almost nil in well cycled samples to 2~ in the ther - momechanicaUy processed wire (Fig. 3). The detai led effects of process ing his tory have not been sys temat - ica l ly explored. In summary , howe'~er, the smal l hys- t e r e s i s that general ly occurs seems to suggest that the f ree energy diagram of Fig. 4 is quali tat ively co r rec t and that the w-like t ransi t ion phase lat t ice waves may be viewed as quasls tat ic in nature.

The bulk of the p rac t ica l Interes t in NiTi has been in the shape-memory or s t r i c t ly mechanical behav io r J The ra the r high negative t empera tu re coefficients of r e s i s t i v i t y (e .g . , up to - 2.2 pct per ~ for the wire ma te r i a l of Fig. 3) combined with i ts abi l i ty to be wire drawn suggest that NiTi may also have p rac t i ca l e lec - t r i c a l applications.

1. C. M. Wayman and K. Shimizu: Met. SeL .four., 1972,wL 6, pp. 175-83. 2. F. E. Wang, B. F. DeSavage, W. J. ~uehler, and W. R. Hosler: I. Appl, Phys.,

1968, vol. 39, pp. 2166-75 3. D. P. Dautovich and G R. Purdy: Can. Met. Quart., 1965, vol. 4, pp. 129-43. 4. J. E. Hanlon, S. R. Bullel, and R. J. Wasilewski: Trans. TMS-AIMtL ] 967, vol.

239, pp. 1323-27. 5. W. B. Cross, A. H. Kariotig, and F. J. Stimler: NASA CR-1433, 1969. 6. G. D. Sandrock, A. J. Perkins, and R. F. Hehemann: Met. Trans., 1971, vol.

2, pp. 2769-81. 7. C. M. Wayman, J. Cornelis, and K. Shimizu: Scr. Met., 1972, vol. 6, pp. 115-22. 8. F. E. Wang, S. J. Pickart, and H. A. Alperin: J. Appl. Phys., 1972, vol. 43, pp.

97-112. 9. K. Chandra and G. R. Purdy: J, Appl. Phy~, 1968, vol. 39, pp. 2176-8 I

10. Private Communication: C M Jackson, Battelle Memorial Institute, Columbus, Ohio; and J. Patri~, Titanium Metals Corporation of America, Toronto, Ohio.

11. D. P. Dautovich, E. Metkvi, G. R. Purdy, and C. V. Stager: J. App~ Phys., I966, voL 37, pp. 2513-I4.

12. D. J. Comello. G. L. Houze, Jr, and R. F. Hehemann: Truns. TMS-AIME, 1965, vol. 233, pp. 30-39.

13. A. J. Perkins, P. F,. Yaffe, and R. F. Hehemann: Met. Trans., 1971), vol. I, pp. 2785-90.

14. F. R. Brotzen, E. L. Harmon, Jr., and A. R. Troiano: Trans. AIME, 1955~ vol. 203, pp. 413-19.

15. D. deFontaine: ActaMet., 1970, vol. 18, pp. 275-79. 16. D. deFontaine, N. E. paton, and J. C. Williams: ActaMet., 1971, vol. 19, pp.

1153-62. 17. R. F. Hehemann and G 13. Sandrock: Scr. Met., 1971, vol. 5, pp. 801-05.

Effect of Plastic Deformation on the

(211) X-Ray Line Width of a Medium

Carbon Martensite V. K. SHARMA AND N. N. BREYER

Breyer et al. have repor ted seve ra l changes accom- panying the p las t ic deformation of an as-quenched mar tens i te . L-4 These include an increase in s trength without any significant loss in ducti l i ty, ~ dec rease ~n e l ec t r i ca l r es i s t iv t ty , 2 sharpening of (110) X- ray dif- f ract ion l ines 3 and an apparent increase in density as indicated by the l inear d i la tomet r ic measurements . 4

V. K. SHARMA, formerly Post-doctoral Research Associate, Illinois Institute of Technology, Chicago, II1., is now Research Engineer, Ma- terials Div., Engineering Research, International Harvester Co., Hinsdale, I11. 60521. N. N. BREYER is Professor, Department of Metallurgical and Materials Engineering, Illinois Institute of Technology, Chicago. 60616.

Manuscript submitted March 26, 1973.

When deformed mar tens t te is subsequently tempered, the normal sequence of precipi ta t ion of carb ides Is also significantly a l t e red , t-s This communication de- scr~bea the r e su l t s of experfments t a t t l e d out to study the effect of p las t ic deformation and e las t ic s t r e s s e s on the (211) X- ray diffraction line width of a medium carbon mar tens i te .

Small rods of AISI 1045 s teel were heat t rea ted and die drawn in a manner s i m i l a r to those descr ibed by Mil ler and Breyer . 4 The predeformat ion d iamete rs for the rods were so se lec ted that deformation by drawing through a 0,175 in. diam die resul ted in r e - ductions ranging f rom 0 to 6 pct. Specimens, about 1~ in. in length, were cut from these ba r s . The specimens were chemical ly polished in a 2:1 mixture of phosphoric acid and 20 pct hydrogen peroxide. Approximately 0.0525 in, was removed from the surface . A XRD-5 General Elec t r ic Dlff rac tometer with f i l te red CrK~ radiat ion and a propor t ional counter tube was used to r eco rd (211) diffraction l ines. A 3 deg beam sl i t , masked to produce a rec tangular beam of size about 0.375 in. • 0.030 in., and a 0.2 deg detector s l i t were used in these exper iments . The beam impinged in a narrow line on the specimen surface pa ra l l e l with the specimen axis . The specimens were continuously scanned at a goniometer speed of 1 deg 20 per min and peaks were char t recorded between the range of 145 to 160 deg. The line width at half maximum helght was de termined graphical ly . A s t ra ight line background was assumed through the char t recording. The peak posit ion was located using the three point parabol ic method developed by Marburger and Koistinen. ~ The (211) line width, repor ted in Fig. 1, was determined f rom the X- ray scan of the cyl indr ical surface along the axis of drawing. The line sharpened with deforma- tion. The c ros s sect ioned surface cut perpendicular to the axis of the specimen was s imi l a r l y scanned with X- rays . However, the beam geometry was changed to a 1 deg sl i t masked to produce a beam size of about 0.1 in. sq. A s imi l a r line sharpening was observed although the line width at half height was less (approx- imately 4.5 deg for the as-quenched specimen). The differences in line width again c lea r ly revealed the line sharpening with deformation. The d ispar i ty in the line widths for the surface and c ros s sect ion studies was a resu l t of the difference in beam geometry r e -

7-0

n- eD

. 6 ' 0

5.0

PEA CENT DEFORMATION

Fig. 1--Effect of p las t i c de format ion of m a r t e n s i t e on the (211) X - r a y line width. AISI 1045 s tee l .

METALLURGtCALTRANSACT~ONS VOLUME S ~ 3 A N U A R Y 1974-30I

1. N. N. Breyer and N. H. Polakowski: Trans. ASM., 1962, vol. 55, p. 667. 2. N. N. Breyer: "Deformation of Martensite," Ph.D. Thesis, Illinois Institute of

Technology, Chicago, 1963. 3. W. Evans: "Discussion t~ Ref. t ," Trans.ASM., 1962, vol. 55, p. 108% 4. M. F. Miller and N. N. Breyer: Trans. ASM., 1969, wfl. 62, p. 891. 5. D. V. Wilson: ActaMet.. 1957, vol. 5, p. 253. 6. R. E. Marburgel and D. P. Koistinen: Trans. ASM., 1961, vol. 53, p. 743. 7. B. D. Cullity: Elements of X-Ray Diffraction, p. 263, Addison Wesley Pub-

lishing Co., 1967. 8. C. J. Alstetter and A. Chaudhuri: "Discussion to Ref. 4" Met. Trans., 1970,

vol. 1, p. 3460.

Discussion Liquid Tin Extensive K. G. DAVIS

Fos te r and

of "Self-Diffusion in and Indium Over Temperature Ranges"*

Reyntk ~ have repor ted m e a s u r e m e n t s on se l f -d i f fus ion in liquid indium and tin. They used a c a p i l l a r y - r e s e r v o i r technique, and obtained D by ana l - ys is of the total concent ra t ion in the i r s amples as a function of the diffusion t ime. These comment s are r e s t r i c t e d to the r e su l t s for tin.

Fos te r and Reynik found a la rge Al effect, wherein m a t e r i a l f rom the mouth of the tube is swept into the r e s e r v o i r by hydrodynamic forces . To co r r ec t for hl , they used a technique in which samples were with- drawn f rom the r e s e r v o i r at va r ious in te rva l s dur ing a s ingle run. The total concent ra t ions in the samples were measu red , and the i r va lues as a function of dif- fusion t ime were analyzed on the a s sumpt ion that Al r e m a i n e d constant throughout the run. In this way both hl and a " c o r r e c t e d " D were es t imated .

The va lues for D obtained in this m a n n e r a re less than half of those repor ted by Ma and Swalin, 2 who used a c a p i l l a r y - r e s e r v o i r technique, and l e s s than half of those repor ted by Ca re r t et al. , 3,4 who used two s e m i - inf ini te rods . Fos te r and Reynik suggest that, in the work of C a r e r i and his coworkers , mixing occur red dur ing the in i t ia l mel t ing and heat ing of the samples which caused an i n c r e a s e in the m e a s u r e d D. This is difficult to r econc i l e with Vicent ini and Pao le t t i ' s s t a tement s that the i r data were reproduc ib le over "ve ry different t ime lengths of d i f fus ion ." Fos te r and Reynik put forward the following r ea sons for the "h igh" diffusion coeff icients r epor ted by Ma and Swaltn.

1) They may have had convect ion in the cap i l l a r i e s . Though this was a lmos t ce r t a in ly so for the h igher - t e m p e r a t u r e runs for which the cap i l l a ry was held o f f -ver t i ca l , it is ex t r eme ly unl ikely that convect ion was p re sen t dur ing the l o w e r - t e m p e r a t u r e runs (up to I000 K). 5'7'8

2) The Al effect was not allowed for. This is i m m a - t e r i a l , for al l the l o w - t e m p e r a t u r e data were obtained by sect ioning. With this technique, the ~ / e f f e c t has

*J. P. FOSTER and R. J. REYNIK: Met. Trans., 1973, vol. 4, pp. 207-16.

K. G. DAVIS is Research Scientist , Metal Physics Section, Physical Metal lurgy Division, Mines Branch, D e p a r t m e n t of Energy, Mines and Resources, Ot tawa, Canada.

Discussion submi t t ed May 17, 1973.

ve ry l i t t le influence on the m e a s u r e d D. 8 3) The p r e sence of Sb 12s was ignored. This would,

however, have had l i t t le effect on the m e a s u r e d values for D. Table I of Fos te r and Reynik shows that, within exper imen ta l sca t t e r , the diffusion coeff icients for Sb 125 and for Sn 11s in l iquid t in a re p rac t i ca l ly ident ical over the t e m p e r a t u r e range examined by Ma and Swalin.

Fur ther published data on se l f -d i f fus ion in liquid t in have apparent ly been overlooked by Fos te r and Reynik. Davis and Fryzuk 6 de te rmined D, between 513 and 1188 K, by a c a p i l l a r y - s o u r c e method. With this tech- nique, there would be no Al effect. At t e m p e r a t u r e s up to 1000 K, ag reemen t between the data f rom this work, that of Ma and Swalin, and that of C a r e r i et al. was good. Some fur ther , unpublished, work has been done on self diffusion in l iquid t in at one t e m p e r a t u r e , 623 K, us ing a c a p i l l a r y - r e s e r v o i r technique. Detai ls of the p rocedures used may be found in Refs. 9 and 10. The r e su l t s f rom five independent runs were within the range 2.95 ~= 0.30 • 10 -s cme/s . Again, this is in good ag reemen t with all previous work except for that of Fos te r and Reynik.

In the above inves t iga t ions , the p re sence of St) 12s was not speci f ica l ly allowed for. This t r a c e r is c r e - ated along with Sn 113 when na tu ra l Sn is i r r ad ia ted . The f rac t ions of the total act ivi ty a t t r ibutable to Sb x2s and to Sn ~3 were es t ima ted as follows. Samples of the i r r ad i a t ed t in, as rece ived , were al loyed with nonact ive t in and sol idif ied d i rec t iona l ly . After growth, the s a m - ples were sec t ioned and counted for X-radiat ion over the same energy band used in counting the diffusion samples . F rom this data, "d i s t r i bu t ion coef f ic ien t s" (k) were calcula ted 11 defined as the act ivi ty in the f i r s t solid to f reeze divided by the act ivi ty of the s t a r t ing ma t e r i a l . If x is the f rac t ion of the total count coming f rom the Sb ~s, it is eas i ly shown that k = 1 + x ( k ~ - 1). The d i s t r ibu t ion coefficient for an t imony in t in (ko sb) is known. ~ x can therefore be found f rom k.

Sb 125 has a longer hal f - l i fe than Sn ~13. The propor t ion of the count coming f rom Sb ~2s, therefore , I nc rea se s with the t ime after i r r ad ia t ion of the t in source . Three months af ter i r r ad ia t ion , Sb ~2s was found to be r e s p o n - s ible for approx imate ly 20 pct of the total count, and all our expe r imen t s were done within this period. Con- s ide r ing that the f rac t ion of the count a t t r ibutable to Sb ~2s was less than 20 pct and that the va lues for the diffusion coeff icients of an t imony in t in h n and of t in in t in a re s i m i l a r , the e r r o r in the va lues for the self diffusion coefficient of t in introduced by the p r e s e n c e of Sb 125 mus t have been sma l l in these exper imen t s .

In sum, the r e su l t s of Fos te r and Reynik are at odds with four independent sets of data, al l of which a re se l f - cons i s t en t , obtained by three separa te techniques . The r eason for the d i sc repancy is not c lea r . However, it is noted that the va lues for A1 calculated by Fos te r and Reynik a re l a r g e r than would be expected f rom the observa t ions on t in a l loys repor ted by Davis. 8 It may also be noted that, con t r a ry to the s ta tement by Fos te r and Reynik, the exis tence of a pa i r of va lues for Al and D that lead to a m i n i mum for the sum in the i r Eq. [6] does not n e c e s s a r i l y mean that h l is independent of t ime. The methods used by Fos te r and Reynik seem to ove re s t ima te Al and to depress the " c o r r e c t e d " D.

In c a p i l l a r y - r e s e r v o i r m e a s u r e m e n t s , de t e rmina t ion of D by sec t ioning the sample and analyzing the concen- t r a t ion prof i le along its length is p re fe rab le to the total

M E T A L L U R G I C A L TRANSACTIONS VOLUME 5, JANUARY 1 9 7 4 - 3 0 3