Low-Temperature Interstitial Hardening of 15-5 Precipitation Hardening Martensitic Stainless Steel

LOW-TEMPERATURE INTERSTITIAL HARDENING OF 15-5 PRECIPITATION HARDENING MARTENSITIC STAINLESS STEEL

AMIRALI ZANGIABADI

Submitted in partial fulﬁllment of the requirements

For the degree of Doctor of Philosophy

Thesis Advisers:

Dr. Arthur H. Heuer

Dr. Frank Ernst

Department of Materials Science and Engineering

CASE WESTERN RESERVE UNIVERSITY

January, 2017 Low-temperature Interstitial Hardening of 15-5 Precipitation

Hardening Martensitic Stainless Steel

Case Western Reserve University

We hereby approve the thesis1 of

AMIRALI ZANGIABADI

for the degree of

Doctor of Philosophy

Dr. Arthur H. Heuer Committee Chair, Research Adviser

Dr. Frank Ernst Committee Member, Academic Adviser

Dr. Sunniva R. Collins Committee Member

Dr. Matthew A. Willard Committee Member

Dr. Farrel J. Martin Committee Member

Date of Defense

2016-11-23

1We certify that written approval has been obtained for any proprietary material contained therein. Dedicated to My Mom Who enlightened my heart with her perpetual love. My Dad Who intrigued my curiosity since my childhood. Table of Contents

List of Tables vi

List of Figures viii

Acknowledgements xxi

Abstract xxiii

Chapter 1. Introduction1

Signiﬁcance of the Study1

Martensite, an Advantageous Alternative2

Chapter 2. Background4

Thermo-chemical Surface Engineering4

Precipitation-Hardening Stainless Steels5

Low-Temperature Carburization/Nitridation 10

Expanded Martensite 14

Interstitial–Induced Phase Transformation 18

Phase Transformations in Steels 20

Nucleation and growth transformations 20

Martensitic transformations 22

Chapter 3. Methodology 32

Low-temperature carburizing/nitriding processes 32

Characterization methods 34

Chapter 4. Experimental 42

iv Non-treated 15-5PH 42

Carburized 15-5PH 45

Nitridation of 15-5PH 56

Phenomenology of martensitic phase transformation 85

Nitrogen-supersaturated martensite 93

Chapter 5. Discussion 105

Martensite to austenite phase transformation 105

Internal shearing of martensitic austenite 109

Highly tetragonal martensite 123

Chapter 6. Conclusions 131

Appendix A. Phenomenology of martensitic phase transformation (Programing

Codes) 134

Appendix B. Correcting Auger Electron Spectroscopy Proﬁle and Calculating

the Diﬀusion Coeﬃcient 140

Appendix C. CALPHAD Modeling to Determine the Stability of Martensite

and Austenite 146

Appendix D. Microstructural Observation of Carburized 13-8 PH 150

Appendix E. Microstructural Observation of Nitrided 13-8 PH 152

Appendix. Complete References 154

v List of Tables

2.1 Chemical composition of several precipitation hardening stainless

steel alloys. All alloys are fully martensitic, except 17-7 PH which

is about 50 vol.% martensitic, 40 vol.% austenitic and 10 vol.%

ferritic6

2.2 The M s temperatures for common martensitic PHSSs calculated

from equation 2.1.7

3.1 Processing parameters to study the eﬀect of nitriding temperature 34

4.1 Crystal structure of H¨aggcarbide (χ–M5C2) with monoclinic

C2/c spacegroup (No. 15). 49

4.2 Crystal structure of θ–Fe3C with an orthorhombic Pnma

spacegroup (No. 62). 54

4.3 The habit planes of martensite in diﬀerent alloys. These indices

are approximate, since the habit planes are in general irrational 66

4.4 Averaged chemical composition of the plate and the matrix

obtained from 3D APT reconstruction, and the normalized

chemical concentrations relative to Fe (at. %). 75

4.5 Relative atomic plane position for the {110}γ planes in austenite

and the {111}α0 planes in martensite shown in Figure 4.28. 83

4.6 Theoretical and experimental data for the crystallography of lath

austenite in 15-5 PH. 91

vi 4.7 Gaussian function parameters of ﬁtted curves after peak

de-convolution in ﬁg. 4.30. 95

5.1 Lattice Parameter of Martensite Measured by Several Researchers.127

vii List of Figures

1.1 Typical phases of iron (i.e. austentie and martensite/ferrite) and

their possible phase transformations.3

2.1 (a) The micrograph of a as-quenched 15-5 PH alloy, showing

martensitic laths (b) Bright-ﬁeld micrograph showing some NbC

carbides.8

2.2 (a) and (b) bright-ﬁeld and dark-ﬁeld micrographs showing the

Cu precipitates in 15-5 PH alloy aged for 230 ks at 773 K, and (c)

an electron DP (diﬀraction pattern)...9

2.3 APT of martensite phase in 17-4 PH aged at 670 K for 360 ks,

which shows a short distance phase decomposition to Cr-enriched

and Cr-depleted zones. Fine spherical Cu-rich precipitates are

also formed after aging. 10

2.4 Morphology of the diﬀerent precipitates formed in the 15-5 PH as

a function of temperature and time. 11

2.5 (a) Carbon concentration depth proﬁle of carburized 15-5 PH at

650 K for 260 ks (data points indicate diﬀerent surface ﬁnishes),

and (b) the corresponding hardness proﬁle (for surface ground

ﬁnish). 13

2.6 Surface hardness 17-4 PH steel as a function of nitriding

temperature. 13

2.7 XRD patterns of 17-4 PH nitrided at 620 K–770 K for 36 ks and

the formation of γ0(Fe4N) and CrN at higher temperatures. 14

viii 2.8 Variation of the lattice parameters c and a of the BCT lattice of

iron–carbon and iron–nitrogen steels with interstitial content. 15

2.9 XRD proﬁles for nitrided of AISI 420 martensitic stainless steel

treated for 14.4 ks at diﬀerent temperatures. 16

2.10 Interstitial (octahedral) sites and their dimensions in (a) BCC,

and (b) FCC structures. 17

2.11 XRD proﬁle of non-treated and carburized 13-8 PH at 650 K,

obtained in Bragg-Brentano and 1◦ grazing incidence. The

unknown shoulder on the left side of the BCC (110) peak is

suggested as a carbide with uncertain stoichiometry. 18

2.12 (a) Equilibrium phase diagram of Fe-carbon system and the

molar free energy of BCC and FCC solid solutions of Fe in

(b) equilibrium condition at 1050 K, (c) possible metastable

solubilities of carbon... 19

2.13 Classiﬁcation of phase transformations in steels 21

2.14 (a) Bain lattice correspondence and lattice deformation, and (b)

the BCT lattice showing the location of interstitials by crosses. 25

2.15 (a) Lattice deformation followed by slip shear, and (b) lattice

deformation leading to twin related regions. 27

2.16 Schematic of habit plane between α0 and γ when (a) no constraint

exists during the transformation, and (b) when a strain energy

constrains the shape of the product phase. 28

ix 2.17 (a) Dark-ﬁeld TEM image of the interface dislocations

(white/black lines) in Fe–20.2Ni–5.4Mn (mass %) steel between

the austenite (γ) and the martensite (α0)... 29

2.18 HRTEM images of the interface in Fe–20.2Ni–5.4Mn (mass %)

steel between austenite (γ) and martensite (α0) in the viewing

directions... 30

2.19 Schematic of interface migration by gliding the interfacial

dislocations on (111)γ planes. The ⊥ symbol indicates a

dislocation (not necessarily an edge-dislocation). 31

3.1 Schematic of nitridation process performed in CVD furnace, which

consists of double-surface-activation and nitridation segments. 33

3.2 Schematic showing the principle of APT. 39

3.3 Schematic of a DSC. 41

4.1 Z-contrast STEM image of a non-treated 15-5 PH, showing

martensite laths. 43

4.2 (a) Dark-ﬁeld image of NbC carbide in non-treated 15-5 PH, and

(b) its corresponding DP in [112] zone axis. (c) XEDS chemical

analysis of the particle, and (d) the crystal structure of the NbC. 44

4.3 Z-contrast STEM image of MnS inclusion and the XEDS proﬁle

containing strong signals of Mn and S elements (point #2). A

brighter region attached to the MnS inclusion (i.e. point #6) is a

NbC particle shown in Figure 4.2. 44

x 4.4 The DSC proﬁle of non-treated 15-5 PH, showing the As and Af

temperatures of the alloy at 735 K and 918 K, respectively. 45

4.5 The results of nano-indentation on the cross-section of 15-5 PH

after low-temperature carburization. The dashed line represents

the hardness of a non-carburized sample. 46

4.6 (a) optical image of carburized 15-5 PH at 720 K for 72 ks and

etched by Fry’s reagent, (b) SEM image of the sample, which is

sputtered by Ar for 300 s to reveal the martensite laths. 47

4.7 STEM image of the carburized 15-5 PH and the corresponding

DP in [100] zone axis. 48

4.8 TKD analysis of carburized 15-5 PH, which shows a carburized

layer at the top 1 µm of the sample. (a) The band contrast

map, (b) orientation map, and (c) phase map (green color is the

matrix and red color is the H¨aggcarbide). The white rectangle is

enlarged in Figure 4.10. 50

4.9 Schematic of N–W relationships and the formation of martensite

laths (twins) rotated by an angle of about 60◦ degrees with

respect to each other. 51

4.10 Enlarged part of the sample from Figure 4.8 and detection of

H¨aggcarbide (M5C2): (a) STEM image, (b) band contrast map,

4.11 (a) Area selected on the martensite and H¨aggcarbide to record

DP, (b) corresponding DP in [1100]¯ χ zone axis, and (c) the

xi simulated H¨aggcarbide DP that is overlaid on the experimental

DP. 52

4.12 (a) Selected area on the martensite and cementite θ–Fe3C to

record DPs in two diﬀerent zone axes. Orange and blue spots are

simulated DPs of cementite and martensite, respectively. 53

4.13 XRD proﬁle of carburized 15-5 PH at 720 K for 72 ks and the

simulated peaks of cementite and Fe(BCC) crystals with a lattice

parameter of aFe = 0.287 nm. 54

4.14 Stereographic projection of OR between cementite and martensite

obtained by analysing Figure 4.12. This OR is known as the

Bagaryatskii relationship. Orange and blue spots represent planes

of cementite and martensite, respectively. 55

4.15 (a) optical image of nitrided 15-5 PH at 670 K for 72 ks and

etched by Fry’s reagent, (b) SEM image of the sample, which is

sputtered by Ga for 300 s and reveals the small plate-like features

inside martensite grains. 57

4.16 (a) Bright-ﬁeld TEM image of one martensite grain in the nitrided

15-5 PH at 670 K, showing a multitude of new plates, and (b)

a higher magniﬁcation image of these plates with some internal

contrast. 59

4.17 (a) TEM bright-ﬁeld image of a plate-containing martensite lath

in 15-5 PH, (b) DP acquired from the circular selecting aperture

shown in (a), and (c) schematic of DP and the calculated plane

xii spacings of the plate and the matrix. (DP obtained from both

the plates and the matrix in the [110]γ and [100]α0 zone axes.) 60

4.18 (a) TEM bright-ﬁeld image of a plate-containing martensite lath

in 15-5 PH, (b) a higher magniﬁcation STEM image showing

shearing of two plates in the 15-5 PH sample, (c) and (d) are DPs

obtained from both the plates and the matrix in the [100]γk[110]α0

and [111]γk[011]α0 zone axes, respectively. 62

4.19 (a) Bight-ﬁeld image of the plate-containing martensite lath in

the 15-5 PH alloy, (b) the corresponding ASTAR phase map of

austenite (red) and martensite (green), and (c) the determined

stereographic projection of the matrix (martensite) and the plates

(austenite). 63

4.20 Orientation of a habit plane (ABCD) in a TEM foil with the

thickness of t, after tilting the foil to α and β angles. The electron

beam (e−) is parallel to ABCD plane. 67

4.21 (a) DP of the austenite plate and the matrix [011]γk[111]α0 zone

axis by using a convergent electron beam and observing image in

the reﬂection, and (b) the stereographic projection of (a), which

shows the location of habit plane normal relative to the (110)α0

plane. 69

4.22 (a) DP of the austenite plate and the matrix in [111]γk[101]α0 zone

axis, and (b) the stereographic projection of (a), which shows the

location of the habit plane normal in the (575) plane (blue line),

xiii in (7 10 7) plane (green line) and their cross product (8 7 2). (872)

is the habit plane which is very close to (541) plane. 70

4.23 (a) and (b) unit cell structure of martensite and austenite, and (c)

and (d) their corresponding densest planes, (111)γ and (011)α0 ,

which also have close plane spacings. These two planes (with

slight deviations from (575)γ and (278)α0 ) are in contact with each

other at the interface, and the interface moves almost normal to

these planes during the phase transformation. 72

4.24 (a) SEM image taken in PHI SAM of 15-5 PH nitrided at 670

K for 20 ks, and the observation of plates inside martensite

laths, and (b) concentration proﬁles of nitrogen and the main

substitutional elements in the alloy. 74

4.25 (a) 2—3D reconstruction of nitrogen atoms revealing bands

with higher nitrogen concentration, (b) and (c) one-dimensional

concentration proﬁles of other elements existing in the alloy. 76

4.26 (a) 2—3D reconstruction of nitrogen atoms revealing bands

with higher nitrogen concentration, (b) and (c) one-dimensional

concentration proﬁles of other elements existing in the alloy. 80

4.27 (a) HRTEM image of the interface in the [011]γ and [111]α0

viewing direction, (b) schematic of atomic conﬁguration and the

eﬀective plane spacings at the interface, (c) the periodogram

(logarithmic intensity of the numerical Fourier transform) of (a)

and the indexed atomic planes. 82

xiv 4.28 (a) Space ﬁlling atomic conﬁguration at the austenite/martensite

interface in the viewing direction [011]γ and [111]α0 . In every 9

atomic planes there is a step to compensate the mismatch. Atoms

are stacked in A and B layers in austenite, and in A, B and C

layers in martensite. 84

4.29 The XRD proﬁles of non-treated and nitrided 15-5 PH at diﬀerent

temperatures. 94

4.30 De-convolution of XRD peaks located at 2θ = 65◦ and 2θ = 68◦

into three peaks. The Gaussian function parameters of each peak

are presented in Table 4.7. 95

4.31 Simulated XRD proﬁle of martensite lattice before imposing any

tetragonality (c/a = 1) and after 2 % and 5 % tetragonality. Note

the location of (110)α0 peak remains exactly in the same position,

but its intensity is reduced. 96

4.32 (a) Bright-ﬁeld image of the matrix and the selected area

for obtaining DPs in diﬀerent zone axes; (b) [100]α0 (smaller

reﬂections are originated from the plate [110]γ), (c) [131]α0 , and

(d) [110]α0 zone axes. The (002)α0 and the (211)α0 reﬂections

are arc-shaped and the (002)α0 reﬂection is elongated to larger

plane-spacings (with slight rotation). 97

4.33 Nano-size beam DPs can be obtained by limiting the acceptance

angle of the electron beam hitting the sample 99

xv 4.34 Nano-sized DP acquired from the plate-containing martensite

lath in 15-5 PH in numbered locations. 100

4.35 Superimposing two DPs 1 and 6 from Figure 4.34 and obtaining

the arc-shaped reﬂections for the (011)α0 and (011)α0 planes. The

(011)α0 and (011)α0 reﬂections still are circular 100

4.36 Superimposing two DPs 1 and 6 from Figure 4.34 and obtaining

the arc-shaped reﬂections for the (011)α0 and (011)α0 planes. The

(011)α0 and (011)α0 reﬂections still are circular 101

4.37 Nano-size DP of both austenite and martensite at their interface,

in the [100]α0 k[011]γ zone axis, and their corresponding sketches

of grids deﬁned by the fundamental g vectors. 103

5.1 The change in the Gibbs free energy between martensite and

austenite by increasing the nitrogen content at T =700 K. 107

5.2 (a) Shearing of {111} planes (parallel to PVQ) along the TQ line

(or the h112i direction) and producing (b) the S0V0Q0 plane as an

{110}BCC plane and (c) the S00V00Q00 plane as an {111}FCC plane,

and (d)–(f) are the cross sectional view of the STQ plane 108

5.3 (a) After performing the shear indicated in Figure 5.2b, and (b)

after completing the transition into a BCC lattice by shearing

1 1 0 successive (110)α over 8 h110iBCC (or 16 h112iFCC). 109

5.4 (Left) Shearing (gliding) of invariant planes {111}γ in the h110i

direction to leave a perfect crystal structure, and (right) the

preferred atomic movement of {111}γ by gliding into two h112i

xvi directions to leave a perfect crystal structure (i.e. Shockley partial

dislocations). 111

5.5 (a) DP of martensitic austenite in [111]γ zone axis, which shows

1 extra reﬂections. The extra reﬂections are in the 6 [121]γ direction,

which deviate from the [110]γ direction by 30◦, (b) the simulated

DP of a Fe-FCC crystal, and (c) the simulated DP of a Fe-HCP

crystal in [0001] zone axis. The extra reﬂection is shown by “x”

and is the strongest reﬂection in [0001]HCP zone axis. 112

5.6 (a) DP of martensitic austenite in [111]γ k[110]α0 zone axis, which

shows extra reﬂections of the austenite, (b) the bright-ﬁeld image,

and (c) and (d) are dark ﬁeld images which are resulted from the

(202)FCC and (1100)HCP crystals, respectively. Due to the defects

(e.g. dislocation) in the plates and the matrix, both bright-ﬁeld

and dark-ﬁeld images have regions with diﬀerent contrasts. 113

5.7 (a) HRTEM image of the interface in the [011]γ and [111]α0

viewing direction, (b) schematic of atomic conﬁguration and the

diﬀerence in the eﬀective plane spacings at the interface, which

necessitates the formation of coherency dislocations. 116

5.8 (a) Space ﬁlling atomic conﬁguration at the austenite/martensite

interface in the viewing direction [011]γ and [111]α0 . In every 9

atomic planes there is a step to compensate the mismatch. Atoms

are stacked in A and B layers in austenite, and in A, B and C

layers in martensite. 117

xvii 5.9 (a) Formation of dislocation due to the dilatational strain in

the habit plane, (b) rotation of the habit plane to reach to an

irrational invariant plane (hypothetically, with no dislocation

formation), and (c) formation of steps at the interface and the

advancement of interface by dislocation climb. 118

5.10 Schematic of atomic plane conﬁguration at the interface and the

formation of coherency dislocation or steps (~d) which can be

dissociated to two vectors (~p and ~q). This conﬁguration is also

called a disconnection. 120

5.11 (a) Formation of steps along the interface by advancing the phase,

(b) the internal shearing of the product phase (austenite) in 3

dimensional view and formation of irrational habit plane, and (c)

the macroscopic habit plane (278)α0 relative to the parent phase. 121

5.12 (a) Atomic conﬁguration in the the (100) plane of a BCC crystal,

and (b)[top] stretching the pattern in the [001] direction caused by

placing nitrogen atom into the octahedral sites, [bottom] placing

several of the initial stretched pattern from the top to form the

stretched (100) plane. It appears that the plane is shearing in the

[011] direction. 124

5.13 (a) The (100) plane of a BCC structure with the lattice parameter

a, (b) after stretching the (100)BCC plane in the [010] direction.

The area of the plane is the same, but the (011) plane spacing

reduces, and (c) maintaining the (011) plane spacing unchanged,

according to the HRTEM observations. The HRTEM images

xviii show the (011) plane spacing does not change; therefore, the

whole volume of the lattice must increase. 125

5.14 The experimental and simulated DPs of the nitrided δ-ferrite

grain in 17-7 PH in the (a) [100]δ, (b) [110]δ, and (c) [113]δ zone

axes. The simulated DPs are obtained by overlapping DPs of

martensite lattices with diﬀerent tetragonalities of c/a = 1.08 and

c/a = 1.04. 129

5.15 Nano-diﬀraction proﬁle along a [001]BCC zone-axis through a

weak-contrast region of a 2205 δ-ferrite grain following nitridation.

The measured angle between the scattering g vectors is oscillating

between 90◦ and 93◦, which are corresponding to c/a = 1 and

c/a = 1.05. 130

B.1 The shape of the nitrogen signal at diﬀerent nitrogen

concentrations. By reaching deeper into the sample the

magnitude of noise is still comparable to the signal. 141

D.1 Formation of cementite in 13-8 PH alloy after carburizing at

650 K for 72 ks. The carbide formation obeys the Bagaryatskii

OR (discussed in section 4.2.2). 151

E.1 Bright-ﬁeld image of the nitrided 13-8 PH at 670 K, which shows

several variants of martensitic austenite are formed. Few variants

cross and shear each other. 152

E.2 Bright-ﬁeld and dark-ﬁeld images of the nitrided 13-8 PH from

the indicated reﬂections in the [111]γ zone axis. The images in

xix (b) and (c) are resulted from the extra reﬂections that originate from the HCP crystal. 153

xx Acknowledgements

This work would not have the spirit that it has without the invaluable academic, educational, psychological, and human support and belief in me as a researcher, provided by the following scholars.

I would like to express my special appreciation and thanks to my research adviser

Professor Arthur H. Heuer, you have been a tremendous mentor for me. Despite my passing perplexities, you encouraged me to continue my journey in search for science, in the land of giants. I would like to thank you for encouraging my research and for allowing me to grow as a research scientist.

I would also like to thank my academic adviser Professor Dr. rer. nat. ha- bil. Frank Ernst. I am very grateful to you for returning to me faith in myself. I have found the manifestation of tact, diplomacy, and sincerity in you as a teacher, adviser, friend, and a human being.

I also want to thank professor Sunniva Collins, professor Matthew Willard and Dr.

Farrel Martin for letting my defense be an enjoyable moment, and for your brilliant comments and suggestions, thanks to you. I would especially like to thank engineers and staﬀ at SCSAM (Swagelok Center for Surface Analysis of Materials). All of you have been there to support me when I worked in the labs and collected data for my

Ph.D. thesis.

A special thanks to my family. Words cannot express how grateful I am to my mom (Akram), dad (Mohammad hossein), brothers (Amirhossein and Amirmasoud) and sister (Nazanin) for all of the sacriﬁces that you have made on my behalf. I would also like to thank all of my friends who supported me in writing, and incented me to strive towards my goal.

xxi This material is based upon work supported by the National Science Foundation under Grant No. DMR-1208812.

xxii Abstract

Low-temperature Interstitial Hardening of 15-5 Precipitation Hardening Martensitic Stainless Steel

Abstract

AMIRALI ZANGIABADI

Surface engineering is a relatively new branch of science and technology. Low-

temperature (≤ 723 K) interstitial hardening via carburization and nitridation are

eﬀective ways to enhance engineering performance of stainless steels surfaces and developed in the past 20 years. At these para-equilibrium processing temperatures, the

substitutional elements in the steels are eﬀectively immobilized, thereby suppressing

carbide or nitride formation. The surface hardness, fatigue resistance, and corro-

sion resistance are signiﬁcantly enhanced due to the resulting “colossal” interstitial

supersaturations achieved during such para-equilibrium interstitial hardening.

The studies on 15-5 PH precipitation hardening martensitic stainless steels re-

sulted in unusual phenomena, following para-equilibrium nitridation. Firstly, isother-

mal martensite-to-austenite phase transformation has been observed after low-

temperature nitridation in the martensite phase. The transformation occurs in the

near-surface regions of the alloy, in which the nitrogen concentration reaches more

than 15 %at. These observations are consistent with the notion that nitrogen is

a strong austenite stabiliser and substitutional diﬀusion is eﬀectively frozen at the

xxiii processing temperature. Our microstructural observations and diﬀraction analyses provide conclusive evidence for the martensitic nature of this phase transformation.

The second response of this alloy (similar to the other alloys, e.g. 13-8 PH, 17-7 PH and 2205) is an anomaly in the martensite (or ferrite) lattice, which can be attributed to the enormous tetragonality, approaching c/a = 1.12. Due to the distortion of both phases at the interface, it is sometimes hard to diﬀerentiate one from another in their

DPs (diﬀraction patterns).

The phenomenological crystallographic theory of the martensite-to-austenite phase transformation has been applied. The theory indicates that the martensitic phase transformation necessitates the closed-packed planes (i.e. {111}γ) of the newly- formed austenite phase undergo shearing. The microstructural studies conﬁrm this internal shearing of the austenite phase. It further appears that the martensitic austenite observed in this work deviates from cubic symmetry. Finally, this study shows that high concentrations of nitrogen interstitials cannot be realized in martensite or ferrite even under “nitrogen paraequilibrium” conditions, because of the formation of martensitic austenite.

xxiv 1

1 Introduction

1.1 Signiﬁcance of the Study

Stainless steels are extensively used in applications where corrosion resistance is im-

portant. Technological applications often demand alloys resistant to mechanical and

chemical forces, including resistance to wear, corrosion, fatigue, etc. Alloys also need

to be formed into parts and therefore, they should be hardened after ﬁrst shaping.

Over the past 20 years, new methods of alloy surface hardening have been developed.

They operate at temperatures between 600 K and 750 K and generate a hard layer

below the surface by incorporating high (non-equilibrium) concentrations of carbon

or nitrogen interstitials. By diﬀusing interstitial solutes (carbon or nitrogen) into

shaped parts, they generate a “case” (hard shell) below the surface without altering

the shape of the part. However, substantially increasing surface hardness requires

interstitial solute atom concentrations orders of magnitudes above the corresponding

equilibrium solubility limits. Surpassing the equilibrium solubility limits potentially

results in formation of very stable metal carbide and/or nitride precipitates. Such

precipitates can dramatically deteriorate the alloy properties: depleting the matrix

of Cr, they locally inhibit formation of the passivating Cr-rich oxide film that makes Introduction 2 the alloy corrosion-resistant (“stainless”), and they can generate local corrosive gal- vanic currents. Moreover, carbide or nitride precipitates – owing to their different crystal structures and different elastic moduli – may degrade mechanical properties

(e.g. fatigue resistance) by concentrating stress and enabling crack formation at the particle–matrix interface.

1.2 Martensite, an Advantageous Alternative

Martensite is the product of a diﬀusionless phase transformation, produced by a crystal lattice shear [1]. In Fe–C or Fe–N steels, martensite results from the attempt to transform from the FCC (face-centered cubic) structure of the high-temperature γ- phase (austenite) to the BCC (body-centered cubic) structure of the low-temperature

α-phase (ferrite) when limited atom mobility does not permit a diﬀusive (nucleation- and-growth) decomposition into α-Fe and carbide. Due to the limited solubility of carbon and nitrogen, the lattice structure of the super-saturated α endures a tetragonal distortion, forming a BCT (body-centered tetragonal) structure denoted as α0 (martensite).

Potentially, the “reverse” transformation of α0 → γ is also possible. However, owing to distortion energy associated with γ → α0 transformations, the As (autenite

start) temperature at which γ begins to form is typically much higher (i.e. several

100 K) than the M s (martensite start) temperature at which α0 begins to form during

cooling (quenching) of γ. Nevertheless, reversion can also occur in a diﬀusionless

transformation, by a shear mechanism. Figure 1.1 shows schematically the crystal

structure of austenite and martensite and the possible phase transformations. C. Project Description

a. Introduction: Reversion of Martensite to Austenite What is martensite? The product of a diffusionless phase transformation, brought about by crystal lattice shear. In Fe–C steel, martensite results from the attempt to transform from the FCC (face-centered cubic) structure of the high-temperature -phase (austenite) to the BCC (body-centered cubic) structure of the low-temperature ↵-phase (ferrite) when limited atom mobility does not permit a diffusive (nucleation-and-growth) decomposition into ↵ and carbide. For carbon fractions XC XH, carbon causes the initially formed primary martensite to transform into “secondary (plate) martensite” with a BCT (body-centered tetragonal) structure denoted as ↵ .1 The structure of ↵ is related to that of ↵ by a tetragonal 0 0 distortion " c 1.02..1.08.1 Similarly, ↵ can form in stainless (Cr- and Ni-containing) steels ⌘ a = 0 and, upon heating, back to . However, owing to distortion energy associated with ↵ $ 0 transformations, the temperature As (“autenite start”) at which begins to form is typically much (several 100 K) higher than the temperature Ms (“martensite start”) at which ↵ begins 0 to form during cooling (quenching) of .2 Usually, therefore, ↵ (BCT FCC) “reversion” of 0! ! martensite in stainless steels is observed at temperatures high enough to permit a diffusive (nucleation-and-growth) transformation, possibly including a decomposition ↵ ↵ carbides 0! + Introduction at intermediate temperatures. Nevertheless, reversion can also occur diffusionless,3 by a shear mechanism.3–7 Depending on alloy composition, a shear mechanism may even be preferred at temperatures that are higher than those required for diffusive transformation.4

Figure 1.1. Typical phases of iron (i.e. austentie and martensite/ferrite) Figure 1: Relation of the newly discovered phase to known phases. and their possible phase transformations. 0 What if dynamical alloying of ↵ gradually builds up a high driving force for the BCT FCC 0 ! Much researchtransformation has been at done a temperature on low-temperature at which metal thermochemical (“substitutional”) processing atom diffusion of is effectively frozen? Then, diffusionless reversion is the only possibility. This scenario can be created by austenitic stainlessinfusing steels8 very [high2–9]. concentrations However, less ofcarbon attention or nitrogen has been into given a martensitic to thermo-stainless steel. Our chemical processing of martensitic stainless steels. In recentC–1 years, the importance of surface hardening has been revealed by successful treatment of martensitic stainless steels [10–12].

This thesis investigates the surface hardening of the 15-5 PH alloy, a precipitation- hardening martensitic stainless steel. The chemical and microstructural evolutions of the substrate have been studied after low-temperature carburization and nitridation. 4

2 Background

2.1 Thermo-chemical Surface Engineering

Surface engineering is a relatively new branch of science and technology. However, from the beginnings of time until the last century, mankind has worked to engineer the surface, while not aware of the concept [13]. As defined in the ASM Handbook, surface engineering is a “treatment of the surface and near-surface regions of a material to allow the surface to perform functions that are distinct from those functions demanded from the bulk of the material” [14]. Introduction of this superficial layer can be carried out by diffusion of specific atoms or ions to the surface which enhance its tribological properties such as hardness, fatigue strength and corrosion resistance. To this goal, thermo-chemical methods employ heat and a chemically active medium with respect to the treated metal, to saturate the surface with given elements, achieving the desired properties by changing the chemical composition and maybe the microstructure of the superficial layer [15].

Saturating the surface by diﬀusion of certain elements (e.g. carbon, nitrogen, silicon, sulfur, aluminum) can be accomplished without engaging other factors in the process (unassisted), or it can be done by the participation of a factor to activate the process by increasing the absorption of diﬀusing elements (assisted)[13]. The latter Background 5 case is usually performed by chemical vapor deposition (CVD) techniques and the surface of the sample is activated by introducing reactive gases. Therefore, less time and lower temperature are required in the assisted process.

Carburizing and nitriding are two examples of diﬀusion-based surface engineering, in which carbon and nitrogen diﬀuse in the interstitial sites of the substrate lattice, without changing its fundamental structure. This thermo-chemical surface treatment aims to improve the hardness, corrosion resistance, fatigue resistance, and other favorable properties.

2.2 Precipitation-Hardening Stainless Steels

Precipitation hardening stainless steels (PHSSs) are frequently classiﬁed in three main categories: martensitic, austenitic and semi-austenitic. Obtaining high strengths without compromising corrosion resistance and ductility are the main features of these classes of stainless steels [16]. Achieving strength and hardness in PHSSs is mainly ascribed to the small fraction of copper, aluminum, titanium and molybdenum. For instance, the 15-5 PH stainless steel has 2–3 at.% copper which is much higher than its solubility in ferrite in room temperature [17]. Upon heat treating between 700 K and

850 K, the strengthening Cu-rich particles will form [18]. The precipitation mechanism throughout heat treatment is diﬀerent for various PHSSs, which will be discussed brieﬂy.

2.2.1 Martensitic PHSSs

In the category of martensitic PHSSs, the microstructure is stable at high working temperature but is accompanied by the precipitation hardening mechanism. This Background 6

Table 2.1. Chemical composition of several precipitation hardening stainless steel alloys. All alloys are fully martensitic, except 17-7 PH which is about 50 vol.% martensitic, 40 vol.% austenitic and 10 vol.% ferritic

at.% Cr Ni Cu Al Mo Mn Si C Fe 15-5 PH 15.8 4.7 3.0 - - 1.0 2.0 0.3 Bal. 17-7 PH 17.6 6.4 - 3.0 - 1.0 1.9 0.3 Bal. 17-4 PH 17.9 3.7 3.4 - - 1.0 1.9 0.3 Bal. 13-8 PH 13.8 7.5 - - 1.1 1.0 2.0 0.3 Bal.

mechanism favors their applicability in harsh working conditions (i.e. corrosive en- vironments under high stresses and high temperatures) such as power plants, and

chemical, aircraft, and naval industries [19]. Table 2.1 shows the composition of

frequently used martensitic PHSSs (note the compositional similarity of 15-5 PH and

17-4 PH). The strengthening contribution from the precipitation hardening is believed

to be attributed to: 1- the coherency strain which prevails between the strengthening

precipitates and the matrix, 2- the dispersion of strengthening precipitates, and 3-

the dissimilarity in the shear moduli of the matrix and the precipitates [20].

The microstructure of this class of PHSSs is martensitic with the BCT crystal

structure. However, negligible amount of retained austenite may be present depending

on the prior solution treatment condition. In order to determine the martensitic start

temperature (M s) for this class of PHSSs, an estimate of M s must be made. Ishida

proposed a formula for calculating the M s temperature as a function of composition

(mass %) for ultra high strength steels [21, 22]. Background 7

Table 2.2. The M s temperatures for common martensitic PHSSs calculated from equation 2.1.

Steel M s (K) 15-5 PH 480 K 17-4 PH 470 K 17-7 PH 465 K 13-8 PH 400 K

Ms(K) = 818 − 33000(%C) + 200(%Al) + 700(%Co) − 1400(%Cr) − 1300(%Cu)

−2300(%Mn)−500(%Mo)−400(%Nb)−1300(%Ni)−700(%Si)+300(%Ti)+400(%V).

(2.1)

According to equation 2.1, the M s for the aforementioned martensitic PHSSs is

calculated and summarized in Table 2.2.

The M s of these martensitic PHSSs are ≈200 K higher than room temperature

(298 K), which indicates a suﬃcient driving force for martensitic transformation at room temperature from the as-solution heat treated condition.

As shown in Figure 2.1 the microstructure of the as-quenched 15-5 PH alloy produced by solution treatment and quenching exhibited lath martensite with a BCC/BCT1

structure and high dislocation density [23].

2.2.2 Precipitation Hardening Mechanism

Two of the PHSSs, 17-4 PH and 15-5 PH are strengthened by precipitation of copper

in the martensitic matrix [24]. The precipitation sequence in these alloys, which

contain approximately 3 at.% Cu, appears complicated. Studies show the ﬁrst stage

of structural hardening occurs in the temperature range 775 K–875 K (Figure 2.2) and

1The tetragonality is not detectable in the DP (diﬀraction pattern). Background 8

(a) (b)

Figure 2.1. (a) The micrograph of a as-quenched 15-5 PH alloy, showing martensitic laths (b) Bright-ﬁeld micrograph showing some NbC carbides [23]. the chemical composition of the precipitates are essentially pure copper [23]. In this early level of aging, the precipitates present either double-lobe or striated contrast in diﬀraction-contrast micrographs and the DP shows streaks. By increasing the aging time, the precipitates grow into partially incoherent phase [24].

Aging of 17-4 PH also reveals the formation of Cu precipitates and moderate

fluctuations of Cr concentration in the alloy. Figure 2.3 shows the atomic probe tomography (APT) results of martensite after aging at 670 K for 360 ks. The elemental mappings of Cu and Cr present fine spherical Cu-rich precipitates and minimal Cr concentration variation. This shows that the aging time (i.e. 360 ks) was sufficient to only start the spinodal decomposition of the martensite to Fe-rich and Cr-enriched phases. However, marked spinodal decomposition of this alloy has been reported for longer times and higher temperatures [25–27].

Figure 2.4 shows diﬀerent types of Cu precipitates as a function of temperature and time [28]. According to the studies on 15-5 PH, the precipitation occurs at Background 9

Figure 2.2. (a) And (b) bright-field and dark-field micrographs showing the Cu precipitates in 15-5 PH alloy aged for 230 ks at 773 K, and (c) an electron DP (diffraction pattern) in the [010]α0 zone axis showing streaks with maxima of intensity from which dark-field were obtained [24]. temperatures higher than 720 K after a long aging periods (i.e. >460 ks). However, the required temperature and time for low-temperature carburization/nitridation are usually below 720 K and 144 ks, respectively. Therefore, it can be inferred that the precipitation hardening phenomenon does not happen to a full extent during low- temperature carburization/nitridation. Background 10

Fig. 8—(a) TEM dark-field image. (b) [001], (c) [011], and (d) [111] SAD patterns of the martensite phase aged 400 7C for 5000 h. The dark- field image was taken using the 1/2(011) reflection.

Figure 2.3. APT of martensite phase in 17-4 PH aged at 670 K for Fig. 7—3DAP elemental mapping of the martensite phase aged at 400 7C 360 ks, whichfor 100 shows h. (a) The a minor phase decomposition phase decomposition into the Cr-enriched to and Cr-enriched depleted and Cr-depletedregions zones. occurs Fine in the spherical martensite Cu-rich phase. (b precipitates) Fine spherical are Cu-rich also formed precipitate. (c) Concentration depth proﬁle obtained from the selected after agingregion [25]. near the Cu precipitate.

having a periodicity of two (011)bcc planes is observed. This 2.3 Low-Temperatureis consistent with Carburization/Nitridation the fringe contrast expected from the G-

hase (Ni16X6Si7,X5 Fe, Mn, or Si, Fm3m, and a 5 0.406 nm). Furthermore, a small particle is observed adjacent to Traditional carburization/nitridationthe G-phase, which is ofbelieved steels to are be usually a Cu precipitate. done at high A temperatures, microdiffraction pattern taken from the region with the Fig. 9—1DAP concentration depth profile of the martensite phase aged at 400 up to 1300 K, enablingFig.Moire 7—3DAP carbon/nitrogen fringes elemental is shown mapping in diffusion Figureof the martensite 11(b). into phaseThe the [111] agedsurface. at micro- 400 7 HighC temperatures7Cfor5000h.Ni,Si,andMnappeartobepartitionedintotheCuprecipitate. for 100 h. (a) The phase decomposition into the Cr-enriched and depleted regions occurs in the martensite phase. (b) Fine spherical Cu-rich precipitate.350—VOLUME (c) 30A, Concentration FEBRUARY depth 1999 profile obtained from the selected METALLURGICAL AND MATERIALS TRANSACTIONS A region near the Cu precipitate.

having a periodicity of two (011)bcc planes is observed. This is consistent with the fringe contrast expected from the G-

hase (Ni16X6Si7,X5 Fe, Mn, or Si, Fm3m, and a 5 0.406 nm). Furthermore, a small particle is observed adjacent to the G-phase, which is believed to be a Cu precipitate. A microdiffraction pattern taken from the region with the Fig. 9—1DAP concentration depth proﬁle of the martensite phase aged at 400 Moire fringes is shown in Figure 11(b). The [111] micro- 7Cfor5000h.Ni,Si,andMnappeartobepartitionedintotheCuprecipitate.

350—VOLUME 30A, FEBRUARY 1999 METALLURGICAL AND MATERIALS TRANSACTIONS A Background 11

Figure 2.4. Morphology of the diﬀerent precipitates formed in the 15-5 PH as a function of temperature and time [28]. lead to the diﬀusion and consequently reaction of chromium with solute atoms to form carbides/nitrides. However, rapid precipitation of chromium carbides/nitrides at the carburized/nitrided surface reduces the corrosion resistance, thus attenuating one of the main attributes of stainless steels [6, 29].

Novel thermochemical methods for surface engineering can be carried out in carbon- or nitrogen-bearing media at temperatures lower than 770 K to enhance the surface properties [30]. Low-temperature carburization/nitridation as a new technique, enhances surface strength of stainless steels without the formation of carbides/nitrides. The process temperature range is usually between 600 K to 750 K. At the lower processing temperature, the process becomes very slow and less economi- cally attractive [30]. Background 12

The very stable passive layer, which mainly forms due to the presence of chromium,

enhances the corrosion resistance of stainless steel [31]. However, the passive layer re-

tards the penetration of carbon and nitrogen atoms and the surface must be activated

by the removal of the passive chromia (Cr2O3) layer.

2.3.1 Surface treatment of martensitic PHSSs

There are limited investigations on surface hardening of 15-5 PH [32–34]. Most of

the research on surface treatment of martensitic PHSS has been done by the plasma

nitridation technique on 17-4 PH (which has similar Cu content as 15-5 PH) [11, 12,

35, 36]. But, the number of research publications on carburization of this alloy is

limited [33, 37].

Low-temperature treatment of PHSSs has been reported as highly successful

[35, 36, 38]. The surface hardness of the treated sample increases up to 3 times that of

the non-treated sample. Precipitation hardening during carburizing/nitriding treat-

ments is also responsible for the hardness increase. Figure 2.5 shows the carbon con-

centration proﬁle and the corresponding hardness of 15-5 PH after low-temperature

carburization. Figure 2.6 shows the variation of hardness at the surface of 17-4 PH

after low-temperature nitridation for 72 ks [38]. By increasing the treatment tem-

perature and time, nitrides such as γ0(Fe4N) and CrN start to form near the surface

(Figure 2.7)[12, 35, 38].

Comparison of the X-ray diﬀraction (XRD) peak shift of samples treated by ni-

tridation and carburization reveals higher peak shift (to larger plane spacings) after

nitridation [37]. Similar observation after nitridation of austenitic stainless steels also

has been reported [8]. Background 13

(a) (b) Figure 4.36: Carbon concentration-depth(a) proﬁles for 15-5 PH stainless steels which (b)

were carburized atFigure 380Cfor72hourswithas-cast,surface-ground,andelectro- 2.5. (a) Carbon concentration depth proﬁle of carburized

polished surface finishes15-5 obtained PH using at 650AES. K for 260 ks (data points indicate different surface finishes), and (b) the corresponding hardness profile (for surface ground finish) [32]. 334 Sun and Bell Low temperature plasma nitriding characteristics of precipitation hardening stainless steel

(c)

Figure 4.33: Hardness-depth6 Surface hardness profilesas a function for 15-5of PHnitriding stainlesstemperature steels which were carbur- Figure 2.6. Surfacefor 17-4PH hardnesssteel 17-4 PH steel as a function of nitriding 4 Nitrogen concentration proéles measured by GDS across nitrided layers produced on 17-4PHtemperatureizedsteel at 380at Cfor72hours(a)withanas-castsurfacefinish,(b)withasurface-ground [38]. various indicated temperatures for 20 h DISCUSSION finish, and (c) with an electro-polished surface finish. Although the atomicThe radiusexperimental of carbonresults isof slightlythe present largerwork than nitrogen (0.08 nm reèection peaks from the untreated substrates, which demonstrate that plasma nitriding of 17-4PH PH correspond to martensite and austenite phases, as stainless steel at temperatures lower than 425°C can expected from the heat treatmentand 0.07history nm,of respectively),the produce thea thin unit-cellnitrided volumelayer characterised of iron-carbonby its martensite is smaller material. However, when applied to the nitrided featureless morphology, slow growth rate, diffuse 84 specimens produced at temperaturesthanbelow iron-nitrogen425°C, the martensitetype nitrogen [39pro].éle Bothand, more carboninterestingly, and nitrogenits X-ray have strong covalent same technique did not generate well deéned Bragg amorphous nature. Although the low temperature peaks. Although attempts have been made to identify layer on PH steels has a ‘white’ and featureless the crystalline phases in the lowbondingtemperature withnitrided surroundingmorphology iron atoms.similar to However,that produced theon carbonaustenitic in iron-carbon bonding layers, this has proved difécult because of the lack of stainless steels at temperatures below 450°C,11 these Bragg peaks and therefore hasthe lack someof positivecrystalline ionicitylayers have whichcompletely transfersdifferent electronicstructures. chargeFigure to8 adjacent iron atoms. feature in the XRD patterns. The lack of crystallinity reproduces the XRD pattern obtained from a 425°C indicates that the low temperature nitrided layers are nitrided austenitic stainless steel specimen.8 It can be X-ray amorphous. Although a more detailed struc- seen that well deéned Bragg reèection peaks (S1 and tural analysis is necessary, from the XRD patterns, S2) were generated from the nitrided layer, indicating coupled with the observed featureless nature of the its crystallinity. Detailed analysis showed that the low nitrided layers it may be concluded that low temperature nitrided layer on austenitic stainless temperature (<425°C) plasma nitriding produced steels is composed of a metastable phase, named an amorphous-like layer on the PH steel investigated. At higher nitriding temperatures (425°C and 450°C), the resultant XRD patterns gradually became crystalline-like, with the appearance of several reèection peaks, which could be indexed as CrN and c9-Fe4N. Such an amorphous to crystalline transition clearly corresponds to the formation of ‘dark’ phases in the nitrided layer.

5 Nitrided layer thickness v. nitriding temperature 7 XRD patterns generated from nitrided layers on relationship for 17-4PH steel, showing transition in 17-4PH steel produced at various temperatures; Cu Ka nitriding kinetics at ~410°C radiation

Surface Engineering 2003 Vol. 19 No. 5 H. Dong et al. / Surface & Coatings Technology 202 (2008) 2969–2975 2971

conventional bright-field (BF) TEM and selected-area diffraction (SAD).

3. Results

3.1. Metallography

It was observed that the microstructure produced during plasma nitriding of 17-4PH stainless steel varied with the treatment temperature and time. Optical microscopy and SEM observations showed that the nitrided layer produced below 420 °C appears not to be attacked by the reagent used, Fig. 4. SEM micrograph of 17-4PH plasma nitrided sample at 500 °C for whereas the substrate was etched. A typical cross-sectional 20 h. microstructure of 390 °C/20 h plasma nitrided specimens is depicted in Fig. 2 showing a thin bright layer on the substrate. TEM studies were carried out using a Philips CM20 A typical SEM micrograph for 420 °C/20 h treated 17-4PH microscope, and both the morphology and crystallography of samples is shown in Fig. 3. It can be seen that the upper part plasma nitridedBackground surface layers were investigated by means of of the 420 °C/20 h treated layer was slightly14 etched, implying

Figure 2.7. XRD patterns of 17-4 PH nitrided at 620 K–770 K for 36 ks and the formation of γ0(Fe4N) and CrN at higher temperatures [35].

But, the nitrogen atoms have more neutral behavior [39]. The lattice distortion of

steel after infusion of carbon and nitrogen is illustrated in Figure 2.8.

2.4 Expanded Martensite

The term “expanded martensite” was coined in 2003 by Kim et al. [10]. They

observed that by doing plasma nitriding, the martensite structure expands and the

peaks obtainedFig. 5.from XRD patternsXRD of shift 17-4PH to samples the treatedleft (i.e. at 350– larger500 °C for lattice (a) 10 h spacings), and (b) 30 h. similar to

the observations on the “expanded austenite”. Figure 2.9 shows the XRD proﬁle of

410 stainless steel samples treated at various temperatures. By doing a comparison

of peak positions (a simple calculation using Bragg’s law; nλ = 2d sin θ, in which

λCu = 0.15406 nm), an expansion of about 3% can be measured after nitridation.

Other authors also reported the expansion of martensite by observing the XRD proﬁle

and no one has reported a phase transformation [10, 35, 41–43]. Background 15

Figure 2.8. Variation of the lattice parameters c and a of the BCT lattice of iron–carbon and iron–nitrogen steels with interstitial content [40].

However, the expanded martensite deduced from the XRD profiles of several nitrided martensitic steels lacks a clear definition. The expansion of the lattice parameters in martensite is different than those of austenite. The lattice parameter expansion in the FCC lattice is symmetric but is asymmetric in the BCC lattice. The reason for this behaviour is the difference in the geometry of interstitial sites of each lattice. Unlike the FCC structure, interstitial (octahedral) sites in BCC are not symmetric (figure 2.10). Carbon and nitrogen preferentially sit in octahedral sites of both lattices2. Placing an interstitial atom in octahedral site in a BCC lattice pushes two closer neighboring iron atoms more apart compared to the four atoms sitting farther

2Although tetrahedral sites in BCC lattice are bigger than octahedral sites, placing an interstitial in octahedral site imposes less strain on the lattice and energetically is more favorable [1]. Background 16

Figure 2.9. XRD proﬁles for nitrided of AISI 420 martensitic stainless steel treated for 14.4 ks at diﬀerent temperatures [10].

from the center. The outcome is the expansion (distortion) of the lattice in only one

geometrical direction. By adding more interstitial atoms, they don’t sit randomly in x, y, and z directions of the crystal to eventually cancel out the large-scale distortion

caused by the previous interstitials. Instead, they prefer to sit in the same spatial

direction as that of the previous interstitial. This has been shown to be energetically

favorable and is known as Zener ordering [39]. This ordering of interstitials leads to

the tetragonality of BCC lattice at large scale or the eventual formation of what is

called BCT structure.

As is explained in chapter4, tetragonality of the martensite is not revealed simply

by the shifting of all XRD proﬁle peaks to the lower angles (i.e. higher plane spacings)

or shrinkage of reciprocal lattice projected in the DP obtained in TEM (transmission

electron microscopy). However, the tetragonal lattice produces extra peaks close Background 17

(a) (b)

� 3/2

�/2 �/ 2

�/2

Octahedral Site Iron Atom

Figure 2.10. Interstitial (octahedral) sites and their dimensions in (a) BCC, and (b) FCC structures [44].

to the primary peaks in XRD proﬁle at slightly lower angles without changing the

position of primary peaks. The extra peak often forms like a shoulder and sometimes with higher intensity which appears that the whole peak is shifted to lower angles

(ﬁgure 2.9). 13-8 PH alloy, which has been carburized by the Swagelok company, revealed this shoulder clearly. Heuer et al. [45] suggested that this peak (which

they have indicated by “?”) is a possible carbide with unknown stoichiometry, and

a similar major element chemistry to the bulk alloy (ﬁgure 2.11). However, the

current study shows that this is an extra peak possibly resulting from the highly

tetragonal martensite (section 4.5). In the same way, the DPs of a tetragonal lattice

can be misleading. Depending on the zone axis of the crystal, the DP shows diﬀerent

distortions (i.e. expansion or rotation of speciﬁc planes). The distortion caused by

tetragonality is discussed in detail in section 5.3. Background 18 Electrochemical and Solid-State Letters, 13 ͑12͒ C37-C39 ͑2010͒ C39

However, some paraequilibrium carbon supersaturation has been achieved by the low temperature carburization in the purely martensitic case below the carbide. This is apparent from the BB XRD pattern, where the small but measurable peak shift in the ͑110͒ 2͑ diffraction angle of the martensite phase suggests a lattice expansion on carburization of 0.32%, which corresponds to a carbon content of 1.4 atom % using the correlation between the lattice parameter and the carbon concentration for ferritic matrices available in Ref. 9. Although the carbon concentration is barely measurable at a case depth ͒2 ␮m, enhanced hardness has been achieved to a depth ͑50 ␮m. Consistent with this enhanced hardness, the wear resistance, as measured in a standard pin-on-disk test ͑dry contact under a 4 N load against an Al2O3 counterface, sliding distance of 1000 m10͒, is enhanced by a factor of ͒50 times compared to the non- treated material ͑Fig. 6͒. Further work is continuing on this alloy, concerned with deter- Figure 5. ͑Color online͒ XRD spectra of a PH13-8 Mo specimen nontreated mining the stoichiometry of the paraequilibrium carbide formed at Figureand 2.11. carburized XRD at 380°C, profile in of BB non-treated geometry and at and 1° grazing carburized incidence. 13-8 PH at380°C, the origin of the enhanced passivity achieved by carburiza- 650 K, obtained in Bragg-Brentano and 1◦ grazing incidence. The un-tion at this temperature, and the severely attenuated passivity result- known shoulder on the left side of the BCC (110) peak is suggested asing from carburization at 450°C. It is also of interest to determine a carbide with uncertain stoichiometry [45]. whether the high cycle fatigue resistance is enhanced by low temperature carburization as is the case for carburized 316L austenitic stainless steel.2 2.5 Interstitial–Induced Phase Transformation Acknowledgments Phase transformation after low-temperature treatment has been reported forThe few authors gratefully acknowledge Dr. Airan Perez of the Office of Naval Research and the Naval Research Laboratory for the finan- stainless steels [46–48]. 17-7 PH and AISI 301 steels, which contain both ferritecial supportand of this work. The authors also thank Peter Williams and Dr. Sunniva Collins of Swagelok Corporation ͑Solon, OH͒ for sig- austenite before treatment, develop fully austenitic hardened case after carburization.nificant technical assistance and for performing treatments of the stainless steel employed in this work. Michal et al. [46] showed by the CALPHAD compound energy-based interstitial solid U.S. Naval Research Laboratory assisted in meeting the publication costs of this article. solution model(a) that ferrite-to-austenite transformation is thermodynamically favor- References able by introducing large amount of interstitials in the system. Figure 2.12a shows 1. F. J. Martin, P. M. Natishan, E. J. Lemieux, T. M. Newbauer, R. Rayne, R. A. the equilibrium phase diagram of Fe-carbon system, which is similar for most ofBayles, the H. Kahn, G. M. Michal, F. Ernst, and A. H. Heuer, Metall. Mater. Trans. A, 40,1805͑2009͒. 2. N. Agarwal, H. Kahn, A. Avishai, G. Michal, F. Ernst, and A. H. Heuer, Acta steels. Figures 2.12b to 2.12d show the molar free energy of BCC and FCC solidMater., 55,5572͑2007͒. 3. F. Ernst, A. Avishai, H. Kahn, X. Gu, G. M. Michal, and A. H. Heuer, Metall. solutions of Fe. The common tangent construction defines the compositions ofMater. the Trans. A, 40,1768͑2009͒. 4. G. M. Michal, F. Ernst, H. Kahn, Y. Cao, F. Oba, N. Agarwal, and A. H. Heuer, α γ coexisting phases, X (equ) and X (equ), under heterogeneous equilibrium, whereActa Mater., 54,1597͑2006͒. C C 5. B. J. Lee, CALPHAD: Comput. Coupling Phase Diagrams Thermochem., 16,121 ͑1992͒. 6. G. M. Michal, F. Ernst, and A. H. Heuer, Metall. Mater. Trans. A, 37,1819͑2006͒. 7. P. Thibaux, A. Metenier, and C. Xhoffer, Metall. Mater. Trans. A, 38,1169͑2007͒. 8. A. W. Bowen and G. M. Leak, Metall. Trans., 1,1695͑1970͒. 9. C. S. Roberts, Trans AIME Journal of Metals, 197,203͑1953͒. 10. L. J. O’Donnell, G. M. Michal, F. Ernst, H. Kahn, and A.H. Heuer, Surf. Eng., 26, 284 ͑2010͒. (b) Figure 6. ͑Color online͒ Wear scars in PH13-8 Mo specimens ͑a͒ nontreated and ͑b͒ carburized at 380°C, after dry sliding tests for 785 m at 0.1 m s−1, with an alumina ball and 5 N force.

Downloaded on 2016-06-12 to IP 129.22.124.89 address. Redistribution subject to ECS terms of use (see ecsdl.org/site/terms_use) unless CC License in place (see abstract). 16

12 1200

10 1000

8 800

6 600

4 400 Hardness (HV) Hardness

2 200 Carbon concentration (at%) concentration Carbon 17 0 0 Background 010203040 17 19 Depth (µm) Fe – C Binary System Figure 2c

Fe – C Binary SystemJ J + graphite

DJ Te = 1013 K D J J + graphite c c Gm D Gm J PD P J DJ CC D XmaxD Te = 1013 K C D + graphite T (K) D J J XC equ XmaxC XC equ XmaxD C D + graphite T (K) D J J XC equ XmaxC XC equ

D J PFeFe P XC (at. fraction) D J XequC XequC Figure 3b 18 XC (at. fraction)

Figure(a) 3b (b) Figure 3a 3c D gra 3d PCC P PJ P gra c c CC c D gra Gm D Gm J Gm D 3c PCC P D gra PCC P

J gra J gra c c PCC P P P Gm D Gm J CC

'Gn

c Gm J

D PFe J PFe X D max X J max C C X D max XequJ XcrJ X J max D J C C C C D XC X C XequC

D J X C max X C max X D X J C C (c) (d) Figure 3c Figure 3d Figure 2.12. (a) Equilibrium phase diagram of Fe-carbon system and Figure 3c the molar free energy of BCC and FCC solid solutions of Fe in (b) 4a equilibrium condition at 1050 K, (c) possible metastable solubilities of

carbon in each phase without the presence of otherD phases, and (d) XLeeC

an open system, in which carburization is takingD place andJ theJ carbon XAppendixC II XLee XN-KC concentration is high enough to induce the α → γ phase transformationC

[46]. T (K)

XC α γ α γ µC = µC and µFe = µFe. It has been realized that the α →Figureγ phase4a transformation happens when the chemical potentials of Fe and carbon are reduced and are suitable for nucleating the austenite embryo. This only occurs when the ﬂuctuation

α in carbon concentration reaches a critical value XC (Cr). The term ∆Gn shown in Figure 2.12d provides the driving force for this transformation which is created due to the “colossal” carbon metastable solubility in α. Background 20

2.6 Phase Transformations in Steels

Phase transformations in steels in response to various thermal and mechanical treat-

ments make steels widely applicable. This is mainly feasible due to the special prop-

erties of iron that exhibits three diﬀerent crystal structures by increasing the temper-

ature (i.e. BCC, FCC and again BCC) [49].

Phase transformations in steel are classiﬁed into two general groups: Thermally

activated (nucleation and growth) and athermal (martensitic) reactions. Most of the

phase transformations in steels happen by thermally activated atomic movements. In

transformations occurring by nucleation and growth, the new phase grows by rela-

tively slow migration of an interphase boundary which is analogous to the transfer

of atoms across this boundary. The second kind of transformation happens by co-

operative movement of many atoms instead of the individual movement of single

atoms. The martensitic transformation occurs at a very high velocity and is almost

independent of temperature. This kind of transformation is often called “diﬀusion-

less”, “shear” or “martensitic”. Figure 2.13 show this classiﬁcation in more detail

[50].

2.7 Nucleation and growth transformations

The rate of nucleation and growth transformations depends on the rate at which nuclei

form and the rate of their growth. Moreover, the activation energy for nucleation and

migration of atoms (diﬀusion) is important. Nucleation and growth transformations

have some general characteristics [50]: Background 21

Heterogeneous Transformations

Thermally Athermal Activated

Coherent Semi-coherent No long-range Long-range Interfase Interfase Transport Transport

Coherent Mechanical Low-angle Continuous Discontinuous Martensite Martensite Twinning boundary Reactions Reactions

Eutectoidal Discontinuous Reactions Precipitation

Figure 2.13. Classiﬁcation of phase transformations in steels after [50].

(1) Dependence of time. The transformation continues until the system reaches

a state of minimum energy. At some temperatures, the transformation may

be so slow that it is not detectable.

(2) Dependence on temperature. If suﬃcient time is provided, the transformation

can continue until ﬁnished at any temperature (unless the equilibrium state

depends on the temperature). However, for homogeneous changes, the rate

of transformation increases exponentially with temperature.

(3) Irreversibility of the transformation. The atoms move independently in this

transformation. So, there is no correlation between the initial and ﬁnal

position of atoms. By reversing the transformation of α0 → γ, the grain

shape and atoms position in the initial and ﬁnal α0 will be diﬀerent. Background 22

(4) Eﬀect of plastic deformation. Plastic deformation may increase the vacant

lattice sites in the system, and temporarily increases the diﬀusion rate of

atoms. Also, nucleation is easier in plastically deformed crystal.

(5) Chemical composition, atomic volume, and shape of the new phase. Necessar-

ily, there is no correlation between parent and product phase in composition,

atomic volume or shape. Except in pure metals which undergo polymorphic

changes, or order-disorder reaction, there is no composition diﬀerence.

(6) Orientation relationship (OR). Usually there is no speciﬁc OR between the

parent and the new phase. However, in some cases (e.g. growth of coherent

precipitates, or eutectoid reactions) there is an OR.

2.8 Martensitic transformations

In martensitic reactions (unlike nucleation and growth reactions), diﬀusion does not play a role. (However, it is not necessarily the case for martensite nucleation). The co-operative movement of many atoms occurs at the speed of sound in the crystal.

Moreover, the composition of the product phase remains unchanged after transformation. In martensitic reaction, the thermal activation energy is not accountable for such a reaction (i.e. athermal). The reaction begins spontaneously at speciﬁc temperature, and below that temperature the parent phase is mechanically unstable. The general characteristics of martensitic transformation is summarized below [50]:

(1) Independence of time. The fraction of transformation is independent of time.

At a constant temperature, an amount of parent phase rapidly transforms to

the martensite phase. Background 23

(2) Dependence on temperature. Temperature plays role in determining the frac-

tion of transformation. However, temperature does not change the velocity

of reaction. By quenching the crystal to diﬀerent temperatures, diﬀerent

amount of parent phase undergoes the martensitic reaction. It is still un-

clear whether the complete transformation is ever possible to happen, spon-

taneously.

(3) Reversibility of the transformation. The martensitic reaction is highly re-

versible. The reverse reaction generally occurs at temperature (As) higher

than the temperature for formation of martensite on cooling (M s). In the

process of transformation and reversion, the size of the crystal and position

of atom are reversible.

(4) Eﬀect of applied stress and plastic deformation. The applied stress can induce

martensitic transformation even at temperatures higher than M s. In contrast

to the transformations with nucleation and growth, plastic deformation of the

parent phase retards the martensitic reaction when the crystal is quenched.

(5) Chemical composition, atomic volume, and shape of the new phase. The

chemical composition of the product phase is similar to that of the original

phase. The transformation may change the atomic volume of the product

phase and they usually form in ﬂat or lenticular plates. The plane of the

lattice where the new phase will form is called habit plane, and the migration

of the interphase boundary occurs along the habit plane.

(6) Orientation relationship. In martensitic reaction, always there is a speciﬁc

OR between the product phase and the parent phase. The product phase

can take the form of a single or twin orientations. Background 24

2.8.1 General theory of martensitic transformation

The ﬁrst mathematical studies on crystallography of martensitic transformation have

been done by Greninger and Troiano [51]. They concluded that the surface relief of

the martensite plate reveals the homogeneous shear along the habit plane, a macro-

scopic interface between the parent and the product phase. While maintaining the

habit plane, a single homogeneous shear is not capable of transforming austenite to

martensite. Therefore, there should be at least two diﬀerent shears accountable for

this transformation, and the ﬁrst shear is acting on the habit plane.

As suggested by Bain and Dunkirk et al. [52], a BCT lattice can be generated in-

side an FCC lattice. A Bain lattice deformation can change the FCC lattice to a BCT

lattice, and is deﬁned by contracting the c lattice parameter by 17% and expanding the a and b parameters by 12% (Figure 2.14). This high amount of strain in the FCC and BCT lattices is not practically possible to be applied on the lattice. Therefore, the Bain transformation is only regarded as hypothetical path and shows the initial and ﬁnal stages of transformation. There are a few other lattice correspondences which have been suggested for the FCC-to-BCT transformation. However, Jaswon

and Wheeler showed that the Bain transformation involves minimal atomic displace-

ments (compared to other lattice correspondences) and is energetically favorable for

ferrous alloys [53].

The lattice correspondence deﬁnes the unique relationship between the atomic

position of the initial and ﬁnal stages of the transformation. The correspondence

matrix of the Bain transformation can be deﬁned as below: 9.5 Diffusionless Transformations; Examples 411

correspond uniquely to specific lattice planes and directions in the martensite lattice (i.e. these corresponding lattice planes/directions pertain to the same atoms (but as before and as after the transformation)). A simple way to conceive the formation of martensite from austenite, revealing the correspondence of certain lattice planes and directions in austenite and martensite is provided by the so-called Bain lattice correspondence, illustrated in Fig. 9.25 (see also Sect. 4.2.2). Consider the two adjacent unit cells (here we refer to the iron sublattice) of the parent austenite phase in Fig. 9.25a. Suppose at the centre of the unit cell at the left-hand side, where an octahedral interstice of the austenite lattice occurs, an interstitial atom resides. At and across the interface of the two adjacent austenite unit cells, a unit cell of b.c.t. type symmetry can be identified. This b.c.t. unit cell can be transformed into a b.c.t. unit cell of the product martensite phase (“Bain deformation”) by contraction (of about 17%) along the c direction and (smaller) expansion (of about 12%) along the a and b directions (see also Fig. 4.25). Two corresponding directions have been explicitly indicated in the figure. The lattice correspondence only implies that the atoms per- taining to certain directions/planes in the parent austenite are the same as those in certain “corresponding” directions/planes in the product martensite; in the specimen frame of reference these corresponding directions/planes of the parent austenite and the product martensite do not coincide (with the exception of the habit plane). For example, in terms of Fig. 9.25,the[10–1]γ direction corresponds with, but as a result of the Bain deformation, is not parallel with the [11–1]α direction. The austenite ′ martensite transformation according to this “Bain model” involves a minimum of → atomic movement, as required for a diffusionless transformation. (2) The lattice invariant deformation.Ifmartensiteformationwouldoccurona planar habit plane in the original austenite lattice, in accordance with the Bain lattice correspondence in association with the Bain deformation, a rotation away from the original habit plane would occur (see the dashed vertical lines in Fig. 9.24bwhich represent the undistorted, unrotated habit plane). To assure that the habit plane can be taken as a plane in the austenite, which does not experience, macroscopically, anetdistortionandrotation,latticeinvariantshears,paralleltothehabitplane,by

Background 25 iron lattice site z-type interstitial site

(a) z (b) z‘

[101] [111] y x‘ y‘ x

Fig. 9.25FigureThe 2.14. Bain lattice (a) Bain correspondence. lattice correspondence (a) A b.c.t. unit cell and can lattice be indicated deformation, for the pair of adjacentand unit (b) cells the of BCT austenite lattice shown. showing (b) This the b.c.t. location unit cell ofcan interstitials be transformed by into crosses a b.c.t. unit cell of[39 the]. product martensite phase (“Bain deformation”) by contraction (of about 17%) along the c direction and (smaller) expansion (of about 12%) along the a and b directions (see also Fig. 4.25). The corresponding [10–1] direction (in (a)) and [11–1] direction (in (b)) have been indicated γ α′

      x0 1 −1 0 x             y  = 1 1 1 y  0           z0 0 0 1 z BCC FCC or

x0BCC = xFCC − yFCC

y0BCC = xFCC + yFCC (2.2)

z0BCC = zFCC.

The formation of martensite can be described by three mathematical entities: a simple shear (P), a lattice deformation (B), and a rigid body rotation (R). Therefore, the combination of these results in shape deformation (P1):

P1 = RBP, (2.3) Background 26 where B is deﬁned as the Bain transformation correspondence in the BCC↔FCC

transformation of ferrous alloys. By using matrix properties, we can change the order

of these factors. Therefore, Eq. 2.3 can be rewritten as:

1 P1P− = RB. (2.4)

3 Since both the P1 and P are invariant plane strains , RB must be an invariant

4 line strain . If the plane and direction of the simple shear are known (e.g. {112}α

plane and h111iα direction in martensite, or equivalently {110}γ plane and h110iγ

direction in austenite), the invariant line strain (RB) can be uniquely deﬁned and all

the elements of each matrix in Eq. 2.4 can be resolved.

For fulﬁlling the three necessary conditions of lattice deformation, simple shear,

and rigid body rotation, martensite phase can be realized equivalently as internally

slipped or internally twinned. In the ﬁrst case, the lattice deformation occurs by

internal slip, which produces an inhomogeneous deformation. In the second case, the

lattice deformation occurs in diﬀerent twins which are crystallographically equivalent

and have similar principal distortion axes. Therefore, in the latter case, it requires

two diﬀerent lattice deformations. The slip and twin mechanism of martensite lattice

deformation are schematically shown in Figure 2.15. Wechsler et al. showed that

the analyses based on the slip and twin nature of the martensite transformation are

mathematically equivalent [54].

3By deﬁnition. 4The intersection of two invariant plane strains results in an invariant line strain Background 27

(a) (b)

Figure 2.15. (a) Lattice deformation followed by slip shear, and (b) lattice deformation leading to twin related regions.

2.8.2 The habit plane and the structure of the interface

At macroscopic scale, the habit plane can be deﬁned as the interface between the

parent and the product phase [55]. This is illustrated as a simple schematic in Fig-

ure 2.16. This plane undergoes very little (or ideally no) change during the transfor-

mation (i.e. movement of the boundary). Otherwise, large-scale plastic distortion of

the surrounding phases would be required to help the boundary movement, and it

is energetically unfavorable [53]. If there is no constraint during phase transforma-

tion, the habit plane ideally forms ﬂat. But, in reality, it is slightly bent (at larger

scales) to accommodate the changes in shape and atomic volume of two phases. The

minimization of interface-energy is responsible for the adoption of particular habit

plane.

A martensitic reaction is the ﬁrst order transformation and is controlled by the

motion of the interface. Therefore, there must be continuity across the interface Background 28

� � ⟷

� Habit Plane

(a)

� � ⟷ � � Habit Plane (b)

Figure 2.16. Schematic of habit plane between α0 and γ when (a) no constraint exists during the transformation, and (b) when a strain energy constrains the shape of the product phase. while it is advancing (i.e. glissile interface) [56]. This continuity can be resolved

by deﬁning a fully- or semi-coherent interphase interface. Due to the shape change

across the interface and having the invariant-plane strain, it is impossible to have a

fully-coherent stress-free boundary between two phases. Therefore, the semi-coherent

interface must form in such a way that dislocations at the interface can glide easily

by advancing the boundary and accommodating the strain.

In order to have a glissile interface, the dislocations which glide at the interface

must have Burger vectors lying out of the interface plane. Only in the case of screw

dislocation, can a Burger vector lie in the interface. Moreover, the dislocation line

must lie in the direction of the invariant-line5. Otherwise, another dislocation is

5Invariant-line is the line in the interface which has no rotation or distortion. 194 T. Moritani et al. / Scripta Materialia 47 (2002) 193–199 sessile dislocations were observed on the broad carbon is enriched in austenite without cementite face of bainitic ferrite. However, no HREM precipitation [18]. Microstructures were observed study has been performed on the bainite/austenite by means of TEM (Philips CM200) and HREM boundary and the characteristic of accommoda- (Jeol JEM4000EX). Orientation relationships (ORs) tion dislocations is not fully understood. between austenite and product were examined by The present authors recently studied interphase analyzing Kikuchi patterns. boundaries of both martensite and bainite by means of HREM [14,15]. In the present study, the characters of accommodation dislocations on 3. Results those two kinds of interphase boundaries are compared to discuss the mechanism of boundary 3.1. Lath martensite/austenite interphase boundary migration. Martensite holds the ORs slightly scattered around K–S 111 c 011 a0; 101 c 111 a0 ,N ðð Þ kð Þ ½ k½ Þ 2. Experimental procedure 111 c 011 a0; 110 c 100 a0 and G–T rela- tionshipsðð Þ kð withÞ respect½ to k austenite.½ Þ The habit plane Fe–20.2Ni–5.4Mn (mass%), in which austenite of lath deviates between 111 c 011 a0 and ð Þ ðkð Þ Þ is stable at room temperature and partly trans- 121 c 132 a0 . In the dark-ﬁeld image of Fig. forms isothermally to lath martensite below room 1(a),ð Þ straightðkð dislocationsÞ Þ with an average spacing temperature [16,17], was used to study lath mar- of 4.8 nm are observed on the broad face of lath. tensite/austenite boundaries. After austenitized at The stereographic projection of Fig. 1(b) shows 1473 K for 3.6 ks and water quenched, the speci- the crystallographic information for this interface. mens were held at 223 K for various periods to Close packed planes of two phases are misoriented promote isothermal martensitic transformation. by 1.0͑ whereas angular deviation of close packed Fe–2.0Si–1.0Mn–0.59C (mass%) was used to study directions is 3.7͑ for this interface. The Burgers bainitic ferrite/austenite boundaries. Specimens vector of dislocations was determined to be b 1 ¼ were austenitized at 1423 K for 0.6 ks, transformed a=2 011 c a=2 111 a0 by contrast analysis. Trace ½ ¼ ½ atBackground 723 K for various periods and water quenched. analysis revealed that the microscopic line direc-29 In this alloy, austenite can be obtained in the gap tion of dislocations is 0:60; 0:57; 0:57 a0 on the ½ between adjacent parallel bainitic ferrite laths since atomic habit plane 111 c 011 a0, indicating ð Þ kð Þ

Fig. 1. (a) Dark-ﬁeld TEM micrographs of the dislocations (see white lines) on the broad face of lath martensite (223 K, 28.8 ks transformed),Figure (b) 001 a 2.17.0 stereographic (a)Dark-ﬁeld projection showing TEM the OR, image the habit of plane the and interface the nature of dislocations dislocations for the interface in ½ (a). (white/black lines) in Fe–20.2Ni–5.4Mn (mass %) steel between the austenite (γ) and the martensite (α0), (b) the corresponding [001]α0 stereographic projection of habit plane and interface dislocation, which reveals the screw characteristic of dislocations [57].

needed to accommodate the misﬁt at the interface. By introducing another disloca-

tion with diﬀerent line direction, they can interact with each other and form jogs.

Jogs require more energy to climb in order to move (i.e. by diﬀusion of vacancies

to help the jogs climb). Therefore, they pin the dislocations, and make the interface

sessile (i.e. immobile). Figure 2.17 shows the crystallographic information of the habit

plane and interface dislocations between martensite and austenite in Fe–20.2Ni–5.4Mn

(mass %) steel. Trace analysis shows these dislocations have a pure-screw character.

The high-resolution TEM (HRTEM) images in Figure 2.18 show the interface

between austenite and martensite. They are viewed in directions of [101]γk[111]α0

and [110]γk[100]α0 corresponding to Kurdjumov–Sachs (K–S) [58] and Nishiyama–

Wassermann (N–W) [59, 60] relationships, respectively. The interface between austen-

ite (γ) and martensite (α0) is indicated by a white serrated line. The regularly spaced

monoatomic steps are regarded as transformation dislocations and the interface has

traces on (111)γk(011)α0 . T. Moritani et al. / Scripta Materialia 47 (2002) 193–199 195

that those dislocations are in a pure-screw orien- parallel close packed planes. A strain of a= tation within an error of 2͑. This result is consis- 12 112 c a=6 011 a0 , which is perpendicular to ½ ð¼ ½ Þ tent with the observation made by Sandvik and 110 c 100 a0, is associated with the stacking ½ k½ Wayman [6]. change per one 111 c layer. By the coalescence of In HREM observation, two diﬀerent beam di- six transformationð dislocations,Þ the shear strain of rections were chosen; the parallel close-packed a=2 112 c is accumulated. This strain can be ac- ½ directions 101 c 111 a0 of the K–S OR and commodated by two kinds of perfect dislocations; ½ k½ 110 c 100 a0 which are parallel in the N OR. b1 a=2 011 c a=2 111 a0 , b2 a=2 101 c ½ k½ ¼ ½ ð¼ ½ Þ ¼ ½ ð¼ Fig. 2 shows the HREM images of the broad a=2 111 a . By introducing these two dislocations ½ Þ face of martensite lath observed along these alternatively on every third layer of (1 1 1)c, the two directions. The broad face of lath, edge-on shear strain due to the stacking change of Fig. 3(a) along 101 c 111 a0 (Fig. 2(a)), contains regularly is fully accommodated. ½ k½ spaced monoatomic steps with the 111 c 011 a0 There is another strain associated with the terrace as previously reported [8]. Theseð Þ stepskð canÞ shape change of parallel close packed planes. To be regarded as transformation dislocations. Along accommodate this component, as shown in Fig. 110 c 100 a0 (Fig. 2(b)), it is seen that many 3(b), the same two sets of dislocations b1 and b2 ½accommodation k½ dislocations with Burgers vectors (the solid lines in the ﬁgure) need to be introduced lying on the parallel close packed planes are pre- on the 111 c 011 a0 plane. Although both of sent on the interface. At the edge of lath, such a those dislocationsð Þ kð areÞ almost of pure-screw type dislocation existed per every third layer of the on the interface when N OR is held across the parallel close packed planes. boundary, they can be visualized as extra half Background Fig. 3(a) schematically shows the shear strain planes when30 they are viewed along 110 c 100 a0. originated from the stacking sequence change of Suppose that those dislocations exist½ as k loops½ on the slip planes inclined on the parallel close packed planes. They can accommodate both of the strain due to the shape change on the parallel close packed planes (i.e., the atomistic habit plane of the broad face) and the strain arising from stacking sequence change at the edge, simultaneously. The dislocations observed in Fig. 2(b) can be explained well by the combination of those two kinds of dislocations. Thus, it is concluded that the shear strain due to the change in the stacking and the shape of parallel close packed planes are fully accommodated by such an arrangement of interphase boundary dislocations.

3.2. Bainitic ferrite/austenite interphase boundary

Bainitic ferrite formed at 723 K is lath shaped with a thickness of about 1 lm. Each lath consists of smaller sub-units whose thickness is in the order of 0.1 lm, as previously reported [19,20]. Sub-units of ferrite exhibit the ORs scattered around K–S, N and G–T relationships and its habit plane deviates around 121 c 132 a0 . In Figure 2.18.Fig. HRTEM 2. HREM images micrographs of the showing interface the broad in Fe–20.2Ni–5.4Mn face of ð Þ ðkð Þ Þ lath martensite viewed along (a) 101 c 111 a0 and (b) the dark-ﬁeld TEM micrograph of Fig. 4(a), (mass %) steel between austenite (γ) and½ martensite k½ (α0) in the viewing 110 c 100 a0, respectively. straight dislocations, 5 nm spaced, are present on directions½ (a) [101]k½ γk[111]α0 , and (b) [110]γk[100]α0 [57].

Figure 2.19 shows schematically how the interface migration occurs by the glide of interfacial dislocations (⊥) on the (111)γ planes. Hirth first proposed the name disconnections to refer to the type of interfacial defects which are a combination of dislocations and steps [61]. Later, Hirth et al. defined disconnection mathematically, and presented a model to differentiate the dislocation and step-like characters of a disconnection [62]. This is further discussed in section 5.2.1. 278 G. J. Mahon et al.

case of diffusional transformations with a rational habit-plane this is frequently done by constructing a Burgers circuit about any interfacial dislocations (Howe, Dahmen and Gronsky 1987).In this instance it is not possible to perform such an analysis due to the close proximity of the steps in fig. 3. However, one can deduce that the primary shear which is responsible for the transformation will be in a direction contained within the unrotated close-packed planes, or (11T), 11 (lOT),. Further, if it is assumed that the two primary shears mentioned in the introduction are the only possibilities, then the primary shear will be in a (112), direction and the magnitude of this shear can be established so as to differentiate between the two different mechanisms of the transformation. The magnitude of the lattice-variant shear can be determined by considering the bending of planes normal to the unrotated planes. This is illustrated in fig. 4, which shows a shear vector of (a/2)[T21], for 12 (ill), planes, or an (a/24)[521], shear corresponding to each (llT), plane. For this experimental observation to be consistent with either of the theories (an (a/12)( 112) or an (a/18)( 112) shear on every { 1 1l}, plane), the shear cannot be occurring in a direction perpendicular to the incident electron-beam (viewing) direction. However, an (a/12)( 112), shear along one of the other (1 12), directions contained in the unrotated (1 11h plane, namely, either [112], or [2Tl],, is consistent with the experimental observations, since when this shear is resolved onto this projection it will appear as an (a/24)[T21], shear. This work therefore supports the idea that the primary shear associated with the f.c.c.+b.c.t. transformation in an (a/12)(112), shear in the case of this martensitic reaction. Using the above information one can construct an overall picture of the interface and how it is able to migrate. The (252), austenite-martensite interface consists of atomic facets on each (1 lT), close-packed plane. The steps of the facets are structural ledges, and associated with each of these is a b =(a/l2)( 112) transformation dislocation. Migration of the interface can then occur by the sweeping of this set of interfacial dislocations across the close-packed planes. This is illustrated schematically in fig. 5. While this analysis has revealed the primary shear responsible for the transformation, the HRTEM image provides only a two-dimensional projection of this complex interface; phenomenological crystallographic theory indicates that a set of Backgroundsimple shears alone cannot account correctly for all the features of the martensite 31

Fig. 5

Downloaded by [University of Pennsylvania] at 08:47 13 January 2015 Austenite (111) Martensite (111) !

Interface InterfaceInterface \\ \ \\\\ \\\\\ Migration \ Migration " \,\\\> - .-.-_-.-.-.I -.-.- -&' \h \/I. \l{ \4 ,4 \.-.-- \.i\\\\\ \\\\\\\ \\\\\\ Martensite Austenite (111)(111")’ Planes Schematic diagram of the dislocation-ledge structure of the austenite-martensite interface. FigureMigration 2.19. Schematic of the interface of interfaceoccurs by glide migration of the interfacial by gliding dislocations the interfacial on the (1lT), planes. Notice that the Isymbols do not⊥ correspond to edge dislocations, but serve to dislocationsillustrate onwhere (111) the dislocationsγ planes. lie. The symbol indicates a dislocation (not necessarily an edge-dislocation) [63]. 32

3 Methodology

3.1 Low-temperature carburizing/nitriding processes

Several methods of surface hardening of stainless steels have been developed; including liquid sodium and cyanide salt bath treatments, plasma nitridation and carburization, ion implantation, and gaseous atmospheric heat treatments [2, 30, 64–66]. Among the above methods, gaseous atmospheric heat treatment has the capability to be expanded to large production scales and meets safety and handling requirements.

Moreover, the hardened case thickness produced by this last method is uniform and the activity of the gases can be controlled. Since 1999, low-temperature gas phase carburization of stainless-steel tube ﬁttings has been carried out by the Swagelok company [30].

In this experiment, carburization of 15-5 PH samples was carried out by Swagelok, and the nitridation process was done with a CVD furnace maintained by Case Western

Reserve University. The conventional time and temperature used by Swagelok are

72 ks and 720 K, respectively.

A schematic of the gas-phase nitridation process used in this project is depicted in Figure 3.1. The procedure of gas-phase carburization is the same, except with a diﬀerent combination of reactive gases: CO, H2,N2. The double HCl gas activation Methodology 33

NH3 + H2 + N2 NH3 + H2 + N2

TN = 670 K TN 7 ks 65 ks

7 ks 7 ks TA 3 1 NH ⟷ H + N HCl + N2 2 2

TA = 600 K

0 185 361036 5415 2072 9025 Time (ks)

Figure 3.1. Schematic of nitridation process performed in CVD furnace, which consists of double-surface-activation and nitridation segments.

segments in all heat treatments (to remove the Cr2O3 passive layer) are performed at

600 K with an activating gases ﬂow of 0.2 L/min HCl and 1.8 L/min N2.

The activity of the nitriding process, aN2 can be deﬁned according to the ammonia

decomposition reaction,

1 3 NH ←→ N + H , (3.1) 3 2 2 2 2 where PNH3 and PH2 are deﬁned as the partial pressure of NH3 and H2, respectively.

Therefore, aN2 is deﬁned accordingly:

!2 PNH3 aN2 = K × , (3.2) P 3/2 H2

in which K is the equilibrium constant for NH3 dissociation. Methodology 34

Table 3.1. Processing parameters to study the eﬀect of nitriding temperature

Gas Composition Nitridation Temperature (K) Activity (aN2 ) Nitridation Time (ks)

NH3 0.007 L/s H2 0.015 L/s 790 7400 72 N2 0.003 L/s

NH3 0.008 L/s H2 0.015 L/s 720 7400 72 N2 0.003 L/s

NH3 0.010 L/s H2 0.015 L/s 650 7400 72 N2 0.003 L/s

NH3 0.007 L/s H2 0.015 L/s 580 7400 72 N2 0.003 L/s

The details of processing temperature and gases ﬂow during nitridation have been

summarized in Table 3.1.

3.2 Characterization methods

Primary studies on microstructural evolution (i.e. phase transformations, nitride/car-

bide formation, and precipitation) after nitridation/carburization were carried out via XRD (X-ray diﬀractometry). An XRD proﬁle provides a quick overview of pos-

sible phases formed during nitridation/carburization. However, the primary peaks

of martensite, austenite and several carbides/nitrides overlap, which makes it hard

to de-convolute the XRD proﬁle. Therefore, more powerful techniques such as TEM

are needed. The microstructure and lattice parameter of the crystals in the sample

can be characterized via TEM in imaging or diﬀraction mode. TEM samples were

mainly prepared by FIB (focused Ion-Beam). Due to the high stress of the samples,

conventional TEM sample preparation was not successful. Methodology 35

Nitrogen/carbon mappings and concentration-depth proﬁles can be studied via

AES (Auger electron spectroscopy), XEDS (X-ray energy dispersive spectroscopy),

EELS (electron energy loss spectroscopy) and APT (atomic probe tomography).

Other microstructural analyses are carried out via SEM (scanning electron microscopy),

TKD (transmission Kikuchi diﬀraction), ASTAR and OM (optical microscopy). Mi-

crohardness testing and nano-indentation are rapid methods for obtaining hardness

proﬁles over the surface and the cross-section of the samples.

3.2.1 XRD

XRD is a rapid analytical method, which provides information about the phase,

crystal structure, and residual stress of the material. Two machines were used in this

study: a Scintag X-1 advanced X-ray diffractometer with Cu radiation (λ =0.15406 nm), CuKα1 and a Rigaku XRD machine (RW100F1) with Cr radiation (λ =0.22898 nm). CrKα1 Two scanning geometries have been used in this study: Bragg-Brentano (θ–2θ) and grazing incidence. In the former geometry, the sample is attached to one axis of the diffractometer and rotated by an angle θ, while a detector rotates on an arm at twice this angle. In the latter geometry, the incoming X-ray beam and the sample are fixed and the beam hits the sample at very small angles (1◦–3◦). This provides superiority compared to the former method in obtaining information only from a very thin top layer of the sample (<1 µm). However, the signal-to-noise ratio is reduced significantly.

The information obtained by XRD originates from a limited depth below the surface. The penetration depth depends on the mean free path of the X-ray photons.

The intensity of the incident X-ray beam attenuates exponentially [67]: Methodology 36

I = I0 exp(−µρL), (3.3)

in which, I0 is the incident intensity and I is the intensity of the beam at depth L of

the sample. µ is the mass absorption coeﬃcient (i.e. 110 cm2/g for iron [68]) and ρ

is the density of the sample (i.e. 7800 kg/m2). A calculation based on (3.3) reveals

that the XRD pattern in Bragg-Brentano geometry mainly originates from a depth of

≈ 3.5 µm below the surface. In the grazing incidence geometry (1◦), the penetration

depth is around 200 nm.

Both machines were calibrated before any scan by a standard polycrystalline Al2O3

plate. All samples were scanned with a step size of 0.04 ◦/step. The scan rate was set

to 1 s/step for the Bragg-Brentano geometry and 6 s/step for the grazing incidence

geometry.

3.2.2 OM/SEM/FIB/TKD

OM and SEM are used as the primary techniques to characterize the microstructure

of samples. Prior to OM, samples were etched by Fry’s reagent1 for 20 s. However, the very ﬁne topographical features of the surface can be revealed by using electrons (with

high energy) instead of photons in an OM. By using the back-scattered detector, it

is even possible to obtain an image with contrast resulting from diﬀerences in atomic

masses (Z-contrast). In this study the FEI Nova Nanolab 200 dual beam SEM/FIB

is used. Before scanning the samples, they were polished to mirror-like surfaces and

sputtered with palladium to increase electrical conductivity and stability of an image

produced by an electron beam.

1 Composition of Fry’s Reagent: 6 ml H2O, 8 ml HCl, 5 ml ethanol, 1 g CuCl2 Methodology 37

FIB is a site-speciﬁc powerful tool that uses heavy Ga ions (with 5 Kv–30 kV accel-

erating voltages) to mill and prepare TEM and APT samples with very high precision.

Samples were cut out from the carburized/nitrided regions in two orientations, cross

section and plan-view.

Preparing TEM samples by FIB leads to the formation of a several nanometer

amorphous (damaged) layer caused by Ga ions. Therefore, samples were further

milled (cleaned) by lower energy ions. A Fischione NanoMill 1040 works with Ar ions

and operates at 900 V, performs the ﬁnal milling after FIB.

By using a special sample holder, TEM foils can be analysed in SEM to study

the phase and orientation of crystals. This method, which is called TKD, recently

has been used to characterise metals with nano-sized grains. This technique is also

called t-EBSD (transmission-electron backscatter diﬀraction) or t-EFSD (transmis-

sion electron forward scatter diﬀraction). TKD provides a great improvement in

spatial resolution compared to the traditional EBSD. In TKD analysis, thin foils are

used instead of bulk samples; therefore, beam broadening is much reduced and the

spatial resolution is lowered to 2 nm–5 nm [69].

3.2.3 TEM

An FEI Tecnai F30 (300 kV) and a Zeiss Libra 200EF (200 kV) TEMs were used to

characterize the microstructure, crystal structure, and chemical composition of car-

burized and nitrided 15-5 PH stainless steel. Both TEM instruments use ﬁeld-emission

guns. The post-column energy ﬁlter used in the Tecnai provides chemical analysis by

EELS and ESI (electron spectroscopic imaging). The in-column Ω energy ﬁlter in

Libra is corrected for 2nd order aberrations and provides large isochromatic sample viewing areas. Dark-ﬁeld and bright-ﬁeld images, DPs and HRTEM images have been Methodology 38

obtained with the Tecnai, and the Libra was used for taking STEM (scanning TEM)

images and for chemical analysis.

Before analysing the HRTEM images, they were ﬁltered by smoothing the edge

according to a Gaussian function to avoid a step function in power spectrum mi-

crographs. The simulations on DPs and stereograms of diﬀerent structures were

performed with the CrystalMaker software.

3.2.4 AES

AES is a surface sensitive analytical technique. In the current studies, a PHI 680

SAM (scanning Auger microprobe) was used to accurately measure the carbon and

nitrogen concentration in 15-5 PH. The detected Auger electron normally can escape

from the top 10 nm of the surface. Therefore, the sample needs to be polished to a

mirror-like surface, and sputtered in vacuum by Ar ions to remove the oxide layer

(for 300 s). Continuous sputtering of the sample is also recommended to avoid the

carbon accumulation during the scan.

3.2.5 APT

APT is a material analysis technique which provides extensive capabilities for both

3-dimensional imaging and chemical composition measurements at the atomic scale.

An APT sample is prepared in the form of a very sharp tip. They were prepared by

a FIB lift-out procedure from the nitrided surface. Cleaning of the tip by ion beam

(5 kV) is performed after the lift-out procedure to minimize the damage layer. The

radius of the tip is less than 50 nm, and the needle length is 300 nm.

In the APT, a high DC voltage (3 kV–15 kV) is applied to the cooled tip. There-

fore, a very high electrostatic ﬁeld is induced at the tip surface, which is below the Methodology 39

Figure 3.2. Schematic showing the principle of APT [72].

point of atom evaporation. A laser or electric pulse is enough to evaporate one or

more atoms from the surface. Atoms are projected onto a position sensitive detector.

Ion detection eﬃciency is normally around 50% and can be as high as 80% [70, 71].

The schematic of APT is shown in Figure 3.2.

A Cameca LEAP 4000 HR Atom Probe (at the School of Engineering, University

of Michigan) was used to study the nitrided 15-5 PH in laser mode at a temperature

of 50 K. Low temperature is used to freeze atoms in their place and increase the

stability of the projected image. The pulse rate for data acquisition is 250 kHz and

the detection rates used are 0.5% and 1%. Increasing the detection rate decreases the

acquisition time.

The projected 14N+ can be mistakenly detected as 28Si2+, since they have similar

mass-to-charge ratios. By considering other peaks that might come from Si or N, the

concentration of nitrogen is corrected (since 15-5 PH has a very small amount of Si). Methodology 40

3.2.6 Hardness

Two hardness indenter instruments were used to measure the hardness of the treated

samples in the plan-view and the cross-sectional surfaces. Plan-view hardness was

acquired by a Buehler Micromet microhardness tester with a Vickers diamond pyra-

mid indenter. A 50 gf load was used for all the samples. To measure the thickness of

the case, cross-sectional hardness values were obtained from an Agilent G200 nano-

indenter. A 5 gf load was used for the nano-indenter. Nano-indentation is sensitive

to surface roughness; therefore, samples were ﬁnely polished to mirror-like surfaces.

3.2.7 Differential scanning calorimetry

DSC (diﬀerential scanning calorimetry) is one of the techniques to observe possible

phase transformations (or any endothermic/exothermic transformation) as a function

of temperature. In a DSC the diﬀerence in heat ﬂow to the sample and a reference

is recorded as a function of temperature. The reference is an inert material such

as an empty aluminum pan. The temperature of both the sample and reference are

increased at a constant rate. The DSC proﬁle reveals the endothermic or exothermic

phase transformation (i.e. heat gain or heat loss) in the sample by diﬀerence of the

two heat ﬂows. The schematic of DSC is depicted in Figure 3.3. The instrument used

in this experiment is a Netzsch 404 F3 Pegasus. DSC of Polymers 2

maintain the holders at the same temperature, is used to calculate ∆dH/dt . A schematic diagram of a DSC is shown in Figure 2. A flow of nitrogen gas is maintained over the samples to create a Methodologyreproducible and dry atmosphere. The nitrogen atmosphere also eliminates air41 oxidation of the samples at high temperatures. The sample is sealed into a small aluminum pan. The reference is usually an empty pan and cover. The pans hold up to about 10 mg of material.

s am p l e re f er e n c e

Li n e a r te m p e r a t u r e s c a n dT = 2 0°C/min T dt + –

H ea t er He a te r Sc a n ∆T Co n t r ol ti m e po w e r po w e r

∆ dq en d o t h e r m – dt + he a t fl ux ex o t h e r m (m c a l / s e c ) ∆Cp

ti m e an d T

Figure 2. Schematic ofFigure a DSC. 3.3. You Schematic choose of the a DSClinear [72 temperature]. scan rate. The triangles are amplifiers that determine the difference in the two input signals. The sample heater power is adjusted to keep the sample and reference at the same temperature during the scan.

en d o t h e r m i c Me l t i ng pe a k gl as s en d i ng tr a n s i t i o n tr a n s i en t he a t f l ux st a r ti ng (m c a l /s e c ) tr a n s i e n t ∆Cp Cp Cr y s t a l l iz a t i on 0 pe a k st a r t 40 0 50 0 st o p ex o t h e r m i c ti m e a n d Te m p e r a t u r e ( ° C ) Figure 3. Typical DSC scan. The heat capacity of the sample is calculated from the shift in the baseline at the starting transient. Glass transitions cause a baseline shift. Crystallization is a typical exothermic process and melting a typical endothermic process. ∆trH is calculated from the area under the peaks. Few samples show all the features in this schematic thermogram.

4 Experimental

4.1 Non-treated 15-5PH

Figure 4.1 shows the microstructure of non-treated 15-5 PH, which contains marten-

site laths. The volume expansion caused by the formation of martensite from austenite

after quenching is often accompanied by the introduction of dislocations and twins.

This Figure reveals a high density of entangled dislocations in the martensite.

Figure 4.1 also shows an MnS inclusion and an NbC carbide. Sulphur is generally

an undesirable element in stainless steels, but a small amount of sulphur can increase

the machinability of steel [73]. Mn is added in a limited amount to steels to avoid the

formation of iron sulphide and to increase hardenability of steels [74]. Nb is a strong

carbide maker and a small amount of it leads to higher wear resistance of stainless

steel [75].

Figure 4.2 demonstrates the existence of a NbC particle with a rock salt crystal

structure (i.e. Fm3m).¯ The DP taken from the particle is taken in the [112] zone axis

of the crystal.

A Z-contrast STEM image of the same area shows a low-density but very stable

MnS inclusion attaching to the NbC particle. From the shape of the NbC particle

(which is partially surrounding the MnS inclusion), it can be inferred that the NbC Experimental 43

Figure 4.1. Z-contrast STEM image of a non-treated 15-5 PH, showing martensite laths.

particles nucleate and form after MnS inclusion during homogenizing of steel at high temperatures, and MnS inclusions provide nucleation sites for NbC carbides.

Figure 4.4 shows the DSC proﬁle of non-treated 15-5 PH, which veriﬁes that the martensite is stable up to 735 K (As). The temperatures used in this study are well below the As temperature of the 15-5 PH alloy. Experimental 44

(a) (b)

{220}

{111}

⨂ [112]

Nb NbC (Fm3m): � = 0.447 nm 5 Energy (keV) 15 20

Figure 4.2. (a) Dark-ﬁeld image of NbC carbide in non-treated 15-5 PH, and (b) its corresponding DP in [112] zone axis. (c) XEDS chemical analysis of the particle, and (d) the crystal structure of the NbC.

Point #2

! !

Figure 4.3. Z-contrast STEM image of MnS inclusion and the XEDS proﬁle containing strong signals of Mn and S elements (point #2). A brighter region attached to the MnS inclusion (i.e. point #6) is a NbC particle shown in Figure 4.2. Experimental 45

DSC /(mW/mg) 0.20 DSC /(mW/mg) [1.1] ↓ exo Peak: 644.8 °C, 0.1732 mW/mg 0.20 [1.1] ↓ exo Peak: 644918.8 K°C, 0.1732 mW/mg

0.15 0.15

End: 674.4 °C End: 674947.4 K °C Onset: 458.5 °C 0.10 Onset: 735458.5 K °C 0.10 Onset: 966.0 °C Onset: 966.0 °C

0.05 0.05

Peak:Peak: 490763 490.1 .1K°C, °C, 0.04793 0.04793 mW/mg mW/mg

0.000.00 200500200 400700400 600900600 8001100800 10001000 TemperatureTemperature /°CK /°C MainMain 2016-04-11 2016-04-11 16:44 User: DXS11 DXS11

Created withCreated NETZSCH with NETZSCH Proteus software Proteus software Figure 4.4. The DSC proﬁle of non-treated 15-5 PH, showing the As and Af temperatures of the alloy at 735 K and 918 K, respectively.

4.2 Carburized 15-5PH

Carburization of a 15-5 PH sample were successfully performed by the Swagelok com-

pany. The carburized sample were characterized using hardness measurement, optical

images, AES and TEM analyses.

4.2.1 Hardness proﬁle

Figure 4.5 shows the nano-indentation results on the cross-section of carburized 15-5 PH.

This hardness proﬁle reveals that the carbon had diﬀused within a depth of ≈ 40 µm which is comparable to AISI 420 (martensitic stainless steel) carburized at a similar

temperature for four hours [76]. Experimental 46

1 2

1 0 ) a

P 8 G (

s s

e 6 n d r a

H n o n - c a r b u r i z e d 4

0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0 D e p t h ( µ m )

Figure 4.5. The results of nano-indentation on the cross-section of 15-5 PH after low-temperature carburization. The dashed line represents the hardness of a non-carburized sample.

4.2.2 Microstructure of carburized 15-5 PH

Figure 4.6a and b show the microstructure of the carburized 15-5 PH taken by OM and

SEM. Etching the sample reveals a higher contrast at the carburized edge (around

50 µm width) compared to the core of the sample, and it shows a very thin layer

(around 5 µm width) with white contrast at the very edge. Unlike austenitic stainless

steels, etching carburized 15-5 PH does not determine the thickness of the carburized

layer. This can be explained based on the previous study on polarization of car-

burized 15-5 PH which showed the corrosion resistance of the sample barely changes

after carburization [77]. The SEM image in Figure 4.6b shows martensite laths after

sputtering the cross-section by Ar ions. In consecutive sputterings of the sample, it is

observed that the edge of the sample (the carburized regions) has higher sputtering

resistance compared to the core of the sample. Experimental 47

(a) (b)

µm 20 µm

Figure 4.6. (a) optical image of carburized 15-5 PH at 720 K for 72 ks and etched by Fry’s reagent, (b) SEM image of the sample, which is sputtered by Ar for 300 s to reveal the martensite laths.

A low magniﬁcation STEM image of carburized 15-5 PH is shown in Figure 4.7.

Analysis of DPs taken from diﬀerent parts of the carburized sample hardly shows

a change from the non-treated sample. The microstructure is still fully martensitic

and no phase transformation has been observed. Comparing Figures 4.6a and b with

Figure 4.7 shows original laths are still composed of smaller laths, which may have

sub-micron dimensions.

Near the edge of the carburized sample, in the top 1 µm from the surface, carbide

precipitates have been observed. The TKD method provides a low magniﬁcation im-

age of the TEM sample and reveals phase and orientation maps. Figure 4.8 shows

that the microstructure of the carburized 15-5 PH is fully martensitic with 3 major

martensite grains. This Figure clearly shows that inside any of these large grains,

there are smaller laths (variant or twins) with smaller misorientations. During the

steel making process, quenching the sample from the austenite phase leads to the Experimental 48

8 nm-1

Figure 4.7. STEM image of the carburized 15-5 PH and the corresponding DP in [100] zone axis.

formation of martensite laths that have similar grain shape as the original austenite

grains. The large grains in Figure 4.8b have large misorientation angle, which origi-

nated from the primary austenite grains. The individual martensite laths inside each

grain usually obey the N–W or K–S relationships with the primary austenite [78–80].

These two relationships are close and only deviate 5.26◦ degrees from each other.

(However, no retained austenite has been observed in this alloy). The schematic of

the N–W relationship is depicted in Figure 4.9. This Figure shows martensite laths

form in twins that have 60◦ angles relative to each other. Three large martensite

laths shown in Figure 4.8b also obey this rule. Figure 4.8c indicates the formation of

H¨aggcarbide (χ–M5C2) and cementite θ–Fe3C near the surface. The H¨aggcarbide is

detected as an ≈ 4 µm-size grain beneath the surface, and the cementite forms at the Experimental 49

Table 4.1. Crystal structure of H¨aggcarbide (χ–M5C2) with monoclinic C2/c spacegroup (No. 15) [81].

a = 1.1552 nm α = 90◦ Lattice Parameters b = 0.4546 nm β = 97.7◦ c = 0.5043 nm γ = 90◦ C 0.107, 0.285, 0.149 Fe 0.097, 0.078, 0.423 Atom positions Fe 0.215, 0.581, 0.306 Fe 0, 0.561, 0.25 very top surface (<400 nm) with ≈ 100 nm grain size. (The cementite is not shown

here).

Higher magniﬁcation TKD analysis on H¨aggcarbide is shown in Figure 4.11. The

formation of H¨aggcarbide after low-temperature carburization also has been reported

by Ernst et al. in 316 stainless steel [81, 82]. However, formation of H¨aggcarbide has not been previously reported for martensitic stainless steel. The morphology of this carbide is not acicular, and it is more similar to an elongated grain. The upper and lower parts of the martensite matrix around the carbide have similar orientation. It is possible that α0 → χ(M5C2) phase transformation had been done partially in the

martensite grain and the carbide was growing during the treatment, but didn’t have

enough time to grow larger.

DPs which are taken from this carbide grain conﬁrm the existence of H¨aggcarbide.

Figure 4.11 shows a selected area containing carbide (in the [1100]¯ χ zone axis) and

the matrix. This DP matches the simulation very well and conﬁrms the results that were obtained by the TKD (Figure 4.10). The crystal structure of the H¨agg carbide

used in this experiment is obtained from [81] and is presented in Table 4.1.

At the top 500 nm of the carburized sample there is another type of carbide which

forms in smaller grain size (which is not very clear in the TKD analyses). This Experimental 50

Hägg Fe (BCT) 5µm

Figure 4.8. TKD analysis of carburized 15-5 PH, which shows a carburized layer at the top 1 µm of the sample. (a) The band contrast map, (b) orientation map, and (c) phase map (green color is the matrix and red color is the H¨aggcarbide). The white rectangle is enlarged in Figure 4.10. Experimental 51 ] 1 2 1 [

(011)α’ (011)α’

(111)� [ 0 1 (011)α’ 1 ]

Figure 4.9. Schematic of N–W relationships and the formation of martensite laths (twins) rotated by an angle of about 60◦ degrees with respect to each other.

a b

c d

Fe (BCT) Hägg Fe7C3 Fe (FCC) 1µm

Figure 4.10. Enlarged part of the sample from Figure 4.8 and detection of H¨aggcarbide (M5C2): (a) STEM image, (b) band contrast map, (c) orientation map, and (d) phase map. Experimental 52

α’

M5C2

b c

8.0nm-1

Figure 4.11. (a) Area selected on the martensite and H¨aggcarbide to record DP, (b) corresponding DP in [1100]¯ χ zone axis, and (c) the simulated H¨aggcarbide DP that is overlaid on the experimental DP.

carbide has formed between martensite laths, and it resembles carbide that grows gradually by consuming the matrix. The DPs in Figure 4.12 show this type of carbide Experimental 53

Pt 100 nm 50 nm Pd

α’

α’ α’

α’

[021]θ [011]θ

[100] 8.0 nm-1 8.0 nm-1 α’

Figure 4.12. (a) Selected area on the martensite and cementite θ–Fe3C to record DPs in two diﬀerent zone axes. Orange and blue spots are simulated DPs of cementite and martensite, respectively.

is cementite θ–(Fe, Cr)3C. The measured plane spacings of the carbide are in good

agreement with the simulated DPs.

XRD is a technique which collects information from the top few micrometers of

the surface. Figure 4.13 shows the XRD proﬁle of the surface of carburized 15-5 PH.

The simulated peaks of cementite θ–Fe3C match very well with the experimental

XRD profile. The peaks from the Häggcarbide were very faint in the XRD profile. Experimental 54

(110)α’ 15-5PH-Carburized-720 K Cementite (simulation) Iron BCC (simulation)

(200)α’

Figure 4.13. XRD proﬁle of carburized 15-5 PH at 720 K for 72 ks and the simulated peaks of cementite and Fe(BCC) crystals with a lattice parameter of aFe = 0.287 nm.

Table 4.2. Crystal structure of θ–Fe3C with an orthorhombic Pnma spacegroup (No. 62).

a = 0.5087 nm α = β = γ = 90 Lattice Parameters b = 0.6744 nm ◦ c = 0.4525 nm C 0.877, 0.250, 0.444 Fe 0.037, 0.250, 0.840 Atom positions Fe 0.182, 0.067, 0.337

(The simulated XRD peaks of H¨aggare not shown here.) This could be related to

the low concentration of H¨aggcarbide formed in the sample and their depth from the

surface (from our TEM observation, i.e. Figure 4.10, the H¨aggcarbide was forming by

growing inside the sample at the depth of ≈ 1 µm). In contrast to the cementite, the

H¨aggcarbide was not observed in other TEM samples prepared from the carburized

15-5 PH. It seems that the cementite phase is the more stable carbide in this alloy.

The lattice parameter of θ–Fe3C is shown in Table 4.2. Experimental 55

011

111

211

011 011 100 100

211

111

011 cementite martensite

Figure 4.14. Stereographic projection of OR between cementite and martensite obtained by analysing Figure 4.12. This OR is known as the Bagaryatskii relationship [83]. Orange and blue spots represent planes of cementite and martensite, respectively.

The OR of cementite to matrix can be obtained by analysing the DPs in Fig- ure 4.12. The consistency between these DPs is the parallelism of the two planes in both crystals with the densest atomic planes (i.e. (011)α0 and (100)θ). Therefore the

OR of cementite to martensite can be deﬁned as:

(011)α0k(100)θ (4.1)

[100]α0k[011]θ The stereographic projection of this OR is depicted in Figure 4.14. This OR is known as the Bagaryatskii relationship [83, 84].

In a summary, the results of the carburized 15-5 PH alloys show an improvement in hardness of the alloy after carbon supersaturation. However, the formation of Experimental 56

carbides at the surface is not enhancing the corrosion resistance of this alloy. Even

the metallographical observations of this alloy after etching by Fry’s reagent show

there is no diﬀerence in the etching of the case and the core of the sample.

4.3 Nitridation of 15-5PH

4.3.1 Microstructural observations

Nitridation of 15-5 PH has been done with a similar procedure to carburization except

in the former case, the diﬀusing element is nitrogen. As explained in section 2.3.1,

due to the more neutral behavior of nitrogen atoms toward the Fe atoms, the lattice

distortion/expansion caused by nitrogen is slightly higher than that caused by carbon.

Austenitic stainless steels which have been processed by low-temperature nitridation

have shown higher lattice parameter expansion [85]. Wu et al. showed that this lattice

parameter expansion can even induce ferromagnetism in 316L austenitic stainless

steel [86], which is not the case in the low-temperature carburized samples. The

expansion caused by nitrogen in the martensitic or ferritic stainless steels was not well understood, since previous DPs and XRD observations on the duplex stainless

steel showed the very interesting but puzzling information that there is no lattice

parameter expansion in the δ-ferrite phase after low-temperature nitridation [87].

However, this concept has been resolved and thoroughly explained in section 5.3.

Nitrided 15-5 PH is primarily studied by OM and SEM. Figure 4.15a shows the white layer near the surface of the nitrided sample after etching with Fry’s reagent. It

is notable that this nitrogen supersaturated layer is more etch resistant. (This result

can be compared with the optical image of the carburized 15-5 PH (ﬁgure 4.6a), which

shows almost no diﬀerence in the etching of the core and the hardened layer.) The Experimental 57

a b

4 µm 50 µm

Figure 4.15. (a) optical image of nitrided 15-5 PH at 670 K for 72 ks and etched by Fry’s reagent, (b) SEM image of the sample, which is sputtered by Ga for 300 s and reveals the small plate-like features inside martensite grains.

magniﬁcation of the image in Figure 4.15a is close to the resolution limit of the OM and no more information can be obtained at this scale. Therefore, an SEM was used to observe this hardened layer. Figure 4.15b shows an SEM image of the hardened layer in the same sample. Before taking the image, the sample was sputtered by Ga ions to show the microstructure. The grain boundaries are more prone to the sputtering and are turned to grooves. The more interesting feature of Figure 4.15b is the evolution of plate-like features inside the grains. Depending on the grains’ orientation relative to the surface, some plates are more prominent than the others, and some plates are only visible as faint contrast. More magniﬁcation on this instrument (i.e. FEI Nova

Nanolab 200 FIB/SEM) did not necessarily provide more information about these nano-size features. Therefore, this sample has been analyzed with TEM. Experimental 58

Figure 4.16 reveals the bright-ﬁeld TEM images of the nitrided 15-5 PH. As shown

in Figure 4.16a, one martensite grain/lath is bounded with many of these plate-like

features. Figure 4.16b shows a higher magniﬁcation of these plates, in which they

have formed in speciﬁc orientations. Two plates on the right side of Figure 4.16b look

like twins.

There are several important features common to the newly formed plates inside

the martensite laths. Firstly, they have been observed mostly near the surface of the

specimen, where the nitrogen concentration is high. Secondly, their size is limited

by grain boundaries or by already-formed plates; otherwise, they end in sharp tips.

Thirdly, they have a high length-to-width ratio i.e. they exhibit a plate-like morphol-

ogy with an average aspect ratio of 0.08. Finally, they tend to grow in a speciﬁc set

of directions relative to the martensite laths and appear to shear each other where

they cross.

4.3.2 DP analyses and ASTARTM

More detailed information about the plates and the matrix can be retrieved by tradi-

tional electron DPs. Electron DPs provide a powerful tool for identifying the struc-

ture and orientation of grains. Figure 4.17a shows a bright-ﬁeld image of the plate-

containing martensite lath. The bright circular area, obtained by double-exposure with an inserted area-selecting aperture, indicates the region from which the DP is

originated. The DP of the plate is also illustrated schematically with dashed lines

in Figure 4.17c. The measured plane spacings and the angles between planes resem-

ble those of the expanded austenite phase. However, there are slight diﬀerences in

lattice plane spacings and angles compared to a simulated austenite lattice (γ-Fe) with a lattice parameter of a = 0.36 nm. Figure 4.17c apparently shows almost no Experimental 59

Figure 4.16. (a) Bright-ﬁeld TEM image of one martensite grain in the nitrided 15-5 PH at 670 K, showing a multitude of new plates, and (b) a higher magniﬁcation image of these plates with some internal contrast. Experimental 60

a b

Plate

Matrix

0.206 nm

0.204 nm

110 0.211 nm 00-2

0.208 nm

53˚ 90˚ 73˚

-1-10 54˚ 011

-200 0.175 nm

Matrix Plate

Figure 4.17. (a) TEM bright-ﬁeld image of a plate-containing martensite lath in 15-5 PH, (b) DP acquired from the circular selecting aperture shown in (a), and (c) schematic of DP and the calculated plane spacings of the plate and the matrix. (DP obtained from both the plates and the matrix in the [110]γ and [100]α0 zone axes.) expansion or contraction of the lattice parameter of martensite although it contains

≈ 15 at. % nitrogen (solid line pattern). However, the (011) spots are elongated and become diﬀused normal to the [011] direction in the viewing plane. This phenomenon is attributed to the tetragonality of the martensite lattice, which will be shown and discussed in more detail in sections 4.5 and 5.3. Experimental 61

Figure 4.18a shows another TEM image of a plate-containing lath in 15-5 PH, lo-

cated ≈ 1 µm from the surface of the sample. (The bright background in Figure 4.18a

is the martensite lath, which is not in a diﬀracting orientation.) Figure 4.18b shows

a striking evidence of two of these plates crossing and shearing each other. Analysis

of the DPs of these plates indicates similar ORs between the parent martensite or

the ferrite phases and the plates in the three alloys. Figures 4.18c, and d show the

DPs of the matrix and the plates in diﬀerent zone axes. The measured plane spacings

and the angles between planes are close to those of the expanded austenite phase

[85, 88]. Not only in 15-5 PH, but also in the martensite phase of 17-7 PH [89] and in

the ferrite phase of 2205 duplex stainless steels [87] similar plates have been observed

after low-temperature nitridation.

In order to unambiguously identify the structure and orientation of the newly

formed austenite in 15-5 PH, we employed a beam-precession-assisted crystal orienta-

tion mapping technique, known as ASTARTM. In this technique, a precessing electron nanoprobe (focused electron beam) is scanned over the specimen and ordinary spot

DPs are recorded at each location. The electron beam is precessed to attenuate dynamical eﬀects and enhance pattern quality. DPs are then matched with simulated templates and are indexed automatically [90]. Figure 4.19b shows a superimposed phase-reliability map of the martensite lath of Figure 4.19a containing these plates.

The green and red colors represent martensite and austenite phases, respectively.

(The darker areas are regions of lower conﬁdence in the orientation determined by the software.) As is evident from Figure 4.19b, these plates are clearly the austenite product phase. Moreover, the information obtained from the orientation of the plates shows that all plates in one lath are formed preferentially in a speciﬁc orientation. Experimental 62

a surface b

200nm a b c ca db c

4 nm-1 4 nm-1 Matrix (martensite) Plate (austenite)

Figure 4.18. (a) TEM bright-ﬁeld image of a plate-containing martensite lath in 15-5 PH, (b) a higher magniﬁcation STEM image showing 59˚ shearing of two plates in the 15-5 PH sample, (c) and (d)59˚ are DPs ob- 63˚ tained from both88˚ the63˚ plates and the matrix in the [100]γk[110]α0 and 88˚ 61˚ [111]γk[011]α0 zone axes, respectively. 64˚ 53˚61˚ 64˚ 53˚

matrix matrix plate plate Experimental 63

a b

400 nm

c 110

312 121

101 011 112 010

112 001 1 111 110 112

011 101 100 011

312 121 matrix (martensite)

110 plate (austenite)

Figure 4.19. (a) Bight-ﬁeld image of the plate-containing martensite lath in the 15-5 PH alloy, (b) the corresponding ASTAR phase map of austenite (red) and martensite (green), and (c) the determined stereographic projection of the matrix (martensite) and the plates (austenite). Experimental 64

Theoretically, one DP from the martensite/austenite interfacial region suﬃces

to determine the OR of the two phases. However, some inaccuracy arises in the

measurement of reﬂections in the DPs (i.e. the lengths and interplanar angles), and

a slight deviation of two phases from the exact OR can occur at diﬀerent locations.

Therefore, several DPs in diﬀerent zone axes were used to decrease this possible

inaccuracy.

Common martensite–austenite ORs reported for Fe-alloys are those of K–S [58]

and N–W [59, 60] relationships, both involving the closed-packed planes (111)γ and

(011)α0 always being parallel. However, diﬀerent preferred ORs deviate in the angle

(φ) between the two closed-packed directions, [101]γ and [111]α0 . In the case of K–S and N–W relationships, φ is 0.00◦ and 5.26◦, respectively. However, in most Fe-alloys, angles between 0.00◦ and 5.26◦ have been reported [78, 91–94]. φ can be measured in

the DP of the martensite and the austenite in [101]α0 and [111]γ zone axes. As shown

in Figures 4.18c and d, φ has been measured for several plates; a range of 2.5◦–5.5◦

has been recorded. Therefore, the martensite–austenite OR can be deﬁned as:

(111)γk(011)α0 (4.2)

[101]γ 2.5◦ to 5.5◦from [111]α0 (4.2) is very close to the martensite–austenite OR found for Fe-19%Ni-5%Mn (at. %) alloy after austenitizing at 1420 K (1147 ◦C) and quenching that alloy in water [78], further evidence in support of the hypothesis of a martensitic (diﬀusionless) transformation mechanism. The stereographic projection of recorded OR (4.2) has been depicted in Figure 4.19c. It shows that there are several other planes of each phase that are almost parallel to each other, including: (110)γk(100)α0 and (121)γk(211)α0 . Experimental 65

The only diﬀerence in our samples from previously studied martensitic alloys is

the nitrogen supersaturation, which expands the lattice plane spacings. Firstly, after

diﬀusion of ≈ 16 at. % nitrogen in the alloy, the DP reﬂections, especially those of

the matrix, become highly diﬀused and elongated in certain directions (as is shown

in section 4.5). Secondly, there are some variations in stress associated with varying

nitrogen concentrations at diﬀerent depths, which possibly leads to the small deviation

between the two most densely packed directions of both phases (i.e. [101]γ and [111]α0 )

from being parallel. More information about the crystallography of the martensitic

austenite, the habit plane, and the interface structure are discussed in sections 4.3.3

and 5.2.1.

4.3.3 Habit plane determination

In the early observations of lath martensite in low carbon steel, the habit plane was mainly determined by measuring the surface relief by OM. The primary results

indicated that the habit plane in the austenite grain is (111)γ [95, 96]. Later, Marder

and Krauss [97] concluded that the habit plane is an irrational plane and is close to

(557)γ. In the past 40 years, there have been more studies on determining the habit

plane between austenite and martensite by TEM. Wakasa and Wayman reported a

mean habit plane 4.5◦ from (111)γ for the Fe-20%Ni-5%Mn alloy [98]. More recent

observation of Fe-C alloys containing various carbon contents from 0.0026 to 0.61

mass % also showed a (557)γ habit plane which is about 9◦ from the (111)γ plane

[79]. Habit planes several angles from (111)γ have also been observed in diﬀerent

types of steels such as Mn-containing interstitial free steels and a maraging steel [99],

Fe-0.3%C-3%Cr-2%Mn-0.5%Mo (mass%) alloy [93], and Fe-24%Ni-6%Ti (mass %)

alloy [100]. The habit planes of several alloys are shown in Table 4.3. However, Experimental 66

Table 4.3. The habit planes of martensite in diﬀerent alloys. These indices are approximate, since the habit planes are in general irrational [102].

Composition (wt.%) Approximate habit plane indices Low-alloy steels, Fe–28Ni {111}γ Plate martensite in Fe–1.8C {259}γ Fe–30Ni–0.3C {3 15 10}γ Fe–8Cr–1C {252}γ

most of the early studies on habit plane determination and the phenomenological

crystallographical theories [54, 101] of austenite-to-martensite phase transformation were formulated for the plate martensite in simple steels with habit plane of (259)γ.

As was explained earlier, due to the stress, the habit plane usually is not a straight plane. In this work, all habit plane have been determined on the straight region of the martensite-austenite interface. Two approaches can be used to determine the habit plane, based on the same principle: by considering the 3-dimensional character of an imperfection and depicting its stereographic projections (Trace Anaysis [103]).

In the ﬁrst approach, the martensite-austenite interface is selected in the TEM foil, in which the interface is roughly perpendicular to the sample surface (edge- on position). A schematic of the interface (ABCD) in the TEM foil is shown in

Figure 4.20. θ is the angle between the interface normal and the TEM foil. Finding an exactly perpendicular interface to the surface is diﬃcult. Therefore, minimal tilting of the sample to α and β angles is inevitable. The perpendicular interfaces to the foil surface are preferred, since tilting of the foil to satisfy the edge-on position is reduced and the projected thickness of the foil (t × sec(θ)) is minimal. Usually

the foil orientation for the edge-on position can be reached by indexing a high-index Experimental 67

� � �

� e- � � � y � � x

Figure 4.20. Orientation of a habit plane (ABCD) in a TEM foil with the thickness of t, after tilting the foil to α and β angles. The electron beam (e−) is parallel to ABCD plane.

DP coming from both phases at the interface. In this case, the edge-on position was

determined by slightly tilting the foil to the [011]γk[111]α0 or [111]γk[110]α0 zone axes.

The procedure for habit plane determination can be summarized as follows

(1) Bringing the sample to the ﬁrst zone axis (ﬁrst projection).

(2) Determining the orientation of habit plane normal relative to the zone axis

(i.e. determining the great circle in stereographic projection which contains

the habit plane normal).

(3) Tilting the sample to the second zone axis, and determining the orientation

of habit plane relative to the second zone axis (second great circle).

(4) The habit plane is located in both great circles, therefore it must be perpen-

dicular to the normal of both great circles. The cross product of great circle

normals is the habit plane.

Obtaining plane (or direction) orientation in TEM could be challenging, since

TEM only shows a 2-dimensional projection of a sample, a vector or a direction. This Experimental 68

is similar to a shadow of a 3-dimensional object on a wall created by a light source.

However, theoretically, one angle of the vectors can still be determined relative to the wall (and the plane containing them). Then, by rotating the object, the direction and

size of the vector would change. Therefore, two diﬀerent projections of the vector are

suﬃcient to uniquely determine two angles of the vector or a plane in 3 dimensions.

The principle is similar to human vision, in which by combining two 2-dimensional

images one from each eye forming at slightly diﬀerent angles, a 3-dimensional image

is reconstructed in the brain.

For instance, Figure 4.21a shows the DP of the austenite plate and the matrix in

[011]γk[111]α0 zone axis. The DP is recorded by converging the electron beam to the

extent that the image of the sample can be seen in each reﬂection. The direction of

the austenite plate can be measured relative to the (110)α0 plane. Figure 4.21a shows

the habit plane projection is around 11◦ away from the (110)α0 plane and it is close

to the (541)α0 plane. The (541)α0 plane is located in the great circle (123)α0 (green line in Figure 4.21b). Since the habit plane in Figure 4.21a is not necessarily parallel to the viewing direction [111]α0 , it can be any plane located in the great circle (123)α0

(which contains it and is also parallel to the viewing direction).

Figure 4.22a shows the second DP which is oriented in the [111]γk[101]α0 zone axis.

This is the same region on the sample which is acquired by tilting the sample and

maintaining the (110)α0 plane parallel to the viewing direction. (Note that in both

Figures 4.21b and 4.22b the (110)α0 plane does not move relative to the transmitted

beam, and it stays in a diﬀracting condition.) The same procedure can be done to

determine the location of the habit plane normal in the second great circle, in the

second zone axis. The great circle (575)α0 which contains the habit plane normal Experimental 69

Location of habit plane normal on (123)α’ plane

a b

(101) α’ 90˚

(123)α’

(110)α’

11˚

[111]α’ [110]ɣ’

11˚

Figure 4.21. (a) DP of the austenite plate and the matrix [011]γk[111]α0 zone axis by using a convergent electron beam and observing image in the reﬂection, and (b) the stereographic projection of (a), which shows the location of habit plane normal relative to the (110)α0 plane.

relative to the second zone axis is indicated by a blue line in Figure 4.22b. Now, the

exact orientation of a habit plane can be determined by having two distinct planes

(great circles) which both contain the habit plane. Therefore, the cross product of

two great circles’ normals is the habit plane:

Great circle 1 × Great circle 2 = habit plane (4.3)

(575)α0 × (7 10 7)α0 = (872)α0

As shown in Figure 4.22b, the determined habit plane (872)α0 is very close to the

1 (541)α0 plane or parallel to the (755)γ plane, based on the determined N–W OR .

1There are ≈3 degrees of error in measurement of the reﬂection spots, which results in similar amount of error in the habit plane determination. Moreover, habit plane can have slight variation depending on its location in macroscopic scale. Experimental 70

a b

interface

(25 26 25)α’ (7 10 7)

(101)α’ 45˚

(541)

[101]α’ (5 7 5)α’ [111]ɣ

Figure 4.22. (a) DP of the austenite plate and the matrix in [111]γk[101]α0 zone axis, and (b) the stereographic projection of (a), which shows the location of the habit plane normal in the (575) plane (blue line), in (7 10 7) plane (green line) and their cross product (8 7 2). (872) is the habit plane which is very close to (541) plane.

(541)α0 plane is the projection of the habit plane in the [011]γk[111]α0 zone axis, and initially was determined in Figure 4.21. Moreover, this shows that the habit plane is almost perpendicular to (011)γ and (111)α0 planes. The habit plane (541)α0 k(755)γ has

been reported in various steels with slight diﬀerences in angle [78, 79, 91–94, 97–100].

Another conclusion from the determined habit plane is that it is very close to

the densest atomic planes in both martensite and austenite phases (i.e. (110)α0 and

(111)γ). These planes have very close plane spacings as well (e.g. (110)α0 = 0.204 nm

and (111)γ = 0.208 nm) in a non-expanded stainless steel. The notion of martensitic

transformation implies that atom movement occurs at a small fraction of a second and

the new conﬁguration is reached by the minimum atomic rearrangement (and mini-

mum movement energy or fully conservative). From the observations on habit plane, Experimental 71

it can be realized that the motion of the transformation interface almost occurs in the

densest planes of both phases (which have very similar lattice spacings). Therefore,

atoms do not need to jump far normal to the interface. Instead, they shift laterally

in the interface plane, as the interface sweeps the atoms (this atomic movement will

be explained later). The atomic conﬁguration of both phases at the interface can

be simpliﬁed in Figure 4.23. This is a simple but important analogy based on the

N–W OR and the habit plane obtained in this study. Note that the determined habit

plane, i.e. (575)γk (278)α0 slightly deviates from the densest planes in both phases.

As will be explained further in section 4.3.5, the slight deviation in the habit plane

(an irrational plane) is caused by the introduction of steps and dislocations at the

interface (disconnections).

The second method of habit plane determination is by identifying two line defects

lying in the habit plane and ﬁnding their crystallographic orientations relative to

the matrix. The ﬁrst line can be a dislocation in the interface and the second line

is the intersection of the plate and the matrix. However, this approach requires

identiﬁcation of an interface dislocation in a highly strained nitrided sample (which

has a high dislocation density). This makes the second approach quite challenging

and with a high chance of error. It is easier to apply this trace analysis to annealed

samples or those of with lower dislocation density.

4.3.4 Chemical Analyses

Chemical analyses of the nitrided 15-5 PH have been done by AES, APT, TEM/XEDS

(energy-dispersive X-ray spectroscopy), and TEM/EELS (electron energy loss spec-

troscopy). The ﬁrst two techniques provided results which were comparable between

the two techniques and were consistent for diﬀerent samples. However, XEDS, EELS Experimental 72

a b

c d 101

111

100 110

Figure 4.23. (a) and (b) unit cell structure of martensite and austenite, and (c) and (d) their corresponding densest planes, (111)γ and (011)α0 , which also have close plane spacings. These two planes (with slight deviations from (575)γ and (278)α0 ) are in contact with each other at the interface, and the interface moves almost normal to these planes during the phase transformation. were not quite able to provide consistent and conclusive measurement of the nitrogen concentration of plate-like features. (The competency of TEM/XEDS and

TEM/EELS on resolving nitrogen in plate-like features has also been discussed for

17-7 PH samples in [89].)

Figure 4.24 is the AES result of nitrided 15-5 PH, which provides nitrogen concentration in the cross-section. The sample has been sputtered by Ar for 300 s before Experimental 73

performing the AES scan. The plate-like features are also observable in this Fig-

ure. The blue line in Figure 4.24(a) indicates where the AES scan has been carried

out. Figure 4.24(b) shows the average concentration of nitrogen near the top 10 µm

of the surface is ≈ 16 at. %. This amount of nitrogen supersaturation in 15-5 PH is

about two orders of magnitude more than its equilibrium condition. (Thermodynamic

calculations are discussed in section 5.1.1.)

There are some ﬂuctuations in the nitrogen and Fe concentrations at the top

≈ 4 µm of the surface which might be related to the difference in nitrogen concentration of different laths with various orientations relative to the surface. Another hypothesis is that the surface roughness after sputtering could result in altering the detection efficiency of Auger electrons with different energies (e.g. N(KLL)=379 eV

and Fe(LMM)=703 eV). However, the importance of the AES result is that the general

shape of the concentration proﬁles are smooth with no spike, which rules out large

segregation or nitride formation (e.g. the Cr concentration proﬁle is almost ﬂat).

The lateral resolution of the AES is limited by a slight sample drift due to the

charging eﬀect of the surface and mechanical vibrations of the stage. Therefore, chem-

ical analysis of sub-micron-size features is not very reliable. APT is another powerful

technique for revealing chemical composition at the nano-scale. This technique solely

cannot reveal directly which region belongs to which phase, unless it is combined with TEM or t-EBSD. However, it provides several clues about chemical composition

and atomic distribution, which make it possible to presume a few facts, draw some

conclusions, and compare them to other known information to conﬁrm the presump-

tions. Here we also provide some APT results from two diﬀerent perspectives, then

draw some conclusions from them, and conﬁrmed them based on the known facts. Experimental 74 surface

N Cr 60 Fe %

. Ni t a 20 Cu

0 0 5 10 15 distance (µm)

Figure 4.24. (a) SEM image taken in PHI SAM of 15-5 PH nitrided at 670 K for 20 ks, and the observation of plates inside martensite laths, and (b) concentration proﬁles of nitrogen and the main substitutional elements in the alloy.

A local electrode atom probe (LEAP) sample was prepared that included two diﬀerent regions. Figure 4.25 shows the reconstructed positions of nitrogen atoms of such a tip. The two diﬀerent regions in the tip show almost homogeneous but Experimental 75

Table 4.4. Averaged chemical composition of the plate and the matrix obtained from 3D APT reconstruction, and the normalized chemical concentrations relative to Fe (at. %).

Elements Fe Cr N Ni Cu Si Mn Mo Nb V C Plate (at. %) 60.6 15.9 14.7 4.4 2.5 1.1 0.5 0.04 0.04 0.02 0.12 Norm. Conc. (X/Fe) 1 0.26 - 0.073 0.041 0.018 0.008 0.0007 0.0007 0.0003 - Matrix (at. %) 62.2 16.2 12.5 4.6 2.6 1.1 0.6 0.04 0.05 0.02 0.02 Norm. Conc. (X/Fe) 1 0.26 - 0.074 0.042 0.018 0.010 0.0006 0.0008 0.0003 -

diﬀerent nitrogen concentrations. A cylindrical region of interest (ROI) was selected

to analyze the composition of these phases in more detail. The concentration proﬁle

along the arrow in Figure 4.25a is shown in Figure 4.25b and c.

To obtain the nitrogen concentration in each region, the atom counts were av-

eraged over a large ROI in each region (table 4.4). Since nitrogen and carbon are

interstitials, the concentration of substitutional elements has been normalized rela-

tive to the main element of the steel (i.e. Fe). Note that the normalized concentrations

of elements are almost the same in both regions, despite the 2.2 at. % diﬀerence in

nitrogen concentration. Moreover, the average nitrogen concentration in both regions

correspond to a “colossal” super-saturation [48].

Another important observation in Figure 4.25(c) is the ﬂuctuation of Ni and Cu

concentrations at the interface between the two diﬀerent N-containing regions. There

is a depletion of these elements on one side of the interface and a corresponding

enrichment on the other. The graph shows these two elements prefer to enrich in the

phase with the higher nitrogen concentration. Nickel and copper crystallize in the A1

(FCC) structure, similar to the austenite phase. Accordingly, while the temperature

of the nitridation process is not high enough for long-range substitutional diﬀusion,

the atomic conﬁguration of the interphase interface is impacted by a short-range

diﬀusion of Ni and Cu. Experimental 76

Figure 4.25. (a) 2—3D reconstruction of nitrogen atoms revealing bands with higher nitrogen concentration, (b) and (c) one-dimensional concentration proﬁles of other elements existing in the alloy. Experimental 77

The morphology of the plates (ﬁgure 4.16) and the similarity in the chemical

compositions of the plates and the matrix (ﬁgure 4.25) suggest that the new phase

have formed by a diﬀusionless transformation, rather than by a diﬀusional phase

transformation. Moreover, the higher capacity of austenite in accommodating more

interstitials compared to the martensite is well-known. Therefore, the ﬁrst assumption

is that the phase with higher nitrogen concentration has an austenitic structure, which

acts as an interstitial absorber (during the long heat treatment process) compared to

the adjacent regions. To strengthen this assumption, the Cu atoms distribution of

each phases are further discussed. (It is possible that the adjacent phases with lower

nitrogen concentrations can also be the transformed austenite phases, which formed

later during the process. However, it still shows that their initial parent martensite

phase had lower nitrogen concentration relative to the adjacent austenite.)

Another LEAP sample was prepared from the nitrided 15-5 PH, which demon-

strates Cu atoms reconstruction. As shown in Figure 4.26a, there are two regions with similar Cu concentration, but diﬀerent Cu distributions. In the top part of the

needle, Cu atoms prefer to cluster, and in the bottom part of the needle, Cu atoms

are dispersed more evenly. The Cu-Cu nearest distance quantiﬁes this dispersion, which is shown in Figure 4.26d. At the early stage of precipitation, the Cu clusters

nucleate and grow coherently in a BCC structure in the Cu-supersaturated BCC ma-

trix. Once they reach a certain size, they lose coherency and grow in a FCC structure

[104, 105]. (3 at.% Cu is easily soluble in the austenite phase and precipitation does

not occur [106].) However, as explained in section 2.2.2, the time and temperature

of heat treatment in this experiment were not suﬃcient to form fully incoherent Cu

particles with FCC structure within the BCC matrix. Moreover, extra reﬂections in Experimental 78

the DPs resulting from the nano-size Cu particles have not been observed in the ma-

trix (martensite). Detailed microstructural observations of the matrix are provided

in section 4.5.

In Figure 4.26, the similarity in the concentrations of major atoms in both regions

also has been observed (except for nitrogen). The concentration proﬁles of elements

obtained from ROI have been shown in Figure 4.26b.

GBs (grain boundaries) generally facilitate atom migration. At the lower part of

the GB in Figure 4.26b, the enrichment of Ni and Cu, and depletion of Cr and N is very notable. The enrichment of Cu and Ni occurs near the phase which has higher

nitrogen concentration and lower Cu clustering. This result is in accordance with

the thermodynamic data which indicates that the austenite phase prefers to dissolve

more Ni and Cu compared to the martensite phase [25].

Figure 4.26 shows the clustering of Cu at the GB. Analysing one of these clusters

at the interface shows that they are almost pure Cu at the core. This result is similar

to previous observations of Cu precipitates in martensitic stainless steels [23, 25].

In summary, after low-temperature nitridation, a newly formed phase appears

in the microstructure of the 15-5 PH alloy, which chemically behaves similar to the

austenite phase (table 4.4). The new phase can easily accommodate 3 at. % Cu in its

crystal structure [25] and can have higher nitrogen concentration [107]. (Note that

the solubility of Cu or nitrogen in martensite crystal structure is less than 1 at. %

[16, 106].) Therefore, it is concluded that the region with higher nitrogen concentra-

tion, no Cu clustering, and higher Ni concentration at the interface probably is the

newly formed austenite, and the adjacent phase with lower nitrogen concentration, Experimental 79

Cu clustering and depletion of Ni at its interface is the martensite phase (or possibly

the newly formed austenite, which didn’t have much time for the diﬀusion).

Moreover, substitutional diﬀusion is eﬀectively frozen at low temperatures. The

microstructural observations and diﬀraction analyses also provide conclusive evidence

for the martensitic nature of martensite-to-austenite phase transformations.

4.3.5 Martensite-austenite interface structure

The interface atomic structure supplies valuable information about the nucleation

and growth mechanisms in phase transformations. The austenite/martensite interface

is fully glissile and can move conservatively during martensitic transformation [57].

Much work have been done on theoretical aspects of austenite/martensite interface

and habit plane determination. However, less information is available regarding the

atomic structure of an austenite/martensite interface. This is probably due to the

technological limitations, even less work has been done with HRTEM of the interface

[57, 63, 108].

Figure 4.27a shows a HRTEM image of the martensite/newly-formed austenite

interface in the 15-5 PH alloy. This image has been obtained in the [011]γ or [111]α0 viewing direction. The atomic planes which meet at the interface are (111)γ and

(110)α0 , and they are almost parallel to each other. The atomic column spacing of (200)γ and (110)α0 are 0.253 nm and 0.238 nm, respectively (ﬁgure 4.27b). The interface is shown by a red dashed line in Figure 4.27b, and it is several degrees away from being parallel to the (111)γ and (110)α0 planes. Their eﬀective plane spacings

(i.e. their projected plane spacings on the interface line) can be estimated by simple trigonometry: Experimental 80

(a) xGrain boundary (b) Region of interest concentration 80

Cr atoms only 70

60 Region of low 50 Fe % Fe nitrogen Grain boundary Cr % Cr concentration 40 N % 30 N 80 7 Si % ConcentraTon (at.%) Si Cr atoms only 70 20 6 60 10 50 Fe % 0 5 40 Cr % 20 30 40 50 60 70 N % 4 30 7 Distance (nm) Ni Si % ConcentraTon (at.%) 20 Mn % Region of 6 3 high nitrogen10 Cu 0 0.18 5 2 concentration 20 30 40 50 60 70 0.16 ConcentraTon (at.%) Distance (nm) 4 Ni Ni 0.14 1 Mn % 0.12 3 Mn Cu 0.1 CuC % 0 0.18 0.08 2 20 30 40 50 60 70 0.16 ConcentraTon (at.%) 0.06 P % 0.14 1 Distance (nm) 0.12 0.04 ConcentraTon (at.%) 0.1 C % 0.02 0 0.08 20 30 40 50 60 70 P % 0 0.06 20 30 Distance (nm) 40 50 60 70 0.04 ConcentraTon (at.%) Distance (nm) (c) 0.02 (d) Copper precipitate0 Cu-Cu nearest distance 100 20 30 40 50 60 70 0.04 Project Customer: Amirali Zangiabadi Distance (nm) Cu is more clustered in [email protected], Case Western Reserve 80 low nitrogen region Project Customer: 0.03 Amirali Zangiabadi [email protected], Case Western Reserve 60 Above GB 0.02

40 Count Below GB

20 0.01 Cu Concentration (at.%) 0 0 0 1 2 3 4 5 6 7 0 0.5 1 1.5 2 Distance (nm) Distance (nm)

Figure 4.26. (a) 2—3D reconstruction of nitrogen atoms revealing bands with higher nitrogen concentration, (b) and (c) one-dimensional concentration proﬁles of other elements existing in the alloy. Experimental 81

eﬀective plane spacing = atomic plane spacing × cos(θplane angle − θinterface angle) (4.4)

Even after considering the eﬀective plane spacings, there is about 6 % mismatch

between atomic layer of phases meeting at the interface. Therefore, dislocations at the

interface should accommodate this strain caused by the lattice mismatch. Since the

interface in martensitic transformation is glissile, the dislocations should be glissile

and lay on the interface to require minimal energy for their movements [109].

However, the mismatch between lattice place spacings and the inclination of the in-

terface can be accommodated by another atomic conﬁguration at the interface, which

is the combination of steps and dislocations with smaller Burgers vectors (i.e. dis-

connections). Disconnection can be deﬁned by the height of the step and a Burgers vector [62, 110]. (Further considerations are provided in section 5.2.1.)

Identifying the exact atomic positions at the interface in the HRTEM image (ﬁg-

ure 4.27) is not possible, since the interface is inclined to the viewing direction (i.e. the

interface (872)α0 is inclined to the viewing direction [111]α0 ). Even though the sample

thickness is less than 50 nm thick, it is still thick enough that the atomic columns

of austenite and martensite overlap at the inclined interface. Therefore, there is an

uncertainty about the atomic positions in this region. The sample could be tilted to

make the interface parallel to the viewing direction; however, the atomic columns of

austenite and martensite would then be oﬀ-axis and not resolvable.

Schematic illustration of the interface (for three atomic layers) based on the

HRTEM observation (ﬁgure 4.27) is illustrated in Figure 4.28. In the viewing direction

([011]γk[111]α0 ), atoms in the austenite phase can only sit in two possible positions A Experimental 82

a [011] � �

�’ 5 nm [111]�’ 36

b � c

�’ 40°

42° 45°

Figure 4.27. (a) HRTEM image of the interface in the [011]γ and [111]α0 viewing direction, (b) schematic of atomic conﬁguration and the eﬀec- tive plane spacings at the interface, (c) the periodogram (logarithmic intensity of the numerical Fourier transform) of (a) and the indexed atomic planes. Experimental 83

Table 4.5. Relative atomic plane position for the {110}γ planes in austenite and the {111}α0 planes in martensite shown in Figure 4.28.

Austentie {110} Martensite {111} Plane (aγ = 0.360nm) (aα0 = 0.288nm) A = 0 A = 0 a Relative atomic B = plane position B = a √3 2√2 C 2a = √3

and B, and in the martensite phase, they can sit in three possible positions A, B, and

C. The depth of each atomic layer are measured and shown in Table 4.5. The illus-

trated interface in Figure 4.28 is one the many possibilities of atomic conﬁgurations

at the interface. The habit plane can bend slightly in diﬀerent regions. Therefore,

the atomic conﬁguration of the interface can be diﬀerent, as well.

Without the introduction of steps at the interface, one dislocation would be needed

in every 16 atomic planes (101)α0 to compensate ≈ 6 % atomic strain mismatch be-

tween the two crystals. However, it is shown in Figure 4.28 that the introduction

of steps at every 9 atomic planes (101)α0 can reduce the size of the Burgers vector

1 to about 6 [111]γ. This illustration also shows that by assuming that the interface

is parallel to the viewing direction, it has an inclination of about 6◦ relative to the

(111)γ plane. This is very close to the measurements obtained from the HRTEM

image (ﬁgure 4.27b).

However, as mentioned earlier, the interface is inclined in two separate axes relative

to the (111)γ and (011)α0 planes, which requires a second set of steps at the interface.

This is explained further in section 5.2.1. Experimental 84

γ (111) γ α ’ (111) (011) A α’ B

(101) layers in martensite. C A and B B , A C B B A C C B . In every 9 atomic planes there is a step to compensate the mismatch. Atoms 0 α layers in austenite, and in B 6˚ 111] and and [ A γ Figure 4.28. (a)direction Space [011] ﬁlling atomic conﬁguration at the austenite/martensite interface in the viewing are stacked in Experimental 85

4.4 Phenomenology of martensitic phase transformation

Phenomenological crystallographic theories for the martensitic transformation evolved

around 1950 by several independent researchers [54, 101, 111]. These theories are

based on the invariant plane strain shape deformation and inhomogeneous or comple-

mentary shear during the transformation. As Christian showed [50], these theories are

equivalent, and they were accepted due to their agreement with several experimental

observations (especially for plate martensite). However, the simple phenomenologi-

cal crystallographic theories are not compatible for some martensitic transformations

observed in steels, e.g. for alloys which have lath martensite with habit plane close

to {110}α0 or {111}γ [112], similar to the lath austenite in 15-5 PH with the {872}α0

habit plane (section 4.3.3). Later, Crocker and Bilby [113] proposed a modiﬁcation to

the theory that the transformation in some alloys can occur by a composite shearing.

Here, we study the basic phenomenological theory of the problem. Then, we con-

sider the more complex mechanism of composite shear (triple shear) for the 15-5 PH

alloy.

All the theories are based on the assumption that the martensite and austenite

lattices coincide at a planar interface, which is the invariant plane of the invariant

2 plane strain P1. (This assumption is based on the primary metallographic observations of the plate which had undergone a uniform shear on a certain plane in the

austenite [51].)

As explained in section 2.8.1 the inhomogeneous deformation required for the

martensitic transformation can be separated into three components: a simple shear

(or “complementary” shear [101]) (P), which displaces regions of the product phase

2The BOLD capital letters stand for 3 by 3 matrices. Experimental 86

relative to each other), a lattice deformation (B), and a rigid body rotation (R); hence:

P1 = RBP. (2.3)

Algebraically, the BP matrix is suﬃcient to produce a macroscopically undistorted interface between the martensite and the austenite. However, the matrix R is necessary to make the undistorted plane unrotated. Therefore, the RBP is an invariant plane strain. The lattice correspondence can be chosen in numerous ways.

However, in all attempts to ﬁnd a solution for experimentally observed crystallography in ferrous alloys, the Bain correspondence has been applied and is considered the most energetically favoured lattice deformation [114]. The simple shear P corresponds to slip or twin-related regions in the product phase and compensates the eﬀect of the Bain strain. Both P1, and P are invariant plane strains with the algebraic form of:

P1 = I + m1d1d10 , (4.5) where d is a unit vector of displacement direction, p0 is the unit normal to the invariant plane, and m is the magnitude of the strain, therefore, md is the displacement vector3.

According to the terminology of Bowles and Mackenzie [101], S is deﬁned as an invariant line strain:

1 P1P− = P1P2 = RB = S, (4.6)

3In Bowles and Mackenzie terminology, lattice directions such as d are written as column vectors and plane normals such as p0 are reciprocal lattice vectors. The prime transposes the column vector to a row vector. Experimental 87

1 in which P− = P2 is a simple shear, and S is the intersection of habit plane p10

(which is invariant to P2) and the inhomogeneous shear plane p20 (which is invariant to P2). Since both P1 and P2 are invariant plane strains, the line of intersection of the two invariant planes is not aﬀected by the strain.

The summarized analysis procedure consists of the following steps:

(1) Unextended lines and unextended normals for the deformation B are cal-

culated so that the former lie in the p20 plane and the latter are along the

directions perpendicular to d2.

(2) An invariant line strain S is calculated so that the unextended lines and

normals are unrotated, following an appropriate rotation.

(3) Elements p10 (habit plane) and d1 of P1 and the magnitude m2 of d2 in P2 are calculated.

(4) The OR is obtained from a calculation of the directional change of the prin-

cipal axes due to the strain S [115].

By assuming we have martensite and austenite with lattice parameters of aα0 =

cα0 =0.288 nm and aγ =0.360 nm, respectively, the Bain distortion can be expressed

as4

  η1 0 0     √ (γBγ) =  0 η 0  , η1 = η2 = 2aα0 /aγ, and, η3 = cα0 /aγ (4.7)  2    0 0 η3

4By assuming we have a cubic martensite for simplicity. Experimental 88

or,   1.132 0 0     (γBγ) =  0 1.132 0  , (4.8)     0 0 0.801 (γBγ) indicates that the Bain distortion matrix is deﬁned relative to the austenite lattice (γ).

By assuming a unit vector xi (xi0 xi = 1) being parallel to the invariant line, the

Bain distortion makes xi transform to xi = Bxi. Since the length of xi is unchanged,

xi0 xi = 1 holds, and then the equation can be rewritten as (Bxi)0Bxi = xi0 B0Bxi =

2 xi0 B xi = 1. Moreover, p20 xi = 0, since the shear plane p20 of the complementary shear must involve xi. Therefore, three equations can be derived to solve for the invariant line [50]:

2 2 2 xi0 xi = 1...x1 + x2 + x3 = 1,

2 2 2 2 2 2 2 xi0 B xi = 1...η1x1 + η2x2 + η3x3 = 1, (4.9)

p20 xi = 0...x1 + x3 = 0.

Similarly, let a unit normal ni0 be the invariant normal. The Bain distortion

1 2 transforms ni0 to ni0 = ni0 B− . Since the length of ni0 is unchanged, ni0 ni = ni0 B− ni=1.

Since the plane with invariant normal must contain the shear direction d2, ni0 d2=0. Therefore, the invariant normal can be obtained:

2 2 2 ni0 ni = 1...n1 + n2 + n3 = 1,

2 2 2 2 n1 n2 n3 ni0 B− ni = 1... 2 + 2 + 2 , (4.10) η1 η2 η3

ni0 d2 = 0... − n1 + n3 = 0. Experimental 89

Within the framework of the theory, the orientation rotation R is determined

from 4.6 by the invariant line xi and the corresponding plane with an invariant normal ni0 . The invariant line matrix, S, must obey the relationships ni0 S = ni0 xi and

Sxi = xi. Therefore, the invariant line matrix can be retrieved. Detailed algebraic manipulations of equations are presented in [116].

Next, by algebraic operations and considering the relationship between invariant lines and normal, the direction of shape deformation (d1), and habit plane normal

(p10 ) can be obtained.

d1 = [Sy − y]/p10 y (4.11)

1 1 p10 = (q0 − q0S− )/q0S− d1 (4.12) where y is any vector other than xi lying in p10 and q is any normal other than ni0 to a plane containing d2. Thus, all relevant quantities are predicted once the lattice parameters are known, the correspondence (and hence Bain strain) is assumed, and the system (plane and direction) for the inhomogeneous shear is chosen (by assumption).

Bowles and Mackenzie [101] alongside Wechsler et al.[54] based their assumption

on the {112}h111iα0 system for inhomogeneous shear in the martensite (twinning

shear), i.e. p20 = {112}α0 and d20 = h111iα0 . The predicted habit plane was close to the experimental results of several alloys. For instance Fe-31%Ni showed the

experimental habit plane close to (259)γ and the theoretical habit plane close to

(268)γ [116]. However, the prediction of habit plane and the magnitude of simple

shear were far from the experimental values for low carbon steel and Fe-28%Ni alloys Experimental 90

with “lath” martensite structure, which had habit planes close to the {111}γ planes.

These alloy have a “nonbehaving” martensitic transformation. In this study, the habit

plane of austenite in 15-5 PH was also determined to be close to the {111}γ planes.

As with 15-5 PH alloy, the nonbehaving martensitic transformations cannot be

easily solved by the basic phenomenological theory. Several attempts to explain the

crystallography of nonbehaving martensitic transformations have been carried out by

extending the lattice invariant shear operation rather than altering the lattice corre-

spondence and distortion. Crocker and Bilby [113] considered several slip/twinning

shear systems to ﬁnd the best match with the experimental results. According to

their computations, the habit plane predicted by assuming the {101}h101iα0 slip sys-

tem matched mostly with the experimental data for those alloys with the habit plate

close to {111}γ planes. However, the problem was that the {101}h101iα0 slip system

is not recognized as a shear system in the martensite. Therefore, they considered the

{101}h101iα0 shear mode as a combination of two shear systems having a common

(110)α0 plane and of similar magnitude, (110)[111]α0 and (110)[111]α0 . In this case,

the estimated habit plane deviated from {111}γ by 3◦ [115].

By assuming a composite double-shear mechanism, Eq. 4.6 is modiﬁed to:

P1 = RBP2P3, (4.13)

in which P2 and P3 are shearing in the (110)[111]α0 and (110)[111]α0 system (or equivalently in the (111)[110]γ and (111)[101]γ system). Since P1 is an invariant

plane strain, one of its principal distortions must be unity, therefore: Experimental 91

Table 4.6. Theoretical and experimental data for the crystallography of lath austenite in 15-5 PH.

Theoretical Experimental p1 (0.21, 0.71, 0.67)α0 (287)α0 m1 0.22 — m2 0.26 — d1 [0.04, -0.17, 0.13] — (111) 1.75 from (011) 0 (111) k(011) 0 OR γ ◦ α γ α [101]γ 1.98◦ from [111]α0 [101]γ 2.5◦ to 5.5◦from [111]α0 p2 (101)α0 or (111)γ d2 [101]α0 or [101]γ

|P10 P1 − I|= 0 (4.14)

|P30 P20 B0BP2P3 − I|= 0 in which the rotation matrix (R) is eliminated in transposition [117]. In our spe-

ciﬁc case in 15-5 PH, the magnitude of shear in the (110)[111]α0 and (110)[111]α0

system can be assumed to be equal, and the calculations were simpliﬁed to a dou-

ble shear transformation. The algebraic calculations have been performed by the

MathematicaTM 11.0 to determine the habit plane, magnitude of shear, and the OR.

A summary of the theoretical and experimental results are presented in Table 4.6.

The programing codes for solving the theoretical phenomenology of α0 −→γ transfor-

mation are shown in AppendixA. The subtle diﬀerence from the case of our studies with the conventional martensitic transformation is that martensite is transforming to

austenite, therefore the codes are written based on the matrix (martensite) reference

system.

As shown in Table 4.6, the theoretical habit plane deviates from the experimental

habit plane only by 2.5◦. The predicted magnitudes of shear in austenite in 15-5 PH Experimental 92 are close to those determined for the martensite in the Fe-20Ni-5Mn alloy [78]. The calculated OR is also close to the experimental values.

Measuring the shear magnitude (m1) experimentally is not straightforward, since plates are small and form below the surface. In conventional martensitic alloys, martensite laths are large (several micrometers), and they can induce surface ﬂuc- tuation. The surface uplift can be measured by OM or SEM to estimate m1. For instance the shearing of two plates in Figure 4.18 indicates the shear magnitude of

≈ tan 13◦ = 0.23, which is very close to the predicted value of m1.

The experimental magnitude of internal shear of the product phase (m2) is also hard to measure, since the observed microstructure (or atomic conﬁguration) of the newly formed austenite is from post-transformation. Therefore, it is almost impossible to track atomic movements after the transformation. However, we can predict the slip/shear planes responsible for simple shear in the austenite. More discussion on this subject is provided in section 5.1.2 Experimental 93

4.5 Nitrogen-supersaturated martensite

Figure 4.29 shows the XRD pattern of the non-treated sample and the samples ni-

trided at 620 K and 670 K. There are several interesting features in the proﬁle of

nitrided samples. Firstly, in the treated samples, two peaks are notable at 2θ = 63◦

and 74◦, which can be roughly matched with the (111) and (200) peaks of expanded

austenite with a ≈ 5 % lattice parameter expansion.

Secondly, in the case of treated samples, the peak located at 2θ = 65◦ has a large

FWHM (full-width half-maximum). This can be attributed to the overlapping of

two peaks: the (111)γ peak of expanded austenite and the (011)α0 peak in tetragonal

martensite. This is further explained after deconvoluting the peaks.

Thirdly, the (110)α0 peak of martensite in treated samples is slightly shifted to the

right relative to the non-treated sample (i.e. smaller lattice parameters). This shift

in the (110)α0 peak corresponds to a 0.5 % contraction in plane spacing. This eﬀect

also has been observed in the carburized 316 stainless steels which were annealed for

a long time (e.g. 50 ks) [118].

Given the normal mass absorption coeﬃcient of Fe, the XRD pattern contains

information from a depth of ≈ 3.5 µm below the surface. The cross-sectional scan

obtained by AES from the sample conﬁrms the average 16 at. % nitrogen concentration within the depth of 3.5 µm from the surface (Fig. 4.24). This amount of nitrogen

concentration corresponds to the ≈ 5 % expansion of lattice parameter in austenitic

stainless steels [119, 120].

A peak analyser software package in OriginTM is used to deconvolute the peak in

ﬁg. 4.29 located between 2θ = 63◦ and 67◦. A Gaussian model has been considered

to ﬁt with the XRD peak: Experimental 94

670 K

620 K (110)�’

(111)�

Austenite (5% exp.) (200)� Non-treated

Figure 4.29. The XRD proﬁles of non-treated and nitrided 15-5 PH at diﬀerent temperatures.

A (x − x )2 y y × − × × c , = 0 + p π exp ( 4 ln 2 2 ) (4.15) w × 4 ln 2 w × √ in which y0 is the oﬀset value, w =FWHM/ ln 4, and xc is the center of the peak.

Fig 4.30 shows two major peaks between 2θ = 65◦ and 69◦, which are de-convoluted to three peaks. The calculated values of Gaussian parameters for these three peaks are presented in Table 4.7.

The primary peak located at 2θ = 68◦ is represented by peak number 3 in

ﬁg 4.30. The calculated peak center is very close to the original peak position of

0 the (110)α plane (i.e. 2θ(110)α’ = 68.42◦ for a martensite with the lattice parameter of a =0.288 nm). However, peak number 2 indicates planes with a rather large and broad Experimental 95

c o m m u l a t i v e

y 1 t

i 2 s n e t n I

1 5 - 5 P H - n i t r i d e d - 6 7 0 K

6 0 6 2 6 4 6 6 6 8 7 0 7 2 7 4 2 θ [ d e g ]

Figure 4.30. De-convolution of XRD peaks located at 2θ = 65◦ and 2θ = 68◦ into three peaks. The Gaussian function parameters of each peak are presented in Table 4.7.

Table 4.7. Gaussian function parameters of ﬁtted curves after peak de- convolution in ﬁg. 4.30.

Peak 1 2 3 y0 288.11 288.11 288.11 xc 64.90 67.18 68.63 A 638.96 1223.10 162.18 w 1.92 3.87 0.92

range of plane spacings. It also has higher intensity compared to peak number 3. This

eﬀect (as shown in the simulated XRD proﬁles of martensite in Figure 4.31) can be

an indication of martensite lattice tetragonality, due to the nitrogen supersaturation.

According to the XRD simulation, the (110)α0 peak remains exactly in the same po-

sition, but its intensity is reduced and it led to an extra peak (i.e. (011)α0 peak) with

a relatively higher intensity. The (011)α0 peak shifts to the left (i.e. larger plane spac-

ings) by increasing the c/a ratio. Finally, peak number 1 (in Figure 4.30) is attributed Experimental 96

3 (011)�′ � = � = 2.88 nm 2

0 3 � = 2.88 nm (011) y �′ � = 2.94 nm t 2 i

s �/� = 1.02 n

e (110)�′ t 1 n I

0 3 � = 2.88 nm (011)�′ 2 � = 3.02 nm �/� = 1.05 (110) 1 �′

0 65 66 67 68 69 70 71 2�[deg]

Figure 4.31. Simulated XRD proﬁle of martensite lattice before imposing any tetragonality (c/a = 1) and after 2 % and 5 % tetragonality. Note the location of (110)α0 peak remains exactly in the same position, but its intensity is reduced.

to the (111)γ plane of expanded austenite (≈4 %). More detailed studies on the eﬀect

of nitrogen supersaturation on the martensite phase have been done by TEM.

Figure 4.32a reveals the bright-ﬁeld image of a low-temperature nitrided 15-5 PH

sample and the selected region for acquiring DPs in diﬀerent zone axes. The DPs

mainly come from the matrix between the plates (the matrix is the darker regions

in this ﬁgure). However, in Figure 4.32b, the DP from the plate is also visible. The

reﬂections from the plate are sharp and circular spots. However, the shape of the

reflection in the martensite (matrix) for the (011)α0 and (211)α0 planes are arc-shaped and diffused, and the (011)α0 reflections are circular and less diffused. Experimental 97

a b

000

100 nm [100] 8 nm -1 c d

000 000

[131] 8 nm -1 [110] 8 nm -1

Figure 4.32. (a) Bright-field image of the matrix and the selected area for obtaining DPs in different zone axes; (b) [100]α0 (smaller reflections are originated from the plate [110]γ), (c) [131]α0 , and (d) [110]α0 zone axes. The (002)α0 and the (211)α0 reflections are arc-shaped and the (002)α0 reflection is elongated to larger plane-spacings (with slight rotation). Experimental 98

Figure 4.32c and d show DPs of the martensite in two other zone axes. The (211)α0

reﬂections in the [131]α0 zone axis are also arc-shaped. On the other hand, the (002)α0

reﬂection in the [110]α0 zone axis has a tail which is directed to the transmitted beam

(i.e. larger lattice parameters). The other aspect of the tail for the (002)α0 reﬂection is that it is slightly rotated. Similar arc-shape and elongated patterns have been observed after low-temperature nitridation of other types of stainless steels such as

17-7 PH [47] and 2205 [87].

Acquiring a nano-size electron beam DP is a very useful method for studying the crystal structure of a sample in an area with a lateral diameter of around 5 nm.

The principle of taking these DPs is shown in Figure 4.33. Using smaller condenser aperture (i.e. smaller diaphragm opening for incoming electron beam) leads to a smaller acceptance angle of the electron beam. Therefore, the electron beam would be focused on a smaller region of the sample. Since the condenser aperture removes the outer portion of the beam, the number of electrons hitting the sample is lowered

(i.e. lower brightness and longer exposure time). For taking DPs, the electron beam should be parallel before entering the condenser aperture (i.e. lower power for the condenser lens).

Figure 4.34 shows several (nano-size electron beam) DPs obtained from the matrix at diﬀerent locations. Interestingly, only one of these patterns has a 90◦ angle between scattering vectors. This angle changes from 85◦ to 91◦. By hovering the electron beam

over the sample, the angle between scattering vectors was oscillating between 85◦ and

95◦.

Figure 4.35 is obtained by superimposing two DPs (number 1 and number 6) from

Figure 4.34. It shows arc-shaped reﬂections can be revealed for the (011)α0 and (011)α0 Experimental 99

(A) (B) (C) Small Medium Large 2α 2α 2α Thin specimen

Kossel-Möllenstedt Kossel Figurepattern 4.33. Nano-size DPs can be obtained by limiting thepattern acceptance α (D)angle of the electron beam (E) hitting the sample (i.e. (F) choosing small 2 ) [121].

planes, but the (011)α0 and (011)α0 reﬂections still are circular and are ﬁxed in their positions. The shape of the superimposed DP is very similar to what is obtained by taking a larger selected area in Figure 4.34b.

FIGUREFurther 20.3. (A–C) studies Ray diagrams by showing HRTEM how increasing of the the C2 matrix aperture size and causes austenitic the CBED pattern plate to change support from one in which our individual previous disks are resolved (K-M pattern) to one in which all the disks overlap (Kossel pattern). (D–F) You can see what happens to experimental CBED patterns on the observationsTEM screen as you select of larger anomalies C2 apertures. in DPs of Figures 4.32, 4.34, and 4.35.

IfFigure you need 4.36 to know shows the value a cross-sectional of a, you should use HRTEM a possible image magnification. of the We matrix reduce L andto < the500mm plate, to known crystal to calibrate its variation with C2 aperture view the low-magnification pattern, sometimes called assizewell for typical as the C2 lens corresponding excitations, as we periodograms. described back (not The surprisingly) fundamental the ‘wholeg pattern’vectors (WP) (spots that contains indi- in Section 9.1 and in equation 5.6. electrons scattered out to high angles. Figure 20.4 shows three CBED patterns obtained over a range of L and cating reflecting plane normals) in the periodogramyou can see that of the if we startplate at a are high relativelyL we can only sharp, see the 20.3.B Selecting the Camera Length 000 disk (Figure 20.4A), then we see the array of ZOLZ whileThe choice those of L depends of the on martensite the information are that youarc-shaped want disks for that the is equivalent (011)α0 toplanes, an SADP and (Figure circular 20.4B) forbut to obtain from the pattern and it’s easy to be confused at the smallest L the HOLZ diffraction effects that we because L controls the magnification of the DP. just mentioned become visible as a ring of intensity at the (011) 0 planes. These priodograms are very similar to the SADP (selected area Typicallyα we adjust the post-objective lenses in the high angles (Figure 20.4C). So it’s often necessary to imaging system to give L > 1500–6000 mm when we record your CBED patterns over a range of L (in addi- diffractionwant to observe pattern) detail in the obtained 000 (BF) disk in at Figure the highest 4.32b.tion This to a range diffuseness of a). in the (011)α0 , (022)α0

and every (0 n n)α0 reﬂections indicates that these planes are not straight in the scale 328 ...... O BTAINING CBED PATTERNS Experimental 100

1 2 3

1 85˚ 85˚ 88˚

3 4 5 6 4

6 400 nm 88˚ 90˚ 91˚

Figure 4.34. Nano-sized DP acquired from the plate-containing martensite lath in 15-5 PH in numbered locations.

1 1+6

+ à 6

Figure 4.35. Superimposing two DPs 1 and 6 from Figure 4.34 and obtaining the arc-shaped reﬂections for the (011)α0 and (011)α0 planes. The (011)α0 and (011)α0 reﬂections still are circular Experimental 101

matrix−�′ [100]�′ [011]�

84˚－96˚

plate−�

52˚ 53˚ 75˚

[100]�′

Figure 4.36. Superimposing two DPs 1 and 6 from Figure 4.34 and obtaining the arc-shaped reﬂections for the (011)α0 and (011)α0 planes. The (011)α0 and (011)α0 reﬂections still are circular

of 50 nm (i.e. sample thickness). By looking closely at the HRTEM image, it is ap-

parent that the atom columns in the (011)α0 plane in the martensite actually are not straight. However, all the atom columns in the plate (austenite) are straight at every direction. This rules out a possibility of misalignment (stigmatism, etc.) in the microscope setup, which could lead to an image warping.

Based on the HRTEM image and the DPs obtained from the matrix (ﬁgures 4.36 and 4.32), it is apparent that the atom columns of the martensite are undulating. Moreover, by encompassing a rectangle on these areas, no extra lattice plane

(i.e. Burgers vector of a dislocation) can be observed. These local areas with wavy Experimental 102

lattice fringes indicate a distortion in the crystal structure of martensite after low-

temperature nitridation. The periodogram of martensite is characterized by diﬀuse

spots that form parallelograms with variable inclination angles of 6◦. The lattice

fringes corresponding to (011) planes have no inclination.

It was very interesting to observe that at the austenite/martensite interface the

crystal structure of both phases are distorted in such a way that it is hard to diﬀer-

entiate one from the other (ﬁgure 4.37). As shown in Figure 4.37, the nano-size DP

shows very similar plane spacings and angles for both phases. Moreover, the DPs

of both phases are highly distorted. For instance, the DP of austenite in the [011]γ viewing direction shows the largest angle observed between the fundamental {111}γ

g vectors of 75◦ instead of the 70.5◦ expected for the FCC crystal. Moreover, in

the [100]α0 viewing direction, the g vector for {011}α0 reﬂection is 85◦, which is far

from the expected angle of 90◦. The 5◦ distortion in g vectors for {011}α0 reﬂection will be explained by the tetragonality of c/a = cot(θ/2) = cot(85◦/2) = 1.09 or 9 %

(section 5.3).

The experimentally observed distorted DP of austenite can also be matched by

assuming an FCC unit cell with a strain of = 1.05 parallel to one of the fundamental

translations, corresponding to an FCT (face-centered tetragonal) lattice. Of course,

the 14 Bravais lattices do not include an FCT lattice, because it corresponds to a √ BCT lattice with parameters a0 = a/ 2, c0 = c. However, the tetragonality values

and DPs can be checked/simulated with crystal simulation software packages.

In conclusion, the transformation of α0 → γ as an attempt to transform the crys-

tal structure from BCT (back) to FCC, is energetically preferred in the presence of Experimental 103

�′

85˚

� 0.210nm

51˚ 52˚ 76˚

8 nm-1

Figure 4.37. Nano-size DP of both austenite and martensite at their interface, in the [100]α0 k[011]γ zone axis, and their corresponding sketches of grids deﬁned by the fundamental g vectors.

high nitrogen concentration. If nitrogen diffuses at low-temperature, under conditions of very sluggish metal atom mobility, the BCT → FCC transformation occurs in a diffusionless manner. However, similar to high carbon concentrations in Fe–C favoring diffusionless formation of α0, not α, high nitrogen concentrations in 15-5 PH do not favor γ, but a distorted version of it: γ0. The underlying principle for the

formation of highly tetragonal martensite can be explained (section 5.3). However,

the tetragonality in the austenite has not been observed before and cannot be easily

explained. It is speculated that the tetragonality in the austenite can originate from Experimental 104 the nitrogen supersaturation and the massive strain energy caused by the phase transformation and volume change. However, more studies are requires to fully understand this phenomenon. 105

5 Discussion

5.1 Martensite to austenite phase transformation

In this section we make connections between diﬀerent aspects of martensitic trans-

formation (i.e. α0 → γ) based on our observations and theoretical considerations on

15-5 PH.

5.1.1 Heterogeneous equilibrium in 15-5PH closed system

It is well known that the concentration of Cr and Ni plays a crucial role in stainless

steel properties; while Cr stabilizes ferrite, Ni stabilizes austenite. [122]. Moreover,

nitrogen is one of the strongest austenite stabilizers. The contribution of nitrogen in

stabilizing the austenite is estimated to be around 25 times higher than that of Ni

[123].

The change in the free energy of the stainless steel undergoing a A2 (BCC) →

A1 (FCC) phase transformation is calculated according to the regular-solution model

[124, 125]:

A2 A1 X A2 A1 X A2 A1 ∆G − = ∆GFe − + Ωij − XiXj, (5.1) Discussion 106

A2-A1 where ∆GFe is the free energy change between αBCC and γFCC phases in pure iron.

A2-A1 Ωij is the diﬀerence in interaction parameter between αBCC and γFCC phases in the ij binary or multi-component system, and X is the atomic fraction. For a quaternary

system composed of Fe, Cr, Ni, and N, the free energy change can be determined by

using thermodynamic data [124, 126, 127]. The equation 5.1 can be expanded for a

α0 → γ transformation in a stainless steel containing three major elements (i.e. Fe,

Cr and Ni) and nitrogen as an interstitial atom is1

α0 γ X α0 γ α0 γ α0 γ ∆G − = ∆GFe − + ΩFe:N− XFeXN + ΩFe:N− XFeXN+

α0 γ α0 γ ΩCr:N− XCrXN + ΩNi:N− XNiXN+

α0 γ α0 γ α0 γ ΩFe:Va− XFeXVa + ΩCr:Va− XCrXVa + ΩNi:Va− XNiXVa+

α0 γ ΩFe,Cr:N− XFeXCrXN(XFe − XCr)+

α0 γ ΩFe,Ni:N− XFeXNiXN(XFe − XNi)+ (5.2)

α0 γ ΩNi,Cr:N− XNiXCrXN(XNi − XCr)+

α0 γ ΩFe,Cr:Va− XFeXCrXVa(XFe − XCr)+

α0 γ ΩFe,Ni:Va− XFeXNiXVa(XFe − XNi)+

α0 γ ΩNi,Cr:Va− XNiXCrXVa(XNi − XCr).

The CALculation of PHAse Diagram (CALPHAD) thermodynamic data of this

study has been provided in [126].

Figure 5.1 shows the change in the Gibbs free energy after the reverse martensite to

austenite phase transformation at T =700 K. It reveals that the martensite structure

1This method of formulating thermodynamical equation is accepted conventionally. However, the unit of the interaction parameter Ωij must change depending on the number of interacting elements. Discussion 107

400 ]

- 1 200 [ J mol 0 α - γ Δ G -200

-400 0.0 0.2 0.4 0.6 0.8 1.0 Nitrogen Concentration[at.%]

Figure 5.1. The change in the Gibbs free energy between martensite and austenite by increasing the nitrogen content at T =700 K.

of 15-5 PH stainless steel becomes unstable by adding around 0.45 at.% nitrogen. The

driving force for this transformation reaches its maximum at near 23 at.% nitrogen

concentration. Diﬀusion of ≈16 at.% nitrogen to the currently studied martensitic

stainless steel provides suﬃcient driving force for the reverse martensite to austenite

phase transformation. By adding nitrogen, the eutectoid temperature of the alloy is

energetically decreased to a temperature lower than the nitriding temperature, which

enables this transformation [89, 128].

5.1.2 Martensitic transformation mechanism

Bogers and Burgers [129] proposed a mechanism for the FCC ←→ BCC martensitic

2 phase transformation . As shown in Figure 5.2a–c, the {111}FCC planes (parallel to

1 PVQ) can shear along the 6 h112i direction to maintain a closed packed stacking.

1 However, in the intermediate position at 18 h112iFCC (ﬁgure 5.2b), the S0V0Q0 plane

2This analysis is based on a cubic martensite, but it can be extended for the FCC ←→ BCT phase transformation. BOGERS AND BURGERS: PARTIAL DISLOCATIONS AND F.C.C. INTO B.C.C. TRANSITION 257 BOGERS AND BURGERS: PARTIAL DISLOCATIONS AND F.C.C. INTO B.C.C. TRANSITION 257 BOGERS AND BURGERS: PARTIAL DISLOCATIONS AND F.C.C. INTO B.C.C. TRANSITION 257 Discussion 108

BOGERS AND BURGERS: PARTIAL DISLOCATIONS AND F.C.C.BOGERS INTO ANDB.C.C. BURGERS: TRANSITION PARTIAL 257 DISLOCATIONS AND BOGERSF.C.C. INTOAND BURGERS:B.C.C. TRANSITION PARTIAL 257DISLOCATIONS AND F.C.C. INTO B.C.C. TRANSITION 257

a b ’’ c

(b) Intermediate position after l/3 of (c) Final position after complete ’’ (a) Original tetrahedral arrangement P (a) Original tetrahedral arrangement (b) Intermediate position after l/3 ofP’’ (c) Final’’ position after complete normal twin shear. The distance twin shear. (a) Original tetrahedral arrangement (b) Intermediate position after l/3 of (c) Final position after complete with four { 111) planes. with four { 111) planes. P’ normal twin shear. The distance twin shear. between successive { 111) planes with four { 111) planes. normal twin shear. The distance twin shear. T T’between successive { 111) planes T’’ between successive { 111) planes parallel to P’V’S’ and P’V’Q’ has parallel to P’V’S’ and P’V’Q’ has increased by 5.4%. parallel to P’V’S’ and P’V’Q’ has increased by 5.4%. increased by 5.4%.

d e ’’ f

(a) Original tetrahedral arrangement (b) Intermediate position after l/3 of(a) Original(c) Final tetrahedral position arrangement after complete (b) Intermediate position after l/3(a) of Original (c) tetrahedral Final position arrangement after complete(b) Intermediate position after l/3 of (c) Final position after complete with four { 111) planes. normal twin shear. The distance with four { 111)twin planes. shear. normal twin shear. The distance with four { 111) twinplanes. shear. normal twin shear. The distance twin shear. between successive { 111) planes between successive { 111) planes between successive { 111) planes parallel to P’V’S’ and P’V’Q’ has parallel to P’V’S’ and P’V’Q’ has parallel to P’V’S’ and P’V’Q’ has increased by 5.4%. increased by 5.4%. increased by 5.4%.

’’ ’’ (d) (4 (d) (4 (d) (4 (d-e-f) Cross section through the (110) plane TQS perpendicular to PV. Figure 5.2. (a) Shearing(d-e-f) Cross of { section111} throughplanes the (parallel(110) plane TQS to perpendicular PVQ) along to PV. the TQ(d-e-f) Cross section through the (110) plane TQS perpendicular to PV. Fro. 2. Normal twin shear in a cubic close-packed arrangement of spheres. The horizontalFro. { 111)2. Normal planes twinare shear in a cubic close-packed arrangement of spheres. The horizontal { 111) planes are sheared in the (112) direction perpendicular to PV.line (or h112i direction) and producing (b) S0V0Q0 plane asFro. an 2.{ 110Normal}BCC twin shear in a cubic close-packed arrangement of spheres. The horizontal { 111) planes are sheared in the (112) direction perpendicular to PV. sheared in the (112) direction perpendicular to PV. plane and (c) S00V00Q00 plane as an {111}FCC plane, and (d)–(f) are the size of the spheres, this shear is again automatically “intermediate” con&ration of the stack of balls crosssize of sectionalthe spheres, viewthis shear of theis again STQ automatically plane [129 ].“intermediate”size con&rationof the spheres, of thisthe shearstack isof again balls automatically “intermediate” con&ration of the stack of balls accompanied by a slight increase in distance between (Fig. 2(b)) in which the planes S’V’Q’ and S’P’Q’ now accompanied by a slight increase in distance between (Fig. 2(b)) in accompaniedwhich the planes by a S’V’Q’ slight increaseand S’P’Q’ in nowdistance between (Fig. 2(b)) in which the planes S’V’Q’ and S’P’Q’ now successive planes. Actually, this shear is analogous represent the “70-planes”, the planes parallel to successive planes. Actually, this shear is analogous represent thesuccessive “70-planes”, planes. the Actually, planes parallelthis shear to is analogous represent the “70-planes”, the planes parallel to to the first shear: by applying that shear to the S’V’Q’ are moved over each other in the direction to the first shear: by applying that shear to the S’V’Q’ are movedto the overfirst eachshear: other by inapplying the direction that shear to the S’V’Q’ are moved over each other in the direction perpendicular to S’Q’ so that they attain the correct perpendicular to S’Q’ so that they attain the correct perpendicular to S’Q’ so that they attain the correct stacking order. In this process these planes and also stacking order. In this process these planes and also stacking order. In this process these planes and also (d) (4 the planes parallel to S’P’Q’ remain unchanged. (d) (4 (d) (4 the planes parallel to S’P’Q’ remain unchanged. the planes parallel to S’P’Q’ remain unchanged. However, now the two planes P’V’Q’ and P’V’S’ (d-e-f) Cross section through the (110) plane TQS perpendicular to PV. (d-e-f) Cross section through the (110) planeHowever, TQS perpendicularnow the two toplanes PV. P’V’Q’(d-e-f) and Cross P’V’S’ section through theHowever, (110) plane now TQS the perpendiculartwo planes P’V’Q’ to PV. and P’V’S’ which had remained invariant during the first shear, takes the geometry of a (110)BCC plane. As shownwhich had in theremained cross-sectional invariant during view the first in shear, which had remained invariant during the first shear, Fro. 2. Normal twin shear in a cubic close-packed arrangement “automcttically”of spheres. The arehorizontal transformed { 111) into planes “70’-plsnes” are Fro. 2. Normal twin shear in a cubic close-packed arrangement of spheres. The horizontal { 111) planes are Fro. 2. Normal twin shear in a cubic close-packed arrangement“automcttically” of spheres. are The transformed horizontal into { 111) “70’-plsnes” planes are “automcttically” are transformed into “70’-plsnes” sheared in the (112) direction perpendicularwhereas P’V’ to PV.becomes longer and equal to S’Q’.sheared in the (112) direction perpendicular to PV. sheared in the (112) direction perpendicular to PV. Figure 5.2d and f, the initial and ﬁnal atomic stackingwhereas is P’V’ similar becomes but longer mirrored. and equal to S’Q’. whereas P’V’ becomes longer and equal to S’Q’. It is now of interest to remark that the displace- It is now of interest to remark that the displace- It is now of interest to remark that the displace- (a) (b) ment taking place in the second(a) shear corresponds (b) ment taking place in the second shear corresponds size of the spheres, this shear is again automatically “intermediate” con&ration of the stack of balls size of the spheres,(a) this shear is again(b) automatically ment taking place in the second shear corresponds FIU. 3. Stacking of “70°-planes”. exactlysize toof onethe The ofspheres, the geometrypartial this dislocations shear of the isconsidered (110)again BCCautomatically plane of Figure“intermediate”exactly 5.2b to is one shown ofcon&ration the in partial Figure dislocations 5.3of a.the Theconsidered stack of balls “intermediate” con&ration of the stack of balls FIU. 3. Stacking of “70°-planes”. FIU. 3. Stacking of “70°-planes”. exactly to one of the partial dislocations considered accompanied by a slight(a) After increase performing in thedistance shear indicated between in Fig. (Fig.2(b). 2(b))in thein paperwhich of theCohen planes et(a) al. After mS’V’Q’ oneperforming of theand ditisociationthe S’P’Q’ shear indicatednow in Fig. 2(b). (b) After completing the transition into a b.c.c. lattice by accompanied by a slight increase in distance between (Fig.in the2(b))accompanied paper in ofwhich (a)Cohen After the by etperforming al. aplanes mslight one theS’V’Q’ ofincrease theshear ditisociation andindicated in S’P’Q’distance in Fig. now 2(b).between in the (Fig.paper 2(b))of Cohen in etwhich al. m onethe ofplanes the ditisociation S’V’Q’ and S’P’Q’ now products of a perfect dislocation(b) After completing l/2 CX,,~.~. the(111). transition It is into a b.c.c. lattice by (b) After completing the transition into a b.c.c. lattice by successive planes. Actually,shearing successive this shear“70’-planes” is analogousover l/8 ar,.o.o. (110).represent the “70-planes”,stacking ofshearing {the110 successive }planesBCC planes “70’-planes” parallel is notoverto correct.l/8 ar,.o.o.(110). Therefore, productssuccessive another of a perfect planes. shearing dislocation Actually, of l/2{ 110CX,,~.~. }BCCthis(111). shearIt is is analogous represent the “70-planes”, the planes parallel to This “shear” is accompanied by a slight increase in successive planes. Actually, this shear is analogous represent the shearing“70-planes”, successive “70’-planes”the planes over parallell/8 ar,.o.o. (110). to products of a perfect dislocation l/2 CX,,~.~.(111). It is important to note thatThis the “shear”direction is accompaniedof that vector by a slight increase in to the first shear: distanceby applying between thethat planes, shear due to theto extensivenessthe S’V’Q’ of are moved over each other in the direction important to noteThis that“shear” the isdirection accompanied of thatby avector slight increase in important to note that the direction of that vector correspondsto the firstto a (112)shear: distancedirection by between inapplying the the corresponding planes, that due to shear the extensiveness to the of S’V’Q’ toare the moved firstdistance overshear: between each theby planes, otherapplying due in to thethat extensiveness direction shear ofto the S’V’Q’ are moved over each other in the direction the spheres. the spheres. 1 corresponds to 1a (112) direction in the corresponding corresponds to a (112) direction in the corresponding perpendicular toplanes S’Q’ so (planes that they parallel attain to the S 0Vcorrect0Q0) along the 8 hperpendicular110iBCC (or 16toh 112S’Q’i FCCso that) is neededthethey spheres. attain to the correct perpendicular to S’Q’ so that they attain the correct stacking order. In this process these planes and also stacking order. In this process these planes and also stacking order. In this process these planes and also the planes parallelmake to a perfectS’P’Q’ BCCremain crystal. unchanged. Therefore the wholethe phaseplanes transformationparallel to S’P’Q’ can beremain sum- unchanged. the planes parallel to S’P’Q’ remain unchanged. However, now the two planes P’V’Q’ and P’V’S’ However, now1 the two planes1 P’V’Q’ and P’V’S’ However, now the two planes P’V’Q’ and P’V’S’ marized into two small shearings of {111}FCC planes along h112iFCC and h112iFCC which had remained invariant during the first shear, which had remained18 invariant16 during the first shear, which had remained invariant during the first shear, “automcttically” directions.are transformed into “70’-plsnes” “automcttically” are transformed into “70’-plsnes” “automcttically” are transformed into “70’-plsnes” whereas P’V’ becomes longer and equal to S’Q’. whereas P’V’ becomes longer and equal to S’Q’. whereas P’V’ becomes longer and equal to S’Q’. It is now of interest to remark that the displace- It is now of interest to remark that the displace- It is now of interest to remark that the displace- (a) (b) ment taking place in(a) the second shear corresponds(b) ment taking place (a)in the second shear corresponds(b) ment taking place in the second shear corresponds FIU. 3. Stacking of “70°-planes”. exactly to one of the FIU.partial 3. Stackingdislocations of “70°-planes”. considered exactly to one of theFIU. partial3. Stacking dislocations of “70°-planes”. considered exactly to one of the partial dislocations considered (a) After performing the shear indicated in Fig. 2(b). in the paper(a) of AfterCohen performing et al. m onethe ofshear the indicatedditisociation in Fig. 2(b). in the paper(a) Afterof Cohen performing et al. mthe one shear of theindicated ditisociation in Fig. 2(b). in the paper of Cohen et al. m one of the ditisociation (b) After completing the transition into a b.c.c. lattice by (b) After completing the transition into a b.c.c. lattice by (b) After completing the transition into a b.c.c. lattice by shearing successive “70’-planes” over l/8 ar,.o.o.(110). products of shearinga perfect successive dislocation “70’-planes” l/2 CX,,~.~. over(111). l/8It ar,.o.o. is (110). products shearingof a perfect successive dislocation “70’-planes” l/2 CX,,~.~. over(111). l/8 ar,.o.o.It is(110). products of a perfect dislocation l/2 CX,,~.~.(111). It is This “shear” is accompanied by a slight increase in important toThis note “shear” that theis accompanied direction ofby that a slight vector increase in importantThis to “shear”note that is accompaniedthe direction by ofa thatslight vector increase in important to note that the direction of that vector distance between the planes, due to the extensiveness of distance between the planes, due to the extensiveness of distance between the planes, due to the extensiveness of the spheres. corresponds to a (112) directionthe in spheres. the corresponding corresponds to a (112) directionthe spheres. in the corresponding corresponds to a (112) direction in the corresponding Discussion 109

a b

(110)

BCC 70.53˚ 70.53˚

Figure 5.3. (a) After performing the shear indicated in Figure 5.2b, and (b) after completing the transition into a BCC lattice by shearing 1 1 0 successive (110)α over 8 h110iBCC (or 16 h112iFCC).

In summary, the martensite −→ austenite phase transformation can occur in a

1 0 0 reverse procedure by shearing along {110}h110iα using the 8 h110iα partial dislocations, which leaves the {110} shear planes unchanged but would transform two other

{110}α0 planes into {111}γ planes. These planes are not in the correct stacking order.

Therefore, another shear on the {101} should be applied along the appropriate [121]

direction, over l/3 of the “Shockley-vector”, to ﬁnish the α0 −→ γ transformation

[129].

Shearing along the {110}h110iα0 and {111}h112iγ are also predicted by the phe-

nomenological theory of α0−→ γ transformation discussed in section 4.4.

5.2 Internal shearing of martensitic austenite

The phenomenological theory of martensitic phase transformation by itself does not

explain the full extent of this transformation, however, it provides clues for further

understanding. In this theory, it is always assumed that the product phase undergoes Discussion 110

internal shearing (i.e. P2) to accommodate the strain energy, since it is easier for the

product phase of the smaller volume fraction with glissile slip system to be sheared

(i.e. m2). (In reality, the martensitic transformation occurs by the advancement of

the interface, which is composed of disconnections.)

In the 15-5 PH alloy, it can be assumed that the newly-formed austenite phase un-

dergoes an internal shearing/slip during the phase transformation (unlike the conven-

tional austenite → martensite phase transformation in which martensite is sheared).

In some martensitic ferrous alloys, it is assumed that the {110}h111iα0 system is

responsible for the internal shearing of the martensite structure [115, 116]. As shown

by Luo et al.[130], the relaxed shear of a BCC metal in the h111i direction on the

{110} or {112} plane is easier.

In the case of FCC structure, it is known that the {111}h110iγ slip system requires

the least energy and is responsible for shearing of {111} planes. As shown in sec-

tion 4.4, the shearing in the {111}γk{110}α0 planes is also presumed by the theoretical

phenomenology of the martensitic transformation in 15-5 PH (table 4.6).

Based on Shockley partial dislocation dissociations, the glide of the {111} planes

in the h110i direction preferentially occurs by two consecutive glides (with lower

energy in total) on the h112iγ directions, as shown graphically in Figure 5.4 and

mathematically in Eq. 5.3:

a a a γ [110] = γ [121] + γ [211]. (5.3) 2 6 6

Eq. 5.3 indicates that by gliding the {111} planes over the h112iγ directions, the

stacking of the product austenite phase can change locally from (ABCABCABCA)

to (ABCACACBCA). It is even possible to assume that the newly formed austenite Discussion 111

Perfect and partial dislocations in FCC C C A r B B b1 A r b r 2 b3

displacement of atoms by b moves them to displacement of atoms by b or b is not a Figure 5.4. (Left)1 Shearing (gliding) of invariant planes {1112} in3 the identical sites ⇒ glide of a perfect dislocation lattice vector ⇒ motion of partialγ dislocation h i leaves perfect110 crystaldirection structure to leave a perfect crystalleaves structure, an imperfect and crystal (right) (stacking the pre- fault is ferred atomic movement of {111}γ bycreated) gliding into two h112i directions to leave a perfect crystal structure (i.e. Shockley partial dislocations). dissociation of perfect dislocation into 2 A Shockley partial dislocations a a a [1 10] = [1 2 1] + [211] phase may have a HCP (hexagonal close2 packed)6 stacking6 in that region (this will discussed further). Partial dislocation outlines a stacking fault area (planar defect): ABCACABCA… instead of ABCABCA… Figure 5.5a shows the experimental DP of the martensitic austenite on the [111]γ University of Virginia, MSE 6020: Defects and Microstructure in Materials, Leonid Zhigilei zone axis. The extra reflections (i.e. smaller reflection such as the reflection indicated by “x”) can not be explained only by assuming a perfect FCC stacking. However, they can exist by assuming an (ABABAB) stacking of {111} planes (e.g. HCP structure). These extra reflections are in the [121]γ direction and deviates from the [110]γ

1 2 direction by 30◦. Also, they are located in the 3 [242]γ or 3 [121]γ. Several crystal structures (as well as nitrides) have been considered as candidates to produce these patterns, however their resulting DPs are not consistent with all experimental DPs.

Fe-HCP crystal is one of the candidates which produces consistent DPs in various zone axes. As shown in a simulated DP of Fe-HCP crystal (figure 5.5c), the extra reflections only exist in the HCP structure and they should have the highest relative intensity. However, the intensity of the similar extra reflection in the experimental

DP is not as strong as the main reﬂections. This shows that the structure is partially Discussion 112

a b c

FCC HCP

Figure 5.5. (a) DP of martensitic austenite in [111]γ zone axis, which 1 shows extra reflections. The extra reflections are in the 6 [121]γ direction, which deviate from the [110]γ direction by 30◦, (b) the simulated DP of a Fe-FCC crystal, and (c) the simulated DP of a Fe-HCP crystal in [0001] zone axis. The extra reflection is shown by “x” and is the strongest reflection in [0001]HCP zone axis.

sheared/faulted to form an (ABABAB) stacking, and the martensitic austenite structure had a combination of both FCC and HCP stacking. The reflections resulting from the HCP stacking are sharp with no streaking, which indicates that the thickness of these layers are sufficient to provide a dynamical effect in the electron DP.

Figure 5.6 shows the dark-ﬁeld image originating from the HCP crystal reﬂection in the [111]FCCk[0001]HCP zone axis. As shown in this Figure, the regions with the HCP crystal are nano-meter size, and are dispersed throughout the product martensitic austenite.

This is strong evidence that these extra reﬂections are the result of both FCC and

HCP crystals. The only diﬀerence between the two crystals is the shearing of {111}γ Discussion 113

a b d c b

160 nm c d

160 nm 160 nm

Figure 5.6. (a) DP of martensitic austenite in [111]γ k[110]α0 zone axis, which shows extra reflections of the austenite, (b) the bright-field image, and (c) and (d) are dark field images which are resulted from the (202)FCC and (1100)HCP crystals, respectively. Due to the defects (e.g. dislocation) in the plates and the matrix, both bright-field and dark-field images have regions with different contrasts.

planes along h112iγ directions to produce regional (ABABAB) stacking. We call the newly formed austenite with HCP crystals an “H-austenite”.

According to the phenomenological crystallographic theory, the product phase undergoes an internal shearing on its invariant planes (i.e. {111}γ) to accommodate the strain energy during the martensitic transformation, i.e. m2. This shear in the Discussion 114

martensitic austenite is also probable, since the shear on the {111} planes of both

FCC and HCP stacking is highly feasible during the near-sonic martensitic phase

transformation.

Similar extra reﬂections also have been observed in a retained austenite of a

martensitic alloy [78]; however, the authors did not mention the source of them.

J. C. Dalton also observed these anomalies in the DPs of the martensitic austenite in

2205 and as he mentioned, they are “considered most germane for future study” [87].

Finally, the internal shear in the martensite crystal structure (BCT) is diﬀerent

than the austenite, since during the austenite-to-martensite phase transformation,

martensite shears on the {110}α0 planes. The shearing of {110}α0 planes only has

one possible stacking (i.e. ABABAB). Therefore, in the conventional austenite →

martensite phase transformation, the product phase always looks the same (i.e. similar

crystal structure, but in diﬀerent variants). However, the ABCABC stacking can have

more options during the transformation (i.e. FCC and/or HCP).

5.2.1 The interface structure of austenite and martensite

Theoretically, two diﬀerent kinds of dislocations can exist in the martensite–austenite

interface: (a) the transformation or coherency dislocations which perform the trans-

formation lattice deformation, maintain continuity across the interface, and are capa-

ble of conservative climb and/or glide, and (b) the misﬁt or anticoherency dislocations which generate an inhomogeneous lattice-invariant deformation and can disturb the

lattice correspondence across the interface [131, 132]. The misﬁt dislocations have the

same properties as lattice dislocations and they are discussed in section 5.2. In this

section, we discuss the transformation and coherency dislocations at the martensite–

austenite interface. Discussion 115

Experimental observations of the newly formed austenite by a martensitic trans-

formation showed that the habit plane is close to the planes with the highest atomic

density in both phases (section 4.3.3). The determined interface of martensitic austen-

ite is around the (287)α0 plane, which is 11◦ from the (011)α0 plane. However, the

angle between the [011]α0 direction and the interface line in Figure 5.7a is around

3◦–6◦. It can be realized that the interface is not only inclined relative to the [011]α0

but it is also inclined slightly relative to the viewing direction (i.e. [111]α0 ). The in-

terface normal (872)α0 (or (872)α0 , depending on the austenite variant) deviates from the viewing direction [111]α0 by 3◦ (or 9◦, respectively).

From Figure 5.7b, it can be calculated that the diﬀerence in the “eﬀective plane

0.252 spacing” of two phases at the interface line is around 6 % (i.e. 0.237 = 1.06). This amount of mismatch between the atomic plane spacing of martensite and austenite

along the [110]α0 line should be accommodated by the coherency dislocations. Ac-

cording to Olson [131], the Burgers vectors of coherency dislocations are usually in

the opposite sign of anticoherency (misﬁt) dislocations. Therefore, it can be con-

cluded that the coherency dislocation at the interface of martensite–austenite are in

the h111iγ or h110iα0 directions.

One diﬃculty of this type of study is the irrationality of the austenite habit

plane. The HRTEM viewing direction is almost parallel to the [111]α0 and [011]γ

directions, but the interface is inclined relative to the viewing direction. Assuming

the thickness of the TEM sample is ≈50 nm, two crystals overlap by about ≈5 nm

(Eq. 5.4). Therefore, it is not possible to observe the correct atomic conﬁgurations

at the interface. On the other hand, due to nitrogen supersaturation of both phases,

there is more uncertainty to resolve atomic column positions. (The spots in the Discussion 116

a [011] b � �

�

�’ 40°

�’ 42° 45°

5 nm [111]�’

Figure 5.7. (a) HRTEM image of the interface in the [011]γ and [111]α0 viewing direction, (b) schematic of atomic configuration and the difference in the effective plane spacings at the interface, which necessitates the formation of coherency dislocations. periodogram are rather diffuse.) However, the atomic model of the interface can be helpful in understanding the formation of coherency dislocations.

Overlap =

= (Sample thickness) × tan (Interface angle) (5.4)

= 50 nm × tan 6◦ = 5 nm

The hard sphere model of the martensite–austenite interface in Figure 5.8 shows how the two diﬀerent crystals can accommodate each other by creating small steps at the interface. Observation of steps at the interface of martensitically transformed phases has been reported by several researchers [110, 114, 133–135]. Discussion 117

(111)γ

(111)

γ B A B A

6˚

C B (101) B A C C B α’ (011)α’

Figure 5.8. (a) Space ﬁlling atomic conﬁguration at the austenite/martensite interface in the viewing direction [011]γ and [111]α0 . In every 9 atomic planes there is a step to compensate the mismatch. Atoms are stacked in A and B layers in austenite, and in A, B and C layers in martensite.

Figure 5.9 shows how the steps form during the advancement of the habit plane over the phase transformation. Figure 5.9a is being produced solely by putting the mostly dense planes of martensite and austenite over each other. (As mentioned theoretically and experimentally in section 4.3.3, in both N–W and K–S relations, the

{111}γ and {011}α0 planes are in contact with each other). During advancement of the interface, dislocations climb, and due to the stress (s) and strain (e) caused by the diﬀerence in the crystals’ volume and their plane spacings, the habit plate rotates slightly according to [109]:

e/s tan θ = , (5.5) E in which E is the elastic modulus of the sample. Discussion 118

a γ

α’ b

Figure 5.9. (a) Formation of dislocation due to the dilatational strain in the habit plane, (b) rotation of the habit plane to reach to an irrational invariant plane (hypothetically, with no dislocation formation), and (c) formation of steps at the interface and the advancement of interface by dislocation climb.

The effect of habit plane rotation is seen in Figure 5.9b. This line between the two phases is undistorted and unrotated, i.e. an invariant line. However, atoms have discrete positions in the plane, and configuration of atoms at the interface in Fig- ure 5.9b is practically impossible. Therefore, atoms rearrange themselves to have the least strain energy on the mostly dense atomic planes of both phases, which leads to the formation of dislocations and steps at the interface (figure 5.9c). This rotation of habit plane by climbing the dislocation is accompanied with internal shearing of Discussion 119

the product phase (i.e. the austenite phase). The interfacial dislocations have sim-

ilar Burgers vectors as an anticoherency dislocation (with partial dislocation along

h112iγ), and they originate from the austenite during the shearing of {111}γ planes.

The result is the step-like conﬁguration of the interface. As mentioned earlier, the

shearing of {111}γ planes is inevitable during the phase transformation (this shearing

is denoted by P2 in the phenomenological theory of section 4.4).

Each step can be deﬁned based on one of the phases meeting at the interface. As

shown in Figure 5.10, the step can be indicated by a vector, ~d, and can be dissociated

into two other vectors, ~p and ~q. The vector ~p is similar to the Burgers vector needed

to ﬁll the gap at the step (which is a basic deﬁnition of Burgers vector). In the

current case study, vector ~p is similar to the internal dislocation of the base crystal

1 (partial dislocation 6 h112i), and vector ~q is deﬁned as the plane spacing of the base crystal parallel to the interface. This plane is also called the “terrace plane”. The

combination of step and dislocation at the interface was predicted more than 30 years

ago. However, Hirth called them “disconnections” for the ﬁrst time in 1994 [61].

The shape of the interface in 3-dimensions can be depicted in Figure 5.11a. There

are steps and terraces along the {111}γ planes. However, the interface is not exactly

perpendicular to the [011]γ plane (see Figure 5.8), and the interface should have steps

along the [011]γ direction as well (ﬁgure 5.11b). Based on our calculations the interface

is rotated 6◦ and 3◦ around the [111]α0 and [110]α0 axes, respectively.

A martensitic interface is capable of moving conservatively; therefore, the misﬁt

dislocations must be able to glide as the interface advances, and they remain paral-

lel to the invariant line (dashed line in Figure 5.11a). Advancement of the interface

and rotation of the habit plane in 3-dimensions, necessitates that the product phase Discussion 120

0.252 nm

(111)γ

q (200)γ d

(011) (110)α’ p

α’

0.237 nm

Figure 5.10. Schematic of atomic plane conﬁguration at the interface and the formation of coherency dislocation or steps (~d) which can be dissociated to two vectors (~p and ~q). This conﬁguration is also called a disconnection.

undergoes shear in closed packed systems at two diﬀerent axes (as proven experimentally earlier). These dislocations must therefore lie along the intersection of their glide plane with the plane of the interface, or habit plane (shown as a terrace plane).

Such a glissile interface is shown in Figure 5.11b. The misﬁt dislocation lines lie in the interface where it intersects their glide planes (i.e. {111}γ planes in Figure 5.11b).

The result of this is the formation of a macroscopic habit plane with irrational Miller

indices (ﬁgure 5.11b). As long as all the glides are happening over the {111}γ planes,

the stacking is still of FCC or HCP. However, their Shockley partial dislocations are

not parallel, and stacking faults in diﬀerent axes can be predicted.

Finally, the samples being studied here are treated by the low-temperature nitrida-

tion process. After the treatment, the samples are under a huge stress (e.g. >2 GPa), which can cause a very high dislocation density in the crystal. The close observation of dislocations and stacking faults in such deformed crystals is tedious. However, the Discussion 121

<112> a ⅙ γ

terrace plane {111}γ

glide/shearing planes{111} b γ

(278)α’ habit plane [001] {111}

α’ γ

[010] ] α’ α’ [100

Figure 5.11. (a) Formation of steps along the interface by advancing the phase, (b) the internal shearing of the product phase (austenite) in 3 dimensional view and formation of irrational habit plane, and (c) the macroscopic habit plane (278)α0 relative to the parent phase. Discussion 122

DP and the theoretical phenomenology of phase transformation are in good agreement and provide clues for further study. Discussion 123

5.3 Highly tetragonal martensite

The BCC crystal structure in our stainless steel has very limited interstitial solubility.

Although after low-temperature nitridation, the carbon and nitrogen concentrations

can reach to more than 20 at.%, previous work on the nitrided δ-ferrite in 2205 [87]

and in 17-7 PH [89] reported no lattice parameter expansion or anomalies in the

crystal structure. This brought more questions, such as “where do the interstitial

atoms go without inducing any distortion in the lattice”. Several other researchers

proposed the idea of “expanded martensite” [10, 35, 41] (in a similar way to the more well-known notion of “expanded austenite”). However, their observations were based

on the XRD patterns and no clear explanation was provided.

Our observations on 15-5 PH showed that there are anomalies in the XRD, DPs

and the HRTEM data of the martensite phase after low-temperature nitridation.

(Note that the as-received martensite with the carbon concentration of <0.3 at.%

shows no measurable expansion or distortion.) The DPs of the nitrided δ-ferrite in

both 2205 [87] and 17-7 PH [89] stainless steel showed similar anomalies to those

observed in the martensite in 15-5 PH alloy.

Our convergent electron beam studies of distorted DPs in 15-5 PH 4.34, followed

by the observation of warped atom columns in the HRTEM image of the martensite

4.36, strengthen the hypothesis that nitrogen atoms might have heavily deformed the

lattice of the martensite. This could also be the case in the nitrided δ-ferrite in both

2205 [87] and 17-7 PH [89] stainless steel.

A schematic Figure provides a better understanding of this eﬀect. Figure 5.12

shows schematically how the infusion of nitrogen atoms into the octahedral spaces Discussion 124

[011]

stretching [001]

[010] BCC BCC BCT Nitrogen atom, x(0) Iron atom, x(0) Iron atom, x(-1/2) [001]

Octahedral site [011]

[011] [010]

- [100] [011] - - (011) (011) (a) (b)

Figure 5.12. (a) Atomic conﬁguration in the the (100) plane of a BCC crystal, and (b)[top] stretching the pattern in the [001] direction caused by placing nitrogen atom into the octahedral sites, [bottom] placing several of the initial stretched pattern from the top to form the stretched (100) plane. It appears that the plane is shearing in the [011] direction.

of the BCC structure leads to the stretching of the lattice in the [001] direction and consequently, the inclination of the originally BCC lattice in the [011] direction.

Figures 5.13a and b show that by shearing a rectangle to a parallelogram, the area must remain unchanged, but the spacing between the (011) planes decreases.

The (011) plane reflection in the DP and the periodogram has an inclination and an arc-shaped variation. The arc-shaped reflection of the (011) plane has a concavity toward the transmitted beam (000). This means that the corresponding planes retain their spacing, although they are rotated (figures 5.13c). This effect can be explained Discussion 125

a a/cos(θ)

(011) (011)

(011) h=a/cos(θ) a

- L=a cos(θ) L=a (011) θ θ a (a) (b) (c)

Figure 5.13. (a) The (100) plane of a BCC structure with the lattice parameter a, (b) after stretching the (100)BCC plane in the [010] direction. The area of the plane is the same, but the (011) plane spacing reduces, and (c) maintaining the (011) plane spacing unchanged, according to the HRTEM observations. The HRTEM images show the (011) plane spacing does not change; therefore, the whole volume of the lattice must increase.

by the stress ﬁeld of a nitrogen atom in (010) planes which resists a decrease in the iron-nitrogen distance in the lattice. Therefore, it can be inferred that on the average, the area of the (100) plane must increase.

On the contrary, the DP and the HRTEM images show that the location of the

(011) planes remains unchanged. For instance, it can be inferred from the peri-

odogram of Figure 4.36 that all the (011) reﬂection almost remains circular with no inclination.

According to Zener ordering in the BCT crystals, high concentrations of interstitials leads to considerable elastic strain energy, which can be minimized by alignment of the tetragonal distortion ﬁelds of neighboring interstitial atoms. Therefore, a relatively large number of interstitial atoms preferably sits on just one of the three types of octahedral interstices [136]. This is why the HRTEM image (ﬁgure 4.36) shows only one set of fringes undulating. Discussion 126

Based on the inclination of the (011) planes, the amount of lattice tetragonality

can be calculated simply from the DPs and the periodogram according to:

90 − |θ| c/a = cotg( ), (5.6) 2 where c and a are lattice parameters of the matrix and θ is the angular deviation

between the (011) normal and the (011) plane of the matrix. Calculations on the

DPs and the periodogram of the matrix shows a local maximum of c/a = 1.12. This amount of tetragonality is higher than the highest c/a = 1.11 reported for conventional martensite in steel (with 10 at.% N) [137–141]. Table 5.1 shows the lattice parameters of martensite after diﬀusion of nitrogen, measured by various researchers.

According to Table 5.1, a was observed not to change much with increasing nitrogen concentration; values range between 0.287 nm and 0.285 nm. This is also observed in the recorded DPs and the periodogram of the martensite in the current work. According to [141], diﬀusion of ≈ 9 at.% nitrogen into the martensite leads to

unit cell volume expansion of up to 7 %. Contrary to the accepted understanding

of the expanded austenite, in which the austenite lattice expands isotropically (since

the octahedral sites in the FCC structure are isotropic), interstitial solutes in the

BCC structure tend to expand the BCC lattice in only one direction, owing to the

anisotropy of the octahedral interstices. The brown or lighter colored iron atoms in

Figure 5.12b are pushed up and down.

Due to the Poisson contraction, one expects that the four atoms sitting farther

from the center of the octahedral site in BCC will get closer to the center after

positioning a nitrogen atom in the center of a tetrahedron and stretching the (011)

plane. The distance between the lateral iron atom and the center of the octahedron is Discussion 127

Table 5.1. Lattice Parameter of Martensite Measured by Several Re- searchers.

Reference Temperature Composition Lattice Parameters (nm) Tetragonality (K) (at. %N) a c c/a Jack [138, 139] 291 0 0.2866 0.2866 1.000 5.30 0.2859 0.3016 1.055 7.06 0.2856 0.3047 1.067 8.09 0.2852 0.3072 1.077 8.23 0.2854 0.3080 1.079 8.55 0.2850 0.3091 1.085 8.68 0.2850 0.3090 1.084 Imai et al. [137] 298 9.17 0.2827 0.3106 1.099 9.30 0.2833 0.3113 1.099 9.49 0.2837 0.3118 1.099 9.92 0.2840 0.3133 1.103 10.18 0.2841 0.3139 1.105 10.28 0.2845 0.3145 1.105 10.64 0.2847 0.3158 1.109 Bell [140] 293 2.86 0.2859 0.2934 3.25 0.2856 0.2951 1.033 4.69 0.2853 0.2932 1.028 6.47 0.2853 0.3029 1.066 7.84 0.2850 0.3062 1.074 8.61 0.2843 0.3091 1.087 8.74 0.2845 0.3097 1.089 9.57 0.2850 0.3116 1.093

79 pm, while the radius of a nitrogen atom in a covalent bond is 75 pm (the radius of iron is estimated to be 125 pm). However, due to the neutral behavior of nitrogen in the covalent iron–nitrogen bond, the eﬀective radius of nitrogen in an iron–nitrogen system is rather larger than its atomic radius [136]. Therefore, in this case, the

Poisson contraction of peripheral atoms does not apply. In other words, the plane spacing contraction in the [001] direction would be negligible. This can be interpreted from the DP and the HRTEM image of martensite in Figure 4.36. Discussion 128

Interstitially dissolved nitrogen tends to increase the tetragonality of martensite without signiﬁcant contraction of the lattice in other dimensions [42, 43, 142]. There-

fore, the average volume of the crystal will increase. The result (in contrast to ex-

panded austenite) is that X-ray diﬀractograms of nitrogen-infused martensite show

the same peak positions as the BCC structure, but with peak splitting that increases with increasing nitrogen concentration. This usually appears as a shoulder on the

left side of the (011) plane or broader peak (overlapping of two peaks) and the center

appears to be shifted to the larger plane spacings (ﬁgure 4.31). In the case of low

instrument resolution or imprecise observation, this issue can be misinterpreted as

an expanded martensite. This shoulder has been observed in references [11, 35, 42].

Likewise, the DPs of highly tetragonal martensite do not show any signiﬁcant change

in plane spacings nor extra reflections; however, they show diffuse arc-shaped spots which originate from locally varying tetragonality (figure 4.17).

Figures 5.14 reveal a comparison between the simulated DPs of highly tetragonal

(c/a = 1.08 and c/a = 1.04) BCT lattices with the recorded DP of δ-ferrite in

the 17-7 PH alloy [89] (the results from the 17-7 PH, 15-5 PH and 2205 steels were

essentially similar). This observed anomaly in the recorded DPs (i.e. arc-shaped

reﬂections) is in good agreement with the simulated martensite lattices. However,

the reason for this slight rotation of the BCT lattice by increasing the tetragonality

possibly is related to the complex stress-strain condition of the sample. However, this

eﬀect can be studied more carefully by observing the corresponding HRTEM images

in a more stable TEM instrument.

Figure 5.15 also retrieved from [87], which shows the nano-diﬀractions proﬁle along

a [001]BCC zone-axis of a nitrided δ-ferrite grain in 2205 stainless steel. The measured Discussion 129

a 011 0 0 1 1 # 1 1 #

011

4 nm-1

11#2 [100]α’

11#0 b

002# 002

1#10

4 nm-1 [110]α’ c 112 121 0 0 1 1 # 1 # 1

4 nm-1

[113]α’ Figure 5.14. The experimental and simulated DPs of the nitrided δ- ferrite grain in 17-7 PH in the (a) [100]δ, (b) [110]δ, and (c) [113]δ zone axes. The simulated DPs are obtained by overlapping DPs of martensite lattices with diﬀerent tetragonalities of c/a = 1.08 and c/a = 1.04. Discussion 130 ..FAUEESFRIECNANN OOSLSUPERSATURATION COLOSSAL CONTAINING FERRITE FEATURELESS 6.4.

91˚ 90˚ 90˚

92˚ 92˚ 92˚ 203

93˚ 92˚ 90˚

FIGURE 6.27: Nano-diffraction profile along a [001]bcc zone-axis through a weak-contrast region of a 2205 δ-ferrite Figuregrain 5.15. following Nano-diffraction nitridation. The dark profile spots runningalong a orthogonal [001]BCC tozone-axis the free surface through in the BF image a weak-contrastrepresent adventitious region carbon of build-up a 2205 fromδ-ferrite the high intensity grain followingof the focused nitridation. electron probe. The measured angle between the scattering g vectors is oscillating between 90◦ and 93◦, which are corresponding to c/a = 1 and c/a = 1.05.

angle between the scattering g vectors oscillates between 90◦ and 93◦, which corre-

spond to c/a = 1 and c/a = 1.05, respectively. This distortion can even be observed

by naked eyes. One might think that this is from the DP artifact, however, at the

same time, it is hard to rule out the possibility of tetragonality in the lattice after

nitrogen-supersaturation. 131

6 Conclusions

Exploring new ways to engineer the surface of a martensitic alloy – a subclass of steels with tremendous technological and economic signiﬁcance – provides great technical importance e.g. for aircraft parts, automotive parts, production tooling, turbines, nuclear reactors, or surgical instruments etc.

Low-temperature carburization and nitridation were successfully applied to 15-5 PH, a martensitic precipitation-hardening alloy. Both procedures resulted in the supersaturation of the martensite lattice with enhanced chemical and structural properties in the near-surface regions (the hardened “case”).

The response of the martensite and the ferrite as lattices which are traditionally known to have less favorability toward interstitial supersaturation was a matter of debate in recent years. The chemical and microstrctural analyses showed that these lattices can have similar or even stronger tendencies to dissolve intersititials.

In the past decade our understanding of “expanded austenite” (due to its pro- nounced changes in crystal structure) has been taken for granted as a known fact, although, we broadly lacked a scientiﬁc concurrence regarding the response of martensite and ferrite crystal structures. Their response (i.e. revealing no obvious expansion Conclusions 132 after the treatment) were sometimes regarded as strange, and other times were simply explained based on the same analogy with the expansion of austenite.

Despite the fact that carbon and nitrogen atoms have similar atomic radii and are located beside each other in the periodic table, the response of the alloy to these elements after the treatment was somehow diﬀerent. After low-temperature nitridation, two diﬀerent but related responses of the martensite crystal have been observed, explained and formulated: enormous tetragonality of the BCT lattice, and isothermal

α0 −→ γ martensitic phase transformation, which we proposed the name “martensitic austenite” for the product phase. From these two responses it is concluded that high concentrations of nitrogen very close to the surface cannot be realized in martensite or ferrite at some point even under “paraequilibrium” conditions, because of the formation of martensitic austenite. The morphology and DPs of the product austenite phase suggest a shear transformation. The new phase products have a lenticular shape that end with sharp tips and they shear each other where they intersect.

The microstructural evolution of martensite after diﬀusion of carbon was more subtle. The alloy mainly responded by the formation of cementite in the depth of

1 µm from the surface. Moreover, the tetragonality of the lattice were also observed to a lesser extend (compared to the nitrided sample).

Finally, this work provided a broader scientiﬁc understanding of the far-from- equilibrium state brought about by interstitial solutes in a martensitic alloy. The martensite-to-austenite martensitic phase transformation provides another pathway for steel (or other alloys) industry to shape and treat future products by manipulating the composition of the alloy and initiate an iso-thermal phase transformation. It is postulated that the microstructure after phase transformation containing a multitude Conclusions 133 of nano-size austenite plates would increase the strength as well as toughness of the product (this requires further studies). Appendix 134

Appendix A Phenomenology of martensitic phase transformation (Programing Codes)

The following programing code is the phenomenological crystallographic algorithm

used to determine the habit plane, magnitude of the shear and the relative OR after

martensitic phase transformation from martensite to austenite. The B matrix is the

lattice deformation (Bain distortion), and x and n are the invariant line and invari-

ant normal, respectively (which are being determined). This formulation is based on

BCC to FCC phase transformation and the Bain distortion, shear plane and direc-

tions are deﬁned based on the parent phase (i.e. martensite). The 3-by-3 matrices

are indicated by capital bold letters. The row or column matrices are indicated by

bold small letters and variables are shown in normal small letters.

ClearAll[“Global`*”]

%B is the Bain transformation matrix with three parameters: b1, b2, and b3: b1=1 .132136; b2=1 .132136; b3=0 .800541;

B = DiagonalMatrix[{b1, b2, b3}];   0.883286 0. 0.     B= 0. 0.883286 0.      0. 0. 1.24916 % x is the invariant line Appendix 135

  x1     x =  x2  ;     x3 % xt is the transpose of x xt = Transpose[x];

% p2 is the shear plane in martensite   1     p2 = (1/2∧0.5)  0  ;     −1

pt2 = Transpose[p2];

sx = NSolve[{((xt.x)[[1]])[[1]] == 1, (((xt.B∧2).x)[[1]])[[1]] == 1, ((pt2.x)[[1]])[[1]] == 0},

{x1, x2, x3}];

% n is the invariant normal   n1     n =  n2  ;     n3 nt = Transpose[n];

% d2 is the direction of shear in martensite

d2 = {{1}, {0}, {1}};   1     d2 =  0  ;     1

sn = NSolve[{((nt.n)[[1]])[[1]] == 1, (((nt.((Inverse[B])∧2)).n)[[1]])[[1]] == 1,

((nt.d2)[[1]])[[1]] == 0}, {n1, n2, n3}]; xbar = B.x; Appendix 136

pt2bar = Simplify[(pt2.Inverse[B])/(((pt2.(Inverse[B])∧2).p2)∧0.5)[[1]]];

% Invariant line x = {{x1/.sx[[2, 1]]}, {x2/.sx[[2, 2]]}, {x3/.sx[[2, 3]]}};   0.530785     x= -0.660708      0.530785 % Invariant normal n = {{n1/.sn[[4, 1]]}, {n2/.sn[[4, 2]]}, {n3/.sn[[4, 3]]}};   0.663032     n= -0.347529      -0.663032 % Building several transient matrices to solve invariant line matrix (S). xbar = B.x; u = Transpose[{Cross[Transpose[x][[1]], Transpose[p2][[1]]]}];

R1 = Transpose[{Transpose[x][[1]], Transpose[p2][[1]], Transpose[u][[1]]}]; v = Transpose[{Cross[Transpose[xbar][[1]], pt2bar[[1]]]}];

R2 = Transpose[{{Transpose[xbar][[1]]}[[1]], {pt2bar[[1]]}[[1]], {Transpose[v][[1]]}[[1]]}];

Transpose[R2]//MatrixForm;

S0 = R1.Transpose[R2].B;

S0i = Chop[Transpose[R2].B.R1];

S0i//MatrixForm; nit = Chop[(Transpose[R1]).n]; nit//MatrixForm;

Rt2BR1 = Chop[(Transpose[R2].B).R1]; Appendix 137

  1 0 0     iSi =  0 cosbeta −sinbeta  .Rt2BR1;     0 sinbeta cosbeta iSi//MatrixForm; nitiSi = Transpose[Transpose[nit].iSi]; nitiSi//MatrixForm; nit//MatrixForm; sbeta = NSolve[{nitiSi[[2, 1]]==(nit[[2]])[[1]], nitiSi[[3, 1]]==(nit[[3]])[[1]]},

{sinbeta, cosbeta}]; sinbeta= sinbeta/.sbeta[[1 , 1]]; cosbeta= cosbeta/.sbeta[[1 , 2]]; beta = ArcSin[sinbeta];

S = R1.iSi.(Transpose[R1]);

% Invariant line matrix   0.8755 0.0288313 0.160388     S= −0.0165036 0.877922 −0.135456      −0.115849 0.0928185 1.23139 habitPlane = Normalize[((pt2.Inverse[S]) − pt2)[[1]]]

{0.209179, 0.709045, 0.673424}

d1 = (S.d2 − d2)/(habitPlane.d2)[[1]]; m1 = Norm[d1] Appendix 138

0.220075 y = Transpose[{Cross[{1, 0, 0}, habitPlane]}];

d2 = Chop[(y − Inverse[S].y)/((pt2.Inverse[S].y)[[1]])[[1]]];

m2 = Norm[d2]

0.256795 alpha = (180/3.141) ArcTan[m2/2]

7.31797

% Orientation relationship

planeMar = {{1, 1, 0}};

scalarP=

(((planeMar/(Norm[planeMar])).

Transpose[{Normalize[Flatten[(planeMar.Inverse[S])/(Norm[planeMar])]]}])[[1]])[[1]];

deviationP = (180/3.141)ArcCos[scalarP]

1.7479

directAus = {{1}, {−1}, {1}};

scalarD=

((Transpose[(directAus/(Norm[directAus]))].

Transpose[{Normalize[Transpose[(S.directAus)/(Norm[directAus])][[1]]]}])[[1]])[[1]];

deviationD = (180/3.141)ArcCos[scalarD]

0.535527 Appendix 139

(111)γ1.74789◦ from (011)α0

[101]γ 0.53553◦ from [111]α0

% Triple shear calculation (assuming two equal shear matrices are acting and

simplifying it to two shears. Therefore, P2 ≈ P3.P3)

p20 = Transpose[p2];

P2 = IdentityMatrix[3] + m2d2p2’;

P2//MatrixForm   0.967028 0. 0.0329718      0. 1. 0.      −0.0329718 0. 1.03297 P3 = MatrixPower[P2, 0.5];

P3//MatrixForm   0.983514 0. 0.0164859      0. 1. 0.      −0.0164859 0. 1.01649 Appendix 140

Appendix B Correcting Auger Electron Spectroscopy Proﬁle and Calculating the Diffusion Coefﬁcient

There is always noise in the AES (Auger electron spectroscopy) system. This

noise is becoming more crucial where the signal-to-noise ratio decreases. The Figure

below shows the detected noise from the regions with the high nitrogen concentration

and a region with the low nitrogen concentration. Ernst recently showed this eﬀect

by mathematical manipulation of the signal [143].

The software of PHI 680 AES instrument is designed to make a ﬁrst order deriva-

tion of the number of received Auger electrons versus their energy (by considering

9 adjacent points in the number/energy diagram). The derivation is being applied

since the received Auger signal is weak and the derivative would help to detect and

quantify the signal. However, the software can not diﬀerentiate noise from the signal

at the region with low atomic concentration, even though the shape of the signal is

completely diﬀerent from the noise. For instance, Figure B.1 shows by reaching to an

area deeper in the sample with low nitrogen concentration, there a notable noise in

the raw data.

Here, I have provided a straightforward method to smooth the signal and remove

the noise at the end of the AES line scan, then, solving the value of diﬀusion coeﬃcient versus nitrogen concentration based on the Boltzmann–Matano method [144].

There are a few step for this evaluation:

(1) The data from the noisy area at the end of the line scan are not correct,

since the concentration never goes to zero. Therefore, the evaluation only

depends on the data sets which have magnitudes higher than the noise. The Appendix 141

Figure B.1. The shape of the nitrogen signal at diﬀerent nitrogen concentrations. By reaching deeper into the sample the magnitude of noise is still comparable to the signal. Appendix 142

average magnitude of noise in the tail is calculated (for example 3 at.% N at

the plateau region). Then, these data sets are suppressed to zero. (Dealing

with this data set at the plateau region can be done by assuming a decrease

in magnitude by second Fick’s law. However, my calculations based on this

assumption showe that this doesn’t make much diﬀerence.)

(2) Fitting the curve to all data according to Gaussian Filter method or Bezier

function.

(3) Inverting the fitted function and solving the diffusion coefficient according

to Boltzmann–Matano method

The programing code written in MathematicaTM software is provided below:

imps =

Import[

"/Users/amiraliza/Documents/Case Western Reserve/Data/Auger/2016-04-19/15-5N400

- N concentration.xls"];

rawX = imps[[1]][[All, 1]];

rawY = imps[[1]][[All, 2]];

rawXY = Transpose[{rawX, rawY}];

GaussFilterY = GaussianFilter[rawY, 20];

GaussFilterXY = Transpose[{rawX, GaussFilterY}];

ListPlot[rawXY, BaseStyle → {FontWeight → “Bold”, FontSize → 12}, AxesStyle → Black,

Frame → True, FrameLabel → {Style[“Distance (µm)”, Black], Style[“N (at.%)”, Black]},

PlotRange → {{0, 20}, Automatic}] Appendix 143

%) 10 at. ( N

0 0 5 10 15 20 Distance (µm)

ListPlot[{rawXY, GaussFilterXY}, AxesLabel → {“Distance (µm)”, “C (at.%)”},

BaseStyle → {FontWeight → “Bold”, FontSize → 12}, AxesStyle → Black,

BaseStyle → {FontWeight → “Bold”, FontSize → 12}, AxesStyle → Black, Frame → True,

FrameLabel → {Style[“Distance (µm)”, Black], Style[“N (at.%)”, Black]},

PlotRange → Automatic]

%) 10 at. ( N

0 0 5 10 15 Distance (µm)

(*Boltzmann-matano*)

(**) Appendix 144

GaussFilterY[[Dimensions[GaussFilterY][[1]]]] = 0;

GaussFilterY[[1]] = Max[GaussFilterY] + 0.01;

ConcenInverve = Transpose[{GaussFilterY, rawX}];

zi = Interpolation[ConcenInverve, InterpolationOrder → 1];

Plot[zi[x], {x, 0, 18}, AspectRatio → 1, PlotRange → {Automatic, {0, 20}},

AxesLabel → {“N at.%”, “Distance(µm)”}]

f1[x ]:=Evaluate[Integrate[zi[t], {t, 0.01, x}]]

(*Flipping the concentration proﬁle to get integration*)

Distance(µm) 20

N at.% 0 5 10 15

Diﬀu[c ]:= − 1 ∗ (10∧(−6))/(72000) ∗ zi0[c] ∗ f1[c]

Plot [Evaluate[Diﬀu[x]], {x, 1, 17}, AxesLabel → {“N at.%”, "D(C) m2/s"}]

(*Plot [Log10[Diﬀu[x]], {x, 1, 17.5}, AxesLabel → {“N at.%”, "Log[D(C)] m2/s"}] ; *) Appendix 145

(*Diﬀusion coeﬃcient versus nitrogen concentration*)

D(C) m2/s

5. × 10-9

4. × 10-9

3. × 10-9

2. × 10-9

1. × 10-9

N at.% 5 10 15 Appendix 146

Appendix C CALPHAD Modeling to Determine the Stability of Martensite and Austenite

α0 γ X α0 γ α0 γ α0 γ ∆G − = ∆GFe − + ΩFe:N− XFeXN + ΩFe:N− XFeXN+

α0 γ α0 γ ΩCr:N− XCrXN + ΩNi:N− XNiXN+

α0 γ α0 γ α0 γ ΩFe:Va− XFeXVa + ΩCr:Va− XCrXVa + ΩNi:Va− XNiXVa+

α0 γ ΩFe,Cr:N− XFeXCrXN(XFe − XCr)+

α0 γ ΩFe,Ni:N− XFeXNiXN(XFe − XNi)+ (C.1)

α0 γ ΩNi,Cr:N− XNiXCrXN(XNi − XCr)+

α0 γ ΩFe,Cr:Va− XFeXCrXVa(XFe − XCr)+

α0 γ ΩFe,Ni:Va− XFeXNiXVa(XFe − XNi)+

α0 γ ΩNi,Cr:Va− XNiXCrXVa(XNi − XCr). ;

Clear[n, Va,T ];

Cr = 0.15;

Ni = 0.05;

Fe = 1 − Cr − Ni;

Va = 1 − n;

T = 600;

GCrVabcc = −8856.94 + 157.48T − 26.908T Log[T ] − 0.00189T ∧2; Appendix 147

GFeVabcc = 1225.7 + 124.134T − 23.5T Log[T ] − 0.0044T ∧2;

GNiVabcc = −5179 + 117.8T − 22.1T Log[T ] − 0.0048T ∧2 + 8715 − 3.556T ;

GCrNbcc = −8856.94 + 157.48T − 26.908T Log[T ] − 0.00189T ∧2+

3/2 ∗ (−3750.675 − 9.45425T − 12.7819T Log[T ] − 0.00176686T ∧2)+

311870 + 29.12T ;

GFeNbcc = 1225.7 + 124.134T − 23.5T Log[T ] − 0.0044T ∧2+

3/2 ∗ (−3750.675 − 9.45425T − 12.7819T Log[T ] − 0.00176686T ∧2)+

93562 + 165.07T ;

GNiNbcc = − 5179 + 117.8T − 22.1T Log[T ] − 0.0048T ∧2+

3/2 ∗ (−3750.675 − 9.45425T − 12.7819T Log[T ] − 0.00176686T ∧2)+

200000 + 200T ;

GCrFeVabcc = +20500 − 9.68T ;

GCrNiVabcc = +17170 − 11.8199T ;

GFeNiVabcc = −956.63 − 1.28726T ;

GCrFeNbcc = −799379 + 293T ;

GFeCrNiVabcc = −2673 + 2.0415T ;

GFeNVabcc = −235433 − 40.5308T ;

GCrNVabcc = −200000;

GCrVafcc = (−8856.94 + 157.48T − 26.908T Log[T ] − 0.00189435T ∧2)+

7284 + 0.163T ;

GFeVafcc = (1225.7 + 124.134T − 23.5T Log[T ] − 0.0044T ∧2) − 1462.4+

8.282T − 1.15T Log[T ] + 0.00064T ∧2;

GNiVafcc = −5179.159 + 117.854T − 22.096T Log[T ] − 0.0048407T ∧2; Appendix 148

GCrNfcc = −8856.94 + 157.48T − 26.908T Log[T ] − 0.00189T ∧2+

0.5 ∗ (−3750.675 − 9.45425T − 12.7819T Log[T ] − 0.00176686T ∧2)−

124460 + 142.16T − 8.5T Log[T ];

GFeNfcc = 1225.7 + 124.134T − 23.5T Log[T ] − 0.0044T ∧2+

0.5 ∗ (−3750.675 − 9.45425T − 12.7819T Log[T ] − 0.00176686T ∧2)−

37460 + 375.42T − 37.6T Log[T ];

GNiNfcc = −5179 + 117.8T − 22.1T Log[T ] − 0.0048T ∧2+

0.5 ∗ (−3750.675 − 9.45425T − 12.7819T Log[T ] − 0.00176686T ∧2)+

38680 + 143.09T − 10.9T Log[T ] + 0.00438T ∧2;

GCrFeVafcc = 10833 − 7.477T ;

GFeNiVafcc = −12054.355 + 3.27413T ;

GCrNiVafcc = +8030 − 12.8801T ;

GCrFeNfcc = −128930 + 86.49T ;

GFeCrNiVafcc = 16580 − 9.783T ;

GFeNVafcc = −26150;

GCrNVafcc = 20000;

Gbcc = Cr ∗ Va ∗ GCrVabcc + Fe ∗ Va ∗ GFeVabcc + Ni ∗ Va ∗ GNiVabcc+

Cr ∗ n ∗ GCrNbcc + Fe ∗ n ∗ GFeNbcc + Ni ∗ n ∗ GNiNbcc+

Cr ∗ Fe ∗ Va ∗ GCrFeVabcc + Cr ∗ Ni ∗ Va ∗ GCrNiVabcc+

Ni ∗ Fe ∗ Va ∗ GFeNiVabcc + Cr ∗ Fe ∗ n ∗ GCrFeNbcc + Fe ∗ n ∗ Va ∗ GFeNVabcc+

Cr ∗ n ∗ Va ∗ GCrNVabcc; Appendix 149

Gfcc = Cr ∗ Va ∗ GCrVafcc + Fe ∗ Va ∗ GFeVafcc + Ni ∗ Va ∗ GNiVafcc+

Cr ∗ n ∗ GCrNfcc + Fe ∗ n ∗ GFeNfcc + Ni ∗ n ∗ GNiNfcc+

Cr ∗ Fe ∗ Va ∗ GCrFeVafcc + Cr ∗ Ni ∗ Va ∗ GCrNiVafcc+

Ni ∗ Fe ∗ Va ∗ GFeNiVafcc + Cr ∗ Fe ∗ n ∗ GCrFeNfcc + Fe ∗ n ∗ Va ∗ GFeNVafcc+

Cr ∗ n ∗ Va ∗ GCrNVafcc; Appendix 150

Appendix D Microstructural Observation of Carburized 13-8 PH

The TEM and XRD studies on the low-temperature carburized 13-8 PH have

been carried out. The XRD pattern reveals the formation of carbide near the surface.

A TEM sample has been prepared from the carburized 13-8 PH sample. Several

plates can be observed in Figure D.1. DP studies of these plate show these plates are

cementite (θ–Fe3C) carbide, which are formed in a speciﬁc orientation to the matrix.

These results are very similar to our ﬁndings in 15-5 PH alloy after low-temperature

carburization. Since the cubic crystal has a three-fold symmetry in the [111] viewing

direction, cementite can form in three diﬀerent variants which deviates 120◦ from

each other (plus three more variants that are similar to the previous plate but are

60◦ rotated relatively. Therefore, the cementite plates can form in every 60◦ relative

to each other in the viewing direction). This can be observed in Figure D.1 for the

cementite plates with smaller dimensions. Appendix 151

[010]θ//[111]! % (001)θ//(110)! 13-8 PH 450°C Matrix with needles

Bagaryatskii OR

Crystal maker software: θ (cementite): a=5.09, b=6.74, c=4.53 α (martensite): a=2.87

400 nm

Martensite + Cementite Cementite

(110)! (002)θ

(002)θ (112)! (200)θ (200)θ

[010]θ -1 -1 [010]θ 10 nm [111]! 10 nm Pic. Courtesy of Maryam

Figure D.1. Formation of cementite in 13-8 PH alloy after carburizing at 650 K for 72 ks. The carbide formation obeys the Bagaryatskii OR (discussed in section 4.2.2). Appendix 152

Appendix E Microstructural Observation of Nitrided 13-8 PH

Low-temperature nitrided 13-8 PH showed necessarily similar results to 15-5 PH.

The XRD pattern reveals a peak at the left side of the (110)α0 peak (e.g. Figure 2.11).

This peak can be related to both distorted martensite and the newly-formed austen-

ite. TEM results show that there are similar plate-like features inside the sample.

Figure E.1 shows speciﬁcally two plates which cross and shear each other. Figure E.2

shows the bright-ﬁeld and dark-ﬁeld images of the austenite martensite. They reveals

that the austenite is defective and have reﬂections from the HCP crystal.

Figure E.1. Bright-ﬁeld image of the nitrided 13-8 PH at 670 K, which shows several variants of martensitic austenite are formed. Few variants cross and shear each other. Appendix 153

Figure E.2. Bright-field and dark-field images of the nitrided 13-8 PH from the indicated reflections in the [111]γ zone axis. The images in (b) and (c) are resulted from the extra reflections that originate from the HCP crystal. Bibliography 154

Complete References

[1] D.A. Porter and K.E. Easterling. Phase Transformations in Metals and Alloys, Third Edition (Revised Reprint). Taylor & Francis, 1992.

[2] D.B. Lewis, A. Leyland, P.R. Stevenson, J. Cawley, and A. Matthews. Metallur- gical study of low-temperature plasma carbon diﬀusion treatments for stainless steels. Surface and Coatings Technology, 60(1):416 – 423, 1993.

[3] P. Stevenson, A. Leyland, M. Parkin, and A. Matthews. The eﬀect of process parameters on the plasma carbon diﬀusion treatment of stainless steels at low pressure. Surface and Coatings Technology, 63(3):135 – 143, 1994.

[4] M.P. Fewell, J.M. Priest, M.J. Baldwin, G.A. Collins, and K.T. Short. Nitriding at low temperature. Surface and Coatings Technology, 131(13):284 – 290, 2000. Proceedings of the 2nd Asian-European International Conference on Plasma surface Engineering.

[5] P.C. Williams and S.V. Marx. Low temperature case hardening processes, Oc- tober 8 2002. US Patent 6,461,448.

[6] Y. Cao, F. Ernst, and G.M. Michal. Colossal carbon supersaturation in austenitic stainless steels carburized at low temperature. Acta Materialia, 51(14):4171–4181, 2003.

[7] Z. Cheng, C.X. Li, H. Dong, and T. Bell. Low temperature plasma nitrocarburis- ing of {AISI} 316 austenitic stainless steel. Surface and Coatings Technology, 191(23):195 – 200, 2005.

[8] M. Tsujikawa, D. Yoshida, N. Yamauchi, N. Ueda, T. Sone, and S. Tanaka. Surface material design of 316 stainless steel by combination of low temperature carburizing and nitriding. Surface and Coatings Technology, 200(1):507–511, 2005.

[9] T. Christiansen and M. A. J. Somers. Low temperature gaseous nitriding and carburising of stainless steel. Surface Engineering, 21(5-6):445–455, 2005.

[10] S.K. Kim, J.S. Yoo, J.M. Priest, and M.P. Fewell. Surface and Coatings Tech- nology, volume 163–164, chapter Characteristics of martensitic stainless steel nitrided in a low-pressure RF plasma, pages 380–385. Elsevier, Jan 2003. Bibliography 155

[11] D. Manova, G. Thorwarth, S. M¨andl, H. Neumann, B. Stritzker, and B. Rauschenbach. Variable lattice expansion in martensitic stainless steel after nitrogen ion implantation. Nuclear Instruments and Methods in Physics Re- search Section B: Beam Interactions with Materials and Atoms, 242(1):285–288, 2006.

[12] M. Esfandiari and H. Dong. The corrosion and corrosion–wear behaviour of plasma nitrided 17-4 PH precipitation hardening stainless steel. Surface and Coatings Technology, 202(3):466–478, 2007.

[13] T. Burakowski and T. Wierzchon. Surface Engineering of Metals: Principles, Equipment, Technologies. Materials Science & Technology. CRC Press, 1998.

[14] ASM International. Handbook Committee. ASM Handbook. Number v. 5 in ASM Handbook. ASM International, 1994.

[15] J.R. Davis. Surface Engineering for Corrosion and Wear Resistance. ASM In- ternational, 2001.

[16] U.K. Viswanathan, S. Banerjee, and R. Krishnan. Eﬀects of aging on the microstructure of 17-4 PH stainless steel. Materials Science and Engineering: A, 104:181 – 189, 1988.

[17] M. Perez, F. Perrard, V. Massardier, X. Kleber, A. Deschamps, H. De Mone- strol, P. Pareige, and G. Covarel. Low-temperature solubility of copper in iron: experimental study using thermoelectric power, small angle x-ray scattering and tomographic atom probe. Philosophical Magazine, 85(20):2197–2210, 2005.

[18] H.R. Habibi-Bajguirani. The eﬀect of ageing upon the microstructure and mechanical properties of type 15-5 PH stainless steel. Materials Science and En- gineering: A, 338(1):142–159, 2002.

[19] M. Aghaie-Khafri and F. Adhami. Hot deformation of 15-5 PH stainless steel. Materials Science and Engineering: A, 527(4-5):1052 – 1057, 2010.

[20] J.K.L Lai, C.H. Shek, and K.H. Lo. Stainless Steels: An Introduction and Their Recent Developments. Bentham Science Publishers, 2012.

[21] K. Ishida. Calculation of the eﬀect of alloying elements on the ms temperature in steels. Journal of Alloys and Compounds, 220(1):126–131, 1995.

[22] W. Xu, P.E.J. Castillo, and S. van der Zwaag. A combined optimization of alloy composition and aging temperature in designing new uhs precipitation hardenable stainless steels. Computational Materials Science, 45(2):467–473, 2009. Bibliography 156

[23] H.R. Habibi-Bajguirani. The eﬀect of ageing upon the microstructure and mechanical properties of type 15-5 PH stainless steel. Materials Science and En- gineering: A, 338(1):142–159, 2002.

[24] H.R. Habibi-Bajguirani and M.L. Jenkins. High-resolution electron microscopy analysis of the structure of copper precipitates in a martensitic stainless steel of type PH 15-5. Philosophical magazine letters, 73(4):155–162, 1996.

[25] M. Murayama, K. Hono, and Y. Katayama. Microstructural evolution in a 17-4 PH stainless steel after aging at 400 c. Metallurgical and Materials Transactions A, 30(2):345–353, 1999.

[26] J. Wang, H. Zou, C. Li, S. Qiu, and B. Shen. The eﬀect of microstructural evolution on hardening behavior of type 17-4 PH stainless steel in long-term aging at 350◦c. Materials Characterization, 57(4–5):274 – 280, 2006.

[27] F. Danoix, J. Lacaze, A. Gibert, D. Mangelinck, K. Hoummada, and E. Andrieu. Eﬀect of external stress on the fe–cr phase separation in 15-5 PH and fe–15cr– 5ni alloys. Ultramicroscopy, 132:193 – 198, 2013. {IFES} 2012.

[28] H.R. Habibi-Bajguirani, C. Servant, and G. Cizeron. Tem investigation of precipitation phenomena occurring in PH 15-5 alloy. Acta metallurgica et materialia, 41(5):1613–1623, 1993.

[29] E.J. Mittemeijer and M.A.J. Somers. Thermochemical Surface Engineering of Steels: Improving Materials Performance. Woodhead Publishing Series in Met- als and Surface Engineering. Elsevier Science, 2014.

[30] P.C. Williams S.R. Collins, F. Ernst S.V. Marx, A. Heuer, and H. Kahn. Low- Temperature Carburization of Austenitic Stainless Steels, pages 451–460. ASM International, 2014.

[31] M.A.J. Somers and T. L. Christiansen. Low-Temperature Surface Hardening of Stainless Steel, pages 439–450. ASM International, 2014.

[32] Chihoon Lee. Phase transformations accompanying low-temperature carburization of martensitic stainless steels under paraequilibrium conditions. Master’s thesis, Case Western Reserve University, 2012.

[33] A. Cohen, M. Boas, and A. Rosen. The inﬂuence of ion nitriding parameters on the hardness layer of 15-5 PH stainless steel. Thin Solid Films, 141(1):53–58, 1986. Bibliography 157

[34] F.G. Yost, S.T. Picraux, D.M. Follstaedt, L.E. Pope, and J.A. Knapp. The eﬀects of n+ implantation on the wear and friction of type 304 and 15-5 PH stainless steels. Thin Solid Films, 107(3):287 – 295, 1983.

[35] H. Dong, M. Esfandiari, and X.Y. Li. On the microstructure and phase iden- tiﬁcation of plasma nitrided 17-4 PH precipitation hardening stainless steel. Surface and Coatings Technology, 202(13):2969 – 2975, 2008.

[36] P. Kochmanski and J. Nowacki. Inﬂuence of initial heat treatment of 17-4 PH stainless steel on gas nitriding kinetics. Surface and Coatings Technology, 202(19):4834–4838, Jun 2008.

[37] A. Leyland, D.B. Lewis, P.R. Stevensom, and A. Matthews. Low temperature plasma diﬀusion treatment of stainless steels for improved wear resistance. Sur- face and Coatings Technology, 62(1-3):608 – 617, 1993.

[38] Y. Sun and T. Bell. Low temperature plasma nitriding characteristics of precipitation hardening stainless steel. Surface Engineering, 19(5):331–336, 2003.

[39] E.J. Mittemeijer. Fundamentals of Materials Science: The Microstructure– Property Relationship Using Metals as Model Systems. Springer, 2010.

[40] L. Cheng and E.J. Mittemeijer. The tempering of iron-nitrogen martensite; dilatometric and calorimetric analysis. Metallurgical Transactions A, 21(1):13– 26, 1990.

[41] K. Marchev, C.V. Cooper, and B.C. Giessen. Observation of a compound layer with very low friction coeﬃcient in ion-nitrided martensitic 410 stainless steel. Surface and Coatings Technology, 99(3):229 – 233, 1998.

[42] S. M¨andland B. Rauschenbach. Comparison of expanded austenite and expanded martensite formed after nitrogen PIII. Surface and Coatings Technology, 186(1):277–281, 2004.

[43] C.X. Li and T. Bell. Corrosion properties of plasma nitrided AISI 410 martensitic stainless steel in 3.5% NaCl and 1% HCl aqueous solutions. Corrosion Science, 48(8):2036–2049, 2006.

[44] Helmut Fll. Octahedral sites, 2016. [Online; accessed 10-October-2016] http:// www.tf.uni-kiel.de/matwis/amat/def_en/kap_1/illustr/t1_3_3.html.

[45] A.H. Heuer, H. Kahn, L.J. O’Donnell, F. Ernst, G.M. Michal, R.J. Rayne, F.J. Martin, and P.M. Natishan. Carburization-enhanced passivity of PH13-8 Mo: A precipitation-hardened martensitic stainless steel. Electrochemical and Solid-State Letters, 13(12):C37–C39, 2010. Bibliography 158

[46] G.M. Michal, X. Gu, W.D. Jennings, H. Kahn, F. Ernst, and A.H. Heuer. Parae- quilibrium carburization of duplex and ferritic stainless steels. Metallurgical and Materials Transactions A, 40(8):1781–1790, 2009.

[47] D. Wang, F. Ernst, H. Kahn, and A.H. Heuer. Cellular precipitation at a 17- 7 PH stainless steel interphase interface during low-temperature nitridation. Metallurgical and Materials Transactions A, 45(8):3578–3585, 2014.

[48] D. Wang, C.W. Chen, J.C. Dalton, F. Yang, R. Sharghi-Moshtaghin, H. Kahn, F. Ernst, R.E.A. Williams, D.W. McComb, and A.H. Heuer. “colossal” interstitial supersaturation in delta ferrite in stainless steels i. low-temperature carburization. Acta Materialia, 86:193 – 207, 2015.

[49] E. Pereloma and D.V. Edmonds. Phase Transformations in Steels: Fundamen- tals and Diﬀusion-Controlled Transformations. Woodhead Publishing Series in Metals and Surface Engineering. Elsevier Science, 2012.

[50] J.W. Christian. The Theory of Transformations in Metals and Alloys. Perga- mon, Oxford, third edition, 2002.

[51] A.B. Greninger and A.R. Troiano. The mechanism of martensite formation. Trans. AIME, 185(9):590–598, 1949.

[52] E.C. Bain and N.Y. Dunkirk. The nature of martensite. trans. AIME, 70(1):25– 47, 1924.

[53] M.A. Jaswon and J.A. Wheeler. Atomic displacements in the austenite– martensite transformation. Acta Crystallographica, 1(4):216–224, 1948.

[54] M.S. Wechsler, Lieberman D. S., and T. A. Read. On the theory of the formation of martensite. Transactions AIME, Journal of Metals, pages 1503–1515, 1953.

[55] H.K.D.H. Bhadeshia. Martensite in Steels, 2002 (accessed June 12, 2016).

[56] H.K.D.H. Bhadeshia. Diﬀusional and displacive transformations. Scripta metallurgica, 21(8):1017–1022, 1987.

[57] T. Moritani, N. Miyajima, T. Furuhara, and T. Maki. Comparison of interphase boundary structure between bainite and martensite in steel. Scripta materialia, 47(3):193–199, 2002.

[58] G. Kurdjumow and G. Sachs. Uber¨ den mechanismus der stahlh¨artung. Zeitschrift f¨urPhysik, 64(5):325–343, 1930. Bibliography 159

[59] Z. Nishiyama. X-ray investigation of the mechanism of the transformation from face centered cubic lattice to body centered cubic. Sci. Rep. Tohoku Imp. Univ, 23:637, 1934.

[60] G. Wassermann. Ueber den Mechanismus der α − γ-Umwandlung des Eisens. Verlag Stahleisen, 1935.

[61] J.P. Hirth. Dislocations, steps and disconnections at interfaces. Journal of Physics and Chemistry of Solids, 55(10):985–989, 1994.

[62] J.P. Hirth and R.C. Pond. Steps, dislocations and disconnections as interface defects relating to structure and phase transformations. Acta Materialia, 44(12):4749 – 4763, 1996.

[63] G.J. Mahon, J.M. Howe, and S. Mahajan. HRTEM study of the {252} γ austenite–martensite interface in an Fe—8Cr–1C alloy. Philosophical magazine letters, 59(6):273–279, 1989.

[64] W.F. Holcomb. Carburization of type 304 stainless steel in liquid sodium. Nu- clear Engineering and Design, 6(3):264 – 272, 1967.

[65] F.B. Litton and A.E. Morris. Carburization of type 316l stainless steel in static sodium. Journal of the Less Common Metals, 22(1):71 – 82, 1970.

[66] G.A. Collins, R. Hutchings, K.T. Short, J. Tendys, X. Li, and M. Samandi. Nitriding of austenitic stainless steel by plasma immersion ion implantation. Surface and Coatings Technology, 74:417 – 424, 1995.

[67] B.D. Cullity and S.R. Stock. Elements of X-ray Diﬀraction. Pearson education. Prentice Hall, 2001.

[68] J.H. Hubbell and S.M. Seltzer. Tables of X-ray mass attenuation coeﬃcients and mass energy-absorption coeﬃcients 1 kev to 20 MeV for elements Z= 1 to 92 and 48 additional substances of dosimetric interest. Technical report, National Inst. of Standards and Technology-PL, Gaithersburg, MD (United States). Ionizing Radiation Div., 1995.

[69] N. Mortazavi, M. Esmaily, and M. Halvarsson. The capability of transmission kikuchi diﬀraction technique for characterizing nano-grained oxide scales formed on a fecral stainless steel. Materials Letters, 147:42 – 45, 2015.

[70] D.J. Larson, T.J. Prosa, R.M. Ulﬁg, B.P. Geiser, T.F. Kelly, and C.J. Humphreys. Local Electrode Atom Probe Tomography: A User’s Guide. SpringerLink : B¨ucher. Springer New York, 2013. Bibliography 160

[71] M.K. Miller and R.G. Forbes. Atom probe tomography. Materials Characteri- zation, 60(6):461 – 469, 2009.

[72] University of Oxford Atom Probe Group. Atom probe tomography, 2016. [On- line; accessed 5-July-2016].

[73] Schmolz & Bickenbach. Making stainless more machinable, 2010. [Online; accessed 22-November-2016] www.goo.gl/IGsKKQ.

[74] The Specialty Steel Industry of North America. Role of alloying elements in stainless steel, 2012. [Online; accessed 22-November-2016] http://www.ssina. com/overview/alloyelements_intro.html.

[75] V. Kuzucu, M. Aksoy, M.H. Korkut, and M.M. Yildirim. The eﬀect of niobium on the microstructure of ferritic stainless steel. Materials Science and Engineer- ing: A, 230(1):75 – 80, 1997.

[76] C.J. Scheuer, R.P. Cardoso, R. Pereira, M. Mafra, and S.F. Brunatto. Low temperature plasma carburizing of martensitic stainless steel. Materials Science and Engineering: A, 539:369 – 372, 2012.

[77] H. Kahn, A.H. Heuer, and F. Ernst. Polarization tests on precipitation hardening stainless steel after low-temperature carburization. Unpublished data.

[78] B.P.J. Sandvik and C.M. Wayman. Characteristics of lath martensite: Part I. crystallographic and substructural features. Metallurgical Transactions A, 14(4):809–822, 1983.

[79] S. Morito, H. Tanaka, R. Konishi, T. Furuhara, and T. Maki. The morphology and crystallography of lath martensite in Fe-C alloys. Acta Materialia, 51(6):1789 – 1799, 2003.

[80] H. Kitahara, R. Ueji, N. Tsuji, and Y. Minamino. Crystallographic features of lath martensite in low-carbon steel. Acta Materialia, 54(5):1279 – 1288, 2006.

[81] F. Ernst, Y. Cao, and G.M. Michal. Carbides in low-temperature-carburized stainless steels. Acta Materialia, 52(6):1469 – 1477, 2004.

[82] F. Ernst, Y. Cao, G.M. Michal, and A.H. Heuer. Carbide precipitation in austenitic stainless steel carburized at low temperature. Acta Materialia, 55(6):1895 – 1906, 2007.

[83] K.W. Andrews. The structure of cementite and its relation to ferrite. Acta Metallurgica, 11(8):939 – 946, 1963. Bibliography 161

[84] Y.A. Bagaryatskii. The probable mechanism of the martensite decomposition. Dokl Akaa1 Nauk SSSR, 71:1161–1164, 1950.

[85] Dandan Wu. Low-Temperature Gas-Phase Nitriding and Nitrocarburizing of 316L Austenitic Stainless Steel. PhD thesis, Case Western Reserve University, 2013.

[86] D. Wu, H. Kahn, G.M. Michal, F. Ernst, and A.H. Heuer. Ferromagnetism in interstitially hardened austenitic stainless steel induced by low-temperature gas-phase nitriding. Scripta Materialia, 65(12):1089 – 1092, 2011.

[87] John C Dalton. Surface Hardening of Duplex Stainless Steel 2205. PhD thesis, Case Western Reserve University, 2015.

[88] H. Dong. S-phase surface engineering of Fe-Cr, Co-Cr and Ni-Cr alloys. Inter- national Materials Reviews, 55(2):65–98, 2010.

[89] Danqi Wang. Low-Temperature Gas-Phase Carburization and Nitridation of 17- 7 PH Stainless Steel. PhD thesis, Case Western Reserve University, 2014.

[90] D. Viladot, M. Véron,M. Gemmi, F. Peiró,J. Portillo, S. Estradé,J. Men- doza, N. Llorca-Isern, and S. Nicolopoulos. Orientation and phase mapping in the transmission electron microscope using precession-assisted diffraction spot recognition: state-of-the-art results. Journal of microscopy, 252(1):23–34, 2013.

[91] Y. Higo, F. Lecroisey, and T. Mori. Relation between applied stress and orientation relationship of α’ martensite in stainless steel single crystals. Acta Metallurgica, 22(3):313 – 323, 1974.

[92] X.M. Zhang, E. Gautier, and A. Simon. Orientation relationships of deformation-induced martensite in Fe-Ni-C alloys. Acta Metallurgica, 37(2):487 – 497, 1989.

[93] P.M. Kelly, A. Jostsons, and R.G. Blake. The orientation relationship between lath martensite and austenite in low carbon, low alloy steels. Acta Metallurgica et Materialia, 38(6):1075 – 1081, 1990.

[94] H. Sato and S. Zaeﬀerer. A study on the formation mechanisms of butterﬂy- type martensite in Fe-30% Ni alloy using EBSD-based orientation microscopy. Acta Materialia, 57(6):1931 – 1937, 2009.

[95] A. Sauveur and C.H. Chih-Hung. The gamma-alpha transformation in pure iron. Trans. ASME, 84:350–365, 1929. Bibliography 162

[96] R.F. Mehl and D.W. Smith. Studies upon the widmanstatten structure, vthe gamma-alpha transformation in pure iron. Trans. AIME, 113:203–210, 1934.

[97] A.R. Marder and G. Krauss. Formation of low-carbon martensite in Fe-C alloys. ASM Transactions Quarterly, 62:957–964, 1969.

[98] K. Wakasa and C.M. Wayman. The morphology and crystallography of ferrous lath martensite. studies of Fe-20%Ni-5%Mn-II. Transmission electron microscopy. Acta Metallurgica, 29(6):991 – 1011, 1981.

[99] S. Morito, X. Huang, T. Furuhara, T. Maki, and N. Hansen. The morphology and crystallography of lath martensite in alloy steels. Acta Materialia, 54(19):5323 – 5331, 2006.

[100] D.S. Sarma, J.A. Whiteman, and J.H. Woodhead. Habit plane and morphology of lath martensites. Metal Science, 10(11):391–395, 1976.

[101] J.S. Bowles and J.K. Mackenzie. The crystallography of martensite transformations i. Acta Metallurgica, 2(1):129 – 137, 1954.

[102] H.K.D.H. Bhadeshia. Steels, 2014.

[103] P.B. Hirsch, A. Howie, R.B. Nicholson, D.W. Pashley, and M.J. Whelan. Elec- tron microscopy of thin crystals. Butterworths, 1965.

[104] C.N. Hsiao, C.S. Chiou, and J.R. Yang. Aging reactions in a 17-4 PH stainless steel. Materials Chemistry and Physics, 74(2):134 – 142, 2002.

[105] S.R. Goodman, S.S. Brenner, and J.R. Low. An ﬁm-atom probe study of the precipitation of copper from lron-1.4 at. pct copper. part ii: Atom probe analyses. Metallurgical Transactions, 4(10):2371–2378, 1973.

[106] P.A. Lindqvist and B. Uhrenius. On the fe-cu phase diagram. Calphad, 4(3):193 – 200, 1980.

[107] G.M. Michal, F. Ernst, and A.H. Heuer. Carbon paraequilibrium in austenitic stainless steel. Metall. Mater. Trans. A, 37(6):1819–1824, 2006.

[108] J.M. Howe and G.J. Mahon. High-resolution transmission electron microscopy of precipitate plate growth by diﬀusional and displacive transformation mechanisms. Ultramicroscopy, 30(1):132 – 142, 1989.

[109] U. Dahmen. Surface relief and the mechanism of a phase transformation. Scripta Metallurgica, 21(8):1029 – 1034, 1987. Bibliography 163

[110] J.P. Hirth and R.C. Pond. Compatibility and accommodation in displacive phase transformations. Progress in Materials Science, 56(6):586 – 636, 2011. Festschrift Vaclav Vitek.

[111] R. Bullough and B.A. Bilby. Continuous distributions of dislocations: Surface dislocations and the crystallography of martensitic transformations. Proceedings of the Physical Society. Section B, 69(12):1276, 1956.

[112] D.P. Dunne and C.M. Wayman. The crystallography of ferrous martensites. Metallurgical Transactions, 2(9):2327–2341, 1971.

[113] A.G. Crocker and B.A. Bilby. The crystallography of the martensite reaction in steel. Acta Metallurgica, 9(7):678 – 688, 1961.

[114] B.P.J. Sandvik and C.M. Wayman. Characteristics of lath martensite: Part iii. some theoretical considerations. Metallurgical Transactions A, 14(4):835–844, 1983.

[115] Z. Nishiyama. Martensitic Transformation. Academic Press, 1978.

[116] C.M. Wayman. Introduction to the crystallography of martensitic transformations. Macmillan series in materials science. Macmillan, 1964.

[117] C.M. Wayman. Crystallographic theories of martensitic transformations. Jour- nal of the Less Common Metals, 28(1):97 – 105, 1972.

[118] Qiong Li. The eﬀect of annealing time and temperature on carburized 316 fer- rules. unpublished thesis, 2016.

[119] A. Saker, C. Leroy, H. Michel, and C. Frantz. Second international conference on plasma surface engineering properties of sputtered stainless steel-nitrogen coatings and structural analogy with low temperature plasma nitrided layers of austenitic steels. Materials Science and Engineering: A, 140:702 – 708, 1991.

[120] D. Wu, H. Kahn, J.C. Dalton, G.M. Michal, F. Ernst, and A.H. Heuer. Orienta- tion dependence of nitrogen supersaturation in austenitic stainless steel during low-temperature gas-phase nitriding. Acta Materialia, 79:339 – 350, 2014.

[121] D.B. Williams and C.B. Carter. Transmission Electron Microscopy: A Textbook for Materials Science. Number v. 2 in Cambridge library collection. Springer, 2009.

[122] K.H. Lo, C.H. Shek, and J.K.L. Lai. Recent developments in stainless steels. Materials Science and Engineering: R: Reports, 65(4-6):39 – 104, 2009. Bibliography 164

[123] R.P. Reed. Nitrogen in austenitic stainless steels. Journal of Materials, 41(3):16– 21, 1989.

[124] J.F. Breedis and L. Kaufman. Formation of Hcp and Bcc phases in austenitic iron alloys. Metallurgical and Materials Transactions B, 2(11):3249–3249, 1971.

[125] K. Tomimura, S. Takaki, and Y. Tokunaga. Reversion mechanism from deformation induced martensite to austenite in metastable austenitic stainless steels. ISIJ International, 31(12):1431–1437, 1991.

[126] John C Dalton. Thermodynamics of paraequilibrium carburization and nitridation of stainless steels. Master’s thesis, Case Western Reserve University, 2014.

[127] K. Frisk. A thermodynamic evaluation of the Cr-N, Fe-N, Mo-N and Cr-Mo-N systems. Calphad, 15(1):79–106, 1991.

[128] M. Sumita, T. Hanawa, and S.H. Teoh. Development of nitrogen-containing nickel-free austenitic stainless steels for metallic biomaterials—review. Materials Science and Engineering: C, 24(6-8):753 – 760, 2004. 2nd International BMC- NIMS Symposium on Biomaterials and Bionanotechnology at the Tsukuba In- ternational Congress Center, Epochal, Japan.

[129] A.J. Bogers and W.G. Burgers. Partial dislocations on the 110 planes in the B.C.C. lattice and the transition of the F.C.C. into the B.C.C. lattice. Acta Metallurgica, 12(2):255 – 261, 1964.

[130] W. Luo, D. Roundy, M.L. Cohen, and J.W. Morris. Ideal strength of bcc molybdenum and niobium. Phys. Rev. B, 66:094110, Sep 2002.

[131] G.B. Olson. Fine structure of interphase boundaries. Acta Metallurgica, 29(8):1475 – 1484, 1981.

[132] B.P.J. Sandvik and C.M. Wayman. Characteristics of lath martensite: Part ii. the martensite-austenite interface. Metallurgical Transactions A, 14(4):823–834, 1983.

[133] R.C. Pond, S. Celotto, and J.P. Hirth. A comparison of the phenomenological theory of martensitic transformations with a model based on interfacial defects. Acta Materialia, 51(18):5385 – 5398, 2003.

[134] L.C. Zhang, T. Zhou, M. Aindow, S.P. Alpay, M.J. Blackburn, and M.H. Wu. Nucleation of stress-induced martensites in a ti/mo-based alloy. Journal of Ma- terials Science, 40(11):2833–2836, 2005. Bibliography 165

[135] J.M. Howe, R.C. Pond, and J.P. Hirth. The role of disconnections in phase transformations. Progress in Materials Science, 54(6):792 – 838, 2009. A collection of invited lectures at the MRS Spring Meeting 2008.

[136] E.J. Mittemeijer. Fundamentals of materials science. Fundamentals of Materi- als Science by Eric J. Mittemeijer. Berlin: Springer, 2011. ISBN: 978-3-642- 10499-2, 1, 2011.

[137] Y. Imai, M. Izumiyama, and M. Tsuchiya. Thermodynamic study on the transformation of austenite into martensite in iron-high nitrogen and iron-carbon binary system. Science reports of the Research Institutes, Tohoku University. Ser. A, Physics, chemistry and metallurgy, 17:173–192, 1965.

[138] K.H. Jack. New interstitial alloy phases relating to the surface hardening of steel. Aust. Inst. Metall. Trans, 3:53–58, 1950.

[139] K.H. Jack. The iron-nitrogen system: The preparation and the crystal structures of nitrogen-austenite (γ) and nitrogen-martensite (α0). Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 208(1093):200–215, 1951.

[140] T. Bell. Martensite transformation start temperature in iron-nitrogen alloys. Journal of the Iron and Steel Institute, 206(10), 1968.

[141] H.A. Wriedt, N.A. Gokcen, and R.H. Nafziger. The Fe-N (iron-nitrogen) system. Bulletin of Alloy Phase Diagrams, 8(4):355–377, 1987.

[142] C.E. Pinedo and Waldemar A. Monteiro. On the kinetics of plasma nitriding a martensitic stainless steel type aisi 420. Surface and Coatings Technology, 179(2):119–123, 2004.

[143] F. Ernst. Background of SAM concentration-depth proﬁles. Unpublished data.

[144] J. Greer. Boltzmann-matano analysis, 2016. [Online; accessed 5-October-2016] http://www.jrgreer.caltech.edu/content/teaching/MS133Files/Notes/ Lect3MS133JRG.pdf.