Switching the soft shearing mode orientation in Ni–Mn–Ga non-modulated martensite by Co and Cu doping
Lucie Bodnárová, Martin Zelený, Petr Sedlák, Ladislav Straka, Oleg Heczko, A. Sozinov, Hanuš Seiner
Abstract
Abstract Resonant ultrasound spectroscopy measurements and density functional theory calculations were used to analyze the effect of Co and Cu doping (3–6 at. %) on elastic constants of non-modulated martensite of the Ni–Mn–Ga ferromagnetic shape memory alloy. Due to the doping, the studied alloys exhibited decreased tetragonal ratios c / a ≈ 1.14. Both the experiments and the calculations revealed that the lowering of the c / a ratio resulted in a change of the orientation of the softest shearing modes of the tetragonal lattice. The newly appearing softest shearing modes for the doped materials have approximately <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">{</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>a</mml:mi> <mml:mspace width="0.33em"/> <mml:mspace width="0.33em"/> <mml:mn>0</mml:mn> <mml:mspace width="0.33em"/> <mml:mspace width="0.33em"/> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>c</mml:mi> <mml:mo stretchy="false">}</mml:mo> <mml:msub> <mml:mrow/> <mml:mrow> <mml:mi>bct</mml:mi> </mml:mrow> </mml:msub> <mml:mo stretchy="false">〈</mml:mo> <mml:mo>−</mml:mo> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>a</mml:mi> <mml:mspace width="0.33em"/> <mml:mspace width="0.33em"/> <mml:mn>0</mml:mn> <mml:mspace width="0.33em"/> <mml:mspace width="0.33em"/> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo stretchy="true">/</mml:mo> </mml:mrow> <mml:mi>c</mml:mi> <mml:msub> <mml:mrow> <mml:mo stretchy="false">〉</mml:mo> </mml:mrow> <mml:mrow> <mml:mi>bct</mml:mi> </mml:mrow> </mml:msub> </mml:math> orientations and indicate a lattice instability directly related to the particularly low twinning stress for compound <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">{</mml:mo> <mml:mn>101</mml:mn> <mml:mo stretchy="false">}</mml:mo> <mml:mo stretchy="false">〈</mml:mo> <mml:mover accent="true"> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:mo>¯</mml:mo> </mml:mrow> </mml:mover> <mml:mn>01</mml:mn> <mml:mo stretchy="false">〉</mml:mo> </mml:math> twins, needed for the magnetically induced reorientation.