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Ni2–based Heusler alloys have received increasing attention due to their shape memory effects and the relevant application properties. It is interesting to explore new Ni2–based shape memory alloys with novel properties. In this work, the site preference, electronic structure, elastic parameters and martensitic transformation of new Ni2Cu-based Heusler alloys Ni2CuZ (Z = Al, Ga, In, Si, Ge, Sn and Sb) are investigated theoretically. Between the two highly-ordered structures of Heusler alloys, Ni2CuZ alloy tends to crystallize in the L21 structure with Cu atom entering the B site in the cubic lattice. In contrast, the XA structure is higher in energy and lower in stability. This is different from the usual rule that transition metal atoms with more valence electrons tend to occupy the A, C sites at first and can be related to the strong covalent hybridization between Ni and main group elements Z in L21 type Ni2CuZ. Ni2CuZ martensites are all lower in energy than the corresponding austenites, which makes them candidates for shape memory alloys. This can be explained by the Jahn-Teller effect characterized by the reduced states near EF in the DOS structure and the mechanical instability of the cubic austenite lattice. The martensite-austenite energy difference ΔEM is strongly influenced by main group elements Z. When Z are in the same group, the ΔEM increases with their atomic number increasing, but when Z are in the same period, an opposite trend is observed. The ΔEM can be regarded as a driving force for the martensitic transformation: a larger ΔEM corresponds to a higher martensitic transformation TM. In Heusler alloys, electron concentration e/a and electron density n are usually used to discuss the variation of TM. An increase of e/a or n tends to increase TM. However, this is in discrepancy with the results in Ni2CuZ, which can be explained by using, the new factors, the negative shear modulus $ C' $ and softening of the elastic constant C44 and their variations with Z elements. These results reveal the close relation between the martensitic transformation and mechanical parameters and indicate that they are important factors to predict new shape memory alloys and analyse their properties in Heusler alloys. It is also found that the Young’s modulus and shear modulus increase and Poisson’s ratio decreases after the martensitic transformation. Thus, the Ni2CuZ martensite has higher stiffness and rigidity but lower ductility than the austenite. -
图 1 Ni2CuAl合金L21与XA晶体结构的示意图
Figure 1. Crystal structure diagrams of L21 and XA type Ni2CuAl.
图 2 L21与XA结构Ni2CuZ的总能量随晶格常数的变化关系. 曲线中能量零点为各成分L21结构的基态能量
Figure 2. Variation of total energy with lattice constant for L21 and XA type Ni2CuZ alloys. Ground state total energy of the L21 structure is set as the zero point of each curve.
图 3 L21与XA结构Heusler合金的电荷差分密度对比 (a) Ni2CuSi; (b) Ni2CuGe; (c) Ni2CuSn
Figure 3. CDD plots of Heusler alloys with L21 and XA structure: (a) Ni2CuSi; (b) Ni2CuGe; (c) Ni2CuSn.
图 4 Ni2CuZ合金马氏体相的结构优化曲线, 图中各曲线零点为对应成分的立方奥氏体能量($ {c {/ } a} = 1 $)
Figure 4. Structural optimization results of different Ni2CuZ martensite, the zero point of each curve is set as the total energy of the corresponding austenite state.
图 5 Ni2CuZ合金的马氏体与奥氏体能量差ΔEM, 价电子浓度e/a, 电子密度n以及合金奥氏体弹性参数$ C' $与C44随主族元素Z的变化关系
Figure 5. Variation of ΔEM, valence electron concentration e/a, electron density n, and mechanical parameters $ C' $ and C44 with main group element Z in Ni2CuZ alloys.
图 6 Ni2CuZ合金奥氏体(a)与马氏体(b)的态密度; (c)两者在费米能级附近态密度的对比
Figure 6. Calculated DOS of Ni2CuZ austenite (a) and martensite (b); (c) compares the enlargement of the austenite and martensite DOS around EF.
表 1 计算得到的L21型Ni2CuZ合金的平衡晶格常数a, 各弹性参数以及L21与XA两结构的能量差ΔE
Table 1. Equilibrium lattice constant a, total energy difference ΔE between the L21 and XA structure and mechanical properties of L21 type Ni2CuZ alloys.
成分 a/Å ΔE/(eV·f.u.–1) C11/GPa C12/GPa C44/GPa B/GPa G/GPa E/GPa ν B/GV Ni2CuAl 5.72 –0.29 145.9 176.3 124.3 166.1 11.0 32.4 0.47 2.42 Ni2CuGa 5.73 –0.28 150.2 181.0 109.6 170.7 5.4 16.0 0.48 2.87 5.75* — 141.3* 177.8* 110.4* 165.6* –0.81* — 0.34* 2.78* Ni2CuIn 6.00 –0.20 123.9 149.5 88.8 140.9 3.8 11.4 0.49 2.93 Ni2CuSi 5.63 –0.46 192.8 195.6 93.8 194.6 26.1 74.9 0.44 3.49 Ni2CuGe 5.74 –0.40 167.9 171.5 92.8 170.3 25.1 71.9 0.43 3.10 Ni2CuSn 5.99 –0.33 143.3 149.7 89.4 147.6 21.9 62.8 0.43 2.82 Ni2CuSb 5.99 –0.45 149.9 148.2 76.3 148.8 24.1 68.7 0.42 3.23 注: *数据引自参考文献[25] 
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表 2 计算得到的Ni2CuZ马氏体的晶格常数V与c/a, 价电子浓度e/a, 电子密度n和马氏体与奥氏体能量差ΔEM
Table 2. Equilibrium lattice parameters V and c/a, valence electron concentration e/a, electron density n and energy difference ΔEM calculated for Ni2CuZ martensite.
成分 V/Å3 c/a e/a n/Å–3 ΔEM/(eV·f.u.–1) Ni2CuAl 187.15 1.24 8.50 0.727 –0.082 Ni2CuGa 188.13 1.26 8.50 0.723 –0.090 Ni2CuIn 216.00 1.28 8.50 0.630 –0.101 Ni2CuSi 178.45 1.28 8.75 0.785 –0.032 Ni2CuGe 189.12 1.30 8.75 0.740 –0.047 Ni2CuSn 214.92 1.30 8.75 0.650 –0.049 Ni2CuSb 214.92 1.18 9.00 0.670 –0.003
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表 3 计算得到的Ni2CuZ马氏体相的弹性参数
Table 3. Calculated mechanical parameters of Ni2CuZ martensite.
成分 C11/GPa C33/GPa C44/GPa C66/GPa C12/GPa C13/GPa B/GPa G/GPa E/GPa ν Ni2CuAl 243.3 196.1 118.9 86.4 100.9 148.6 164.3 71.4 187.1 0.31 Ni2CuGa 236.8 198.2 104.1 76.7 112.5 150.6 166.6 64.8 172.1 0.33 Ni2CuIn 194.6 178.8 80.2 65.4 104.8 126.2 142.5 54.1 144.2 0.33 Ni2CuSi 232.9 234.5 95.8 83.9 155.7 165.4 186.0 63.0 169.7 0.35 Ni2CuGe 220.8 203.7 77.1 69.2 135.3 157.5 171.7 51.9 141.3 0.36 Ni2CuSn 189.8 176.7 77.8 42.7 83.6 123.8 134.8 49.3 131.7 0.34 Ni2CuSb 217.3 153.1 76.6 16.1 79.9 147.3 148.4 28.7 81.0 0.41
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