Surface Hardening of Titanium Alloys By

Home , Nitriding, Titanium nitride

SURFACE HARDENING OF TITANIUM ALLOYS BY

GAS PHASE NITRIDATION UNDER KINETIC CONTROL

LIZHI LIU

Submitted in partial fulfillment of the requirements

For the degree of Doctor of Philosophy

Dissertation Advisor: Prof. Arthur H. Heuer

Co-Advisor: Prof. Frank Ernst

Department of Materials Science and Engineering

CASE WESTERN RESERVE UNIVERSITY

January, 2005

CASE WESTERN RESERVE UNIVERSITY

SCHOOL OF GRADUATE STUDIES

We hereby approve the dissertation of

Lizhi Liu candidate for the Ph.D. degree *.

(signed) Arthur Heuer

(chair of the committee)

Frank Ernst

Gary Michal

Roberto Ballarini

John Lewandowski

Harold Kahn

(date) 6 August, 2004

*We also certify that written approval has been obtained for any proprietary material contained therein.

I grant to Case Western Reserve University the right to use this work, irrespective of any copyright, for the University’s own purpose without cost to the University or to its students, agents and employees. I further agree that the University may reproduce and provide single copies of the work, in any format other than in or from microforms, to the public for the cost of reproduction.

Lizhi Liu

(sign)

Dedicated to my wife Yin Tang

Table of Contents

Table of Contents...... 1

List of Tables ...... 5

List of Figures...... 6

Acknowledgments...... 13

Abstract...... 14

Chapter 1 INTRODUCTION ...... 16

1.1 History and Current Applications of Titanium ...... 16

1.2 Surface Hardening Methods ...... 17

1.3 The Goal...... 18

Works Cited ...... 20

Chapter 2 LITERATURE REVIEW ...... 22

2.1 Titanium and Titanium Alloys...... 22

2.2 Basic Properties of Titanium Alloys...... 31

2.3 Current Surface Hardening Methods ...... 34

2.3.1 Physical vapor deposition and chemical vapor deposition ...... 36

2.3.2 Ion implantation techniques...... 37

2.3.3 Laser nitriding...... 39

2.3.4 Plasma nitriding...... 41

2.3.5 Gas nitriding...... 42

2.4 Gas Adsorption Kinetics...... 45

2.4.1 Physisorption and chemisorption...... 45 1

2.4.2 Nitrogen adsorption on metal surface...... 46

2.4.3 The interaction of nitrogen with titanium ...... 47

2.5 Diffusion Model of Nitridation...... 51

2.5.1 Solution of the diffusion equation...... 51

2.5.2 Diffusion in titanium...... 53

2.5.3 Diffusivity of nitrogen in titanium...... 54

2.6 Kinetic Control of Gas Nitriding ...... 59

Work Cited...... 62

Chapter 3 THERMODYNAMIC AND KINETIC CALCULATIONS ...... 69

3.1 Equilibrium Nitrogen Pressure...... 69

3.2 Gas Concentration...... 79

3.3 Kinetic Equilibrium Nitrogen Partial Pressure ...... 80

3.4 Nitrogen Pressure for Si3N4/Si Powder Pack...... 87

3.5 Sticking Coefficient...... 91

3.6 Nitrogen pressure for CrN/Cr powder packs ...... 93

3.7 Nitrogen pressure for Cr2N/Cr powder packs...... 96

3.8 Summary...... 99

Work Cited...... 99

Chapter 4 EXPERIMENTAL PROCEDURES...... 101

4.1 Selection of Materials ...... 101

4.2 Heat Treatment...... 103

4.3 Characterization Techniques...... 107

4.3.1 Light optical microscopy ...... 107

4.3.2 Microhardness measurement ...... 107

4.3.3 XRD Analysis...... 111

4.3.4 XPS and AES...... 116

4.3.5 SEM ...... 117

Work Cited...... 119

Chapter 5 CrN/Cr2N/Cr POWDER PACK TREATMENT ...... 120

5.1 CrN/Cr Powder Pack Treatment ...... 120

5.2 Cr2N/Cr Treatment...... 133

5.3 CrN/Cr and Cr2N/Cr Powder Packs...... 141

5.4 Treatment at Other Conditions...... 144

5.5 Goal-Oriented Nitriding Practice...... 149

5.6 Discussion...... 157

5.6.1 Nitrogen pressure for CrN/Cr and Cr2N/Cr powder pack...... 157

5.6.2 Surface adsorption kinetics...... 159

5.6.3 Nitridation kinetics...... 162

5.6.4 Microstructural analysis...... 164

Work Cited...... 170

Chapter 6 MECHANICAL PROPERTIES ...... 172

6.1 Tensile Testing...... 172

6.2 Microhardness Profile...... 182

6.3 Discussion...... 184

Chapter 7 CONCLUSION AND FUTURE WORK ...... 185

APPENDIX A. TiN/Ti POWDER PACK TREATMENT...... 188

A.1 Surface Properties of CP Titanium after Heat Treatment...... 188

A.1.1 Heat Treatment at 860 °C ...... 190

A.1.2 Heat Treatment at 1150 °C ...... 195

A.2 Surface Properties of Ti-6Al-4V after Heat Treatment ...... 199

A.3 Microhardness Measurement...... 204

A.4 Discussion...... 207

A.5 Summary...... 209

Work cited...... 210

APPENDIX B. Si3N4/Si POWDER PACK TREATMENT...... 211

B.1 Si3N4/Si Powder Pack Treatment without getter ...... 211

B.2 Si3N4/Si Powder Pack Treatment with Getter...... 217

B.3 Discussion...... 220

B.4 Summary...... 222

APPENDIX C. Non-linear Viscoelastic Properties of Cucumaria frondosa

Dermis...... 223

Bibliography ...... 261

List of Tables

Table 2.1 Some of the most important commercial titanium alloys in each of these

three groups: α, β, and α+β alloys (Donachie, 2000)...... 30

Table 2.2 Physical data for titanium alloys and alloys based on iron, nickel and

aluminum (Boyer et al., 1994)...... 33

Table 3.1 G-HSER data for selected phases for nitrogen and titanium...... 75

Table 3.2 Effect of Ti2N on the solubility of nitrogen in the α-Ti...... 75

Table 3.3 Calculated nitrogen partial pressure for CrN/Cr powder pack ...... 95

Table 3.4 Calculated nitrogen partial pressure for Cr2N/Cr powder pack at different

temperatures...... 98

Table 4.1 Chemical composition for commercial pure titanium and Ti-6Al-4V alloy

(in weight percent)...... 102

Table 4.2 Metal and metal nitride powders used in this work ...... 102

Table 5.1 Summary of heat treatment, the phase development and the

microhardness (Vickers) measured with a 50 g load...... 124

Table 6.1 Mechanical properties of Ti-6Al-4V tensile bar...... 175

List of Figures

Figure 2-1 The unit cell of hexagonal α phase and cubic β phase. Shaded planes are

the mostly close-packed planes...... 26

Figure 2-2 Schematic drawing shows the effect of alloying element classified as (a)

α stabilizer, (b) β stabilizer, and (c) neutral...... 27

Figure 2-3 Pseudo-binary section through a β isomorphous phase diagram shows the

classification of α, β, and α+β alloys...... 28

Figure 2-4 Isothermal sections through the Ti-rich corner of the Ti-Al-V system at

1000°C, 900°C and 800°C. the black dot marks the composition of Ti-6Al-4V.

(Collings, 1994) ...... 29

Figure 2-5 Schematic drawing of laser nitriding ...... 40

Figure 2-6 Gas nitriding setup...... 44

Figure 2-7 Combination of chemisorption and physisorption potential (ϕ) diagram as

a function of distance z of adsorbed nitrogen atom or molecule on a metal surface; z0

is the equilibrium distance for chemisorption, QDiss is the dissociation energy of N2

in the gas phase, Eact is the activation energy for adsorption of N2, Edes is the

activation energy for desorption of 2N, EB is the binding energy in the

chemisorption state 2M-N. (Luth, 1993) ...... 48

Figure 2-8 The four chemisorbed states of molecular N2 are classified in Greek

letters (α’, α, δ and γ) (Mortensen et al., 1999)...... 49

Figure 2-9 The two interstitial sites for adsorbed nitrogen atoms in α titanium (HCP

structure) (Frickel et al., 1997)...... 50

Figure 2-10 Arrhenius diagram of various alloying elements in titanium as well as

titanium self-diffusion (Lutjering & Williams, 2003) ...... 57

Figure 2-11 The Diffusivities of nitrogen in pure titanium ...... 58

Figure 3-1 The Ti-N phase diagram (Wriedt & Murray, 1987)...... 76

Figure 3-2 Thermodynamic calculation for the relationship between free energy

change ∆G and conmposition xN...... 77

Figure 3-3 Supersaturation and equilibrium nitrogen partial pressure ...... 78

Figure 3-4 The model to simulate the diffusion profile...... 84

Figure 3-5 Nitrogen diffusion profile at different pressure ...... 85

Figure 3-6 Nitrogen diffusion profile for different treatment time...... 86

Figure 3-7 Equilibrium nitrogen pressure generated by several powder packs...... 90

Figure 4-1 Heat treatment setup ...... 105

Figure 4-2 Heating protocol...... 106

Figure 4-3 Schematic illumination of Vickers pyramid diamond indenter indentation;

d1 and d2 are diagonal lengths and h is the penetration depth...... 108

Figure 4-4 SEM image of the Berkovich diamond tip ...... 110

Figure 4-5 A typical load/depth curve recorded during nanoindentation...... 110

Figure 4-6 Plane-stress elastic model. dφψ marks the plane stress at a free surface

showing the change in lattice spacing from dφ0 with tilt ψ for a uniaxial stress σφ

parallel to one edge. (Prevey, 1986) ...... 115

Figure 5-1 XRD patterns for Ti-6Al-4V samples treated at 860°C with CrN/Cr

powder pack at various temperatures for 24 h...... 125

Figure 5-2 XRD patterns for the Ti-6Al-4V samples treated at 860°C with CrN/Cr

powder pack at 750°C for various times...... 126

Figure 5-3 XRD patterns for the Ti-6Al-4V samples after a longer-time treatment

(860°C, 72h) and the formation of nitrides...... 127

Figure 5-4 XRD patterns for the Ti-6Al-4V samples treated at 860°C with CrN/Cr

powder pack at different temperatures for various times which have all formed

nitride (Ti2N) on the surface...... 128

Figure 5-5 SEM image of the titanium treated at 860°C for 120 h with CrN/Cr

powder pack at 750°C...... 129

Figure 5-6 SEM image of the titanium treated at 860°C for 240 h with CrN/Cr

powder pack at 750°C...... 130

Figure 5-7 SEM image of the titanium treated at 860°C for 72 h with CrN/Cr powder

pack at 775°C...... 131

Figure 5-8 SEM images of the titanium treated at 860°C for 24 h with CrN/Cr

powder pack at 800°C. (Top: SE image; bottom: BSE image.) ...... 132

Figure 5-9 XRD pattern of titanium treated at 860°C for 72 h with Cr2N/Cr powder

pack at 750°C...... 136

Figure 5-10 SEM image of the cross-section from the sample treated at 860°C for 72 h

with Cr2N/Cr powder pack at 750°C ...... 137

Figure 5-11 The glancing incidence XRD (GIXRD) results for the titanium treated at

860°C for 72 h with Cr2N/Cr powder pack at 700, 650, and 625°C, and the

comparison to the annealed sample (from bottom to top)...... 138

Figure 5-12 SEM images of cross-section from the samples treated at 860°C for 72 h

with Cr2N/Cr powder pack at (a) 700°C, (b) 650°C and (c) 625°C...... 139

Figure 5-13 XRD pattern for the CrN/Cr and Cr2N/Cr powder packs before heat

treatment...... 142

Figure 5-14 The XRD patterns of CrN/Cr and Cr2N/Cr powder packs after heat

treatment...... 143

Figure 5-15 GIXRD patterns of Ti-6Al-4V sample has been treated at 860°C for 24 h

with CrN/Cr powder pack at 800°C under 105 Pa (solid line) and 1 Pa (dotted line)

argon pressure respectively...... 146

Figure 5-16 XRD patterns of Ti-6Al-4V sample treated at 860°C for 24 h with

5 Cr2N/Cr powder pack at 700°C under 1 Pa and 10 Pa argon pressure, and the

comparison to the annealed sample (from top to bottom) ...... 147

Figure 5-17 XRD patterns of Ti6-Al-4V samples at 950, 860 and 800°C (from up to

bottom), with Cr2N/Cr powder pack at 625°C under vacuum, and the comparison to

the annealed sample ...... 148

Figure 5-18 GIXRD pattern of Ti-6Al-4V tensile bar treated at 860°C with Cr2N/Cr

powder pack at 650°C for 72 h ...... 152

Figure 5-19 Microhardness for the nitrided sample (without nitride on the surface) as

in Figure 5-16, and the comparison to that for the annealed sample...... 153

Figure 5-20 Heating treatment practice with 4 segments: gettering, high temperature,

reduced temperature, and low temperature treatment...... 154

Figure 5-21 XRD patterns for two samples treated with new heat profile shown in

Figure 5-20. The temperatures shown in the figure are for Cr2N/Cr powder packs

heat-treatment protocol...... 155

Figure 5-22 Microhardness for the sample treated with Cr2N/Cr powder pack at 675,

625 and 600°C protocol, and the comparison to the annealed sample...... 156

Figure 5-23 Cross-section image of annealed Ti-6Al-4V alloy. Bright area is β phase,

dark, equiaxial grains are α phase...... 168

Figure 5-24 Cross-section image of nitrided Ti-6Al-4V alloy away from surface,

which shows an α + β two phase structure...... 169

Figure 6-1 Engineering stress-strain curve (a) and stress curve as function of time (b)

for annealed and nitrided samples...... 174

Figure 6-2 Plan view surface (a) and fracture surface (b) of annealed sample after

deformation...... 176

Figure 6-3 Plan view surface (a) and cross-section (b) of nitrided sample after

deformation. This nitridation formed a thick nitride layer on the surface...... 177

Figure 6-4 Fracture surface of nitrided sample with nitrides layer shows ductile

feature in the center but brittle feature near the surface...... 178

Figure 6-5 Plan view surface of nitrided sample after deformation...... 179

Figure 6-6 SEM image shows plan view surface of nitrided sample after deformation,

slip bands can be observed and there is no crack in this area...... 180

Figure 6-7 Fracture surface of nitrided sample without nitride layer...... 181

Figure 6-8 Microhardness depth profile for nitrided titanium without nitride ...... 183

Figure A-1 Surface morphology of grade 4 titanium before heat treatment and after

treatment at 860°C for 48 h in vacuum...... 189

Figure A-2 XRD patterns for TiN/Ti powder pack before and after heat treatment 192

Figure A-3 XRD patterns for Grade 4 titanium before and after heat treatment...... 193

Figure A-4 SEM of cross-section for Ti4 treated with TiN/Ti at 860°C for 48 h..... 194

Figure A-5 Photograph of CP titanium (with a flat on the circle) and Ti-6Al-4V

sample treated with TiN/Ti powder pack at 1150°C for 1hr ...... 196

Figure A-6 XRD for Grade 4 titanium sample treated at 1150°C for 1 h compared

with untreated sample ...... 197

Figure A-7 SEM of cross-section for Ti4 treated with TiN/Ti powder pack at 1150°C

for 1 h, (a) surface area and (b) center area ...... 198

Figure A-8 The optical micrograph of Ti-6Al-4V samples...... 201

Figure A-9 XRD patterns for Ti-6Al-4V samples treated with TiN/Ti powder pack at

different conditions...... 202

Figure A-10 SEM for Ti-6Al-4V samples treated with TiN/Ti powder pack at 860°C

for 48 h, and at 1150°C for 1 h...... 203

Figure A-11 SEM photo of Microhardness Indents ...... 205

Figure A-12 The comparison of microhardness for CP titanium and Ti-6Al-4V by

different treatments ...... 206

Figure B-1 XRD pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at

300°C for 48 h...... 213

Figure B-2 XPS pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at

300°C for 48 h...... 214

Figure B-3 XRD pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at

500°C and 700°C for 16 h...... 215

Figure B-4 XRD pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at

860°C for 48 h...... 216

Figure B-5 XRD pattern of gettered sample ...... 218

Figure B-6 XPS of gettered sample with powder pack at 1130°C...... 219

Acknowledgments

I would like to thank my advisors, Professor Arthur Heuer and Professor Frank

Ernst, for their tremendous support, patience, and encouragement. This research endeavor

would not have been possible without their determination and vision.

I also want to thank Professor Gary Michal, for his help in calculating the thermodynamic predictions throughout this research effort.

I also like to thank Peter Williams, Sunniva Collins, and Steven Marx in

Swagelok Company for their support during this endeavor.

I am extremely grateful to my wife for her assistance and support to all my work.

Surface Hardening of Titanium Alloys by Gas Phase Nitridation under

Kinetic Control

Abstract

Lizhi Liu

This work describes a nitriding process for titanium and its alloys, which will

improve the wear and corrosion resistance by forming a single phase Ti (N) solid solution

that has the same lattice properties as the substrate, but not forming any nitrides on the

surface. By kinetically controlling the chemical potential of nitrogen as diffusional

interstitials, a large solubility can be achieved, which results in a super-hard surface. The

nitrogen pressure, heat treatment temperature, and heat treatment time were investigated

to form a desired diffusion profile without the formation of surface nitride compounds.

This process can improve the wear resistance without the cost of reduced corrosion and fatigue resistance.

A thermodynamic calculation has shown that the partial pressure of nitrogen acquired to avoiding the formation of nitrides is extremely low. A kinetic calculation, however, has indicated that a much higher nitrogen partial pressure can be afforded to nitride titanium alloys without forming nitrides. This kinetic calculation considers the

impingement rate at the gas-solid interface, the sticking coefficient, and the interstitial

diffusion coefficient.

The conception of nitridation under kinetic control is verified in a laboratory-scale

system, the design and construction of which is part of this work. Nitridation under well-

defined and reproducible conditions was achieved by using a long fused silica tube as the

reactor and sealing it with a hydrogen/oxygen torch. To clean the gas atmosphere in the

tube prior to nitridation, titanium foil was integrated into the system as a getter material.

After the titanium getter has cleaned the atmosphere from undesired impurities,

the titanium or titanium alloy specimen was nitrided by exposing it to a well-controlled

but very low nitrogen partial pressure, generated by a metal nitride/metal powder pack.

-4 -1 With the Cr2N/Cr powder pack, for example, nitrogen pressure from 10 Pa to 10 Pa can be achieved by adjusting the powder pack temperature. Thermodynamic and kinetic calculation indicated that this pressure range is suitable for nitridation under kinetic control.

By carefully controlling the nitrogen pressure, the sample temperature, and treatment time, a thickness of hardened layer equal to 25 µm was achieved without the formation of nitrides. The surface microhardness is more than 10 GPa, The cross-section microhardness measurements showed the nitrogen concentration profile resulted from diffusion. Tensile testing indicated that nitridation under kinetic control increases the yield strength and reduces the ductility.

Chapter 1 INTRODUCTION

1.1 History and Current Applications of Titanium

Titanium was first identified as a metallic element by Gregor in England in 1791.

In 1795, Klaproth, a German chemist, rediscovered this metal and named it titanium,

after the Titans, the powerful son of earth in Greek mythology (Lide, 1995). The element

Ti is the fourth most abundant metal in the earth's crust. Because of its great affinity for

oxygen and nitrogen, pure titanium had not been produced in a commercial process until the late 1930's. Interest in the properties of titanium started in the late 1940’s and early

1950’s when the Second World War passed. In the following decades titanium research and application received tremendous development. The production of sponge titanium already reached more than 100,000 tons annually in the early 1980's, and still increased steadily (Froes, Eylon, & Bomberger, 1985).

From about 1950, alloy development of titanium progressed rapidly because of the recognition of aluminum additions for strengthening purpose. Some other alloying elements combined with aluminum have been attempted, such as Ti-5Al-2.5Sn for high temperature applications, and Ti-7Al-4Mo for high strength applications. The appearance of Ti-6Al-4V alloy, which combined excellent properties and good producibility, was a major breakthrough. Today, Ti-6Al-4V is still the most widely used titanium alloy.

Titanium alloys possess a unique combination of good mechanical properties, low density, corrosion resistance and biocompatibility, which make them attractive candidates for structural and biomedical applications. The two classical application areas are airframes and aeroengines which are driven by the superior structural efficiency of

titanium alloys (Boyer, 1992). In the traditional areas of chemical and power industries,

using titanium alloys as corrosion resistant material has become more common in recent years (Schutz & Watkins, 1998). A well-established area of titanium is the biomedical field. Several alloys have been used as implant materials. Efforts have been made to develop new alloys in order to improve the fatigue strength and biocompatibility (Froes,

Allen, & Niinomi, 1998). The need of titanium in consumer products area is growing very fast. Watches and jewelries are made from titanium because of the preservation of the appealing metal surface. And various kinds of sporting goods, such as golf club heads and bicycle frames, are made because of the high strength and low density of titanium alloys.

1.2 Surface Hardening Methods

Light weight, low modulus, high strength, and high corrosion resistance are the inherent advantages for titanium alloys. But at the same time, titanium has a tendency to

gall when in sliding contact with other materials under load, which results in poor

abrasive and adhesive wear resistance. So their usefulness in many engineering

applications is severely hampered. Therefore substantial efforts have been put into the

surface engineering area of research in order to obtain protective and durable coatings

and thereby to widen the potential range of applications beyond that of construction

materials. Several kinds of surface treatments have been proposed to achieve the desired

surface properties. Basically there are two distinctive techniques used: depositional

techniques and diffusional techniques.

Depositional techniques are characterized as transporting a substance from

derivative sources and depositing it onto the surface of the treated materials, and include

electroplating, physical vapor deposition (PVD), and chemical vapor deposition (CVD).

In the CVD process, theoretically any element or compound can be deposited on the substrate. But for titanium alloys, the deposited substances are usually TiN, TiC, and diamond, which are hard materials and can provide a protective surface and also have good adherence with titanium substrates.

Diffusional techniques, namely nitriding, carburizing, carbonitriding, ferritic nitrocarburizing, and boronizing, are characterized by diffusing an element, usually small diameter atoms, such as carbon, nitrogen, sulfur, boron, and oxygen, into the surface of the treated material by the application of the appropriate amount of heat, time, and the surface catalytic reaction. Traditional gas carburizing and nitriding have been favored by metallurgists and engineers for many years. More efficient surface treatment techniques, such as controlled gas treatment, ion implantation, and plasma nitriding, are now commercially available to improve the surface properties. Laser surface treatment and arc melting treatments are also under investigation.

1.3 The Goal

In this work, nitriding is the process that has been studied. It is well known that the surface compounds on titanium substrates have adherence problems and a tendency to degrade the fatigue resistance. So far a variety of surface engineering techniques, such as

PVD/CVD coating, direct gas nitriding, plasma, and laser thermochemical processing, have generated surface layers with considerable thickness. The improved wear resistance has a cost in mechanical properties, such as ductility and fatigue resistance. The present work focuses on trying to find a nitriding process that will improve the wear and corrosion resistance by forming a single phase Ti(N) solid solution, which has the same

lattice properties as the substrate but in the absence of forming any nitrides on the surface.

A similar problem has been encountered in surface engineering of austenitic

stainless steels. In these materials, surface properties have been successfully improved by carburization process at low temperatures, that introduces a colossal supersaturation

(LTCSS) of interstitially dissolved carbon without the formation of carbides (Cao, 2003).

By controlling the mobility of alloying elements and the chemical potential of diffusing interstitials, a large solubility of interstitials can be achieved, which can result in a super- hard surface and high residual compressive stress. This process can improve the wear resistance without compromising corrosion and fatigue resistance.

The surface properties of titanium and its alloys could be dramatically improved by applying a similar process using nitrogen as the interstitial solvent. Based on the concept of gas nitriding and other nitridation practice (Maksymovych, Fedirko, &

Pohrelyuk, 1991; Panaioti, 1998; Shenhar, Gotman, Gutmanas, & Ducheyne, 1999), a new nitriding technique is introduced and investigated to form a desired nitrogen concentration profile in the surface layer of titanium and its alloys. The experimental results show that this process does improve the surface hardness and wear resistance.

Based on the experience of carburization (LTCSS) in austenitic stainless steel, it is hoped that the nitridation process will improve the fatigue properties of titanium and its alloys and may also improve the corrosion resistance.

Works Cited

Boyer, R. (1992). New Titanium Applications on the Boeing-777 Airplane. Jom-Journal

of the Minerals Metals & Materials Society, 44(5), 23-25.

Cao, Y. (2003). Surface hardening of austenitic stainless steels via low-temperature

colossal supersaturation. Unpublished Ph. D. Dissertation, Case Western Reserve

University, Cleveland.

Froes, F. H., Allen, P. G., & Niinomi, M. (1998). Non-aerospace applications of titanium.

Warrendale, Pa.: TMS.

Froes, F. H., Eylon, D., & Bomberger, H. B. (1985). Titanium technology : present status

and future trends. Dayton, Ohio: Titanium Development Association.

Lide, D. R. (1995). CRC Handbook of Chemistry and Physics (76th ed.). New York:

CRC Press.

Maksymovych, H. H., Fedirko, V. M., & Pohrelyuk, I. M. (1991). A mechanism of

formation of near-surface hardened layers on titanium alloys in a rarefied

dynamic atmosphere of nitrogen. Fizyko-Khimichna Mekhanika Materialiv, 27(2),

38-42.

Panaioti, T. A. (1998). Effect of the pressure in the gas-discharge chamber on the depth

of nitrogen diffusion in titanium alloys. Metal Science and Heat Treatment, 40(9-

10), 381-384.

Schutz, R. W., & Watkins, H. B. (1998). Recent developments in titanium alloy

application in the energy industry. Materials Science and Engineering a-

Structural Materials Properties Microstructure and Processing, 243(1-2), 305-

315.

Shenhar, A., Gotman, I., Gutmanas, E. Y., & Ducheyne, P. (1999). Surface modification

of titanium alloy orthopaedic implants via novel powder immersion reaction

assisted coating nitriding method. Materials Science and Engineering a-

Structural Materials Properties Microstructure and Processing, 268(1-2), 40-46.

Chapter 2 LITERATURE REVIEW

2.1 Titanium and Titanium Alloys

Pure titanium has an allotropic phase transformation at 882°C from a body- centered cubic (BCC) β phase at high temperature to a hexagonal close-packed crystal structure (HCP) α phase at low temperature. The transformation is diffusionless. During

the transformation, titanium atoms in the BCC beta structure shift only slightly to convert

to the HCP alpha structure. Therefore in pure titanium, even very rapid cooling has been

unable to suppress the transformation.

The unit cell of hexagonal α phase and cubic β phase is shown in Figure 2-1. At

room temperature, the lattice parameters of the α phase are a = 0.2951 nm and c = 0.4684

nm. The resulting c/a ratio = 1.5871, is smaller than the ideal ratio of 1.633 for the HCP structure. The lattice parameter of the β phase at 900°C is a = 0.3306 nm. Also indicated

in Figure 2-1, are the most densely packed planes of these two phases. In β, it is one of

the six {1 10} planes, while in α, there are three types of densely packed planes: (i):

(0001) plane, also called basal plane; (ii): one of the three {1010} planes, also called the

prismatic planes; and (iii): one of the six {1011} planes, also called pyramidal planes. In

β, the close-packed directions are the four <111 > directions. In α, they are the three

<>1120 directions.

The α/β transformation temperature of titanium alloys is strongly influenced by interstitial and substitutional elements, and therefore depends on the purity of the metal.

Alloying elements in titanium are usually classified as α or β stabilizing additions,

depending on whether they increase or decrease the α/β transformation temperature.

The substitutional element Al and the interstitial elements C, N, and O are all strong α stabilizers. The transus temperature from HCP to BCC increases with increasing concentrations of these alloying elements (see Figure 2-2(a)). Aluminum is the most widely used alloying element in titanium alloys, because it is the only common metal that can raise the transus temperature and it has large solubility in both α and β phases. Some other α stabilizers include B, Ga, Ge, and the rare earth elements, but their solid solubilities are much lower as compared to aluminum. And none of these elements is used commonly as an alloying element.

Figure 2-2(b) shows the schematic phase diagram for β stabilizers. The most commonly used β stabilizers in titanium alloys are V, Mo, and Nb. Sufficient concentration of these elements make it possible to stabilize the β phase to room temperature. Hydrogen is a β stabilizer, too. But the maximum practical hydrogen content in titanium alloys is strictly limited to about 125 - 150 ppm because of hydrogen embrittlement. Some other β stabilizer elements, i.e. Cr, Fe, and Si, are also used in many titanium alloys, whereas Ni, Cu, Mn, W, Pd and Bi have only very limited usage.

In addition, there exist some elements which behave more or less neutrally

(Figure 2-2(c)), because they have essentially no effect on the α/β transformation temperature. Zr, Hf, and Sn are some of these. Especially, Zr and Hf are isomorphous with titanium and both exhibit the same β to α allotropic transformation. These elements have complete solubilities in the α and β phases of titanium. However Zr and Sn, when present in many commercial multicomponent alloys, are considered as α stabilizing elements. This is because of the chemical similarity of Zr to titanium and because Sn can

replace aluminum in the hexagonal ordered Ti3Al phase. The interactions between alloying elements make it difficult to understand titanium alloying behavior just on the basis of binary Ti-M system.

Commercial titanium alloys are classified conventionally as α, β and α+β alloys according to their position in a pseudo-binary section through a β isomorphous phase diagram. It is shown schematically in Figure 2-3. Table 2.1 lists the most important commercial titanium alloys in each of these three groups (Donachie, 2000).

The group of α alloys consists of the alloys which upon annealing well below the

β transus temperature contains only small amounts of β phase (2 - 5 vol%) stabilized by iron. Commercially pure titanium is an α alloy. Usually it contains impurities (maximum wt%) of Fe (0.3 - 0.5%), C (< 0.10%), H (< 0.015%), N (0.03 - 0.05%) and O (0.18 -

0.40%). The total is less than 1%. Pure titanium has good corrosion resistance, formability and weldability, but relatively low strength. Some other α alloys have better corrosion resistance or higher yield strength. Classifying titanium alloys by their constitution (α, α+β, and β) is convenient but can be misleading for α alloys, because essentially all α alloys contain a small amount of β phase as mentioned above. Perhaps a better criterion for α alloys is the lack of heat treatment response (Lutjering & Williams,

2003).

The group of α+β alloys consists of the alloys which transform martensitically upon rapid cooling from the β phase field to room temperature. In the phase diagram

(Figure 2-3), it has a range from the α/α+β phase boundary up to the intersection of the

Ms line with room temperature. The most widely used titanium alloy, Ti-6Al-4V is in this group. It contains about 15 vol% β phase in equilibrium at 800°C. It has an exceptional

good balance of strength, ductility, fatigue, and fracture properties.

The group of β alloys is actually metastable β alloys because they are located in the equilibrium (α+β) phase region of the phase diagram (Figure 2-3). Stable β alloys that are located in the β single phase field do not exist as commercial alloys yet. The characteristic feature of the β alloys is that they do not transform martensitically upon fast cooling from the β field.

Up to the data on 1998 (Eylon & Seagle, 2000), CP titanium accounted for about

26% of the total USA titanium market, while Ti-6Al-4V covered about 56%, whereas all other alloys together sum up to 18%. In this study, Grade 4 (Commercial Pure, CP) and

Grade 5 (Ti-6Al-4V, Ti64) titanium alloy samples are studied.

It should be emphasized that most commercial titanium alloys are multicomponent alloys. So the binary phase diagram can serve only as a qualitative guideline. In principle, ternary or quaternary phase diagrams should be used. Figure 2-4 is an example that shows isothermal sections through the Ti-rich corner of the Ti-Al-V system at 1000°C, 900°C and 800°C (Collings, 1994). However, not all the necessary higher order phase diagrams have been determined and binary phase diagrams are still the most useful tools for the material scientist.

HCP structure of α phase BCC structure of β phase

Figure 2-1 The unit cell of hexagonal α phase and cubic β phase. Shaded planes are the mostly close-packed planes.

Temp. (a) β

α+β

Ti Metal

Temp. (b)

α α+β β

Ti Metal

Temp. (c)

Ti Metal

Figure 2-2 Schematic drawing shows the effect of alloying element classified as (a) α stabilizer, (b) β stabilizer, and (c) neutral.

Temp.

α α+β β

alloys alloys alloys

Ti Metal

Figure 2-3 Pseudo-binary section through a β isomorphous phase diagram shows the classification of α, β, and α+β alloys.

Figure 2-4 Isothermal sections through the Ti-rich corner of the Ti-Al-V system at 1000°C, 900°C and 800°C. the black dot marks the composition of Ti-6Al-

4V. (Collings, 1994) 29

Table 2.1 Some of the most important commercial titanium alloys in each of these three groups: α, β, and α+β alloys (Donachie, 2000).

Unalloyed grades ASTM grade 1 (0.18 wt% oxygen)

ASTM grade 2 (0.25 wt% oxygen)

ASTM grade 3 (0.35 wt% oxygen)

ASTM grade 4 (0.40 wt% oxygen)

α alloys Ti-5Al-2.5Sn

Ti-8Al-1Mo-1V

Ti-6Al-2Sn-4Zr-2Mo

Ti-5.5Al-4.5Sn-4Zr-0.5Mo (IMI834)

α+β alloys Ti-6Al-4V (ASTM Grade 5)

Ti-6Al-4V-ELI (extra low interstitial)

Ti-3Al-2.5V

Ti-6Al-6V-2Sn

β alloys Ti-13V-11Cr-2Al

Ti-8Mo-8V-2Fe-3Al Ti-10V-2Fe-3Al

2.2 Basic Properties of Titanium Alloys

Some of the basic characteristics of titanium are listed in Table 2.2 and compared to those of other metallic materials (Boyer, Welsch, & Collings, 1994). Titanium has the highest strength to density ratio, which makes it a perfect material for structural application. The much higher melting temperature compared to Al (also a lightweight structural material), gives titanium advantage for high temperature applications. However, the high reactivity with oxygen, not only results in its high price, but also limits the maximum use temperature of titanium alloys to about 600°C. Above this temperature, the diffusion of oxygen through the oxide surface layer becomes too fast, which results in excessive growth of the oxide layer and embrittlement (Lutjering & Williams, 2003).

Besides the low density high strength advantage, titanium alloys have other valuable characteristics. Compared to aluminum, another low density metal, titanium and its alloys have better fatigue properties, higher elevated-temperature-strength, and better crack growth resistance and do not corrode in conditions in typical aircraft usage.

Compared to other widely used metals, e.g. steel, titanium alloys have higher corrosion resistance.

For commercial pure (CP) titanium and Ti-6Al-4V, the thermal conductivity and the electrical resistivity vary significantly. These two factors both depend on the density and extent of scattering of conduction electrons. But these differences are relatively small if compared with the difference between Ti alloys and other three structural metallic materials. It can be seen that the thermal conductivity of Ti alloys is significantly lower, and the electrical resistivity is very high. This will limit the use of titanium as an electrical conductor. The linear thermal expansion coefficient is similar for CP titanium

and Ti-6Al-4V. And the value is lower compared to other three metallic materials.

Consequently, titanium alloys are an excellent choice for applications, i.e. casings for aero-engineering and connecting rods in automobile engineering.

Titanium has excellent corrosion resistance in most environments. This is due to a stable protective surface TiO2 layer, which passivates titanium as long as the integrity of this film is maintained. On the other hand, titanium is not corrosion resistant under reducing conditions, where the protective nature of the oxide film breaks down. TiO2 layer can form on the surface simultaneously because of the high affinity of titanium to oxygen. Below this layer, there is an oxygen-rich layer in the bulk titanium originating from inward diffusion of oxygen (d'Agostino, Fracassi, Pacifoco, & Capezzuto, 1992).

This “case” can result in the formation of surface cracks under tension loading and limit the titanium application temperature at about 600°C to avoid embrittlement. In order to decrease the diffusion rate of oxygen through TiO2 layer, various additions of alloying elements have been studied. Aluminum is commonly used for this purpose. It can form a very dense and thermally stable oxide, which can retard the diffusion of oxygen (Mishin

& Herzig, 2000).

The excellent properties of titanium continuously increase the range of application in the aerospace, chemical, medical, and automobile industries.

Table 2.2 Physical data for titanium alloys and alloys based on iron, nickel and aluminum (Boyer et al., 1994).

cp-Ti Ti-6Al-4V Fe Ni Al (grade 4)

General

Density (g/cm3) 4.5 4.4 7.9 8.9 2.7

Comparable price Very High Very High Low High Medium

Thermal

Melting point (°C) 1670 1650 1538 1455 660 Thermal cond. 20 7 80 90 237 (W/m·K) Thermal expansion 8.4 9.0 11.8 13.4 23.1 (10-6/K) Specific heat 523 530 450 440 900 (J/kg·K) Mechanical Young's modulus 100 110 220 200 70 (GPa) Poisson's ratio 0.36 0.36 0.29 0.31 0.35 Tensile strength 500 1000 1000 1000 500 (MPa) Hardness (Vickers) 260 350 610 640 170

Chemical Corrosion Very high Very high Low Medium High resistance Reactivity with Very high Very high Low Low High oxygen

2.3 Current Surface Hardening Methods

Titanium alloys possess a unique combination of good mechanical properties, low density, good corrosion resistance and biocompatibility, which make them attractive candidates for structural and biomedical applications. On the other hand, the higher costs and poorer machinability are two major disadvantages. Titanium alloys are also characterized, especially in sliding contact, by poor tribological properties, including high and unstable friction coefficients, severe adhesive wear, susceptibility to fretting wear, and a strong tendency to seize. Titanium alloys have a tendency to gall when in sliding contact with other materials under load, which results in a poor abrasive and adhesive wear resistance. This severely hampers tribological applications of Ti-based alloys.

To improve the wear resistance and the hardness of titanium alloy surface, many methods have been developed in recent years: surface nitride coating by PVD (Khaled,

Yilbas, & Shirokoff, 2001; Lim, McCulloch, Russo, Bilek, & McKenzie, 2002; B. S.

Yilbas, Hashmi, & Shuja, 2001; B.S. Yilbas & Shuja, 2000); oxygen or nitrogen thermo- diffusional treatment (Dong & Li, 2000; Spies, Reinhold, & Wilsdorf, 2001; Zhecheva,

Malinov, & Sha, 2003); surface modification by means of ion implantation and plasma nitriding (Alonso et al., 1997; Fukumoto et al., 1999; Han, Kim, Lee, Lee, & Kim, 1996); laser or arc nitriding (Labudovic & Khan, 1998; L'Enfant, Laurens, St Catherine, Dubois,

& Amouroux, 1997; Masse & Mathieu, 1996; B. S. Yilbas, Khalid, & Shuja, 1999); and so on.

Hardening the surface of titanium alloys by heat treatments results in microstructural and heterogeneity changes that will also change the material properties.

The surface oxide would definitely be changed, possibly altering resistance to corrosion.

Also, the increased wear resistance would only last as long as the surface layer was not removed by wear. Once the surface is removed, the surface will revert back to its untreated properties. The effects of different treatments will vary depending on the processing parameters, such as temperature, atmosphere, composition, and time.

Interstitial hardening is a common method in surface treatment especially in steel products. Mostly carbon and nitrogen are used (Blawert et al., 2000). Sometimes other small radius atoms, such as oxygen and boron, are also used to improve the surface properties (Baazi, Knystautas, & Fiset, 1993; Boettcher, 2000). Carbon has only a small solubility in titanium. Oxygen has a large solubility, but high concentrations of oxygen in titanium, forming what is known as an “α case” are known to cause embrittlement and therefore must be avoided. Nitrogen also has a large solubility. The effect of nitrogen on mechanical properties is still under investigation.

Several surface treatments compared in this section are common in industry. They include physical (chemical) vapor deposition (PVD or CVD), nitrogen ion implantation, laser nitriding, plasma nitriding, and conventional gas nitriding. PVD and CVD are coating techniques, which grow new layers of harder materials. Ion implantation and plasma nitriding are two examples of thermochemical treatments, where there is a gradual change from the substrate material to the surface material. Laser nitriding is a liquid phase alloying technique.

The surface modifications are on the order of µm; therefore, evaluation techniques for thin films need to be developed, since traditional methods of indenter hardness tests

(>10 µm) and torsional tests are no longer applicable.

2.3.1 Physical vapor deposition and chemical vapor deposition

Physical vapor deposition (PVD) and Chemical Vapor Deposition (CVD) are coating techniques which give a completely different chemistry, structure and property to the surface compared to the substrate (Quinto, 1996). Basically, PVD involves evaporating a coating metal, and then depositing that metal on the substrate. These coatings are applied at substrate temperatures of several hundreds degree Celsius and are accomplished in high-vacuum chambers. The coating metal is vaporized by induction coils. Electrical resistance or electron beams heat the source and thus coating materials evaporate in the presence of reactive gases, in most case N2 (Bardos & Barankova, 2001;

Murawa, 1986; Navinsek, Panjan, & Milosev, 1997; Wiklund & Larsson, 2000). Nitride compounds form and deposit on the surface of substrates.

Chemical vapor deposition (CVD) involves supplying a source of several reactant gases, and then depositing the chemical reaction products on the substrate (Ultramet,

2002). Gaseous compounds of the materials to be deposited are transported to a heated substrate surface where a thermal reaction/deposition occurs. The reactions of gases occur at the surface of the hot substrate to form a solid deposit. A more detailed interpretation of CVD mechanism would include chemical reactions that take place in the vapor phase prior to adsorption, as well as surface diffusion of the reactive adsorbents.

The most advanced CVD systems allow control over the extent of these processes, thus allowing control of the morphology of the deposit (Pierson, 1992).

Compared with the PVD processes, the CVD processes exhibit better throwing power, which allows even intricately shaped parts to be provided with a uniform coating.

A major disadvantage of the classic CVD processes is the high process temperature, in

the range from 800 to 1400°C, which is necessary for coating formation. Lower process temperatures are possible with the PACVD process (Plasma Assisted CVD). In this process the gas/substrate system is exposed to a low-temperature plasma that supplies the necessary energy to activate the reaction. The process temperatures used in PACVD lie between 450 and 650°C.

In surface coating technique, a short time treatment resulting in a thin hard coating layer can improve surface properties. However, longer process time is detrimental to fatigue properties due to the poor adherence between thick coating layers and the substrate, although the hard coating surface provides very good improvement in the sliding wear performance (Ashrafizadeh, 2000).

2.3.2 Ion implantation techniques

The surface modification of titanium and its alloys by ion implantation with N or

C has been studied as a means to improve the wear, fatigue, or fretting fatigue behavior of the alloys. During ion implantation, accelerated ions are driven into a substrate surface.

An ion source is bombarded with electrons that ionize the molecules by striking an arc discharge between an anode and a cathode. The ions are extracted by an electrostatic field, then will be magnetically accelerated, separated and scanned on a substrate. If the implantation dose is controlled under a suitable level, it will correspond to the formation of a stoichiometric or near-stoichiometric balance between the implanted species (N or C) and the host lattice, i.e. TiN or TiC near the surface. This leads to the transition of the wear mechanism from adhesive wear to abrasive wear, with a corresponding enhancement of the wear-resistant properties of the base metal. In a review paper, Elder

et al. (1988) concluded that an implantation dose that can form stoichiometric or near- stoichiometric nitride will optimize the wear properties.

The ion implantation process is carried out at room temperature, however, the surface temperature increases dramatically. The high energy ions enter the lattice and produce vacancy-interstitial point defects. The penetration depths are typically less than

500 nm and depend upon the implantation energy (Minkoff, 1992). The range distribution of ions follows a Gaussian distribution; the penetration depths may be increased with repeated treatments at various beam energies (Mozetic et al., 1999).

According to the most recent Ti-N phase diagram (Lengauer, 1991), room temperature implantation should lead to the formation of the Ti2N phase when N/Ti<0.5, and to TiN when N/Ti>0.65 (Backovic, Weatherly, & Elder, 1994). Zheng et al. (1988)

+ observed a complete transformation of Ti to Ti2N at relatively low N doses, the direct formation of TiN in Ti, the formation of “patches” of fine-grained TiN and the development of a preferred epitaxy in most of the grains. The orientation relationship which develops during a phase transformation induced by implantation has been reported by a number of studies. The most common orientation relationship which has been found is (0001) || (010) || (111) or (1100) || (101) || (111) (Zheng et al., 1988). Ti Ti2 N TiN Ti Ti2 N TiN

These particular planes are the close packed or nearly close packed planes in these three crystal structures. This orientation relationship can be rationalized by noting the close geometric similarity and spacing of the Ti atoms in these planes with these three crystal structures.

These surface modifications form intimate mixtures and do not have the adhesion problems that coatings might experience. However, ion-plated thin coatings are

compromised by the poor load-bearing capacity of the substrate, which can cause rapid degeneration of the bond at the coating/substrate interface under repetitive stress conditions (Torrisi, 1996). Furthermore, although nitrogen-ion implantation is able to convert the alloy surface into a hardened compound nitride layer, this is typically achieved only across a very thin region, providing little improvement in load support from the substrate.

2.3.3 Laser nitriding

In recent years there has been widespread interest in using lasers to modify surface structures and compositions of titanium alloys (Deevi, Sikka, Swindeman, &

Seals, 1997). In this case, the use of gaseous nitrogen interaction with the laser melted surface is utilized, since elemental titanium has a strong affinity for nitrogen. Very high incident power is brought by CO2 or YAG lasers to bear on the substrate surface, producing extremely rapid heating. Since there is a steep temperature gradient, the bulk of the material remains unaffected and acts as a heat sink to provide self-quenching. A relatively thick and hard nitrided layer on Ti-alloys can be obtained. Primarily this will improve their tribological properties. Laser beam moving velocities, processing pressure as well as nitrogen/argon ratio, gas flow rates are major controlling factors (Figure 2-5).

Laser surface modification of Ti-6Al-4V alloy was investigated by Akgun and

Inal (1992; 1994) under nitrogen gas atmosphere. The results showed that laser-treated

Ti-6Al-4V alloy produced a hardened surface layer due to TiN formation. Laser surface melting followed by an aging treatment resulted in uniform hardness distribution in the melted zone. Ignatiev et al. (1993) also produced a laser-nitrided surface with very small roughness, free from cracks. They demonstrated that the wear properties of laser-treated

surfaces improved considerably, which encouraged the use of laser nitriding as a potential surface treatment technique for the industry. Yilbas and Shuja (2000) have described that laser melting plus PVD TiN coating duplex treatment can improve the surface wear property considerably.

Although laser nitriding can generate a hardened layer about hundreds of microns in a very short time and without affecting the substrate properties, the melting-solidifying process totally changes the surface microstructure. Surface roughness is comparably high and it is very hard to have a crack-free surface. Significant reduction in ductility and fatigue strength also occurs after laser melting and alloying with nitrogen. This cracked, brittle surface layer has limited the application of laser nitrided titanium alloy products.

Nitrogen

Figure 2-5 Schematic drawing of laser nitriding

2.3.4 Plasma nitriding

Plasma Nitriding is one of the most widely used surface hardening processes which involves diffusion of nitrogen atoms into the metal surface in the presence of a plasma environment. This process is also called ion nitriding.

If two electrodes of different potential are placed in a gas at reduced pressure and an increasing voltage is applied, at a certain voltage a glow discharge will be set up around the electrode at lower potential. Plasma nitriding is carried out in the region of abnormal glow discharge where the workpiece to be plasma nitrided is completely covered with glow and the voltage and current increases simultaneously. The workpieces themselves can be heated through the transfer of energy associated with the action of ionic bombardment. As a result, highly energetic nitrogen is transferred to the workpieces, and then penetrates inside by diffusion.

Nitrogen in plasma nitriding is introduced in the form of NH3 gas or nitrogen and argon mixtures. The sample to be coated is made cathodic or negative relative to the chamber walls. A direct current potential is applied between the work piece and the chamber walls, usually between 500 and 730 V. Nitrogen atoms are much smaller than titanium atoms, and can penetrate the materials to form an interstitial solid solution. As the nitrogen concentration is built up on the surface, a surface compound layer will form and the nitrogen atoms will diffuse into the structure. Thus, the surface hardness of titanium gets enhanced.

In the case of nitriding of titanium, the surface layers are comprised of an outermost TiN layer, followed by a Ti2N layer, then the Ti alloy substrate (Raveh, 1993).

The thickness of the compound layer increases with nitriding temperatures and time. The

grain size, surface roughness, thickness of diffusion layer and superficial microhardness also increase with coating thickness. At the same time, the diffusion process also depends on the temperature.

The enhanced energetic bombardment produced unique nucleation characteristics resulting in the formation of nanostructures. Processing can be achieved at significantly lower temperatures (typically ~ 500°C), allowing nitriding of materials with temperature- sensitive microstructures. The intensified plasma treatment can cause a significant increase in the nitride growth kinetics. Intensified plasma-assisted processing treated surfaces (Meletis, 2002) exhibit significant increase in hardness that can have a beneficial effect on wear resistance while maintaining other desirable material properties such as corrosion and/or fatigue behavior.

The major negative of plasma processing is its cost. The initial acquisition costs are very high. And installation is also expensive due to the large electric power supplies required. Water usage is also very high to provide sufficient cooling.

2.3.5 Gas nitriding

Although many techniques are commercially available to modify the surface properties of titanium alloys, conventional gas nitriding is still considered to be the most promising method for engineering applications because it can easily form a hardened nitrided layer on the surface of material and it is not as expensive as those newly developed technologies. Gas nitriding technology offers the right set of conditions for thermodynamically based process control (Spies et al., 2001).

Gas nitriding as a process, has been used industrially since the early 1920's. The treatment is usually conducted in a furnace with a gas atmosphere control. Pure nitrogen,

nitrogen/argon gas mixture, nitrogen/hydrogen gas mixture, or ammonia can be used as the nitriding gas resource (Figure 2-6). The general procedure is first the furnace is evacuated, then a flow of gas is introduced in order to reach atmospheric pressure. The thickness of the surface layer and the value of the microhardness depend on two parameters-temperature and time.

Traditional gas nitriding, which has been favored by metallurgists and engineers for many years, now is being challenged by more recent techniques such as controlled nitriding, ion nitriding, enhanced ion nitriding and RF nitriding. Controlled nitriding and ion nitriding have gained acceptance and now are commercial techniques. Controlled nitriding is a development of the traditional gas nitriding in which all of the process parameters are computer-controlled, including a gas panel for precise gas mixing and flow measurements, the process gas-analysis system, the process gas pressure within the process retort and process temperature and time. Process parameters are monitored on a continuous basis via computer, and precise adjustments are made to the process systems to ensure repeatable metallurgy in relation to the load surface area and the load mass.

In the gas nitriding practice, the oxygen contamination is very hard to control.

The processing gases all have a certain level of oxygen impurities in the form of oxygen gas or water vapor. Gas leakage through heat treatment facilities also introduces the contamination. Titanium alloys with a high level of oxygen have a tendency to form the brittle α phase on the surface which has a detrimental effect on mechanical properties.

Figure 2-6 Gas nitriding setup.

2.4 Gas Adsorption Kinetics

2.4.1 Physisorption and chemisorption

Nitriding is a surface modification process in which nitrogen is supplied from a gaseous phase. At the solid-gas interface, one important process is adsorption. The adsorption of an atom or molecule on a solid surface involves the same basic forces that are known from the theory of chemical bonding. Actually many concepts in adsorption theory are transferred from the theory of chemical bonding. Basically there are two principal modes in the theory of adsorption: physical adsorption (physisorption) and chemical adsorption (chemisorption) (Luth, 1993).

General speaking, physisorption is a process in which the electronic structure of the molecule of atom is hardly perturbed upon adsorption. The only bond between adsorbed molecule (adsorbate) and substrate is a van der Waals type force. Physisorption is virtually independent of surface atomic geometry. It’s a non-dissociative, reversible process. After monolayer coverage, gas molecules can still be adsorbed on the surface to allow multilayer uptake. Physisorption usually happens at low temperature. Since it is a non-activated process, it happens very fast.

In contrast, chemisorption is an adsorption process that a chemical bond, involving substantial rearrangement of electron density, is formed between the adsorbate and substrate. The nature of this bond may lie anywhere between the extremes of virtually complete ionic or complete covalent character. This strong reaction limits the chemosorption to one monolayer. And if the gas molecule consists of several atoms, dissociation is very likely to happen. And this reaction may be irreversible. Like other

chemical reactions, chemisorption is often an activated process, and the characteristics of chemisorption varies profoundly with crystallographic orientation of the surface.

2.4.2 Nitrogen adsorption on metal surface

The interaction of nitrogen in a gas nitridation system with a solid surface is very complex. Among the large number of possible interactions, the following have been considered as relevant to nitridation processes: adsorption of nitrogen, desorption of nitrogen, recombination of nitrogen, and diffusion of nitrogen. The first and the last mechanisms are source terms for nitriding, while the other two mechanisms are loss terms for nitriding. These effects can occur simultaneously.

The energetics of adsorption are shown in Figure 2-7 (Luth, 1993). N2 molecules are adsorbed in different states on the surfaces of transition metals. The N2 molecule approaching the substrate surface is firstly attracted by van der Waals (including electrostatic polarization) forces between the substrate and molecule itself. On further approaching the surface, the molecule encounters the outer electrons in the d-orbital of the metal atoms, and is repelled with an increase in energy. This state of adsorption is a minimum energy into which the N2 molecule can be accommodated and is termed physisorption. Physisorbed N2 is a state of weak adsorption. The coverage is a function of nitrogen pressure, while it is less related to the substrate temperature.

Given enough thermal energy, physisorbed N2 draws even closer to the surface and has to surmount an energy barrier to achieve a state of strong adsorption -- chemisorption. The energy barrier arises because of repulsion between the N2 non- bonding electrons and electrons in the surface atoms. Because of the energy evolving nature of this process, chemisorption is an overall thermodynamically down hill process.

In the chemisorbed state, the N2 molecule can have the molecular axis perpendicular to the surface of the metal (end-on orientation) with one of the N atoms in the molecule forming the adsorption bond with the metal atom. It can also assume the side-on orientation, in which the molecular axis is parallel to the metal surface. In this case both N atoms form a chemisorption bond with the metal atoms on the surface. The chemisorbed states of molecular N2 are classified in Greek letters (α’, α, δ and γ) depending on the strength of interaction with the surface (Mortensen, Hansen, Hammer,

& Norskov, 1999). The α’ state is also termed the precursor state since α’-N2 dissociates into atoms on warming to higher temperatures. Dissociatively chemisorbed nitrogen

(atomic species) is labeled as the β state. The four molecular states of nitrogen are illustrated in Figure 2-8.

2.4.3 The interaction of nitrogen with titanium

Adsorption processes on the surface of titanium have been studied to a far less degree as compared to other metals. Shih et al. (1976) analyzed nitrogen adsorption on the Ti(0001) surface at room temperature by the LEED method. They found two chemically nonequivalent states of adatoms. Nitrogen is localized under the first monolayer of titanium at the initial stage of adsorption, and subsequently nitrogen starts to fill the low-coordination surface states (Figure 2-9). The adsorption of N2 on titanium surface forms a TiN-like layer. Frickel et al. (1997) have done the same investigation with XPS and XRD. They verified the two chemically nonequivalent states of adsorbed nitrogen. And at elevated temperature, nitrogen starts to dissolve in to α-Ti. That is the beginning of diffusion process.

Figure 2-7 Combination of chemisorption and physisorption potential (ϕ) diagram as a function of distance z of adsorbed nitrogen atom or molecule on a metal surface; z0 is the equilibrium distance for chemisorption, QDiss is the dissociation energy of N2 in the gas phase, Eact is the activation energy for adsorption of N2, Edes is the activation energy for desorption of 2N, EB is the binding energy in the chemisorption state 2M-N. (Luth, 1993)

Figure 2-8 The four chemisorbed states of molecular N2 are classified in

Greek letters (α’, α, δ and γ) (Mortensen et al., 1999).

Figure 2-9 The two interstitial sites for adsorbed nitrogen atoms in α titanium (HCP structure) (Frickel et al., 1997).

2.5 Diffusion Model of Nitridation

After nitrogen atoms are adsorbed onto the surface layer, the high chemical potential of nitrogen constitutes the driving force for the interstitial diffusion of nitrogen into the solid bulk. Using Fick’s law of diffusion and appropriate boundary conditions, the observed diffusion profile can be explained to some extent.

2.5.1 Solution of the diffusion equation

Consider interstitial atoms in a solid solution where the parent atoms are arranged in a simple cubic lattice. If any atom has an equal probability of jumping into any of the adjacent sites (total are 6), the result is a net flux of interstitial atoms from the regions of high concentration to those of low concentration. If the jump frequency for the interstitial atoms is ν, and the interatomic spacing in the simple cubic lattice is α, then random atom jumping leads to a flux of interstitial atoms of (Porter & Easterling, 1992):

dc J =−(1 6να 2 ) (2.1) dx

The term in brackets is a constant, and defines the flux for a given concentration gradient. This is the diffusion coefficient, D, and making the appropriate substitution gives Fick’s first law of diffusion:

dc JD=− (2.2) dx

In general, the jump frequency ν is not constant, even within a given alloy. This makes the diffusion coefficient D a function of composition. For example, the diffusivity of C in Fe increases with increasing C concentration because of two important factors:

the concentration dependence of the activity of carbon and the existence of a strain in Fe lattice originating from interstitial C atoms.

Fick’s first law of diffusion can be applied in all cases, using a diffusion coefficient which depends on composition where appropriate. However, it cannot be used to calculate composition profiles in materials except under steady–state situations, i.e. when the composition at all points remains constant with time. But in the majority of cases we are concerned with the development of composition profiles as a function of time. We need to have a more general equation which defines time–dependent diffusion.

Nitridation is a non-steady state diffusion process in which the nitrogen concentration at the surface region increases with increasing time. This kind of time- dependent diffusion is described by the general differential equation which is called

Fick’s second law:

dc d d dc ==−()JD (2.3) dt dx dx dx

This equation specifies the time-dependent change of the diffusion in one direction, or, the time-dependent change of the local concentration gradient at that position for specific materials (diffusion coefficient). This means that the concentration profile is a function of time. If D is constant or the variations of D with concentration can be ignored, this equation (2.3) can be simplified to:

dc d2 c =−D (2.4) dt dx2

With given boundary conditions, Fick’s second law can be solved to give analytical expression of concentration profile. In the carburization and nitridation practice, the common boundary conditions are given as: (i) c = cs, at x = 0 (surface concentration),

and (ii) c = c0, at x = ∞ (original concentration). By taking a constant value of D, a simple one-dimensional solution of the differential equation can be obtained:

x ccxs=−() ccerf s −0  (2.5) 2 Dt where cs is a constant concentration at surface, cx is the variable concentration at distance x, and c0 is the initial concentration of the diffusing species in the sample solid. The term

‘erf’ stands for error function, which is an indefinite integral defined by

2 z erf( z )=− exp( y2 ) dy (2.6) π ∫0

2.5.2 Diffusion in titanium

The diffusion coefficient for interstitial atoms, D, follows an Arrhenius type dependency, with an activation energy which is equal to the enthalpy barrier to atomic migration. It can be expressed by:

DD=−0 exp( QRT / ) (2.7) where D0 is a temperature-independent pre-exponential constant, Q is the activation energy for the diffusion of nitrogen into metal substrate, T is the absolute temperature in

Kelvin, and R is the gas constant (8.314 J mol-1 K-1).

Many titanium production processes, such as solution and aging heat treatments, hot working and recrystallization, are diffusion dependent. The knowledge of the diffusion rates of interstitial and substitutional alloying elements in α and β titanium is of great importance to the research, design and treatment of titanium alloys. Much diffusivity data were measured especially during the first twenty years of commercialization of titanium. Liu and Welsch (1988)have done a literature survey on

diffusion of oxygen, aluminum, and vanadium in α and β titanium. However, their data scattered from each other a lot since several methods were employed for the measurements. Mishin and Herzig (2000) summarized recent experimental results for Ti and Al diffusion in α-Ti(Al), β-Ti(Al), and intermetallic phases α2-Ti3Al and γ-TiAl. The results for interdiffusion and impurity diffusion in these phases and the improvement in the understanding of diffusivities are discussed in detail.

A selection of diffusivity data is shown in Figure 2-10 (Lutjering & Williams,

2003) in the form of Arrhenius plots. It can be seen that the self-diffusion of titanium in the β phase is about 3 orders of magnitude faster than the self-diffusion in the α phase.

The discontinuity of the Arrhenius curve at the transformation temperature is a unique phenomenon for the IVa elements (Douglas, 1971). The diffusion coefficient of substitutional elements can be either faster (for example, Fe) or slower (i.e. Al) than the self-diffusion rate of titanium. For interstitial atoms, hydrogen has the highest diffusion coefficient. The diffusivity of oxygen is much lower than hydrogen and decreased greatly with decreasing temperature. Every diffusion coefficient data has a discontinuity at the transformation temperature.

2.5.3 Diffusivity of nitrogen in titanium

The interstitial diffusion of N atom increases with substrate temperature. The depth of the diffusion zone is observed to depend on the available amount of nitrogen, the concentration gradient, temperature, time, material composition and composition of phases formed dynamically. The diffusion zone consists of nitrogen in solid solution as long as the temperature-dependent solubility limit is not exceeded. If the solubility limit is exceeded, nitrides form.

Reaction of titanium with nitrogen is reported to be slower than that with hydrogen (Papazoglu & Hepworth, 1968) and oxygen (Wasilewski & Kehl, 1954).

Diffusion data for N in Ti have been investigated for a long time (Anttila, Raisanen, &

Keinonen, 1983; Bars, David, Etchessahar, & Debuigne, 1983; Metin & Inal, 1989;

Wood & Paasche, 1977). They all have an assumption that the diffusion coefficient is independent of nitrogen concentration. The Arrhenius plots of diffusion coefficient (D) are summarized in Figure 2-11. Compare these data with those shown in Figure 2-10, the diffusion coefficient of nitrogen is about 2 orders of magnitude lower than that of oxygen.

The nitrogen diffusion data fall into a narrow band and are in good agreement. The scattering is due to different measurement technique employed and due to different considerations of phase boundary composition. The Ti-N phase diagram has been revised several times since those studies were conducted. Till now, there are still some uncertainties about the position of phase compositions.

The diffusional case in Ti-6Al-4V has not been investigated systematically. But

Wang et al. (2001) have observed that the alloying elements Al and V retard the diffusion of nitrogen. Chen et al. (1992) tried to estimate the diffusion coefficient of nitrogen in Ti-

6Al-4V. Although not accurate, their results show a smaller diffusion coefficient than that in pure titanium. To give a direct evidence, when comparing the thickness of nitrogen diffusion layer of Ti-6Al-4V alloy as well as CP titanium at the same treatment condition

(Foi, Deramaix, Atale, & Jacquot, 2000; Muraleedharan & Meletis, 1992; Swagelok,

2002), the thinner diffusional case in Ti-6Al-4V alloy indicates a smaller diffusion coefficient in this alloy. Metin and Inal (1991) also observed a slower nitriding rate for

Ti-6242S alloy than for pure titanium, which addressed the influence of alloying elements on nitrogen diffusion coefficient.

Since there is no available data for the diffusion coefficient of nitrogen in titanium alloys, the diffusion coefficient of nitrogen in pure titanium is employed to calculate a suitable diffusion profile. Despite the scattering in the diffusion data, the most recently data from Metin and Inal (1989) is chosen.

Figure 2-10 Arrhenius diagram of various alloying elements in titanium as well as titanium self-diffusion (Lutjering & Williams, 2003)

Figure 2-11 The Diffusivities of nitrogen in pure titanium

2.6 Kinetic Control of Gas Nitriding

In section 2.3 several nitriding methods have been described. It’s very clear that all those methods form a hard, brittle compound layer, usually TiN, on the treated surface.

This hardened surface layer can significantly improve the tribological properties, however, with a sacrifice of ductility and fatigue resistance and so on (Bell, Bergmann,

Lanagan, Morton, & Staines, 1986). In some applications, the outer layer has to be removed after nitriding treatment. This step will increase the product cost.

In order to optimize the nitriding effects, the thermodynamics and kinetics of Ti-

N system should be investigated more thoroughly. The nitridation process can be divided into the following steps:

1. Nitrogen is supplied or generated from sources such as NH3, nitrogen gas,

or decomposition from nitrogen-containing compounds.

2. Nitrogen transport from the near source area to near the titanium parts

being treated by gas diffusion.

3. Nitrogen molecules impinge the titanium surface and then are adsorbed on

the surface (physisorption).

4. Decomposition of N2 into atomic N and uptake of atomic N in the titanium

surface (chemisorption).

5. Nitrogen atoms diffuse through the bulk material.

6. Reactions may happen on the surface to form Ti2N and TiN compounds

when the nitrogen concentration becomes high enough.

If the nitrogen partial pressure goes too high (as in traditional gas nitriding, about

103 Pa to 105 Pa), the impingement rate is high enough that surface nitrogen adsorption

can easily build up and get into equilibrium. However, because of the high chemical

potential of nitrogen, the reaction Ti + N → Ti2 N, TiN in step 6 always occurs. The surface nitride layer is not so good for the desired surface properties, and it will slow down the diffusion.

This work concerns seeking a certain range of nitrogen partial pressures such that the impingement rate will be kept at a moderate level and the chemical potential of nitrogen on the sample surface is still not high enough to overcome activation energy to form nitrides, i.e. to seek the balance between steps 3, 4, and 5 while still suppressing those reactions in step 6. In such a case, the nitrogen atoms immediately diffuse into the bulk after absorption, so that there is no surface condensation and no possibility of nitride formation.

Temperature is another key factor to control the diffusion process, which may affect step 5. The diffusion coefficient of nitrogen in titanium is lower than that of nitrogen in iron. So the treatment of titanium is much harder to perform than the treatment of iron and steel. Even worse, titanium nitrides are so stable that it is not easy to get rid of them once formed. A particular temperature window is needed to achieve the desired diffusion case without the formation of nitrides.

Based on the work with stainless steel, the role of alloying elements is very important. As we mentioned before, in titanium alloys, different alloying elements serve as either α stabilizers or β stabilizers. They may also affect the solubility of nitrogen. In this nitrogen transport mechanism, alloying elements may affect the process in steps 3, 4,

5, and also 6. The understanding of the effect of different alloying elements will enlighten the further task of seeking optimization of the surface treatment process.

Compared with PVD and CVD, kinetically controlled gas nitriding may successfully suppress the formation of the hard nitride compound layer which could cause adherence problems. The improvements of mechanical properties mainly result from the functional gradient diffusion layer, which has the same structure as the substrate.

There is no sharp interface to cause large changes of physical or chemical properties. The thickness of the diffusion layer in this nitriding process can reach tens or hundreds of microns. It’s much thicker than ion implantation-treated material. So the service life of the workpiece can be dramatically extended.

Kinetically controlled gas nitriding is based on the traditional gas nitriding technique, which has a very low cost. Its economy should be more attractive than plasma nitriding. Titanium and its alloys are expensive. If the kinetically controlled gas nitriding treatment can be successfully applied to titanium, it will significantly increase the profit margin. Another major advantage of kinetically controlled gas nitriding is that the processing protocols can be designed to harden already fabricated components, so that they seamlessly integrate with existing manufacturing processes.

When put Ti and TiN together, Ti2N is formed by reaction TiN + Ti ÆÆ Ti2N.

The nitrogen partial pressure is then defined by equilibria between titanium and the nitrides. The chemical potential of nitrogen in such a case is well controlled that titanium substrate will not form nitrides. This is the starting point to investigate the kinetically controlled gas nitriding process.

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Chapter 3 THERMODYNAMIC AND KINETIC

CALCULATIONS

3.1 Equilibrium Nitrogen Pressure

For the Ti-N system, to avoid the phase transformation of Ti and have a relatively simple system, we are most interested in the equilibrium at low temperatures, especially below the α/β transus temperature, 882°C. According to a published Ti-N binary phase diagram (Figure 3-1) (Wriedt & Murray, 1987), there are three major phases below the transformation temperature: α-Ti, δ-TiN, and ε-Ti2N . The solubility of nitrogen in α-Ti reaches its maximum of 23 at% at about 1050°C. But with decreasing temperature, the solubility drops very rapidly. This Ti-N phase diagram was published in 1987, the dotted line in the phase diagram meaning that the nitrogen composition is uncertain. Up to now, some new information has been pulled out to get a better understanding of the phase boundaries and obtain a more precise phase diagram.

In 1991, Dinsdale (1991) tabulated thermodynamic data for condensed phases of

78 elements as used by Scientific Group Thermodata Europe (SGTE). The data for each phase of each element are presented as expression showing the variation of G-HSER as a function of temperature. The subscript SER means “Standard Element Reference”, i.e. the enthalpies of the pure elements in their defined reference phase at 298 K and 105 Pa.

The data presented in this form are very convenient to use because all data in a database stored relative to this reference state are selfconsistent and can be combined for the calculation of chemical and metallurgical equilibria.

In his work, titanium solid phase has several possible structures such as HCP_A3,

BCC_A2, FCC_A1, and DIAMOND_A4. However, at temperature below the α/β transformation temperature, we are only concerned with the HCP and FCC structures.

The interest in nitrogen data are only for gas phase. The data for both titanium and nitrogen in the form of G-HSER are listed in Table 3.1.

The first edition of JANAF Tables was published in 1964 to critically evaluate and compile consistent tables of thermodynamic properties of propellant combustion products. Its objective is to have one single source of best available data prepared for the entire aerospace industry. In 1998, the fourth edition of JANAF Tables (Chase, 1998) is used and far transcends the original needs. It is the invaluable resource for reliable thermochemical data for modeling of complex chemical process.

The JANAF thermochemical tables consist of thermal functions and formation functions. The thermal functions consist of heat capacity, enthalpy, entropy, and Gibbs energy. The formation functions consist of enthalpy of formation, Gibbs energy of formation, and the logarithm of the equilibrium constant of formation. Both functions are temperature dependent.

Thermochemical data for stoichiometric compounds, such as pure titanium α

(HCP) and β (BCC), δ-Ti1N1 (FCC), and ε-Ti2N1 (anti-rutile structure) as well as nitrogen gas are listed the JANAF Tables (Chase, 1998).

Binnewies and Milke (1999) in their book collected the thermochemical data of elements of many inorganic and some organic compounds. Although they only included enthalpy and entropy data to a temperature of 298 K, they gave out the Cp data also. By using the Cp data it is very simple to calculate thermochemical data for other

temperatures.

All those data listed in the above references are for stoichiometric compounds only. In the Ti-N system, titanium and nitrogen form solid solutions. To assess the Ti-N phase diagram, the Gibbs energy of those phases need to be determined first. Recently

Ohtani and Hillert (1990) published an assessment of the Ti-N system in 1991. Jonsson

(1996), Zeng and Schmid-Fetzer (1996) gave out their calculation separately in 1996.

Their methods and calculations are critically reviewed by Dumitrescu et al. (1999). As

Dumitrescu pointed out there are discrepancies between their calculations, so are the phase diagrams they assessed. By comparing their phase diagrams with the published one, the data from Jonsson are chosen for the calculations in this work.

The model for α-Ti (HCP) phase is to have nitrogen occupying the octahedral interstitial vacancy sites. Vacancy and nitrogen on the interstitial sites are randomly mixed with an exception that two nitrogen atoms cannot occupy two neighboring interstitial sites in the c-direction at the same time. This can be expressed by Ti1(Va,N)0.5, where Va is for interstitial vacancy sites and N for the interstitial sites occupied by nitrogen. The Gibbs energy of α-Ti solid solution referred to one mole of formula units is given by (Jonsson, 1996):

11 GyGyGαα=+DD α + RTyyyy[]ln + ln − 4743 yy (3.1) mVaTiN22 TiN2 VaVaN N VaN

D α D α here G and G represent the Gibbs energy of pure α-Ti and α-Ti2N respectively. Ti Ti2 N

The variables yVa and yN are sites fraction of vacancies and nitrogen in the interstitial

sites. The last term − 4743yyVa N is an excess term which is added to simulate the interaction between atoms in the lattice. The value of the coefficient (-4743) is

determined by fitting the equation to the experimental data.

The model for δ-TiN (FCC) phase is presented by the formula Ti1(Va,N)1 as there is one octahedral interstitial site for each Ti atom. And the Gibbs energy is given by

(Jonsson, 1996):

GyGyGδδδ=+DD mVaTiNTiN (3.2) +++−−−RTy[][]Valn y Va y N ln y N yy Va N 47739 9877( y N y Va )

D δ D δ here GTi and GTi are the Gibbs energy of pure δ-Ti and stoichiometric TiN respectively.

Again the last term is for the interactions between lattices and the two coefficients are experimentally determined.

In Jonsson’s work (1996), the ε-Ti2N phase is treated as stoichiometric compound.

The Gibbs energy is given relative to δ phase by

DG ε =DG δ + DG δ − 63220.14 + 22.42085T Ti2 N Ti TiN (3.3)

At certain temperature, the standard Gibbs energy for each stoichiometric compound can be derived from those listed thermochemical data in Table 3.1 and should be able to be verified by data in JANAF tables (Chase, 1998). And then the Gibbs energy for solid solution as a function of composition can be calculated by those equations. The

Gibbs energy curves of α-Ti and δ-TiN solid solution phases vs. composition (G(Xn)) at

727°C (1000K) are shown in Figure 3-2. The red curve is for δ-TiN, and the blue curve is for α-Ti phase. ε-Ti2N phase is considered as a stoichiometric compound, so its Gibbs energy is a single dot in the Figure 3-2.

The common tangent line between different phases phase defined the phase composition. In Figure 3-2, the common tangent between α-Ti and ε-Ti2N gives out the solubility of nitrogen in α-Ti of 12.9 at%. Correspondingly, the equilibrium between ε-

Ti2N and δ-TiN gives the composition of δ-TiN solution of 43.5 at% nitrogen, which is far from the stoichiometric composition. These two points define the phase boundaries at this particular temperature for the T-N phase diagram. At a different temperature, Gibbs energies will change, so does the equilibrium solubility of nitrogen in α-Ti. After a series of calculation, the phase boundary data of α-Ti and δ-TiN for each particular temperature can be obtained. Table 3.2 lists the calculated solubilities of nitrogen in titanium at selected temperatures. Based on these data, one can reproduce the Ti-N phase diagram again.

In all calculated Ti-N phase diagrams, the ε-Ti2N phase is assumed unstable at high temperature, it will decompose to δ-TiN or other complex nitrides. Only at temperature below 1100°C, it is a stable phase (Figure 3-1). Theoretically, if the formation of ε-Ti2N phase at low temperature can be suppressed, then the system only involves equilibrium between α-Ti and δ-TiN phases (Figure 3-3). By applying a common tangent between the α-Ti and δ-TiN Gibbs energy curves, we can define this situation as a “new” equilibrium system. At 727°C, the solubility of nitrogen in α-Ti is

26.1 at%. This situation is so-called “supersaturation”. Again, after doing this study for different temperature, we get a series data of nitrogen solubility in supersaturation system, and a “new” phase boundary between α-Ti and δ-TiN can be established.

The comparison between this calculation and the published phase diagram

(Wriedt & Murray, 1987) has shown a good consistency. The error between this work and literature works on the α-Ti phase boundary and TiN phase boundary is less than 2 at%. Considering the uncertainty of the calculation, they show good agreement. The phase boundaries calculated from Figure 3-3 is called “supersaturation”. These lines

extended from high temperature phase boundaries, and gave out huge nitrogen solubility.

This big difference gives much encouragement for a low temperature nitriding process.

Another parameter that can be obtained from the Gibbs energy diagram is the equilibrium nitrogen pressure. As shown in Figure 3-3, the extension of the common tangent line has an intercept with the y axis at XN = 1. This intercept point is called the chemical potential of nitrogen, or the free energy change ∆G(N). It has a relationship with nitrogen pressure as

∆=−GN() RT ln() P (3.4) N2

So the common tangent line is a direct measurement of equilibrium nitrogen pressure. Table 3.2 lists some calculated data at selected temperatures. From those numbers we can see that, titanium nitrides are so stable that to suppress the formation of nitrides is very hard.

Table 3.1 G-HSER data for selected phases for nitrogen and titanium

N (GAS) -3750.675-9.45425T-12.7819Tln(T)-0.001767T2+2.6807e-9T3-32374T-1

(298.15

-7358.85+17.2003T-16.3699Tln(T)-6.5107e-4T2+3.0097e-8T3+563070T-1

(950

Ti (HCP_A3) -8059.921+133.615T-23.9933Tln(T)-4.7780e-3T2+0.1067e-6T3+72636T-1

(298.15

-7811.815+132.988T-23.9887Tln(T)-4.2033e-3T2-0.0909e-6T3+42680T-1

(900

(FCC_A1) (HCP_A3)+6000-0.1T

Table 3.2 Effect of Ti2N on the solubility of nitrogen in the α-Ti

Temperature 1000K 900K 800K

Equilibrium with Ti2N (at%) 12.9 6.2 3.5

Corresponding nitrogen pressure (Pa) 7.9×10-25 1.3×10-29 1.6×10-35

suppress the formation of Ti2N (at%) 26.1 27.4 28.6

Corresponding nitrogen pressure (Pa) 1.6×10-22 2.0×10-26 2.5×10-31

3500 3290 °C 47.4

3000 L

2500 2350 °C 15.2 20.5 28 δ–TiN 4.0 2020 °C 2000 6.2 12.5

1670°C 1500 β– Ti α–Ti 1050°C 33.3 1100 °C 1000 23 30 33 800 °C 882 °C 39 34 37.5 ε–Ti2N δ’–TiN 500 0 510152025303540455055 Ti nitrogen (at%)

Figure 3-1 The Ti-N phase diagram (Wriedt & Murray, 1987).

Figure 3-2 Thermodynamic calculation for the relationship between free energy change ∆G and conmposition xN.

Figure 3-3 Supersaturation and equilibrium nitrogen partial pressure

3.2 Gas Concentration

Following the above calculation, if we want to suppress the formation of nitrides, the thermodynamic equilibrium nitrogen pressure is the right choice. But the magnitude of this pressure is very low. So we should give it another thought.

The nitridation treatment will be done in a sealed container with a finite volume,

V. The size of V in this work is between 100 - 1000 cm3. Assuming the tube is sealed at room temperature (27°C, 300K), and using the ideal gas equation PV=⋅ N kT , the total number of molecules of a given gas in the tube can be calculated as NPVkT= / , where k is the Boltzman constant. Substituting actual values for P, V and T, we can have

N ≅ 0.1. This number means that on the average, there is less than one nitrogen molecule in the tube at any time.

To have a 10 at% nitrogen on the titanium surface, at least 1014 atoms/cm2 are needed. It will take forever to cumulate such a surface concentration at the equilibrium nitrogen pressure. The prediction of nitridation treatment at equilibrium nitrogen pressure is solely based on thermodynamic calculations: lowering the chemical potential of nitrogen below the critical value will suppress the formation of nitrides. To form a nitride layer, a high nitrogen chemical potential is necessary but this high potential will not always result in the formation of nitride. It needs a certain surface concentration of nitrogen to stabilize the nitrides. Otherwise the already formed nitrides can be adsorbed by the substrate. Nitridation is not only a surface accumulation process to increase the concentration, but also a bulk diffusion process which will decrease the surface concentration. When we consider the two processes together, a kinetic model can be

proposed to simulate the adsorption and diffusion behavior and find out suitable solution for the nitrogen concentration distribution.

3.3 Kinetic Equilibrium Nitrogen Partial Pressure

From both the calculation and experimental results, we know that, when a titanium surface is treated with thermodynamic equilibrium (Ti-TiN) nitrogen pressure, nitrogen can hardly accumulate on the surface to get enough improvement for hardness

(APPENDIX A). Therefore, a higher nitrogen partial pressure is demanded for the nitriding process. Gas nitridation process should consider not only thermodynamics but also kinetics. Because two processes, an adsorption process and an inward diffusion process, are involved here, and they are competing to form the surface compounds as well as the diffusion layer.

When a solid surface is put in a gas atmosphere, the gas molecules will collide with the solid surface and some of the molecules will adsorb on the surface. From the ideal gas law, the frequency of impingement of gas molecules, or the impingement rate Γ in atoms/cm2/s, is defined by the Hertz-Knudsen equation:

1/2 Γ=Npa ()2π MRT (3.5)

23 -1 where Na is the Avogadro number (Na = 6.022×10 mol ), p is the partial pressure of the gas species in units of Pa, and M is the molecule weight in g/mol. R is the gas constant (R

= 8.314 Jmol-1K-1) and T is the temperature in Kelvin. For instance, nitrogen gas at 25°C

(298 K) and 105 Pa, Γ = 2.9×1023 atoms/cm2/s. The impinging molecules can adsorb and cover the solid surface. The monolayer coverage time (τ) is then related to the inverse of the gas impingement rate (or flux). If assuming a solid surface has about 1015 sites/cm2, and every molecule that strikes the solid surface remains adsorbed, we have τ =Γ1015 / .

Still, for nitrogen gas at 25°C and 105 Pa, taking the impingement rate of Γ = 2.9×1023 atoms/cm2/s, the monolayer coverage time is only τ = 3.4×10-9 s. Even at a relatively low pressure such as 10-1 Pa, the surface concentration will build up in 3 ms. The surface concentration of adsorbed species is rather non-controllable.

From equation 3.5, the change from room temperature to a higher temperature won’t affect the impingement rate too much because Γ∝1/T 1/2 . For example, changing the temperature from 300K to 1300K can only reduce the Γ by a factor of 2. However, since Γ∝P and the gas pressure can be varied by several orders of magnitude, it has a dramatic effect on the impingement rate. So in most of the gas phase nitridation treatments, high nitrogen pressure will build up the surface concentration very rapidly, and this favors the formation of nitride compounds. Only at high vacuum level (10-3 Pa -

10-7 Pa) is the surface coverage time in a controllable range.

At elevated temperature, the nitrogen atoms adsorbed on the solid surface will diffuse into the bulk solid. In the nitridation practice, the diffusion process is highly concerned. In the case of nitrogen diffusing interstitially into a titanium alloy, if a titanium specimen is heated to a specific temperature at a specific nitrogen partial pressure, the nitrogen will strike the titanium surface and then be adsorbed onto it. Then it will move from the surface inward to the bulk by chemical diffusion. If the flux of the impinging species is comparable to the diffusion flux, the surface concentration of nitrogen will be stable at a certain level which can be low enough to suppress the formation of nitrides.

To simulate the nitriding process in this work, a model which is shown in Figure

3-4 has been proposed. A plate sheet material (titanium) with a thickness of L is put in a

nitrogen atmosphere, in which the nitrogen has an impingement rate of Γ. This constant rate is for the nitrogen to get into the substrate. The length and width of this plate can be considered as infinite when compared with the thickness. If the thickness (L) is big enough, this is the same as semi-infinite one dimensional diffusion model. For convenience, the initial nitrogen concentration in the bulk is set to 0. During the nitridation process, the impingement flux is also the diffusion flux at the surface, which is

dC Γ=−Dx ⋅,0 = (3.6) dx where dC/dx is the concentration gradient and D is the diffusion coefficient which takes

on the typical form of D = D0 exp( -Q RT) . In this work, the value of D is adopted from

Metin and Inal (1989). Equation (3.6) is Fick’s first law, which quantitatively describes the diffusion process with the relationship with the concentration. The diffusion profile of a substance into a sheet, at a constant flux (Γ) and with an initial constant concentration

(C0 = 0), has already been solved by others and is given by (Moore, 2001):

Γ−4Dt x2  x Cxt(,)=−⋅ exp xerfc (3.7) DDtπ 4 4Dt where x is the distance from the center of the sheet and t is the amount of time the material is exposed to the gas atmosphere. The impingement rate Γ, which was discussed earlier, is a function of nitrogen pressure. And the diffusion coefficient, D is a function of temperature. So if nitrogen pressure, the titanium heat treatment temperature and treatment time are selected, we can solve those equations to get the nitrogen distribution along the cross-section.

Figure 3-5 shows the simulated nitrogen depth profile in titanium at 860°C at different nitrogen pressure for a treatment time of 100 h. Since Γ ∝ P and Cxt ( , ) ∝ Γ , so the nitrogen concentration at a given position and given time is proportional to the nitrogen pressure (Cxt ( , ) ∝ P). Figure 3-5 shows that the nitrogen partial pressure has a huge impact on the diffusion profile. At 1.0×10-3 Pa, the surface nitrogen concentration reaches more than 100 at%, which is not realistic because the nitrides will form as soon as the nitrogen concentration reaches the solubility at that temperature. On the other hand, at 1.0×10-5 Pa, 100 h treatment only accumulates less than 2 at% nitrogen on the surface.

Only the nitrogen pressure of 1.0×10-4 Pa gives a satisfactory surface concentration and an acceptable thickness of diffusion layer.

From equation (3.7), the surface nitrogen concentration is

Γ 44Dtt Ct(0, ) ==Γ (3.8) D π π D

This means that surface nitrogen concentration increases following a parabolic law. After setting the nitrogen pressure of 10-4 Pa, the nitrogen diffusion profile is calculated for different treatment time. Figure 3-6 shows those calculated profiles. Notice that a time between 30 and 100 h should form a satisfactory surface concentration and an acceptable thickness of the diffusion layer.

Γ Γ

x L/2

Figure 3-4 The model to simulate the diffusion profile

Figure 3-5 Nitrogen diffusion profile at different pressure

Figure 3-6 Nitrogen diffusion profile for different treatment time

3.4 Nitrogen Pressure for Si3N4/Si Powder Pack

From the calculation in Section 3.3, a nitrogen partial pressure of the order of 10-4

Pa is suitable to nitride titanium samples. However, this nitrogen pressure can not be achieved by diluting the pure nitrogen gas with an inert gas such as argon. It is simply because both the nitrogen gas and argon gas, with the highest purity grade, still have a ppm level of impurities, which have partial pressures higher than 10-2 Pa with the base pressure of 105 Pa. It is very hard to stop the contamination and have a truly low pressure of nitrogen. Even with the highly purified gas mixtures, controlling the dilution system to achieve such low partial pressure of nitrogen may not be practical. Some other nitrogen sources need to be created.

An ultrahigh vacuum (UHV) system can be deployed to study the nitridation process. Blush (2004) is working on that system and has made some progress to nitride

Grade 4 commercial pure titanium alloy. But the capital investment of UHV system is high, and it may not suitable for mass production.

Inspired by the reaction between Ti and TiN, when other metal nitride and corresponding metal are in thermal equilibrium, a certain nitrogen partial pressure can also be defined. The nitrogen pressure depends on the free energies of both solid phases.

When considering the commercial availability, some nitrides/metal combinations, such as

CrN/Cr, Si3N4/Si, and VN/V, are able to generate different nitrogen partial pressure at reasonable temperature range. Powder forms of those chemicals are commercially available and they are not expensive. The mixture of metal nitride powder and corresponding metal powder is called “powder pack”.

Assuming these nitrides and metals are all stoichiometric compounds, the

equilibrium nitrogen partial pressure on the surface of powder packs at selected temperatures can be easily calculated from thermodynamic data. For example, the reaction between Si3N4 and Si is

Si3N4 (s) ÅÆ 3Si (s) + 2N2 (g) (3.9)

The reaction rate is expressed as

KPaa= 23/ (3.10) NSiSiN234 where P is the pressure for gases and a is the chemical activity for solids. Commonly, the chemical activity of solids is set as unity, so

KP= 2 (3.11) N2

Also the free energy change for this reaction is

∆=GG32DDD + G − G = RTK ln (3.12) Si N234 Si N

The value of °G for all compounds can be found in the JANAF thermodynamic database (Chase, 1998). The calculated nitrogen pressure for Si3N4/Si powder pack at selected temperature is shown in Figure 3-7. The same simple calculation can be easily transferred to VN/V powder pack and CrN/Cr powder pack. The calculated results are also shown in Figure 3-7.

-4 To achieve the desired 10 Pa nitrogen partial pressure, Si3N4/Si powder pack at temperature around 1100K (830°C) is suitable. This temperature is near the designed heat treatment temperature for titanium. For VN/V powder pack, a temperature around 1300K

(1030°C) is needed to have this nitrogen pressure. This temperature is much higher than the α-β transus temperature of titanium. So VN/V powder pack can not be heat together with a titanium sample. They have to be treated separately to achieve the desired nitrogen pressure and the diffusion profile. CrN/Cr powder pack at 830°C will have a nitrogen

pressure of 102 Pa, which will definitely form nitride compound on the surface. But at lower temperature CrN/Cr powder pack also can reach the 10-4 Pa. Low temperature treatment has economical benefit, CrN/Cr powder pack is another good choice for nitridation experiments. Again, the treatment will involve at least two heating zones, one is for CrN/Cr powder pack to generate the desired nitrogen pressure and the other is for the titanium part to have the designed diffusion profile.

Figure 3-7 Equilibrium nitrogen pressure generated by several powder packs

3.5 Sticking Coefficient

Gas nitridation not only deals with thermodynamics but also kinetics. At the surface of titanium, an adsorption process and an inbound diffusion process are competing to form certain surface nitrogen concentration. In Section 3.3, when assuming every atom striking the surface will stick onto it, a kinetically suitable nitrogen pressure range has been calculated to have a 15 at% of nitrogen on the surface without forming any nitride phase.

But actually, the assumption that every atom striking the surface will stick onto it is not reliable. At least, if the surface is almost full of adsorbed atoms, the following impingement will result only a little additional adsorption coverage. The probability that a striking atom will be adsorbed on the surface is called the sticking coefficient (Hayward

& Trapnell, 1964). A lot of work has been done on the sticking coefficient for gas molecules on different substrates. The results show that, with a smaller sticking coefficient, it does need a higher nitrogen pressure to get the same adsorption rate. The modified surface flux equation then is expressed as (Luth, 1993)

1/2 Γ=απpMRT()2 (3.13)

The α in the equation is the sticking coefficient. Several important factors affect the quantity α:

(i) Activation energy: In many cases the adsorption process is an activated

process. Only those atoms having impact energy higher than the

activation barrier Eact can stick to the surface. Or it can be expressed as

α ∝−exp(ERTact / ) .

(ii) Steric factor: Not every atom possessing the required activation energy

will necessarily be adsorbed on the substrate surface. The electronic

orbitals of impinging atoms must have a particular interaction with the

dangling-bond orbitals of the surface. So the adsorption potential varies

locally along the surface due to the atomic structure of the substrate.

(iii) Energy transfer: During the adsorption, the incident atom must transfer

part of its kinetic energy to the substrate. Otherwise it will bounce back.

(iv) Site availability: The impinging atom can only be adsorbed on a site

which is not occupied by other atoms. The more sites are occupied, the

fewer particles can be adsorbed. So the sticking coefficient is a function

of surface coverage.

The experiments in APPENDIX B show that under the kinetic equilibrium nitrogen pressure of 10-4 Pa, the surface nitrogen concentration of treated samples is much lower compared with the calculated model. It clearly showed that α<<1. In order to have the predicted nitridation result, a much higher nitrogen pressure is needed. For

Si3N4/Si powder pack, a temperature higher than 1200°C is needed to get nitrogen pressure into the range of 10-1 Pa. But such a high temperature is not feasible for some furnaces and also it’s not economic. High temperature also generates high silicon vapor pressure, which is a potential contamination source. CrN/Cr powder packs, which can have a high nitrogen pressure at low temperature, should be chosen to conduct the nitridation experiments. Since the sticking coefficient is not certain, a wide nitrogen pressure range need to be attempted to find the suitable treating parameters.

3.6 Nitrogen pressure for CrN/Cr powder packs

The nitrogen pressure generated from CrN/Cr powder pack is predicted by the thermodynamic data. At high temperature, when the reaction (3.14) is in equilibrium, the nitrogen pressure is defined by P(N2) = exp(∆G/RT) for CrN/Cr powder pack, where ∆G is the molar formation energy of CrN. Again the thermodynamic data can be found in

JANAF tables and other reference books. The nitrogen pressure of CrN/Cr powder pack calculated at selected temperature is listed in Table 3.3.

2CrN (s) ÅÆ 2Cr (s) + N2 (g), (3.14)

Binnewies and Milke (1999) have collected the thermal data including heat capacity, enthalpy and entropy for thousands of common compounds. From the

C thermodynamic equations HCdT= , SdT= p , and GHTS= − , the molar ∫ p ∫ T formation energy data for CrN, Cr, and N2 compounds can be calculated. By considering the reaction above, the nitrogen pressure can be derived. The calculated nitrogen pressure is also listed in Table 3.3. Comparing this result with the result got from JANAF tables, we can see the nitrogen pressures for CrN/Cr powder pack between these two calculations have a good agreement.

All these data are for stoichiometric compounds only. Just like TiN, the CrN is not a stoichiometric compound. The non-stoichiometry of CrN will affect the molar formation energy and the equilibrium nitrogen pressure. Frisk (1991) has compared previous works and gave out some equations to calculate the molar energy as a function of composition. Same as the Ti-N system, the whole Cr-N phase diagram can be accessed by doing the thermodynamic calculations. And equilibrium nitrogen pressure at various

conditions can all be calculated. This result shows a good agreement with Binnewies and

Milke’s book, but still differs by a factor of ~1.5.

Recently some experimental data have been observed that may or may not be consistent with the old calculation model. There is no reliable experimental data clearly showing the equilibrium nitrogen pressure for nitride compounds. The agreement between those calculations only confined the pressure in a certain range. This difference in pressure will affect the kinetic predictions in a small level.

Table 3.3 Calculated nitrogen partial pressure for CrN/Cr powder pack

Equilibrium nitrogen pressure (Pa) from references T(°C) By Binnewies and Milke By Frisk By JANAF

527 8.55×10-3 4.44×10-3 8.63×10-3

625 0.353 0.204

627 0.377 0.219 0.375

650 0.801 0.473

675 1.74 1.05

700 3.63 2.22

727 7.71 4.79 7.55

750 14.2 8.87

775 26.7 16.8

800 48.7 30.9

827 90.3 58.3 87.1

860 185 120

927 698 449 667

3.7 Nitrogen pressure for Cr2N/Cr powder packs

From Cr-N phase diagram (Frisk, 1991), besides Cr and CrN there is another solid phase: Cr2N. Same as CrN/Cr powder pack, the Cr2N/Cr powder pack should also be able to generate a certain nitrogen pressure. The reaction in the powder pack is

2 Cr2N (s) ÅÆ 4 Cr (s) + N2 (g) (3.15)

From the thermodynamic data, same calculation of nitrogen pressure has also been done. Table 3.4 lists the calculated nitrogen pressures. The result from Binnewies and Milke has a good agreement with that from Frisk. But their result is one order of magnitude lower than the result from JANAF tables. This discrepancy made it very difficult to define the true nitrogen pressure for the Cr2N/Cr powder pack. So only by a series of heat treatments with powder packs at different temperature can we obtain ideal nitridation parameters. Some other experiments, such as use mass spectrometry in high vacuum system can measure the nitrogen pressure of powder pack. But it is not covered in this research.

When comparing Table 3.3 and Table 3.4, it is clearly shown that the CrN/Cr and

Cr2N/Cr powder packs give different equilibrium nitrogen pressure at the same temperature. But the nitrogen pressure is calculated solely based on the mass equilibrium between CrN and Cr powder pack, or Cr2N and Cr powder pack. This is different than the actual chemical reaction. When mixing CrN and Cr powders, there is a reaction to form

Cr2N:

CrN + Cr Æ Cr2N (3.16)

The free energy change for (3.16) is negative, so the chemical reaction favors forming Cr2N. If there is enough Cr powder and heating the powder pack for a sufficient

time, all CrN powder will convert to Cr2N powder and then the equilibrium nitrogen pressure will be the same as Cr2N/Cr powder pack.

Table 3.4 Calculated nitrogen partial pressure for Cr2N/Cr powder pack at different temperatures

Equilibrium nitrogen pressure (Pa) from references T(°C) By Binnewies and Milke By Frisk By JANAF

527 4.88×10-5 6.61×10-5 3.37×10-4

625 2.63×10-3 3.75×10-3

627 2.83×10-3 4.03×10-3 1.91×10-2

650 6.33×10-3 9.06×10-3

675 1.45×10-2 2.08×10-2

700 3.17×10-2 4.58×10-2

727 7.07×10-2 0.102 0.470

750 0.135 0.195

775 0.264 0.380

800 0.500 0.715

827 0.963 1.36 6.31

860 2.05 2.87

927 8.34 11.3 54.0

3.8 Summary

Heat treatment with thermodynamic equilibrium nitrogen pressure will ensure that no nitride forms during nitridation. But the equilibrium nitrogen pressure is extremely low, and there is no nitrogen accumulation on the work piece. By considering both the surface impingement and bulk diffusion processes, a kinetic nitrogen pressure of 10-4 Pa has been calculated and the method of generating such low nitrogen pressure by nitride powders has been introduced. With the chemical reaction of nitrides and corresponding metal, a certain nitrogen pressure can be determined by thermodynamics.

Work Cited

Binnewies, M., & Milke, E. (1999). Thermochemical Data of Elements and Compounds.

New York: Wiley-Vch.

Blush, J. (2004). High Vacuum Gas Phase Nitridation of Titanium via Kinetic Control.

Unpublished Master Thesis, Case Western Reserve University, Cleveland.

Chase, M. W. J. (1998). NIST-JANAF Thermochemical Tables (4th ed.): American

Chemical Society.

Dinsdale, A. T. (1991). SGTE Data for Pure Elements. CALPHAD, 15(4), 317-425.

Dumitrescu, L. F. S., Hillert, M., & Sundman, B. (1999). A reassessment of Ti-C-N

based on a critical review of available assessments of Ti-N and Ti-C. Zeitschrift

Fur Metallkunde, 90(7), 534-541.

Frisk, K. (1991). A Thermodynamic Evaluation of the Cr-N, Fe-N, Mo-N and Cr-Mo-N

Systems. Calphad-Computer Coupling of Phase Diagrams and Thermochemistry,

15(1), 79-106.

Hayward, D. O., & Trapnell, B. M. W. (1964). Chemisorption (2nd ed.). Washington:

Butterworths.

Jonsson, S. (1996). Assessment of the Ti-N system. Zeitschrift Fur Metallkunde, 87(9),

691-702.

Luth, H. (1993). Surfaces and interfaces of solids. New York: Springer-Verlag.

Metin, E., & Inal, O. T. (1989). Kinetics of Layer Growth and Multiphase Diffusion in

Ion- Nitrided Titanium. Metallurgical Transactions a-Physical Metallurgy and

Materials Science, 20(9), 1819-1832.

Moore, R. (2001). Kinetic Processes in Materials, from

http://pruffle.mit.edu/~ccarter/3.21/Lecture_11/Lecture_11.html

Ohtani, H., & Hillert, M. (1990). A Thermodynamic Assessment of the Ti-N System.

Calphad-Computer Coupling of Phase Diagrams and Thermochemistry, 14(3),

289-306.

Wriedt, H. A., & Murray, J. L. (1987). Assessed Ti-N Phase Diagram (Condensed

System). Bulletin of Alloy Phase Diagrams, 8(4), 378.

Zeng, K. J., & SchmidFetzer, R. (1996). Critical assessment and thermodynamic

modeling of the Ti-N system. Zeitschrift Fur Metallkunde, 87(7), 540-554.

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Chapter 4 EXPERIMENTAL PROCEDURES

4.1 Selection of Materials

ASTM Grade 4 (commercial pure titanium, CP) and ASTM Grade 5 (Ti-6Al-4V,

Ti64) alloys are studied in this work for nitridation experiment. Two kinds of samples were treated: small coupons were made of both CP titanium and Ti-6Al-4V; tensile bars

(“dog bone”) were made of Ti-6Al-4V sheet. Coupon samples evaluated in this work were provided by the Swagelok Company. Their thickness is about 2 mm and they were all sectioned from a bar stock with a diameter of 9.6 mm (3/8 in). The Ti-6Al-4V sheet was bought from Vulcanium Metals International (Northbrook, IL). The tensile bars were machined from the sheet with the dimension defined in ASTM standard E8. Table 4.1 lists the chemical compositions of the materials studied.

In order to control the nitrogen pressure, a new technique, called “powder pack” technique has been introduced. The mixture of metal and its nitride, all in the powder form, is called “powder pack”. Based on the calculation in Chapter 3, at certain elevated temperatures, when the metal nitride is in equilibrium with the corresponding metal, a well-defined nitrogen pressure is generated and maintained. To ensure equilibrium, both nitrides and metal should be in powder form and be mixed thoroughly. Several types of powder packs were used in this work: Ti and TiN powders, Si and Si3N4 powders, Cr and

CrN powders, and Cr and Cr2N powders. Detailed information of these powders are listed in Table 4.2.

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Table 4.1 Chemical composition for commercial pure titanium and Ti-

6Al-4V alloy (in weight percent).

Elements C N O Fe Al V Ti

CP titanium 0.08 0.05 0.40 0.50 - - Balance

Ti-6Al-4V 0.08 0.05 0.20 0.25 6.2 4.5 Balance

Ti-6Al-4V Sheet 0.012 0.006 0.16 0.12 6.19 3.87 Balance

Table 4.2 Metal and metal nitride powders used in this work

powder source purity

Ti Goodfellow 99.95 wt%

TiN Goodfellow 99.5 wt%

Si Alfa Aesar 99 wt%

Si3N4 Alfa Aesar 98 wt%

Cr Alfa Aesar 99.5 wt%

CrN Alfa Aesar 98 wt%, mixed with Cr2N phase

Cr2N Alfa Aesar With CrN phase up to 10 wt%

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4.2 Heat Treatment

The samples used for heat treatment had a disk shape with a diameter of 9.6 mm and a thickness of 2 mm, sectioned from bar stocks provided by Swagelok Company. All samples were polished using SiC paper up to 4000 grit and ultrasonically cleaned before heat treatment.

The heat treatments were conducted in fused silica tubes (The Quartzplus Inc.,

Brookline, NH) with a high temperature furnace. The softening point of fused silica tubes is greater than 1700°C, so a hydrogen/oxygen torch was used to make the seal. After closing one end of the tube, the samples, the powder pack and a titanium getter were put into the tube at the position showed in Figure 4-1. Then the tube was connected to an argon flushing/vacuuming system. A rotary pump was used to evacuate the tube down to a base vacuum of 1 Pa. Then the argon gas was introduced into the tube to flush out residual air. This vacuuming-flushing cycle was repeated at least 3 times to remove the air and finally the tube is evacuated to 1 Pa. During this pumping procedure, the whole length of the tube was heated homogeneously by a natural gas torch or an electric heating tape up to a temperature greater than 300°C. Any gas or water molecule adsorbed on the tube wall will be baked out. After the final evacuation, the open end of the tube was again sealed by hydrogen/oxygen torch. Inside the tube are the titanium sample and powder pack and the getter in a defined closed system.

Several tube furnaces were used in this work. A Mellen (Concord, NH) furnace with three heating zone controller can minimize the temperature gradient inside the furnace. A Linderburg furnace has a 500 mm (18 in) heating zone which can treat large samples. It has only one heating controller. Some other small tube furnaces were used to

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control the temperature differences. All furnaces can reach temperature up to 1100°C.

And the heat treatments are taken at temperatures usually below 900°C.

Figure 4-2 shows the heating protocol used in this work. There are three furnaces to control the temperature of powder pack, getter and the treating sample, respectively and independently. At the beginning of heat treatment, the getter and powder pack are heating up to desired temperature. This step usually takes 24 h to remove any residual reactive gas species and ensure that the reaction in the powder pack has reached equilibrium. Then the getter is cooled down to room temperature and will have no effect to the ongoing nitridation. The gas phase in the tube will be the argon at the base pressure and the nitrogen at a certain partial pressure defined by the powder pack. At last, the sample is heated up to the desired temperature to finish the nitriding process. The treatment time can last from 16 to 240 h depending on the need.

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Figure 4-1 Heat treatment setup

105

Figure 4-2 Heating protocol

106

4.3 Characterization Techniques

Light optical microscopy, X-ray diffraction (XRD), and scanning electron microscopy (SEM) were the main techniques used to analyze the nitrided samples. In addition, X-ray photoelectron spectroscopy (XPS), also known as electron spectroscopy for chemical analysis (ESCA), was used to investigate the chemical composition of the surfaces. Auger electron spectroscopy (AES) was used to analyze element distribution along cross-section. Surface hardness measurement was also employed.

4.3.1 Light optical microscopy

A Buehler Versamet 3 optical microscope was used to examine the microstructure of the metallographic specimens. A CCD camera was connected to the microscope for image acquisition. The magnification is from 50× to 1000×. Usually the treated surface is examined. Cross-section samples can be prepared by cutting, grinding and etching, which is same as the SEM sample preparation method (section 4.3.5)

4.3.2 Microhardness measurement

The mechanical properties of the nitrided layers were characterized by surface microhardness and hardness depth profile measurements. The surface hardness of the nitrided surfaces was measured using a Buehler Micromet 2100 microhardness tester.

The load varied from 1000 g to 10 g. The holding time at the peak load is 10 s which is according to ASTM B721-91.

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Figure 4-3 Schematic illumination of Vickers pyramid diamond indenter indentation; d1 and d2 are diagonal lengths and h is the penetration depth.

The Vickers Diamond Pyramid harness number is the applied load (kgf) divided by the surface area of the indentation (mm2)

HV=≅2 P sin(136D / 2) / d22 1.8544 P / d (4.1) where P is the load in kilogram; d1 and d2 are the length of indentation two diagonals in mm, d is the arithmetic mean of the two diagonals, d = (d1 + d2) / 2. The Vickers

Diamond Pyramid indenter is ground in the form of a squared pyramid with an angle of

136obetween faces. The depth of indentation is about 1/7 of the diagonal length. When calculating the Vickers Diamond Pyramid hardness number, both diagonals of the indentation are measured and the mean of these values is used in the above formula with the load used to determine the value of HV.

The hardness depth profile measurements were conducted by using TriboScope® system (Hysitron Inc., Minneapolis, MN), which is designed for nanoindentation and

108

mechanical properties testing. A Berkovich diamond tip (Figure 4-4) is used to indent a surface and immediately image the indentation. Also during indentation, the indentation depth versus time and the load versus time are recorded simultaneously. A standard load/depth curve can be displayed once the indentation is made (Figure 4-5). Hardness and modulus can be determined from the load/depth curve.

Cross-section sample were made by sectioning and polishing. Then nonoindentation were made perpendicular to the nitrided surface. The microhardness is calculated by TriboScope® software package.

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Figure 4-4 SEM image of the Berkovich diamond tip

/nm

Figure 4-5 A typical load/depth curve recorded during nanoindentation

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4.3.3 XRD Analysis

4.3.3.1 Lattice spacing measurement

XRD technique was used to identify the phases present, determine the lattice parameters, and measure the residual stress at the surface. In this work, X-ray diffraction patterns were obtained with XGEN-4000 (Scintag). This XRD equipment has a Scintag

X-1 diffractometer equipped with a high-purity Ge solid state detector; monochromatic

Cu Kα (Cu Kα1 λ = 0.154056 nm) radiation was used. The tube voltage is set at 45 kV and the current at 40 mA are used in this work. The software package DMSNT was used to control the diffractometer, acquire raw data and for analysis of diffraction peaks. A database of the Joint Committee for Powder Diffraction Standards (JCPDS) with search software was available on the computer-based system to help interpret the results.

For XRD, diffracted beams can only exist in special directions that satisfy the

Bragg condition. If one considers “reflection” of waves at 2D layers of lattice points, the

Bragg condition for constructive interference can be described as

2sind θ = λ (4.2) where d is the space between the two crystal planes that contribute to the diffraction peak at θ position, and λ is the wave length of the X-ray source.

When nitrogen is incorporated into the titanium, the lattice parameter will increase with increasing nitrogen concentration. An empirical equation is given by Bars

(1983), which shows that the lattice parameters, a and c, increase linearly with increasing nitrogen concentration. Since λ is constant, the increase in d spacing will result in a decrease in θ, which will show as a peak shift towards lower angles in the XRD pattern.

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The microhardness is also related with nitrogen concentration. So the peak shift is a visualization of microstructure change and hardness increase.

Two geometries were used for the diffraction analysis. The most common geometry was the conventional θ - θ geometry. In this geometry, the sample is held stationary with its surface in a horizontal plane, while the detector and the X-ray tube move in opposite directions above the center of the specimen. The focal point of the X- ray beam remains at the same location on the sample surface.

For the study of thin crystalline films on the surface, the conventional θ - θ technique loses its sensitivity because the X-rays generally penetrate several micrometers into the substrate. In a conventional diffractometer, the effective depth of penetration of

X-rays varies as sinθ / µ , where µ is the linear mass-absorption coefficient of the sample.

Thus, at low Bragg angles, the penetration depth is small, and at a Bragg angle of 90°, it is at its maximum. If the sample surface is placed at a low glancing angle to the incident

X-ray beam, penetration of the X-rays into the sample will be decreased by an order of magnitude. The glancing angle XRD (GAXRD) geometry was used for this purpose. X- rays pass through a suitable slit system and are made to fall on the sample at a fixed glancing angle α, while the detector on the 2θ axis scans the XRD pattern. The diffracted beam optics are modified to parallel optics by removing the conventional slits and replacing them with a set of soller collimators. The conventional powder methods are applicable in analyzing the GAXRD patterns. Typically the incidence angle α is varied from 0.5° to 5°.

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4.3.3.2 Residual stress measurements

XRD stress measurements can be a powerful tool for failure analysis or process development studies. Quantifying the residual stresses present in a component, which may either accelerate or arrest fatigue or stress corrosion cracking, is frequently crucial to understanding the cause of failure. Successful machining, grinding, shot peening, or heat treatment may hinge upon achieving not only the appropriate surface finish, dimensions, case depth or hardness, but also a residual stress distribution producing the longest component life. The engineer engaged in such studies can benefit by an understanding of the limitations and applications of XRD stress measurement.

Stress is an extrinsic property, and must be calculated from a directly measurable property such as strain, or force and area. In X-ray diffraction methods, strain is measured in the crystal lattice, and the residual stress producing the strain is calculated, assuming a linear elastic distortion of the crystal lattice.

XRD residual stress measurement is applicable to fine grained crystalline materials that produce a diffraction peak of suitable intensity, and are free of interference in the high back-reflection region for any orientation of the sample surface. Surface measurements are nondestructive. Both the macroscopic residual stresses and line broadening caused by microstresses and damage to the crystals can be determined independently.

Figure 4-6 shows the plane-stress elastic model. In the exposed surface layer, a condition of plane stress is assumed to exist. That is, a stress distribution described by principal stresses σ1 and σ2 exists in the plane of the surface, and no stress is assumed perpendicular to the surface, i.e. σ3 = 0. However, a strain component perpendicular to

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the surface ε3 exists as a result of the Poisson's ratio contractions caused by the two principal stresses.

In Figure 4-6, the angle ψ, defining the orientation of the sample surface, is the angle between the normal of the surface and the incident and diffracted beam bisector.

The strain in the sample surface at an angle φ from the principal stress σ1 is then given by the following equation (Hilley, 1971):

1+νν2  εφψ=−+σψ φ sin  ( σσ12 ) (4.3) EE  where ν is the Poisson’s ratio and E is the elastic modulus. If dφψ is the spacing between the lattice planes measured in the direction defined by φ and ψ, the strain can be expressed in terms of changes in the linear dimensions of the crystal lattice:

εφψ=∆dd//000 =() d φψ − d d (4.4) where d0 is the stress-free plane spacing. Substitution into equation (4.3) yields,

1+νν2  ddφψ=−++σψ φ 00120sin  dd ( σσ ) (4.5) EE()hkl  () hkl

By changing the ψ tilt angle, the measured dφψ shows a linear relationship to

2 2 sin ψ, and from the slope of the dφψ vs. sin ψ plot, σφ can be calculated as,

11+ν ∂dφψ σφ =  2 (4.6) Ed()hkl 0 ∂ sin ψ

2 2 and the intercept of the dφψ vs. sin ψ plot at sin ψ = 0 is:

ν ddφ 00=−1() σσ 12 + (4.7) E ()hkl

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If the lattice spacing is determined precisely at two extreme values of ψ, typically

0° and 45°, the method to calculate the stress is called the two-angle technique. If the lattice spacing is determined for multiple ψ tilts, and the stress is calculated from the slope of the least-squares fitted line, the method is called the sin2ψ technique (Hilley,

2 1971). The primary advantage of the sin ψ technique is in establishing the linearity of dφψ as a function of sin2ψ to demonstrate the possibility of X-ray diffraction residual stress measurements.

Figure 4-6 Plane-stress elastic model. dφψ marks the plane stress at a free surface showing the change in lattice spacing from dφ0 with tilt ψ for a uniaxial stress σφ parallel to one edge. (Prevey, 1986)

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4.3.4 XPS and AES

X-ray Photoelectron Spectroscopy (XPS) or Electron Spectroscopy for Chemical

Analysis (ESCA) is a technique used to study the surface chemical structures of inorganic and organic materials. When X-rays bombard a material, the photon interaction results in the ejection of electrons which may be photoelectrons or Auger electrons. The kinetic energy distribution of the ejected electrons is analyzed by a high resolution electrostatic spectrometer. The energy of the incident photon (x-ray) minus the kinetic energy of the photoelectron line yields its binding energy.

XPS is very sensitive to the surface atoms. Basically it is used to determine the surface concentration. Also it can measure the impurities deposited on the surface during heat treatment. Combining with XRD analysis, detailed information of surface phases and compositions can be obtained. With argon sputter etching, nitrogen concentration profile also can be achieved in the nitrided samples. The depth profile could be used to calculate the diffusion coefficient and other parameters.

In this work, the XPS spectra were obtained using a Perkin-Elmer PHI-5600 system. Monochromatic Al Kα radiation (1486.6 eV) was used to irradiate the sample.

The X-ray generator was operated at 250 W (15 kV and 17 mA). The specimens were analyzed using a spherical capacitance analyzer (SCA) at an electron take-off angle of

45°. The analyzer energy resolution (∆E / E) was about 1 eV. Argon ion sputter-etching was used to remove surface contaminants, which is particularly useful when removing adventitious hydrocarbons and the native oxides from surfaces. To produce the ion beam,

Ar gas is leaked into the ion gun source chamber and ionized by electron bombardment.

The resulting Ar+ ions are extracted from the source, accelerated and focused onto the

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sample surface by a set of electrostatic lenses. In certain circumstances it is preferable to have a low ion beam energy in order to minimize surface damage hence maximize the analysis of the “true” surface. In this work, the energy is usually set at 4 keV, and the sputter rate was about 3.6 nm/min based upon calibration with Ta2O5.

In Auger spectroscopy, the excitation source is a finely focused electron beam.

Upon sample bombardment, a transfer of energy occurs which excites a core electron into an orbital of higher energy. Once in this excited state, the atom has two possible modes of relaxation: emission of an X-ray, or emission of an Auger electron. In both processes, the emitted particle will have an energy characteristic of the parent element. An energy spectrum of the detected electrons shows peaks assignable to the elements present. The ratios of the intensities of Auger electron peaks can provide a quantitative determination of surface composition.

In this work, AES spectra were obtained by using a PHI 680 system with field emission gun. Very small spot sizes are available, down to 7 nm for imaging. Inert gas sputtering (using a PHI-04-303 ion gun) is used to clean surface contamination from samples and to remove material from a small area on the surface for depth profiling.

Several modes of operation are available to the user, including survey, line, profile, and elemental mapping.

4.3.5 SEM

SEM was used to observe the surface morphology. If nitrides formed on the surface during heat treatment, SEM can be used to investigate the surface morphology, particle shape and size, compound layer and diffusion layer morphology and thickness, crystal distribution, and growth direction. Also SEM is helpful in measuring the size of

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small microhardness indents that can give more accurate data for the hardness when small load is used.

A Hitachi S-4500 scanning electron microscope (SEM) and a Philips XL30

Environmental SEM were employed to reveal the surface morphology of Ti samples. The

Hitachi S-4500 SEM is equipped with a field-emission gun, two secondary electron detectors, a backscatter detector, and an infrared chamber scope. In addition, it has a

Noran XEDS (X-ray energy-dispersive spectrometry) system. The microscope is capable of operating at a spatial resolution of 1.5 nm at 15 keV energy.

For the cross-section study of Ti samples, the disk samples are mounted using thermosetting resin (Buehler, phenolic powder), with the sample thickness direction parallel to the mounting plane. The process is conducted under the high temperature and high pressure provided inside the mounting machine (Simplimet 2000, Buehler). The mounted samples are cut using a SiC blade (machine model Struers Accutom-50) to reveal the cross section of the Ti samples. Then the samples are ground and polished using SiC paper up to 4000 grit. Due to the insulation property of mounting materials, all samples are coated with a thin Au layer before being put inside the SEM.

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Work Cited

Bars, J.-P., David, D., Etchessahar, E., & Debuigne, J. (1983). Titanium alpha-Nitrogen

Solid Solution Formed by High Temperature Nitriding: Diffusion of Nitrogen,

Hardness, and Crystallographic Parameters. Metallurgical Transactions A, 14A,

1537-1543.

Hilley, M. E. (1971). Residual Stress measurement by X-ray Diffraction. Warrendale, PA:

SAE J784a, Society of Automotive Engineers.

Prevey, P. S. (1986). X-Ray Diffraction Residual Stress Techniques. In K. Mills (Ed.),

Metals Handbook (9th ed., Vol. 10, pp. 380-392). Metals Park, OH: American

Society for Metals.

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Chapter 5 CrN/Cr2N/Cr POWDER PACK TREATMENT

5.1 CrN/Cr Powder Pack Treatment

According to the discussion in Chapter 3, CrN/Cr powder packs were selected to perform the nitriding treatments. The treatment procedure is described in Chapter 4.

Grade 5 titanium alloy (Ti-6Al-4V) has much more market prospect than commercial pure titanium. So the heat treatments in this Chapter are all done for Ti-6Al-4V alloy only.

In the treatment, powder pack temperature, heat treatment time, and sample temperature are the controlled parameters.

Figure 5-1 displays the XRD patterns for Ti-6Al-4V samples treated with powder pack for 24 h. The samples heat treatment temperature is 860°C for all four experiments, while the powder packs are treated at different temperatures. When the powder pack was

750°C, the Ti peaks for treated sample only shows a small shift compared with annealed sample. Although the nitrogen pressure for CrN/Cr at this temperature is 8.9 Pa, there is no formation of nitrides. By increasing the temperature of powder pack to 775°C the nitrogen pressure will reach 17 Pa. After 24 h treatment, the titanium peaks shifted more, which indicate more nitrogen atoms diffused into titanium. Still, no nitrides exist on the surface. Then increasing the temperature of powder pack to 800°C, at which the nitrogen pressure reaches 31 Pa, the Ti2N peak appeared in the pattern along with titanium peaks which shifted towards lower angle by 0.14° - 0.18°.

Since the titanium samples are all at 860°C, the diffusion coefficient of nitrogen is the same. With a higher nitrogen pressure, the impingement rate is higher too. For the same treatment time, surface concentration is built up faster on the surface with CrN/Cr

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powder pack at a higher temperature. When the nitrogen concentration reached the limit of solubility, it results in the formation of nitride. Although both the high nitrogen concentration solution layer and the nitrides phases will give significant hardening effect for the surface, the formation of nitride phase has detrimental effect on the material ductility.

Figure 5-2 compares the XRD patterns for the Ti-6Al-4V samples (860°C) treated with CrN/Cr powder pack (750°C) for various times. After treatment for 24, 72, and 120 h, the titanium peaks (100) and (101) basically show no change. While the 2θ position for titanium (002) peak at about 38.3o, which corresponds to the basal plane, shifted a little bit to the low 2θ value, and the shape is gradually broadened. For much longer treatment time (240 h), the nitride formed on the surface and occupied a small volume fraction. We

o can see (111) peak of Ti2N appeared at about 39.3 . The equilibrium nitrogen pressure for

CrN/Cr powder pack at 750°C is 8.9 Pa, which is 3.5 times less than that for powder pack at 800°C (31 Pa), and the time needed to form the nitride is about 10 times longer.

Figure 5-3 shows the XRD patterns for the Ti-6Al-4V samples after a longer treatment time and the formation of nitrides. When powder pack is at 750°C, with an equilibrium nitrogen pressure of 8.9 Pa, it took 240 h to form Ti2N phase on the surface.

For the treatment less than 240 h, only titanium peaks showed up in the pattern (see

Figure 5-2). The equilibrium nitrogen pressure is 17 Pa when powder pack is at 775°C.

Then after 72 h treatment, Ti2N phase formed. If increasing the powder pack temperature to 800°C, only 24 h is needed for the Ti2N phase to form. The nitrogen pressure is 31 Pa for the CrN/Cr powder pack at 800°C. The relationship between nitrogen pressure and

2 the time to form Ti2N phase can be roughly considered as P × t = constant. This can be

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derived from kinetic calculations which will be discussed later. Moreover, after 60 h treatment with CrN/Cr powder pack at 800°C, the surface already covered by a thin layer of Ti2N, and TiN also formed.

Figure 5-5 shows the SEM image of the titanium treated at 860°C for 120 h with

CrN/Cr powder pack at 750°C. On the very surface there is a continuous layer which is titanium α phase with interstitial solute of nitrogen. This layer is about 5 µm. Beneath the topmost layer the material shows an equiaxed microstructure. The α grain size is fairly large due to the annealing effect. The β phase formed irregular-shape grains which are located mostly at the triple junction (Lutjering & Williams, 2003). The size of α grains is about 15 µm, and is homogeneous from beneath the diffusion layer to the center.

However, the morphology of the near surface area is different from the center area. This can be contributed by surface texture, so that grains near the surface have different orientation from those in the center area.

Figure 5-6 shows a SEM image of the titanium treated at 860°C for 240 h with

CrN/Cr powder pack at 750°C. On the surface there is no continuous nitride layer formed.

Only some small particles, which are Ti2N phase, formed isolated island on the titanium substrate. Because of the inward diffusion of nitrogen, the surface formed a thick α- titanium layer with nitrogen interstitial (about 10 µm). Beneath that, equiaxed α grain and irregular β phase coexist. The grain size of α titanium is very large (about 20 µm) after such long time treatment, and is homogeneous from beneath the diffusion layer to the center. Again, the morphology of the near surface area is different from the center area which has already shown in the sample treated only for 120 h.

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Figure 5-7 shows a SEM image of titanium sample treated at 860°C for 72 h with

CrN/Cr powder pack at 775°C. A continuous Ti2N layer forms on the surface. Beneath that, it is α-titanium phase with nitrogen interstitial. The grain size of α-Ti is about 10

µm. And the α+β Ti is the substrate material at the core. The part of α-Ti which near the surface has different morphology with the part of α Ti which near the core, even though both are α-Ti phase. Some researchers explained that the near surface part of α-Ti is the area of Al and V enriched α-Ti, since the formation of Ti2N on the surface, which doesn’t contain the alloy elements and then drive these elements beneath the compound layer.

Figure 5-8 shows a SEM image of titanium sample treated at 860°C with CrN/Cr powder pack at 800°C. After 24 h treatment, the sample has a continuous Ti2N layer on the surface, while after 60 h treatment, both TiN and Ti2N layer form on the surface. The

TiN layer is porous. And the interface between TiN and Ti2N is very rough. Some researchers even consider it is a mixture region of nitride compounds below a porous TiN layer. The interface between the nitride compound region and α-Ti is relatively clear and smooth. The average α grain size is about 15 µm, which is slightly bigger than 12 µm for the sample treated for 24 h.

As a summary, Table 5.1 list the 860°C treated Ti-6Al-4V samples with selected powder pack temperature and heat treatment time. The resulting phases on the surface are listed for each experiment. Nitrides formed when a high powder pack temperature is used or a long treatment time is used for the sample.

Correspondingly, the surface hardness of every treated sample has been measured.

The result is also shown in Table 5.1. For a powder pack at 750°C, the equilibrium nitrogen pressure is low. So less nitrogen can be diffused in to titanium part. This results

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in a small value of surface hardness. Only after 240 h treatment, Ti2N phase formed as some spots, and so that the hardness increased. At 775°C, nitrogen pressure increasing led to the nitrogen concentration increasing on and beneath the titanium surface. After 24 h treatment, surface hardness increased 30%. After 72 h treatment, Ti2N formed, and the hardness is 670. The titanium sample treated for 24 h with powder pack at 800°C formed

Ti2N phase on the surface. The hardness of 740 is also indicated the presence of harder surface layer.

Table 5.1 Summary of heat treatment, the phase development and the microhardness (Vickers) measured with a 50 g load

Temp.\Time 24 h 72 h 120 h 240 h

860 °C Ti2N / TiN

Ti / Ti2N Ti2N / TiN 800 °C 740

Ti Ti / Ti2N 775 °C 535 670

Ti Ti Ti Ti / Ti2N 750 °C 440 460 440 500 Ti Ti 700 °C 360 360

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Ti2N Ti

Figure 5-1 XRD patterns for Ti-6Al-4V samples treated at 860°C with

CrN/Cr powder pack at various temperatures for 24 h.

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Ti Ti

Ti2N

Figure 5-2 XRD patterns for the Ti-6Al-4V samples treated at 860°C with

CrN/Cr powder pack at 750°C for various times.

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Ti2N

Ti Ti

Ti2N Ti2N

Figure 5-3 XRD patterns for the Ti-6Al-4V samples after a longer-time treatment (860°C, 72h) and the formation of nitrides.

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Ti2N Ti

Figure 5-4 XRD patterns for the Ti-6Al-4V samples treated at 860°C with

CrN/Cr powder pack at different temperatures for various times which have all formed nitride (Ti2N) on the surface.

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α Ti

α+β Ti

Figure 5-5 SEM image of the titanium treated at 860°C for 120 h with

CrN/Cr powder pack at 750°C

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Nitrides

α Ti

α+β Ti

Figure 5-6 SEM image of the titanium treated at 860°C for 240 h with

CrN/Cr powder pack at 750°C

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Nitrides

α Ti

α+β Ti

Figure 5-7 SEM image of the titanium treated at 860°C for 72 h with

CrN/Cr powder pack at 775°C

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α Ti

α+β Ti

Nitrides

α Ti

α+β Ti

Figure 5-8 SEM images of the titanium treated at 860°C for 24 h with

CrN/Cr powder pack at 800°C. (Top: SE image; bottom: BSE image.)

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5.2 Cr2N/Cr Treatment

Heat treatments with Cr2N/Cr powder packs were conducted in the same way as for CrN/Cr powder packs. Figure 5-9 shows the XRD pattern of titanium treated at 860°C for 72 h with Cr2N/Cr powder pack at 750°C. The glancing incidence scan provides the information of material structure presented near the surface. The result shows the existence of TiN and Ti2N. But the normal scan shows a very strong signal for TiN phase with a very small peak at 39.3°, which is for Ti2N.

As we know, the normal scan provides the information from the bulk material as well as from the surface. We can explain this result as that TiN is the dominant phase of the thick nitride region, while Ti2N is the minor part. For the normal scan, with the large percentage of signal from TiN, the Ti2N signal is relatively weak. While for the glancing scan, since the incident angle is very small (1o in this case), the total collected signal is in much less, thus the difference between these two nitride phase is less obvious. The color of the surface is yellow which directly showed the formation of nitrides. This indicated that the equilibrium nitrogen pressure for Cr2N/Cr powder pack at 750°C is way too high.

So TiN phase formed and the nitride layer is very thick.

Figure 5-10 shows a SEM image of the cross-section near the surface. The outmost layer is TiN phase followed by Ti2N phase. The TiN layer is porous. And the interface between TiN and Ti2N is not very clear, so we can consider it may be a mixed region. The nitride region is about 10 µm in thickness, which is consistent with XRD result. Beneath the nitride layer, the microstructure is the same as the CrN/Cr powder pack treated samples: the interstitial diffusion region in the α-Ti phase and equiaxed α grain co-existing with β phase. The interface between Ti2N and α-Ti is relatively smooth.

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Since the titanium sample is always treated at 860°C, the change of powder pack doesn’t affect the core structure.

Since a thick nitride layer is formed, the nitrogen pressure of Cr2N/Cr powder pack at 750°C is probably too high for the nitridation. So the treatments with powder pack at 700, 650, and 625°C were performed. Figure 5-11 shows the glancing scan XRD results for these three samples.

The pattern for 700°C is almost identical to that 750°C treated sample. TiN is still the major phase and two peaks have shown up. Again the small peak at 39.3° is the sign of the Ti2N phase. And it hardly can be seen in the normal scan mode.

The treatment with powder pack at 650°C shows a big change. TiN peaks are no longer the strongest; instead it is the Ti2N peak that is the strongest. Still there is no titanium peaks in the pattern which indicated that the nitrides layer is at least several micrometer size thick.

Finally the titanium peaks appeared in the XRD pattern of sample treated with powder pack at 625°C. The titanium (100), (002) and (101) peaks all showed up and (101) peak is the strongest one. So α-Ti is the major phase on the surface. As the same time

Ti2N peak also appear, indicating that the nitrogen pressure is still not low enough to suppress the formation of nitrides. In glancing scan, the TiN peaks are very weak and they have almost disappeared in the normal scan mode. This indicated that the formation of nitrides is restricted on the surface. So for glancing scan, the nitrides may occupy a certain volume fraction. But for normal scan mode, the volume fraction of nitrides is so small that XRD can only give out a very weak signal.

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Figure 5-12 shows SEM images of cross-section from the samples treated for 72 h with Cr2N/Cr powder pack at 625, 650 and 700°C. Compared with powder pack at 750°C, the microstructures of Ti-6Al-4V sample treated with powder pack at 700°C is fairly identical. The same thickness of nitrides layer indicated that the nitrogen pressure has no effect on the formation kinetics. For 650°C, the thickness of nitride compounds layer is thinner, and beneath the nitrides there is a layer of α titanium grains that show different morphology than the center area. Powder pack at 625°C didn’t form a continuous nitride layer on the surface. The α titanium layer is about the same thickness as that treated with powder pack at 650°C.

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TiN TiN

Ti2N

Figure 5-9 XRD pattern of titanium treated at 860°C for 72 h with

Cr2N/Cr powder pack at 750°C.

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Nitrides

α Ti

α+β Ti

Figure 5-10 SEM image of the cross-section from the sample treated at

860°C for 72 h with Cr2N/Cr powder pack at 750°C

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Ti2N Ti

Ti TiN TiN

Ti2N

Figure 5-11 The glancing incidence XRD (GIXRD) results for the titanium treated at 860°C for 72 h with Cr2N/Cr powder pack at 700, 650, and 625°C, and the comparison to the annealed sample (from bottom to top).

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Nitrides

α Ti

α+β Ti

(a)

Nitrides

α Ti

α+β Ti

(b)

Figure 5-12 SEM images of cross-section from the samples treated at

860°C for 72 h with Cr2N/Cr powder pack at (a) 700°C, (b) 650°C and (c) 625°C.

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Nitride

α Ti

α+β Ti

(c)

Figure 5-12 SEM images of cross-section from the samples treated at 860°C for

72 h with Cr2N/Cr powder pack at (a) 700°C, (b) 650°C and (c) 625°C.

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5.3 CrN/Cr and Cr2N/Cr Powder Packs

The heat treatments with CrN/Cr powder pack and with Cr2N/Cr powder pack showed a contradiction for the nitrogen pressure. The thermodynamic calculations

(section 3.6 and 3.7) show that at the same temperature, the CrN/Cr powder pack has a higher nitrogen pressure than the Cr2N/Cr powder pack. However, the treatment of Ti-

6Al-4V at the same condition with both powder packs showed that apparently Cr2N/Cr powder pack has a much higher nitrogen pressure.

Figure 5-13 shows the XRD pattern for the CrN/Cr and Cr2N/Cr powder packs before heat treatment. As described in Chapter 4, both the CrN powder and Cr2N powder are actually a mixture of these two phases. In CrN there is 1 wt% of Cr2N and in Cr2N there is up to 10 wt% of CrN. In the XRD patterns, the peaks for all three phases are present. The intensities of peaks roughly represent the volume fraction. So both CrN and

Cr2N powders are actually a mixtures of those two compounds. Those compounds in the powder pack may have some reaction that can affect the nitrogen pressure.

Figure 5-14 shows the XRD pattern of those powder packs after heat treatment.

The CrN/Cr powder pack still has the CrN as the major phase. The volume fraction of Cr has not changed and volume fraction of Cr2N shows a small increase. So during the heat treatment, CrN is slowly converted to Cr2N. But for less than 100 h treatment, all three solid phases, CrN, Cr2N, and Cr still coexist. On the other hand, the Cr2N/Cr powder pack after heat treatment only has Cr2N and Cr phases. The CrN phase in the raw powder has all changed to Cr2N. So in solid phase we only have Cr2N and Cr, in gas phase we only have nitrogen and Cr.

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Figure 5-13 XRD pattern for the CrN/Cr and Cr2N/Cr powder packs before heat treatment.

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Figure 5-14 The XRD patterns of CrN/Cr and Cr2N/Cr powder packs after heat treatment.

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5.4 Treatment at Other Conditions

So far all the heat treatments have been conducted in a vacuum environment with sample temperature at 860°C, and the base vacuum pressure is 1 Pa of argon. Some other conditions have been tried to get a better understanding of the kinetics of the powder pack techniques.

The pressure inside the sealed tube can be controlled using argon as the filled gas.

Before sealing the tube, if we don’t evacuate the tube, 105 Pa argon will remain in the tube. Ti-6Al-4V sample has been treated at 860°C for 24 h with CrN/Cr powder pack at

800°C under 105 Pa argon pressure. Figure 5-15 shows the XRD pattern. All three titanium peaks have been detected and the position shift is negligible. The XRD pattern of Ti-6Al-4V sample treated under 1 Pa vacuum is also shown in the figure for the convenience of comparison. Under the vacuum condition the nitrides formed on the surface. For this temperature, the nitrogen pressure of CrN/Cr powder pack is somewhat around 1 Pa (This is not certain. This estimation is given based on the treatment condition of Cr2N/Cr powder pack.). This pressure is comparable to the base vacuum pressure (1

Pa). But if the tube is filled with 105 Pa argon, the volume fraction of nitrogen is significantly reduced. Although the impingement rate is only determined by partial pressure, this small volume fraction will significantly reduce the gas molecules sticking coefficient on the solid surface; further it will effect the formation of nitrides and diffusion of nitrogen. The XRD results indicate that the base pressure in the tube has a big effect on the nitridation.

Ti-6Al-4V sample treated at 860°C for 24 h with Cr2N/Cr powder pack at 700°C under 105 Pa and 1 Pa argon pressure have been performed respectively. Figure 5-16

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shows the XRD patterns. With low base pressure, the nitrogen volume fraction in the gas phase is large, so the nitrides formed on the surface. But with 105 Pa of argon in the tube, the treated Ti-6-Al-4V surface virtually has no change. Again, this verified the effect from the base pressure.

Heat treatments of Ti-6Al-4V samples at temperatures other than 860°C were also performed to verify the effect of temperature on nitriding kinetics. The heat treatment of

Ti6-Al-4V samples at 800 and 950°C, with Cr2N/Cr powder pack at 625°C under vacuum have been conducted. Figure 5-17 shows the XRD patterns. At 950°C, the diffusion coefficient of nitrogen in titanium is very high. In contrast, the impingement rate is not high enough to deposit a certain amount of nitrogen. After 72 h treatment, the titanium peak shifted a little and no nitrides formed on the surface, which is consistent with low nitrogen concentration. At 800°C, the diffusion coefficient is smaller than 860°C. At the same surface flux rate, more nitrides formed on the surface since less nitrogen can diffuse inward. This is evidence that shows that the surface nitrogen concentration is a kinetic balance between the surface adsorption process and bulk diffusion process. And the results are consistent with the kinetic calculation in Chapter 3.

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Ti2N

Figure 5-15 GIXRD patterns of Ti-6Al-4V sample has been treated at

860°C for 24 h with CrN/Cr powder pack at 800°C under 105 Pa (solid line) and 1

Pa (dotted line) argon pressure respectively

146

Ti2N TiN TiN

Ti2N

Ti Ti

Figure 5-16 XRD patterns of Ti-6Al-4V sample treated at 860°C for 24 h

5 with Cr2N/Cr powder pack at 700°C under 1 Pa and 10 Pa argon pressure, and the comparison to the annealed sample (from top to bottom)

147

Ti2N

Ti TiN

Ti2N TiN Ti Ti2N

Figure 5-17 XRD patterns of Ti6-Al-4V samples at 950, 860 and 800°C

(from up to bottom), with Cr2N/Cr powder pack at 625°C under vacuum, and the comparison to the annealed sample

148

5.5 Goal-Oriented Nitriding Practice

Based on the above heat treatments, a protocol for nitriding under kinetic control has been developed to optimize the desired properties of treated titanium alloys. In order to measure mechanical properties of treated Ti-6Al-4V sample, tensile bar materials are treated with Cr2N/Cr powder pack. The heating profile described in Chapter 4 is used.

Figure 5-18 shows the XRD pattern of Ti-6Al-4V tensile bar treated at 860°C with Cr2N/Cr powder pack at 650°C for 72 h. The pattern is obtained by glancing incidence scan so the peaks are from the top surface. The three major peaks at 35.3°,

38.1°, and 40.4° are from titanium. There are two small peaks. The one at 39.2° is from

Ti2N phase and the one at 36.7° is identified as TiN. Although the strong titanium peaks indicate that the sample surface was mostly α-titanium phase, Ti2N was formed on some places. And the weak TiN peak demonstrated the existence of final nitride product. Three phases coexist on the surface is evidence of inhomogeneous nucleation and growth of nitrides.

Surface hardness measured with different loads is shown in Figure 5-19.

Compared with annealed sample, the improvement when tested with 50g load is only about 50%. The microhardness is related with nitrogen concentration. This small increase in hardness reflected a small nitrogen concentration on the surface. To increase the concentration, we need either to raise the nitrogen pressure or treat the sample for a longer time. But since nitrides are already forming on the surface, raising pressure or prolonging the treatment time will promote the nitrides growth, and we will never have a titanium sample without compound layer.

149

The contradiction between surface hardness and nitride formation indicated the heat treatment procedure is not successful in one respect. Ti-6Al-4V alloy is an α+β two- phase alloy. On the surface we have both α and β phase as well as lots of grain boundaries. The sticking coefficient and diffusion coefficient for different phase are different. So when put the titanium substrate into the nitrogen atmosphere, some area of the surface only accumulated a small amount of nitrogen, while some other area already formed nitride. The nitride is so stable that once formed on the surface it is very hard to dissolve it under that nitrogen pressure. The treatment with one nitrogen pressure combined with surface inhomogeneity of titanium alloy make the goal of hardening the surface without nitride formation inaccessible. To achieve the goal, a more practical method should be conducted.

From the diffusion profile equation discussed in Chapter 3, we can see that the surface inward diffusion flux is a function of time. By calculation, a conclusion can be drawn from Equation (3.7): at constant nitrogen pressure (constant impingement rate) and temperature (constant diffusion coefficient), the surface inward diffusion flux will decrease with increasing time. So in the heat treatment the surface nitrogen concentration increases faster when treatment time is longer. In order to reduce the accumulation rate, the nitrogen pressure should be lowered after a certain time. Actually this kind of strategy is common in industrial practice. Swagelok Company uses an atmosphere of gradually reduced CO concentration in the carburization of stainless steel (Cao, 2003). And some other companies use boost-diffusion cycles to achieve the same control (Edenhofer,

1995).

150

For the convenience of experimental process, a 4-segment heat treatment is proposed. The schematic heating profile is shown in Figure 5-20. The difference compared with the 2-segment heat treatment (Figure 4-2) is after a certain treatment time, the temperature of Cr2N/Cr powder pack is lowered. So the nitrogen pressure is reduced.

This step is repeated once at another time. Lowering the nitrogen pressure will lower the rate, and so lower the surface nitrogen accumulation rate. In this 4-segment heat treatment, the impingement flux is controlled to be balanced with diffusion flux so that the nitrogen concentration on the surface would never be high enough to form the nitride.

Figure 5-21 shows XRD patterns of two titanium samples treated with the 4- segment heating profile. The temperatures indicated in the figure are the Cr2N/Cr powder pack temperature at different segments. For the sample treated with higher nitrogen pressure, the XRD pattern only shows the peaks from Ti2N phase. This indicated that a homogeneous Ti2N layer is formed on the surface. For the other sample treated with lower nitrogen pressure, the XRD pattern only shows the peaks of titanium. There is no trace of nitrides. Compared with the peaks of annealed titanium, the peaks from nitrided titanium are greatly shifted toward lower 2θ angles. This indicated a significant change in the lattice parameters which is caused by the nitrogen diffusion.

Figure 5-22 shows the microhardness measurement with different loads on the surface of nitrided titanium without the nitrides. At 50g load, the hardness is more than twice that of the annealed sample. This significant improvement is a proof of the success of heat treatment.

151

Ti5bar+Cr2N/Cr(650)-860-72.glancing

Ti Ti Ti

Ti2N TiN

34 35 36 37 38 39 40 41 42

Figure 5-18 GIXRD pattern of Ti-6Al-4V tensile bar treated at 860°C with

Cr2N/Cr powder pack at 650°C for 72 h

152

600 Annealed Nitrided 500

400

300 Vicker Microhardness Vicker 200

100

0 50 g 200 g 1000 g

Figure 5-19 Microhardness for the nitrided sample (without nitride on the surface) as in Figure 5-16, and the comparison to that for the annealed sample.

153

Figure 5-20 Heating treatment practice with 4 segments: gettering, high temperature, reduced temperature, and low temperature treatment.

154

Ti5 Annealed 700C, 650C, 600C 675C, 625C, 600C

Ti N Ti 2

Ti N 2

34 35 36 37 38 39 40 41 42

Figure 5-21 XRD patterns for two samples treated with new heat profile shown in Figure 5-20. The temperatures shown in the figure are for Cr2N/Cr

powder packs heat-treatment protocol.

155

900 Annealed 800 Nitrided

700

600

500

400 Vicker Microhardness 300

200

100

0 50 g 200 g 1000 g

Figure 5-22 Microhardness for the sample treated with Cr2N/Cr powder pack at 675, 625 and 600°C protocol, and the comparison to the annealed sample.

156

5.6 Discussion

5.6.1 Nitrogen pressure for CrN/Cr and Cr2N/Cr powder pack

The CrN/Cr and Cr2N/Cr powder packs can generate nitrogen at elevated temperatures. The possible chemical reactions are

2CrN ÅÆ 2Cr + N2 (5.1)

2Cr2N ÅÆ 4Cr + N2 (5.2)

CrN + Cr ÆÆ Cr2N (5.3)

In Chapter 3, those reactions (Equations (3.14), (3.15), and (3.16)) have been discussed. Since the actual powder packs have all three solid phases, those chemical reactions can take place at the same time. Both (5.1) and (5.2) can generate nitrogen, so when three solid phases coexist, the nitrogen pressure can not be defined by either reactions.

For CrN/Cr powder pack, during the nitriding, all three compounds, CrN, Cr2N, and Cr, coexist in solid phase. The gas phase consists of both nitrogen and Cr vapor. The conversion between CrN and Cr2N is governed by reaction (5.3). The free energy change of reaction (5.3) is less than 0, so it is a spontaneous reaction converting CrN into Cr2N.

However, this reaction is also a solid phase reaction. The mass transaction between two these solid phases has a limited speed. 100 h treatment is not long enough to exhaust all the CrN phase. So during the nitriding, the chemical reactions in the powder pack didn’t reach equilibrium state, the nitrogen pressure can not be determined by the simple reaction of either (5.1) or (5.2).

157

And if assuming the CrN/Cr powder pack has the equilibrium nitrogen pressure, it will be at the order of 10 Pa. To fit this nitrogen pressure into the kinetic model, the sticking coefficient has to be set as 0.00001. Although there is no direct analysis of the sticking coefficient of nitrogen on titanium surface at high temperature, a value of

0.00001 seems not reasonable. From the XRD pattern for the CrN/Cr powder pack, we learned that three solid phases, CrN, Cr2N, and Cr are co-existing (Figure 5-14). So the equilibrium nitrogen pressure that is simply calculated by the thermal equilibrium between CrN and Cr as described in equation (5.1) can not be realistic.

Although CrN phase is continuously converted into Cr2N phase, in CrN/Cr powder pack the CrN is always the major component. So the nitrogen pressure can not be the same as Cr2N/Cr powder pack. But eventually the CrN phase will all convert into

Cr2N phase, then the nitrogen pressure will reach the equilibrium as Cr2N/Cr powder pack.

For Cr2N/Cr powder pack, the equilibrium nitrogen pressure is determined by reaction (5.2). By adopting a suitable sticking coefficient (about 0.01 – 0.1), the nitrogen pressure is very consistent with the kinetic calculation. However, the calculated nitrogen pressure of Cr2N/Cr powder pack from different references has a discrepancy of one order of magnitude (Table 3.4). So the real equilibrium nitrogen pressure for the Cr2N/Cr powder pack used in this work need to be clarified by some other methods. The experiments in this work just assume that a certain range of nitrogen pressure is generated, and the pressure is monotonic to the temperature of powder pack.

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5.6.2 Surface adsorption kinetics

In the overall nitriding process, the impingement, sticking, and desorption of nitrogen is a key step to affect the surface concentration and further diffusion. The nitrogen pressure determines the impingement rate at a certain temperature. Then, the sticking coefficient controls how often the striking will result in a stay, or adsorption.

When nitrogen atoms start to build up surface concentration, they will also diffuse into the titanium substrate by the driving force originating from chemical potential. Some nitrogen atoms can also combine together to form nitrogen molecules and leave the surface. The surface concentration is then determined by the balance of these processes.

The sticking coefficient may be written as

α =−σθf ( )exp(ERT / ) (5.4)

In this equation, σ is the probability that a molecule is adsorbed, provided it possesses the necessary activation energy E and collides with a vacant site. f(θ) is a function of the surface coverage θ and represents the probability that a collision will take place at an available site. It can be seen that α is a function of activation energy E and surface coverage θ. Directly measuring θ is not easy. In general f(θ) is not known. The adsorption processes is differ from case to case. Adsorption processes on the surface of titanium have been studied to a far lesser degree as compared to other metals. It is almost impossible to solve the equation above to get the solution for sticking coefficient.

The calculation shows that at 105 Pa pressure, the impingement rate is extremely high and the surface monolayer coverage time is about nanoseconds. This kind of time scale usually is non-detectable. Therefore, the surface is always covered by adsorbed atoms. A lower sticking coefficient will increase the coverage time. However, for the

159

case of nitrogen adsorbed on metal surface, the sticking coefficient is mostly in the range of 0.1~1. Even with the sticking coefficient as low as 0.001, the monolayer coverage time is still in the order of microseconds. Compared to the treatment time (usually hours), this short transient state can be neglected and the surface still can be considered as fully covered at all the time. The high surface concentration will result in the formation of nitrides.

So from equation (5.4), controlling the nitrogen pressure is a better strategy to control the accumulation of surface concentration. It can be seen that a very low nitrogen pressure (in the range of 10-3 Pa to 10-1 Pa) is desirable. At this pressure, when assuming the sticking coefficient to be 1, the monolayer coverage time is about several seconds. An order of magnitude change in sticking coefficient will result in a much longer coverage time. The diffusion process will lower the surface concentration. By carefully controlling the nitrogen pressure and temperature, a good diffusion profile without nitride formation can be obtained.

Equation (5.4) describes the process of a pure gas adsorbed on the metal surface.

However, in the present heat treatment, the sealed quartz tube is filled with argon, which has a comparably high pressure. The mixture of inert gas with reactant gas showed some effect on the nitriding practice. Even though no quantitative analysis is reported, our heat treatment at different base pressures clearly showed the influence of argon on the nitriding process. It seems that argon acts like a sputtering agent which can remove adsorbed nitrogen atoms from the surface. High argon pressure reduced the apparent sticking coefficient.

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From equation (5.4), temperature is also a factor that can affect the sticking coefficient. Low temperature will result in a higher sticking coefficient. So changing the treatment temperature will change the surface flux. Also the temperature change will affect the diffusion coefficient. Suppose the surface flux and the diffusion flux are in equilibrium at a certain temperature. Then decreasing the sample treatment temperature will increase the surface flux but decrease the diffusion flux. So the surface concentration will be accumulated faster. In contrast, raising the treatment temperature will decrease the surface flux but increase the diffusion flux. In this case the surface concentration will be accumulated more slowly. The treatments of Ti-6Al-4V samples at different temperature in section 5.3 (Figure 5-17) totally proved this hypothesis.

From all the nitriding experiments, the lowest nitrogen pressure that needed to form nitride is one order of magnitude higher than the kinetic calculation. In the kinetic calculation, the gas is assumed to be pure nitrogen at very low pressure, and the diffusion coefficient of nitrogen is adopted from that in pure titanium. In the nitriding experiments,

Ti-6Al-4V alloy is treated. In which the nitrogen diffusion coefficient is different than that in pure titanium. Some nitriding experiments have shown that the diffusion coefficient of nitrogen in Ti-6Al-4V is smaller than that in pure titanium (Foi, Deramaix,

Atale, & Jacquot, 2000; Muraleedharan & Meletis, 1992). Another big difference from kinetic calculation is that in the nitriding experiments a nitrogen/argon gas mixture is used.

Inoue et al. (1999) observed that the nitrogen partial pressure in nitrogen/argon gas mixture has big influence on mechanical properties for reactively sputtered Ti-N films. Kang and Pu also observed that the mixture of nitrogen/argon can affect the

161

electronic properties of nitrogen (Kang & Pu, 2002). In this work, when increasing the argon pressure in the sealed tube, the partial pressure of nitrogen is not affected, but the nitriding effect is reduced dramatically. In the sticking coefficient argument, only the interaction between nitrogen gas and titanium substrate is considered. Apparently the argon gas in the tube has some influence on the nitriding process. However, the consideration of argon in the nitriding system will make it too much complicated and that is beyond this work.

5.6.3 Nitridation kinetics

We have established the model for the nitridation kinetics. It is a balance between surface adsorption and bulk diffusion (section 3.3). And it is a function of nitrogen pressure, sample temperature, and treatment time. However, the results from those experiments in section 5.1 and 5.2 tell another story: a simple heat treatment profile with a certain nitrogen pressure, sample temperature, and treatment time will either result in high hardness with nitrides on the surface or a barely improved surface without nitrides.

The goal of having a treated sample with high surface hardness but without nitrides is not achievable by the simple heat treating profile.

Ti-6Al-4V is an α+β alloy which has α and β phases coexisting ("Metals

Handbook," 1980). Figure 5-23 shows the SEM image of the cross-section of an annealed sample, which has been treated with the Ti getter for 48 h at 860°C in vacuum. The bright, irregular shaped grains are the β phase, which has a high solubility of vanadium. The dark, equiaxial grains are α phase, which has more aluminum. On the surface, we have both α and β phase and of cause, a lot of grain boundaries. The structure of surface layer is identical to that of the core.

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According to the calculated surface impingement rate, if the nitrogen pressure is sufficiently high during heat treatment, the Ti-6Al-4V surface will be covered by a layer of nitrogen in milliseconds. The affinity of titanium to nitrogen is high and soon the surface will be covered by nitrides. So for the high nitrogen pressure nitridation experiments, the sample surface always forms a homogeneous titanium nitride layer. It shows a golden yellow color, and gives a very high surface hardness. But the brittle nature of the nitrides and the interface adhesion problem between the nitride layer and the substrate limit the material in many engineering applications.

To avoid the formation of nitrides, nitrogen pressure has to be kept low. But when the nitrogen pressure is lowered to the kinetic equilibrium range, the surface impingement rate is not high enough to cover the titanium surface in a short time to form a sufficient surface concentration. Moreover, once the nitrogen is adsorbed on the surface, it starts to diffuse inward the substrate. The diffusion process reduces the surface concentration and makes it difficult for the nitrogen to accumulate on the titanium surface.

No decent diffusion profile can be generated with the thermodynamic equilibrium nitrogen pressure.

At the calculated kinetic equilibrium nitrogen pressure, the chemical potential of nitrogen is much higher than that to form nitride. During the heat treatment, adsorbed nitrogen atoms may react with titanium to form nitride at the very earlier stage. Since the surface of titanium is not homogeneous, those nitrides could form clusters or islands at the grain boundaries or around the surface defects. Later on, the nitridation process is a balance between local nitride particles, adsorbed nitrogen atoms, and the very active titanium substrate. During heat treatment, the nitrogen pressure is kept constant and

163 higher than the equilibrium nitrogen pressure for the TiN/Ti system, and the diffusion

rate is always balanced with the surface impingement rate. So those already formed

nitrides won’t disappear but will grow until they cover the whole surface.

So during the heat treatment, lowering the nitrogen pressure is a right strategy to make the impingement rate comparable to the diffusion rate. If the final nitrogen pressure is low enough to make the impingement rate smaller than the diffusion rate, the already formed nitrides may loose nitrogen and finally be dissolved in the substrate. This is the reason why the 4-segments heat treatment can have the best result so far.

5.6.4 Microstructural analysis

The annealed Ti-6Al-4V sample shows identical α+β two-phase microstructure

through the cross-section (Figure 5-23). Comparing it with those SEM micrographs

(Figure 5-6, Figure 5-8, and Figure 5-12) of nitrided samples, it is evident that the nitrided zone is composed of several layers, with microstructures that are different from

the core (Figure 5-24). The treatment conditions of annealing and nitriding are only

different by an atmosphere of nitrogen. So the microstructure transformation is solely

owing to the diffusion of nitrogen.

After treatment with a low nitrogen pressure or for a short time, there is no nitride

on the surface, and the outer layer is α phase of large grain size. This layer is also the

diffusion layer with nitrogen as interstitial solute. In this layer, β phase no longer exists.

It is consistent with XRD observation, which didn’t show any β phase peaks for nitrided

samples. Beneath this diffusion layer is the α + β two-phase base material. On the other

hand, after treatment with a high nitrogen pressure for a short time or with a low nitrogen

pressure for a longer time, nitrides formed on the surface. The nitrides form either

164 isolated particles (Figure 5-6 and Figure 5-12) or a fully covering layer (Figure 5-7 and

Figure 5-10) on the surface, depending on the nitrogen pressure and treatment time. The contrast in those SEM images showed the diffusional α layer has two sub-layers. The sub-layer which is adjacent to the nitride is believed to be an aluminum-rich titanium phase. Several groups (Ponticaud, Guillou, & Lefort, 2000; Swagelok, 2002) have also observed this kind of morphology.

In titanium substrate, the diffusion coefficient of nitrogen is two orders of magnitude higher than the diffusion coefficient of Ti, Al, or V. During the nitriding process, only nitrogen is the effective diffusing element. In the Ti-6Al-4V alloy, β phase is stabilized by vanadium. But with more nitrogen interstitially dissolved in the lattice, β phase is no longer stable and will transform to α phase since nitrogen as an alloying element is a α stabilizer in titanium alloys. If the nitrogen concentration is high enough to form a nitride, the aluminum and vanadium was expelled from the surface layer into the core. Since the diffusion coefficient of Al is much smaller than nitrogen, it formed the aluminum-enriched area in the α layer (Ponticaud et al., 2000).

There are 3 possible explanations for the large grain size of diffusional α phase.

First is the DIGM theory. Although there is no direct measurement of the grain boundary diffusion rate of nitrogen in titanium substrate, it should be much faster than the diffusion rate in grains (Porter & Easterling, 1992). Hillert and Purdy have observed that grain boundary motion can be induced by fast grain boundary diffusion, which is called

“diffusion-induced grain boundary migration” (DIGM) (Hillert & Purdy, 1978). The diffusion process in the nitriding has similarities with their experiments. The fast diffusion of nitrogen along grain boundary could nucleate new nitrogen-enriched α

165 titanium phase at grain boundaries or on the surface. Then the transport of nitrogen into

the titanium substrate was accomplished by grain boundary diffusion coupled with grain

boundary sweeping on the surface. However, the diffusion profile of nitrided titanium

substrate more or less agreed with that predicted using the bulk diffusion coefficient. So

DIGM theory is less likely able to be applied here.

The second explanation is dynamic recrystallization. Nitrogen is an interstitial

solute which can induce distortion of the titanium substrate lattice. If the internal stress

induced by distortion is large enough, the grain will undergo a certain deformation. But

since the nitridation temperature is higher than the annealing temperature of titanium,

recrystallization will also happen simultaneously with deformation. The strength of

titanium Ti-6Al-4V alloy at the nitriding temperature of 860°C is lower than 20 MPa

(Ogawa, Fukai, Minakawa, & Ouchi, 1993), which makes the dynamic recrystallization

less likely.

The third explanation is the phase transformation and grain growth. In the Ti-6Al-

4V substrate, we have both α and β phase and of cause, a lot of grain boundaries. The β

phase is BCC structure and α phase is HCP structure. Nitrogen is an α stabilizer in titanium alloys. During the nitriding process, β phase, which is enriched with vanadium, will transform into α phase by dissolving nitrogen. This phase transformation will form small α grain at several sites on the grain boundaries of the β phase. Simultaneously, new grain boundaries are created. These small-size grains and new-formed grain boundaries store high free energy, which must be released by the grain growth at high temperature.

The orientation of those grown grains might have some preferred direction with XRD

166 patterns (Figure 5-1 and Figure 5-2) that show the relative intensity change for different peaks as evidence for this hypothesis.

The nitridation of Ti-6Al-4V alloy involves phase transformation and grain growth. These processes may also affect the diffusion property of nitrogen in the titanium substrate. The dynamic recrystallization and phase transformation mechanism can be utilized to explain the very complex structure of nitrided titanium substrate. But the detailed progress during the nitriding is still difficult to describe. Nevertheless, a desirable nitrogen depth profile has been achieved by changing the nitrogen pressure during the nitridation, which is a good strategy to balance the diffusion flux and the impingement flux, to control the nitrogen surface concentration, and to avoid the formation of nitride.

167

Figure 5-23 Cross-section image of annealed Ti-6Al-4V alloy. Bright area is β phase, dark, equiaxial grains are α phase.

168

Figure 5-24 Cross-section image of nitrided Ti-6Al-4V alloy away from surface, which shows an α + β two phase structure.

169

Work Cited

Cao, Y. (2003). Surface hardening of austenitic stainless steels via low-temperature

colossal supersaturation. Unpublished Ph. D. Dissertation, Case Western Reserve

University, Cleveland.

Edenhofer, B. (1995). Carburizing and Nitriding Industry in the Eastern Hemisphere. In J.

Grosch, J. Morral & M. Schneider (Eds.), 1995 Carburizing and Nitriding with

Atmospheres (pp. 3-8). Materials Park, Ohio: ASM International.

Foi, R., Deramaix, C., Atale, O., & Jacquot, P. (2000). Tinitron process for low pressure

nitriding of titanium and its alloys. Surface Engineering, 16(3), 205-209.

Hillert, M., & Purdy, G. R. (1978). Chemically induced grain boundary migration. Acta

Metallurgica, 26, 333-340.

Inoue, S., Ohba, T., Takata, H., & Koterazawa, K. (1999). Effect of partial pressure on

the internal stress and the crystallographic structure of r.f. reactive sputtered Ti-N

films. Thin Solid Films, 344, 230-233.

Kang, Z. D., & Pu, Y. K. (2002). Electron temperature control in inductively coupled

nitrogen plasmas by adding argon/helium. Chinese Physics Letters, 19(8), 1139-

1140.

Lutjering, G., & Williams, J. C. (2003). Titanium. New York: Springer.

Metals Handbook. (1980). In (9th. ed., Vol. 3, pp. 367). Materials Park, OH USA: ASM

International.

Muraleedharan, T. M., & Meletis, E. I. (1992). Surface Modification of Pure Titanium

and Ti-6al-4v by Intensified Plasma Ion Nitriding. Thin Solid Films, 221(1-2),

104-113.

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Ogawa, A., Fukai, H., Minakawa, & Ouchi, C. (1993). In D. Eylon, R. R. Boyer & D. A.

Koss (Eds.), Beta Titanium Alloys in the 1990's (pp. 513). Warrendale, USA:

TMS.

Ponticaud, C., Guillou, A., & Lefort, P. (2000). Direct gaseous nitridation of the Ti-6Al-

4V alloy by nitrogen. Physical Chemistry Chemical Physics, 2(8), 1709-1715.

Porter, D. A., & Easterling, K. E. (1992). Phase transformations in metals and alloys.

Cheltenham, UK: Chapman & Hall.

Swagelok. (2002). Quantative Depth Profile of Nitrided Titanium Alloys Measured by

GDOES.

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Chapter 6 MECHANICAL PROPERTIES

6.1 Tensile Testing

Tensile tests have been performed on annealed and nitrided Ti-6Al-4V bars. A strain gauge was used to determine the elastic modulus and yield strength. Since the full scale of the strain gauge can not cover the whole elongation, it was removed during the tensile test. The total elongation can only be estimated.

Figure 6-1(a) shows the engineering stress-strain curve. The stress is calculated as

σ = PA/ 0 , where P is the load and the A0 is the initial cross-section area. The strain is

calculated as ε = ()/ll− 0 l, where l is the strain gage length and l0 is the initial length.

The annealed sample is the tensile bar heat treated in the sealed silica tube with the getter, but without any powder pack. The treatment temperature and time are the same as the nitrided samples, which are 860°C and 72 h. The nitrided samples are treated with

Cr2N/Cr powder pack at gradually reduced temperatures, which are 675, 625, and 600°C respectively. The one treated with Cr2N/Cr powder pack at higher temperature (i.e. 900°C) formed a very thick nitride layer on the surface. Compared with annealed sample, which has the same heat treatment history as the nitrided sample, all nitrided samples show higher yield strength. The data are shown in Table 6.1. The elastic modulus also increased for nitrided sample. But when nitrides formed on the surface, the modulus is reduced. Figure 6-1(b) shows the stress as a function of loading time. When making a parallel line to the elastic deformation region from the point of fracture, the interception with the time line is approximately proportional to plastic deformation. It clearly shows that all nitrided samples have smaller total elongation compared to the annealed sample.

172

With nitrides on the surface, the material is very brittle. The ultimate strength of all samples is very close to the yield strength, and nitrided sample have higher strength than the annealed one. This trend is consistent with the reported results in many places.

Figure 6-2 shows the SEM images of the annealed sample after deformation. The plan view surface shows the feature of irregular bended steps all over the observed area.

And there are some small cracks (Figure 6-2a) which were nucleated at the grain boundaries. The feature of the fracture surface (Figure 6-2b) is the shear dimples, which is the proof of ductility.

Figure 6-3 shows the SEM images of a nitrided sample with a thick nitride layer.

From the plan view surface, many transverse cracks formed in the surface layer. The cross-section image clearly shows the width and depth of one crack. When the crack propagates to the subsurface layer, it is along the grain boundaries.

Figure 6-4 shows the SEM image of fracture surface of a nitrided sample with a thick nitride layer. Shear dimples still show up in the core of the material. But the surface has a very smooth fracture facet. It indicates that the surface is quite brittle, but the core still keeps some ductility.

Figure 6-5 shows the SEM images of a nitrided sample without nitrides. The density of surface cracks is higher than the annealed sample but much smaller than the sample with the nitride layer. And the high magnification shows the crack is the same as the annealed sample that goes along the grain boundaries.

Figure 6-6 is another high magnification image, which shows the slip bands on the nitrided sample surface. It is evidence of the surface ductility. The fracture surface shown in Figure 6-7 also shows ductile features.

173

1200

1000

800

600

stress (MPa) ANNEALED 400 nitrided-1 nitrided-2 200 Nitrides on the surface

0 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 strain (%)

1200

1000

800

annealed 600 nitrided-1

Stress (MPa) Stress nitrided-2 400 Nitrides on the surface

200

0 0 50 100 150 200 250 300 time (s)

Figure 6-1 Engineering stress-strain curve (a) and stress curve as function of time (b) for annealed and nitrided samples.

174

Table 6.1 Mechanical properties of Ti-6Al-4V tensile bar

Elastic Yield Ultimate Total

Modulus Strength Strength Elongation

(MPa) (MPa) (MPa) (%)

Annealed 106 910 1010 16

Nitrided-1 115 970 1050 6

Nitrided-2 123 1000 1060 8

With Nitrides 106 940 1035 3

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Figure 6-2 Plan view surface (a) and fracture surface (b) of annealed sample after deformation.

176

Figure 6-3 Plan view surface (a) and cross-section (b) of nitrided sample after deformation. This nitridation formed a thick nitride layer on the surface.

177

Figure 6-4 Fracture surface of nitrided sample with nitrides layer shows ductile feature in the center but brittle feature near the surface.

178

Figure 6-5 Plan view surface of nitrided sample after deformation.

179

Figure 6-6 SEM image shows plan view surface of nitrided sample after deformation, slip bands can be observed and there is no crack in this area.

180

Figure 6-7 Fracture surface of nitrided sample without nitride layer.

181

6.2 Microhardness Profile

The microhardness profile is measured by nanoindentation. Two areas are selected to measure the hardness with same load of 5000 µN. The position of the first indentation, which is not exactly on the surface but within 0.5 µm is considered as 0 distance from the surface. Figure 6-8 shows the measurement for the Ti-6Al-4V sample treated with Cr2N/Cr powder pack for 72 h. The surface hardness is more than 10 GPa while the substrate is only 4 GPa. The hardening layer is about 25 µm thick. The thickness of the diffusion layer measured by this nanoidentation method is consistent with the α layer in the cross-section images observed by SEM (Figure 6-7).

This result shows that by the nitridation under kinetic control, the titanium sample achieved a high surface hardness with an effectively thick diffusion layer and without the formation of nitrides (XRD results, see Chapter 5).

182

Figure 6-8 Microhardness depth profile for nitrided titanium without nitride

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6.3 Discussion

Nitriding increases the tensile strength of Ti-6Al-4V. It slightly increases the elastic modulus. It’s because the elastic modulus of TiN is almost 6 times larger than the titanium substrate. Because of the difference of modulus, if nitrides formed on the surface, tensile deformation will cause higher stress in the nitride layer. Cracks in the surface nitride layer will form in the very earlier stage. So the effective cross-sectioned area is reduced and the apparent elastic modulus is reduced. If there is no nitride formation on the surface, the surface diffusion layer will not have such a stress concentration problem and there are no transverse cracks formed during tensile test.

Nitriding treatment formed a diffusion layer with a high concentration of nitrogen.

The more nitrogen is dissolved, the more brittle is the material. This brittle layer will cause crack formation and decrease the total elongation. If the nitride layer is formed, the material is apparently brittle. This is consistent with references.

With the goal-oriented heat treatment process, the formation of nitride is avoided.

Still the surface hardness is higher than 10 GPa, which is twice more than the hardness of substrate. By balancing the impingement flux and the diffusion flux, a hardened layer of the thickness of 25 µm was achieved. These properties can significantly improve the ware resistance of Ti-6Al-4V alloy.

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Chapter 7 CONCLUSION AND FUTURE WORK

Conclusion:

1. Titanium alloys have a great affinity for nitrogen. The equilibrium

nitrogen pressure for the TiN/Ti system is lower than 10-25 Pa. The

common nitridation practice with nitrogen pressures higher than 10 Pa

always forms nitride layers. This has a detrimental effect on some

mechanical properties.

2. Based on thermodynamic calculations, nitride/metal powder packs can

define the nitrogen pressure from 10-30 Pa to 105 Pa. Some powder packs

are suitable to perform the kinetically controlled nitridation treatment,

such as Si3N4/Si, CrN/Cr2N/Cr, etc.

3. By adjusting the heat treatment parameters, such as nitrogen pressure,

sample temperature, and treatment time, a desirable nitrogen diffusion

profile can be achieved without the formation of nitrides.

4. Ti-6Al-4V treated at 860°C for 72 h with Cr2N/Cr powder pack at varies

temperature (675, 625, and 600°C) produced a successful treated sample.

5. The microhardness of nitrided Ti-6Al-4V alloy is related to nitrogen

concentration. For the successfully treated sample, the diffusion of

interstitial nitrogen provides very good surface hardness (>10 GPa), and

formed a hardened layer of 25 µm.

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6. Tensile test proved that the nitridation dose not affect the elastic modulus,

increases the tensile strength, but decreases the ductility. The nitride layer

is brittle, as evidenced by its cracking during tensile testing.

Future Work:

1. Optimize the nitriding condition

Although the treatment with Cr2N/Cr powder pack provided the desired nitriding result, the surface hardness, the thickness of hardened layer and the mechanical and chemical properties are far from optimized. The effect of heat treatment temperature of substrate, the effect of nitrogen/argon gas mixture, and the effect of pressure change on the nitriding process still need to be systematically investigated.

2. Effect of alloying element on the nitridation treatment

In order to investigate the influence of substitutional alloying elements on the kinetics and the solubility limit of nitrogen in the kinetically controlled nitridation treatment, titanium alloys with different compositions should be treated at same condition.

Beside Ti-6Al-4V, Ti-3Al-2.5V, IMI384, Ti6242 alloys are attractive candidates for further heat treatment studies.

3. Investigation of ductility of the nitrided layer

Titanium nitride is a brittle phase while titanium has good ductility. The ductility of nitrided layer lies between those two. From the tensile test in Chapter 6, the nitridation will reduce the ductility of titanium, and surface cracks formed during test. But what is the exact ductility of nitrided layer and when does the crack form during the tensile test still need to be investigated. An in situ tensile test in the SEM will provide valuable

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insight of the crack initiation and propagation. Also TEM observation of deformed layer can provide microstructural information for the deformation mechanism.

4. Fatigue testing and corrosion testing

Fatigue resistance and corrosion resistance are the most common mechanical and chemical properties of structural materials. A lot of literature has reported that nitridation will increase the corrosion resistance, but it will lower the fatigue strength. However, in their treatment, nitride compound layers inevitably formed. The new nitridation treatment under kinetic control can eliminate the formation of nitrides. So the effect on fatigue and corrosion resistance still needs to be investigated.

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APPENDIX A. TiN/Ti POWDER PACK TREATMENT

In order to get a better understanding of the nitridation process, heat treatments of titanium alloys with TiN/Ti powder pack, which will generate a thermodynamic equilibrium environment, were conducted. Ti and TiN powder pack contributed as the sources to generate the balanced partial pressure of nitrogen. Both titanium Grade 4

(Commercial Pure, CP) and Grade 5 (Ti-6Al-4V, Ti64) samples were studied.

A.1 Surface Properties of CP Titanium after Heat Treatment

There is an easy method to roughly examine if there are nitrides formed on the surface since the colors of titanium nitrides and titanium are different. Titanium nitrides

(both TiN and Ti2N) have a golden to brown yellow color, which can be easily distinguished from the metallic silver white color of titanium. Figure A-1 shows the surface of both untreated and annealed samples. The surface of untreated sample shows the lustrous, white color. After annealing at 860°C for 48 h, the samples still show the same metallic colors as untreated materials. For higher treatment temperature of 1150°C, the samples shows golden yellow color, which indicates the formation of nitrides on the surface. XRD results for these two treatment temperature also verify that nitrides exist after 1150°C but not after 860°C (see section A.1.1 and A.1.2).

The optical micrograph shows a very small crystallite structure in untreated samples (see Figure A-1.). After heat treatment, the grain size grows to about 10 µm. It is a clear evidence of recrystallization. The heat treatment has little effect on the surface roughness, and for both samples the surface roughness is estimated to be 1 micron. The etchant has no effect on titanium nitrides, so it is not easy to see the surface structure on

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the sample treated at 1150°C.

Polished & Etched

After Treatment @ 860 °C for 48 h

Figure A-1 Surface morphology of grade 4 titanium before heat treatment and after treatment at 860°C for 48 h in vacuum

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A.1.1 Heat Treatment at 860 °C

Figure A-2 displays the XRD patterns of TiN/Ti powder packs before and after heat treatments at 860°C for different time. The major peaks for untreated powder pack are from the TiN phase, which can be identified at 36.7° and 42.6°. They are (111) and

(200) peaks respectively. This 2θ data are consistent with JCPDF file #87-0633. The peaks at 35.1°, 38.2° and 40.2°, which are consistent with JCPDF file #44-1294, are titanium (100), (002) and (101) peaks. After heat treatment TiN peaks still showed up at the same position. The presence of TiN phase in the powder pack clearly shows that the nitrogen resource is not exhausted under these experimental conditions. However, titanium peaks shifted to low 2θ angle, indicating that nitrogen has dissolved in titanium and changed the lattice parameter.

Before heat treatment, the powder pack only has Ti powder and TiN powder.

They are distinguished by XRD peaks. After 16 h heat treatment, a new set of peaks appeared in the pattern. They are at 36.3°, 39.2°, and 40.8°. These peaks fitted with

JCPDF file #76-0198 very well, which is the Ti2N phase. This shows the TiN has reacted with Ti to form Ti2N, and it is consistent with the Ti-N phase diagram. After 120 h treatment, the relative intensity of Ti2N phase is increased. At the same time, the peaks for titanium phase become weaker. This can be explained by the fact that the reaction of

Ti2N consumed titanium, and newly formed Ti2N phase may also cover the surface of titanium powder.

Figure A-3 displays the XRD results of titanium grade 4 samples treated at 860°C for different times. The untreated grade 4 titanium has three peaks at 35.2°, 38.5° and

40.2°, which all belong to α-Ti. The peaks are broadened due to small grain size. After

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heat treatment with TiN/Ti powder pack for 16 h, those peaks are much sharper. Again this is attributed to recrystallization. The relative intensity of the peak at 38.5°, which corresponds to the basal plane (002), became weaker after heat treatment. After treatment with TiN/Ti powder pack for 120 h, the (002) peak disappeared, only the other two peaks are conserved. The reason of this disappearance is not clear but it is believed to be related to surface texture.

Compared with untreated samples, these titanium peaks have no peak shift. This indicated no change of lattice parameter by interstitial solution of nitrogen. The nitridation process with TiN/Ti powder pack at 860°C has little effect on the surface.

Since the nitrogen concentration is so low, no nitride peaks show up for all treated samples. Also the color of the sample surface is the same with the untreated sample.

Figure A-4 displays the SEM photo of the cross-section of grade 4 titanium sample treated with TiN/Ti powder pack at 860°C for 48 h. The grain size is very large about 50 microns. It’s homogeneous through the cross-section. And there is no compound layer formed on the surface. However, the morphology of the surface area is different from the center area. This can be attributed by surface texture, so that grains near the surface have different orientation from those in the center area.

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TiN Ti2N TiN

Ti2N Ti2N Ti Ti

Figure A-2 XRD patterns for TiN/Ti powder pack before and after heat treatment

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Figure A-3 XRD patterns for Grade 4 titanium before and after heat treatment

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Figure A-4 SEM of cross-section for Ti4 treated with TiN/Ti at 860°C for

48 h

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A.1.2 Heat Treatment at 1150 °C

In contrast to the 860°C treatment that shows no evidence of a nitrogen-enriched phase, the sample treated at 1150°C for only 1 h showed a golden color on the surface which means a nitrides layer has formed (Figure A-5).

Figure A-6 displays the XRD results of Grade 4 titanium sample treated with

TiN/Ti powder pack at 1150°C for 1 h. The three titanium peaks expected in this 2θ range can not be found; instead the peaks of TiN phase and Ti2N phase appear. This verified the formation of nitrides on the surface which cause the golden yellow color.

Since the X-ray can roughly penetrate 5 microns of sample, the compound layer formed on this sample is at least 5 microns or thicker.

Figure A-7 is the SEM micrograph of the cross-section of grade 4 titanium sample treated with TiN/Ti powder pack at 1150°C for 1h. Three different morphologies show up gradually along the thickness direction of the sample. A porous surface layer can be easily identified as TiN phase. Beneath it there is a layer with very little contrast which should be the Ti2N phase. The grain size of the substrate is more than 50 µm. The thickness of diffusion layer can be estimated as 40 µm.

As expected in the experiments, with nitrogen diffused into the titanium substrate, the nitrided titanium surface (here TiN and Ti2N) should be harder than the untreated sample. The sample treated at 1150°C for 1 h gives very high surface hardness, about

1300HV0.2, compared to the untreated sample, about 250HV0.2.

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Figure A-5 Photograph of CP titanium (with a flat on the circle) and Ti-

6Al-4V sample treated with TiN/Ti powder pack at 1150°C for 1hr

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TiN

Ti2N

Ti Ti

Figure A-6 XRD for Grade 4 titanium sample treated at 1150°C for 1 h compared with untreated sample

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(a)

(b)

Figure A-7 SEM of cross-section for Ti4 treated with TiN/Ti powder pack at 1150°C for 1 h, (a) surface area and (b) center area

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A.2 Surface Properties of Ti-6Al-4V after Heat Treatment

Similar heat treatments for Grade 5 (Ti-6Al-4V, Ti64) samples also have been carried out. Grade 5 titanium alloy is an α+β alloy which has two coexisting phases at room temperature. The mean hardness of the base materials is slightly higher than CP titanium. The major XRD peaks show low-angle-shift due to alloying elements

(vanadium and aluminum), which have smaller radii than titanium and the lattice parameter is then reduced.

Figure A-8 shows the optical micrograph of grade 5 titanium both untreated and treated with a TiN/Ti powder pack at 860°C for 120 h. Similar to grade 4 titanium samples, the color of treated Ti-6Al-4V is not changed. The treated sample shows an equiaxed structure, with some irregular shapes at the grain boundaries, which should be β phase. The average grain size (10 µm) is smaller than the same condition treated grade 4 titanium (30 µm).

Unlike grade 4 titanium which has only one Ti phase, the Ti-6Al-4V alloy is an

α+β alloy. Figure A-9 displays the XRD pattern of Ti-6Al-4V heat-treated at different conditions. From the XRD pattern of untreated sample, the three peaks at 35.5°, 38.5° and 40.5° are from α-titanium, and the broadened peak at 39.6° is from β-titanium. In the

Ti-6Al-4V sample, the β phase has a volume fraction about 10%. So the XRD peak intensity is much lower than α phase. Compared with CP titanium, the peak positions shift to higher 2θ angle. This is because of the alloying elements, vanadium and aluminum. After heat treatment with the TiN/Ti powder pack at 860°C for 16 and 120 h, the XRD patterns showed no change for the titanium peak positions. This indicates that

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no nitrogen deposition happened. However, after treatment with TiN/Ti powder pack at

1150°C for 1 h, the XRD pattern totally changed to a new set of peaks at 2θ as 36.7° and

42.6°. They belong to TiN phase. The absence of titanium peaks indicates the compound layer is very thick.

Figure A-10 shows the SEM photo of treated grade 5 titanium alloy. Treatment with the TiN/Ti powder pack at 860°C for 48 h just like annealing, the sample show a homogenous equiaxed structure with β phase along α grain boundaries. No surface compound layer is observed. After heat treatment with the TiN/Ti powder pack at

1150°C for 1 h, a porous surface layer is appeared. This is the TiN phase. Beneath it is another compound layer Ti2N.

200

Polished & Etched

After Treatment with TiN/Ti @ 860 °C for 120 h

Figure A-8 The optical micrograph of Ti-6Al-4V samples

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TiN TiN

Ti Ti Ti Ti

Figure A-9 XRD patterns for Ti-6Al-4V samples treated with TiN/Ti powder pack at different conditions.

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Figure A-10 SEM for Ti-6Al-4V samples treated with TiN/Ti powder pack at 860°C for 48 h, and at 1150°C for 1 h.

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A.3 Microhardness Measurement

As expected in the heat treatment at 860°C, with nitrogen diffused into the titanium substrate, the microhardness of treated samples shouldn’t change too much.

However the sample treated with TiN/Ti powder pack at 1150°C for 1 h shows the formation of nitrides on the surface. It should be a very hard surface since the nitride compounds, both TiN and Ti2N, are very hard.

Figure A-11 shows the SEM micrograph of indents made by different loads.

Large loads made large indents for which the diagonal lengths are easy to measure, while small loads made tiny indents which interact with the surface roughness and it is very hard to measure the diagonal lengths accurately.

Figure A-12(a) shows the comparison of hardness data of untreated/treated CP titanium samples. The average microhardness for untreated samples is 252HV0.2. While for all treated sample, the microhardness is less. For the annealed samples, the hardness is

230HV0.2. After heat treatment with TiN/Ti powder pack at 860°C for 16, 48, and 120 h, the surface microhardness has little change with increasing heat treatment time. Treated samples give lower surface hardness data, which can be explained as the increase in grain size.

Microhardness measurement also has been done on treated Ti-6Al-4V samples.

The average microhardness for untreated samples is 350, higher than CP samples, which is due to the alloying elements. After heat treatment with TiN/Ti powder pack at 860°C for 16 h, 48 h, and 120 h, the microhardness on the surface changed. The data is shown in

Figure A-12(b). From the figure we can see that the surface microhardness has little

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change with increasing heat treatment time. The 860°C treated samples give lower surface hardness data, which can be explained as the increase in grain size. However the sample treated at 1150°C for 1 h shows a very hard surface, because of the nitride compound layer. TiN and Ti2N are very hard.

Figure A-11 SEM photo of Microhardness Indents

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1500 50 g 1000 200 g 1000 g 500

300

200 Vicker Microhardness Vicker

100

0 s hr 1 hr , treated 120 hrs o C o C, 16 o un C, 48 hrs o C, 860 1150 860 860

1500 50 g 200 g 1000 1000 g 500

400

300 Vicker Microhardness 200

100

0 s s hr ated hr e 16 tr 48 120 hrs o C, 1 hr o , C, o un C o C, 50 860 11 860 860

Figure A-12 The comparison of microhardness for CP titanium and Ti-

6Al-4V by different treatments

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A.4 Discussion

Titanium is very active. When exposed to air, it only takes milliseconds to form a thin TiO2 layer (~ 3 nm) on the surface. Underneath this layer, a diffusional TiO2-x region about 60 nm also formed (d'Agostino, Fracassi, Pacifoco, & Capezzuto, 1992). The oxide layer will affect many surface properties of titanium, especially for corrosion resistance.

The diffusion coefficient of oxygen in titanium is 2 orders of magnitude higher than nitrogen, and 4 orders of magnitude higher than titanium self-diffusion coefficient.

At elevated temperature, oxygen can get into titanium substrate very easily This oxygen diffusional layer in titanium alloy can also achieve deep case-hardening (Dong & Li,

2000). However, high oxygen concentration will result in a brittle case usually called a

“white layer”. This brittle layer is very detrimental to fatigue resistance.

Some authors have noticed that the oxide layer will retard the diffusion of nitrogen in the metal substrate. So in the gas nitridation process, the oxygen contamination has to be limited to the lowest level. In this powder pack technique, the contamination is well controlled. All reactants are sealed in the fused silica tube. Fused silica is virtually permeable only for hydrogen, helium, and neon. So in the sealed system, no outside reactant will affect the nitridation process.

One thing should be carefully considered is that the tube was filled with argon gas.

Definitely there are impurities such as oxygen and water vapor in the argon gas. This might be a source of contamination. However, let’s consider the volume of the tube which is about 15 cm3 and the base pressure inside the tube which is 1 Pa. According to the ideal gas law, PV=⋅ N kT , the total gas substance in the tube (consider the

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temperature is at 300K.) is N = PV/kT = 4.8×1015 atoms. If all the residual gas in the tube can be considered as the impurities, and the surface sites of titanium is roughly 1015 atoms/cm2, those impurities can only form a couple of monolayers at the beginning of nitridation process. Later on, those atoms will diffuse into the substrate. For a treatment lasting for tens of hours, the effect generated from these impurities is actually negligible.

With all the treatments discussed in this chapter, no significant hardness improvement has been seen. This is contradictory with the understanding of the nitriding process. At the equilibrium nitrogen partial pressure, nitrogen diffused in the sample for a long treatment time, and then the surface should be hardened. But the microhardness measurement didn’t support this hypothesis. The microhardness is within the standard deviations for all different treatment times.

Again, let’s consider the volume of the tube, which is approximate 15 cm3, and the equilibrium partial pressure of nitrogen in the reaction TiN ÍÎ Ti + 1/2 N2, which is p = 10-17 Pa at 860°C. Use the ideal gas equation PV= N⋅ kT once more, we find that inside the tube there is only N = 0.9 molecules. If the titanium solid substrate has 1015 atoms on the surface, and to have 10 at% of nitrogen at the surface boundary, at least we need 1014 atoms. It’s not a surprise that hardly there is any nitrogen in the substrate.

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A.5 Summary

1. Thermodynamic calculations show that if the formation of Ti2N is suppressed, the solubility of nitrogen in α-Ti phase can increase several times. It can be considered as supersaturation. These calculations provide a theoretical framework for the experiments in this work, which is try to obtain a high nitrogen concentration in α-Ti phase without the formation of nitrides.

2. Thermodynamic calculations also show that the equilibrium partial pressure of nitrogen to avoid the formation of nitrides is extremely low. Even modern UHV technique can’t achieve that level of pressure. However, when some gas-solid reactions are in thermodynamic equilibrium, they can establish a certain level of nitrogen pressure.

3. Sealing reactants in a fused silica tube constructs a well-defined closed system.

The residual gas sealed in the tube has no effect on the nitridation process. The permeability of active gases such as oxygen or nitrogen in the fused silica is virtually zero. The reaction between a powder pack and titanium is the only possible process in this system.

4. TiN/Ti powder pack can generate the equilibrium partial pressure of nitrogen at any given temperature. However, since the volume of the tube is very small, at such a low nitrogen pressure, that are almost no nitrogen atoms that can be decomposed from the powder pack and deposited on the titanium samples.

5. TiN powder is the nitrogen reservoir used in the heat treatment. However, the decomposition rate of TiN is not fast enough compared with the adsorption and diffusion to supply a certain surface concentration of nitrogen.

6. Different heat treatment history will change the microstructure of the substrate.

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So the mechanical properties are also changed. A surface hardened layer will have better wear resistance and corrosion resistance, but the ductility and fatigue strength may be reduced.

7. Although high temperature (above the α-β transus temperature) heat treatment can induce some nitrogen into the titanium substrate and harden the surface, the microstructure totally changed due to the phase transformation during heating up and cooling down. This microstructural change will have a negative effect on the strength and fatigue properties.

Work cited d'Agostino, R., Fracassi, F., Pacifoco, C., & Capezzuto, P. (1992). Plasma Etching of Ti

in Fluorine-containing Feeds. J. App. Phy., 71(1), 462-471.

Dong, H., & Li, X. Y. (2000). Oxygen boost diffusion for the deep-case hardening of

titanium alloys. Materials Science and Engineering a-Structural Materials

Properties Microstructure and Processing, 280(2), 303-310.

210 APPENDIX B. Si3N4/Si POWDER PACK TREATMENT

B.1 Si3N4/Si Powder Pack Treatment without getter

To get titanium nitrided without forming titanium nitride compounds, the nitrogen partial pressure has to be reduced. This can be achieved by lowering the temperature of the powder pack. However, temperature is a key factor to determine the diffusion coefficient of nitrogen in titanium. And the diffusion coefficient drops very quickly with decreasing temperature. A low diffusion coefficient will result in a thin case depth, which isn’t very useful for improving the hardness. So the temperature of treated samples should be kept at a certain level to have a better case depth without sacrificing other properties too much. Therefore, the treatment temperature for titanium samples is still kept at 860°C.

To get the temperature gradient from powder pack to sample, two furnaces are needed which can give separate heating. In order to do so, a long tube is needed to provide enough space. The middle zone of the tube then can be kept at room temperature.

And this design also helps to trap any silicon vapor that is generated from powder pack.

Since silicon has a very low equilibrium pressure of 10-20 Pa at 25°C, most of silicon would condense on the cold wall at the middle zone of the tube.

Figure B-1 displays the XRD pattern of grade 5 titanium sample treated in the long tube with Si3N4/Si powder pack at 860°C for 48 h. The temperature of the powder pack was kept at 300°C. The reason of choosing this very low temperature to do the nitridation is to see the bottom line temperature of the hardening effect. At 300°C, the

-12 nitrogen partial pressure of the Si3N4/Si powder pack is 10 Pa. From the XRD pattern

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we can see that at such a low nitrogen pressure, titanium nitrides don’t form on the surface. But the titanium peaks are shifted, which indicated that nitrogen has diffused into the titanium lattice as interstitial atoms. The surface hardness value of 360HV0.05 is slightly higher than the annealed material but within the standard deviation.

Figure B-2 displays the XPS spectrum for this sample. Besides the titanium peak, strong oxygen and carbon peaks are due to surface contamination. And silicon peaks have totally disappeared. So this long tube setup does eliminate the silicon contamination under this treatment condition. But we can hardly find the peak nitrogen, which indicate that the diffused nitrogen atoms, if there are any, are present in very small amount. So the effect on improving hardness is very limited.

The nitridation powder pack experiments at 500°C and 700°C are performed. The corresponding nitrogen pressure is 10-11 Pa, and 10-7 Pa respectively. Figure B-3 displays the XRD pattern for the 16 h treatment. In the 2θ range from 34° to 44°, only the titanium

(100) peak at 35.5° and the titanium (101) peak at 40.5° showed up for these two heat- treated samples. Compared with the annealed sample, the titanium peaks all shifted to the left side. And the shift displacement increases with increasing powder treatment temperature. This can be interpreted as higher nitrogen pressure resulting in higher nitrogen content on the surface layer. No silicon is found for these two heat-treated samples by XPS analysis. This agree with the XRD results

No nitride peaks are present in any pattern which is consistent with kinetic prediction. This may be caused by low powder pack temperature and a short treatment time. To study the limitation of equilibrium pressure, the treatment with higher powder pack temperature and longer treatment time are conducted. Figure B-4 shows the XRD

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pattern of grade 5 titanium sample treated with Si3N4/Si powder pack for 48 h. The powder packs are at 500°C and 860°C respectively. Still, only two titanium peaks in the pattern and both are shifted. But the peak shift is not larger than the 16 h treatment. The one treated at 860°C showed hardly any difference with the one treated at 500°C, although the nitrogen pressure differed by 7 orders of magnitude.

Figure B-1 XRD pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at 300°C for 48 h.

213

*104 Ti5+Si3N4/Si(300)-860C-48hrs 12 sputtered 10 min

6 N(E)/dE

0 600 550 500 450 400 350 300 250 200 150 100 50 0 Bonding energy (eV)

Figure B-2 XPS pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at 300°C for 48 h.

214

Figure B-3 XRD pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at 500°C and 700°C for 16 h.

215

Figure B-4 XRD pattern of Ti-6Al-4V treated at 860°C with Si3N4/Si powder pack at 860°C for 48 h.

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B.2 Si3N4/Si Powder Pack Treatment with Getter

To obtain a theoretically “clean system”, a titanium getter is used in the tube system as described in Chapter 4. Figure B-5 shows the XRD pattern of titanium treated at 860°C with Si3N4/Si powder pack also at 860°C in this kind of tube with getter for 24 h.

The pattern shows no peak shift at all. This is a surprising result. Since we assume that nitrogen pressure is determined by the powder pack temperature, then there is only one possible explanation for this results: the getter material also collects nitrogen gas (which is generated from powder pack) so that prevents the nitridation process.

The sample temperature is at 860°C but the temperature of the powder pack is now at 1130°C. The corresponding nitrogen pressure is 0.56 Pa. The XRD pattern is shown in Figure B-5. Compared with annealed sample, all α and β titanium peaks still showed up. However, the peaks shift is very small. This indicates that not much nitrogen has accumulated on the surface, although the nominal nitrogen pressure is already 0.56

Pa. XPS analysis was performed and the spectrum is displayed in Figure B-6. Titanium, oxygen and carbon are all on the surface, nitrogen has a very tiny peak. This result is consistent with XRD analysis. Still the absence of a silicon peak in the spectrum, proved this treatment can successfully stop the environmental contamination.

217

Ti5+Si3N4Si(1130vg20)-860-24

Ti5+Si3N4/Si(860)-860-24

Ti5 annealed

34 35 36 37 38 39 40 41 42 2θ

Figure B-5 XRD pattern of gettered sample

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Figure B-6 XPS of gettered sample with powder pack at 1130°C

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B.3 Discussion

Silicon nitride, like some other nitrides, usually is made by carbonthermal reduction method. A high level of impurities is always present in the Si3N4. Also Si3N4 is very easily oxidized. The particle surface is always covered by a SiO2 layer about several nanometers. So during heating up, the powder pack will have a lot of transient reactions before it reaches the final thermodynamic equilibrium. Silicon powder in the powder pack is also a reactive element.

Besides silicon contamination, nitrogen is also released. Unlike silicon which can condense on a cold surface, nitrogen can easily fill up the tube and get on to the titanium surface. The calculation in section 3.2 clearly shows that at a temperature lower than

700°C, the equilibrium nitrogen pressure generated from the Si3N4/Si powder pack is very low. Based on the kinetic theory of gases, the amount of nitrogen that can strike the titanium surface is very limited. However, the Ti peak shift is easily observed for treated samples and the hardness is increased. This is an unexpected result for such a low nitrogen pressure. As we discussed in APPENDIX A, the residual gas in the tube won’t affect the hardness of treated samples. These results have to be attributed by the nitrogen that comes out during the transient states. Since it is a non-equilibrium situation, we have no way to know the quantity of this nitrogen pressure, and it is very hard to control. But we can by-pass this problem if we eliminate these uncertain factors before doing the sample nitriding.

Using a getter in the sealed tube is the key factor to reduce any unwanted reactions during the heat treatment. In industrial activities, titanium is a very common gettering material to adsorb and remove unwanted materials. In APPENDIX A, TiN/Ti

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powder pack treatment won’t introduce any contaminations to titanium samples. One reason is there are only titanium and nitrogen involved in that system. Even if there are some impurities on the samples or in the powder pack, the titanium powder will act as a perfect getter for all unwanted materials. When powder pack is changed, other elements are also introduced in the system and the contamination is generated. For the heat treatment with Si3N4/Si powder pack, the getter not only eliminates the Si vapor and other impurity effects, but also adsorbs the excessive nitrogen generated at the transient states. After the powder pack has reached thermodynamic equilibrium, which means the pressure of nitrogen is at the right level, we can cool down the getter and then heat up titanium to start the nitridation process.

Considering the loss of some nitrogen in the getter, with the new experimental setup, a suitable nitrogen pressure for nitridation in the system is about 0.1 Pa. After 24 h treatment, the surface hardness improves without the formation of nitrides. To pursue a greater hardening effect, a higher nitrogen partial pressure must be achieved by a higher powder pack treatment temperature. But increasing the temperature is not favorable for industrial energy saving.

As we discussed in chapter 2, adsorption and diffusion of nitrogen is the main source terms for nitriding. We assume that the adsorbed nitrogen is the starting point for the nitrogen diffusion. The diffusion coefficient is a function of temperature. The adsorption rate is mostly affected by gas partial pressure. The diffusion zone consists of nitrogen in solid solution as long as the temperature-dependent solubility limit is not exceeded. If the solubility limit is exceeded, nitride formation occurs. And for powder pack technique, the thermodynamics and kinetics of the gas-solid reaction is of equal

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importance.

B.4 Summary

1. A titanium getter was integrated in the heat treatment setup. By using the getter, the effect from all unwanted reactions has been removed. After that, we can consider that the titanium samples are treated in a well-controlled, clean system.

2. Kinetic calculations show that a much higher nitrogen partial pressure can be utilized to do titanium nitridation without forming the nitrides. This calculation is based on gas-solid interface impingement rate and the interstitial diffusion coefficient. This pressure range can be achieved by the decomposition of other metal nitrides at certain temperatures.

222 APPENDIX C Non-linear Viscoelastic Properties of

Cucumaria frondosa Dermis

Non-linear Viscoelastic Properties of Cucumaria frondosa Dermis

Lizhi Liu(a), Zhien Liu(a), Arthur H. Heuer(a)*, and John A. Trotter(b)

a) Department of Materials Science and Engineering, Case Western Reserve

University, Cleveland, OH 44106

b) Department of Cell Biology and Physiology, School of Medicine, University of

New Mexico Health Science Center, Albuquerque, NM 87131

* To whom correspondence should be addressed. Email: [email protected]

Key Words: echinoderms, collagen, connective tissue, Cucumaria frondosa,

sea cucumber, mechanical properties, mechanical model, stress relaxation, creep,

viscoelasticity, tensile strength, displacement rate, water loss

223 Abstract

The mechanical properties of frozen-thawed tensile specimens taken from the inner dermis of Cucumaria frondosa have been studied using tensile and creep tests and stress relaxation experiments. The tensile studies were conducted under various displacement rates and the stress relaxation tests with various prestrains; in particular the prestrain effect on mechanical properties of sea cucumber dermis was systematically investigated. C. frondosa dermis displays linear viscoelasticity at low strains but non- linear viscoelasticity at high strains. Mechanical models for the stress relaxation were developed and relaxation curves could be simulated. Although specimens were tested while immersed in artificial sea water (ASW), water was expressed from these specimens during testing; this water loss was characterized as a function of the extent of viscoplastic

deformation.

Introduction

The echinoderm phylum consists of five classes – sea urchins, sea lilies, starfish,

brittle stars and sea cucumbers. The connective tissues in these organisms display

mutable mechanical properties, changing reversibly from a stiff to a flexible state under

physiological time scales. We have studied this phenomenon in specimens of the North

Atlantic species, Cucumaria frondosa. The dermis consists of the following components:

1) collagen fibrils to which proteoglycans are tightly bound; 2) other proteoglycans which

are not tightly bound to fibrils; 3) micro-fibrils that surround bundles of collagen fibrils;

4) other (non-collagenous) proteins; and 5) nerve processes, morula cells, and granular

cells (Trotter and Koob, 1995; Thurmond and Trotter, 1996; Trotter et al., 1997).

Physically, the dermis can be divided into an inner dermis, which is relatively stiff, and

224 an outer dermis, which is more compliant. Sea cucumber dermis is a convenient vehicle

to study mutable mechanical properties. The mutability can be observed by means of electrical, mechanical, or chemical stimulation (Motokawa, 1981).

Biomechanical studies of sea cucumber dermis have employed a variety of testing modalities, including creep studies (Motokawa, 1981, 1982, Byrne, 1985), stress-strain studies (Motokawa, 1982, Eylers, 1989), stress relaxation studies (Motokawa, 1984), bending studies (Trotter and Koob, 1995), and dynamic oscillatory shear studies (Szulgit and Shadwick, 2000). Two mechanisms for the mutable properties of the dermis have been put forward. In one, the stiffness change of the dermis is attributed to the viscous components of the matrix (Eylers, 1982, Motokawa, 1984; Eylers and Greenberg, 1988,

1989). In the stiff state, collagen fibrils sliding through the matrix are thought to encounter increased resistance due to interaction with the surrounding, primarily viscous, matrix components. In the second model, the stiffness change is attributed to the elastic components (Harris, 1980, Szulgit, 1998), for example, by adjacent fibrils becoming linked together. Szulgit and Shadwick (2000) have discussed the two types of mechanisms.

Models involving springs and dashpots have been used to predict the mechanical properties of mutable connective tissue (Eylers, 1982; Motokawa, 1984; Eylers and

Greenberg, 1988, 1989). However, these models do not provide general understanding of the mechanical behavior of sea cucumber dermis. For example, up to three kinds of spring and dashpot models have been suggested, including the Maxwell model and the standard linear solid model, but it is not clear which model is applicable under specific conditions.

225 The mechanical properties of C. frondosa dermis have been described by Trotter and Koob (1995), Szulgit and Shadwick (2000), and others. In this present work, stress-

strain tests, stress relaxation tests, and creep tests were performed to characterize the mechanical properties of C. frondosa dermis in the frozen-thawed state. The process of freezing and thawing lyses cells and thereby puts the dermis into the maximally stiffened state. Studies on the dermis in this state are quite relevant to the rheological properties of the dermis in its maximally stiffened state. Mechanical models were developed to predict relaxation behavior of the dermis. It was found that C. frondosa dermis displays non- linear viscoelastic behavior. By simulating the master curve, the mutable rheology displayed by the dermis is attributed to the interactions between collagen fibrils, consistent with the model used by Szulgit (1998).

Materials and Methods

Specimens

Sea cucumbers of the genus C. frondosa were collected in the Gulf of Maine

during September or October. The animals were sectioned longitudinally along the ventral surface with a razor blade so that the viscera and muscle layers on the inside of the body wall could be removed. As noted above, the body wall of sea cucumber dermis consists of inner and outer segments. The pigmented outer dermis was removed with a razor blade. The white inner dermis was cut into pieces approximately 2×4×30 mm and fast frozen and stored at -70°C. Before testing, frozen dermis was thawed in artificial sea water (ASW, 0.5 M NaCl, 0.05 M MgCl2, 0.01 M CaCl2, 0.01 M KCl, and 0.01 M 3-(N-

morpholino) propane sulfonic acid (MOPS), pH 7.8-8.0).

All of the mechanical tests to be reported here were conducted on these frozen-

226 thawed dermis specimens. Because of possible variability in the mechanical properties of

the tissue, which could depend on the position from which the specimen was selected and

the age of the animals, most tests were repeated several times and conclusions were

drawn from tests conducted using specimens from one animal. All tests were performed

in ASW at 12°C.

Stress-Strain and Relaxation Tests

An Instron 1125 Universal Testing machine (Canton MA) was used for both

stress-strain and stress relaxation tests. Specimens were cut into 2×2×30 mm pieces, and the thickness and width measured using a digital caliper with an accuracy of 0.01 mm.

They were mounted onto two screw-loaded epoxy/acrylate grips, using a cyanoacrylate

"Superglue" for initial mounting. The specimen span was about 8 mm. One grip was fixed to the bottom of a beaker containing ASW solution, located at the base of the

Instron machine. The other grip was connected to an MDB-25 load cell (Transducer

Techniques, Temecula, CA) mounted on the cross head of the Instron machine; full scale of the load cell is 100 N, with an accuracy of ±0.05 N. For the stress calculation an assumption of constant volume is applied. So the stress is the load divided by calculated cross-section area.

In the stress/strain tests, the crosshead moved at a constant rate in the range 0.1 to

100 mm/min, until the specimen fractured. Inasmuch as the gauge sections were 8-10 mm, the strain rates were in the range of 1% to 1000 %/min. In the stress relaxation tests, the cross head of the Instron machine was stopped at a certain strain, and the stress was recorded as a function of time. The typical displacement rate during loading for these tests was 5 mm/min. Unless otherwise indicated, all tests were conducted under standard

227 conditions – immersion in ASW at 12°C and pH 7.8. The test specimens in the stress relaxation tests (and in the creep tests to be described next) were identical to those used for the stress-strain test. Each specimen was stretched under loads ranging from 0.12 to

16 N, corresponding to initial stresses of 50 kPa to 6.3 MPa.

Creep Tests

Creep tests were conducted for frozen-thawed tissues in ASW at 12°C and pH

7.8, using an apparatus similar to that described by Trotter and Koob (1995); its most important component is a linear variable differential transducer (LVDT) (Lucas Shaevitz,

Pennsauken, NJ, U.S.A.). During the creep tests, length changes were recorded by the

LVDT every 6 seconds for times up to 20 minutes.

Weight Loss Measurement

During this work, water was “expressed” or exuded from the samples during testing, even though the specimens were completely immersed in ASW. The following protocol was employed to measure this weight loss. Before conducting the mechanical test, a specimen was first mounted onto the specially designed grips, which can hold the specimen tightly without applying Superglue. During this specimen mounting, the portion of the specimen within the grips was compressed; water was exuded from this region.

The specimen was then removed from the grips and its weight determined. This weight,

Ws1, represents the original weight of the test specimen after mounting. The specimen was remounted and the test conducted. As soon as the test was completed, the specimen was removed from the grips and the weight, Ws2, determined. Ws1-Ws2 represents the water loss during testing. The last step was to cut off the two ends of the specimen that were within the grips and determine the weight of the tested span, Wg2. Then Ws1-

228 Ws2+Wg2 is the effective weight that experienced the water loss. The percentage of

water loss (w%) is then calculated as

Ws12− Ws w%100%=× (1) (Ws 1−+ Ws 2) Wg 2

Results

Mechanical Behavior ---Tensile and Stress Relaxation Behavior

Representative stress-strain and stress relaxation curves of C. frondosa dermis are

shown in Figure 1 and 2. Specimens l and 2 in Figure 1 are from a single 2×4×30 mm

piece of tissue and show similar rheological behavior; the same is true for specimens 3 and 4. All of the specimens in Figure 1 are from a single individual. All specimens show a “toe region” at very low strains, which may correspond to true elastic deformation.

Above a (strain-rate dependent) strain, non-recoverable strain commences and the

“stiffness” (the slope of the σ-ε curves) increases. For the displacement rate of Figure 1, the stiffness is ~ 45MPa. Failure occurs at strains between 60 and 70%, corresponding to ultimate tensile strengths between 20 and 25 MPa.

Table 1 shows the mean tensile strength, facture strain, and stiffness, and their standard deviations for the data of Figure 1, and the range in these properties from 12 individuals. While there is animal-animal variability, the rheology of the tissue from a

single individual appears to be well behaved and suitable for parametric studies.

Stress relaxation tests (again from a single individual) are shown in Figure 2.

Specimens 2 and 3 are from a single 2×4×30 mm piece of tissue and show nearly

identical relaxation behavior, the same is true for specimens 4 and 5. The range of

relaxation behavior from a single animal is clearly as small as the behavior under tensile

229 Effect of Displacement Rate on Tensile Behavior

The stress-strain curves of C. frondosa dermis (again from a single individual),

tested under different displacement rates of 0.1, 0.5, 2, 20, and 100 mm/min, are shown in

Figure 3. The displacement rate does not affect the fracture strain, which is between 65

and 75% for all specimens. However, the fracture stress increases systematically with increasing displacement rate, varying from 15 MPa to 23.5 MPa, as does the stiffness.

The stress-strain curves of Figure 3 can be divided into two regimes: Region I up to about

30% strain, and Region II from ~30 to 60% strain. The stiffness in Region I increases

very rapidly when increasing the displacement rate from 0.1 mm/min to 100 mm/min, whereas in region II, the stiffness change is much more modest. This probably indicates some relaxation during deformation at the slower displacement rates.

Effect of Prestrain on Stress Relaxation of C. frondosa Dermis

Figures 6 and 7 show stress relaxation curves of C. frondosa dermis specimens tested under different prestrains from 8.4% to 68.1%, plotted in two different ways. In the stress-time plots, the stress was normalized (σ(t)/σmax is actually plotted) in order to

facilitate comparison for different prestrains. There is a very strong prestrain effect on the

relaxation curves, the higher prestrain causing hardening of the dermis, i.e. prestrain

reduces the total relaxation. Thus, the characteristic relaxation time, the time when the

stress decayed to 1/eth of the original stress, becomes unmeasurable in the time period

used in these tests when prestrains are larger than 34.2%. In log(stress)-log(time) plots

(Figure 7), the relaxation curves tend to be linear with increasing prestrain. The slope, m, of the relaxation curves changes from 0.160 to 0.037 when prestrain was increased from

8.4% to 68.1%.

230 Creep Tests

Creep tests were conducted under different initial stress, from 50 kPa to 6.3 MPa; the data are shown as strain versus time plots in Figure 8. The creep strains at 10 and 20 minutes were plotted versus initial stress, see Figure 9. At low stresses (up to 1 MPa) the creep strain increases linearly with initial stress. At high stresses (greater than about 1

MPa) this relationship was non-linear.

Water Exudation during Mechanical Testing

During the cyclic loading tests, we found that the stress history affected the stress state, which we attribute to water exudation during loading. The average water loss, using a displacement rate of 5 mm/min (strain rate of 50 %/min), was 24 wt.%, while at a rate of 0.5 mm/min, the water loss was 39 wt.% (Figure 10).

Water loss from the dermis continues during the stress relaxation tests, as shown in Figure 11. This implies that the water loss during tensile testing under a given displacement rate is a non-equilibrium process; “equilibrium” water loss, if such exists, may be attained only at very low displacement rates.

Water loss also occurred during the creep tests; water loss as a function of time at constant load is shown in Figure 12a, while water loss after a 5 minute creep test at different stress is shown in Figure 12b. The range of water loss is similar in these tests to that already demonstrated.

We also measured dimensional changes after stress relaxation tests; the results are shown in Table 2. After the tests, the specimens were kept in ASW for about 30 minutes together with the grips. Then the specimen dimensions were measured and the permanent strain calculated. When tissue was stretched at low strains, the tissue underwent such

231 extensive recovery that further shrinkage was observed, i.e. specimens experienced

negative permanent strain. At prestrain greater than about 20%, the strain is non-

recoverable, and the permanent strain is positive.

Discussion

Springs and Dash-Pot Models

A wide range of synthetic materials show some combination of linear elastic and

viscous behavior – linear polymers and rubbers are familiar examples. For comparing and

understanding these materials in relation to C. frondosa dermis, it is useful to rigorously

define the term “linear viscoelasticity”. If a stress σ1 produces a strain ε1 in time t, while

stress σ2 produces strain ε2 in the same time t, then stress (σ1 + σ2) will produce strain (ε1

+ ε2) in time t. More generally if a sequence of stresses σ1 σ2 σ3 ... σn is applied at times t1

t2 t3...tn, then the strain at some time t is given by:

n ε(t) = ∑σ i D(t − ti ) (2) i=1

where D is a material constant.

Combining springs and dashpots is the commonly accepted method of modeling viscoelastic materials. The Maxwell model and the three element standard linear solid model are two well-known examples. The following equations can be used to predict relaxation behavior of such linear viscoelastic materials:

σ (t) = E0 exp(−t / λ) (3) ε 0

for the Maxwell model and

σ (t) = E∞ [1− exp(−t / λ)] + E0 exp(−t / λ) (4) ε 0

232 for the three element model, where t is time, λ is a characteristic relaxation time

th when the stress decays to 1/e of the initial stress, E0 is an apparent modulus at time=0, ε0 is the prestrain, E∞ is the relaxation modulus when t is infinite, and σ(t) is stress at time t.

The viscosity of the Maxwell element is defined as η=E0λ.

The Maxwell model, the standard linear solid model, and a four element model

(two Maxwell elements in parallel) were used to model the relaxation behavior of dermis from Holothuria, Actinopyga, and C. frondosa in ASW (Motokawa, 1984, Szulgit and

Shadwick, 2000), with reasonable matches to the experimental data. In Motokawa's work, the prestrain and stress are the same for the two species, 50% and 0.5MPa, respectively.

The relaxation time is 1.8s for Holothuria and 82s for Actinopyga, respectively.

Apparently, Holothuria and Actinopyga dermis are much softer than C. frondosa dermis.

Unfortunately, Motokawa randomly selected one prestrain for the stress relaxation tests.

We do not know whether under the high strain selected, the dermis studied in his work will display linear viscoelasticity. Szulgit predicted the mechanical property change when the modulus of the spring and the viscosity of the dashpots changed separately and gave a helpful discussion. However, they did not simulate the stress relaxation behavior using the standard linear solid model and compare it with the experimental curves.

When using the Maxwell model, we treat E0 and cross-section area as constants, i.e., as independent of the magnitude of the prestrain. This work shows that this assumption is reasonable when the stress, and therefore the prestrain, is small. This situation is then comparable to the behavior of an elastic material within the elastic limit.

If the material meets the foregoing conditions, we call the material linear viscoelastic.

Therefore, in principle, these time dependent spring and dashpot models can be used for

233 linear viscoelastic materials. However, Matsuoka (1992) pointed out that a model of springs and dashpots has a serious deficiency. If it is made to fit a set of real relaxation data, it cannot fit the creep test data for the same material. A valid mathematical model must fit all experimental data without changing the values of the parameters. No combinations of springs and dashpots can satisfy this simple requirement. According to

Matsuoka's work, springs and dashpots models are not even good for linear viscoelastic materials. C. frondosa dermis displays linear viscoelasticity only at low strains. At high prestrains, the stress or relaxation modulus during stress relaxation obviously depends on both time and prestrain, and the material by definition is not linear viscoelastic. Thus, different models are needed to predict the mechanical properties of C. frondosa dermis at low and high strains, respectively.

Kohlrausch-Williams-Watts (KWW) and Power Law Models

Stress relaxation curves record the time-dependent change in stress at constant strain and temperature. However, for linear viscoelastic materials (such as amorphous polymers), time and temperature are equivalent to the extent that data at one temperature can be superimposed upon data taken at a different temperature, merely by shifting the relaxation curves (Leaderman, 1943). By doing this, it is possible to treat stress relaxation data at widely different temperatures using a single curve covering many decades of time at some reference temperature. First of all, the relaxation curves can be plotted as log

(stress) vs. log (time) (or log (modulus) vs. log (time)), see the left of Figure 13 (modulus is defined as σ(t)/ε0)). Then, these curves can be shifted, one at a time, with respect to the reference curve (at TR = 25°C), until portions of the curves superimpose to give a master curve, such as shown on the right side of Figure 13. The amount each curve has to be

234 shifted along the logarithmic time axis in making the master curve, the so-called shift factor, is a function of temperature (Williams, et al., 1955, Krevelen and Hoftyzer, 1976).

An equation is available to calculate the time change at constant temperature.

Generally, the curve can be divided into three stages: 1) glassy state; 2) leathery state (above the glass transition temperature, Tg, of the material); and 3) rubbery state.

There are two equations that can be used to predict the master curve. The Kohlrausch-

Williams-Watts (KWW) model (Donth, 1992) is usually used for stage 1 and 3:

σ (t) β = E0 exp[−(t / λ) ] (5) ε 0

where λ is the relaxation time and β encompasses all material-related parameters.

For polymers, β is generally around 0.5.

A power law is used for stage 2:

σ (t) E t = 0 ( ) −n (6) ε 0 e λ

where n is constant.

Although only the first and second stages are revealed by the data. It can be seen that the relaxation curve of C. frondosa dermis tested under standard conditions (12°C,

ASW, and pH7.8) corresponds to the glassy state of polymeric materials. Thus, the

KWW model can be used to predict the relaxation behavior of C. frondosa dermis.

A simulated relaxation curve for a prestrain of 8.4%, which was obtained using equation (5), is shown in Figure 15 and compared with the experimental data. The parameters used for simulation are: prestrain ε0 = 8.4%, initial modulus E0 = 10MPa, relaxation time λ = 201s, and β = 0.48. The simulations match very well with the experimental data. Well-matched simulation curves can also be obtained for the

235 relaxation curves with higher prestrain. However, β decreased to 0.45 for a prestrain of

11.5% and to 0.40 for a prestrain of 21.7% (Figure 15). At strains of ~50%, the relaxation curve can be simulated using a power law, that is, equation (6). The n value, which has a similar meaning to β in equation (5), is even lower -- 0.21 for a prestrain of 34.2% and

0.085 for 68.1%. However, the relaxation times are too long to be measured -- 1700s and

4.8×105s for prestrains of 34.2% and 68.1%, respectively (Figure 16).

According to the definition of linear viscoelasticity, equation (2), these results clearly show that C. frondosa dermis displays non-linear viscoelasticity. However, when the prestrain is low, between 8.4% and 11.5%, the relaxation curves are very similar and the relaxation times are essentially constant. This indicates that the sea cucumber dermis investigated in this work displays nearly linear viscoelastic properties at low strains, but becomes non-linear at high strains.

From these simulations, we also note that the viscosity of the tissue increases with increasing prestrains. It is important to note that during the relaxation tests, water content in the tissue is continuously being exuded, with water loss increasing with increasing prestrain. With insufficient water to act as both solvent and lubricant, the fluid in the tissue becomes more viscid, and the viscosity of the simulated Maxwell element is also increased.

The water content of the dermis is clearly a key factor in determining stiffness, because it is more than 50wt% in the dermis of C. frondosa tissue. The smaller increases in stiffness between Regions I and Region II in the high displacement rate (100 mm/min) test is attributed to the difficulty of "squeezing" water out of the tissue at the higher displacement rates. In fact, the difference in stiffness between the two regions is also

236 associated with water exudation during tensile elongation, in spite of the fact that specimens were immersed in water during testing. This can also explain the appearance of two regions in the stress-strain curves and the effect of displacement rate on the apparent modulus in Figure 3. Since exuding water from the tissue is a time-dependent process, at low displacement rates, there is enough time for water to diffuse out of the tissue. In region I, the apparent modulus is only 13 MPa, whereas in region II, the apparent modulus increased to 33 MPa. At very high displacement rates, the tests were finished in a very short time, and only a small amount of water was exuded. Therefore, the two regions are difficult to distinguish. For example, the apparent modulus of the tissue tested at a displacement rate of 100 mm/min increased by only 26% from 34 MPa to 43 MPa.

The dimensional changes (Table 2) we measured can also be explained by water- exudation. When tissue was stretched at low strains, only small amounts of water were squeezed out and caused deformation of the tissues. At this time, the collagen fibrils are still separated from each other by a liquid film. When the stress is removed, the collagen fibrils tend to be pulled together under the capillary forces inherent in the water-collagen two-phase system. Therefore, the stretching strain was recovered completely and caused further shrinkage, i.e. specimens experienced negative permanent strain. At low strains, in fact, the mechanical properties (such as the apparent elastic modulus) of the tissues represented that of the mixture of collagen fibrils, protein and water. With increasing prestrain, more water was squeezed out during stretching, allowing adjacent collagen fibrils to come closer together. At a critical prestrain, which is about 20% in this investigation (Table 2), adjacent collagen fibrils apparently touch each other. With

237 further increases in prestrain, sliding between collagen fibrils occurs. After removing the stress, the stretching strain is non-recoverable, and the permanent strain is positive. At high strains, the mechanical properties of the tissue appear to reflect the interaction of collagen fibrils with one another. Also, the phenomenon of a saturation strain in load- unload cycles is also believed to be associated with water exudation.

Our data in total is consistent with the model that attributes the mutable rheology of the dermis to the interactions between adjacent collagen fibrils (Szulgit and Shadwick,

2000). In particular, the ability to derive a master curve of the type used to describe the rheology of engineering polymers (Figure 13 and 14) is good evidence of the dominance of collagen interactions in the rheology of the sea cucumber dermis.

Conclusions

1) The mechanical properties of C. frondosa dermis can be reliably and reproducibly

determined using standard rheological tests.

2) The dermis displays linear viscoelasticity at low strains and non-linear viscoelasticity

at high strains. Stress relaxation behavior depends on both time and prestrain.

3) During mechanical testing, water in the dermis is exuded. The water content of the

dermis is a key factor in determining stiffness, viscosity and other mechanical

properties.

4) The stress-strain curves of C. frondosa dermis are relatively insensitive to

displacement rates in stress/strain tests. The toe region in stress-strain curve is

attributed to the “expression” of water from the tissue under load.

5) Similar to engineering polymers, a master curve can be constructed for C. frondosa at

low prestrains. The relaxation curves tested under standard conditions (below Tm)

238 correspond to the glassy state for polymers. Therefore, the KWW model can be used to predict stress relaxation. This is interpreted to indicate the dominance of collagen interactions in the mutable rheology displayed by the dermis.

Acknowledgement

This work was supported by the Defense Advanced Research Projects Agency

(DARPA).

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242 Table 1. Tensile data of dermis taken under standard conditions (ASW,

12°C, pH = 7.8) at a displacement rate of 10mm/min

One animal (Figure 1) † Range from animal to animal ‡

Tensile strength (MPa) 22 ± 3 15 – 35

Fracture strain (%) 65 ± 7 40 – 75

Stiffness (MPa) 45 ± 2 40 – 68

†: Mean value ± standard deviation.

‡: Specimens from 12 animals were studied.

243 Table 2 Dimensional change of frozen-thawed dermis specimens after stress relaxation tests at different prestrains

1 2 3 4 5

Initial length, L0 (mm) 7.45 8.11 7.88 7.66 8.28

Maximum stress, σ0 (MPa) 0.28 0.55 1.14 2.84 5.64

Maximum strain, ε0 (%) 4.0 7.0 6.9 14.1 23.7

Final length, Lf (mm) 7.07 7.75 7.57 7.22 8.42

Permanent strain, εp (%) -5.1 -4.4 -3.9 -4.0 1.6

244

30 * Specimens 1-6 are from same batch Specimen-1 1-2, 3-4, and 5-6 specimens are from Specimen-2 25 one piece dermis Specimen-3 Specimen-4 Specimen-5 20 Specimen-6

15 Stress (MPa) 10

toe region 5

0 0 1020304050607080 Strain (%)

Figure 1 Stress-strain curves of frozen-thawed sea cucumber dermis

(repeatability test)

245 Specimen-2 8 Specimen-3 Specimen-4 Specimen-5 Specimen-6 6 Specimen-1

4 Stress (MPa)

Specimen 2 and 3 are from same strip of dermis, as are Specimen 4 and 5. 0 0 200 400 600 800 1000 1200 Time (s)

Figure 2 Stress relaxation of frozen-thawed sea cucumber dermis (standard conditions)

246

25 100 mm/min 20 mm/min 20 2 mm/min 0.5 mm/min Region II 0.1 mm/min

10 Region I Stress (MPa)

0 0 10203040506070 strain (%)

Figure 3 Stress-strain curves of sea cucumber dermis at different displacement rates

247

1.4

(a) Maximum load: 5 N 1.2

1.0

0.8

0.6 Stress (MPa)

0.4

0.2

0.0 0123456789101112 strain (%)

12 (b) Maximum load: 30 N

Stress (MPa) 4

0 0 5 10 15 20 25 30 35 40 strain (%)

Figure 4 Stress-strain curve of C. frondosa dermis during load-unload cycles

248

Stress (MPa) 5

0 5 1015202530 strain (%)

Figure 5 Stress vs. saturation strain curve of frozen-thawed tissue after 5 cycles of load-unload testing. (An exponential curve has been fit to the data; it has no theoretical implication.)

249

1.2 σ = 68.1%, ε = 31 MPa 0 0 σ = 50.5%, ε = 19 MPa 0 0 σ = 44.0%, ε = 13 MPa 1.0 0 0 σ = 37.8%, ε = 10 MPa 0 0 σ = 34.2%, ε = 8.6 MPa 0 0 σ = 21.7%, ε = 5.7 MPa 0.8 0 0 σ = 11.5%, ε = 1.9 MPa 0 0 σ = 8.4%, ε = 0.84 MPa 0 0 0.6

Normalized Stress 0.4

0.2

0.0 0 200 400 600 800 1000 1200 Time (s)

Figure 6 Stress relaxation of frozen-thawed sea cucumber dermis with different prestrains, ε0 (standard condition).

250

7.5 m=0.037 7.0

6.5

6.0

ε = 68.1% 5.5 0 (Stress) [Pa] ε = 50.5% 10 0 ε = 44.0%

log 0 5.0 ε = 37.8% 0 ε = 34.2% m=0.160 0 ε = 21.7% 4.5 0 ε = 11.5% 0 ε = 8.4% 0 4.0 0123 log (Time) [s] 10

Figure 7 Stress relaxation of frozen-thawed sea cucumber dermis with different prestrains (log scales)

251 50 load = 1600g load = 800g load = 400g load = 200g 40 load = 100g load = 50g load = 25g 30 load = 12.5g Strain (%)

0 0 5 10 15 20 Time (minutes)

Figure 8 Creep test of frozen-thawed sea cucumber dermis under different initial stress

252

10 minutes 20 minutes 40

20 Strain (%)

0 01234567 Stress (MPa)

Figure 9 Strain vs stress of frozen-thawed sea cucumber dermis during creep tests for 10 and 20 min

253

water loss average water loss 35

water loss (%) loss water 30

15 012345 displacement rate (mm/min)

Figure 10 Water loss as a function of displacement rate during tensile tests

254

32 water loss (%) 30 water loss average water loss 28 displacement rate: 1mm/min 26

0 5 10 15 20 120 130 relaxation time (min)

Figure 11 Water loss during stress relaxation tests

255

Water loss (%) 20 applied stress σ=1.5MPa

0 0 5 10 15 20 25 130 140 150 creep time (min)

water loss (%) creep time: t = 5 min 10

0 0.00 0.75 1.50 2.25 3.00 Applied Stress (MPa)

Figure 12 Water loss as a function of (a) creep time, and (b) applied stress

256

Figure 13 Time temperature superposition principle illustrated with polyisobutylene data. The reference temperature of the master curve is 25 oC. The inset graph gives the amount of curve shifting required at the different temperatures (after

Catsiff and Tobolsky, 1955).

257

6.8

0 6.6 12 C 300C 0 6.4 45 C

6.2

6.0

(Stress) [Pa] (Stress) 10

log 5.8

5.6

5.4

5.2 012345 log (time) [s] 10

Figure 14 Master curve of C. frondosa dermis at low strains

258

6 Simulation parameters: (1) (2) (3) Prestrain (ε ): 8.4% 11.5% 21.7% 5 0 Relaxation time (λ): 201 s 253 s 487 s (3) Initial modulus (E ): 10 MPa 16.8 MPa 25 MPa 0 β: 0.48 0.45 0.40 4

Stress (MPa) 2 (2)

1 (1)

0 0 200 400 600 800 1000 1200 time (s)

Figure 15 Experimental and simulated Stress relaxation of C. frondosa dermis at prestrain of 8.4%, 11.5% and 21.7%

259

35 Simulation parameters: (1) (2) 30 Prestrain (ε ): 34.2% 68.1% 0 Relaxation time (λ): 1700 s 470000 s (2) Initial modulus (E ): 25.3 MPa 46 MPa 0 25 n: 0.211 0.085

Stress (MPa) Stress (1)

0 0 200 400 600 800 1000 1200 time (s)

Figure 16 Simulation of relaxation of C. frondosa at prestrains of 34.2% and

68.1%

260

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