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Phase separation and crystallization in amorphous Pd-Si-Sb
Journal of Non-Crystalline Solids 30 (1979) 317-335 © North-Holland Publishing Company
PHASE SEPARATION AND CRYSTALLIZATION IN AMORPHOUS P d - S i - S b Matthew A. MARCUS Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA Received 28 May 1978
It is found that replacing some of the Si in a Pd-Si-Sb glass with Sb can make it more resistant to crystallization than the pure binary material. This is shown by the calorimetric results, in which the crystallization temperature increases and the glass temperature decreases with increasing Sb substitution, and also by the finding that certain alloys, such as Pd80 .5 Sil 6.5 Sb3 may be quenched into amorphous rods (by the gradient-quench method) up to 0.5 mm thick. • Calorimetry and small-angle X-ray scattering data show that certain alloys in this system phase separate in the amorphous state• The two phases thus produced independently crystallize. Isothermal measurements indicate that the rate of crystallization of one of the phases is interface-limited, with most nuclei initially present. The other crystallization process does not fit an Avrami law, possibly due to a transformation of the crystalline phase. A method called "gradient-quenching" (GQ) was used to prepare samples from the melt in such a way that the quench-rate was non-uniform, so all stages of crystallization in slowlyquenched alloys are displayed. Nucleation was frequently found to take place on voids and inclusions. The use of the calorimetric and GQ methods in conjunction to gather information about crystallization processes in metallic glasses is discussed.
1. Introduction The subject of transformation behavior in metallic glasses is of technical and fundamental interest. There has been much work done in this field on ternary glasses of the form (Pd, M ) - X , where M is a transition metal and X i s a metalloid [ 1 - 3 ] . That is, the metallic part of a metal-metalloid glass consists of a combination of metals, while the metalloid part is a single element. However, there has been little work on systems of the form P d - ( X , Y), i.e., systems with the single metalloid replaced by a combination of metalloids. Many glasses of technical interest are of the latter form or are quarternary glasses (too complex to understand without understanding ternary glasses) with more than one metalloid• The object of this investigation is to characterize the formation and crystallization behavior of P d - S i - S b glasses b y calorimetric and metallographic methods. The transformation properties of P d - S i - S b glasses as a function of composition were systematically investigated. A differential scanning calorimeter was used to 317
318
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
measure the glass transition and crystallization temperatures of a number of glasses and isothermal crystallization rates as a function of time and temperature. Crystal growth morphologies have been examined by a method known as "gradient-quenching". In it, a sample of molten alloy is quenched in such a way that parts of it have been rapidly quenched and are totally amorphous, parts have been quenched slowly so are totally crystalline, and parts show crystals growing in an amorphous matrix. The general effect is like a movie; the rapidly-quenched portions of the sample show the beginning stages of crystallization while the less-rapidly quenched portions display more-advanced stages.
2. Experimental The crystalline alloys from which the samples used in this experiment were made were prepared by melting 4-9's Pd (from Engelhard Industries), 5-9's Sb and 9-9's Si (both from Alfa Inorganics) in fused-quartz test-tubes under an Ar atmosphere. To assure homogeneity, the alloys were remelted and stirred several times in the test-tubes and they then proved to be metallographically uniform. Amorphous samples in ribbon form were produced by quenching a stream of molten alloy (melted under Ar and squirted through a fused-quartz nozzle) onto the edge of a spinning AI disk [4]. The ribbons were about 0.5 mm wide by 20/a thick. A DSC-2 calorimeter was used to make the calorimetric measurements. The machine was run in the scanning mode to obtain glass and crystallization temperatures for alloys with a wide range of compositions, thus providing the systematic data referred to in the introduction. Isothermal measurements were done on a few alloys and yielded detailed results concerning crystallization kinetics. Scanning data were taken at a heating rate of 40 ° min -I. The samples used for both scanning and isothermal tests weighed 10-25 mg, and were encapsulated in aluminum pans. The melting transitions of lead and zinc were used for temperature and heat calibration as described in the DSC-2 instruction manual [5]. A typical scanning thermogram is shown in fig. 1, along with the def'mitions of glass transition temperature, heat of crystallization, and crystallization temperature used in this paper. My definitions of the first two quantities are the same as those used by Chou [6]. However, his definition of crystallization temperature differs from that used here. He defines it as the temperature at which the first observable crystallization appears. Thus, only one Tc is defined even if there are two crystallization peaks. I define Tc for each peak as the temperature at which the crystallization rate reaches a maximum. If the peaks overlap, an attempt is made to subtract the tail of the first peak from the second before finding Tc2, and likewise for Tcl. The above nomenclature assumes that both peaks are due to crystallization. The evidence for this assumption will be discussed below. To minimize drift in isothermal measurements the calorimeter had to be as nearly as possible in thermal equilibrium as soon as it reached the holding tempera-
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
--->1 ............
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Fig. l. Typical calorimetric thermogram showing definitions of Tcl , Tc2, Tg, AHc, and the shapes of the crystallizationpeaks. ture, designated TI. Let/'2 be the highest temperature at which the sample may be held for two hours without detectable crystallization occurring, yet as close as possible to T 1. With the cooling water on, the calorimeter was held at T2 until the drift in the observed signal was constant. It was then run up to T] as quickly as possible. This procedure reduced the machine's settling time from one or two hours to about three minutes. The temperature calibration of all calorimeters (the DSC-2 included) varies with the heating rate. Thus, to calibrate the calorimeter in the isothermal mode, it was necessary to extrapolate the calibration results for several heating rates to the isothermal limit. The temperature error (actual temperature-temperature displayed by the calorimeter) was found to be linear in the temperature for all scan rates, and linear in the scan rate for all temperatures. A simple computer program performed least-squares fitting and extrapolated the calibration to zero heating rate. Isothermal calorimetry data were analyzed in the context of the Avrami formalism. A digitizing tablet was employed to pick data off thermograms. These data were processed by a computer program which produced plots of:
dXt/dt versus t
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X t versus t
(2)
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(3)
logloXe versus log]ot
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d(logl oXe) versus lOglot d(logl ot)
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M.A. Marcus / Phase separation and crystallization in amorphous, Pd-Si-Sb
320
where X t is the transformed volume fraction, t the time since reaching T~, and X e the extended volume fraction. The assumption was made that the heat evolved when a unit volume of the sample crystallizes is constant throughout the crystallization process. Thus, the observed signal is proportional to dXt/dt. The proportionality factor is computed by requiring that oo
.;
1,
(6)
o
in other words, that the transformed fraction be unity at long times. In computing this integral, the data are extrapolated to zero and to infinity. The first four points are used to derive a power-law fit to the short-time behavior of the observed signal, while the last three are used to fit the long-time behavior to an exponential. Some samples were annealed in order to produce phase separation without crystallization. The annealing was done in a molten-solder bath heated in a box furnace. The samples were wrapped in aluminium foil to prevent them from deforming and reacting with the solder. Annealing was performed at 13° below the glass transition (635 K) for 2.5 min, conditions chosen by analogy with the work of Chou [6]. SmaU-angle X-ray scattering measurements were done on the annealed samples using a Kratky camera (with 80 g slit), Mo-Ka radiation, and photographic detection. GRADIENT QUENCHING .,,..~ Ca pil la r y
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Fig. 2. Operating principles of the GQ apparatus.
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
321
The gradient-quenching apparatus and the kind of sample it was used to make are shown in fig. 2. The fumace is an alumina tube wound with Kanthal wire, insulated with Ceramic Paper (from Edmund Scientific) and held in a vertical position. Just below it sits a beaker of water. The capillary is a fused-quartz tube, about ~ m long, with a 2 mm id, whose end is drawn into a tapered capillary about 4 cm, long by 0.1 m m i d (at the small end). In operation, the capillary is placed inside the furnace. A lump of alloy about 300 mg in mass is placed in the capillary where it sits on the shoulder of the tapered part. The capillary is pumped out with a rotary pump and the furnace is heated. When the alloy melts, the capillary is backfilled with Ar at atmospheric pressure, which forces the alloy into the thin end. The drop of molten alloy acts like a gasket in preventing Ar from getting into the thin end. The tube is now pushed downward so that the alloy is immersed in water. The sample thus produced is a tapered cone of alloy, which is often amorphous at the thin end, and crystalline at the thick end. The thickness gradient produces a corresponding gradient in quench-rates. Metallography was done on gradient-quenched samples using standard procedures. They were etched in a solution of 4 vol.% bromine in methanol. The etching process pitted the amorphous material and acted as a contrast etch toward crystalline phases. X-ray and hardness tests confirmed that the pitted phase was amorphous.
3. Calorimetric results Depending on its composition, a given sample exhibited one of four behaviors: Type I - fully amorphous; thermogram shows glass transition, one exothermic peak. Type II - fully amorphous; thermogram shows glass transition transition, two exothermic peaks. Type IIa - l i k e Type II, but no visible glass transition (on the Type II-Type Ill border). Tupe III - partially crystalline; two or more broad exothermic peaks, not reproducible. Fig. 3 shows the composition ranges over which these behaviors occur. The closed circles represent alloys displaying Type I behavior, the open circles indicate Type II, the open triangles Type III, and the dashes Type IIa. The variation of Tg, Tcl, and Tc2 with composition is plotted in fig. 4. As silicon is replaced by antimony, the glass transition temperature decreases, as shown in fig. 4. The temperature of the first crystallization is near that of the second, for the lowest Sb contents for which both are seen. As the Sb concentration increases, the first crystallization temperature decreases. For Pd concentrations less than 82%, the second crystallization temperature is a monotonically increasing function of the Sb content. For greater Pd concentrations, Tc2 decreases with Sb
Pd~Si 2 2 . ~
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1.50 10.00 12.50 15.00 IT.50 20.00 22.50 25.00 XSb --~
Fig. 3. Composition range over which Type I (closed circles), Type II (open circles), Type IIa (dashes), and Type III (triangles) behaviors are found. The marked segment of the P d - S i line is the amorphous-forming range for binary Pd-Si glasses. The marked segment of the P d - S b line is the (Pd) phase field at 740°C as determined by X-ray diffraction and metallography.
[Pd]= 79%
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Fig. 4. Crystallization and glass temperatures as functions of x for alloys of the form PdySiloo_x_ySbx,fory = 79, 80.5, 82, 83;5. and 85.
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
323
content when the alloy has much less Sb than Si, then goes through a minimum, and increases for higher amounts of Sb. At the highest Sb concentrations, Type Iti behavior occurs, and the scatter of the data makes it meaningless to plot Tc's. At the Type I - T y p e II boundary, the curves of Tc versus x(Sb) (on the Type I side) join continuously with those of Tc2 versus x(Sb) (on the Type II side). Both the value of T c and its derivative with respect to x(Sb) are continuous across the I - I I boundary. It is therefore plausible to identify the Type I Tc with the Type II Tc2, as is done in fig. 4. The I - I I boundary is marked by the appearance of the first crystallization, whose peak area varies continuously from zero (at the boundary) to about half the total (at higher Sb contents). In the above, it has been assumed that the second peak is actually due to crystallization, and not to a transformation of an already present crystalline phase. The evidence for this assumption is as follows: (a) the foregoing continuity argument implies that the peak observed in low-Sb glasses (and, in fact, Pd-Si) is due to the same type of process which produces the second peak seen in Type II thermograms. Since the binary alloy transforms by crystallization, this process is identified as crystallization. (b) Samples taken through the first peak, but not the second, show bend ductility, which is indicative of the presence of some amorphous material; however, this observation does not rule out the possibility that the first crystallization produced a supersaturated fcc (Pd) phase which then decomposed, producing the second peak. (c) X-ray diffraction indicates that samples treated as in (b) above are about 50% amorphous (the scattering from amorphous and crystalline phases are equally intense). (d) The two peaks show similar activation energies in isothermal tests (see below), indicating that they may be due tc similar processes. Taking the above evidence as conclusive, one might wonder how one glass could have two crystallization temperatures. It is possible that phase separation of the
Fig. 5. Kratky photograph of phase-separated Pd82Si1sSb3. The total height of the image corresponds to an s = 20/h of 0.14 A-1 .
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
324
glass into two amorphous phases (as observed by Chou [6] for Pd-.Si-Au) also occurs in Pd-Si-Sb. As a test of this theory, some samples were annealed and examined by small-angle X-ray scattering as explained in the experimental section. Samples so annealed were totally amorphous (as verified by calorimetry), and .6 THERMOGRAMS WERE TAKEN AT THE FOLLOWING TEMPERATURES: a) 646.16° K b] 644.16° K c} 640.16e K d) 658.16 ° K e) 634.16" K f) 652.16" K
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Fig. 6. (a) Plots of dXt/dt versus t for Pd80.5 Sil 9.5 at temperatures of 646.16,644.16,640.16, 638.16,634.16, and 632.16 K. (b) Plots of log iOXe versus loglo t corresponding to fig. 6a.
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
325
showed scattering comparable to that shown by a crystalline sample. As-quenched samples showed no detectable scattering. A photograph, taken with a 220 mm Kratky camera and Mo-Ka radiation, of the scattering from an annealed sample is shown in fig. 5. The X-ray data thus shows that when a sample is annealed, it may
ISOTHERMAL
DATA FOR Pde3.sSi14.5Sb a
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I 2.0
Fig. 7. (a) Plots of dxt/dt versus t for Pd83.sSi14.sSb 2 at temperatures of 608.19, 610.17, 629.96, and 636.89 K (all temperatures are ±0.05 K). (b) Plots o f l o g l o X e versus loglo t corresponding to fig. 7a.
326
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
become non-uniform without crystallizing. Phase separation of this kind will be discussed again in the context of isothermal data. Isothermal plots taken at various temperatures for Pd 8o. sSil 9. s are shown in fig. 6a, with log-log Avrami plots in fig. 6b. The Avrami exponent is between three and four, which suggests an interface-limited process with some sporadic nucleation; other interpretations are possible but less plausible. The times to maximum crystallization rate show Arrhenius behavior, with an activation energy of 72.4 kcal/mole. These results are in accord with Chou's findings on Pd 83. sSil 6. s. Similar plots are shown in figs. 7a and 7b for the two peaks exhibited by the ternary alloy Pdaa.sSi14.sSb 2. The results for the second peak are similar to those for Pdao.sSit9.s. An Arrhenius plot for both peaks is shown in fig. 8. The activation energies are 128 -+ 6 kcal/mole (first peak) and 89 -+ 5 kcal/mole (second peak). In this glass, the first crystallization occurs so rapidly that it proceeds to completion long before the second begins; thus, both crystallizations may be studied independently. The first crystallization peak decays too slowly in its later stages to fit an Avrami shape. There may be a transformation of the initial crystalline phase which causes a delayed thermal effect. The rate of heat release beyond the maximum fits a power law J"t = t -2"5. In fig. 9 a thermogram is seen in which both peaks appear. The latter part of the
6c 5C
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I
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1.70
Fig. 8. Arrheniusplotsfor first and secondpeaksof Pd83.sSi14.sSb2.
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
327
ISOTHERMAL -656"K Pdao.5 Sil4.5 Sb5 [Tg "649"K1
~/ 0
I lO
I
20
~'1.
30
I
I
I
40
50
60
I 7O
t (minutes)
Fig. 9. Isothermal plot of Pdso.sSil4.sSb 5 at 656 K.
second peak fits an Avrami law with an exponent of three and no incubation time. The inferred profile shown for the first peak resembles that found in Pdsa.sSi14.sSb 2. That the second peak can best be fit by assuming a zero incubation time suggests that the processes giving rise to the two peaks operate in parallel, not in series. This is further evidence for phase separation in the amorphous state, followed by independent crystallization of the separate phases, as an explanation for the appearance of two peaks in isothermal and scanning thermograms. The general features outlined here hold for all Type II glasses tested. The differing shapes of the two peaks are evident in scanning thermograms, as shown in fig. 1. In all cases, both crystallizations show similar activation energies as in the case discussed above, and the second-peak Avrami exponents are between three and four. This similarity, plus the continuity of Tc's as a function of composition, indicate that the same mechanisms operate over the entire Type I and II regions.
4.
Gradient-quenching
The gradient quenching method outlined above provides qualitative information on the morphology of crystals formed during quenching. The crystallites in most parts of a GQ specimen are at least five microns long, while those obtained by the annealing of fully amorphous samples are too small to resolve with an optical microscope. Thus, crystallization morphologies can be seen on a convenient size.scale in GQ material. However, these morphologies are acharacteristic of slow-quench processes and don't necessarily tell us anything about other types of treatments. An overall view of a GQ Pdso.sSil6.sSb3 sample is shown in fig. 10. The start of
328
M,4. Marcus/Phase separation and crystallization in amorphous Pd-Si-Sb
?- . . ~
t
4
1ram
Fig. 10. Overallview ofGQ Pd83.sSi13.sSb 3.
copious crystallization can be seen as the U-shaped edge of the dark region which extends towards the thick end of the sample. It is plausible that this edge represents a contour of constant quench-rate. The gas-bubbles, shown as semicircular "bites" cut out of the edge of the sample, acted as thermal insulators. Thus, the part of the alloy in their vicinity did not cool as rapidly during the quenching process as it would have had there been no bubbles. The contours of constant quench-rate were thus distorted, as reflected by the shape of the crystallization edge. The progress of crystallization in Pdao.sSi~2.sSb 7 can be seen in fig. 11. The first crystals form irregular spherulitic aggregates and are often nucleated on voids or
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
329
100,1.1
Fig. 11. Progressof crystallization of GQ Pd80.5Sil 2.5 Sb7. inclusions. This is direct evidence of the role of heterogeneous nucleation in crystallization of Pd-base alloys. As the aggregates get bigger, they become more rounded. These pictures were taken with polarized light and show that the aggregates are really spherulites with radial symmetry, and not round agglomerations of equiaxed grains. At the point shown by fig. 1 ld, the crystallization suddenly became almost complete, and the average spherulite size increased. The large spherulite size (compared with those shown in figs. 1 la--c) suggests that the growth rate (not the num-
330
M.A. Marcus/Phase separation and crystallization in amorphou s Pd-Si-Sb
ber of nuclei) suddenly increased due to the slow quench rate. Fig. 1 ld is shown at half the magnification of figs. I l a - c . The alloy just discussed is one in which phase separation is indicated by calorimetric tests. However, only one crystallization process is seen in GQ samples, possibly due to the large size of the crystallites obtained in the GQ process. Phase separation produces composition fluctuations over distances on the order of 100 A. When a 1/a wide crystal grows, it picks up material from many 100 A-wide zones, so sees an "average" composition.
i
lO0.1J
!,
C Fig. 12. Progress of crystallization of GQ Pd80.5Sil 6.5Sb3.
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
331
Figure 12 shows another crystallization morphology as observed in Pds0.sSi16.sSb3. The final state is a "wheat-sheaf" lamellar structure. The initial crystallites are needles, often nucleated on inclusions or voids as above. In the upper right corner of fig. 12a is seen the first signs of a developing lameUar structure. Figs. 12b, c, however, show this initial mode of crystallization to be an exception; the crystals first adopt a "rosette" growth-pattern in which they grow as pairs of bundles, which then impinge on each other to form the final structure. The quench-rate gradient can clearly be seen in figs. 12c, d by its effect on the crystallized fraction. Figure 13 shows the morphology of crystallization of a Type III alloy, Pd82Si11SbT. The matrix is amorphous, as shown by X-ray and mechanical tests. Here we see the primary crystals forming first, followed by a lameUar eutectic structure which replaces the amorphous matrix. An example of dendritic growth in Pdso.sSilT.sSb 2 is shown in fig. 14. Here a crystallization front has moved from the thick to the thin end of the sample. Probably there was a large temperature gradient during quenching. In. Pdso.sSi 17.5Sb 1 is seen (figs. 15a, b) a crystallization morphology quite different from that described above for Pdso.sSilT.sSb 2. The two alloys, when diskquenched, show very similar calorimetric properties, so it is somewhat surprising that they would exhibit such different crystallization modes. There may have been
Fig. 13. GQ Pd82Si I 1Sb7 showing primary and lamellar eutectic structures.
332
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
Fig. 14. GQ Pd8o.5Si17.5Sb2 showingdirected dendritic growth. large differences in quenching conditions between the two samples. In figs. 15a, b what appear to be spherulites are seen, with some larger crystals protruding from them. The "spherulites" do not show birefringence under polarized light; it was impossible to determine their texture, and thus confirm or deny their spherulitic character. However, their internal microstructure appears equiaxed, rather than radial, so it is probable that what is observed are cellular colonies of circular shape. True spherulitic growth is shown in fig. 16 for Pds3.sSi14.sSb2. Under unpolarized light, the crystal aggregates look like those just described, but under polarized light, as in fig. 16, the crystals are seen to be radially oriented. It should be possible to use the maximum thickness of the amorphous part of the sample as a rough measure of the "quenchability" of a given alloy to a glassy state. For instance, binary Pd-Si alloys show less glass-forming tendency (must be quenched at higher rates in order to form glasses) than ternary alloys. In fact, there is no amorphous material in a GQ binary sample as there is in one made of a ternary alloy. 5. Conclusions I have discussed two ways of probing kinetic phenomena in metallic glasses, with application to an unusual metallic glassy alloy system. Calorimetry provides infor-
M.A. Marcus/Phase separation and crystallization in amorphous Pd-Si-Sb
Fig. 15; "Spherulitic" morphology of GQ Pd 8o.5 Si 18.5 Sb 1-
333
334
M,4. Marcus /Phase separation and crystallization in amorphous 2~d-Si-Sb
Fig. 16. Spherulitein GQ Pd83.sSi14.5Sb2.
mation on the rate of crystallization and of configurational relaxation (i.e., the glass temperature), allowing one to deduce the rate-limiting process in crystallization and the effect of alloying on transport behavior. By making systematic measurements as a function of composition, it is sometimes possible to construct continuity arguments, which allow extrapolation of properties from binary to ternary alloys. By such arguments, and some of the isothermal data, it was possible to make a strong case for the occurrence of phase separation in the amorphous state in Pd-Si-Sb alloys, with small-angle X-ray scattering used for confirmation. The GQ method provides useful data of another kind. With it, one probes the crystallization process in a qualitative, pictorial sense, obtaining data on the nucleation and shape of the growing crystals. The size of the crystals observed removes the complicating effect of phase separation, so it is the crystallization of the singlephase glass that is studied. The two techniques used in the investigation reported here can be used to extract a wide variety of information about crystallization and alloy effect in any metallic glass that can be quenched from the melt; the Pd-Si-Sb system is by no means unique or peculiar in this respect.
Acknowledgements This work was supported by ONR contract N00014-76-C-0020, and made possible by the encouragement and advice of D. Tumbull. Additional t'mancial support was provided by the Harvard University Division of Applied Science, and the Schlumberger Foundation.
M.A. Marcus/Phase separation and crystallization in amorphous Pd-Si-Sb
335
References [1] [2] [3] [4] [5]
H.S. Chen, Mat. Sci. Eng. 23 (1976) 151-154. E. Coleman, Mat. Sci. Eng. 23 (1976) 161-167. B.G. Lewis and H.A. Davies, Mat. Sci. Eng. 23 (1976) 182-197. R. Pond and R. Maddin, Trans. AIME 245 (1969) 2475. Instruction Manual, Mod. DSC-2 Differential Scanning Calorimeter (Perkin-Elmer Corp., Instrument Div., Norwalk, Ct., USA, April, 1972). [6] P. Chou, Thesis, Division of Applied Sciences (Harvard University, Cambridge, Mass. USA, 1974).
PHASE SEPARATION AND CRYSTALLIZATION IN AMORPHOUS P d - S i - S b Matthew A. MARCUS Division of Applied Sciences, Harvard University, Cambridge, MA 02138, USA Received 28 May 1978
It is found that replacing some of the Si in a Pd-Si-Sb glass with Sb can make it more resistant to crystallization than the pure binary material. This is shown by the calorimetric results, in which the crystallization temperature increases and the glass temperature decreases with increasing Sb substitution, and also by the finding that certain alloys, such as Pd80 .5 Sil 6.5 Sb3 may be quenched into amorphous rods (by the gradient-quench method) up to 0.5 mm thick. • Calorimetry and small-angle X-ray scattering data show that certain alloys in this system phase separate in the amorphous state• The two phases thus produced independently crystallize. Isothermal measurements indicate that the rate of crystallization of one of the phases is interface-limited, with most nuclei initially present. The other crystallization process does not fit an Avrami law, possibly due to a transformation of the crystalline phase. A method called "gradient-quenching" (GQ) was used to prepare samples from the melt in such a way that the quench-rate was non-uniform, so all stages of crystallization in slowlyquenched alloys are displayed. Nucleation was frequently found to take place on voids and inclusions. The use of the calorimetric and GQ methods in conjunction to gather information about crystallization processes in metallic glasses is discussed.
1. Introduction The subject of transformation behavior in metallic glasses is of technical and fundamental interest. There has been much work done in this field on ternary glasses of the form (Pd, M ) - X , where M is a transition metal and X i s a metalloid [ 1 - 3 ] . That is, the metallic part of a metal-metalloid glass consists of a combination of metals, while the metalloid part is a single element. However, there has been little work on systems of the form P d - ( X , Y), i.e., systems with the single metalloid replaced by a combination of metalloids. Many glasses of technical interest are of the latter form or are quarternary glasses (too complex to understand without understanding ternary glasses) with more than one metalloid• The object of this investigation is to characterize the formation and crystallization behavior of P d - S i - S b glasses b y calorimetric and metallographic methods. The transformation properties of P d - S i - S b glasses as a function of composition were systematically investigated. A differential scanning calorimeter was used to 317
318
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
measure the glass transition and crystallization temperatures of a number of glasses and isothermal crystallization rates as a function of time and temperature. Crystal growth morphologies have been examined by a method known as "gradient-quenching". In it, a sample of molten alloy is quenched in such a way that parts of it have been rapidly quenched and are totally amorphous, parts have been quenched slowly so are totally crystalline, and parts show crystals growing in an amorphous matrix. The general effect is like a movie; the rapidly-quenched portions of the sample show the beginning stages of crystallization while the less-rapidly quenched portions display more-advanced stages.
2. Experimental The crystalline alloys from which the samples used in this experiment were made were prepared by melting 4-9's Pd (from Engelhard Industries), 5-9's Sb and 9-9's Si (both from Alfa Inorganics) in fused-quartz test-tubes under an Ar atmosphere. To assure homogeneity, the alloys were remelted and stirred several times in the test-tubes and they then proved to be metallographically uniform. Amorphous samples in ribbon form were produced by quenching a stream of molten alloy (melted under Ar and squirted through a fused-quartz nozzle) onto the edge of a spinning AI disk [4]. The ribbons were about 0.5 mm wide by 20/a thick. A DSC-2 calorimeter was used to make the calorimetric measurements. The machine was run in the scanning mode to obtain glass and crystallization temperatures for alloys with a wide range of compositions, thus providing the systematic data referred to in the introduction. Isothermal measurements were done on a few alloys and yielded detailed results concerning crystallization kinetics. Scanning data were taken at a heating rate of 40 ° min -I. The samples used for both scanning and isothermal tests weighed 10-25 mg, and were encapsulated in aluminum pans. The melting transitions of lead and zinc were used for temperature and heat calibration as described in the DSC-2 instruction manual [5]. A typical scanning thermogram is shown in fig. 1, along with the def'mitions of glass transition temperature, heat of crystallization, and crystallization temperature used in this paper. My definitions of the first two quantities are the same as those used by Chou [6]. However, his definition of crystallization temperature differs from that used here. He defines it as the temperature at which the first observable crystallization appears. Thus, only one Tc is defined even if there are two crystallization peaks. I define Tc for each peak as the temperature at which the crystallization rate reaches a maximum. If the peaks overlap, an attempt is made to subtract the tail of the first peak from the second before finding Tc2, and likewise for Tcl. The above nomenclature assumes that both peaks are due to crystallization. The evidence for this assumption will be discussed below. To minimize drift in isothermal measurements the calorimeter had to be as nearly as possible in thermal equilibrium as soon as it reached the holding tempera-
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
--->1 ............
~
I" ""
.
i
zxP
319
le--Morgin of Stobility :2":~. ~ ~
~
i~ i - ~
~--~~ -
~
__
=-: ~ - :- - --: - -
iiiii~;~i::i::::::L:::::::::ii~::::ii~i~~t~ c~-cg
I ~i: :ii!i
I
V
j
I I
Tg
I I
I
t
Tcl
Tc2
T
Fig. l. Typical calorimetric thermogram showing definitions of Tcl , Tc2, Tg, AHc, and the shapes of the crystallizationpeaks. ture, designated TI. Let/'2 be the highest temperature at which the sample may be held for two hours without detectable crystallization occurring, yet as close as possible to T 1. With the cooling water on, the calorimeter was held at T2 until the drift in the observed signal was constant. It was then run up to T] as quickly as possible. This procedure reduced the machine's settling time from one or two hours to about three minutes. The temperature calibration of all calorimeters (the DSC-2 included) varies with the heating rate. Thus, to calibrate the calorimeter in the isothermal mode, it was necessary to extrapolate the calibration results for several heating rates to the isothermal limit. The temperature error (actual temperature-temperature displayed by the calorimeter) was found to be linear in the temperature for all scan rates, and linear in the scan rate for all temperatures. A simple computer program performed least-squares fitting and extrapolated the calibration to zero heating rate. Isothermal calorimetry data were analyzed in the context of the Avrami formalism. A digitizing tablet was employed to pick data off thermograms. These data were processed by a computer program which produced plots of:
dXt/dt versus t
(1)
X t versus t
(2)
Xe versus t
(3)
logloXe versus log]ot
(4)
d(logl oXe) versus lOglot d(logl ot)
(5)
M.A. Marcus / Phase separation and crystallization in amorphous, Pd-Si-Sb
320
where X t is the transformed volume fraction, t the time since reaching T~, and X e the extended volume fraction. The assumption was made that the heat evolved when a unit volume of the sample crystallizes is constant throughout the crystallization process. Thus, the observed signal is proportional to dXt/dt. The proportionality factor is computed by requiring that oo
.;
1,
(6)
o
in other words, that the transformed fraction be unity at long times. In computing this integral, the data are extrapolated to zero and to infinity. The first four points are used to derive a power-law fit to the short-time behavior of the observed signal, while the last three are used to fit the long-time behavior to an exponential. Some samples were annealed in order to produce phase separation without crystallization. The annealing was done in a molten-solder bath heated in a box furnace. The samples were wrapped in aluminium foil to prevent them from deforming and reacting with the solder. Annealing was performed at 13° below the glass transition (635 K) for 2.5 min, conditions chosen by analogy with the work of Chou [6]. SmaU-angle X-ray scattering measurements were done on the annealed samples using a Kratky camera (with 80 g slit), Mo-Ka radiation, and photographic detection. GRADIENT QUENCHING .,,..~ Ca pil la r y
I
~
Crystol
i
,~,~Heater
(~uenchj Rote
Contours
l
.~Sample
IH20~1
Sample (Width Exaggerated)
Fig. 2. Operating principles of the GQ apparatus.
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
321
The gradient-quenching apparatus and the kind of sample it was used to make are shown in fig. 2. The fumace is an alumina tube wound with Kanthal wire, insulated with Ceramic Paper (from Edmund Scientific) and held in a vertical position. Just below it sits a beaker of water. The capillary is a fused-quartz tube, about ~ m long, with a 2 mm id, whose end is drawn into a tapered capillary about 4 cm, long by 0.1 m m i d (at the small end). In operation, the capillary is placed inside the furnace. A lump of alloy about 300 mg in mass is placed in the capillary where it sits on the shoulder of the tapered part. The capillary is pumped out with a rotary pump and the furnace is heated. When the alloy melts, the capillary is backfilled with Ar at atmospheric pressure, which forces the alloy into the thin end. The drop of molten alloy acts like a gasket in preventing Ar from getting into the thin end. The tube is now pushed downward so that the alloy is immersed in water. The sample thus produced is a tapered cone of alloy, which is often amorphous at the thin end, and crystalline at the thick end. The thickness gradient produces a corresponding gradient in quench-rates. Metallography was done on gradient-quenched samples using standard procedures. They were etched in a solution of 4 vol.% bromine in methanol. The etching process pitted the amorphous material and acted as a contrast etch toward crystalline phases. X-ray and hardness tests confirmed that the pitted phase was amorphous.
3. Calorimetric results Depending on its composition, a given sample exhibited one of four behaviors: Type I - fully amorphous; thermogram shows glass transition, one exothermic peak. Type II - fully amorphous; thermogram shows glass transition transition, two exothermic peaks. Type IIa - l i k e Type II, but no visible glass transition (on the Type II-Type Ill border). Tupe III - partially crystalline; two or more broad exothermic peaks, not reproducible. Fig. 3 shows the composition ranges over which these behaviors occur. The closed circles represent alloys displaying Type I behavior, the open circles indicate Type II, the open triangles Type III, and the dashes Type IIa. The variation of Tg, Tcl, and Tc2 with composition is plotted in fig. 4. As silicon is replaced by antimony, the glass transition temperature decreases, as shown in fig. 4. The temperature of the first crystallization is near that of the second, for the lowest Sb contents for which both are seen. As the Sb concentration increases, the first crystallization temperature decreases. For Pd concentrations less than 82%, the second crystallization temperature is a monotonically increasing function of the Sb content. For greater Pd concentrations, Tc2 decreases with Sb
Pd~Si 2 2 . ~
X s i ~ . ~ / ~
0.00 2.50 5.00
1.50 10.00 12.50 15.00 IT.50 20.00 22.50 25.00 XSb --~
Fig. 3. Composition range over which Type I (closed circles), Type II (open circles), Type IIa (dashes), and Type III (triangles) behaviors are found. The marked segment of the P d - S i line is the amorphous-forming range for binary Pd-Si glasses. The marked segment of the P d - S b line is the (Pd) phase field at 740°C as determined by X-ray diffraction and metallography.
[Pd]= 79%
80.5%
82%
83.5% 85%
T(*K)
75C T¢2
700
..J
650 3,
600
,
;,
;.;, 3 [s.]--.(~)
, , . . . . . . . 6 T o ~ 2 3 4 5 8 o ~ 2
;;.
o
2o~2
,
,
Fig. 4. Crystallization and glass temperatures as functions of x for alloys of the form PdySiloo_x_ySbx,fory = 79, 80.5, 82, 83;5. and 85.
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
323
content when the alloy has much less Sb than Si, then goes through a minimum, and increases for higher amounts of Sb. At the highest Sb concentrations, Type Iti behavior occurs, and the scatter of the data makes it meaningless to plot Tc's. At the Type I - T y p e II boundary, the curves of Tc versus x(Sb) (on the Type I side) join continuously with those of Tc2 versus x(Sb) (on the Type II side). Both the value of T c and its derivative with respect to x(Sb) are continuous across the I - I I boundary. It is therefore plausible to identify the Type I Tc with the Type II Tc2, as is done in fig. 4. The I - I I boundary is marked by the appearance of the first crystallization, whose peak area varies continuously from zero (at the boundary) to about half the total (at higher Sb contents). In the above, it has been assumed that the second peak is actually due to crystallization, and not to a transformation of an already present crystalline phase. The evidence for this assumption is as follows: (a) the foregoing continuity argument implies that the peak observed in low-Sb glasses (and, in fact, Pd-Si) is due to the same type of process which produces the second peak seen in Type II thermograms. Since the binary alloy transforms by crystallization, this process is identified as crystallization. (b) Samples taken through the first peak, but not the second, show bend ductility, which is indicative of the presence of some amorphous material; however, this observation does not rule out the possibility that the first crystallization produced a supersaturated fcc (Pd) phase which then decomposed, producing the second peak. (c) X-ray diffraction indicates that samples treated as in (b) above are about 50% amorphous (the scattering from amorphous and crystalline phases are equally intense). (d) The two peaks show similar activation energies in isothermal tests (see below), indicating that they may be due tc similar processes. Taking the above evidence as conclusive, one might wonder how one glass could have two crystallization temperatures. It is possible that phase separation of the
Fig. 5. Kratky photograph of phase-separated Pd82Si1sSb3. The total height of the image corresponds to an s = 20/h of 0.14 A-1 .
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
324
glass into two amorphous phases (as observed by Chou [6] for Pd-.Si-Au) also occurs in Pd-Si-Sb. As a test of this theory, some samples were annealed and examined by small-angle X-ray scattering as explained in the experimental section. Samples so annealed were totally amorphous (as verified by calorimetry), and .6 THERMOGRAMS WERE TAKEN AT THE FOLLOWING TEMPERATURES: a) 646.16° K b] 644.16° K c} 640.16e K d) 658.16 ° K e) 634.16" K f) 652.16" K
~=_ .5 E -x ~.4
(CI)
6o
.2
a
.I
b f
o ~ -~J~----------~E-~6 2~ ~ ~ -2 0
8
16
4
-"r----~----------',----~
32 40 Time in Minutes
48
56
64
I
I
72
80
1.25 -
-0.25
--
- 1.75
-
'
0
2
4
6
8
10
12
14
1.6
1.8
2.0
Loglo Time
Fig. 6. (a) Plots of dXt/dt versus t for Pd80.5 Sil 9.5 at temperatures of 646.16,644.16,640.16, 638.16,634.16, and 632.16 K. (b) Plots of log iOXe versus loglo t corresponding to fig. 6a.
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
325
showed scattering comparable to that shown by a crystalline sample. As-quenched samples showed no detectable scattering. A photograph, taken with a 220 mm Kratky camera and Mo-Ka radiation, of the scattering from an annealed sample is shown in fig. 5. The X-ray data thus shows that when a sample is annealed, it may
ISOTHERMAL
DATA FOR Pde3.sSi14.5Sb a
.4 E
._m (/3
#:
636.89°K •~ I
.'11 ~ 0
(0)
610.'170K z 2nd peak '1st peak / / / 608'19°K
4
lstpeak
8
12
629.960K
'16 20 24 Time in Minutes
28
32
I 36
I 40
1.25
0.5(3
•
-0.2 ~=
U~o-1.(~
ff .J
-1.7~
) -2.5(]
-3.25 -4.00
•0
I .2
I .4
I .6
I .8
I I 1.0 '1.2 Log }o Time
I 1.4
I 1.6
I 1.8
I 2.0
Fig. 7. (a) Plots of dxt/dt versus t for Pd83.sSi14.sSb 2 at temperatures of 608.19, 610.17, 629.96, and 636.89 K (all temperatures are ±0.05 K). (b) Plots o f l o g l o X e versus loglo t corresponding to fig. 7a.
326
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
become non-uniform without crystallizing. Phase separation of this kind will be discussed again in the context of isothermal data. Isothermal plots taken at various temperatures for Pd 8o. sSil 9. s are shown in fig. 6a, with log-log Avrami plots in fig. 6b. The Avrami exponent is between three and four, which suggests an interface-limited process with some sporadic nucleation; other interpretations are possible but less plausible. The times to maximum crystallization rate show Arrhenius behavior, with an activation energy of 72.4 kcal/mole. These results are in accord with Chou's findings on Pd 83. sSil 6. s. Similar plots are shown in figs. 7a and 7b for the two peaks exhibited by the ternary alloy Pdaa.sSi14.sSb 2. The results for the second peak are similar to those for Pdao.sSit9.s. An Arrhenius plot for both peaks is shown in fig. 8. The activation energies are 128 -+ 6 kcal/mole (first peak) and 89 -+ 5 kcal/mole (second peak). In this glass, the first crystallization occurs so rapidly that it proceeds to completion long before the second begins; thus, both crystallizations may be studied independently. The first crystallization peak decays too slowly in its later stages to fit an Avrami shape. There may be a transformation of the initial crystalline phase which causes a delayed thermal effect. The rate of heat release beyond the maximum fits a power law J"t = t -2"5. In fig. 9 a thermogram is seen in which both peaks appear. The latter part of the
6c 5C
Pd83"5 Sil4"5Sb2
4C 3C
Pea k
/
128kcol/mole
2C c ~ 8 ~ 6
k
I
1.58
I
1.60
I
I
1.62 1.64 1000 a K / T
I
1.66
I
1.68
J
1.70
Fig. 8. Arrheniusplotsfor first and secondpeaksof Pd83.sSi14.sSb2.
M.A. Marcus / Phase separation and crystallization in amorphous Pd-Si-Sb
327
ISOTHERMAL -656"K Pdao.5 Sil4.5 Sb5 [Tg "649"K1
~/ 0
I lO
I
20
~'1.
30
I
I
I
40
50
60
I 7O
t (minutes)
Fig. 9. Isothermal plot of Pdso.sSil4.sSb 5 at 656 K.
second peak fits an Avrami law with an exponent of three and no incubation time. The inferred profile shown for the first peak resembles that found in Pdsa.sSi14.sSb 2. That the second peak can best be fit by assuming a zero incubation time suggests that the processes giving rise to the two peaks operate in parallel, not in series. This is further evidence for phase separation in the amorphous state, followed by independent crystallization of the separate phases, as an explanation for the appearance of two peaks in isothermal and scanning thermograms. The general features outlined here hold for all Type II glasses tested. The differing shapes of the two peaks are evident in scanning thermograms, as shown in fig. 1. In all cases, both crystallizations show similar activation energies as in the case discussed above, and the second-peak Avrami exponents are between three and four. This similarity, plus the continuity of Tc's as a function of composition, indicate that the same mechanisms operate over the entire Type I and II regions.
4.
Gradient-quenching
The gradient quenching method outlined above provides qualitative information on the morphology of crystals formed during quenching. The crystallites in most parts of a GQ specimen are at least five microns long, while those obtained by the annealing of fully amorphous samples are too small to resolve with an optical microscope. Thus, crystallization morphologies can be seen on a convenient size.scale in GQ material. However, these morphologies are acharacteristic of slow-quench processes and don't necessarily tell us anything about other types of treatments. An overall view of a GQ Pdso.sSil6.sSb3 sample is shown in fig. 10. The start of
328
M,4. Marcus/Phase separation and crystallization in amorphous Pd-Si-Sb
?- . . ~
t
4
1ram
Fig. 10. Overallview ofGQ Pd83.sSi13.sSb 3.
copious crystallization can be seen as the U-shaped edge of the dark region which extends towards the thick end of the sample. It is plausible that this edge represents a contour of constant quench-rate. The gas-bubbles, shown as semicircular "bites" cut out of the edge of the sample, acted as thermal insulators. Thus, the part of the alloy in their vicinity did not cool as rapidly during the quenching process as it would have had there been no bubbles. The contours of constant quench-rate were thus distorted, as reflected by the shape of the crystallization edge. The progress of crystallization in Pdao.sSi~2.sSb 7 can be seen in fig. 11. The first crystals form irregular spherulitic aggregates and are often nucleated on voids or
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
329
100,1.1
Fig. 11. Progressof crystallization of GQ Pd80.5Sil 2.5 Sb7. inclusions. This is direct evidence of the role of heterogeneous nucleation in crystallization of Pd-base alloys. As the aggregates get bigger, they become more rounded. These pictures were taken with polarized light and show that the aggregates are really spherulites with radial symmetry, and not round agglomerations of equiaxed grains. At the point shown by fig. 1 ld, the crystallization suddenly became almost complete, and the average spherulite size increased. The large spherulite size (compared with those shown in figs. 1 la--c) suggests that the growth rate (not the num-
330
M.A. Marcus/Phase separation and crystallization in amorphou s Pd-Si-Sb
ber of nuclei) suddenly increased due to the slow quench rate. Fig. 1 ld is shown at half the magnification of figs. I l a - c . The alloy just discussed is one in which phase separation is indicated by calorimetric tests. However, only one crystallization process is seen in GQ samples, possibly due to the large size of the crystallites obtained in the GQ process. Phase separation produces composition fluctuations over distances on the order of 100 A. When a 1/a wide crystal grows, it picks up material from many 100 A-wide zones, so sees an "average" composition.
i
lO0.1J
!,
C Fig. 12. Progress of crystallization of GQ Pd80.5Sil 6.5Sb3.
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
331
Figure 12 shows another crystallization morphology as observed in Pds0.sSi16.sSb3. The final state is a "wheat-sheaf" lamellar structure. The initial crystallites are needles, often nucleated on inclusions or voids as above. In the upper right corner of fig. 12a is seen the first signs of a developing lameUar structure. Figs. 12b, c, however, show this initial mode of crystallization to be an exception; the crystals first adopt a "rosette" growth-pattern in which they grow as pairs of bundles, which then impinge on each other to form the final structure. The quench-rate gradient can clearly be seen in figs. 12c, d by its effect on the crystallized fraction. Figure 13 shows the morphology of crystallization of a Type III alloy, Pd82Si11SbT. The matrix is amorphous, as shown by X-ray and mechanical tests. Here we see the primary crystals forming first, followed by a lameUar eutectic structure which replaces the amorphous matrix. An example of dendritic growth in Pdso.sSilT.sSb 2 is shown in fig. 14. Here a crystallization front has moved from the thick to the thin end of the sample. Probably there was a large temperature gradient during quenching. In. Pdso.sSi 17.5Sb 1 is seen (figs. 15a, b) a crystallization morphology quite different from that described above for Pdso.sSilT.sSb 2. The two alloys, when diskquenched, show very similar calorimetric properties, so it is somewhat surprising that they would exhibit such different crystallization modes. There may have been
Fig. 13. GQ Pd82Si I 1Sb7 showing primary and lamellar eutectic structures.
332
M.A. Marcus /Phase separation and crystallization in amorphous Pd-Si-Sb
Fig. 14. GQ Pd8o.5Si17.5Sb2 showingdirected dendritic growth. large differences in quenching conditions between the two samples. In figs. 15a, b what appear to be spherulites are seen, with some larger crystals protruding from them. The "spherulites" do not show birefringence under polarized light; it was impossible to determine their texture, and thus confirm or deny their spherulitic character. However, their internal microstructure appears equiaxed, rather than radial, so it is probable that what is observed are cellular colonies of circular shape. True spherulitic growth is shown in fig. 16 for Pds3.sSi14.sSb2. Under unpolarized light, the crystal aggregates look like those just described, but under polarized light, as in fig. 16, the crystals are seen to be radially oriented. It should be possible to use the maximum thickness of the amorphous part of the sample as a rough measure of the "quenchability" of a given alloy to a glassy state. For instance, binary Pd-Si alloys show less glass-forming tendency (must be quenched at higher rates in order to form glasses) than ternary alloys. In fact, there is no amorphous material in a GQ binary sample as there is in one made of a ternary alloy. 5. Conclusions I have discussed two ways of probing kinetic phenomena in metallic glasses, with application to an unusual metallic glassy alloy system. Calorimetry provides infor-
M.A. Marcus/Phase separation and crystallization in amorphous Pd-Si-Sb
Fig. 15; "Spherulitic" morphology of GQ Pd 8o.5 Si 18.5 Sb 1-
333
334
M,4. Marcus /Phase separation and crystallization in amorphous 2~d-Si-Sb
Fig. 16. Spherulitein GQ Pd83.sSi14.5Sb2.
mation on the rate of crystallization and of configurational relaxation (i.e., the glass temperature), allowing one to deduce the rate-limiting process in crystallization and the effect of alloying on transport behavior. By making systematic measurements as a function of composition, it is sometimes possible to construct continuity arguments, which allow extrapolation of properties from binary to ternary alloys. By such arguments, and some of the isothermal data, it was possible to make a strong case for the occurrence of phase separation in the amorphous state in Pd-Si-Sb alloys, with small-angle X-ray scattering used for confirmation. The GQ method provides useful data of another kind. With it, one probes the crystallization process in a qualitative, pictorial sense, obtaining data on the nucleation and shape of the growing crystals. The size of the crystals observed removes the complicating effect of phase separation, so it is the crystallization of the singlephase glass that is studied. The two techniques used in the investigation reported here can be used to extract a wide variety of information about crystallization and alloy effect in any metallic glass that can be quenched from the melt; the Pd-Si-Sb system is by no means unique or peculiar in this respect.
Acknowledgements This work was supported by ONR contract N00014-76-C-0020, and made possible by the encouragement and advice of D. Tumbull. Additional t'mancial support was provided by the Harvard University Division of Applied Science, and the Schlumberger Foundation.
M.A. Marcus/Phase separation and crystallization in amorphous Pd-Si-Sb
335
References [1] [2] [3] [4] [5]
H.S. Chen, Mat. Sci. Eng. 23 (1976) 151-154. E. Coleman, Mat. Sci. Eng. 23 (1976) 161-167. B.G. Lewis and H.A. Davies, Mat. Sci. Eng. 23 (1976) 182-197. R. Pond and R. Maddin, Trans. AIME 245 (1969) 2475. Instruction Manual, Mod. DSC-2 Differential Scanning Calorimeter (Perkin-Elmer Corp., Instrument Div., Norwalk, Ct., USA, April, 1972). [6] P. Chou, Thesis, Division of Applied Sciences (Harvard University, Cambridge, Mass. USA, 1974).