Tungsten solubility in the matrix increases with a higher nickel content. In turn, the rate of grain growth during liquid phase sintering is dependent on the tungsten sol- ubility in the matrix. [~8] By increasing the Ni/Fe ratio, there is more solubility for tungsten in the matrix, giving a slightly larger grain size with a lower contiguity. Both factors contribute to a higher ductility and lower strength. I5,~9] Similar behavior is attained with changes in the sintering temperature, since there are concomitant increases in solubility, grain growth kinetics, and sin- tered grain size that lead to greater ductility and lower strength. 12~ Alternatively, molybdenum and other re- fractory metals, such as rhenium and tantalum, reduce the tungsten solubility in the matrix during sintering, tt4] This leads to a smaller grain size as well as solid solution strengthening of the alloy. The current findings indicate the Ni/Fe ratio effect on tensile properties is small in comparison with the role of Mo alloying, but there is some benefit from the 8/2 Ni/Fe ratio.

This research was performed under sponsorship of the United States Army Research Office. The encourage- ment of Dr. Andrew Crowson of the ARO is appreciated.

REFERENCES

1. W.E. Gurwell: Prog. Powder Metall., 1986, vol. 42, pp. 569-90.

2. S.G. Caldwell: Prog. Powder MetaU., 1987, vol. 43, pp. 123-38.

3. A. Bose and R.M. German: Metall. Trans. A, 1988, vol. 19A, pp. 2467-76.

4. V. Srikanth and G.S. Upadhyaya: Int. J. Refract. Hard Met., 1986, vol. 5, pp. 49-54.

5. R.M. German, L.L. Bourguignon, and B.H. Rabin: J. Met., 1985, vol. 37 (8), pp. 36-39.

6. V. Srikanth and G.S. Upadhyaya: Proc. l l t h Int. Plansee Seminar, H. Bildstein and M.H. Ortner, eds., Metallwerk Plansee, Reutte, Austria, 1985, vol. 2, pp. 203-18.

7. H. Takeuchi: Nippon Kinzoku Gakkaishi, 1967, vol. 31, pp. 1064-69.

8. A. Fernandez-Guillermet and L. Ostlund: Metall. Trans. A, 1986, vol. 17A, pp. 1809-23.

9. D.J. Jones and P. Munnery: Powder Metall., 1967, vol. 10, pp. 156-73.

10. E.C. Green, D.J. Jones, and W.R. Pitkin: Syrup. on Powder Metallurgy, Special Report 58, Iron and Steel Institute, London, 1956, pp. 253-56.

11. J. Spencer and J. Mullendore: Chemical and Metallurgical Prod- ucts, GTE Corp., Towanda, PA, unpublished research, 1987.

12. A. Bose and R.M. German: Modern Developments in Powder Metallurgy, P.U. Gummeson and D.A. Gustafson, eds., Metal Powder Industries Federation, Princeton, NJ, 1988, vol. 19, pp. 139-53.

13. A. Bose, D. Sims, and R.M. German: Prog. Powder Metall., 1987, vol. 43, pp. 79-92.

14. A. Bose and R.M. German: Metall. Trans. A, 1988, vol. 19A, pp. 3100-03.

15. A. Bose, G. Jerman, and R.M. German: Powder Metall. Int., 1989, vol. 20 (3), pp. 9-13.

16. J.W. Burlingame: U.S. Army Armament RD&E Center, Picatinny Arsenal, N J, private communication, Oct. 1987.

17. R.M. German and K.S. Churn: Metall. Trans. A, 1984, vol. 15A, pp. 747-54.

18. R.M. German: Liquid Phase Sintering, Plenum Press, New York, NY, 1985, pp. 133-43.

19. V. Srikanth and G.S. Upadhyaya: Metallography, 1986, vol. 19, pp. 437-45.

20. L.L. Bourguignon and R.M. German: Int. J. Powder Metall., 1988, vol. 24, pp. 115-21.

An X-Ray Diffraction Line Profile Analysis in Cold-Worked Fcc Ag-lSn-Zn Alloys: Role of 1 Wt Pet Sn

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

Recently, we have undertaken a study on the states of cold-worked deformed materials with fcc Cu-Ni-Zn, 121 Cu-Sn-Zn, t21 and Cu-Mn-Zn TM ternary alloy systems, employing detailed analyses of the X-ray powder dif- fraction line profiles. In all these systems, the solvent metal is copper, and the additions of transitional solutes Ni, Mn in the solid solution range and also nontransi- tional solute Sn in the dilute range (to the a-brass sys- tem) have been made to obtain a clear picture of the role of the addition of a third component. In the present com- munication, the studies have been extended to the silver- base alloy system (Ag-1Sn-Zn) to see the role of dilute Sn in binary Ag-Zn. l+~

Five compositions (in weight percent), namely, Ag- 1Sn-5, 10, 15, 20, and 25Zn, were prepared in the usual way t5,61 from accurately weighed quantities of spectro- scopicaUy pure component metals obtained from Johnson, Matthey and Co., Ltd., London. Melting was done at about 1000 ~ and the final compositions were deter- mined considering weight loss and atomic absorption analyses. The cold-working and annealing treatments (annealing temperature lying in the range of 400 ~ to 450 ~ for 8 hours) were done following the usual method. [5] Both cold-worked and annealed samples, sieved through a 250-mesh screen, were prepared for diffrac- tometer flat specimens, and powder profiles from (111), (200), (220), (311), (222), (400), (331), (420), and (422) reflecting planes were recorded at room temperature (-28 ~ --- 1 ~ with a standard PHILIPS* Geiger counter

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

X-ray diffractometer (PW 1050, 1051) and using LiF- monochromated copper radiation. The profile analyses (peak-shift, peak-asymmetry, and peak-broadening) were done using the methods adopted earlier, t~l

The stacking fault probability (a) has been measured from (a) peak shifts (PS) of (111), (200), (220), and (311) reflections for both cold-worked and annealed specimens (Eq. [2], Reference 1) and also from (b) scatter of ah+t lattice parameter (LP) values for cold-worked samples only (Eq. [3], Reference 7). The calculated (aps) and (aLp) values (Table I) from two different considerations agree fairly well. Figure 1 shows the changes in (aps) values with solute Zn (weight percent) in binary as well as in ternary silver- and copper-base systems. It is quite ap- parent that the addition of 1 wt pct Sn to fcc Ag-Zn al- loys helps to increase the fault probability only to a small extent, maintaining nearly constant slopes until 20 wt pct

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 August 24, 1989.

METALLURGICAL TRANSACTIONS A VOLUME 2IA, MAY 1990--1327

Table I. Values of Stacking Fault Probability (a), Lattice Parameter a (/~), and (fl + 4.5a") from Peak-Shift and Peak-Asymmetry Analyses in Cold-Worked Ag-I Wt Pct Sn-Zn Alloys

Composition cw cw cw ac~c ac~lc ae(x~ka~ol Wt Pct Zn (O/ps) x 103 (o~Lp) X l03 (O/LS) • 103 a0 (/~) (/~) (LS) (]k) (eL) = 0 (fl + 4.5a") • 103

5 11.3 11.5 11.2 4.0828 4.0789 4.0798 4.0809 2.6 10 20.5 17.1 20.3 4.0703 4.0659 4.0674 4.0670 1.2 15 27.8 28.7 27.7 4.0499 4.0496 4.0486 4.0505 2.6 20 39.5 43.9 40.0 4.0356 4.0403 4.0387 4.0375 2.5 25 57.1 65.3 56.7 4.0244 4.0328 4.0287 4.0295 0.7

Ag-Sn-Zn O-Present Work / Ag-Zn A - De (1969) / Cu-Sn-Zn a-Ghosh& SenGupta(1983) /

4O

"o x

2C

60

I I I I 0 5 10 15 20 2 5

Wt*/, Zn

Fig. 1 - - P l o t s of average stacking fault probability (aps) as a function of solute concentration (wt pct) in Ag-lSn-Zn, Cu-lSn-Zn, and Ag- Zn alloys.

Zn. However, there is a tendency for the fault proba- bility to increase near the solubility limit, as evidenced from the two sets of o~ values (Table I), and the nature of variation is entirely different when compared with the Cu-1 wt pct Sn-Zn system in the solid solution range.

Considering Eq. [1'] of Reference 1, the values of (OtLs) and Aa/ao causing the peak shifts simultaneously have also been evaluated from the least-squares (LS) analysis. That the a values in Table I agree well with the other two sets of a values as determined above indicates the sole influence of deformation stacking faults and the negligible influences of lattice parameter change and re- sidual stresses (for deformed samples) on the observed peak shifts. The lattice parameter values for the cold-

81- \ ,3

V

-10

2t Ii I 1 I

1.0 I. I I. 2 1.3 1.4

e/A

Fig. 2 - - P l o t s of dislocation density ~o) and stacking fault energy pa- rameter (y/iz) as a function of valence electron to atom (e/A) ratio in Ag- 1Sn-Zn alloys.

worked (CW) materials, as determined from least-squares calculations and considering (eL) = 0 (Eq. [7.126], Ref- erence 8) and extrapolation function, tsj are also in close agreement.

The peak-asymmetry measurements for the (111) and (200) profiles from the shifts of centers of gravity with

Table II. Values of De (~), DSF ( / ~ ) , Train (~), Rms Strain (e2=s0x) 1/2, [1.5(a' + a") + fl], and V0 (for pure Ag) from Peak-Broadening Analysis in Cold-Worked Ag-1 Wt Pct Sn-Zn Alloys

a ' • 103 (~Ls~ (~" = 0,/~ = 0)

C o m p o s i t i o n De (~') DSF (~) T-,i, • 103 [1.5(a' + a") + r] from Peak Wt Pct Zn [111] [100] [111] [100] ()~) [111] [100] • 10 3 Broadening

3'0 (Extrapolated) for Pure Ag

(mJ/m 2)

5 172 109 390 169 193 3.8 4.0 24.2 16.1 10 140 87 301 130 164 3.8 3.9 31.2 20.8

15 128 77 253 I10 162 3.6 3.9 37.0 24.7

20 113 58 156 68 256 3.2 4.2 59.8 39.9 25 85 46 131 57 151 4.0 4.4 70.9 47.3

(30) Voigt (23) Reuss

1328--VOLUME 21A, MAY 1990 METALLURGICAL TRANSACTIONS A

respect to peak position maximum (Eq. [3], Reference 1) failed to indicate, as before, TM any detectable presence of either double deformation or extrinsic (a") or defor- mation twin (/3) stacking faults (Table I).

Using Warren and Averbach's method t91 of Fourier analysis of line shapes, the plots of the Stokes u~ cor- rected normalized Fourier coefficients AL(L ,~) for (111), (222) and (200), (400) reflections have been made to separate the components of effective domain sizes, De (/~), and the rms microstrains, (e2) I/z, along [111] and [100] (Table II). The (De)[hkl I values are comparable to (DsF)[hgt], the domain size due to stacking faults (SFs), and decrease with increasing solute Zn. This, therefore, indicates that the stacking faults do influence signifi- cantly the observed domain size broadening of the line profiles. However, the average experimental ratio of (De)llll]/(Oe)[lOO l ( -1 .7) reveals that D, the average co-

herent domain size, and T, the domain size in the fault- ing plane (Train is slightly greater than (Oe)[hkt], Table II), do also take part in the domain size broadening. The magnitudes of Trmn decrease with the increase of solute Zn, signifying increased influence of deformation faults in the (111) faulting plane, tH~ However, the changes in the values of (Oe)tllll,t10o] are very small (within error limits), Ill and this is reasonable in view of the role of stacking faults in the concerned temary alloys (Figure 1). The (e2_50~) ~/2 values (Table II) tend to increase grad- ually with solute Zn, and they are relatively pronounced, possibly due to the introduction of lattice strains with the addition of a third solute (Sn) in the binary Ag-Zn system.

The line-shape analysis also yields the values of com- pound fault probability, [1.5(a' + t~") + /3] (Eqs. [5] and [6], Reference 1), as shown in Table II. Considering both/3 = 0 and a" = 0 (as evident from peak-asymmetry

(a) (b)

(c) (d)

Fig. 3 - - T r a n s m i s s i o n electron micrographs showing the faulted structures in specimens marked with arrows and their corresponding electron diffraction patterns. (a) 5 wt pct Zn: Magnification 54,280 times and (b) zone axis = [111]; (c) 25 wt pct Zn: Magnification 70,840 times and (d).

METALLURGICAL TRANSACTIONS A VOLUME 21A, MAY 1990-- 1329

analysis), the values of single deformation or intrinsic fault probability a ' are determined (Table II), which are in good agreement with those of (aps) (Table I).

The above analyses also lead to the estimations of p (dislocation density) and 3' (stacking fault energy), m Both the parameters (p) and (3'//x) as functions of valence electron to atom ratio (e/A) vary nonlinearly (Figure 2) and depict normal variation with increasing solute effect. Using the values of shear moduli (/Z)Ag for Voigt (V) and Reuss (R) schemes, t12J 3'0, the stacking fault energy for pure silver, comes out to be 30 and 23 mJ/m 2, respec- tively (Table II), when the curve of 3'//.~ is extrapolated to e/A = 1.0. The values for pure silver are in good agreement with the values reported previously from (a) X-ray diffraction (21 and 16 mJ/m 2) due to Halder and Sen Gupta t13J and (14 - 3.5 rnJ/m 2) due to Vassamillet and Massalski t~41 and (b) electron microscopic measure- ments (16 to 31 mJ/m 2) due to Reed and Schramm. tlSJ The values of (p) and 3'//x, however, are considerably higher when compared with Cu-1Sn-Zn alloys.t2J

Fine powder samples from two alloy compositions, namely, 5 and 25 wt pct Zn, were also observed under an electron microscope (PHILIPS CM 12). The diffrac- tion patterns conforming single and polycrystalline na- tures and corresponding micrographs are shown in Figures 3(a) through (d). The weak fringe patterns (stacking fault nature) do appear in the micrographs, in- dicating the faulted structures.

The authors are thankful to Dr. M. De for his kind interest in the work. They are also extremely grateful to

Professor O.N. Srivastava, Banaras Hindu University, for the electron microscopy work.

REFERENCES

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

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

3. S.K. Ghosh and S.P. Sen Gupta: J. Appl. Phys., 1984, vol. 56, pp. 1213-17.

4. M. De: Indian J. Pure Appl. Phys., 1969, vol. 7, pp. 16-21. 5. S.P. Sen Gupta and M.A. Quader: Acta Crystallogr., 1966, vol. 20,

pp. 798-803. 6. A.K. Malty, S.K. Pradhan, M. De, and S.P. Sen Gupta: Metall.

Trans. A, 1989, vol. 20A, pp. 1142-44. 7. C.N.J. Wagner and J.C. H61ion: J. Appl. Phys., 1965, vol. 36,

pp. 2830-37. 8. C.N.J. Wagner: Local Atomic Arrangements Studied by X-ray

Diffraction, AIME, New York, NY, 1966, vol. 36, ch. 7. 9. B.E. Warren: X-ray Diffraction, Addison-Wesley, Reading, MA,

1969, ch. 13. 10. A.R. Stokes: Proc. Phys. Soc., London, 1948, vol. B61,

pp. 382-91. l l . R.P.I. Adler and C.N.J. Wagner: J. Appl. Phys., 1962, vol. 33,

pp. 3451-58. 12. G. Simmons and H. Wang: Single Crystal Elastic Constants and

Calculated Aggregate Properties, MIT Press, Cambridge, MA, 1971, p. 264.

13. S.K. Halder and S.P. Sen Gupta: J. Appl. Phys., 1977, vol. 48 pp. 5306-10.

14. L.F. Vassamillet and T.B. Massalski: J. Appl. Phys., 1963, vol. 34, pp. 3398-3402.

15. R.P. Reed and R.E. Schramm: J. Appl. Phys., 1974, vol. 45, pp. 4705-11.

1330--VOLUME 21A, MAY 1990 METALLURGICAL TRANSACTIONS A