The structural polymorphism in transition metal dichalcogenides (TMDs) provides exciting opportunities for developing advanced electronics. For example, MoTe$_2$ crystallizes in the 2H semiconducting phase at ambient temperature and pressure, but transitions into the 1T$^prime$ semimetallic phase at high temperatures. Alloying MoTe$_2$ with WTe$_2$ reduces the energy barrier between these two phases, while also allowing access to the T$_d$ Weyl semimetal phase. The MoWTe$_2$ alloy system is therefore promising for developing phase change memory technology. However, achieving this goal necessitates a detailed understanding of the phase composition in the MoTe$_2$-WTe$_2$ system. We combine polarization-resolved Raman spectroscopy with X-ray diffraction (XRD) and scanning transmission electron microscopy (STEM) to study MoWTe$_2$ alloys over the full compositional range x from 0 to 1. We identify Raman and XRD signatures characteristic of the 2H, 1T$^prime$, and T$_d$ structural phases that agree with density-functional theory (DFT) calculations, and use them to identify phase fields in the MoTe$_2$-WTe$_2$ system, including single-phase 2H, 1T$^prime$, and T$_d$ regions, as well as a two-phase 1T$^prime$ + T$_d$ region. Disorder arising from compositional fluctuations in MoWTe$_2$ alloys breaks inversion and translational symmetry, leading to the activation of an infrared 1T$^prime$-MoTe$_2$ mode and the enhancement of a double-resonance Raman process in 2H-MoWTe$_2$ alloys. Compositional fluctuations limit the phonon correlation length, which we estimate by fitting the observed asymmetric Raman lineshapes with a phonon confinement model. These observations reveal the important role of disorder in MoWTe$_2$ alloys, clarify the structural phase boundaries, and provide a foundation for future explorations of phase transitions and electronic phenomena in this system.
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