temperatures agree reasonably with experimentally de- termined volume fractions for the alloy. The Nb content increases in the/30 phase and decreases in a2 at 1020 ~

We gratefully acknowledge the kind permission of the Director of the DMRL to publish these results.

REFERENCES

1. M.J. Blackburn and M.P. Smith: Air Force Technical Report, AFWA L-TR-80-4175, 1980.

2. A.K. Gogia, T.K. Nandy, D. Banerjee, and Y.R. Mahajan: Proc. of the 6th World Conf. on Titanium, Cannes, France, June 6-9, 1988, in press.

3. A.K. Gogia, T.K. Nandy, and D. Banerjee: Defence Metallur- gical Research Laboratory, Hyderabad, India, unpublished re- search, 1988.

4. D.B. Williams: Practical Analytical Electron Microscopy in Materials Science, Philips Electronics Instruments, Mahwah, NJ, 1984, pp. 55-90.

5. G. Cliff and G.W. Lorimer: J. Microscopy, 1975, vol. 103, p. 203. 6. V.D. Scott and G. Love: Mater. Sci. & Tech., 1987, vol. 3,

pp. 600-08. 7. P.M. Kelly, A. Jostsons, R.G. Blake, and J.G. Napier: Phys.

Stat. Sol. A, 1975, vol. A31, p. 771. 8. R.G. Blake, A. Jostsons, P.M. Kelly, and J.G. Napier: Phil.

Mag. A, 1978, vol. 37A, p. 1. 9. S.M. Allen: Phil. Mag. A, 1981, vol. 43A, pp. 325-35.

10. F.R. Castro-Fernandez, C.M. Sellars, and J.A. Whiteman: Phil. Mag. A, 1985, vol. 52A, pp. 289-303.

An X-Ray Diffraction Line Profile Analysis in Cold-Worked Hexagonal (()-Phase and Mixed + r)-Phase of Copper-Germanium Alloys

A.K. MALTY, S.K. PRADHAN, M. DE, and S.P. SEN GUPTA

The additions of solute germanium to the solvent metal copper in the fcc (a)- as well as in the hexagonal (if)- phases were investigated earlier.II.21 It has been observed that, in both the alloy phases, the deformation stacking faults of intrinsic type occur in a characteristic manner (i.e., for the fcc phase, the fault probability increases sharply and nonlinearly with increasing solute concen- tration until the a-phase boundary is reached; and, for the hcp phase, which occurs just after the very narrow re- gion of mixed phase of fcc and hcp, the fault probability decreases in an identical manner with increasing solute). In both the phase regions, the twin or growth fault prob-

A.K. MALTY and S.K. PRADHAN, Senior Research Fellows, M. DE, Senior Lecturer, and S.P. SEN GUPTA, Professor and De- partmental Head, are with the Department of Materials Science, Indian Association for the Cultivation of Science (IACS), Jadavpur, Calcutta 700 032, India.

Manuscript submitted April 8, 1988.

ability has been found or considered to be negligible. The present study considers the hexagonal phase along with the intermediate mixed phase, separating the fcc phase with the following objectives in mind: (1) the pic- ture of the deformed state in the mixed phase is not known, and, as such, it will be interesting to see for the first time whether this region truly behaves as an intermediate one or not, being evenly influenced by the adjacent fcc and hcp phases; and (2) the hexagonal ~-phase is re- analyzed in a more general way to establish the absence of twin stacking faults. The analysis has been done fol- lowing Warren and Averbach's method, TM as applied to our earlier studies with a number of hexagonal materials; namely, Cu-Ge, [21 Ag-Sb, [41 Zr, Ti, Mg, Zn, [5,61 thin films of Zn I7] and Te, t81 and Zn-Ag. t9]

Altogether, six compositions of copper-germanium alloys, namely, 11.01 and 12.05 at. pct of germanium in the (a + ()-phase and 12.55, 14.63, 16.60, and 18.03 at. pct of germanium in the ~'-phase, were prepared I2,91 from spectroscopically pure component metals. Prepa- rations of flat powder diffractorneter specimens and re- cordings of the line profiles were done in the usual manner, f2,91 Altogether, ten reflections were recorded from both cold-worked and annealed samples for profile analyses, namely the fault-unaffected 10.0, 00.2, 11.0, 20.0, 1 1.2, and 00.4 reflections and fault-affected 10.1, 10.2, 10.3, and 20.1 reflections for all the hcp alloy compositions. The tails of certain profiles overlapped with adjacent ones, and these were separated, assuming sym- metrical broadening for both halves of the peak. Each profile originating from the deformed sample was cor- rected for instrumental broadening using the standard method of Stokes, Iml which requires the corresponding profile from the respective annealed sample. For the mixed-phase alloys, the unfaulted profiles 10.0 and 20.0 and the faulted profiles 10.1, 10.2, and 10.3, which were isolated from the fcc constituents, were considered for independent analysis. For the fcc component, only peak shift analysis was done with the reflections 11 1, 200, 220, and 31 1, assuming that the overlapped hcp com- ponent is unaffected by the stacking faults for any peak displacement.

The evaluations of the domain size, r.m.s, strain, and stacking fault density were carried out by the method outlined by Warren. 13,91 In addition, the dislocation den- sityE~l] and the stacking fault energy r~2-151 have been eval- uated following the procedure as adopted earlier for hexagonal alloy systems. 191

The results obtained from the Fourier analysis t31 for the (- and (a + ()-phases are shown in Figures 1, 3, and 4 and compared with those obtained earlier 12r for the ~'-phase.

Figure 1 shows the solute dependence of the stacking fault probability for the fcc tll and hcp r2j phases as ob- tained earlier, along with the present investigations with mixed and hexagonal phases. It is seen clearly that the deformation stacking fault probability (a) for the fcc phase increases roughly parabolically with increasing solute Ge; and for the hcp phase, the fault probability decreases with increasing solute as the composition moves away from the initial fcc and intermediate heterogeneous two-phase (a + ~') region, where the stacking fault probability tends to reach the maximum from both ends of the single-phase

1142--VOLUME 20A, JUNE 1989 METALLURGICAL TRANSACTIONS A

t00 / r re Present value(p~=O) i ,cq~ . . . . cp=o) / L a Sen Gupta & Goswam I~ / 1967 ( '=0) \

80{- l / IFCC �9 Ghosh, De ~ SenGupta

1983 \

/ rv com,o.e., ' , \ NIXED b.\x I

. 60~ . . . . . }o HCP corn onent 03*0) , - \ ~ / O ~r I~11~ I P I k \ I

/! ! \\\ 40 / ' , ', \ \

I I I

I 20 / I I ~--~\

4 4o \ \ F,,CC , , ~ ' , ~ T . ~ , H C P ~.

- I 1.00 1.15 1.30 1.45 1.60

e/a

Fig. 1 - Plots of stacking fault probability c~ vs electron atom ratio (e /a) for fcc, mixed, and hcp phases.

component. This clearly indicates the normal feature of the solute effect and can be explained qualitatively from the phase stability and free energy consideration, as dis- cussed earlier, u61 It may be seen that there exists a con- tinuity in the faulting parameter as one proceeds from the fcc to the hcp region through the narrow two-phase region. For the hcp phase, the results for the two cases (/3 #= 0 and/3 = 0) show no significant variation in o~, and the growth fault probability (/3), which was earlier assumed t21 to be zero, is either negative or small positive (ranging between -+5.0 x 10-3), confirming the earlier assumption of complete absence of twin or growth fault in both fcc m and hcp t2~ phases. The value of a for the first composition (12.46 at. pct) in the if-phase calculated earlier [21 probably is high (91.3 x 10-3). However, overall observations with regard to the presence of deformation stacking faults are quite consistent in both the analyses.

For the two constituents in the mixed-phase region, which is a mixture of both fcc and hcp components with

an interdependence, the deformation stacking fault prob- abilities have been calculated considering each compo- nent separately. The value of the stacking fault probability

for the first composition for fcc components in the mixed-phase region is 54.9 x 10 -3 (Figure 1), which is in good agreement with the extrapolated plot of c~ v s sol- ute concentration. However, the value of ~ for the sec- ond composition was not calculated, as it is too close to the hexagonal if-phase region, and the isolated fcc peaks are not at all prominent to make any reasonable calcu- lation. Similarly, the values for deformation stacking fault probability (c0 for the hcp component of the first com- position in the mixed phase are close to the present value evaluated for the pure hexagonal alloy phase (Cu-12.55 at. pct Ge), thus showing an identical behavior in the mixed-phase region. For the second composition, slightly less values have been obtained which, to some extent, are due to uncertainty in the measurements of the cold- worked profiles, many of which are too diffuse and overlapping to be analyzed accurately, as evidenced from the diffractogram (Figure 2).

The r .m.s , strain, (E2) 1/2, increases sharply with in- creasing solute Ge in the fcc region, m and near the two- phase region, strain-value increases (ranging from 8.4 to 7.5 X 10 .3 for L = 30 ,~) and is close to the hcp phase, wherein this decreases (from 5.4 to 4.5 x 10 3 for L = 30 ,~), similar to earlier observation, ~21 as the composi- tion moves away from the two-phase region. This pic- ture also is consistent with the presence of imperfections and their interactions with the solutes.

Figure 3 gives the plots that compare the variations of Def f v s at. pct of solute Ge for the three separate regions. As the solute Ge increases, the domain size decreases sharply in the fcc region in a linear way, attaining a minimum value in the two-phase region, and then in- creases gradually in the hcp region in a nonlinear manner with increasing solute Ge. Here, the solute Ge has an effect also, and the variation is consistent with the de- formation effect in creating imperfections. In the hcp re- gion (Figure 3), the average domain sizes, Day, obtained from the unfaulted reflections are found always to be larger than those from the faulted reflections. The values of the domain sizes also are close in the present and ear- lier casesJ 21

Finally, Figures 4(a) and (b) show, respectively, the variation of the dislocation density, p, and the stacking fault energy parameter, y//x, with at. pct of solute Ge. While the p v s concentration plot follows, in general, the same pattern as that of the stacking fault probability

(11,2) &(311) (11.0) &(220) (222)8(00,4") . ~ r ? o ~ / (t0,3) ~ (10.2)

(100

(200)

" ~ #5 ~ 'o ~ @ ~~ r ~ 7 "~ #~ 2# 6'o ~ ~~ Loo ,'5 ~

Fig. 2 - - X - r a y diffractogram for mixed phase Cu-12.55 Ge alloy (CuK~j 40 KV, 20 mA).

315 o -o ~

METALLURGICAL TRANSACTIONS A VOLUME 20A, JUNE 1989--1143

300 150 FCC �9 �9 Ghosh, De a Sen Gupta

\ HCPvo-c- {4- Present work

10,3

2OO

~, Deft

MIXEO - - F C C ,~-~, N C P - -

o~ ~ ~o ~s 2o at % of Ge

Fig. 3 - -P lo t s of average (DaJ and effective (Derf) domain sizes vs at. pct of solute Ge for fcc, mixed, and hcp phases.

o <

1oo O

2 ,-E

v

5O

FCC o -o- Ghosh, De ~ Sen Gupta 1983 HCP tx v Present work

Smallrnan & Westmacott 1957

(Pure Copper ) !j/ 4

I

I

(a)

I 20 "i

T_ o 15 ~ I

~- lO

FCC ___ L ~ ~ ~ . ~

o ~ ~ 9 12 15 1~ o a t '/i of Ge

Fig. 4 - - ( a ) and (b) Plots of dislocation density p and stacking fault energy parameter 3'/# vs at. pct of solute Ge for fcc, mixed, and hcp phases.

vs s o l u t e Ge plot for the three regions (Figure 4(a)), the plot of the parameter y/ /~ with solute concentration Ge shows a roughly parabolic variation in both the fcc and hcp regions, with a minimum in the proximity o f the mixed (a + ~')-phase region. This variation is consistent with the creation of stacking faults, as is apparent in the plot o f Figure I. There also exists a continuity in the variation of y / / z from fcc to hcp through the hcp com- ponent of the narrow mixed-phase region, indicating a smooth transition from the a ~ ~'-phase so far as this parameter is concerned. This type of continuous varia- tion in the three distinct phases of an alloy system is

rather interesting to note from the point of view of free energy relationships.

Therefore, from these observations, it may be con- cluded that the solute content, as well as the phase sta- bility, has a pronounced influence on the defect structures, such that the solute dependence of the different micro- structural parameters becomes prominent. Thus, the di- minishing effects of all the parameters in the hcp region are possible, as there lies a mixed hcp + bcc (ff + e)- phase just after the hcp (#)-phase.

REFERENCES

1. S.K. Ghosh, M. De, and S.P. Sen Gupta: J. Appl. Phys., 1983, vol. 54, pp. 2073-78.

2. S.P. Sen Gupta and K.N. Goswami: Brit. J. Appl. Phys., 1967, vol. 18, pp. 193-98.

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

4. M. De and S. Sen: Brit. J. Appl. Phys., 1968, Ser. 2, vol. 1, pp. 1141-44.

5. S.K. Chatterjee and S.P. Sen Gupta: J. Mater. Sci., 1974, vol. 9, pp. 953-60.

6. S.K. Chatterjee and S.P. Sen Gupta: J. Mater. Sci., 1975, vol. 10, pp. 1093-104.

7. S. Sen, R.K. Nandi, and S.P. Sen Gupta: Thin Solid Films, 1978, vol. 48, pp. 1-16.

8. E. Chatterjee and S.P. Sen Gupta: Thin Solid Films, 1984, vol. 122, pp. 73-91.

9. S.K. Ghosh and S.P. Sen Gupta: Metall. Trans. A, 1985, vol. 16A, pp. 1427-35.

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

1 I. G.K. Williamson and R.E. Smallman: Phil. Mag., 1956, vol. 1, pp. 34-46.

12. R.E. Smallman and K.H. Westmacott: Phil. Mag., 1957, vol. 2, pp. 669-83.

13. L.F. Vassamillet: J. Appl. Phys., 1961, vol. 32, pp. 778-82. 14. D. Hull: Introduction to Dislocation, Pergamon Press, London,

1975, chs. 5 & 6. 15. A.H. Cotla-ell: Dislocation and Plastic Flow in C~stals, Clarendon

Press, Oxford, 1933, ch. 7. 16. J.H. Foley, R.W. Cahn, and G.V. Raynor: Acta Metall., 1963,

vol. 11, pp. 355-60.

Effect of Oxygen on Tungsten Filament Sag Kinetics

JOHN W. PUGH

The objective of this work was to determine how small quantities of oxygen, such as might be found in the at- mosphere of an incandescent lamp, affect the creep of tungsten filaments. While some attention has been given to the effect of oxygen on porosity, ll 51 little is known about the effect on creep. In at least one instance, con- tributions to creep from the geometric effect of porosity formation were recognized. 161 Since oxygen was known to cause more porosity formation in some tungsten wire

JOHN W. PUGH, Senior Consulting Metallurgist, is with the Advanced Technology Department, General Electric Company, Nela Park, Cleveland, OH 44112.

Manuscript submitted October 27, 1988.

1144--VOLUME 20A, JUNE 1989 METALLURGICAL TRANSACTIONS A