Ionic and electronic transport in liquid metals: Relation between longitudinal and transverse effects

Utilizing relations due to Moreau and to Bridgman, plus the Wiedemann-Franz law, it is first demonstrated that a longitudinal effect, the Thomson thermoelectric coefficient, σ T is given by LP R , where L is the Lorenz number while P and R characterize transverse effects, represented by Ettingshausen and Hall coefficients, respectively. Corresponding effects are then defined for ionic transport, motivated by the observed Haeffrer effect for isotopes but written initially for an isotopically pure liquid metal. In this way, we have related a longitudinal ionic density gradient to a similar transverse gradient in the Hall configuration in a transverse magnetic field. The latter gradient is shown to be precisely determined by the ratio eE H k B T , where E H is the Hall electric field. Generalizing to a binary mixture of isotopes, the Haeffner effect follows directly by momentum transfer arguments.