Calculation of the extra‐resistivity of GPZ using the T‐matrix formalism

Abstract

I t is well known froiii experiiiient, that the foriiiutiori of GPZ is accotnpaiiied with characteristic changes in the residual resistivity. Brorri theoreticul point of view this supposecl stateinerit becoriies a coiiiplicutetl problem of the electronic structure of alloys. A series of triodels have beerr developed during the last twenty years (see for exaniple HILLEL, HOSSITER; LUIGQI et al. ; RICHTER, SCKUBERT). Although soiiie progress was uchieved in both the detailed calculations for real systerns (HILLEL, ItOSSITER; LUIGCI e t al.) un(1 the iiiodel calculations (RICHTER, SCHUBERT) soiiie essential points remained unclear : (i) What is the physical reason for the extra resistivity? (ii) How deteriiiines the sign of Lhe extra resistivity? (iii) The lack of calculations for real systetns without fitting any etiipirical paraineters.These three points are closely related to each other and the aim of the present paper is to contribute to answer these questions.The residual resistivity of alloys of simple rnetals can be described within the Zirnan upproximation ( 0'I'hrts in the fraule of the present iiiodel the extra resistivity is cuused by the coherent scattering of the iftipurities within a Gl'Z. It nmy be positive or negative depending on the interference terms I( It) ant1 the pair distribution n( ft), i.e. the size, shape anti crystallic structure of the GI'Z. Pigure 1 contuiris the interference term for apair of ZII utouis in at1 A1 host. l t is a quickly oscillutirig function of lt with inagnitudes not larger thun about 3 % of the residuul resistivity per atoiii in the interesting region up from nearest rieighbour distance. Note that uccording to (3) only discrete values of f < contribute to the extra resistivity. Jhie to the oscillations sign and magnitude of the interference terms depend very sensitively on the scattering properties of the impurities. This means that the extru resistivity is Inuch more influenced by details of the electronic structure than the residual resistivity itself.On the other hand the existing practical calculations of the extra resistivity use severul pseudopotentials, in the case of AlZn the Harrisson forrnfactor ( HARRISSON) 4 n ) = ( 4 n s 2 Z h 2 + B)lQo/42) ( 4)