  Using elastic neutron scattering on single crystals of MoTe$_{2}$ and
Mo$_{1-x}$W$_{x}$Te$_{2}$ ($x \lesssim 0.01$), the temperature dependence of
the recently discovered T$_{d}^{*}$ phase, present between the low temperature
orthorhombic T$_{d}$ phase and high temperature monoclinic 1T$^{\prime}$ phase,
is explored. The T$_{d}^{*}$ phase appears only on warming from T$_{d}$ and is
observed in the hysteresis region prior to the 1T$^{\prime}$ transition. This
phase consists of four layers in its unit cell, and is constructed by an "AABB"
sequence of layer stacking operations rather than the "AB" and "AA" sequences
of the 1T$^{\prime}$ and T$_{d}$ phases, respectively. Though the T$_{d}^{*}$
phase emerges without disorder on warming from T$_{d}$, on cooling from
1T$^{\prime}$ diffuse scattering is observed that suggests a frustrated
tendency toward the "AABB" stacking.
