Thermal-expansion and elastic constants of dilute Cr-Al alloys

The thermal-expansion and elastic constants of dilute Cr-Al alloys containing 0.67, 1.06, 1.70, 2.19, 2.74, and 3.22 at.% Al are reported in the temperature range $4<T<\mathrm{}400\mathrm{}$ K. Magnetic anomalies were found at $T_N$ in both the thermal-expansion coefficients ($\alpha$) and bulk moduli ($B$) of all the alloys. At the Néel temperature these anomalies display a $\lambda$-type behavior for $c<\mathrm{}2\mathrm{}$ at.% Al and a jumplike behavior for $c>\mathrm{}2\mathrm{}$ at.% Al. The magnetic contribution to $B$ at 0 K reaches a large peak value of about 1.1×${10}^{11}$ ${\mathrm{Nm}}^{-2\mathrm{}}$ for alloys near 2 at.% Al. It is concluded that antiferromagnetism is not suppressed for $2<c<\mathrm{}4\mathrm{}$ at.% Al in contrast with suggestions based on previous resistivity and susceptibility measurements. The magnetovolume, $\Delta \omega$, of all the alloys as well as of pure chromium is found to vary as $\Delta \omega \mathrm{}\left(T\right)=a+b{T}^2+c{T}^4$ at $T<\mathrm{}{T}_N$. This type of relation is predicted by itinerant-electron theories which, however, fail to produce the correct temperature variation of the magnetic contribution ($\Delta B$) to $B$. The measured values of $\Delta \omega$ and $\Delta B$ are used to calculate the concentration dependence of $\frac{d{T}_N}{\mathrm{dp}}$. It decreases rapidly with Al concentration in the range $2<c<\mathrm{}4\mathrm{}$ at.% Al where the absence of resistivity anomalies at $T_N$ previously precluded the direct determination of $\frac{d{T}_N}{\mathrm{dp}}$.