Electron-phonon scattering times in crystalline disordered titanium alloys between 3 and 15 K

We have successfully fabricated bulk crystalline disordered titanium alloys (Ti_1-xSnₓ,{Ti}_{1{-}x}{Ge}ₓ,$and ${Ti}_{0.97{-}x}{Sn}0.03{Sc}ₓ$) with nominal concentration $x$ of the order of a few at. %. The impurity atoms are gradually introduced into a titanium host to tune the degree of disorder, resulting in residual resistivities ${{ρ}}₀$ varying from ${≈}$ 40 to 160 ${μ}{Ω}cm$ (corresponding to values of ${k}Fl{≈}5--20$, with ${k}F$ being the Fermi wave number and $l$ being the electron elastic mean free path). With this wide range of experimentally accessible ${{ρ}}₀$, we are able to perform systematic studies of the disorder ${{ρ}}₀$, or electron elastic mean free path $l$, behavior of the electron-phonon scattering time ${{τ}}ₚₕ.$ We have measured the magnetoresistivities of these alloys between 3 and 15 K, and compared our results with weak-localization theoretical predictions to extract ${{τ}}ₚₕ(T,l)$. Unexpectedly, we obtain a rather diversified temperature dependence and disorder dependence of ${{τ}}ₚₕ$ as follows. (a) In ${Ti}_{1{-}x}{Sn}ₓ$ alloys with ${{ρ}}₀{}100$ ${μ}{Ω}{{0ex}{0ex}}cm$ we find $1/{{τ}}ₚₕ{~}{T}²/l$. (b) In ${Ti}_{1{-}x}{Sn}ₓ$ alloys with ${{ρ}}₀{}70$ ${μ}{Ω}$ cm we find $1/{{τ}}ₚₕ{~}{T}³/l$. (c) In ${Ti}_{1{-}x}{Ge}ₓ$ alloys with $50{}{{ρ}}₀{}130$ ${μ}{Ω}$ cm we find $1/{{τ}}ₚₕ{~}{T}³$ in some alloys and $1/{{τ}}ₚₕ{~}{T}⁴$ in others, while at a given temperature $1/{{τ}}ₚₕ$ is essentially independent of disorder. (d) In ${Ti}_{0.97{-}x}{Sn}0.03{Sc}ₓ$ alloys with $55{}{{ρ}}₀{}75$ ${μ}{Ω}$ cm we obtain $1/{{τ}}ₚₕ{~}{T}²$. These experimental observations altogether imply that electron-phonon interactions in the presence of strong impurity scattering are very sensitive to the local material environment (the microscopic quality) of a particular sample system, which might be variously modulated with the doping of different kinds of impurity atoms. Our results are compared with existing theoretical predictions for electron-phonon scattering in disordered conductors.