Communications An X-Ray Diffraction Line Profile Analysis in Cold-Worked Fcc Cu-lZn-Sn and Ag-lZn-Sn Alloys: Role of 1 Wt Pct Zn

A.K. MAITY and S.P. SEN GUPTA

The role of addition of 1 wt pet Sn to fcc Cu-Zn u] and Ag-Zn t2] alloys has been investigated earlier, and the sig- nificant observations with regard to the addition of a third element in the dilute range have been reported. The pres- ent investigation concerns two other alloy systems, namely, the solid-solution phase of Cu-Sn and Ag-Sn having solute Zn in the dilute range of 1 wt pct only.

Spectroscopically pure (99.999 pct) metals, supplied by M/S Johnson, Matthey, and Co. Ltd. (London), were used to prepare five compositions of Cu-I wt pct Zn-Sn alloys and also Ag-1 wt pct Zn-Sn alloys in the solid- solution range; the X-ray diffractograms from respective cold-worked and annealed standards were recorded in the usual way. t3] The recorded diffractograms were sub- jected to detailed profile analyses for peak shift, peak asymmetry, and peak broadening following the standard methods adopted earlier, t41

The average values of the stacking fault probabilities, (Ups), have been determined from measurements of rel- ative peak shifts, t41 and the reflections involved are (111), (200), (220), and (311). The values are shown in Table I, and the variations of the (Ups) with solute Sn concentra- tions in weight percent are shown in Figure 1.[3.5.6] It is apparent from Figure 1 that the fault probabilities (Ups), in general, increase rapidly with the addition of solute Sn, and the addition of dilute solute 1 wt pct Zn to binary alloys of Cu-Sn and Ag-Sn helps to increase the fre- quency of faulting, which is identical to observations made in Ag-lSn-Zn alloys t21 and unlike the case with Cu-lSn-

A.K. MAITY, Senior Research Fellow, and S.P. SEN GUPTA, Professor and Head, are with the Department of Materials Science, Indian Association for the Cultivation of Science, Jadavpur, Calcutta 700 032, India.

Manuscript submitted October 11, 1989.

Zn alloys, u] in which the role of 1 wt pct Sn is quite different.

The plots of (Ups) have also been made as a function of the chemical valence electron to atom ratio, (e/A), considering monovalent (Figure 2(a)) t3,51 as well as pos- sible divalent (Figure 2(b)) t3'5] states of copper (Cu-lZn- Sn). It may be seen from both Figures 2(a) and (b) that the values of (aps) change in a similar way when e/A changes from a value of 1.00 to 1.30 and from 2.00 to 2.17, and this, therefore, suggests that the identical sit- uation may be obtained in cases when the solvent metal copper exists in a divalent state. The variation of (aps) as a function of e/A for Ag-lZn-Sn alloys is also similar in nature to the binary system and to copper-base alloys under consideration.

Using (111) and (200) reflections, the shifts of the centers of gravity from the peak maxima of the respec- tive broadened profiles, APMcc(20 deg)hkt, have been measured t71 to calculate the contributing factor,/3 + 4.5u" (Table I). The values of the compound fault probability are found to be negligibly small, similar to earlier cases, II'2] signifying near absence of extrinsic or double defor- mation faults (u") and deformation twin faults (/3) as compared to intrinsic or single deformation faults (u ') .

o Cu-tZn-Sn'[,~r t w "3 /_,~ ~p~, 6C v Ag-lZn-Sn.J ~ esen OrK / ~ �9 Ag-Sn (Adler&Wagnermez) / , , ~ /

Cu-Sn {Wagner& He'lionlges) /_~" / • "~ o co-,o e , . , . o . , / y e

V2c

I I I 0 4 8 t2 16

Wt % Sn

Fig. 1--Plots of average stacking fault probability, (aps), as a func- tion of solute concentration (weight percent) in Cu-lZn-Sn, Ag-lZn- Sn, Cu-Sn, and Ag-Sn alloys.

Table I. Experimental Values for Cu-1 Wt Pct Zn-Sn (Upper) and Ag-1 Wt Pct Zn-Sn (Lower) Alloys

(aps) (/3 + 4.5t~") De (/~) DSF (]k) T "n (e2=50A) 1/2 x 103 [1.5(a '

Wt Pct Sn x 103 x 103 [111] [100] [111] [100] (/~i [111] [100] + a") +/3] X 103

3 6.6 -1 .2 151 90 291 126 196 2.5 3.7 28.8 6 20.5 1.8 116 67 208 90 164 2.9 3.7 40.6 9 28.1 -1 .0 85 50 159 69 114 3.0 3.8 53.3

12 43.2 1.1 75 45 147 64 95 3.2 3.9 57.8 15 60.0 2.3 67 40 130 56 86 3.7 4.5 65.7

2 11.4 1.0 156 97 336 145 182 3.0 3.4 28.1 4 20.3 2.1 137 86 302 131 157 3.1 3.2 31.3 6 32.2 2.6 125 77 263 114 149 3.1 3.4 36.1 8 41.2 2.6 107 65 220 95 128 3.3 4.0 43.2

10 61.0 -5 .0 83 51 173 75 100 3.8 4.4 54.9

METALLURGICAL TRANSACTIONS A VOLUME 21A, MAY 1990--1319

4C

r

V

2O

60 o Cu-IZn-Sn (Present work) / u Cu-Sn (Goswami et al. 1966) ~ "

Cu-Sn (Wagner & He'lion 1 9 ~

o

I I ~O 1.1 1.2

e/A

I 1.5

(a)

~_o

6C

4C

20

0 :~.00 2.20

Cu-Sn (Wagner& H~lion tges) /

o �9

I I 2.05 2.~10 2.15 e/A

(b)

Fig. 2 - - P l o t s of average stacking fault probability, (ePs), as a func- tion of valence electron to atom (e/A) ratio in (a) Cu- lZn-Sn and Cu- Sn alloys (monovalent Cu) and (b) Cu- lZn-Sn and Cu-Sn alloys (divalent Cu).

Fourier analysis of profile broadening has been made using Warren-Averbach's approach [81 considering first- and second-order reflections, namely, (111), (222) and (200), (400). The Stokes corrected [9] normalized Fourier coefficients, At(hkl), have been used, and the values of anisotropic effective coherent domain sizes, De, the do- main size due to stacking faults, DsF, the minimum value of T (the domain size in the faulting plane), and root mean square microstrains, (e~> 1/2, have been determined (Table I). To see the effect of DsF on the observed pro- file broadening, the ratio for the completely extended stacking faults (which is (DsF)[nu/(DsF)[IOO] -- 2.3), has been determined, whereas the ratio due to all contrib- uting factors (i.e., T, DsF, and D, the coherent domain size normal to the reflecting plane) to De, i.e., (De)tim/ (De)[~001, is --1.6, for both Cu-lZn-Sn and Ag-lZn-Sn alloy systems. This clearly suggests that both the param- eters T and D contribute to the parameter De, the domain size broadening. The decreasing tendency of Tmi, with

increasing solute Sn reveals a deformation stacking fault on the (111) faulting plane. The values of the compound fault probability [1.5(a' + ~x") + /3] are found to in- crease with increasing solutes. All of these factors in- dicate that the observed domain size broadening originates mainly from the creation of an appreciable density of deformation stacking faults (of intrinsic nature) in the cold-worked materials in a similar way to the binary system.

e/A Z.OO 2,05 2,10 Z. 15 Z.20

I I I

\~ Cu-lZn-Sn

'!,

\

1.0 1.t t.2 t,3 e/a (a)

45

35

25 ~

1.4

f Ag-lZn-Sn 7\ \ \

\

\\ \

\ \

\ \

\ \

\ \

o \

O v

( I I 1.0 1.1 1.2

e/A

/ X3--

!z4

x

16~

4

t.3

(b)

Fig. 3 - - P l o t s of dislocation density, (p), and stacking fault energy ( ' / /# ) as a function of valence electron to atom (e/A) ratio in (a) Cu- 1Zn-Sn and (b) Ag- lZn-Sn alloys.

1320--VOLUME 21A, MAY 1990 METALLURGICAL TRANSACTIONS A

The values of the dislocation density, Pay, and the pa- rameter 3//ix (% the stacking fault energy and/x, the shear modulus) have also been calculated t41 and plotted as a function of e/A (Figures 3(a) and (b)). It may be seen from Figure 3(a), where y/ /s ' s have been plotted as a function of e/A, that for both monovalent and divalent states of copper, the curves are identical and quite close. The curves, when extrapolated to e/A = 1.00 and 2.00, yield the values of 3///x for pure copper. Using the value of/~,t~ol the shear modulus for pure copper, the stacking fault energies, 3/0, for pure copper have been obtained, and these are 49 (monovalent copper) and 51 (divalent copper) mJ /m 2 in the Voigt scheme and 36 (monovalent copper) and 37 (divalent copper) m J / m 2 in the Reuss scheme. The agreement with the reported values of 55 mJ/m 2 by Gallagher till and 62 mJ/m 2 by Reed and Schramm t~21 is found to be quite good. The plot of 3///x

vs e/A for the Ag-lZn-Sn alloy system similarly gives a value of 3/0 for pure silver by extrapolating the curve to e/A = 1.00. Thus, 3/0 is found to be 24 (Voigt scheme) and 19 mJ /m 2 (Reuss scheme). These values are also quite reasonable and are comparable to the reported val- ues of 14 mJ/m2, [~31 21 m J / m 2 (Voigt) and 16 mJ /m 2 (Reuss), t14~ and 16 to 31 mJ /m 2 (the range, in general, from all of the observations, is due to Reed and Schrammt~21). The satisfactory evaluations of the stack- ing fault energy parameter, % in all of these cases of ternary systems with solute in the dilute range present a consistent picture of the deformed states of the alloys influenced by the additions of solutes (Zn, Sn) in the sol- vent copper and silver.

Polycrystalline specimens of Cu-lZn-Sn alloys pre- pared in the form of thin foils and of Ag-lZn-Sn alloys in the form of fine powders have been observed under

(i) (ii) (a)

(iii) (iv) (b)

Fig. 4 - - ( a ) Transmission electron microscope images showing the microstructures in samples with their SAED patterns (insets) of Cu-lZn-Sn alloys. (i) 3 wt pct Sn: magnification 47,000 times and zone axis of the pattern = [213] and (ii) 15 wt pct Sn: magnification 37,000 times and zone axis of the pattern = [001]. (b) Microstructures with their SAED patterns (insets) of Ag- lZn-Sn alloys. (iii) 2 wt pct Sn: magnification 23,780 times and zone axis of the pattern = [111] and (iv) 10 wt pct Sn: magnification 30,340 times and zone axis of the pattern = [111].

METALLURGICAL TRANSACTIONS A VOLUME 21A, MAY 1990--1321

transmission electron microscope (PHILIPS* CM 12).

*PHILIPS is a trademark of Philips Instruments Corporation, Mahwah, NJ.

The micrographs of the deformed microstructures and their corresponding selected area electron diffraction (SAED) patterns (insets) are shown in Figures 4(a) and (b) [(i) through (iv)]. Figure 4(i) exhibits the extinction contours t15] from Cu-1 wt pct Zn-3 wt pct Sn alloy with foil orientation [213]. In its SAED pattern, a poly- crystalline ring pattern is observed. Figure 4(ii) shows the bright-field image from Cu-1 wt pet Zn-15 wt pet Sn alloy containing high dislocation density, t~6] as also evi- denced from the X-ray diffraction analysis, and its foil orientation is along [001], as indicated by its SAED pat- tern. Figure 4(iii) represents the bright-field image from Ag-1 wt pct Zn-2 wt pct Sn alloy showing the disloca- tion network with foil orientation along [111 ]. Figure 4(iv) shows the microstructure with the presence of pre- cipitation t171 of one of the constituents of Ag-I wt pct Zn-10 wt pct Sn alloy. This, however, requires the composition analysis of energy-dispersive X-ray spectrum.

The authors are indebted to Professor O.N. Srivastava, Banaras Hindu University (BHU), for the help in the electron microscopic work.

REFERENCES

1. S.K. Ghosh and S.P. Sen Gupta: J. Appl. Phys., 1983, vol. 54, pp. 6652-57.

2. A.K. Malty and S.P. Sen Gupta: Metall. Trans. A, 1990, vol. 21A, pp. 1327-30.

3. K.N. Goswami, S.P. Sen Gupta, and M.A. Quader: Acta Metall., 1966, vol. 14, pp. 1559-65.

4. S.K. Halder, M. De, and S.P. Sen Gupta: J. Appl. Phys., 1977, vol. 48, pp. 3560-65.

5. C.N.J. Wagner and J.C. HElion: J. Appl. Phys., 1965, vol. 36, pp. 2830-37.

6. R.P.I. Adler and C.N.J. Wagner: J. Appl. Phys., 1962, vol. 33, pp. 3451-58.

7. S.K. Chatterjee, S.K. Halder, and S.P. Sen Gupta: J. Appl. Phys., 1976, vol. 47, pp. 411-19.

8. B.E. Warren: X-ray Diffraction, Addison-Wesley, Reading, MA, 1969, ch. 13.

9. A.R. Stokes: Proc. Phys. Soc., London, 1948, vol. B61, pp. 382-91.

10. G. Simmons and H. Wang: Single Crystal Elastic Constants and Calculated Aggregate Properties, MIT Press, Cambridge, MA, 1971, p. 182, p. 264.

11. P.C.J. Gallagher: Metall. Trans., 1970, vol. 1, pp. 2429-61. 12. R.P. Reed and R.E. Schramm: J. Appl. Phys., 1974, vol. 45,

pp. 4705-11. 13. L.F. Vassamillet and T.B. Massalski: J. Appl. Phys., 1963, vol. 34,

pp. 3398-3402. 14. S.K. Halder and S.P. Sen Gupta: J. Appl. Phys., 1977, vol. 48,

pp. 5306-10. 15. R.D. Heidenreich: J. Appl. Phys., 1949, vol. 20, pp. 993-1010. 16. M.J. Klein and R.A. Huggins: Acta Metall., 1962, vol. 10,

pp. 55-62. 17. T.N. Baker: Proc. 7th Eur. Congr. on Electron Microscopy in-

cluding the 9th Int. Conf. on X-Ray Optics and Microanalysis, The Hague, The Netherlands, Aug. 24-29, 1980, 7th Eur. Congr. on Electron Microscopy Foundation, Leiden, The Netherlands, 1980, vol. 3, pp. 44-45.

Study of Phase Transition in TisoNI47.5 Fezs Alloy

JIANXI RAO, YUSHENG HE, and RUZHANG MA

The premartensitic phase transitions in Ti-Ni-Fe alloy are the incommensurate transition (I) and commensurate transition (R). tl] This paper describes an investigation of the R transition in TisoNi47.sFe2.5 alloy. Samples were spark-cut from a lump of the alloy, heated at 1073 K in vacuum for 1 hour, and then slowly cooled.

The temperature dependence of the relative attenua- tion (Ate) and the velocity change (AV) measured in TisoNiaT.sFe2. 5 alloy between 135 and 335 K for cooling and heating runs are shown in Figures 1 and 2, respec- tively. The ultrasonic frequency used was 13.9 MHz. The rates of change of temperature for both cooling and heating runs were 1 K/min. It can be seen clearly from Figure 1 that the curve of sound velocity in the second cooling run coincides most closely with the curve in the first cooling run and that there are two sound velocity minima within the experimental region. The first valley is deep and rapid, and the second is shallow and gentle. This shows that mode softening has occurred twice and suggests that the mechanisms of the two mode softenings are different.

Gui et al. reported two soft modes in Ti-Ni-Fe alloy and considered that they correspond to I and R transi- tions, respectively, t21 What exactly do our two softenings correspond to? We can identify them unambiguously as we made simultaneous ultrasonic and resistance mea- surements. The resistance curves are shown in Figure 3. From Figure 3, we can easily determine that 284 K is the Td described by Nishida et al.]3] (denoted as Tdl in Figure 3) and 273 K is the Td described by Hwang et al. ]4] (denoted as Td2 in Figure 3). Hwang et al. considered that Td was the inflection point on the anomaly region of the electric resistance curve, but Nishida et al. con- sidered that the curve increased abruptly at Td. It seems to us upon more careful examination of Figure 1 that the discrepancy between Tdl and Td2 is not due to some kind of uncertainty or accident but has a more profound phys- ical origin. It is generally believed that when the I phase transforms into the R phase, a corresponding soft mode should occur. The phason should change considerably but the amplitudon should not. tS] These are the charac- teristics of this soft mode. Therefore, the ultrasonic ve- locity should not obviously change. However, it can be seen that there is a slight change in slope of the velocity curves near 284 K in Figure 1 (as shown in the inset). The changes in attenuation curves are even more spec- tacular; only between 284 and 273 K is the increase in attenuation rapid, whereas below 273 K, the increase appears as a flight of steps with decreasing temperature.

JIANXI RAO, Professor, is with the Physics Division, Naval Academy of Engineering, Wuhan 430033, People's Republic of China. YUSHENG HE, Professor, is with the Physics Department, Tsinghua University, Beijing 100084, People's Republic of China. RUZHANG MA, Professor, is with the Department of Metal Physics, Beijing University of Science and Technology, Beijing 100083, People's Republic of China.

Manuscript submitted August 7, 1989.

1322--VOLUME 21A, MAY 1990 METALLURGICAL TRANSACTIONS A