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Recent studies on the constituent binaries of common NiTi-based shape memory alloys (NiTi, NiZr, NiHf, PdTi, PtTi) have led to questions regarding the accuracy of current phase diagrams, including the existence of theoretical phases, and the atomistic nature of stability in observed martensitic and austenitic phases. These issues are investigated here with ab initio molecular dynamics. Theoretically identified ground state structures are found to become mechanically unstable well below room temperature, while the experimentally determined martensite structures are found to be stabilized by anharmonic effects at elevated temperatures. The martensite phases of all binaries are found to transition to a common austenite structure (cubic B2), with transition temperatures in agreement with available experiments. Interestingly, the B2 structures are unstable at low temperature but are stabilized by large anharmonic …