First Principles Calculation of Residual Resistivity
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First Principles Calculation of Residual Resistivity 2 1 R. H. Brown, W. H. Butler, D. M. Nicholson, 4 5 P. B. Allen, A. Mehta, and L. M. Schwartz 6
1
H. Yang,
3
J.
W. Swihart,
3
I Metals and Ceramics Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831-6114 Department of Physics, Luther College, Decorah, IA 52101 3 Department of Physics, Indiana University, Bloomington, IN 47405 4 Department of Physics, State University of New York at Stony Brook, Stony Brook, New York 11794-3800 5 Department of Physics, Brandeis University, Waltham, MA 02254 6 Schlumberger-Doll Research, P.O. Box 307, Ridgefield, CT 06877 2
ABSTRACT The list of physical properties which are important in the design of materials and which are routinely calculated from first principles within the local density approximation to density functional theory is continually growing. In this paper we discuss the application of multiple scattering theory to the calculation of the residual resistivity of disordered alloys. Progress has been made on two fronts. First, the coherent potential approximation for the resistivity, which sums to all orders a limited set of multiple scattering diagrams, has given resistivities in agreement with experiment for alloys where the site occupation is roughly random. Second, the linearized KKR was used to evaluate the Kubo formula for several large configurations of atoms and obtain the resistivity with all multiple scattering paths included. This method is not limited to random alloys, but can be applied to short range ordered and amorphous alloys provided the resistivity is high enough to limit the mean free path to a single unit cell.
INTRODUCTION Materials are a collection of nuclei held together by a gas of electrons. Many would argue that the value of multiple-scattering-theory (MST) is its ability to calculate the state of the electron gas and extract the behavior of the nuclei, for example the energetically preferred lattice or the occupation of lattice sites by particular species, or the vibrational modes of the lattice i.e., phase stability and mechanical properties. Often the electrons draw attention only because they coerce the nuclei into particular motions or positions. Counter to this, our contribution to this symposium takes aim at the behavior of the electrons in an electric field. We are interested in the positions of the nuclei because they affect the motion of the electrons. The electrons are assumed to act as if they move independently in a potential determined by the electron density and the electrostatic field of nuclei in fixed positions. This restricts the discussion to the "ordinary conductivity" at zero temperature calculated in the local density approximation. The appropriate procedure is to evaluate the Kubo formula1 which gives the linear response of the current to a perturbative electric field in terms of the Green function of the unperturbed system. In keeping with the topic of this symposium MST will be called upon to provide the Green functions. The "ordinary conductivity" h
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