Although the TM-Si-C ternary compounds are promising advanced ceramics, the solution mechanism of C element in TM-Si matrix is entirely unclear. In particular, the influence of C on the mechanical properties of TM-Si matrix is no clear. To solve the problem, we apply the first-principles calculations to study the occupied mechanism of C in TM 5 Si 3 silicides. In addition, the influence of C element on the mechanical properties of TM 5 Si 3 is further studied. Here, two typical TM 5 Si 3 phases: D8 l -Ta 5 Si 3 and D8 m -Mo 5 Si 3 are considered. For C-doping, six C interstitial sites,
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