Ab initio modeling of TWIP and TRIP effects in $$\beta$$-Ti alloys

Abstract Transformations in bcc- $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> , hcp- $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> , and the $$\omega$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ω</mml:mi> </mml:math> phases of Ti alloys are studied using density functional theory for pure Ti and Ti alloyed with Al, Si, V, Cr, Fe, Cu, Nb, Mo, and Sn. The $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> -stabilization caused by alloying Si, Fe, Cr, and Mo was observed, but the most stable phase appears between the $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> and the $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> phases, corresponding to the martensitic $$\alpha ''$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup> <mml:mi>α</mml:mi> <mml:mrow> <mml:mo>′</mml:mo> <mml:mo>′</mml:mo> </mml:mrow> </mml:msup> </mml:math> phase. Next, the $$\{112\}\langle 11\bar{1}\rangle$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>112</mml:mn> <mml:mo>}</mml:mo> <mml:mo>⟨</mml:mo> <mml:mn>11</mml:mn> <mml:mover> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> bcc twins are separated by a positive barrier, which further increases by alloying w.r.t. pure Ti. The $$\{332\}\langle 11\bar{3}\rangle$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mo>{</mml:mo> <mml:mn>332</mml:mn> <mml:mo>}</mml:mo> <mml:mo>⟨</mml:mo> <mml:mn>11</mml:mn> <mml:mover> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mo>⟩</mml:mo> </mml:mrow> </mml:math> twinning yields negative barriers for all species but Mo and Fe. This is because the transition state is structurally similar to the $$\alpha$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>α</mml:mi> </mml:math> phase, which is preferred over the $$\beta$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>β</mml:mi> </mml:math> phase for the majority of alloying elements. Lastly, the impact of alloying on twin boundary energies is discussed. These results may serve as design guidelines for novel Ti-based alloys with specific application areas. Graphical Abstract