The diffusion of carbon into tungsten

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Authors Withop, Arthur, 1940-

Publisher The University of Arizona.

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Link to Item http://hdl.handle.net/10150/347554 THE DIFFUSION OF CARBON INTO TUNGSTEN

by Arthur Withop

A Thesis Submitted to the Faculty of the

DEPARTMENT OF METALLURGICAL ENGINEERING In Partial Fulfillment of the Requirements .For the Degree of

MASTER OF SCIENCE

In the Graduate College

THE UNIVERSITY OF ARIZONA

1966 STATEMENT BY AUTHOR

This thesis has been submitted in partial ful­ fillment of requirements for an advanced degree at The University of Arizona and is deposited in the University Library to be made available to borrowers under rules of the Library,,

Brief quotations from this thesis are allowable without special permission, provided that accurate acknowledgment of source is made. Requests for permis­ sion for extended quotation from or reproduction of this manuscript in whole or in part may be granted by the head of the major department or the Dean of the Graduate College when in his judgment the proposed use of the material is in the interests of scholarship. In all other instances, however, permission must be obtained from the author.

SIGNED:

APPROVAL BY THESIS DIRECTOR

This thesis has been approved on the date shown below:

/ r / r ~ t / r t e //Date Professor of Metallurgical.Engineering ACKNOWLEDGMENTS

I wish to express my appreciation to my advisor, Dr0 K 0 L 0 Keating, for his valuable guidance and advice with this project, to Mr, A, W, Stephens for his assist­ ance with the equipment, and to all the graduate students in the Department of Metallurgical Engineering for their encouragement and confidence. Finally, I am grateful to my wife, Toni, for her sacrifices and patience during my academic years. TABLE OF CONTENTS

Page

LIST OF ILLUSTRATIONSooooeooooo o O deoooeoooeoooooooooe vi

LIST OF TABLES,0„OOOOOOO-OOOOOOOOOOOOOOOOOOOOOQOOOOOOO vii

ABSTRACT0 .0 „o.oeo OOOOOOOOOOftOOOOOOOOOOOOOOOOOOOOOOOOO viii

lo INTRODUCTIONOOOOOOOOOOOOOOOOOOOOOOOOOO.O 1

II. THEORY. 00000000000000006000000000 00 0.0 o O o 4

2.1 * S Laws oooooooooooooooooooaoooo 4

2.1.1 Steady-State-Diffusion..= 4 2.1.2 Non-Steady State DiPPxisaon...... oo.oo o. 5 2.2 Solution to Flck's Law...... 5

2.3 Diffusion Lengch.ooooooo.ooooooo.oo 8

2.4 Arrhenius Relation...... oo.oo....o 9

2.5 Meohanisms....ooooooooooooooooooooo • 9

2.5.1 Interstitial Diffusion... 10

2.5.2 Meaning of D^...... 10

2.6 van1t Hoff Equation...... I. 12

III. EXPERIMENTAL PROCEDURE.. . ’ 15

3 o l Diffusion Couple...... ooooo.o. 15

3o2 F U m a G e OO.O.O.OOOOOO.OOOOOOOOOOOOO* 16

3.3 S e C t l O m n g o OQ.OOO.OOOOOOOOOOO.OOOOO 20

3.4 X —Ray Diffraction..ooo.ooo.oooooooo 23

4 ir V

TABLE OF CONTENTS— Continued

Page

IV, EXPERIMENTAL RESULTS,,,,,,,,,,,,,,,,,,,, 30

V o DISCUSSION OOOOOOOOOOOOOOOOOOOOOOOOOOOOOO '35 5.1 Comparison of''Results' with.... Literature, o,,,,-,,,,000,0,00000000 35 5.2 Equilibrium Analysiso,,,,*,,,,,,,,, 37

VI , CONCLUSIONS ,,00000 <>00000000,,0000000,,og 35

REFERENCES o,,,,o,,,,,,,,,,00,0,00,0000000,0,0o,,,,,,, LIST OF ILLUSTRATIONS

Figure Page

2-1 Tungsten-Carbon Diffusion Couple 0 „ „ 0«= <,»<,«o = = 7

2-2 Interstitial Mechanism,,, 0 »=,,, »6,,, o = = 11

3-1. Tungsten Microstructure , 18 3-2 Vycor Tube Furnace0000000000,00000,00000,0000 15

3-3 Induction Piirnace 0,0,0000000,000,00000 0,00000 21 3-4 Diamond Grinding Unit,„,,«,,o,,, =,, =,,,,o«, =, 24

3-5 X —Ray Diffractometer000,000,oooooooooooooo,,, 25 ' 3-6' Tungsten Carbide Microstrueture,,,„,,„„0,,=0, 27

4-1 Loge K vs'Dlffuslon-Anneal'Temperature at'... 6 h o u r s OOOOOOOOOOO OOOOOO, 00000 00000,0009000 32

5-1 Loge D vs Diffusion-Anneal Temperature- Curves From Literature0,000000000000ooooo,, 3 6

vi LIST OF TABLES

Table Page

1 Results of Literature Survey0 =>«, <> = <>» <> = „. <,00000 2 2 Chemical Analysis' of Diffusion' Couple'"' "... - MatenalS 00000 ooooeooooooo*oo<>ooo»QOO 00 0000 17

3 Dl f fu s 1 on - Annea 1 Data. 00 000=. 00 000000 = 00 000000 22 4 Surface Reactlon-Rate Data. = = o o 0 = = = o ======» 31

vll ABSTRACT

This investigation was concerned with the kinetics of the tungsten carbide reaction of cylindrical specimens of graphite and tungsten in the temperature interval 979° -

1382° C 0 The kinetics of the carbide formation were studied in relation to Pick's Laws of diffusion and the van't Hoff relation for reaction-rate constants0 Analysis of the surface reaction and penetration was determined by x-ray diffraction techniques0 The results showed that in the temperature range

studied, diffusion was not controlling but rather the

chemical reaction rate.of carbide formation determined the amount of tungsten carbide. The activation energy

for the reaction, W -f C = WC, was- found to be -10,090 +

1200 cal/mole.

viii- Io INTRODUCTION

During the past decade there has been considerable energy expended in an effort to study solid state diffusion in body-centered cubic metals (Thomas and Leak, 195^5

Ranthenau, 1958; Adda and Kiriananko, 1959J Smith, 19621 Federer and Lundy, 19635 Murdock, Lundy, and Stansbury, 1964)o This is due in part to the formation of inter- metallic compounds in this lattice system, and currently

is of interest as new materials for high temperature structural applications* Because these compounds exhibit

various crystal structures, lattice imperfections, and bonding types, knowledge of their diffusion mechanisms and activation energies is of basic valuee Concerning the diffusion of carbon into tungsten there is wide disagreement among previous investigators

(Pirani and Sandor, 19475 Kottrel, 19565 Aleksandrov, i9605 Becker, Becker, and Brandes, I96I5 Aleksandrov, 1962) on the experimental values of the frequency factor,

D^, and the activation energy, Q, in the Arrhenius relation*

Their results appear in Table 1* Values of D0 vary by many orders of magnitude and the values of Q differ by JO Kcal/

mole*

1 TABLE 1

Results of Literature Survey

2 Temperature Investigator D , cm /sec Q, Kcal/mole Range, °C

PIrani and Sandor, 1947 0.31 59 ± 5 1535-1805

Kottrel, 1956 2.54 x 10 -112 + 3 above 1400

6 Aleksandrov, i960 1.80 x 101 39o5 + 13.4 above 1400

Becker, Becker, and Brandes, -6 . 1961 . . 1.60 x 10 50.34 1400-2400

Aleksandrov, 1962 0.31 - 61«5 + lo5 900 ...... 3 These discrepancies suggested that a study of the kinetics of the reaction forming tungsten carbide was

neededo It was felt that a study of diffusion, in terms

of Pick's Laws, for the tungsten-carbon system would resolve this problem* However, in the temperature inter­

val studied, 980° - 1380° C, no measurable diffusion was

observed. Examination of the carbide concentration at the diffusion couple interface, in relation to the van't Hoff equation, showed that in the temperature range investigated

a diffusion mechanism was not controlling the reaction.

It was found that the reaction kinetics were controlled by the ability of carbon and tungsten to react to form

tungsten carbide. II. THEORY

2,1 Pick's Laws

It was proposed.by Pick in 1855 that the mass flow of solute through an isotropic solvent material could be expressed mathematically„ Based upon the heat- flow equations derived by Pourier (Birchenall, 1959)^ Pick proposed two laws to describe this diffusion,, Pick's two laws are based upon the equilibrium conditions of the system, i.e., steady-state or non-steady-state diffusion,

2,1.1 Steady-State Diffusion, Pick's first law states that the atomic flux, J, across a given plane of area. A, will be proportional to the atomic concentra­ tion gradient, d c/ d x, across that plane, i,e,,

J (2|S S ) = -D( £ ) £f (SSgg£g). 2-1 ( - ll t - - where D, the proportionality constant, is called the diffusion coefficient. The negative sign indicates that if a concentration gradient exists in a system, matter will flow in such a manner as to decrease the gradient.

As the material becomes homogeneous the flux approaches zero, which satisfies Eq» (2-1). 20lo2 Non-Steady-State Diffusion0 If the concentration at some point, x, is a function of time,

Eqe (2-1) is not a convenient form to use. To obtain

Pick's second law it is necessary to use Eq„ (2-l) and a material balance to find another differential equation

(Shewmon, 1963)0 The resulting relation then is

8c/81 = 8/8 x (D 8 c/8x) „ (2-2)

It is desirable in diffusion studies to describe the concentration of solute as a function of position and time, c(x,t)0 That is, in a given diffusion couple composed of materials A and 33, it is of value to know the depth of penetration of A into B 0

2,2 Solution to Pick's Law

If the diffusion distance is short relative to the length of the solvent material, c(x,t) can be ex­ pressed in terms of error functions. When the diffusion couple approaches homogeneity an infinite trigonometric series can describe e(x,t) (Crank, 1956), The present study will be concerned with non-steady-state diffusion; therefore, it shall deal with error functions.

Solution of Eq, (2-2) in terms of c(x,t) requires a knowledge of the boundary conditions of the system. The geometry of the diffusion couple will be discussed in

Section 3.1; however, it is necessary to know that the couple has an extended, or semi-infinite, solute source, as shown in Pig. 2-1. When pure carbon and pure tungsten are used as a diffusion couple, the boundary conditions are

c = 0 for x > 0 , at t = 0

c = e ! for x < 0 , at t = 0 where positive values of x indicate a direction from the interface into tungsten, and c represents the con­ centration of carbon. Solution of Ecu (2-2) then be­ comes

c(x,t) = e '/2 [_ 1-erf(x/2 lfDt) ] „ (2-

The function erf(Z), where Z = x/2lfx)t is called an error function. Since the error function appears frequently in diffusion and heat conductivity solutions, its values have been tabulated to fifteen places in a

Table of Error Function Values (Federal Works Agency,

1941). Pig. 2-1. Tungsten-Carbon Diffusion Couple 2 o3 Diffusion Length

To obtain Eq0 (2-4) an assumption was made that the diffusion distance was -small compared to the total length of solvent material, i„e0, the solvent bar length was considered to be semi-infinite in relation to the diffusion length* It is now necessary to justify this assumption* A solute-free bar of length x 1 can be considered semi-infinite if a quantity of solute which would have diffused past this length is an insignificant part of the total solute diffusing in the bar* Assuming that a value of 0*1 percent is an insignificant amount of solute, x ! can be evaluated in the equation,

r m J x' 0*001 • = (2 A-

J- CM

The numerator is proportional to that amount of solute that has diffused past x' and the denominator is proportional to the total amount of solute that has diffused, into the bar* Solution of Eq* (2-5) yields x' % 4lfDt* Therefore, a bar can be considered semi­ infinite if its length is greater than 4 VDt.* 9 2.4 Arrhenius Relation

Since diffusion is a thermally-activated rate processj, in general, diffusion coefficients may be described by an Arrhenius equation of the form

D = Dq exp (-Q/RT) o (2-6)

The activation energy, Q, and the frequency factor, Dq, are characteristics of the diffusion system. The quantity R is the perfect gas constant and T is the absolute temperature» The interpretation of Dq will be described in Section 205o2e

2.5 Mechanisms

Contemporary discussions on the explanation for bulk diffusion in solids are mainly limited to three possibilities: interstitial diffusion, vacancy diffusion, and diffusion by a ring mechanism. Since carbon atoms are much smaller than tungsten atoms (size ratio of 0 .55), carbon diffusion in tungsten

is based upon an interstitial mechanism. 2o5ol Interstitial Diffusion. At elevated temperatures atoms oscillate violently about their equilibrium positions in a crystal0 When an atom in an interstitial site in a crystal jumps to a nearest- neighbor interstitial site, without any permanent dis­ placement of the atoms in the structure, it has diffused by an interstitial mechanism (Shewmon, 1963)0 This is shown schematically in Fig, 2-2 (Huntington, 1951)» The energy required for an interstitial solute atom to move from position 1 to position 3 Is given by AH, The posi­ tion shown as No, 2 is termed the saddle point. This mechanism is believed to operate in a solid in which the diffusing solute interstitial atoms do not distort the structure greatly. When the solute atom size approaches that of the solvent atoms on the normal lattice sites, then the distortion is too great and some other mechanism becomes dominant, such as vacancy diffusion,

2,5,2 Meaning of Do„ In the case of inter­ stitial diffusion, which is the suggested mechanism for the tungsten-carbon system (Pirani and Sandor, 1947)? the diffusion coefficient can be expressed by a relation derived from equilibrium thermodynamics (Beshers, 1965;

LeClaire, 1965), (a)

E

2 3

Dist

Fig. 2-2. Interstitial Mechanism, (a) FCC Alloy, View of a (100} plane, (b) Energy vs. Displacement for a [1001 plane (Huntington, 1951) 12

D = (7a()2^> exp ASm/R) exp (-AHm/RT1) (2-7) where 7 Is a geometric factor, aD Is the lattice constant, and V is the jump frequency of an interstitial solute atom, loe0, the mean vibrational frequency of an atom about its interstitial equilibrium site* The product of these three factors is the probability that an inter­

stitial atom will jump into an adjoining interstitial site. The term ASm is the entropy of mixing and in the exponential form, represents the probability that an

interstitial site will be available for a jump. The

enthalpy of mixing is termed AHm and, as an exponential

term, represents the probability that the interstitial

atom will have enough energy to jump. Comparing Eq, (2-7) to Eq, (2-6), it is obvious

that E>0 = 7aQ2'? exp ASm/R and Q = AHm.

2.6 van't Hoff Equation

The formation of tungsten carbide from tungsten

and graphite is governed by the reaction

kl W -t- C ^ WC ; AH° (2-8) ■^2 ' '

where and kg are the reaction rate constants in each 13 of the directions shown, and AH0 Is the activation energy for the process. The rate of reaction, r, in each direc­ tion depends upon k and the concentrations of the reactants or products, as shown below.

fw][o] , (S-9a) ri = ki

r2 “ k2 [ W0J • (2-9b)

At equilibrium, r^ = rg and it is seen that

kl/k2 “ "jTWJ" 0 (2 -10)

However, the equilibrium-reaotion constant, K, is

K “ |[W ] X G J ° (2 -11)

kl ' Therefore, K = ,

Levenspiel (1962) derived a differential equation

showing the change in K with temperature, i,e„.

dlnK AH° fn

t = i ? ’ ( 2 " 1 2 ) which becomes a In k -AH0 fn a (i/t) = "T™ (2-13) ana is known as the van't Hoff equation*

From Eq» 2-13 it can be seen that by plotting the

In k vs. 1/T one shouia obtain a straight line of slope equal to AH°/R. III. EXPERIMENTAL PROCEDURE

Experimental methods for producing diffusion data have been well developed and may be divided into four steps. Specimen preparation to produce a diffusion

couple is the first step. The couple is then heat treated at a constant temperature for a determined length of time. A method to determine the concentration profile of the diffusion couple comprises the third step. The last step is the graphical analysis of the data.

The four sections of this chapter will discuss the diffusion couple preparation, heat treatment, and the determination of the concentration profile by means

of sectioning and x-ray diffraction.

3.1 Diffusion Couple

The diffusion couple is illustrated in Pig. 2-1. It consists of a 1/2 in.-diameter tungsten cylinder that

is 1 in. in length. Both ends are sandwiched with

graphite cylinders that are 5/8 in. in diameter and 3/8 in. long. A typical chemical analysis of the materials

is shown in Table 2. The microstructure of the tungsten

15 is shown in Fig0 3-1 at 100 X and 1000 X 0 It is a fine- grain material, ASTM grain size 6-7, with no apparent preferred orientation, as determined metallographically0 The tungsten was sandwiched by graphite to produce dupli­ cate couples at each diffusion anneal„ Each couple length was established at 0„5 in0 by calculating the approximate diffusion length, using an over-estimate of the diffusion coefficient at the maximum annealing temperatureo This length is 0*044 in* which is signifi­ cantly less than 0,5 in* Matching specimen faces were carefully polished mechanically so that oxidation on these surfaces was reduced to a minimum, Firm contact was produced by imposing an axial load of 5®75 psi,

3.2 Furnace

The temperature range in which the reaction to form ¥0 was studied was 979° 0 - 1382° 0 * In the, interval from 979° - 1208° C, a vertical Vycor tube furnace was used, as shown in Fig. 3-2, The diffusion couple was supported on a column of refractory brick and loaded in compression axially. A dry hydrogen atmosphere was maintained in the furnace during the anneal. The temperature was measured by a chrome1-alume1 thermocouple which was attached to a recorder. 17 TABLE 2

Chemical Analysis of Diffusion-Couple Materials

Material: Graphite - National Carbon Co,, CS grade

Typical Typical Impurity Analysis % Impurity Analysis $

Fe 0,03 A1 0,035 V 0,0049 B 0,00013 S 0,145 Li <0,001 Oa 0,0116 Cd <0,001 Ti 0,006 Ash "0,09

Material: Tungsten

Typical Typical Impurity Analysis,ppm Impurity Analysis,ppm

0 10 Si 30 N 10 Ti <10

. 0 30 Mn <10 A1 10 Mg <10 Ca 10 Or <10 Fe 20 Ag <10 Mo 50 Cb <50 Ni 20 ■' (b)

Fig. 3-1. Tungsten Microstructure, (a) 100 X (b) 1000 X 19

Fig. 3-2. Vycor Tube Furnace 20 At higher temperatures, 1362° C - 1382° C, a

10 Kc induetion furnace, Pig. 3-3, was used to heat the diffusion couple. The couple was inserted into a graphite susceptor, 4-1/4 in. high and 2 in. in diameter, with a 5/8 -in. hole drilled to a depth of 3 in. A heat shield of tantalum was placed against the quartz tube to protect the tube from the heat and to reflect the heat back to the susceptor. A vacuum of 35 microns was established prior to the anneal. Temperature measure­ ment was achieved by use of an optical pyrometer corrected for non-black body conditions. Annealing time was determined from the point at which the temperature was 95 percent of the desired temperature. The time to heat up the couple to 95 per­

cent of actual temperature was in all cases less than • 5 percent of the total diffusion time and was neglected. Table 3 shows the temperatures and times for

annealing treatments. The confidence limits were cal­

culated for a probability of 0 .9 5 *

3.3 Sectioning

The sectioning operation was carried out on a

grinding disc loaded with 20-micron diamond dust. A special support was attached to the unit making it 21

Fig. 3-3. Induction Furnace TABLE 3

Diffusion Anneal Data

Diffusion Temperature Time Phases Depth - Couple oc hrs. Present Inches

1 979*2 ± 3.6 6 . ¥ + ¥0 surface 2 1016 0.8 + 3.4 6 . ¥ + ¥0 surface 3 1086,8 ± 1,7 6 ¥ + we surface 4 1142,6 + 2,2 6 ¥ + ¥C surface 5 OXIDIZED

6 . 1208,4 ± 11,5 ' 6 " ' ¥ + ¥0 <0,0011 7 1198.5 ± 35.5 24 . ¥ + ¥0 . >0,0006 8 OXIDIZED 9 1381,9 ± 22,7 12,5 ' - ¥ + ¥0 <0.0005 10 1362,7 +7.3 12,5 ¥ + ¥0 <0,0005 possible to align the surface of the couple perpendi­ cular, within 1°, to the grinding unit axis, as shown in Fig. 3-4. The support held a jig which presented the face of the couple to the diamond disc. This jig has a micrometer head which indexes the specimen Vertically by 0.01 mm. The actual amount of material removed was measured by means of a dial gauge indicator accurate to + 0.00005 in. or + 0.00127 mm. Table 3 shows the thickness of the sections removed.

3.4 X-Ray Diffraction

Since the intensities of diffraction lines due to one material in a mixture depends upon the relative amount of that constituent in the mixture, a quantitative analysis can be performed by means of x-ray diffraction techniques. Diffraction enables one to determine the presence of a material as it occurs in the specimen. A

General Electric XRD-5 Diffractometer, shown in Fig. 3-5> was used to determine the presence and the amount of tungsten carbide, WO, at the diffusion couple interface.

A chromium target x-ray tube with a vanadium filter was selected because the chromium characteristic emission line is of longer wavelength than the 24

Pig. 3-4. Diamond Grinding Unit Fig. 3-5. X-Ray Diffractometer characteristic emission line of tungsten* A 3° beam slit (medium resolution) and a 0 *2° detector slit (medium resolution) were used so that the x-ray beam would cover as large a surface area as possible on the

'diffusion-couple face* Since detection of x-ray quanta is a statisti­ cal function, the greater the intensity incident upon the proportional counter the smaller the statistical fluctuation. A large time constant enables one to achieve an effective integration over a larger time period. A time constant of 8 seconds was used. A sample of pure WC, shown in Fig. 3-6, was used to locate the 20 angles of the diffraction peaks. A 4°/min scan was used first to locate the peaks. Then a 0 .2°/min scan was conducted in the region of the peaks to determine the 20 angles more accurately.

The depth of the WG in the specimen was found by successive surface diffraction and section removal, until the WC peaks no longer appeared on a scan. Surface concentration of ¥0 was determined by the internal standard method (Oullity, 1959)» This method uses a comparison of the intensity of a sample with the intensity"of a known concentration to determine a relative concentration of a phase. 27

wmm■

(a) sat

(b) Fig. 3-6. Tungsten Carbide Microstructure, (a) 100 X (b) 1200 X 28 . Due to the fact that x-ray quanta arrive ran­ domly# accuracy is governed by the laws of probability0 Cullity (1959) defines a probable error relation as a percentage of the true count value# N 0 At a 0o96 prob­ ability level# the equation for counting error is

Eh = 20l/(N)1/2 % (3-1) where N is the total count. To reduce the statistical error# intensity counts of about 20#000 were made. This yielded an EM of 1.42 • . * J,\j » ♦ percent or 20#000 + 284 with a O.96 probability.

The depth of penetration of the x-ray beam into the diffusion couple is of importance. The beam pene­ tration should be less than the section removal so that concentration obtained represents the material in the section. The depth of penetration of an x-ray bean at a diffraction angle of 20 is given by the absorption equation (Cullity# 1959),

I/lo = exp (-2y&t/sin 9) (3-2) where I is the intensity of the diffracted radiation# Iq is the incident radiation# ju, is the linear absorption coefficient of the material, and t represents the depth of penetration of the beam0 The WC peak of interest occurs at an angle of

2© = 53ol3° and sin © = 0.446. At 99 percent return of the beam, i.e., l/l0 = 0 .0 1 , the beam depth is 0.001167 mm or 0.000046 in. This is an order of magni­ tude smaller than the thinnest section removed. IV. EXPERIMENTAL RESULTS

The original objective of this investigation was to study the reaction kinetics of tungsten carbide for­ mation from tungsten and graphite by means of a diffusion study. However, in the temperature range studied, no diffusion of carbon into tungsten to form WC could be measured, as shown in Table 3=

In order to determine why this result ,was obtained, a study was made of the reaction-rate constants and the equilibrium, constant for the surface reaction that did develop during the anneals. These data are presented in

Table 4. A plot of the natural log of the equilibrium constant vs. reciprocal absolute temperature for the

experimental data is presented in Fig. 4-1, The method

of least squares was used to determine the best line

through the data points. A line representing a theoreti­ cal calculation for equilibrium of the reaction forming MG based upon the free energy values of Kubachewski and

Evans (1958) is also shown in Fig, 4-1. The relation

used to determine K theoretically was

AF° = - RT In K . (4-1)

30 TABLE 4 ■

Surface Reaction-Rate Data

Diffusion Surface Cone, .Couple (K), mole % In K T orr K . 10^ VT Time, hrs,

1 ' 37.45 -0.9821 1253 7.98 6 2 41.63 ■ -O.8764 1289 7.76 6

3 49=14 -O.7105 1358 7=36 6

4 44.03 -0.8173 1415 7=07 6 5 OXIDIZED

6 70.55 -0.3489 " 1483 6.74 6

7 79=77 -0.2260 1472 6.79 24

U) H Log K, mole fraction +0 - - -0.4 -0.3 - -0.5 - -0.7 - -0.9 - 0.0 0.1 0.2 0.8 0.6 1.1 1.0 . 1 Pig. 4-1. Loge K vs0 Loge Diffusion-AnnealK Temperature at6hrs. Pig. 4-1. 1300 6.4 1200 x 24hr. 4 Theoretical , °CT, Experimental AH = -10,090 1200 = + AH 10001100 As can be seen from the figure, the data point representing 1142° 0 is much below the curve„ In the least-squares calculation this point was first included and then excluded. Inclusion of this data point resulted in a correlation coefficient of 0,6667 and a AH° of -8,337 + 4,436 cal/mole at 0,95 probability. When the point was neglected the correlation coefficient became 0=9970 and the AH0 was -10,090 + 1200 cal/mole, also at

O .95 probability. Volk (1958) describes a test for discarding data in which it is reasonable to discard data which deviate from the mean by five times the value

' of the standard deviation of the mean. When this test was applied to the data it was found that the point representing 1142° 0 was not representative of the popu­

lation of the mean, i.e., it was discarded with a prob­

ability of error of 0.000063. The point labeled 24 hr. shows a four-fold

increase in the diffusion-anneal time with respect to the experimental curve. An estimate of the time neces­ sary to reach the equilibrium curve at that temperature

is several days. The experimental curve was extrapolated to log

0.00 (100 percent MG) for determination of the tempera­

ture at which a distinct phase would result at the diffusion-couple interface0 This point is at ture of 1387° C0 V„ DISCUSSION

5»1 Comparison of Results with Literature

The Arrhenius equation developed by PIrani and

Sandor (1947) was selected for comparison because the values of Dq and Q, they reported are of the correct order of magnitude for an interstitial mechanism. The other investigators (see Table l) have values either excessively large or small to describe the diffusion mechanism, Aleksandrov (1962)5 however, has reported values for and Q which agree quite well, A plot of the Arrhenius line for the five investigators is shown in Fig, 5-1o Extrapolation of Pirani's line and Aleksandrov's line down to the temperature region in which this investigator's diffusion treatments were con­ ducted shows that their values for the diffusion coeffi­ cient are nearly identical. Examination of Table 3 for diffusion couple No, 7 shows the depth of diffusion to be greater than

0,0006 in, but less than 0,0016 in. Using the Arrhenius equation developed by Pirani and Sandor in the tempera­ ture range of 1535° 0 - 1805° C, one obtains the depth of diffusion to be 0,00231 in, for the annealing

35 2000 1750 1500 1250 1000 10

o

E o -10 Q

-20

-30

4.40 6.56 10^/T, °K"1 Fig. 5-1. Loge D vs. Diffusion-Anneal-Temperature Curves From w Literature (numbers in parentheses refer to references) 37 temperature of specimen No0 7* PIrani and Sandor!s' value is 201 times greater than the author1 s,0 This deviation increases with lower temperature„ - Since the diffusion-anneal time enters into cal­ culations as the author’s diffusion couple would require four times the annealing time it had been given, i„e0, four days of annealing at temperature would be required to approach the diffusion depth comparable to that found by PIrani and Sandor, To investigate, this lack of significant diffusion at lower temperatures a suggestion (Keating, 1966) was made to study the temperature dependence of the equili­ brium reaction constant, as determined by the van't Hoff equation,

5,2 Equilibrium Analysis .

Again examining Pig, 4-1, the experimental curve is lower than the theoretical curve, indicating that the surface reaction is not yet complete and equilibrium has not been established. Therefore, control of the carbide formation in the temperature range studied is believed to be by the ability of tungsten and carbon to react, since both are available at the interface. It has been established, by previous investiga­ tors (Pirani and Sandor, 1947j Aleksandrov, i960) that once a carbide layer has formed at the interface, diffu­ sion must take place through this layer and chemically react at the tungsten-tungsten carbide interface. Extra­ polation of the experimental curve to 100 percent WC at the surface shows that this would occur at 13870 C. Therefore, at higher temperatures, control of the react­ ion would be by diffusion of carbon through the carbide, i.e., the availability of carbon to react with tungsten. This is a possible explanation as to the lack of diffusion observed in the present investigation. VIo CONCLUSIONS

The following conolusions were drawn from the results of this investigation: 1„ Control of tungsten carbide formation in

the temperature range 979° 0 - 1382° C is by means of chemical reaction rates„ 20 At higher temperatures, the diffusion of carbon through the carbide layer controls the formation of tungsten carbide. 3o The activation energy for the reaction - between tungsten and carbon in the tempera­

ture range 979° 0 - 1208° 0 was determined to be -10,090 + 1200 cal/mole0

39 REFERENCES

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