Densification of α- and β-Si3N4 under pressure

Densification of α- and β-Si3N4 under pressure

CERAMICS INTERNATIONAL. 93 Vol. ‘3. ” 3. 1982 Densification of a- and ,&Si3N4 under Pressure TETSUO YAMADA*, ATSUHIKO TANAKA*, MASAHIKO MITSUE KO...

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CERAMICS

INTERNATIONAL.

93

Vol. ‘3. ” 3. 1982

Densification of a- and ,&Si3N4 under Pressure TETSUO YAMADA*,

ATSUHIKO TANAKA*, MASAHIKO MITSUE KOIZUMI

SHIMADA’

and

The Institute of Scientific and industrial Research, Osaka University, Suita, Osaka 565, Japan * Central Research Laboratory, UBE Industries, Ltd. Ube, Yamaguchi 755, Japan

Effect of phase transformation on densification, microstructural changes and bonding beetween grains of Si3N4, without additives was studied by high pressure hot-pressing using CX-and ,9-Si3N4 as starting materials. Densification of Si3N4 did not depend on the difference of the phase in starting materials.

During the hot pressing of &33N4, a drastic change in grain morphology took place with the progress of phase transformation, and the final microstructure showed the existence of self bonding and the development of polyhedral grains. In the hotpressing of @%N4,no appreciable change in grain morphology was observed and densification was proceeded only due to a plastic deformation mechanism. Phase transformation seems to play a significant role in the bonding between grains.

1 - INTRODUCTION

There has been much effort in recent years for the application of ceramic materials to engineering purposes by overcoming the fault of ceramics with is intrinsically brittle material. Among these efforts, silicon nitride (Si3N4) has emerged a material with outstanding potential for high temperature structural applications. However, Si3N.I is known as a material which is difficult to consolidate, because of its high degree of covalent bonding and the small self-diffusion coefficients of constituent elements. Highly dense Si3N4 ceramics are in general fabricated in the presence of oxide additives which cause the precipitation of glassy phase at grain boundaries. This glassy phase has been found to deleteriously affect the mechanical properties at high temperatures’. In order to evaluate the intnnsic thermal and mechanical properties of S&N4 into highly dense self-bonded ceramic bodies without additives have been using high pressure hotpressing or hot isostatic pressing techniques. Prochazka and Rocco performed high pressure hot-pressing of S&N4 and obtained fully dense self-bonded S&N4 ceramics.’ But they did not refer in detail to the relation between densification and phase transformation under pressure. Recently, we have studied the relation between densification and phase transformation under pressure using various kinds of SbN4powders as starting materials.3 In the present paper we describe the experimental results of high pressure hotpressing of (Y- and P-SiJNd with respect to the role of phase Table I. Characteristics

Sample powder

B ( B-Si3N4)

2 - EXPERIMENTAL 2.1

- Starting

microstructural

PROCEDURE

materials

Two kinds of powders consisting of w and B- SiIN4, denoted as samples A and B, were used as starting materials in the present study, and their characteristics are listed in Table 1. Sample A is mainly composed of LYphase, which was obtained by thermal decomposition of Si (NH)? prepared by ammonolysis of SiC14.4*5Sample B is only consisted of pSi3N4, which was obtained from a-&N4 by heating at 1850% for 2 hours in nitrogen at 5 MPa. 2.2 - High pressure hot-pressing High pressure hot-pressing was conducted using DIA 15 cubic anvil type apparatus. The magnitude of pressure generated inside the cell was calibrated at room temperature by the change of electrical resistivity in Bi I-II, Bi 11-111 and Ba I-II transitions at 2.55, 2.70 and 5.5 GPa, respectively. The temperature of the sample was monitored with a PtlPt-13% Rh thermocouple inserted in the cell. Starting powders were compressed to pellets 5mm@ x2.5mm at 150 MPa and charged into pressure cell. The powder compacts were heated at fixed pressure Of 1.5 or 3.0 (3% and at various temperatures from 1200 to 1700°C for 60 min. The heating rate was about 30%/s. After the samples were subjected to the desired high pressure hotthey were quenched to room pressing conditions, temperature and pressure was released. 2.3 - Density

measurements

The bulk density of the hot-pressed measured by means of water displacement

bodies method.

density of porous specimens was also measured the surfaces with nitrocellulose lacquer. 2. 4 - X-ray powder

diffraction

was

The by coating

measurements

The phases of the hot-pressed bodies were determmed by X-ray powder diffractometry using Ni-filtered CUK~Yradia-

of Si3N4 starting powders

I

I

I Phase (wt%)

I

c1 A(a-Si3N4)

transformation to be played in densification. change and bonding between grains.

86

a 14

0 100

* To whom correspondence

I

I

Contents

N*

cl**

of elements

Cl

C

Specific

(wt%)

Al

Ca

39.0 0.87

0.2

co.01

0.03

0.01

0.03


6.9

38.0 0.45

-

-

-

-

-

-

0.95

should be addressed.

’ A/h/r

fusion

method

’’ lnerrgasfusfon

method

TETSUO

YAMADA

ATSUHIKO

TANAKA

MASAHIKO

SHIMADA

and MITSUE

KOIZUMI

In. The weight fractions of LX and /3 phases of the hotessed bodies were determined by the method reported by azzara and Messier’ using the diffraction peaks of (201), 02) and (210) for a-Si3N4 and of (200), (101) and (210) for 83N4. 5 -

Vickers microhardness

measurements

The hot-pressed bodies were polished with various ,ades of diamond paste (8-O.lpm). Vickers microhardness ‘MH) measurements were made at room temperature in acuum by a Nixon &M Typen microhardness tester using a ickers indenter with load of 200 g.

.6 - Microstructure

observations

,’

.’

licrostructures of the fracture surfaces of the hot-pressed odies were observed by scanning electron microscopy ;EM) after etching the specimens with HF based etchants t0 wto/o HF-20 wt% HNO.3 aqueous solution).

I

I

t

cwmSi3NL

15GPa

c-

B- SisNc

3.0GPa

I

I

AND DISCUSSION

i. 1 - Effect of the temperature

on phase transformation

The effect of temperature on the phase transformation, from c&&N4 to P-Si3N4, under pressure is shown in Fig. 2. Phase transformation occurred above 1400°C at 3.0 GPa and above 1500°C at 1.5 GPa. As seen in this figure, the extent of transformation from c&&N4 to @-S&N4 in 60 min seems to be enhanced by the application of pressure. 3.3 - Relationship transformation

between

densification

(“C)

on relative density of the FIGURE 1 - Effect of temperature bodies hot-pressed under 1.5 or 3.0 GPa for (Y-and $- Si?N+ (hold time: 60 min.).

on densification

Densification behavior of the compacts was evaluated by he bulk density. The effect of the temperature on final densiy after high pressure hot-pressing is shown in Fig. 1. When r-S&N4 was hot pressed, at 3.0 GPa for 60 min, the relative iensity of the hot-pressed bodies began to increase at = 1200% and a highly dense Si3N4 body was obtained above 1600°C. A rapid increase in density was observed at 1300-15OO’C. Comparing the relative densities of the two >odies obtained from powders of A and B, it could be seen :hat the temperature dependence was similar, although the ,elative density of the hot-pressed body obtained from sample B (P-Si3N4) was slightly lower than that from sample A (aSi3N4). This result indicates that the phase difference in the starting powders did not significantly affect the densification behavior of the Si3N4 without additives. The relative density of the hot-pressed bodies obtained for sample A at 1.5 GPa (shown in Fig. 1) was considerably lower than that at 3.0 GPa for a given temperature, although a rapid increase in density was observed at 1400-l 600%. 3.2 - Effect of temperature

1800

1600

Temperature

- RESULTS

1

I

I

1400

1200

/----If

--_-_-_---___--_-_-----

100

0

80

/ +

3.0GPa

-k

1.5GPa

i i



1200

1400

1600

Temperature

(“C)

FIGURE 2 - Effect of temperature on (Yto p phase transformation in S&N4 at 1.5 or 3.0 GPa for 60 min.

and phase

The relationship between the relative density of the hot pressed body and the amount of P-phase in the high pressure hot-pressing of sample A is shown in Fig. 3. A definite correspondance was observed between densification and phase transformation in the later stage of densification, but most of the densification occurred with little or no phase transformation. The densification mechanism of solids under hotpressing conditions was explained by mass transport such as grain boundary sliding and phenomena fragmentations-“, plastic deformation’2-‘6, evaporation and condensation”-“, stress enhanced diffusion and mechanisms’9-25. In the present case, the fragmentation and rearrangement of the particles was the operative mechanism for the initial cold pressing, and then on heating, it was considered that densification of a-Si3N4 in the first strage proceeded mainly by plastic flow of the a-grains. The effective stress applied to the particles by the external high pressure, which calculated using the following equation employed by

I 0

20

-o-

3.0 GPa

-A-

1.5 GPa

I

I

I

40

60

80

Wt %

100

fFSi3N,

FIGURE 3 - Relation between relative density and the amount of !3 phase in the bodies hot-pressed at 1.5 or 3.0 GPa for 60 min.

DENSIFICATION

OF o- AND &!3iN,

UNDER

95

PRESSURE

McClelland’“, was enough high in magnitude to provoke strain rate greater than 10-‘/s by dislocation glide or climb mechanisms as seen in the deformation mechanism map*’ where (TVis efof S&N4 calculated by us *‘; ue= P,/[l-(l-~)~‘~], fective stress, P, is applied pressure and Q is relative density. The yield stress of 3.1 GN/m2 at 1200% for S&N4 estimated from VMH using the ralation 2’ of H = 4.5Y (H: hardness, Y: yield stress) was almost of the same magnitude as the applied pressure. In the next stage, densification occurred with an accompanying$hase transformation due to diffusion controlled process Since the experimental evidence for the present hypothesis is reflected a little in the microstructure of the hot-pressed bodies, it requires much more extensive work. As for the phase transformation under high temperaturepressure conditions, it is considered that P-grains formed on the plastically deformed a-grains, simultaneously releasing the stored strain energy. as proposed by Weh and Silora’g. 3.4 - VMH of hot-pressed

4

Si7N4

d

I

I 1200

Densification is considered to be distint from bonding as proposed by Nadeau”, who conducted very high pressure hot-pressing of SIC. Therefore, the distinction between udensificationa and ([bonding between grainsn was made as follows in the present study. Density is the measurable indicator of the degree of densification and VMH is one of the indicator of the degree of bonding between grains. The evidence concerning bonding between grains was examined by VMH measurements. VMH data for the hotvarious hot-pressing pressed bodies obtained at temperatures at 3.0 GPa, measured at room temperature, are shown in Fig. 4. The VMH began to increase rapidly accompanying the progress of densification at = 1400°C, and self-bonding between grains seemed to be achieved above 1500%. The VMH of the highly dense hot-pressed body obtained from sample A was 22 GN/m*, higher than that of the highly dense hot-pressed body obtained for sample B (18 GNlm’). According to a recent study on VMH of the S&N4 bodies consolidated under high pressure3”, there was little density dependance of VMH after the relative density was greater than 97%. Therefore, it is expected that the difference in VMH of the hot-pressed bodies reflects the degree of self-bonding between grains, which is dependent on the fabrication temperature and the phase of the starting materials. Since VMH is a relative value of yield strength or critical shearing strengthens”, there are two relations concerning the temperature dependence of VMH3’; ho-Shishokins

equation

Ha eeA’

(A is costant)

and Schwab’s

I

I

1400

1600

Temperature

(“C )

FIGURE 4 - VMH of the SijNI bodies hot-pressed at various temperatures at 3.0 GPa using w and o- S&N4 powders as starting materials.

“E

\

12

Z

2

30

.~

8

6

T/10’

RT

I

2

,,/

I

30GPa-1600’C-6Omin

P -L--V--’

(‘c)

4

.

A

(from

cx phase)

o

B

(from

13 phase)

I

I 2 l/T

x 10)

I

I 3

I

( K’)

FIGURE 5 - Temperature dependance of VMH values for A and B samples hot pressed at 3.0 GPa und 1600°C for 60 min.

Hccl/e-r”kT.

equation

In the present study, Schwab’s

equation was adopted.

Temperature dependence of the VMH of the SiqN4 bodies obtained from sample A and sample B hot-pressed at 3.0 GPa and 1600°C for 60 min is shown in Fig. 5. Hot-pressed bodies obtained from sample A exhibited higher VMH from room temperature to 1200°C, 14 GN/m2 at 1200°C, whereas, the VMH of the hot-pressed bodies from sample B decreased abruptly above 900°C. This difference in VMH at high temperature would not be due to the difference in grainsize, but to the bonding between grains. Therefore, phase transformation seems to be important in the consolidation of Si3N4 without additives. 3.5 - Microstructure

I

of hot-pressed

Si3NJ

microstructure of etched fracture surfaces of the hot-pressed bodies were observed by scanning electron microscopy (SEM). Changes in the microstructure of the hot-pressed bodies obtained from sample A at 3.0 GPa and 1400-1700°C are shown In Fig. 6. As seen in these SEM photographs, a

marked change in the grain morphology of Si,Nl was observ ed at 1500-155O’C (formation of polyhedral grains), where the most progress In densrfrcatron and phase transformation occurred. In the micrograph of the specimen obtained at 1400°C (b), a certain degree of plastic deformation of particles occurred after the fragmentation of acicular particles of the starting powder (a). Grains with rather sharp edges and corners were only agglomerated by the application of pressure. In the micrograph of the specimen obtained at 1500% (c), grain refinement due to recrystallization of plastically deformed a-grains occurred, and a fine spheroidal matrix, whose grain size was smaller than that of the specimen at 14OO’C developed. In the micrographs of the specimens obtained above 1550% (d, e, f) fine polyhedral grains whose average grain size was -0.3 pm were developed. These micrographs showed sharp grain boundary morphology, and it was expected that self-bonding between grains was achieved, which was consistent with the increase of VMH shown in Fig 4 There were many twins in these micrographs which provided evidence for the recrystallization concept.

TETSUO

YAMADA.

ATSUHIKO

TANAKA,

MASAHIKO

SHIMADA

and MITSUE

KOIZUMI

(a)

00

(e)

-lGURE 6 - SEM photographs of the fracture surfaces of the bodies hot-pressed lb) 1400°C, (c) 1500°C, (d) 1550°C, (e) 16OOT, and (f) 1700(bar= lpm).

W

(e)

FIGURE 7 - SEM photographs of the fracture surfaces of the bodies hot-pressed (b) 1400°C, (c) 1500°C, (d) 1550% (e) 16OO”C, and(f) 17OOT (bar= 10pm).

(0 using a-S&N4 at 3.0 GPa for 60 min.;(a) starting powder,

(f) using /X%ilN~ at 3.0 GPa for 60 min.; (a) starting powder,

DENSIFICATION

OF of AND ,:-S,*N, UNDEH

Table II. Summary of experimental I\-,temp.

starting powders

N

results

qfJ

I’:

densification process

1_jlj_ ]__ ijfpq;;aa-

[_b;::_.1 ““0 _jfi

plates needles

texture

L-Si3N4

97

PRESSURE

plates needles

qrain arowth

/ fragmentation / rearranqement

polyhedrons plates

plates

cont.

polyhedrons

phase _* transformatioc

qrain

qrowth +

;39.Ga; sa, (6. %&/
relative density

(8)

c Vickers microhardness (GN,'m2) fragmented franqmented

texture

plastic

prisms columns

deformation

P-Si3N4 N cont.

(38.0%)

relative density

(%I

I-

I

-

Microstructures of the etched fracture surfaces of the hotpressed bodies obtained from sample B at 3.0 GPa and 1400-1700°C are shown in Fig. 7. In the micrograph of the starting powders (a), remarkably columnar, or prismatic, grains elongated in the c-axis direction were grown, since the powders were prepared from sample A by the heat treatment under nitrogen pressure. In the micrograph of the specimen obtained at 1400°C (b), large columnar or prismatic grains were only agglomerated by the application of pressure, and large voids were observed between grains. The micrograph of the specimen obtained at 1500% (c) indicated that grain morphology was almost same as the specimen fabricated at 1400% and grains had still sharp edges and corners, but the fraction of voids decreased. In the micrographs of the specimens obtained above 1550% (d, e, f), plastic deformation of p-grains became dominant and only a little voids are seen. Although a considerable degree of densification was achieved, the edges or corners of the grains were rather round, and grain boundary migration by diffusion process during heating was expected to be little in the observed microstructure.

86

95

97

98

99

3.8

14.8

16.7

17.0

18.4

____--__

10

from

8-SiaN,

8 6

__ --_--4

$2

z 0.8

from ol-SixNL

3i C .$

T

0.6

3.6 - Grain growth during high pressure hot-pressing Grain size measurements in the hot-pressed bodies were made on SEM photographs. The temperature dependences of the grain size of the hot-pressed bodies obtained from both powders A and B are shown in Fig. 8. The points in the figure represent the mean grain-size derived by the intercept method reported by Fullman3’, and the bars represent the ranges of the dimension of the long axis of a grain measured directly from SEM photographs. When sample A was hotpressed at 3.0 GPa for 60 minutes, coarse grains disappeared and the mean grain size decreased slightly at 1400-1500°C, probably due to recrystallization. An increase in grain size was observed in the temperature range from 1500 to 1550°C, and finally grain growth occurred slowly above 1550%. When sample B was hot-pressed at 3.0 GPa for 60 minutes, the change in grain size was very little.

0.4

0.2

0

I

I

I

I

I

I

1200

1300

1400

1500

1600

1700

Temperature

(“C

FIGURE 8 - Temperature dependence of grain size of the bodies hot-pressed using $Y-and ,&Si,N, at 3.0 GPa for 60 min.

98

TETSUOYAMADA.

The results of the present experiment with respect to the texture of the hot-pressed body, the densification process, the weight of /3-Si3N4, bulk density and VMH are summarized in Table II. It is evident from these data that these parameters are correlated with the densification of S&N4 under high pressure.

4 - CONCLUSION The mechanism of densification and the roles of phase transformation to be played in densification, microstructural changes and bonding between grains of SisNl without additives were studied in high pressure hot-pressed bodies obtained from cr-Si,N4 and fi-Si,N, powders. The results are as follows. 1) The densification behaviour of S&N4 did not depend on the difference of phase in the starting material, and fully dense Si,N4 ceramics were obtained from both &iJN4 and P-SisNb at 3.0 GPa and 1700%.

2) Phase transformation from CY-to p- phase in S&N4 occurred completely at 3.0 GPa and 1600°C within 60 minutes, and the rate of phase transformation was enhanced by the application of pressure. 3) When a-Si3N4 was hot-pressed under 3.0 GPa, most of the densification resulting from plastic deformation of a-grains on heating proceeded with little or no phase transformation, but the intermediate and final stages, densification was accornpained by the phase transformation. 4) Marked changes in grain morphology occurred with the progress of phase transformation, and the microstructure showed the existence of self-bondig and the formation of polyhedral grains. 5) When &Si3N4 was hot-pressed under 3.0 GPa, densification proceeded by the plastic deformation of P-grains, and there was no appreciable change in grain morphology. 6) VMH of the highly dense S&N4 ceramics obtained from QSi3N4 was 22 GNlm , higher than that obtained from P-SI~N~. Phase transformation seemed to play a significant role in the bonding between grains.

REFERENCES 1. F.E. RICHERSON, Effect of Impurities on the High Temperature Proprieties of Hot-pressed Silicon Nitride, Am. Warn. SOC. Bull., 52 (1973) 560-62. 2. S. PR06HAZkA and W.A. ROCCO, High Pressure Hot Press-

ina of Silicon Nitride Powders, Hiph TemD.-High _ Pressure, 10

3.

4. 5.

6.

(1378) 87-95. T. YAMADA, M. SHIMADA, and M. KOIZUMI, Densification of S&N4 by High Pressure Hot-pressing, Am. Ceram. Sot. Bull., 60 (1981) 1281-83. M. BILLY, Preparation et Definition du Nitrure de Silicium. Ann. Chim., (1959)795-851. 0. GLEMSER and P. NAUMANN, Uber den Thermischen Abbau von Siliciumdiimide Si(HN)*, Z. Anorg. Allgem. Chem., 298 (1959) 134-41. M. SHIMADA, N. OGAWA, M. KOIZUMI, F. DACHILLE, and R. ROY, Crystallization and Sintering of Amorphous S&N4 under Pressure, Am. Ceram. Sot. Bull.. 58 (1979) 519-21.

ATSUHIKOTANAKA

7. C.P. GAZZARA

MASAHlKOSHlMADAa”d

and D.R. MESSIEh.

MITSUE

Determination

KOIZUMI

of Phase

Content of S&N3by X-ray Diffraction Analysis, Am. Ceram. Sec. Bull., 56(1977) 777-80. 8. E.J. FELTON, Hot-Pressing of Alumina Powders at Low Temperatures, J. Am. Ceram. Sot., 44 (1961) 381-85. 9. R. CHANG and G. RHODES. Hiah-Pressure Hot-Pressina of Uranium Carbide Powders and ?vlechanism of Sink&i of Refractory Bodies, J. Am. Ceram. Sot., 45 (1962) 379-82. 10. W. POCH, Hochdruckpressen von Oxiden, Ber. Dtsh. Keram. Ges., 46 (1969) 65-68. 11. G.S. NADEAU, Very High Pressure Hot Pressing of Silicon Carbide, Am. Ceram. Sot. Bull., 52 (1973) 170-74. 12. J.K. MACKENZIE and R. SHUTTLEWORK, Phenomenogical Theory of Sintering, Proc. Phys. Sot. (London), 62 (1949) 833-52. 13. P.W. CLARK and J. WHITE, Some Aspects of Sintering, Trans Brit. Ceram. Sot., 49 (1950) 305-33. 14. E.B. ALLISON and P. MURAY, Fundamental Investigation of Mechanism of Sintering, Acta Met., 2 (1954) 487-512. 15. J.D. MCCLELLAND. A Plastic Flow Model of Hot Pressinn, J. Am. Ceram. Sot., 44 (1961) 526. 16. F.V. LENEL and G.S. ANSELL, The Role of Plastic Deformation in Conventional Sintering and. Hat Pressing, in Sintering and Related Phenomena, Ed. by G.C. Kuczynski, N.A. Hooton and CF. Gibbon, Gordon and Breach, Science Publishers, New York-London-Paris (1967) 351-68. 17. G.C. KUCZYNSKI, Trns. AIME, 185 (1949) 169. 18. W.D. KINGREY and M. BERG, Study of the Initial Stages of Sinterina Solids bv Viscous flow. Evaooration-Condensation, and SelKDiffusion, 2. Appl. Phys., 26 (1955) 1205-12. 19. C. HERRING, Diffusional Viscosity of a Polycrystalline Solid, J. Appl. Phys., 21 (1950) 437-45. 20. T. VASILOS and R.M. SPRIGGS, Pressure Sintering: Mechanisms and Microstructures for Alumina and Magnesia, J. AM. Ceram. Sot., 46 (1963) 493-96. 21 T. VASILOS and R.M. SPRIGGS, Pressure Sintering of Ceramics, in Progress in Ceramic Science, 4, Ed. by J.E. Burke, Pergamon Press, New York, (1966) 95-132. 22 R.L. COBLE, Mechanisms of Densification During hot Pressing, in Sintering and Related Phenomena, Ed. by G.C. Kuczynski, N.A. Hootan and C.F. Gibbon, Gordon and Breach, Science Publishers. new York-London-Paris (1967) 329-50. 23 R.L.COBLf& Diffusion Models for ‘Hot tiressing with Surface Enerav and Pressure Effects as Drivina Forces, J. Appl. Phys., 41 (1 ti0) 4798-4807. 24 G.M. FRYER, Hot Pressing of Alumina-A New Treatment of Final Densification, Trans. Brit. Ceram. Sot., 66 (1967) 127-34. 25. D. KALISH and E.V. CLOUGHERTY, Densification Mechanisms in High-Pressure Hot-Pressing of HfBz, J. Am. Ceram. Sac., 52 (1969) 26-30. Maos. 26. M.F. ASHBY. A First Reoarf on Deformation-Mechanism Acta Met., 20’(1972) 887:97. 27. T. YAMADA, M. SHIMADA and M. KOIZUMI, The Relation between Densification and Phase Transformation of S&N4 under Pressure, Yogyo-Kyokai-Shi, 90 (1982) 118-23. 28. D.L. KOHLSTEDT, The Temperature Dependence of Microhardness of the Transition-Metal Carbides, J. Mater. Sci., 8 (1973) 777-86. 29. H.C. WEH and P.F. SIKORA, Consolidation of S&N4 by Hot isostatic Pressing, Am. Ceram. Sot. Bull., 58 (1979) 444-47. 30. T. YAMADA, A. TANAKA, M. SHIMADA and M. KOIZUMI, High Temoerature Hardness of SilNa Ceramics Fabricated under High’Pressure, Yagyo-Kyokai-Shi, 90 (1982) 202-8. 31 G.M. SCHWAB, Some New Aspects of the Strength of Alloys Trans. Faraday Sot., 45 (1949) 385-96. 32. R.L. FULLMAN. Measurement of Particle Sizes in Opaque Bodies. Trans. AIME, 197 (1953) 447-52. Received December 22, 1981; final text received April 4, 1982