Effect of Pressure on the Order-Disorder Transition Temperature of Vacancies inNiVTi2S4

The order-disorder transition of vacancies in $\mathrm{Ni}V{\mathrm{Ti}}_2{\mathrm{S}}_4$ has been studied by electrical-resistivity measurements at hydrostatic pressures up to 7 kbar. The measured resistivity values indicate that the order-disorder transition is first order. The transition temperature as a function of pressure can be expressed by the empirical relations $T_c^h=(348.5+9.2P-0.31\mathrm{}{P}^2)$ K in heating and $T_c^c=(343.5+9.7P-0.32\mathrm{}{P}^2)$ K in cooling runs, where $P$ is the applied pressure in kbar. Application of the Bean-Rodbell method gives the ordering energy ${\Xi }_0=-0.030\mathrm{}$ eV/Ni atom, its volume dependence $\left(\frac{V}{\Xi }\right)\times \left(\frac{d\Xi }{\mathrm{dV}}\right)=-40\mathrm{}$, and the compressibility $\kappa =7\mathrm{}\times {10}^{-4\mathrm{}}$ ${\mathrm{kbar}}^{-1\mathrm{}}$ at the transition temperature at 0 kbar. The critical pressure for the first-order-to-second-order transition is estimated to be 14 kbar which nearly agrees with the value 12 kbar obtained from linear extrapolation of experimental ($T_c^h-T_c^c$) values. The initial pressure slopes of the transition temperature are considerably larger than those of the order-disorder systems without vacancies. The pressure effect can be explained by the volume-dependent differences in the following terms: (i) the Madelung energy of the Ni ions screened by the conduction electrons, (ii) the core-core interaction energy between Ni atoms, and (iii) the self-energy of $e^T$ orbital electrons split from $t_{2g}$ states in Ni Wigner-Setiz cell, between the ordered and the disordered states.