Effects of band shape on the magnetic and thermal properties of metals and alloys

Abstract

The temperature variations of the electronic contributions to the paramagnetic susceptibility, χ , and specific heat C , of metals are calculated for various forms of electronic energy bands. The band shapes considered are those corresponding to density of states relations of the form d ν /d ε = ν ' = 2 a n ε n for n = 1, 2, 3 and ν ' = 2( a 0 + a 3 ε 3 ) for a range of values of ( a 3 / a 0 ). The variations of χ and C are presented graphically for effectively the whole temperature range in each case. It is shown, in particular, that with ν ' = 2 a n ε n , χ decreases monotonically with increasing temperature, T , but that with ν ' = 2( a 0 + a 3 ε 3 ) the χ , T curve may have a maximum for a certain range of values of ( a 3 / a 0 ). The effects of band closure and band overlap are also considered, and results are presented graphically for χ and C as functions of temperature for ( a ) a single closed rectangular band, ( b ) two overlapping infinite rectangular bands and ( c ) two overlapping closed rectangular bands. The status of the collective electron treatment of metals, on which the present work is based, is briefly discussed with respect to the more general theory of metals. A short discussion is also given of the theoretical results in relation to the relevant experimental results, and, in particular, in relation to the properties of palladium and of some of its alloys with silver.