The composition dependence of the structural transition between the monoclinic 1T$^{prime}$ and orthorhombic T$_{d}$ phases in the Mo$_{1-x}$W$_{x}$Te$_{2}$ Weyl semimetal was investigated by elastic neutron scattering on single crystals up to $x approx 0.54$. First observed in MoTe$_{2}$, the transition from T$_{d}$ to 1T$^{prime}$ is accompanied by an intermediate pseudo-orthorhombic phase, T$_{d}^{*}$. Upon doping with W, the T$_{d}^{*}$ phase vanishes by $x approx 0.34$. Above this concentration, a phase coexistence behavior with both T$_{d}$ and 1T$^{prime}$ is observed instead. The interlayer in-plane positioning parameter $delta$, which relates to the 1T$^{prime}$ $beta$ angle, decreases with temperature as well as with W substitution, likely due to strong anharmonicity in the interlayer interactions. The temperature width of the phase coexistence remains almost constant up to $x approx 0.54$, in contrast to the broadening reported under pressure.
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