Ab initio study of anomalous temperature dependence of resistivity in V-Al alloys

TL;DR

This work tackles the long-standing Mooij correlation by performing ab initio transport calculations for V1-xAlx alloys using a Kubo-Greenwood formalism embedded in a KKR-CPA framework and a CPA-based model for thermal vibrations. The conductivity is decomposed into a local term sigma_0 and a Boltzmann-like term sigma_1, with sigma_0 showing a temperature growth that, when comparable to sigma_1, drives the negative TCR observed experimentally in the intermediate-to-high temperature range; sigma_0 correlates with the DOS at the Fermi level and is dominated by multi-orbital pd and df channels near V, while sp channels dominate in Al-rich compositions. The results reproduce the Mooij correlation and explain the negative TCR without invoking quantum coherence, highlighting the crucial role of multi-orbital interband processes and the DOS, though they acknowledge limitations of CPA at low T and possible beyond-CPA mechanisms. Overall, the study provides a quantitative, first-principles account for anomalous resistivity in highly disordered metallic alloys and clarifies the microscopic origin of the non-Boltzmann contribution.

Abstract

V$_{1-x}$Al$_x$ is a representative example of highly resistive metallic alloys exhibiting a crossover to a negative temperature coefficient of resistivity (TCR), known as the Mooij correlation. Despite numerous proposals to explain this anomalous behavior,none have provided a satisfactory quantitative explanation thus far. In this work, we calculate the electrical conductivity using an ab initio methodology that combines the Kubo-Greenwood formalism with the coherent potential approximation (CPA). The temperature dependence of the conductivity is obtained within a CPA-based model of thermal atomic vibrations. Using this approach, we observe the crossover to the negative TCR behavior in V$_{1-x}$Al$_x$, with the temperature coefficient following the Mooij correlation, which matches experimental observations in the intermediate-to-high temperature range. Analysis of the results allows us to clearly identify a non-Boltzmann contribution responsible for this behavior and describe it as a function of temperature and composition.

Figures (8)

• Figure 1: Comparison of calculated ('theory') and experimental values (a) of the resistivity normalized by the residual resistivity for Al atomic fraction $x=0.34$ and (b) of the temperature coefficient of resistivity (TCR) as a function of Al concentration. Experimental data is taken from Ref. Alekseevskii1975.
• Figure 2: Temperature dependence of the conductivity for V$_{1-x}$Al$_x$ alloys. The three columns are related to the Al concentrations $x=0.2, 0.3, 0.38$. The first row shows the on-site $\sigma_0$, the second row -- the $\sigma_1$ conductivity term, while the third row corresponds to the total conductivity as a function of $T$. Several positions of the Fermi levels have been used, with the plots for the true Fermi level $\Delta E_F = 0$ shown with thick green lines.
• Figure 3: Conductivity terms, $\sigma_0$, $\sigma_1$, for V$_{1-x}$Al$_x$ as functions of the Al concentration, $x$, at $T = 0$ K.
• Figure 4: $\sigma_0$ conductivity term plotted against the DOS at the respective energy for various V$_{1-x}$Al$_x$ alloys and two temperatures: 0 K and 1000 K.
• Figure 5: The component-resolved DOS for V$_{1-x}$Al$_x$ alloys at three different temperatures 0K, 500K, 1000K. The three columns are related to the Al concentrations $x=0.2, 0.3, 0.38$. Upper row: The DOS of the vanadium component; inset: Zoom-in around the Fermi level. Lower row: The DOS of the aluminum component.