| Summary: | The crystal structures and martensitic transformation of Ti<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mn>50</mn></msub></semantics></math></inline-formula>Ni<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mrow><mn>50</mn><mo>−</mo><mi>x</mi></mrow></msub></semantics></math></inline-formula>Pt<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mrow></mrow><mi>x</mi></msub></semantics></math></inline-formula> alloys (<i>x</i> = 0, 6.25, 8.33, 10.42, 12.5, 18.75, 25) were studied by means of density functional theory (DFT). The computational results indicate that the lattice parameters of Ti-Ni-Pt alloys continuously increase with increasing the Pt content. It is found that at ≤ 12.5 at.% Pt, the martensite structure is monoclinic B19<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>′</mo></msup></semantics></math></inline-formula> phase, and the energy differences between parent and martensite phases (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>E</mi></mrow></semantics></math></inline-formula>) decrease slightly with a minimum observed at 6.25 at.% Pt. However, when the Pt content is increased to around 15 at.%, the most stable martensite phase is the orthorhombic B19 structure, and the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>E</mi></mrow></semantics></math></inline-formula> increases sharply with Pt concentration. It was found that the phase transition temperatures are closely related to the energy differences <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>E</mi></mrow></semantics></math></inline-formula> between parent and martensite phases. The electronic structures of martensite B19 and B19<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>′</mo></msup></semantics></math></inline-formula> phases are also discussed.
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