Correlation between the composition-dependent properties and phase stability of ${\mathrm{Co}}_{2}Y\text{Ga}(Y=\text{Cr},\text{V})$ shape-memory alloys from first-principles study

The composition-dependent properties and phase stability of ${\mathrm{Co}}_{2}Y\text{Ga}(Y=\text{Cr},\text{V})$-based shape-memory alloys are investigated by using the first-principles exact muffin-tin-orbital method in combination with the coherent potential approximation. It is shown that both ${\mathrm{Co}}_2\mathrm{CrGa}$ and ${\mathrm{Co}}_2\mathrm{VGa}$ alloys possess $L{2}_1$ structures at the ferromagnetic (FM) state but tetragonal structures at the paramagnetic (PM) state. In off-stoichiometric ${\mathrm{Co}}_{2}Y\mathrm{Ga}$ alloys, the excess Ga atom has a strong tendency to take the $Y$ sublattice, whereas the excess Co atom tends to take the $Y$ site in the FM $L{2}_1$ phase when $Y=\text{Cr}$ but the Ga site in the other phases when $Y=\text{V}$. The off-stoichiometric Cr78 and Cr79 alloys can occur in the normal martensitic transformation (MT) at the PM state but the reentrant martensitic transformation (RMT) at the FM state, whereas only the normal MT is obtained in the V50 and V15 alloys, where the small difference of the magnetization between the austenite and martensite is supposed to suppress the RMT. In all four groups of off-stoichiometric alloys, the correlation between the composition-dependent properties with the experimental $T_M$ values for the normal MT has been established. In the Cr78 and Cr79 alloys, $T_M$ for the RMT is also predicted to decrease with increasing $e/a$. The PM ordering tends to soften the elastic constants of all these $L{2}_1$ alloys. In the four groups of FM $L{2}_1$ alloys, $C^{\prime },G,E,\mathrm{\Theta }$, and G/B decrease whereas $A$ increases with increasing $e/a$, which favors $T_M$ for their RMT decreasing but that for their normal MT increasing with $e/a$. The composition dependence of the MT of these alloys could be explained from their minority density of states around the Fermi level of the $L{2}_1$ phase by means of the Jahn-Teller effect.

Figure 1

Electronic total energy change $\left(\mathrm{\Delta }E\right)$ with respect to the tetragonal lattice distortion (c/a) of ${\mathrm{Co}}_{2}Y\mathrm{Ga}(Y=$ Sc, Ti, V, Cr, Mn, Fe, Ni, and Cu) alloys with both the FM (a) and PM (b) states. The energy of the $L{2}_1$ structure is taken as reference in each FM and PM alloy.

Figure 2

Electronic total energy change $\left(\mathrm{\Delta }E\right)$ with respect to $c/a$ of the four groups of FM and PM off-stoichiometric alloys: $\text{Cr}78\left({\mathrm{Co}}_x{\mathrm{Cr}}_{78-x}{\mathrm{Ga}}_{11}{\mathrm{Si}}_{11},48\le x\le 56\right),\text{Cr}79\left({\mathrm{Co}}_x{\mathrm{Cr}}_{79-x}{\mathrm{Al}}_{10.5}{\mathrm{Si}}_{10.5},53\le x\le 57\right),\text{V}50\left({\mathrm{Co}}_x{\mathrm{V}}_{50-0.5x}{\mathrm{Ga}}_{50-0.5x},56\le x\le 64\right)$, and $\text{V}15\left({\mathrm{Co}}_{64}{\mathrm{V}}_{15}{\mathrm{Si}}_{21-x}{\mathrm{Ga}}_x,4\le x\le 12\right)$. Here, both results calculated with the normal and the abnormal but stable site occupations corresponding to the Co-rich alloys are presented. The energy of the FM $L{2}_1$ phase evaluated with the normal site occupation is a reference for each composition.

Figure 3

Equilibrium volume $\left(V\right)$ of the $L{2}_1$ phase (a), c/a of the tetragonal phase (b), ${\mu }_{\text{tot}}^{L{2}_1}$ and ${\mu }_{\text{tot}}^{\text{Tet}}$ (c), the electronic total energy difference between the FM state of the martensite and austenite $(-\mathrm{\Delta }{E}_{\text{FF}}^{\text{AM}})$ and that between the PM state of the austenite and martesnite $\left(\mathrm{\Delta }{E}_{\text{PP}}^{\text{AM}}\right)$ (d), and the experimental $T_M$ values (e) of the $\text{Cr}78\left(48\le x\le 56\right),\text{Cr}79\left(53\le x\le 57\right),\text{V}50\left(56\le x\le 64\right)$, and $\text{V}15\left(4\le x\le 12\right)$ alloys as a function of e/a. The cited experimental $V$ and c/a data are from Refs. [3, 7, 9, 58], and the experimental $T_M$ values are from Refs. [4, 5, 7, 9].

Figure 4

e/a dependence of the static tetragonal shear elastic constant $\left(C^{\prime }=(C_{11}-C_{12})/2\right)$ (a), shear modulus $\left(G\right)$ (b), Young modulus $\left(E\right)$ (c), Debye temperature $\left(\mathrm{\Theta }\right)$ (d), elastic anisotropy $\mathrm{[}A=2C_{44}/(C_{11}-C_{12}\left)\right]$ (e), and G/B (f) of the FM $L{2}_1$ phase of $\text{Cr}78\left(48\le x\le 56\right),\text{Cr}79\left(53\le x\le 57\right),\text{V}50\left(56\le x\le 64\right)$, and $\text{V}15\left(4\le x\le 12\right)$ alloys.

Figure 5

Total density of states (DOS) of the FM and PM $L{2}_1$ and tetragonal $\text{Cr}78(x=48$ (a) and 56 (b)), $\text{Cr}79\mathrm{[}x=53$ (c) and 57 (d)], $\text{V}50\mathrm{[}x=56$ (e) and 64 (f)], and $\text{V}15\mathrm{[}x=4$ (g) and 12 (h)] alloys. The vertical lines indicate the Fermi level.