Sintering kinetics in tungsten powder

JOURNAL OF THE LESS-COMMON METALS

140

SINTERING KINETICS IN TUNGSTEN POWDER N. C. KOTHARI Department

of Mining

and Metallurgical Engineering, Brisbane, Queensland (Australia) (Received

October

University

of Queensland,

r5th, 1962)

SUMMARY An experimental study of the initial sintering kinetics in tungsten powder has been made in the temperature range of ~roo”C to 1500%. The influential factors involved include compacting pressure, sintering time and temperature. Isothermal changes in volume and density were studied. The experimental results were evaluated by two methods of analysis: (a) The degree of sintering 6 was evaluated from the time-temperature relationship. (b) An empirical equation of the Arrhenius-type, based on volume change as a function of sintering time, was derived to evaluate the rate constant of the sintering process. The rate controlling step is believed to be diffusion dependent. Using method (a), the activation energy, IOO f 5 kcal/mole was calculated for various fractions of 6. The activation energy associated with the sintering of tungsten powder was calculated by method (b), and found to be 102 * 2 kcal/mole. This value is in good agreement with the calculated activation energy by method (a). The ratios between the activation energy of surface diffusion and volume self-diffusion and between grain boundary diffusion and volume self-diffusion were examined in tungsten and other metals. They were found to give support to tlfe theory that sintering of tungsten powder in the temperature range of I 100°C to 1500°C is controlled by grain boundary diffusion and not volume self-diffusion.

INTRODUCTION

The term “sintering” is generally applied to one or more complex bonding processes involved in the densification of particles which are either loosely packed or compacted and heated to a temperature which is below the melting point of the material. It is generally recognized that surface tension is the predominant driving force responsible for particle bonding and reduction of pore volume. Excess surface energy in a mass of powder particles make the system thermodynamically unstable. The purpose of sintering is to bring such a system to a stable state and its mechanism may be considered as consisting of three stages: (i) The contact area between the adjacent particles increases. (ii) The pores spheroidize and gradually diminish in number. The compact decreases in volume, indicating rapid movement of material into the pores. (iii) Densification ceases, but the pores and grains continue to change in shape without a change in the volume of the system. J. Less-Common

Metals,

5 (1963) 140-150

SlNTERING KINETICS IN TUNGSTEN

r4r

POWDER

The mechanisms by which the material transport may occur have been suggested to be: plastic or viscous flow, evaporation-condensation and diffusion mechanisms such as volume, surface or grain boundary diffusion. The plastic flow mechanism suggested by FRENKEL~, and supported by SHALER~ and MACKENZIE AND SHUTTLEWORTH~ isnolongeraccepted. The possibility of an evaporation-condensation mechanism is generally disregarded where the material has a low vapour pressure. In recent years, sintering mechanisms based on diffusion models have been presented by the following authors: KUCZYNSK~~-~, CABRERA', HERRING*, RHINES~, SCHMED~~, ALEXANDER AND BALLUFFI 11,12,KINGERY AND BERGEN, COBLE~~, ZA16.Their studies indicated that material transPLATYNSKI~~ and JORDANANDDUWEZ

port in sintering is due to volume self-diffusion. Most of the experimental studies for determining the kinetics of sintering were conducted on more common metals such as copper, silver, nickel, and iron. The first attempts to investigate the sintering of tungsten were made by COOLIDGE~~, who developed sintering of tungsten filaments for electric lamps. Since then most of the studies on sintering of tungsten have been undertaken to determine the effects of particle size, compacting pressure, sintering time, temperature and atmosphere on physical and mechanical properties, but little attention has been paid to the kinetics of the process. The purpose of this investigation was to determine the mechanism of material transport involved during the sintering of pressed tungsten compacts. An attempt is made to correlate the effects of compacting pressure, sintering time and temperature on the sintering kinetics of tungsten powder. An empirical equation for the rate of sintering from the rate of volume change has been derived. EXPERIMENTAL

PROCEDURE

Pressing The compacts were made from a single batch of hydrogen-reduced tungsten powder with an average particle size of 3 ,I..J.Table I gives the chemical composition and size distribution of the powder. Cylindrical compacts, 0.25 in. in diameter and 0.5 in. in height, were made employing pressures in the range of 30 . 103 to 120 . 10~ p.s.i. in a hardened-steel die using a hydraulic press. No trouble was experienced with slip cracks and no lubricant was used. Compacts pressed at pressures of 40 . 10~ p.s.i.

TABLE CHEMICAL

COMPOSITION

Elements

02

C

Fe Ni CU MO CO w

AND

PARTICLE

I

SIZE

wt. y0

ANALYSIS

Pa&de

size

c/J)

OF

TUNGSTEN

POWDER

wt.%

0.20

0.5

0.01

I

10.02

0.05

2

0.02

20.16 33.0'

0.02

3 4

0.03

2

0.61 5.10

IO

0.59

8.50

22.OI

0.01

Remaining

J. Less-Common

Metals, 5 (1963) 140-150

N. C. KOTHARI

142

and above had uniform density and could be handled with a reasonable amount of care. The pressures recorded are believed to be accurate to + 3%. Sintering All experimental studies on sintering were carried out in the temperature range from IIOO’C to 15oo’Y in a tungsten-wound resistance furnace. The furnace was evacuated to 10-5 mm Hg pressure. To prevent any time lag in heating of the compacts, the furnace was brought to a temperature 25°C higher than the required temperature. The recrystallized alumina crucible containing the compacts was then inserted in the hot zone of the furnace. The temperature was controlled with the platinum VS. platinum-130/o rhodium thermocouple, and also was measured with an optical pyrometer. The sight glass correction was obtained by calibration with a standard tungsten filament lamp. The temperature of the hot zone was held to & 5°C over the 2 in. length of the crucible containing the compacts. At the end of the sintering cycle, the crucible and compacts were quickly removed from the hot zone and cooled in a watercooled jacket. The technique of sintering described above was found to give satisfactory and reproducible results. THEORETICAL

CONSIDERATIONS

Derivation of the degree of sintering “6” SEITZ~~, HOLLOMON AND JAFFE~S, FISHER rate of diffusion

AND MACGREGOR~O have shown

K can be expre’ssed in terms of the following equation K

=

that

the

:

Ae-QIRT

(1)

where K is the rate, expressed as the reciprocal of the time for some fractional change of property, A is a constant, Q is the activation energy, R is the gas constant, T is the absolute temperature. By taking the logarithms of eqn. (I), it can be reduced to the following: Q 2.3 RT

Log A + log t = ___ HOLLOMON time

and

AND JAFFE~~ derived temperature

successfully premise

to creep

that

assumed applicable During

that

they

for

eqn.

(2) to show

the relation

between

tempering

given hardness. Since then eqn. (2) has been applied

and rupture21

are rate

sintering

a

and recrystallization

processes

dependent

is also dependent

upon

upon diffusion,

and grain diffusion. eqn.

growth22 As

on the

it is generally

(2) should

be directly

to the rate of sintering. sintering

the maximum

theoretical

density

which

a metal

powder

compact

If PO, Ps and Pm represent the pressed, sintered and theoretical densities respectively, a dimensionless parameter can be defined as the degree of sintering 6 : where Ps - PO 8=_ (3) p* - PO can attain

This

is that

parameter

of the solid metal.

represents

the fraction

of total

density

change

J. Less-Common

after

sintering

time

t,

Metals, 5 (1963) 140-150

SINTERING

KINETICS

IN TUNGSTEN

POWDER

143

at a given temperature. The initial value of this parameter is zero and it becomes unity when the compact attains theoretical density. Thus a plot of sintering parameter 6 versus sintering time t gives a set of approximately parallel straight lines on a lognatural scale. Derivatiolz of sintering equation

Isothermal sintering studies suggest that the decrease in pore volume is caused by growth across contact interfaces of the particles. Then the fraction dV of the total volume change in the compact after sintering time t is given by eqn. (4) AV

v* v,

VP -

= ___

v,-

(4)

where VP and V, are the compacted and theoretical volumes of the compact and V, is the sintered volume of the compact after sintering time t. If we consider the sintering mechanism to be similar to precipitation and austenitemartensite transformations 23, then the fraction of total volume change, “85’” becomes proportional to the product of sintering time t raised to a power n, and the fraction of unchanged volume (I - d V). Thus eqn. (4) becomes AV = K’(I - AV) et”

(5)

where K’ is the rate constant. The term (I - AL’) introduced in eqn. (5) is used to correct for one or more of the following effects : (I) Impingement of two or more particles. (z) Decrease in the free surface area or in volume by means of surface or grain boundary or volume self-diffusion. (3) Changes which occur in the size and shape of pores at constant volume. Substituting d V from eqn. (4) into eqn. (5) and rewriting leads to :

Substituting

V for d V/(I -

AV ____=_=

vp -

V*

(I

v*-

v'm

-

AV)

(6)

K’ . t”

A V), then

v, - vs v, - Vm

I’=-=

K’ * tn

(7)

On differentiating eqn. (7) with respect to time, an expression for the rate of volume change in the compact is obtained dV

%.

K’

.

tm-’

(8)

z=

Since t = (V/K)ll* be re-written :

(from eqn. (7)) and substituting

say, D = n . K’ll*,

eqn. (8) can

dV - = D . V(l-1/n, dt J. Less-Co?rLmcW Metals,

5 (1963)

140-150

N. C. KOTHARI

144

where D is an apparent diffusion coefficient or a temperature-dependent rate constant for sintering. This expression suggests that the rate of the volume change of pores depends upon the fraction of total volume change. The influence of temperature enters through the constant D. Therefore constant D can be related to temperature by the usual relation D =

Doe-Q/ET

(10)

where DO is a constant. RESULTS AND THEIR INTERPRETATION

The reported experimental sintering results were obtained on compacts pressed only at 40 . 103 and 80 . 103 p.s.i. Density

The as-pressed and sintered densities of the compacts were determined by weighing them and calculating volume from micrometer measurements. Occasionally a check on the density was made by weighing the compact in water and air, a thin coating of lacquer being applied to prevent ingress of water into the pores during the tests. The results of as-pressed density measurements for the total range of pressures used are presented in Table II. TABLE EFFECT

OF

COMPACTING

Pressure (P.s.i. 103)

0/OTheoretical green density

30 40 60 80 IO0 120

60.938 64.070 69.375 73.020

75.520 76.130

II

PRESSURE

ON

DENSITY*

Observation Weak, easily crumbled Easy to handle Good strength, easy to handle Strong, no slip cracks Strong, no slip cracks Strong, slip cracks began to appear

* Results are average of ten samples. SMITHELLSz4 reported a green density of 12.70 g/cm3, when tungsten powder was subjected to the pressure of 60 . 103 p.s.i. The value obtained in this investigation for the as-pressed density using 60 . 103 p.s.i. is x3.32 g/cm3. This difference in the initial density may be due to differences in the initial particle size and the chemical purity of the two powders. The pressed compacts were sintered for 30,60, IOO, 200, 240, 300,400, and 500 min at each of the following temperatures: 1100”; 1200~; 1300’; 1400’; 1450” and 15oo~C. At the end of each experimental run, the fractional volume change V and degree of sintering 6 were determined. Experimental results for the increase in density of compacts pressed at each pressure are given in Fig. I (a) and (b). It is apparent that the densification in tungsten powder compact is very slow. The sintering parameter 6 plotted as a function of sintering time t on log-natural scale in Fig. z (a) and (b), gives a set of approximately parallel straight lines. Then Fig. 2 (a) and (b) permits the selection of various sintering times and temperatures for

J. Less-Common Metals, 5 (1963) 140-150

SINTERINC

KINETICS

IN TUNGSTEN

POWDER

X4.5

the constant vahx of sintering parameter 6. By plotting these selected values as log t ofQj2.3R in Fig. 3 (a) and (b}. The cakulated activation energy is not constant, and is probably an average value for severai processesoccurring together. The stapes in Fig. 3 fa) and fb) carrespcmd to

werms IIT, straight fines are &t&ned with slope

Sintering time

(a) Pressed al

40

.

103

fmin)

p.s.i.

[a) Pressedat 40 * 103p.s.E. (b) Pressed at 80 . 103 pd. Fig. 2. Isothermal plot of degree of sintering “6” ~wszcs log sin&ring time (minutes).

an ~~vation energy Q between

95 and rag kca~~m~~~, The volume parameter Y calculated from the valume change (eqn. (2)) is also plotted as a function of sintering time d, on log-log scale for a constant sintering temperature in Fig. 4 (a) and (b). The straight lines dram through the experimental points at

J. Lass-CorPzmorr,n/let&, 5 (~963) 140-191

N. C. KOTHARI

146

the various temperatures are approximately parallel and the slope (n) is about 0.2 (Table III). Substituting the value of n = 0.2 in eqn. (9) gives: dV _ = D.

v-4

dt

I-

7 .-

c

z _ .+ .-F : t; IOO5

_

1OL 5

I 6

-

Sintering

1/T ~10~

I 6

I

’

I

1/Tx104

Sintering

temperature

temperature

(b) Pressed at 80

(a) Pressed at 40 . 103 p.s.i.

8

’

. 103p.s.i.

Fig. 3. Sintering time OWSZ~S reciprocal of absolute temperature for constant degree of sintering “S”.

0.01 10

100

Sintering (a) Pressed at 40

1000

time (min) . 103

p.s.i.

10

100

Sintering

1000

time

(b) Pressed at 80.

(min)

103p.s.i.

Fig. 4. Relation between log volume parameter “ V” and log sintering time (minutes).

,I. Less-Common Metals, 5 (1963) 140-150

SINTERING KINETICS IN TUNGSTEN POWDER

I47

Equation (II) thus allows an estimate of the apparent diffusion coefficient, D. The dependence of D on temperature is represented by the conventional plot given in Fig. 5 and straight lines are drawn through the derived points. The slope yields an activaTABLE VALUES

compacting ptzsswe

(P.s.i.

III OF ?Z

Temfmzture

n

PC)

x 103) 4o

1200

1300 14.50 I500 1200

80

1300 1400 1500

Sin&kg

0.193

0.185 0.179 0.205 0.203 0.531 0.199 0.200

temperature

Fig. 5. Apparent diffusion coefficient D (calculated from the sintering eqn. (I I)) versus reciprocal of absolute temperature.O- -0 Pressed at 40 . 103p.s.i. ; . - - - 0 Pressed at 80. Io3p.s.i.

tion energy 102 & 2 kcal/mole for the process. It should be noted that this value is comparable with the activation energy IOO _C 5 kcal/mole derived by the method (a) (Fig. 3 (a) and (b)). The effect of varying compacting pressures on the initial densities was investigated. It was found that the initial densities increased with the compacting pressures as shown in Table II. Compacts pressed at 40.103 p.s.i. showed excellent unfired strength; the appearance of lamination cracks was first observed in compacts pressed at 120 . J. Less-Common

Metals,

5 (1963)

140-150

N. C. KOTHARI

148 103

p.s.i.

should

noted

show a definite decrease with increase in initial compacting pressure. The activation energy derived in this work is less than that reported elsewhere for the volume self-diffusion of tungsten. A comparison with related values is given below. DISCUSSION VAN

LIEMPT~~

diffusion

estimated

in tungsten.

an activation

energy

of 143 kcal/mole

His value for the activation

that of 135.8 kcal/mole

for volume

energy

for volume

self-

is in good agreement

with

or lattice self-diffusion

derived

by VASILEV

AND

CHERNOMORCHENKO~~. LANGMUIR~~ analysed the data of BRATTAIN AND BECKER~~ and calculated

the activation

for the thorium-tungsten

energies

for grain boundary

Q Bb and volume self-diffusion

system (see Table IV) using DUSHMAN-LANGMUIR

Q1

equation.

M~~LLER~~ derived the activation energy 106 & 8 kcal/mole for tungsten by following the progress of shape changes of a fine tungsten point with time and temperature. He assumed that the change in the shape is due to surface diffusion. Recently, a detailed investigation of surface diffusion in tungsten has been carried out by BARBOUR

et al.30 using the field emission microscope

technique.

ergy Qs 72.0 kcal/mole for the surface diffusion TABLE ACTIVATIONENERGIESFORVARIOUS Element

(a) Volume self-diffusion Ag in Cu Ag in Ag Ag in Ag Ag in Ag Fe in Fe Fe in Fe Pb in Pb W in W W in W ThinW Zn in Cu (b) Grain boundary diffusion Ag in Cu Ag in Ag Ag in Ag (at low temp. 500 to 65o’C) ThinW C in W Pb in Pb Zn in Cu (c) Surface diffusion Ag in Ag ThinW W in W NiinW

Activation energy (kcallmole)

QL

38.0 45.7 45.9 49.5 73.2 72.0 27.9 143.0 135.8 120.0

They

of tungsten

found the activation into tungsten.

IV DIFFUSION

MECHANISMS

Reference

Method

Diffusion couple Sintering method Radioactive isotope Radioactive isotope Radioactive isotope Sintering method Radioactive isotope Solute experiment

35 3: 37 38 39 40 25 26

Calculated from Ref. (28)

27

41

34.0

Qsb

23.8 20.2

26.4 90.0 108.0 15.7 24.0 Qli 10.3 66.4 72.0

en-

Comparing

Diffusion couple Radioactive isotope Radioactive isotope Calculated from Ref. Carburizing exp.

Radioactive isotope Field emission Field emission

70.0 (aver.) J. Less-Common

35 36 37 27 42 43 41

(28)

44 28 30 31 and45

Metals, 5 (1963)

140-150

SINTERINGKINETICS IN TUNGSTENPOWDER

I49

M~~LLER’Svalue of Q8 with that of VAN LIEMPT’S value of Qr gives a ratio QJQr = 0.7 which is much higher than is normally encounted in silver or other metals or alloys. From the earlier worka*JOJi, it appears that the activation energy for thesurface diffusion in tungsten is about one-half of Ql. It is possible that the activation energy derived by MULLER of about 0.7 Ql may thus be QSb or Q1, (the activation energy for diffusion along dislocations and other defects). Assuming that no experimental value of Q were available from this work, an estimation of its magnitude would still be possible by assuming that it is equal to the activation energy of grain boundary diffusion. This assumption is based on the fact that grain boundary diffusion should have an activation energy smaller than volume selfdiffusion. The ratios of the activation energy of grain boundary diffusion to that of the volume self-diffusion for tungsten and other metals obtained from Table IV give the following values: Ag into Ag 0.5 to 0.8; Ag into Cu 0.63; Pb into Pb 0.65 ; Zn into Cu 0.72; C into W 0,74 and Th into W 0.75. Although the majority of reported results apply to binary systems a rough consistancy of the ratio QgblQl is apparent. Taking 0.7 as the mean value and 143 kcal/mole as the activation energy for volume selfdiffusion25, a value of 100.1 kcal/mole for grain boundary diffusion of tungsten is obtained. This value is in good agreement with the experimental values obtained in this work. The experimental value obtained is also comparable to a value of go.0 kcal/mole reported by LANGMUIRfor the grain boundary diffusion of thorium in tungsten27. Isothermal sintering studiesi3~14~16 on copper, Al2O3, ZrOs and Fez03 powders indicated that volume self-diffusion is the predominant mechanism of material transport. The authors’ arguments are based on the activation energies derived from their experiments. However ALEXANDER AND BALLUFFI~~ reported an activation energy of 47.0 instead of accepted value of 56.0 kcal/mole for copper. CIZERONAND LACOMBE~~derived activation energies 37.0 and 54.0 kcal/mole for sintering of iron which are lower than those associated with volume self-diffusion. These values closely approachthosetobeexpectedforsurfaceorgrainboundarydiffusion.Thissuggeststhata mechanism, such as surface or grain boundary diffusion may be responsible for sintering. The models of NABARRO~~and HERRING* suggest that the vacancies diffuse from the surface of pores to the grain boundaries or to the outer surface of the specimen. If this mechanism prevails in sintering, then densification of a compact occurs by the migration of individual ions into the voids from nearby grain boundaries. The space originally occupied by the vacancies is filled by the grain material, resulting in a decrease in compact volume. BALLUFFI ANDSIEGLE 34 studied the distribution of pores in a thin sheet of dezincified or-brass. Dezincification produced an excess of lattice vacancies. On annealing, a shrinkage in the specimen was observed. Their results indicate that grain boundaries act as sinks. Pores disappear much more rapidly in the neighbourhood of a grain boundary than those within the grains. This suggests that at low temperatures the detectable shrinkage during the sintering of tungsten is due to grain boundary diffusion. The comparison between known activation energies for similar systems has been made in an attempt to determine the controlling mechanism. However these comparisons cannot in themselves confirm the nature of the process. They suggest that the sintering of tungsten may be governed by some diffusion mechanism other than volume self-diffusion. J. Less-Common

Metals,

5 (1963) 140-150

N. C. KOTHARI

150

In general, all the results, experimental grain boundary diffusion is the predominant the sintering

of tungsten

in the temperature

and theoretical, support the idea that mechanism of material transport during range of IIOO’C to 15oo’C.

ACKNOWLEDGEMENTS It is a pleasure to thank Professor F. T. M. WHITE for suggesting the problem and providing the research facilities. The author wishes to express his deep gratitude to Mr. J. WARING for many valuable discussions during the course of investigations; to Dr. B. RUSSELL and Dr. W. BOAS for constructive criticism of this written presentation; and Mr. G. JUST for his assistance in preparing this manuscript. REFERENCES 1 YA. I.FRENKEL,J. Phys. U.S.S.R.,9 (1945) 385 (English translation). 2 A. J.SHALER,Trans. AIME, 185 (1949) 796. 3 J. K. MACKENZIE AND R. SHUTTLEWORTH, Proc. Phys. Sot. (London),62 (1949) 833. 4 G. C. KUCZYNSKI,Trans. AZME, 185 (1949) 169. 5 G. C. KUCZYNSKI,J.Appl. Phys., 21 (1950) 632. e G. C. KUCZYNSKI,Acta Met., 4 (1956) 58. 7 N. CABRERA, Trans. AZME, 188 (1950) 667. 8 C. HERRING,].Appl.Phys.,2I (1950) 301 and437. 9 F.N.RHINES,C.E.BIRCHENALLAND L. A.HUGHES,Trans. AZME, I88 (1950) 378. 1” P. SCHMED,TY(E~S. AIME, 191 (Ig51)245. II B.H.ALEXANDERANDR.W.BALLUFFI,J. Metals, 2 (1950) 1219. 12 B.H.ALEXANDERAND R.W. BALLUFFI,Acta Met.,5 (Ig57)666. 13 W. D. KINCERY AND M. B. BERG, J. Appl. Phys., 26 (1955) 1205. 14 R. COBLE,J. Am. &ram. Sot., 4I (1958) 55. 15 I. ZAPLATYNSKI, Planseeber. Pulvermet., 6 (1958) 89. 16 C. B. JORDAN AND P. DUWEZ, Trans. AIME, 185 (1949) 96. 17 W. D. COOLIDGE,J. Am. Inst. Elec. Engrs., 29 (Igog) 953. 1s F. SEITZ, The Physics of Metals, McGraw Hill& Co.,New York, 1943,~.177. IQ J. H. HOLLOMON AND L. D. JAFPE,Trans. AZME, 162 (1945) 223. 20 J. C. FISHER AND C. W. MACGREGOR, J. Appl. Mech., 67 (1945) 824. 21 F.R. LARSON AND J.MILLER,T~~~~.ASME, 174(1952)765. 22 F. R. LARSON AND J.SALMOS,Trans. ASM, 46 (1954) 1377. 23 J.B.AusTINANDR.L.RIcKETT,T~~~~. AZME,I35(1939)396. 24 C. J. SMITHELLS, Tungsten, Chapman & HallLtd.,London, 1952.~.124. 25 J.A.M.VAN LIEMPT,Rec. Trav. Chim.,64 (1945) 239. 26 V.P.VASILEVANDS.G.CHERNOMORCHENKO, Zavodsk.Lab..22 (1956)688. 27 I. LANGMUIR,J. Franklin Inst., 217 (1934) 543. 2s W.M.BRATTAIN AND A.J. BECKER, Phys.Rev.,43 (1933)428. 29 E.W. M~~LLER,~.Physik, 126 (1949) 642. 30 J.P. BARBOUR,F.M.CHARBONNIER,~~~~.,II~(I~~~) 1752. 31 B.I.PINEs AND I.V. SMUSHKOV, SovietPhys.,28 (1958) 626. 32 G. CIZERONAND P.LACOMBE, Rev. Met., 52 (1955) 771. 33 F. R. N. NABARRO, Rept. Conf. on Strength ofSolids, Bristol, 1947. 34 R.W. BALLUFFIAND L.L.SIEGLE,ActaMet., 3 (1955)170. 35 M.R. ACHTERANDR.J.SMOLUCHOWSKI, Phys.Rev.,76(1949)470. 36 W. JOHNSON,Trans.AZME, 143 (1941)107. 37 R.E.HOFFMANANDD.TURNBULL, J.Appl.Phys.,22 (195I)634. 38 C. E. BIRCHENALLAND R.F.MEHL, Trans.AZME, 188(Ig5o)144. 39 G.BOCKSTIEGEL,G.MASINGAND G.ZAPF,AppZ.Sci.Res.,4 (1954) 284. 40 W. SEITHAND A. KEIL,~.MetaZZk.,z5 (1933) 104. 41 R.FLANAGANAND R.J.SMOLUCHOWSKI.J. Appl.Phys., 23 (1952) 785. 42 M. ANDREWS AND S.DUSHMAN, J. Phys. Chem., 29 (1925) 462. 43 B. OKKERSE, Acta Met., 2 (1954) 551. 44 R.A.NICKERSON AND E.R. PARKER,T~~~s.ASM,42 (Ig5o)376. 45 R.A. SWALINANDA.MARTIN,T~~%. AZME,S (1956)567. J. Less-Common

Metals,

5 (1963)

140-150