  Any of two or more two-dimensional (2D) materials with similar properties can
be alloyed into a new layered material, namely, 2D alloy. Individual monolayer
in 2D alloys are kept together by Van der Waals interactions. The property of
multilayer alloys is a function of their layer number. Here, we studied the
shear (C) and layer-breathing (LB) modes of Mo$_{0.5}$W$_{0.5}$S$_2$ alloy
flakes and their link to the layer number of alloy flakes. The study reveals
that the disorder effect is absent in the C and LB modes of 2D alloys, and the
monatomic chain model can be used to estimate the frequencies of the C and LB
modes. We demonstrated how to use the C and LB mode frequency to identify the
layer number of alloy flakes deposited on different substrates. This technique
is independent of the substrate, stoichiometry, monolayer thickness and complex
refractive index of 2D materials, offering a robust and substrate-free approach
for layer-number identification of 2D materials.
