internal friction in titanium and titanium-oxygen alloys

6
INTERNAL FRICTION IN TITANIUM AND TITANIUM-OXYGEN ALLOYS* J. N. PRATT?, W. J. BRATINAt and B. CHALMERS5 A low-frequency torsional pendulum technique has been used to study internal friction in alpha- titanium and in some titanium-oxygen alpha-solid-solutions containing up to 4.5 atomic per cent oxygen. Characteristic grain-boundary relaxation peaks are exhibited by the pure titanium and by the alloys; the respective heats of activation were found to be 46,000 cal/mol and 75,000 cal/mol. The introduction of oxygen results in the appearance of an additional relaxation peak at approxi- mately 700°K; the mechanism involved is not established but the associated heat of activation is estimated as 48,000 cal/mol. LE FROTTEMENT INTERNE DANS LE TITANE ET LES ALLIAGES TITANE-OXYGENE La methode du pendule de torsion B basse frequence a et.6 utilisee pour I’Ctude du frottement interne dans le titane alpha et dans quelques solutions solides, du type alpha, d’oxygbne dans le titane. Sur les courbes de frottement interne du titane pur et des alliages, apparaissent les maxima caracteristiques de la relaxation aux joints intercristallins; les energies d’activation furent &al&es respectivement a 46000 cal/mol et 75090 cal/mol. L’introduction d’oxygene conduit a I’apparition d’un autre maximum de relaxation aux environs de 7OO”K, le mdcanisme implique dans ce second cas n’est pas Ctabli, mais l’energie d’activation associke & ce phenomene est evaluee a 48000 cal/mol. DIE INNERE REIBUNG IN TITAN UND TITAN-SAUERSTOFF LEGIERUNGEN Die innere Reibung von a-Titan und einigen festen a-Liisungen von Titan und Sauerstoff, die bis zu 4, 5 Atom% Sauerstoff enthielten, wurde mit Hilfe einer Niederfrequenz-Torsionspendel- methode untersucht. Reines Titan und die Legierungen zeigen charakteristische Korngrenzen Relaxationsmaxima; die entsprechenden Aktivierungsenergien betrugen 46,000 cal/mol bezw. 75,090 cal/mol. Der Zusatz von Sauerstoff rief ein weiteres Maximum bei etwa 700°K hervor. Der dazugehorige Elementarvorgang ist noch nicht bekannt, aber die damit verbundene Aktivierungs- energie kann zu ca. 48,000 cal/mol abgeschatzt werden. Introduction The profound effect of certain interstitial solute elements on the physical properties of a-titanium is well established. Previous work has shown, for example, that while pure titanium has a high ductility, contamination by very small quantities of nitrogen or oxygen induces marked embrittlement [l; 2; 31. A rigorous interpretation of the influence of these elements on a-titanium is not possible on the basis of the existing data; the effects are not attributable to the equilibrium precipitation of a second phase since they become significant at compositions far below the equilibrium solubility limits and cannot be explained in terms of the observed lattice parameter changes [2; 4; 5; 61. It is possible that the fundamental embrittlement mechanism involves an inhomogeneous distribu- tion of solute atoms within the specimen, accom- panied by incipient precipitation or lattice faulting. With the aim of obtaining further information concerning the exact role of the interstitial solutes in a-titanium, an investigation is being made of *Received October 6, 1953. tDepartment of Metallurgical Engineering, University of Toronto: now I.C.I. Research Fellow, Department of Metal- lurgy, University of Manchester. SDepartment of Metallurgical Engineering, University of Toronto. IDivision of Applied Science, Harvard University, Cam- bridge, Massachusetts. ACTA METALLURGICA, VOL. 2, MAR. 1954 their influence on its internal friction characteris- tics, particularly their modification of grain boun- dary relaxation phenomena [7; 81. The present publication reports the results of experiments on commercially pure titanium and titanium-oxygen alloys. Experimental Details The titanium employed in the present investiga- tion was in the form of wire of 0.05-inch diameter. It was supplied by the Titanium Metals Corp. of America who reported its analysis to be: 0.10% Fe; 0.02% N; trace 0; 0.04% C; 0.039& W; remainder Ti. Heat treatment of specimens was carried out either in situ in the Internal friction apparatus or in evacuated quartz capsules in an auxiliary tube furnace; in the latter case the specimens were wrapped in similar titanium wire to prevent con- tamination by reaction with the containers. Oxy- gen-bearing samples were prepared by heating lengths of the wire under suitable conditions to give a uniform oxide coat, followed by prolonged anneal- ing in vacua until a uniform distribution of the oxygen throughout the specimen had been achieved. The change of the weight of the specimen was taken as a measure of its oxygen content. Owing to the inherent difficulties, it was not possible to prepare alloys with a high degree of precision by this method. All annealing procedures were such as

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Page 1: Internal friction in titanium and titanium-oxygen alloys

INTERNAL FRICTION IN TITANIUM AND TITANIUM-OXYGEN ALLOYS*

J. N. PRATT?, W. J. BRATINAt and B. CHALMERS5

A low-frequency torsional pendulum technique has been used to study internal friction in alpha- titanium and in some titanium-oxygen alpha-solid-solutions containing up to 4.5 atomic per cent oxygen. Characteristic grain-boundary relaxation peaks are exhibited by the pure titanium and by the alloys; the respective heats of activation were found to be 46,000 cal/mol and 75,000 cal/mol. The introduction of oxygen results in the appearance of an additional relaxation peak at approxi- mately 700°K; the mechanism involved is not established but the associated heat of activation is estimated as 48,000 cal/mol.

LE FROTTEMENT INTERNE DANS LE TITANE ET LES ALLIAGES TITANE-OXYGENE

La methode du pendule de torsion B basse frequence a et.6 utilisee pour I’Ctude du frottement interne dans le titane alpha et dans quelques solutions solides, du type alpha, d’oxygbne dans le titane. Sur les courbes de frottement interne du titane pur et des alliages, apparaissent les maxima caracteristiques de la relaxation aux joints intercristallins; les energies d’activation furent &al&es respectivement a 46000 cal/mol et 75090 cal/mol. L’introduction d’oxygene conduit a I’apparition d’un autre maximum de relaxation aux environs de 7OO”K, le mdcanisme implique dans ce second cas n’est pas Ctabli, mais l’energie d’activation associke & ce phenomene est evaluee a 48000 cal/mol.

DIE INNERE REIBUNG IN TITAN UND TITAN-SAUERSTOFF LEGIERUNGEN

Die innere Reibung von a-Titan und einigen festen a-Liisungen von Titan und Sauerstoff, die bis zu 4, 5 Atom% Sauerstoff enthielten, wurde mit Hilfe einer Niederfrequenz-Torsionspendel- methode untersucht. Reines Titan und die Legierungen zeigen charakteristische Korngrenzen Relaxationsmaxima; die entsprechenden Aktivierungsenergien betrugen 46,000 cal/mol bezw. 75,090 cal/mol. Der Zusatz von Sauerstoff rief ein weiteres Maximum bei etwa 700°K hervor. Der dazugehorige Elementarvorgang ist noch nicht bekannt, aber die damit verbundene Aktivierungs- energie kann zu ca. 48,000 cal/mol abgeschatzt werden.

Introduction

The profound effect of certain interstitial solute elements on the physical properties of a-titanium is well established. Previous work has shown, for example, that while pure titanium has a high ductility, contamination by very small quantities of nitrogen or oxygen induces marked embrittlement [l; 2; 31. A rigorous interpretation of the influence of these elements on a-titanium is not possible on the basis of the existing data; the effects are not attributable to the equilibrium precipitation of a second phase since they become significant at compositions far below the equilibrium solubility limits and cannot be explained in terms of the observed lattice parameter changes [2; 4; 5; 61. It is possible that the fundamental embrittlement mechanism involves an inhomogeneous distribu- tion of solute atoms within the specimen, accom- panied by incipient precipitation or lattice faulting. With the aim of obtaining further information concerning the exact role of the interstitial solutes in a-titanium, an investigation is being made of

*Received October 6, 1953. tDepartment of Metallurgical Engineering, University of

Toronto: now I.C.I. Research Fellow, Department of Metal- lurgy, University of Manchester.

SDepartment of Metallurgical Engineering, University of Toronto.

IDivision of Applied Science, Harvard University, Cam- bridge, Massachusetts.

ACTA METALLURGICA, VOL. 2, MAR. 1954

their influence on its internal friction characteris- tics, particularly their modification of grain boun- dary relaxation phenomena [7; 81. The present publication reports the results of experiments on commercially pure titanium and titanium-oxygen alloys.

Experimental Details

The titanium employed in the present investiga- tion was in the form of wire of 0.05-inch diameter. It was supplied by the Titanium Metals Corp. of America who reported its analysis to be: 0.10% Fe; 0.02% N; trace 0; 0.04% C; 0.039& W; remainder Ti. Heat treatment of specimens was carried out either in situ in the Internal friction apparatus or in evacuated quartz capsules in an auxiliary tube furnace; in the latter case the specimens were wrapped in similar titanium wire to prevent con- tamination by reaction with the containers. Oxy- gen-bearing samples were prepared by heating lengths of the wire under suitable conditions to give a uniform oxide coat, followed by prolonged anneal- ing in vacua until a uniform distribution of the oxygen throughout the specimen had been achieved. The change of the weight of the specimen was taken as a measure of its oxygen content. Owing to the inherent difficulties, it was not possible to prepare alloys with a high degree of precision by this method. All annealing procedures were such as

Page 2: Internal friction in titanium and titanium-oxygen alloys

204 ACTA METALLURGICA, VOL. 2, 1954

to result in uniform a-titanium structures. In the subsequent internal friction experiments the final temperature of the preliminary anneal was gener- ally not exceeded in order to avoid grain growth during their progress. Nor in the present work were observations made above approx. 86O”C, since it was desired to exclude any possible complications resulting from the allotropic transformation of titanium.

Measurements of internal friction were made by the standard method [7] of studying the free decay of the oscillations of a simple torsion pendulum, the suspension of which consisted of a wire of the material under investigation. The normal appara- tus was elaborated to permit the experiments to be carried out in high vacuum (approx. 5 X low6 mm Hg.). This eliminated the possibility of contamina- tion of the specimens during the experiments and also greatly increased the sensitivity of the method. Frequencies of vibration of approximately 1 cycle per second and 0.5 cycle per second were used. The maximum pendulum deflection employed corre- sponded to a maximum torsional strain of the order of lob5 at the surface of the specimen. The variation of temperature along the length of the specimen was found to be little more than 1°C.

Internal friction is here defined as

(1) tan 6 = logarithmic decrement/* where the logarithmic decrement is the natural logarithm of the ratio of the amplitudes of succes- sive swings. The variation of tan 6 with tempera- ture has been studied and the relaxation spectra plotted. From the frequency dependence of tan 6 the heat of activation, H, for a relaxation process may be calculated using the expression

(2) H = R *lnb fi / A(l/T)

where A(l/T) is the shift to superpose the curves of tan 6 versus (l/T) obtained from experiments on a single specimen using two frequencies of vibration, fi and fi, and where T is expressed in degrees absolute. The temperature dependence of the rigidity modulus may be observed by determining the vibrational frequency, f, at each temperature, since for a torsional pendulum

(3) G =*128-J- r. I.fz

d4

where 1, d and G are respectively the length, dia- meter and shear modulus of the suspension and I the moment of inertia of the oscillating member.

Experimental Results and Discussion 1. Titanium

The variation of internal friction with tempera- ture has been determined for a number of specimens of pure titanium; the results were found to be satisfactorily reproducible. Typical tan 6 versus l/T plots are shown in Figure 1. Curves (a) and (b) were obtained from the same small-grained sample (mean grain diameter 0.019 mm) using two differ- ent frequencies of vibration, while curve (c) is that obtained under similar conditions for a sample having a very large grain size.

Tempwature F 00 7Do wa sat2 4w 400

I ’ I

I I 0.9 1.0 I.1 1.2 1.3 1.4 l.S I.6

100011%

FIGURE 1. Variation of internal friction with lOOO/(abso- lute temperature) in pure titanium (frequency of vibration is equal 0.5 cycles/set and 1 cycle/set for grains of mean grain diameter = 0.019 mm, and 0.5 cycles/set for very large grains).

It is evident that the relaxation spectrum of polycrystalline titanium consists of two compon- ent parts, a background steadily increasing with temperature and a peak confined to a limited temperature range. The nature of the peak is revealed by its behavior as the grain size of the specimen is modified. As the grain size increases but remains small compared with the diameter of the specimen the peak is observed to occur at higher temperatures but remains unchanged in magnitude. However, when the point is reached where some grains extend completely across the specimen, the peak begins to be reduced in size. These observa-

Page 3: Internal friction in titanium and titanium-oxygen alloys

PRATT ET AL.: INTERNAL FRICTION IN TITANIUM 205

tions show that the peak is due to stress relaxation by grain-boundary slip. It is difficult to assess precisely the contribution of the background internal friction in the vicinity of the peak; h:w- ever, it is certain that at the temperatures where tan 6 first begins to rise most rapidly the form of the curve is mainly determined by that of the relaxa- tion peak. The magnitude of the shift, A(l/T), to superpose the curves in this region should, there- fore, on substitution in equation (2), give a value for H which corresponds to the heat of activation for the grain-boundary slip process responsible for the peak. The observed value is 46,000 cal/mol.

No detailed study of the background internal friction has been made in the present work, but it is evident that its magnitude decreases rapidly with increasing grain size; this would appear to be in accord with the views of Pearson et al [9], who regard it as due to creep at regions of stress concen- tration arising from shear stress relaxation along grain boundaries. Few measurements are available which can be considergd to be wholly attributable to this source; however, examination of such high- temperature regions of spectra as were obtained suggests that the heat of activation for the back- ground internal friction in polycrystalline titanium is identical with that for grain-boundary relaxation.

The variation of the rigidity modulus with tem- perature is illustrated in Figure 2, where values of

I .6 -

j ‘,:_.~~ ,y if

w aw 100 Te%Lut.Y 600 700 800

FIGURE 2. Variation of rigidity modulus with temperature in pure titanium (Gt and GSO are rigidity moduli at PC and 20°C; GM is “unrelaxed modulus”).

Gt/Gzo (i.e., f”/fi,,), Gt being the modulus at t”C, are plotted. The results shown are those associated with internal friction curve (a) in Figure 1. Most rapid reduction of the modulus begins when the temperature reaches that at which the amount of

grain-boundary slip starts to become significant. At temperatures well below that of the relaxation peak, the “unrelaxed modulus,” G,, is observed and in this region the curve for polycrystalline specimens should be identical with that for a single crystal of titanium. G, falls slowly and approxi- mately linearly with increasing temperature. The extent of the modulus variation directly associated with grain-boundary slip is best illustrated by a plot of GJG, versus temperature; this is shown also in Figure 2. A computation of the maximum effect that stress relaxation at the grain boundaries can have on the elastic modulus has been made by Zener [lo]. Theoretically, with increasing tempera- ture, the modulus should approach a limiting value known as the “relaxed modulus,” G,, where

GIG = 2 (7 + 5u) 5 (7 - 4u) ’

d = Poisson’s ratio.

For titanium u = 0.36 [11] so that G,/G, = 0.63. As indicated by the graph of Gt/G, (Figure 2), the modulus relaxation exhibited in the temperature range corresponding to the relaxation peak is close to this theoretical value, providing confirmation that both these effects are associated with grain- boundary slip. It appears, however, that the modulus will continue slowly to fall below the theoretical limit, the further reduction of the modulus being associated with the mechanism responsible for the background internal friction.

2. Titanium-oxygen alloys

Alloys ranging in composition from approxi- mately 0.8 to 4.5 atomic per cent oxygen have been examined and typical of the relaxation spectra observed are those shown in Figure 3. They may be resolved into three component parts, a back- ground increasing with temperature and two characteristic peaks.

The peak appearing in the temperature range around 1000/T = approx. 1.0 has been shown, by its dependence on grain size and the magnitude of the associated modulus decrement, to be due to grain-boundary relaxation. This peak is found at higher temperatures in titanium-oxygen alloys than is the corresponding one in pure titanium; it has been calculated that in the 4.5 atomic per cent oxygen alloy the grain-boundary peak occurs at a temperature 95’C above that in pure titanium of the same grain size, the frequency of vibration being approximately 0.5 cycles per second. How- ever, the grain-boundary peak in the alloys is reduced in size as the oxygen content increases,

Page 4: Internal friction in titanium and titanium-oxygen alloys

206 ACTA METALLURGICA, VOL. 2, 1954

and there is some evidence of a simultaneous tendency to move to slightly lower temperatures.

It is considered, therefore, that the grain- boundary peaks in pure titanium and in the oxygen alloys are distinct phenomena, characteristic of the individual materials, and are not simply related by a temperature transition. This type of phenomenon has been observed by Pearson [12] in copper- and silver-base substitutional alloys. In certain speci- mens he was able to distinguish two grain-boundary relaxation peaks, one typical of the pure metal, the other of the solid solution; the first was rapidly eliminated while the latter increased to its maximum value as the solute content was increased. It was not possible to resolve two grain-boundary peaks in any of the alloys examined in the present work.

This view of the effect of oxygen on the grain- boundary relaxation of titanium seems necessary to account for the superficially contradictory observation that although the characteristic tem- perature of the peak in alloys is higher than in pure titanium it falls as the oxygen content increases.

The gradual reduction of size and characteristic temperature, with increasing solute content, of the grain-boundary peak in alloys may be attributed respectively to the reduction in the amount of slip and of the mean relaxation distance arising from a locking effect of oxygen segregated at the grain boundaries.

The heat of activation for grain-boundary relaxation in the alloys is considerably larger than that for the corresponding process in pure titanium. From the results plotted in Figure 3, a value for H

,Lo ,I, “p- ’ ,i.>- A, 1: -44 tooo,r’-:

FIGURE 3. Variation of internal friction with loOO/ (absolute temperature) in titanium-ox$gen alloy.

of 75,000 cal/mol. is found for the 4.5 atomic per cent oxygen alloy; very similar values for H were observed for alloys with other oxygen concentra- tions.

The value of the background internal friction of

titanium at both high and low temperatures is reduced by the addition of oxygen. The near ide?tity of the maxima in the relaxation spectra for the two frequencies suggests that the heat of activation for the background internal friction mechanism is again the same as that for grain- boundary slip.

The introduction of oxygen also results in the appearance of the very small additional relaxation peak at approximately 1000/r = 1.4. The addi- tional peaks observed in three specimens having increasing oxygen contents are shown on an en- larged scale in Figure 4. It is clear that the size of

,.I I.2 1.3 1.4 I.5 1.6 1.7 I.6 1000/T*K

FIGURE 4. Oxygen-induced relaxation peak in titanium- oxygen alloys of different composition.

peak increases with the oxygen content. However, if allowance is made for the internal friction from other sources it appears that the ‘size is not directly proportional to the solute content and possibly approaches a limiting value at comparatively low percentages of oxygen. The position of the peak appears to be independent of grain size but the dependence of its magnitude upon this factor has not been determined owing to the difficulty of separating other contributions in fine-grained specimens. It will be seen that at temperatures well above the peak the internal friction is greater the greater the oxygen content; since oxygen re- duces the magnitude of the background and of the grain-boundary slip relaxation effects, this increase must be due to the movement of the grain-boundary peak to lower temperatures.

The frequency dependence of the additional peak in a 3.5 atomic per cent oxygen alloy is illustrated in Figure 5, and from these curves it is found that the associated heat of activation is 48,000 cal/mol. Similar calculations using data from other samples indicate that the heat of activation is independent of composition. Examination of the half-maximum width of the peaks obtained for several specimens

Page 5: Internal friction in titanium and titanium-oxygen alloys

PRATT ET AL.: INTERNAL FRICTION IN TITANIUM 207

suggests only a very slight spread of relaxation times for the process involved.

Micrographic examination revealed all the ti- tanium-oxygen alloys to consist entirely of a uniform a-solid solution. No signs of precipitation of any second phase were found; neither were there any indications of twinning or any similar modifica- tion having occurred in the a-phase. The second peak cannot be attributed, therefore, to either of these sources, so that it would seem that it must be associated more directly with the diffusion of

Tempwotur~ Z

.x4 600 , 500 450 400 350 300 I

/ I

I I

Titanium-Oxygen Alloy _

i3.50t.x 0 1

l 0.5 cystc ,*ec

0 I cyct*/s*c

I I I I 1.1 1.2 I.3 1.4 1.5 1.6 1.7 I.8

. IOOO/T *K

FIGURE 5. Frequency dependence of the oxygen-induced relaxation peak in a 3.5 atomic per cent oxygen alloy.

oxygen in solution in titanium. However the values of 48,000 cal/mol for the heat of activation and of approximately 0.4 for Do (estimated by means of the Dushman-Langmuir equation [13] are con- siderably higher than are normally observed for the diffusion of interstitial solutes, while the diffusion distance indicated by the relaxation time is very small. Furthermore, no suitable diffusion process is readily apparent.

The work of Ehrlich [4] indicates that in ti- tanium-oxygen alloys the solute atoms occupy the octahedral interstices at the ($, 3, 2) and (p, $, 2) positions in the close-packed hexagonal unit cell. Thus simple stress-induced diffusion, analogous to that of the interstitial solutes in body-centred cubic structures [14; 151 does not provide a mechanism in the present case.

An atom pair process [16] could operate for an interstitial solid solution in a closed-packed lattice; the occupation of neighbouring pairs of interstices will give rise to an anisotropic strain, so that in the presence of an oscillating stress diffusion should take place in a continual striving to maintain coincidence between the interstitial pair axis and the direction of maximum applied strain. However, a significant number of such pairs could only occur at fairly high oxygen contents, which would indicate

it to be improbable that such a mechanism is responsible for the peak given by the small amounts of oxygen involved in the present alloys.

A possible stress-induced diffusion process might result from the effect of applied stress on the equi- librium distribution of oxygen between the grains and the grain boundaries. Since the solution of oxygen increases the axial ratio of the titanium lattice, a grain on which the net effect of the applied stress was also to increase the axial ratio might be expected to absorb oxygen from that adsorbed at the grain boundary, while ejection of solute into surrounding interfaces would occur from grains whose axial ratios were reduced by the applied stress. However, this mechanism would seem to be precluded as an interpretation of the present results because of the excessive relaxation time which it would involve.

Thus it is not possible at present to define the mechanism responsible for the additional oxygen- induced relaxation peak. Further experiments are being made in an effort to establish its exact nature and in order to obtain a more precise relationship between the oxygen content and the detailed form of the relaxation spectrum. An analogous series of experiments are proposed on titanium-nitrogen alloys.

Summary

The internal friction characteristics of pure (Y- titanium have been examined using a low-frequency torsion pendulum method of high sensitivity. The relaxation spectrum was found to consist of a back- ground which rises continuously with temperature and a peak arising from stress relaxation by slip at the grain boundaries. The heat of activation for the latter process was found to be 46,000 cal/mol.

The investigation of titanium-oxygen alloys has shown their relaxation spectra to be characterised by a background curve, a grain-boundary relaxa- tion peak and a small additional relaxation peak. In the alloys, the peak characteristic of grain- boundary slip occurs at higher temperatures than in pure titanium and the heat of activation for the process is increased to approximately 75,000 cal/ mol. It has been established that the additional relaxation peak is due to the presence of oxygen. The process involved has not been determined, but the associated heat of activation has been shown to be 48,000 cal/mol. While the grain-boundary relaxation peak in alloys is reduced in size and temperature by additional oxygen, the second peak increases in size with increasing solute content,

Page 6: Internal friction in titanium and titanium-oxygen alloys

208 ACTA METALLURGICA, VOL. 2, 1954

but not apparently in any direct proportion. The References background internal friction decreases with in- 1. FINLAY, W. L. and SNYDER, J. A. Trans. A.I.M.E. 1

creasing oxygen content. (1950) 277.

The rigidity moduli of titanium and of the alloys 2. JAFFEE, R. I., OGDEN, H. R. and MAYKUTH, D. J. Tra

3.

4.

decrease in the usual manner with increasing tem- perature. It was observed that, at room tempera- ture, the addition of approximately 4.5 atomic per cent of oxygen raised the rigidity modulus of titanium to approximately 4500 kg/mm2; the corresponding value for the original material was 3840 kg/mm2.

A.I.M.E. 188 (1950) 1261. JENKINS, A. E. and WORNER, H. W. J. Inst. Metals (1951) 157.

Acknowledgements

The authors wish to thank Professor L. M. Pidgeon for his interest and for the provision of laboratory facilities, and Mr. D. H. Laing for his assistance in constructing the apparatus. The financial support of the Defence Research Board of Canada is also gratefully acknowledged (Grant No. 289).

5. 6. 7.

8.

9.

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University of Chicago Press, 1948). PEARSON, S., GREENOUGH, G. B., and SMITH, A. D. Nature 167 (1951) 1021. ZENER, C. Phys. Rev. 60 (1941) 966. K&TER, W. American F.I.A.T. Rev. 31, 56. PEARSON, S. R.A.E. Report No. Met. 67, 1951; R.A. Report No. Met. 71, 1953. DUSHMAN, S. and LANGMUIR, I. Phys. Rev. 20 (1922) 11 SNOEK, J. Physica (1939) 591; 8 (1941) 711; 9 (1942) 8f

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