Experimental evidence for nonintegral direct-force valence in electromigration

The effective valence number $Z^{\mathrm{*}}$ of hydrogen in ${\mathrm{VB}}_{\mathrm{x}}$, ${\mathrm{NbH}}_{\mathrm{x}}$, and ${\mathrm{TaH}}_{\mathrm{x}}$ (with x≃0.01) has been measured by means of a new experimental technique. From the temperature dependence of $Z^{\mathrm{*}}$ it is concluded that the valence associated with the direct force in electromigration differs significantly from the bare valence of the migrating ion. The results are discussed on the basis of Landauer’s work on the carrier-density modulation effect and the very recent theory of Sorbello on the direct force for a strong scatterer in a free-electron gas.