Abstract
The excess resistivityΔ ρ of binary alloys is calculated in the Born approximation for the scattering of quasifree electrons from the atomic disorder.Δ ρ can be represented as the convolution of the structure functionS(q) and the fourier transform of the effective potential. The critical anomaly ofΔ ρ is derived from scaling expressions forS(q), both for alloys which undergo unmixing and for order-disorder transitions. The variation ofΔ ρ with concentration and temperature in the vicinity of a critical point is obtained. The time-dependence of the resistivity of alloys after a sudden quench into the two-phase region is also calculated, using computer simulation data forS(q,t), and a maximum ofΔ ρ is found for zones with linear dimension of 8–12 lattice spacings. All these results are in fair agreement with the available experiments. As a further possible application, we obtain the critical exponent for the nonlinear relaxation of the resistivity of an alloy close to the order-disorder transition.
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Asch, A.E., Hall, G.L.: Phys. Rev.132, 1047 (1963)
Rossiter, P.L., Wells, P.: J. Phys. C4, 354 (1971)
Rossiter, P.L., Wells, P.: Phil. Mag.24, 425 (1971);28, 505 (1973)
Bhatia, A.B., Thornton, D.E.: Phys. Rev. B2, 3004 (1970) Hillel, A.J., Edwards, J.T., Wilkes, P.W.: Phil. Mag.32, 189 (1975)
Pseudopotentials in metals are reviewed by H. Jones: In: Handbuch der Physik (edited by S. Flügge), Vol. 19, p. 269. Berlin-Göttingen-Heidelberg: Springer 1956
Suezaki, H., Mori, H.: Progr. Theor. Phys.41, 1177 (1969)
For a related treatment at structural and magnetic phase transitions cf. Binder, K., Meissner, G., Mais, H.: Phys. Rev. B13 (1976, to be published)
This assumption is invalid for many alloys of practical interest like ZnAl, for instance, as pointed out by Labusch, phys. stat. sol.3, 1661 (1963). There the region of allowed wavevectors rather is similar to a region between two spheres of slightly different radius, and lies completely within the second Brillouin zone. The adaption of our treatment to this situation is in principle straightforward, if the geometry of the Fermi surfaces is known
Fisher, M.E., Aharony, A.: Phys. Rev. B10, 2818 (1974)
Fisher, M.E., Langer, J.S.: Phys. Rev. Lett.20, 665 (1968) Richard, T.G., Geldart, D.J.W.: Phys. Rev. Lett.30, 290 (1973)
Thomas, G.A., Giray, A.B., Parks, R.D.: Phys. Rev. Lett.31, 241 (1973)
Simons, D.S., Salamon, M.B.: Phys. Rev. Lett.26, 750 (1971)
For an early experiment in AuCu-alloys, cf. Johansson, C.H., Linde, J.O.: Ann. Physik25, 1 (1936). These data are reproduced in Figure 14 of [1]. For a more recent experiment see: Fisher, G., Godel, D., Steeb, S.: Z. Metallk.64, 200 (1973)
Note that this is analogous to the behavior of an antiferromagnet in a field, whereT N(H)=T N(O) −a′H 1/φ,H→0, and the magnetization—which corresponds to |c B −c B crit| — varies linearly withH. At larger values ofH, however, the phase transition may change from second order to first order at a tricritical point. Cf. e.g. Fisher, M.E.: AIP Conf. Proc.24, 273 (1975). For a discussion of crossover scaling see e.g. Riedel, E.K., Wegner, F.J.: Z. Physik225, 195 (1969)
Kadanoff, L.P.: In: Critical Phenomena (M.S. Green, Ed.), p. 100. New York: Academic Press 1971 Griffiths, R.B.: Ibid., p. 283
Fisher, M.E.: In: Ref. 17, p. 1 Stanley, H.E.: An Introduction to Phase Transitions and Critical Phenomena. Oxford: Oxford University Press 1971
Binder, K.: Adv. Phys.23, 917 (1974)
For a recent review, see Binder, K.: In: Fluctuation, Instabilities and Phase Transitions (T. Riste, Ed.) p. 53. New York: Plenum Press 1975
For a recent review, see Langer, J.S.: In: Ref. 20, p. 19
Guinier, A.: Nature142, 569 (1938) Preston, G.D.: Proc. R. Soc. A167, 526 (1938)
Panseri, C., Federighi, T.: Acta met.8, 218 (1960) Federighi, T., Passari, L.: Acta met.7, 422 (1959) Panseri, C., Federighi, T., Ceresara, S.: Trans. metall Soc. A.I.M.E.227, 1122 (1963) Ceresara, S., Federighi, T., Fiorini, P.: Phil. Mag.18, 49 (1968)
Gerold, V.: Z. Metallkde.53, 341 (1962)
Geisler, A.H.: In: Phase Transformations in Solids (R. Smoluchowsky, Ed.) p. 387. New York: J. Wiley 1951 Kelly, A., Nicholson, R.B.: Progr. Mater. Sci.10, 149 (1963)
Wilkes, P.: Acta Met.16, 153 (1968) Smugeresky, J.E., Herman, H., Pollack, S.R.: Acta met.17, 883 (1969) Higgins, J., Wilkes, P.: Phil. Mag.25, 599 (1972) Williams, R.O., Paxton, H.W.: J. Iron and Steel Inst.185, 358 (1957) Richter, F., Bendick, W., Pepperhoff, W.: Z. Metallkde.65, 42 (1974) Kosamura, K., Hiraoka, Y., Murakami, Y.: Phil. Mag.28, 809 (1973)
Mott, N.F.: J. Inst. Metals60, 267 (1937) Harrison, W.A.: Acta met.8, 168 (1960) Asdente, M.: Acta met.9, 587 (1963) Matyas, Z.: Phil. Mag.39, 277 (1948)
Wilkes, P.: Acta met.16, 863 (1968) Hillel, A.J.: Acta met.18, 253 (1970)
Fine, M.E.: Acta met.7, 228 (1959)
Cahn, J.W.: Acta met.9, 785 (1961);10, 179 (1962) Cook, H.E.: Acta met.18, 297 (1970)
Binder, K.: Z. Physik267, 313 (1974)
Langer, J.S., Bar-on, M., Miller, H.D.: Phys. Rev. A11, 1417 (1975) Langer, J.S.: Ann. Phys.65, 53 (1971) Langer, J.S., Bar-on, M.: Ann. Phys.78, 421 (1973)
Binder, K., Stauffer, D.: Phys. Rev. Lett.33, 1006 (1974)
Bortz, A.B., Kalos, M.H., Lebowitz, J.L., Zendejas, M.A.: Phys. Rev. B10, 535 (1974) Lebowitz, J.L., Kalos, M.H.: Scripta Met.10, 9 (1976) Marro, J., Bortz, A.B., Kalos, M.H., Lebowitz, J.L.: Phys. Rev. B12, 2000 (1975) Flinn, P.A.: J. Statist. Phys.10, 89 (1974)
Rundman, K.B., Hilliard, J.E.: Acta met.15, 1025 (1967) Rundman, K.B.: Ph. D.-Thesis (The University of Illionois, 1967, unpublished)
Lifshitz, I.M., Slyozov, V.V.: J. Phys. Chem. Solids19, 35 (1961)
Marro, J.: Ph. D.-Thesis, Yeshiva University (New York 1975, unpublished)
Collins, M.F., Teh, H.C.: Phys. Rev. Lett.30, 781 (1973) Earlier less precise data on nonequilibrium slowing down obtained by other methods are due to Siegel, S.: J. Chem. Phys.8, 860 (1940) Lord, N.W.: ibid.21, 692 (1953)
Suzuki, M.: Int. J. Magn.1, 123 (1971) Binder, K.: Phys. Rev. B8, 3423 (1973)
Racz, Z.: Phys. Rev. B13, 263 (1976) Fisher, M.E., Racz, Z.: Phys. Rev. B13 (1976, to be publ.)
Kretschmer, R., Binder, K., Stauffer, D.: J. Stat. Phys., to be publ.
Halperin, B.I., Hohenberg, P.C., Ma, S.: Phys. Rev. Lett.29, 1548 (1972)
Hashimoto, T., Miyoshi, T., Ohtsuka, H.: Phys. Rev. B13, 1119 (1976)
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Binder, K., Stauffer, D. Behavior of the electrical resistivity at phase transitions in binary alloys. Z Physik B 24, 407–415 (1976). https://doi.org/10.1007/BF01351533
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DOI: https://doi.org/10.1007/BF01351533