PrintedS°lid StateinGreatC°mmunicati°nS'Britain. Vol.65,No.12, pp.1461-1462, 1988.
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CORRELATION BETWEEN THERMAL STABILITY AND DYNAMICAL PROPERTIES IN Cu-Zr AMORPHOUS ALLOYS J. Chevrier Institut Laue-Langevin, 156X, 38042 Grenoble Cedex, France (Received by E.F. Bertaut on the 27th November 1987) For Cu-Zr amorphous alloys, a relationship is established between crystallization energy and the variation, during crystallization, of dynamical properties as described by Debye temperature. The large reduction of Debye temperature 8D usually found in non equilibrium solids like Cu-Zr amorphous alloys as compared to crystalline values is analysed within this correlation. Therefore beside the well established link of eO and the latent heat of melting, Lf, for metals at equilibrium, we present an extension to alloys in a non equilibrium state using the crystallization energy Nix, and therefore to an irreversible solid state transformation.
As the Debye temperature OD is mainly determined by the shear modulus of solids in the Debye theory, relation (I) relates the energy associated with the appearance of a rigid lattice during the solid liquid transition to t h e s h e a r r e s i s t a n c e o f t h i s lattice. Amorphous m e t a l s a r e i n a non e q u i l i b r i u m s t a t e , t h e r e f o r e r e l a t i o n (1) i s no longer valid because the latent heat of melting is not defined. Nevertheless the Debye temperature is still experimentally well defined and amorphous metals are solid phases often obtained through rapid quenching from the melt. Therefore in order to compare the amorphous state with the liquid state as it is done for pure crystalline metals by relation (1), we have to find what is the characteristic energy associated with the shear resistance in amorphous metals. The latent heat of melting, Lf, is the energy difference between the crystalline state and the liquid state and Nix, the crystallization energy, is the energy difference between the crystalline state and the amorphous state:
In the past few years, several experimental features have been shown to be consistent differences between non equilibrium amorphous and equilibrium crystalline states. The crystallization as an irreversible solid state transformation, is a universal behavior of amorphous metals with an enthalpy variation Nix of several kJ/mole (about 5kJ/mole for crystallization of Cu-Zr amorphous alloysl, 2) at the crystallization temperature T x. Moreover experiments on mechanical properties and low temperature specific heat measurements have raised a widely observed difference: the density of low frequency transverse acoustic phonons is much higher in amorphous metals than in their crystalline counterparts. For example, the difference in the shear modulus is as large as 35% in Pd-Si-Cu 3. This effect is even larger in Cu-Zr 4,5 where the decrease of the Debye temperature after crystallization is about 30% as compared with 15% for Pd-Si-Cu 3. These specific dynamical properties of amorphous metals have been measured in detail by neutron inelastic scattering 6 and compared to those of the crystalline phases. As the large increase o f ~) during crystallization is associated with an important irreversible exothermal effect, the non equilibrium state of amorphous metals seems to be an important condition to observe their characteristic dynamical properties at low f r e q u e n c i e s . Thus t h e p u r p o s e o f t h i s l e t t e r i s to establish a relationship between the crystallization energy NIx of amorphous metallic alloys and the variation of eO during crystallization. Cu-Zr alloys have been chosen because a complete set of experimental data exists for this system. In the case of metallic alloys in equilibrium state, it has already been suggested that alloy stability and Debye temperature could be correlated at least in some cases 7. For the solid-liquid transition, Grlmvall et al. have shown that the Debye temperature (90 is strongly linked to the latent heat of melting Lf 8. For pure crystalline metals this result can be written using relation (1): e0 = C x (Lf/M) I/2 where C metals.
L*= Lf - Nix
appears to be, at least approximately, the energy difference between amorphous and liquid states and therefore the energy associated with the rigidity of amorphous metals. Therefore relation (1) can be written for amorphous metals in a non equilibrium state characterized by NIx, the crystallization e n e r g y , i n the following way: eD ffiC x (L*/M) I/2
In order to establish this analysis on an experimental basis, relation (3) has to be compared with the measured eO and NIX . Taking the crystalline alloy as a reference, we use relation (I) and (3) with the same mass M and constant C. This enables us to write the following relation which will be used to analyse experimental data: eoa =co c x (I - Nix/Lf) I/2
Although el)a and Niv have been measured by different authors 4,5,1,2, the crystalline values eoc and Lf are known with less precision. For copper concentrations between
CORRELATION BETWEEN THERMAL STABILITY AND DYNAMICAL PROPERTIES
30% and 50%, the Debye temperature 80c is nearly constant 80c = 310K 4. The available experimental values of Lf for different copper concentrations reveal only small changes. In fact using Agf=8.5 J/mole/K, the usual values for metals, and as, in this part of the CuZr phase diagram, the melting temperature is within IOX a constant, Tm=1200K, we find Lf=10kJ/mole. This is the average of values measured by Kleppa et al. 9. The experimental valueSreferences 1,°f ~Sx. are taken from two different Using these experimental values and relation (4), 8Da can be calculated from the Debye temperature in the crystalline state,eD c, and compared with experimental values. Figure 1
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As only ~/4x and Lf are required to describe the Debye temperature decrease, this model emphasizes the fact that the origin of the enhancement of specific heat at low temperature in amorphous metals could be the non equilibrium state of amorphous metals as compared to the crystalline state. Moreover any change on 6Hx due to an irreversible solid state transformation would be, within our analysis, the cause of 8D variation. A well known experimental example of such an irreversible change on 8O is its increase after thermal relaxation in the amorphous state. Lasjaunias et al. 10 have measured the OD increase after relaxation at T=200°C for 2 hours of a Cuo.24ZrQ.76 amorphous alloy prepared by sputter depositlon at-77-K--and simultaneously the energy released during relaxation . AHof0.8kJ/mole as measured by calorimetry 11. The crystallization energy of the unrelaxed sample was ~Hx=6kJ/mole and the Debye temperature of respectively the relaxed state and the unrelaxed state were 8Dr=170K and eDa = 154K . Therefore relation (4) can be readily applied in the following way:
8Dr=eDa x (I+ 6Ho/(L f - /~Hx))I/2
40 50 % a l Cu
Figure 1: Comparison of e x p e r i m e n t a l Debye temperatures in amorphous state ( 0 Ref. 4; o Ref. 5) and calculated values (e) using equation (4), crystallisation energy from Ref. 1,2 and Debye temperature of crystalline alloys from Ref. 5 (X). with both calculated and experimental values shows that the agreement is good for the CuZr systems in the composition range considered. This indicates that, with no further hypothesis, relation (4) gives the Debye temperature difference between amorphous and crystalline state.
The calculated value of Debye temperature in relaxed state using 8Da= 154K is eDrf169K in a good agreement with the aforementioned experimental value. Then our model can explain not only the Debye temperature difference between a non equilibrium amorphous state and an equilibrium crystalline state but also between an unrelaxed Cu0.24Zr0.76 amorphous alloy and the same sample annealed in the amorphous state. As a conclusion, this analysis is based only on one system and further investigations on others systems would probably emphasize the importance of other parameters like the chemical short range order in amorphous metals especially when crystalline compounds exist with a large latent heat of melting (i.e. a high melting point). But as throughout this letter no attention has been paid to the actual atomic structure, we can ask if such a llnk between the energy associated vlth irreversible solid state reaction and Debye temperature change could also be found among the large number of non equilibrium crystalline phases produced by means of rapid solidification.
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D.G. Ohn i n "Amorphous M e t a l l i c A l l o y s " Ed. F.E. Luborsky B u t t e r w o r t h s Monographs i n M a t e r i a l s (1983) p. 217 G. G r i m v a l l and S. S j o i n Phys. S c r i p t a . i0 (1974) 340-352 O.J. Kleppa and S. Watanabe Met. Trans. B Vol. 13B (1982) 392 A. Ravex, J.C. Lasjaunias and O. Bethoux J. Phys. F: Met. Phys. 14 (1984) 329-346 J.C. Lasjaunlas, F. Zugmore and M. Harmelin (private communication)