Abstract <p>Transformations in bcc-<InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>, hcp-<InlineEquation ID="IEq4"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation>, and the <InlineEquation ID="IEq5"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq5.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\omega$</EquationSource> <EquationSource Format="MATHML"><math> <mi>ω</mi> </math></EquationSource> </InlineEquation> 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 <InlineEquation ID="IEq6"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation>-stabilization caused by alloying Si, Fe, Cr, and Mo was observed, but the most stable phase appears between the <InlineEquation ID="IEq7"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> and the <InlineEquation ID="IEq8"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> phases, corresponding to the martensitic <InlineEquation ID="IEq9"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq9.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="21" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha ''$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>α</mi> <mrow> <mo>′</mo> <mo>′</mo> </mrow> </msup> </math></EquationSource> </InlineEquation> phase. Next, the <InlineEquation ID="IEq10"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq10.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">$\{112\}\langle 11\bar{1}\rangle$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mn>112</mn> <mo stretchy="false">}</mo> <mo stretchy="false">⟨</mo> <mn>11</mn> <mover accent="true"> <mrow> <mn>1</mn> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation> bcc twins are separated by a positive barrier, which further increases by alloying w.r.t. pure Ti. The <InlineEquation ID="IEq11"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq11.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="84" /> </InlineMediaObject> <EquationSource Format="TEX">$\{332\}\langle 11\bar{3}\rangle$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">{</mo> <mn>332</mn> <mo stretchy="false">}</mo> <mo stretchy="false">⟨</mo> <mn>11</mn> <mover accent="true"> <mrow> <mn>3</mn> </mrow> <mrow> <mo stretchy="false">¯</mo> </mrow> </mover> <mo stretchy="false">⟩</mo> </mrow> </math></EquationSource> </InlineEquation> twinning yields negative barriers for all species but Mo and Fe. This is because the transition state is structurally similar to the <InlineEquation ID="IEq12"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq4.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="14" /> </InlineMediaObject> <EquationSource Format="TEX">$\alpha$</EquationSource> <EquationSource Format="MATHML"><math> <mi>α</mi> </math></EquationSource> </InlineEquation> phase, which is preferred over the <InlineEquation ID="IEq13"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="43578_2025_1657_Article_IEq1.gif" Format="GIF" Height="17" Rendition="HTML" Resolution="72" Type="Linedraw" Width="15" /> </InlineMediaObject> <EquationSource Format="TEX">$\beta$</EquationSource> <EquationSource Format="MATHML"><math> <mi>β</mi> </math></EquationSource> </InlineEquation> 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.</p> Graphical Abstract <p></p>

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

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2025年8月4日

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David Holec,
Johann Grillitsch,
José L. Neves,
David Obersteiner,
Thomas Klein

摘要

Abstract

Transformations in bcc- $\beta$ $β$ , hcp- $\alpha$ $α$ , and the $\omega$ $ω$ 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 $\beta$ $β$ -stabilization caused by alloying Si, Fe, Cr, and Mo was observed, but the most stable phase appears between the $\beta$ $β$ and the $\alpha$ $α$ phases, corresponding to the martensitic $\alpha ''$ $α^{''}$ phase. Next, the $\{112\}\langle 11\bar{1}\rangle$ ${112} ⟨ 11 \bar{1} ⟩$ bcc twins are separated by a positive barrier, which further increases by alloying w.r.t. pure Ti. The $\{332\}\langle 11\bar{3}\rangle$ ${332} ⟨ 11 \bar{3} ⟩$ twinning yields negative barriers for all species but Mo and Fe. This is because the transition state is structurally similar to the $\alpha$ $α$ phase, which is preferred over the $\beta$ $β$ 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

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

摘要