Strain-aging behavior of irradiated and denitrided mild steel

Materials Science and Engineering, 59 (1983) 207-215

207

Strain-aging Behavior of Irradiated and Denitrided Mild Steel K. LINGA MURTY North Carolina State University, Raleigh, NC 27650 (U.S.A.) (Received October 12, 1982; in revised form November 3, 1982)

SUMMARY

Influences o f neutron irradiation and dry hydrogen treatment on yield point phenomena in mild steel were examined. Static strain-aging studies were performed on vacuum-annealed, dry-hydrogen-treated and neutron-irradiated samples. Hardening due to neutron radiation damage exhibited a cube root dependence o f the fluence. In addition to an increase in the lower yield stress, the Litder strain increased with dose up to 10 is neutrons cm -2, and at higher doses an apparently rounded yield was observed because o f fracture during the Liider straining. The increase in the Liider strain followed a (apt) 1/3 law, similar to that for radiation hardening. Static strain-aging studies revealed a complex time dependence o f the strain-aging index f and seem to illustrate a two-stage process: initially, atmosphere locking and, for long aging times, locking due to precipitation. The effect of neutron irradiation was very similar to the effect of dry hydrogen treatment; the rate o f aging decreased and, at high fluences (or longer exposures to dry hydrogen), essentially non-aging steel was obtained. However, the kinetics and/or mechanism o f strain aging are not affected by neutron radiation (or dry hydrogen treatment).

1. INTRODUCTION

The influence of irradiation-induced defects such as vacancies and interstitials on the mechanical properties of metals has been well d o c u m e n t e d in the literature through microstructural and mechanical property investigations. The significance of interactions between extrinsic impurities and radiationproduced defects is beginning to be recog0025-5416/83/0000-0000/803.00

nized [1]. The interaction of interstitial impurities such as carbon and nitrogen with point and line defects in steels is one such example and these interactions are best investigated through studies on yield point phenomena. These interactions between impurities and intrinsic defects can have practical significance such as in the critical role played b y residual copper on the notch impact properties of reactor pressure vessel steels [1, 2]. As pointed o u t b y Wechsler [1], experiments on the influence of nitrogen in irradiated iron may have a bearing on the radiation embrittlement of ferritic steels. The interstitial impurities such as carbon and nitrogen play a major role in radiation hardening and strain-aging phenomena [ 3-7 ]. Earlier work b y Hall [8] and others [9, 10] clearly indicated that these interstitial impurities combine with irradiation-induced point defects, such as vacancies and interstitials, either as individual defects or as loops, to form complexes. These complexes are probably responsible for part of the hardening [8]. At the same time the creation of these complexes results in a reduced net concentration of interstitial atoms in solution [10] and thus the irradiated steel becomes non-aging at sufficiently high neutron doses [8, 9]. Indeed, Hall's work indicates that mild steel samples with initial carbon and nitrogen concentrations of 0.03% and 0.002% respectively exhibited a " r o u n d e d " yield and became non-aging when irradiated to a dose of a b o u t 1019 neutrons cm -2. The parallel study b y McLennan and Hall [ 10] using internal friction methods revealed that the concentration of carbon in solution decreases on irradiation, although the residual amount is quite sufficient to show strain aging. In addition, there seems to be no experimental investigation of the strain-aging kinetics in steels irradiated at incremental neutron doses to observe the gradual decrease © Elsevier Sequoia/Printed in The Netherlands

208

in the rate of aging [ 11 ]. A very interesting study o f the role of interstitials in irradiation hardening and strain aging was made by Little and Harries [9]; t h e y studied the contribution of nitrogen to the aging kinetics by appropriately heat treating and quenching the samples. However, such processes will no doubt involve complications due to the contribution of quench aging. During the same study, Little and Harries observed in irradiated (about 10 is neutrons cm -2) mild steel that serrations appeared at a higher temperature and also after a finite plastic strain (cf. the PortevinLe Chatelier effect in solid solution alloys) in contradistinction to the unirradiated samples for which the serrations appear from the very beginning of the stress-strain curve [ 7 ]. These results were different from those reported by Murty and Hall [3]. The present study was undertaken to investigate the effects of incremental neutron dose as well as the concentration of nitrogen on the static strain-aging behavior of mild steel. Although both carbon and nitrogen are believed to be responsible for dislocation locking in steels, the effect of nitrogen is more pronounced in annealed material, mainly because most of the carbon precipitates as cementite [9]. In this paper the static strain-aging kinetics of vacuum-annealed mild steel samples are described and compared with those of samples irradiated at four different neutron doses ranging from about 4 × 101~ to about 1019 neutrons cm -2. The effect of dry hydrogen treatment at about 675 °C for various times (leading to different concentrations of nitrogen with essentially the same original carbon content) is also considered. In all cases, samples were furnace cooled to avoid any additional complications due to quenching.

2. E X P E R I M E N T A L P R O C E D U R E

Mild steel wires of 0.001 m diameter and 0.0385 m gauge length were used. The main

advantage o f wires is that the deformation proceeds by a single Liider band, usually nucleated in one of the grips, and the lower yield stress is thus extremely constant [12]. The material used was cold
TABLE 1 C o m p o s i t i o n o f steel (1 m m wires) Element

C

N

O

Si

AI

Ni

Mn

S

Cr

Cu

Sn

Fe

A m o u n t (wt.%)

0.05

0.004

0.012

<0.001

0.002

0.032

0.39

0.012

0.041

0.091

0.003

Balance

209

irradiation temperature can be taken as 80 °C, the heavy-water temperature [8]. The irradiated specimens all became radioactive because of the relatively large capture cross section of 58Fe, and thus the specimens were stored in lead coffins until the 7 activity decayed to tolerable levels. All tension tests were performed on a "hard" tensile machine of the t y p e designed by Adams [13]. The cross-head speeds can be varied from 1.8 × 10-7 to 1.0 × 10-5 m s-1 with seven intermediate steps. The major part of the testing was done at a cross-head speed of 5.2 × 10-6 m s -1 which corresponded to a nominal strain rate of a b o u t 1.36 × 10-4 s-1. The desired temperatures were attained by immersing the specimen and the holder assembly in an electrically heated stirred oil or salt bath, and the temperatures were controlled to +1 °C. Static strain-aging studies were made following the m e t h o d of Sylwestrowicz and Hall [12]; if a Liider band is run part of the way along a wire specimen, the load removed and the specimen aged then, when the specimen is re-strained, a small upper yield point " p i p " appears before the band moves on. If a' is the lower yield stress and o" the upper yield stress after aging and re-straining, then the aging parameter f is defined as* f

0"" --

-

-

(7'

(/'

(1)

Thus, experimental determination of f after different aging times at fixed temperatures yields the static strain-aging characteristics. 3. R E S U L T S AND D I S C U S S I O N

3.1. Radiation hardening: effect o f neutron dose Load-elongation curves for unirradiated and irradiated samples with a grain size of ASTM 7.5 at a fixed strain rate of 1.35 × 10-4 * T h e m o r e c o m m o n l y used p a r a m e t e r t o characterize t h e static strain aging is t h e d i f f e r e n c e b e t w e e n t h e t w o stresses [14]: A 7 = a" - - o' Preliminary data [ 15] i n d i c a t e d t h a t n o r m a l i z i n g b y the l o w e r yield stress a ' gave m o r e c o n s i s t e n t results o n m u l t i p l e s p e c i m e n s t e s t e d u n d e r identical cond i t i o n s . Thus, t h e aging p a r a m e t e r f as d e f i n e d in eqn. (1) is r e g a r d e d as a b e t t e r p a r a m e t e r t h a n A%

s -1 and room temperature are d o c u m e n t e d in Fig. 1. It is clear that radiation hardening and embrittlement occur and they in turn increase with integrated neutron flux. In addition to an increase in the lower yield stress, the Ltider strain increases with dose until the lower yield stress after irradiation approaches the ultimate tensile stress. At higher doses (about 1019 neutrons cm-2), an apparently rounded yield is observed; as will be discussed later, fracture probably occurred during the Liider straining. The increase in the lower yield stress due to radiation was found to vary as the cube root of the integrated flux: A G L y = OLy i - - OLy u =

A(cbt) lla

(2)

Figure 2(a) is a plot of yield stress versus (qbt) ~a for the three grain sizes, and leastsquares analyses of these data yield the following values for A (kgf mm -2 (neutrons cm-2)-l/a) : 10.15 × 10 -6 (14.43) for ASTM 7.5 9.35 × 10 -6 (13.30) for ASTM 6.5 8.30 × 10 -6 (11.81)

(3)

for ASTM 5.5

The numbers in parentheses correspond to the A values with Ao in kilopounds-force per square inch and ~ t in 1018 neutrons per square centimeter. Cottrell [ 16] obtained a value of 8.0 for A (with Aa in kilopoundsforce per square inch and qSt in 10 TMneutrons per square centimeter) for En2 mild steel irradiated at 100 °C in the BEPO reactor. Considering the differences in the composition of En2 and the present mild steels, the present A values compare well with Cottrell's results; other factors, such as the neutron spectrum which is a characteristic of the particular reactor, also influence the parameter A. The parameter A seems to decrease with increasing grain size, implying that coarse-grained material is relatively more resistant to radiation damage. These results confirm the earlier findings of Castagna et al. [17] on Fe-Ti alloys and of Trudeau [18] on 3.25% Ni steel but are in conflict with Cottrell's prediction regarding the superiority of fine-grained steels to radiation hardening [19]. In the same figure the effect of radiation on the yield stress of decarburized material is illustrated, and Oy

=

5.41 + 1.29 X 10-5(ept) ~a

(4)

210

50 "~ 1.4x1019 5

%

4O

E Q

o~

30 nirradiated

~0

20

3.~)x 1016

10 0

I 12

I

I 24

36

Elongation

48

(%)

Fig. 1. L o a d - e l o n g a t i o n curves at r o o m t e m p e r a t u r e , d e p i c t i n g t h e e f f e c t o f n e u t r o n fluence, t h e values o f w h i c h are s h o w n o n t h e curves in n e u t r o n s p e r s q u a r e c e n t i m e t e r (grain size o f t h e samples, A S T M 7.5; T = 22 °C).

30 ¸

15 2O

E

10 m

/, I

10

(a)

I

15

I 0 - 5 ( ~ t ) ~la

0

0

20

(b)

0

I

4

I

8

I

12

I 16.

J

20

I

24

10-5 ( ¢ t ) 1/3

Fig. 2. (a) E f f e c t o f grain size a n d d e c a r b u r i z a t i o n o n t h e f l u e n c e d e p e n d e n c e o f yield stress i n c r e m e n t ( T - - 22 °C): A, d = 0 . 0 2 7 m m ( A S T M 7.5); o, d = 0 . 0 3 8 m m ( A S T M 6.5), v a c u u m a n n e a l e d ; ~, d = 0 . 0 5 3 m m ( A S T M 5.5); v, d = 0 . 0 4 4 ram, d e c a r b u r i z e d . ( b ) F i u e n c e d e p e n d e n c e o f t h e Liider s t r a i n : A, e x t r a p o l a t e d .

This implies that the interstitial-free steel is less resistant to radiation hardening. A plausible albeit n o t necessarily convincing explanation may be put forward. Neutron irradiation creates a high concentration of linear and point defects, b o t h vacancies and interstitials. The point defects migrate to dislocations, creating jogs which result in an increased yield stress [8]. In mild steels, however, free carbon and nitrogen are

interstitially dispersed and the presence of a large concentration of point defects will mean a sizable number of sinks for carbon and/or nitrogen. Consequently, the interstitial impurity element, which is quite mobile at the irradiation temperature (about 80 °C in this work), will migrate to these point defects and be held there. This implies that the presence o f free interstitial elements results in the elimination of some of the radiation-induced

211 involved room temperature propagation of the Lfider band, strain aging under zero load and room temperature unlocking of the Liider band (Fig. 3). The main advantage of this method is that a limited number of samples are enough to obtain an adequate amount of data on the temperature and aging time dependences of the strain-aging index f; thus specimen-to-specimen scatter is minimized.

defects responsible for jogging the dislocations, thereby decreasing the radiation hardening. The fluence dependence of the Liider strain was similar to that of the yield stress, namely a cube root function (eqn. (4)). Figure 2(b) depicts the linear relationship between the Liider strain and (~t) ~3. Thus, the Liider strain increased with fluence, and at the highest fluence of 1.4 × 1019 neutrons cm -2 we predict the Liider strain to be 13%. It is clear from Fig. I that fracture occurred during the Liider straining at this fluence.

3.2.1. Vacuum-annealed samples Figure 4 shows f versus t at various test temperatures for vacuum-annealed samples (d = 7.5). The index f is an indication of the d e ~ e e of locking and is proportional to the number Nt of interstitial atoms removed from solution after the aging time t [14]. According to the theory of CottreU and Bilby [20] which is based on dislocation locking by carbon atmospheres, Nt o: t 2[3. Later modifications of the theory by Bullough and Newman [21] and Ham [22] indicate essentially the same relationship at short aging times. However, Suzuki and Tomono [23] and McLennan and Hall [10] indicate that the aging process should be divided into two parts; initially, Nt ~ t 1"5 and, at long times, Nt cct 0.a. The present results support such a contention. However, the experimental data are too scattered to fix the value for the time index. All the experimental results are better correlated with sigmoidal-type curves described by

3.2. Static strain-aging studies Static strain-aging studies were made using the method of Blakemore and Hall [ 7] which

]1% I Fig. 3. Experimental method used in static strainaging studies (irradiated, 2.8 × 1017 neutrons cm-2; Tage = 120 °C; f= AO/O0).

I x

i

?o=5 /

.~'".

7 5 0 min

0o o

o~

ex { 1

_

. . -

0.1

Og,~J ~-'~ 0

J 50

I 100

I 150

I 200

250

t (rain}

F)g. 4. Static strain-aging index f vs. aging time for vacuum-annealed samples: <>, T = 59 °C; v, T = 61 °C; O , T = 70°C; ~, T = 75°C; D, T = 81°C; ©, T = 90°C.

(5)

212 1000 -

e,,,j

,' (2.sxtd

/

500

/

/

,'

e/ , , / ,

/

,/

/

/

/ / 85 min J J c y / / / ,/ / I J(////

// 5

I

rain

/

."

,'~15 mi./ / / / / ' Vacuum .' A n n e a l e d /(Q~._3 k c a t . / . / tool I)

/

'] 2.7

2,

//,o

,~ / , ' /

Treated

10 --

/,(3.gxld%

"//~ry H2 / /Treated/'

/<7/

"2

7)

Irradiated

.'

~._ 100 .EE ® 50-Dry

where T is a constant dependent on temperature [ 8 ]. The static strain-aging studies at various temperatures indicate a thermally activated process as shown in Fig. 5 where aging times for an f value of 0.07 are plotted versus reciprocal temperature (in kelvins) on a semilogarithmic scale. The slopes o f the lines yield an average value of 23.84 + 3.18 kcal mol-1 for the activation energy which agrees with earlier studies [7, 9 ]. This value is greater than that for the migration of carbon and/or nitrogen by about 5 kcal mol-Z. Identical results were obtained for samples with different grain sizes.

Irradiated

I

IO00/T

I 2.9

3.2.2. Effects o f irradiation and nitrogen concentration The static strain-aging studies were performed on irradiated and dry-hydrogentreated samples. Figure 6(a) depicts data on irradiated material (2.8 × 10 z7 neutrons cm -2)

I 3.1

(K-1)

Fig. 5. Arrhenius plot of aging time at f - 0.07 for vacuum-annealed, irradiated and dry-hydrogentreated mild steel. 0.2

1O C O.

//,ooo

C

,=

y./ 100

500 t (rain)

1000

5000

(a) 0.3

0.2

90 °C

,-

0.1 6 8 °C

¢n

0

--

, 5

1 10

i 5

I 100

J I 5 1000

t (rain) (b) Fig. 6. Static strain-aging index f vs. aging time for (a) irradiated (~bt = 2.8 × 1017 neutrons cm -2) and (b) dryhydrogen-treated (75 min at 675 °C) mild steel at various temperatures.

213 0.3

Unirradiated

,_ ..... r x

0.2

Irradiated

.,./.,~.Sxld 7

~0.1 /

(a/

~,

0.0 10

50

.t

2.0x1018

100 t (min)

500

~ 1000

0.3

Annealed

tacuum , ~ - - - -i....-----.~ D r y H y d r o g e n "x

0.2

min Trea~,~60 min

" f 4 5

'~ 0.1

.o- . . . . --~--- T ~ - - - = - - v - - e

0

1

lO (b~

1

s0

lOO

1

s o o lOOO

t (min)

Fig. 7. Effect of (a) irradiation and (b) partial denitriding o n s t a t i c strain aging at 90 °C.

as the strain-aging index f versus aging time at various temperatures. These data are very similar to those obtained for vacuum-annealed material except that much longer aging times are required to attain identical f values. Similar results were obtained on samples treated in a dry hydrogen atmosphere, resulting in reduced nitrogen concentrations in solution (Fig. 6(b)). The neutron dose dependence o f the strain-aging characteristics at a constant temperature (90 °C) is illustrated in Fig. 7(a) which clearly indicates that, as the neutron dose increases, the rate of aging decreases and at doses greater than about 10 is neutrons cm -2 a non-aging steel is obtained. Essentially identical results were obtained on dry-hydrogen-treated samples. Figure 7(b) depicts the effect of denitriding on static strain aging and, as the duration of dry hydrogen treatment increased from 2700 s (45 min) to 10 800 s (3 h), the rate of aging decreased and samples treated for 3 h or more were found to be non-aging. These observations indicate that nitrogen is

primarily responsible for strain aging in furnace-cooled mild steel. It was unfortunately n o t possible to determine the concentration of nitrogen in solution which precluded a quantitative analysis of these data. Although irradiation and denitriding reduced the rate of strain aging, the kinetics of aging seem to be unaffected. Arrhenius plots of the aging times for f = 0.07 for irradiated and dry-hydrogen-treated samples are included in Fig. 5 together with the vacuum-annealed data; essentially parallel lines were noted with an activation energy for strain aging of a b o u t 23 kcal mo1-1. Little and Harries [9] reported a value of 24 kcal mo1-1 for an En2 steel irradiated to 1.5 × 1017 neutrons cm -2 and attributed the difference between this value and that for migration of nitrogen in iron (19 kcal mo1-1) of 5 kcal mo1-1 to the binding energy of nitrogen to manganese. The present results lend support to the conclusions reached earlier b y Hall [8], namely that nitride locking of the dislocations is responsible for strain aging in mild steel. Although vacancy and interstitial concentrations increase to a b o u t 10 -2 at.% because of irradiation, the amount o f free carbon and nitrogen present in the damaged material (about 7 × 10-4wt.%) [10] is sufficient to lock all the dislocations [8]. If it is assumed that the dislocations in annealed material are decorated b y carbide and nitride precipitates, the effect of neutron irradiation results in jogging the dislocations and freeing them from the precipitates. The amount of jogging increases with neutron dose level. During deformation these jogs produce more point defects which act as further sinks to interstitial carbon and nitrogen. If the level of impurity concentration is not sufficiently small, the free impurity atoms migrate to the free dislocation loops and nucleate new carbide and nitride precipitates although the rate of aging decreases. However, as the dose increases, the amount of jogging of the dislocations increases and the level of impurity concentration in solution decreases further and eventually at sufficient neutron dose levels the material becomes non-aging. Since precipitation takes place through the matrix, the activation energy will be that for the migration of nitrogen (about 19 kcal m o V 1) plus the binding energy of free nitrogen to the

214

defect complexes. In slowly cooled or furnacecooled samples the concentration of free nitrogen is quite large compared with that of carbon, and thus nitrogen is believed to be responsible for the strain aging. The present experimental results on dry-hydrogen-treated and irradiated samples (Figs. 6 and 7) support these arguments. The amount of nitrogen available for precipitation on the dislocations will thus be a function of the neutron dose (dry hydrogen treatment) as well as the aging temperature. Since higher temperatures mean larger amounts of precipitates on dislocations and larger neutron fluences (a longer dry hydrogen anneal) imply smaller amounts of free nitrogen available for precipitation, each f value tends to a limiting value dependent on the aging temperature and the irradiation fluence (the duration of dry hydrogen treatment). Again, the present results as depicted in Fig. 6 are in accord with these arguments. Quantitative comparison between internal friction data [10] and theories based on atmosphere and precipitation locking indicate that dislocation locking may be due to atmosphere formation for short times of aging whereas it is probably due to precipitation for long times; however, both the theories fail in the quantitative predictions of the experimental data. 4. SUMMARIZING REMARKS AND CONCLUSIONS

The effects of neutron irradiation and dry hydrogen treatment on yield point phenomena in mild steel were examined. Static strainaging studies were performed on vacuumannealed, dry-hydrogen-treated and neutronirradiated samples. The hardening due to neutron radiation damage exhibited a cube root dependence of the fluence. In addition to an increase in the lower yield stress, the Ltider strain increased with dose up to 10 is neutrons cm -2, and at higher doses an apparently rounded yield was observed. The increase in the Liider strain followed a (~t) 1/3 law, similar to that for radiation hardening. Static strain-aging studies revealed a complex time dependence of the strain-aging index f and seem to illustrate a two-stage process: initially, f c0 t 1-5 and, at longer times, f ccto.5. The effect of neutron irradiation (dry hydrogen treatment) is to decrease the rate

of aging and, at high fluences (longer exposures to dry hydrogen), essentially non-aging steel was obtained. However, the kinetics and/or mechanism of strain aging are not affected by neutron radiation (dry hydrogen treatment).

ACKNOWLEDGMENTS

I wish to express my sincere appreciation to the Australian Institute of Nuclear Science and Engineering for the support of the experimental work described herein. Thanks are due to Professor E. O. Hall, University of Newcastle, for various suggestions and discussions. Acknowledgments are due to Mr. E. A. Palmer, Australian Institute of Nuclear Science and Engineering, and Mr. R. Hilditch, Australian Atomic Energy Commission, for irradiation arrangements. Thanks are due to Mr. Hugh Munn for preparing the manuscript.

REFERENCES 1 M. S. Wechsler, J. Eng. Mater. Technol., 101 (1979) 114. 2 J. A. Spitznagel, R. P. Shogan and J. H. Phillips, in Irradiation Effects on the Microstructure and Properties o f Metals, A S T M Spec. Tech. Publ. 611, 1976, p. 434. 3 K. L. Murty and E. O. Hall, in Irradiation Effects on the Microstructure and Properties o f Metals, A S T M Spec. Tech. Publ. 611, 1976, p. 53. 4 E. O. Hall, J. Iron Steel Inst, London, 170 (1952) 331. 5 B. J. Brindley and J. T. Barnaby, Acta Metall., 14 (1966) 1765. 6 A. S. Keh, Y. Nakada and W. C. Leslie, in A. R. Rosenfield (ed.), Dislocation Dynamics, McGrawHill, New York, 1968, p. 381. 7 J. S. Blakemore and E. O. Hall, J. Iron Steel Inst., London, 204 (1966) 817. 8 E. O. Hall, J. Aust. Inst. Met., 7 (1962) 44. 9 E. A. Little and D. R. Harries, in Irradiation Effects in Structural Alloys, A S T M Spec. Tech. Publ. 457, 1969, p. 215. 10 J. E. McLennan and E. O. Hall, J. Aust. Inst. Met., 8 (1963) 191. 11 K. L. Murty and E. O. Hall, Effect of neutron irradiation on static strain-aging kinetics in mild steel, A N S Winter Meet., San Francisco, 1975, American Nuclear Society, Hinsdale, IL, 1975. 12 W. Sylwestrowicz and E. O. Hall, Proc. Phys. Soc., London, Sect. B, 64 (1951) 495. 13 M. A. Adams, J. Sci. lnstrum., 36 (1959) 444. 14 E. O. Hall, Yield Point Phenomena in Metals and Alloys, Macmillan, London, 1970.

215 15 K. L. Murty, Yield point phenomena in mild s t e e l - - e f f e c t of neutron irradiation, A I N S E Final Rep., 1975 (Australian Institute of Nuclear Science and Engineering, Lucas Heights, Australia). 16 A. H. CottreU, Proc. Uonf. on Brittle Fracture in Metals, 1957, in UKAEA Rep. IG145 (RD/C), May 1959 (U.K. Atomic Energy Authority). 17 M. Castagna, A. Ferro, F. S. Ross and J. Sebille, in The Effects o f Radiation in Structural Metals, A S T M Spec. Tech. Publ. 426, 1967, p. 3. 18 L. P. Trudeau, J. Iron Steel Inst., London, 69

(1961) 382. 19 R. W. Nichols and D. R. Harries, in Radiation Effects on Metals and Neutron Dosimetry, A S T M Spec. Tech. Publ. 341, 1963, p. 162. 20 A. H. Cottrell and B. A. Bilby, Proc. Phys. Soc., London, Sect. A, 62 (1949) 49. 21 R. BuUough and R. C. Newman, Proc. R. Soc. London, Ser. A, 266 (1962) 189. 22 F. S. Ham, J. Appl. Phys., 30 (1959) 915. 23 T. Suzuki and Y. Tomono, J. Phys. Soc. Jpn., 14 (1959) 597.