- Email: [email protected]
Correlations in binary liquid and glassy metals
Solid State Communications, Vol. 21, pp. 129—132, 1977.
Pergamon Press.
Printed in Great Britain
CORRELATIONS IN BINARY LIQUID AND GLASSY METALS* S.R. Nagelt and J. Tauc Division of Engineering and Department of Physics, Brown University, Providence, RI 02912, U.S.A. (Received 14 January 1977 by J. Tauc) It is shown, starting from a nearly-free electron approximation, how correlations can occur in the atomic positions of binary liquid and glassy alloys. In particular, it follows from energy considerations that for an alloy of a transition metal with a metalloid there is a concentration region where there should be no metalloid—metalloid nearest neighbors. This concentration region is just the same as that where glass formation is often observed in these systems. RECENTLY there has been considerable interest in alloys of the form M~X1_~ (where Mis a transition or a
and glassy alloys identical correlations as the assumption
noble metal and Xis a polyvalent atom such as a metalbid.) It is from alloys of this type (with c 0.8) that the majority of metallic glasses are made [1] and much effort has been spent in determining the structure of these glasses and of the binary eutectic liquids. The most recent evidence [2—71 is that for many of these alloys the partial interference functions of the liquid or glassy solid cannot be described simply as a random packing of dissimilar sized hard spheres. In order to get reasonably good agreement between the experimental results and the calculated partial interference functions an additional assumption must often be introduced. This hypothesizes strong chemical bonding between the two dissimilar atoms so that a metalloid atom would always prefer to be completely surrounded by metal atoms rather than have another metalloid as a nearest neighbor. For example, in the model calculations of Sadoc et a!. [8] an ad hoc assumption of this kind was made explicitly. The necessity of making such an assumption raises some serious difficulties. The nearly-free electron approximation has been very successful in describing much of the electronic transport data in these alloys [9] and a model based on it has recently [10, 111 been suggested to account for the phenomena of glass formation. If strong chemical bonds are really present one might wonder at all, correespecially whether insofar asthis theapproximation determination isofvalid structural lations is concerned. It is the purpose of the present paper to resolve this question by demonstrating how nearly-free electron t1-~orywill produce in these liquid * Work supported by NSF grant DMR7 1-01814-AOl and ARO grant DAAG29.76G0221.
t Present address: James Franck Institute, University of
of chemical bonding between the dissimilar elements. In particular, we show that this effect is not related to bond formation between the metal and the metalloid atoms. In addition to the questions raised about the validity of the nearly-free electron theory there are some additional serious anomalies with the assumption of strong metal—metalloid bonds. For example in recent studies of eutectic Au: Ge [4], Au: Si [4] and Ag: Ge [5] systems it was concluded that in the liquid there were strong bonds between the noble metal and the metalloid which produced a structure with no Si—Si or Ge—Ge nearest neighbors. This result is somewhat unexpected since in the solid phase all three systems phase separate and there are no intermetallic compounds [12] indicating that the bonding between the metal and the metalloid is relatively weak. If this bonding is so dominant in the liquid, it is surprising that it does not manifest itself also in the solid. In order to compare the energies for the different configurations of the liquid in the nearly-free electron approximation it is necessary to write down the total electronic energy of the system. Following Heine and Weaire [13] we can separate out the contribution to the cohesive energy which depends sensitively on the structure of the liquid 2e(q)x(q)d3q (I) Ub8 oJ U(q)~ where e(q) is the dielectric function, ~(q) is the perturbation characteristic and for a monoatomic system IU(q)12 = S(q)~v(q)l2.Here S(q) is the interference function describing the correlation in the positions of the ions and v(q) is the screened pseudopotential of the ion. For a binary alloy, M~X 1_~, the result becomes more complicated because there are now two pseudopotentials v~(q)and z~(q)and three partial interference functions
Chicago, Chicago, IL 60637, U.S.A. 129
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describing the correlation both between like atoms we would expect the distance between the M and X SMM(q) and S~~(q), and between unlike atoms, S~~(q). atom to be somewhat smaller than that between two M In this case [14] atoms. IU(q)12 = jv~(q) v~(q)I2c(l c)+S~~(q)Iz~(q)I2c2 At this point a few words should be said about the validity of using pseudopotential theory in the case +Sx~(q)IV~(q)~2(l —c)2 + 2SM~(q)v~(q)v~(q)c(l —c). where transition or noble metals are involved. The first (2) point to be made is that we are only concerned with In a binary liquid system where the pseudo-potential the metalloid part of expression 2 for which pseudomay be very differnet for the two elements, the magnipotential formalism clearly is valid. The second point tude of U(q)12 and therefore Ubs can be increased if is that for most of our applications the metal atom is certain correlations are set up in the liquid. Thus the either Ag or Au, that is a noble metal. In this case for liquid can favor those configurations in which the three the states above the d-bands a pseudopotential can be partial interference functions are significantly different used [13, 15]. Since we are alloying with a polyvalent from those predicted by a simple hard sphere model. metal the d-bands in the alloy are even further below This is just the case for alloys of the form we are EF than they are in the pure element. All the electronic discussing. states that are important in this approach lie in the The contribution to the band structure energy will nearly-free electron region near EF where the pseudobe increased if each partial interference function has its potential formalism is appropriate. Finally, in dealing first large peak at a value of q where the corresponding with the transition metals the metal pseudopotential pseudopotential in equation (2) is large. (It is also neces- z~(q)will have to be replaced by a scattering matrix sary that the product e(q)x(q) also is large. This will be but the expression for the perturbed electronic states true only if the value of the wavevector is less than 2kF.) will be formally equivalent to that using pseudopotenIn particular if Sx~(q)has a peak at a value of q where tials [16]. Our conclusions will remain unaltered since Vx(q) has its first node the contribution of the third the metalloid term which is important for our theory term in (2) to the cohesive energy will be negligible, will not be effected. The transport properties, even for In the alloys we are concerned with here, the X-ray these transition metal—metalloid systems can be deintereference function [which is dominated by the parscribed in terms of the nearly-free electron theory. In tial interference function S~~(q)] has its first peak, at particular the Hall effect shows that the metalloid atom q~,at a value of q where the metalloid pseudopotential donates all its valence electrons to the free electron gas is near zero;i.e. v,~(q~)~O. Ifthere were to be metalloid— [17]. This would not be consistent with strong chemical metalloid nearest neighbors, then Sx~(q)would also bonding of the metalloid with the d-bands of the metal. have a peak near q~and there would be only a small We will now examine the available data to see the contribution to the cohesive energy. (If the hard sphere validity of these arguments. The prototype system radius of the two elements were the same, the partial would appear to be the eutectic Au: Si or Au : Ge alloys. interference function would be identical in the hard X-ray diffraction has shown [4] that for both cases sphere model.) In order to gain structural energy for qp = 2.73 A-1. If we now look at the pseudopotentials the alloy it is clearly favorable to have metalloid atoms for Au, Ge, and Si (taken from Cohen and Heine [15]) be only next nearest neighbors to each other so that the we find several interesting results. The pseudopotential peak in S~~(q) would move to a smaller value of q. for Au has a maximum within 10% of qp, that is at q = This does not cost the system any volume energy since 2.95 A-’. For Ge and the Si, on the other hand, qp is by merely rearranging the order of the atoms we have very close to the first node in both pseudopotentials. Si not changed the volume. Since qp 2kF in these alloys has a node q 1 and Ge has one at q 0 2.8 A0 2.9 A’. [10], the peak in S~~(q) cannot avoid the node in For both cases the value of v(q~) 0.02 Ryd. If the v~{q)by moving to a higher value of q ~> qp since in peak in Sxx(q) corresponded to having only second that case the term e(q)x(q) would act to decrease the nearest neighbors than we would evaluate the pseudocontribution to the energy. Thus the metalloid atoms potential at this new peak position, q~,which is roughly must move apart, not closer together, in order to in0.74q~.At q~the pseudopotentials are about an order crease the energy. of magnitude larger than they are at qp so that the Another general point about these alloys is that contribution to the energy, which is proportional to since z~(q~)0 the last term in (2) which contains the square of the potential, will be increased by almost SMX(q) will also produce some deviations from a hard two orders of magnitude. Thus we would expect sphere model. In this case, the expression is linear in ordering in both systems as was observed. V~(q)so that in order to increase the structural energy In the case of amorphous Co081P019, where neutron the peak in SMx(q) will move to larger values. Therefore data does exist [2,3], a similar situation prevails. The —
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CORRELATIONS IN BINARY LIQUID AND GLASSY METALS
phosphorous pseudopotential also has a node close to 1. The where S~0~0(q) a peak, is atone qp =would 3.13 expect A value of v~(q~)has —0.02 Ryd.that Again each P atom to be completely surrounded by Co atoms. This is indeed what is observed in the data, where the three partial interference functions exist, showing that Spp(q) has a peak at approximately 3/4 the wavevector where S~, 0Co (q) has its peak. In the Pd0 8Si02 system ordering is also observed 1 [6, 7]. Since Sp~p~(q) has its first hold peak as at qp 2.8AuA-: Si exactly the same situation should for =the alloy system and silicon should prefer not to be in contact with other silicon atoms. This is what was concluded from the structural study. Also in both the CoP and the PdSi alloys the S~x(q) partial interference function had a peak at a higher value of q than did the SMM(q) interference function. As we have already said this is also a consequence of the theory. At this point we must emphasize that this approach is not equivalent to the assumption of a chemical bonding between the dissimilar atoms. The term which was important for our argurrents was the third term in equation (2). This term only contained the pseudopotential and interference function which described the metalloid, The parameters for the metal atom did not even enter in this term. However some other qualitative effects of these interactions can be similar to those associated with chemical bonds. The chemical bond model was used in analyzing some thermodynamic properties [18] and the temperature dependence of the magnetic susceptibility [19] and the Knight shift [20] for the eutectic Au : Si system. We expect to have qualitatively the same temperature dependence with the nearly-free electron model. States lying far below the Fermi level can have a significant contribution to the magnetic susceptibility [21]. This is in con-
131
trast to the case of resistivity where the states at the Fermi energy are of dominant importance. The susceptibiity, but not the resistivity, should therefore be sensitive to the correlations between two metalloid atoms since this involves wavevectors, q~,less than 2kF and therefore energies less than EF. As the temperature is increased the system will eventually become completely disordered in the sense that metalloid—metalloid nearest neighbors would no alonger be qp forbidden. In that caseone Sxx(q) would have peak at and no longer have at q~.Since vx(q~) 0, for both the resistivity and susceptibility the effect of this peak should have little effect. There would be a strong temperature dependence to the susceptibility at lower temperatures as the system becomes more disordered followed by a region of more gradual dependence at temperatures where the ordering is already completely destroyed. This temperature dependence is what the experimental data indicates [19]. The same would not be true for the resistivity. This explanation, based on pseudopotential theory, for why the metalloid atoms are not nearest neighbors in the liquid or glassy alloys, helps to clarify why some of the geometrical models such as the Polk model [22] for glass formation have been so successful. In this model it was assumed that the metal atoms formed a hard sphere Bernal random packed network. The metalloid atoms, assumed to be smaller, would fill the holes inherent in such a structure, and thereby stabilize the amorphous phase. This implicitly assumes that no two metalbid atoms are nearest neighbors. Our explanation based on pseudopotential theory now explains why this is a good assumption. It also explains why the distance between metal and metalloid atoms can be considerably smaller than expected. Acknowledgement We would like to thank B.G. Bagley for many stimulating conversations. —
1.
REFERENCES CARGILL G.S., III, Solid State Physics (Edited by EHRENREICH H., SEITZ F. & TURNBULL D.), Vol. 30, p. 227. Academic Press, New York (1975).
2.
BLETRYJ. & SADOC J.F.,J. Phys. F: Metal Phys. 5, LllO (1975).
3. 4.
SADOC J.F. & DIXMIER J., Proc. 2nd mt. Conf on Rapidly Quenched Metals, (Section II).’ MIT, Cambridge, Mass (1975) (Edited by GRANT N.J. & GIESSEN B.C.). J. Mat. Sci. Eng. 23, 187 (1976). WAGHORNE R.M., RIVLIN V.G., & WILLIAMS G.I.,J. Phys. F: Metal Phys. 6, 147 (1976).
5.
BELLISENT-FUNELM.C. & DESRE P.J.,Proc. 3rdlnt. Conf on Liquid Metals Bristol, U.K. (1976) (in press).
6.
SUZUKI K., FUKUNAGA T., MISAWA M. & MASUMOTO T., Proc. 2nd mt. Conf on Rapidly Quenched Metals (Section II): MIT, Cambridge, Mass (1975) (Edited by GRANT NJ’. & GIESSEN B.C.). J. Mat. Sd. Eng. 23, 215 (1976).
7.
SUZUKI K., FUKUNAGA T., MISAWA M. & MASIJMOTO T.,Sci Rep. RITUA26, 1,1(1976).
8.
SADOC J.F., DIXMIER J. & GUINIER A., J. Non-Ciyst. Solids 12,46 (1973).
132 9. 10. 11. 12. 13. 14.
CORRELATIONS IN BINARY LIQUID AND GLASSY METALS
Vol. 22, No.2
BUSCH G. & GUNTHERODT H.-J., Solid State Physics (Edited by EHRENREICH H., SEITZ F. & TURNBULL D.), Vol. 29, p. 235. Academic Press, New York (1974). NAGEL S.R. & TAUC J., Phys. Rev. Lett. 35, 380 (1975). NAGEL S.R. & TAUC J.. Proc. 2nd mt. Conf. on Rapidly Quenched Metals (Section I): MIT, Cambridge, Mass (1975) (Edited by GRANT N.J. & GIESSEN B.C.). MIT Press, Cambridge, Mass. (1976) p. 337. HANSEN H., Constitution ofBinary Alloys. McGraw-Hill, New York (1958). HEINE V. & WEAIRE D., Solid State Physics (Edited by EHREMREICH H., SEITZ F. & TURNBULL D.), Vol. 24, p. 250. Academic Press, New York (1970). FABER T.E. & ZIMAN J.M., Phil. Mag. 11, 153 (1965).
15.
COHEN M.V. & HEINE V., in Solid State Physics (Edited by EHRENREICH H., SEITZ F. & TURNBULL D.), Vol. 24, p. 38. Academic Press, New York (1970).
16. 17. 18.
SCHWARTZ L. & EHRENREICH H.,Ann. Phys. 64, 100 (1971). GUNTHERODT H.-J., KUNZI H.U., LIARD M., MULLER M., MULLER R. & TSUEI C.C., Conf on Amorphous Magnetism. Troy, New York, September (1976) (in press). CHEN H.S. & TURNBULL D., .1. Appl. Phys. 38, 3646 (1967).
19. 20.
BAGLEY B.G. & DISALVO F.J.,Bull. Am. Phys. Soc. 21, 385 (1976). BAGLEY B.G., D1SALVO F.J., WARREN W.W. & DUPREE R. (to be published).
21.
TIMBIE J.P. & WHITE R.M., Phys. Rev. 81,2409 (1970).
22.
POLK D.,Acta Met. 20,485 (1972).
Pergamon Press.
Printed in Great Britain
CORRELATIONS IN BINARY LIQUID AND GLASSY METALS* S.R. Nagelt and J. Tauc Division of Engineering and Department of Physics, Brown University, Providence, RI 02912, U.S.A. (Received 14 January 1977 by J. Tauc) It is shown, starting from a nearly-free electron approximation, how correlations can occur in the atomic positions of binary liquid and glassy alloys. In particular, it follows from energy considerations that for an alloy of a transition metal with a metalloid there is a concentration region where there should be no metalloid—metalloid nearest neighbors. This concentration region is just the same as that where glass formation is often observed in these systems. RECENTLY there has been considerable interest in alloys of the form M~X1_~ (where Mis a transition or a
and glassy alloys identical correlations as the assumption
noble metal and Xis a polyvalent atom such as a metalbid.) It is from alloys of this type (with c 0.8) that the majority of metallic glasses are made [1] and much effort has been spent in determining the structure of these glasses and of the binary eutectic liquids. The most recent evidence [2—71 is that for many of these alloys the partial interference functions of the liquid or glassy solid cannot be described simply as a random packing of dissimilar sized hard spheres. In order to get reasonably good agreement between the experimental results and the calculated partial interference functions an additional assumption must often be introduced. This hypothesizes strong chemical bonding between the two dissimilar atoms so that a metalloid atom would always prefer to be completely surrounded by metal atoms rather than have another metalloid as a nearest neighbor. For example, in the model calculations of Sadoc et a!. [8] an ad hoc assumption of this kind was made explicitly. The necessity of making such an assumption raises some serious difficulties. The nearly-free electron approximation has been very successful in describing much of the electronic transport data in these alloys [9] and a model based on it has recently [10, 111 been suggested to account for the phenomena of glass formation. If strong chemical bonds are really present one might wonder at all, correespecially whether insofar asthis theapproximation determination isofvalid structural lations is concerned. It is the purpose of the present paper to resolve this question by demonstrating how nearly-free electron t1-~orywill produce in these liquid * Work supported by NSF grant DMR7 1-01814-AOl and ARO grant DAAG29.76G0221.
t Present address: James Franck Institute, University of
of chemical bonding between the dissimilar elements. In particular, we show that this effect is not related to bond formation between the metal and the metalloid atoms. In addition to the questions raised about the validity of the nearly-free electron theory there are some additional serious anomalies with the assumption of strong metal—metalloid bonds. For example in recent studies of eutectic Au: Ge [4], Au: Si [4] and Ag: Ge [5] systems it was concluded that in the liquid there were strong bonds between the noble metal and the metalloid which produced a structure with no Si—Si or Ge—Ge nearest neighbors. This result is somewhat unexpected since in the solid phase all three systems phase separate and there are no intermetallic compounds [12] indicating that the bonding between the metal and the metalloid is relatively weak. If this bonding is so dominant in the liquid, it is surprising that it does not manifest itself also in the solid. In order to compare the energies for the different configurations of the liquid in the nearly-free electron approximation it is necessary to write down the total electronic energy of the system. Following Heine and Weaire [13] we can separate out the contribution to the cohesive energy which depends sensitively on the structure of the liquid 2e(q)x(q)d3q (I) Ub8 oJ U(q)~ where e(q) is the dielectric function, ~(q) is the perturbation characteristic and for a monoatomic system IU(q)12 = S(q)~v(q)l2.Here S(q) is the interference function describing the correlation in the positions of the ions and v(q) is the screened pseudopotential of the ion. For a binary alloy, M~X 1_~, the result becomes more complicated because there are now two pseudopotentials v~(q)and z~(q)and three partial interference functions
Chicago, Chicago, IL 60637, U.S.A. 129
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describing the correlation both between like atoms we would expect the distance between the M and X SMM(q) and S~~(q), and between unlike atoms, S~~(q). atom to be somewhat smaller than that between two M In this case [14] atoms. IU(q)12 = jv~(q) v~(q)I2c(l c)+S~~(q)Iz~(q)I2c2 At this point a few words should be said about the validity of using pseudopotential theory in the case +Sx~(q)IV~(q)~2(l —c)2 + 2SM~(q)v~(q)v~(q)c(l —c). where transition or noble metals are involved. The first (2) point to be made is that we are only concerned with In a binary liquid system where the pseudo-potential the metalloid part of expression 2 for which pseudomay be very differnet for the two elements, the magnipotential formalism clearly is valid. The second point tude of U(q)12 and therefore Ubs can be increased if is that for most of our applications the metal atom is certain correlations are set up in the liquid. Thus the either Ag or Au, that is a noble metal. In this case for liquid can favor those configurations in which the three the states above the d-bands a pseudopotential can be partial interference functions are significantly different used [13, 15]. Since we are alloying with a polyvalent from those predicted by a simple hard sphere model. metal the d-bands in the alloy are even further below This is just the case for alloys of the form we are EF than they are in the pure element. All the electronic discussing. states that are important in this approach lie in the The contribution to the band structure energy will nearly-free electron region near EF where the pseudobe increased if each partial interference function has its potential formalism is appropriate. Finally, in dealing first large peak at a value of q where the corresponding with the transition metals the metal pseudopotential pseudopotential in equation (2) is large. (It is also neces- z~(q)will have to be replaced by a scattering matrix sary that the product e(q)x(q) also is large. This will be but the expression for the perturbed electronic states true only if the value of the wavevector is less than 2kF.) will be formally equivalent to that using pseudopotenIn particular if Sx~(q)has a peak at a value of q where tials [16]. Our conclusions will remain unaltered since Vx(q) has its first node the contribution of the third the metalloid term which is important for our theory term in (2) to the cohesive energy will be negligible, will not be effected. The transport properties, even for In the alloys we are concerned with here, the X-ray these transition metal—metalloid systems can be deintereference function [which is dominated by the parscribed in terms of the nearly-free electron theory. In tial interference function S~~(q)] has its first peak, at particular the Hall effect shows that the metalloid atom q~,at a value of q where the metalloid pseudopotential donates all its valence electrons to the free electron gas is near zero;i.e. v,~(q~)~O. Ifthere were to be metalloid— [17]. This would not be consistent with strong chemical metalloid nearest neighbors, then Sx~(q)would also bonding of the metalloid with the d-bands of the metal. have a peak near q~and there would be only a small We will now examine the available data to see the contribution to the cohesive energy. (If the hard sphere validity of these arguments. The prototype system radius of the two elements were the same, the partial would appear to be the eutectic Au: Si or Au : Ge alloys. interference function would be identical in the hard X-ray diffraction has shown [4] that for both cases sphere model.) In order to gain structural energy for qp = 2.73 A-1. If we now look at the pseudopotentials the alloy it is clearly favorable to have metalloid atoms for Au, Ge, and Si (taken from Cohen and Heine [15]) be only next nearest neighbors to each other so that the we find several interesting results. The pseudopotential peak in S~~(q) would move to a smaller value of q. for Au has a maximum within 10% of qp, that is at q = This does not cost the system any volume energy since 2.95 A-’. For Ge and the Si, on the other hand, qp is by merely rearranging the order of the atoms we have very close to the first node in both pseudopotentials. Si not changed the volume. Since qp 2kF in these alloys has a node q 1 and Ge has one at q 0 2.8 A0 2.9 A’. [10], the peak in S~~(q) cannot avoid the node in For both cases the value of v(q~) 0.02 Ryd. If the v~{q)by moving to a higher value of q ~> qp since in peak in Sxx(q) corresponded to having only second that case the term e(q)x(q) would act to decrease the nearest neighbors than we would evaluate the pseudocontribution to the energy. Thus the metalloid atoms potential at this new peak position, q~,which is roughly must move apart, not closer together, in order to in0.74q~.At q~the pseudopotentials are about an order crease the energy. of magnitude larger than they are at qp so that the Another general point about these alloys is that contribution to the energy, which is proportional to since z~(q~)0 the last term in (2) which contains the square of the potential, will be increased by almost SMX(q) will also produce some deviations from a hard two orders of magnitude. Thus we would expect sphere model. In this case, the expression is linear in ordering in both systems as was observed. V~(q)so that in order to increase the structural energy In the case of amorphous Co081P019, where neutron the peak in SMx(q) will move to larger values. Therefore data does exist [2,3], a similar situation prevails. The —
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Vol. 22, No.2
CORRELATIONS IN BINARY LIQUID AND GLASSY METALS
phosphorous pseudopotential also has a node close to 1. The where S~0~0(q) a peak, is atone qp =would 3.13 expect A value of v~(q~)has —0.02 Ryd.that Again each P atom to be completely surrounded by Co atoms. This is indeed what is observed in the data, where the three partial interference functions exist, showing that Spp(q) has a peak at approximately 3/4 the wavevector where S~, 0Co (q) has its peak. In the Pd0 8Si02 system ordering is also observed 1 [6, 7]. Since Sp~p~(q) has its first hold peak as at qp 2.8AuA-: Si exactly the same situation should for =the alloy system and silicon should prefer not to be in contact with other silicon atoms. This is what was concluded from the structural study. Also in both the CoP and the PdSi alloys the S~x(q) partial interference function had a peak at a higher value of q than did the SMM(q) interference function. As we have already said this is also a consequence of the theory. At this point we must emphasize that this approach is not equivalent to the assumption of a chemical bonding between the dissimilar atoms. The term which was important for our argurrents was the third term in equation (2). This term only contained the pseudopotential and interference function which described the metalloid, The parameters for the metal atom did not even enter in this term. However some other qualitative effects of these interactions can be similar to those associated with chemical bonds. The chemical bond model was used in analyzing some thermodynamic properties [18] and the temperature dependence of the magnetic susceptibility [19] and the Knight shift [20] for the eutectic Au : Si system. We expect to have qualitatively the same temperature dependence with the nearly-free electron model. States lying far below the Fermi level can have a significant contribution to the magnetic susceptibility [21]. This is in con-
131
trast to the case of resistivity where the states at the Fermi energy are of dominant importance. The susceptibiity, but not the resistivity, should therefore be sensitive to the correlations between two metalloid atoms since this involves wavevectors, q~,less than 2kF and therefore energies less than EF. As the temperature is increased the system will eventually become completely disordered in the sense that metalloid—metalloid nearest neighbors would no alonger be qp forbidden. In that caseone Sxx(q) would have peak at and no longer have at q~.Since vx(q~) 0, for both the resistivity and susceptibility the effect of this peak should have little effect. There would be a strong temperature dependence to the susceptibility at lower temperatures as the system becomes more disordered followed by a region of more gradual dependence at temperatures where the ordering is already completely destroyed. This temperature dependence is what the experimental data indicates [19]. The same would not be true for the resistivity. This explanation, based on pseudopotential theory, for why the metalloid atoms are not nearest neighbors in the liquid or glassy alloys, helps to clarify why some of the geometrical models such as the Polk model [22] for glass formation have been so successful. In this model it was assumed that the metal atoms formed a hard sphere Bernal random packed network. The metalloid atoms, assumed to be smaller, would fill the holes inherent in such a structure, and thereby stabilize the amorphous phase. This implicitly assumes that no two metalbid atoms are nearest neighbors. Our explanation based on pseudopotential theory now explains why this is a good assumption. It also explains why the distance between metal and metalloid atoms can be considerably smaller than expected. Acknowledgement We would like to thank B.G. Bagley for many stimulating conversations. —
1.
REFERENCES CARGILL G.S., III, Solid State Physics (Edited by EHRENREICH H., SEITZ F. & TURNBULL D.), Vol. 30, p. 227. Academic Press, New York (1975).
2.
BLETRYJ. & SADOC J.F.,J. Phys. F: Metal Phys. 5, LllO (1975).
3. 4.
SADOC J.F. & DIXMIER J., Proc. 2nd mt. Conf on Rapidly Quenched Metals, (Section II).’ MIT, Cambridge, Mass (1975) (Edited by GRANT N.J. & GIESSEN B.C.). J. Mat. Sci. Eng. 23, 187 (1976). WAGHORNE R.M., RIVLIN V.G., & WILLIAMS G.I.,J. Phys. F: Metal Phys. 6, 147 (1976).
5.
BELLISENT-FUNELM.C. & DESRE P.J.,Proc. 3rdlnt. Conf on Liquid Metals Bristol, U.K. (1976) (in press).
6.
SUZUKI K., FUKUNAGA T., MISAWA M. & MASUMOTO T., Proc. 2nd mt. Conf on Rapidly Quenched Metals (Section II): MIT, Cambridge, Mass (1975) (Edited by GRANT NJ’. & GIESSEN B.C.). J. Mat. Sd. Eng. 23, 215 (1976).
7.
SUZUKI K., FUKUNAGA T., MISAWA M. & MASIJMOTO T.,Sci Rep. RITUA26, 1,1(1976).
8.
SADOC J.F., DIXMIER J. & GUINIER A., J. Non-Ciyst. Solids 12,46 (1973).
132 9. 10. 11. 12. 13. 14.
CORRELATIONS IN BINARY LIQUID AND GLASSY METALS
Vol. 22, No.2
BUSCH G. & GUNTHERODT H.-J., Solid State Physics (Edited by EHRENREICH H., SEITZ F. & TURNBULL D.), Vol. 29, p. 235. Academic Press, New York (1974). NAGEL S.R. & TAUC J., Phys. Rev. Lett. 35, 380 (1975). NAGEL S.R. & TAUC J.. Proc. 2nd mt. Conf. on Rapidly Quenched Metals (Section I): MIT, Cambridge, Mass (1975) (Edited by GRANT N.J. & GIESSEN B.C.). MIT Press, Cambridge, Mass. (1976) p. 337. HANSEN H., Constitution ofBinary Alloys. McGraw-Hill, New York (1958). HEINE V. & WEAIRE D., Solid State Physics (Edited by EHREMREICH H., SEITZ F. & TURNBULL D.), Vol. 24, p. 250. Academic Press, New York (1970). FABER T.E. & ZIMAN J.M., Phil. Mag. 11, 153 (1965).
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