First-principle study on effects of Zn-doping on electronic structure, magnetism and martensitic transformation of Heusler type MSMAs Ni2FeGa1–xZnx (x = 0–1)
Fund Project:Project supported by the Natural Science Foundation of Hebei Province, China (Grant Nos. E2018202097, E2019202143)
Received Date:21 December 2020
Accepted Date:05 February 2021
Available Online:28 June 2021
Published Online:05 July 2021
Abstract:The magnetic shape memory alloys (MSMAs) have both martensitic transformation and ferromagnetism in the same material, thus external magnetic field can be used to induce/control the phase transformation or the reorientation of martensite variant. MSMAs have received considerable attention for their interesting properties and wide applications in different fields. For practical applications, the martensitic transformation temperature TM is an important factor and a high TM is preferable. Recently, Zn-doping has been found to be a possible way to elevate the value of TM of Ni-Mn based MSMA, but this effect on other kinds of MSMAs is not very clear yet. Heusler alloy Ni2FeGa is a typical MSMA with unique properties, however, its TM is relatively low. So it can be meaningful to find possible ways to increase its phase transition temperature. In this paper, the influences of Zn-doping on the electronic structure, martensitic transformation and magnetic properties of Heusler-type magnetic shape memory alloy Ni2FeGa are investigated by first-principle calculations. Total energy calculation and charge density difference indicate that Zn atom prefers to occupy the Ga (D) site when substituting for Ga in Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1). This main-group-element-like behavior is related to the closed 3d shell of Zn. Due to the similar atomic radii of Ga and Zn, Zn-doping does not lead the lattice constant to change greatly. The variation of the energy difference ΔEM between the martensite and austenite with Zn content increasing is calculated, and the result shows that ΔEM increases with Zn-doping increasing, and thus conducing to increasing the stability of the martensite phase and to evaluating the transformation temperature TM in Ni2FeGa1–xZnx. This trend can be explained by the Jahn-Teller effect observed in the DOS structure. The Zn-doping does not change the magnetic structure of Ni2FeGa. A ferromagnetic coupling between Fe spin moment and Ni spin moment can be observed within the whole range studied. The calculated total spin moment increases with Zn content increasing. The variation of formation energy Ef with Zn-doping is investigated. In Ni2FeGa1–xZnx a negative Ef is retained within the whole range studied, though it increases slightly with the doping of Zn. It is also found that the Zn-doping can increase the stability of L21 Heusler phase in Ni2FeGa1–xZnx and suppress the formation of the FCC L12 phase. Keywords:Heusler alloys/ magnetic shape memory alloys/ electronic structure/ martensitic transformation
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3.结果与讨论Heusler合金的物性与合金中的原子占位和有序度密切相关, 因此首先通过结构优化对Zn在Ni2FeGa1–xZnx中的择优占位进行讨论. 在Heusler合金X2YZ的立方晶格中, 有四个不同的晶体学位置, 分别标记为A(0, 0, 0), B(0.25, 0.25, 0.25), C(0.5, 0.5, 0.5)和D(0.75, 0.75, 0.75). 其中A, B和C位置被过渡金属元素X和Y如Fe、Co等占据, 而D位置被主族元素Z如Ga等占据. 已经发现, Heusler合金存在两种可能的高有序结构: L21和XA. 在L21结构中, 两个相同的X原子占据等效的A和C晶位; 而在XA结构中, 两个X原子分别占据A和B位, Y, Z原子分别位于C和D位. 具体到Ni2FeGa, 理论和实验研究均表明其具有L21结构[5], 两个Ni原子进入A, C晶位, 一个Fe原子进入B位. 主族元素Ga占据D位. 这与Heusler合金中的“价电子数规则”, 即具有较多价电子的过渡金属原子优先占据A和C位是一致的[23]. 在Ni2FeGa1–xZnx中用Zn代替Ga时, Zn存在两种可能的占位方式: 一种是Zn直接进入所取代Ga的D位, 另一个是考虑到Zn价电子数较多, 可能优先进入A/C位, 而原本此晶位的Ni原子进入D位. 图1给出了Ni2FeGa1–xZnx结构优化的结果. 对于未掺杂的Ni2FeGa, L21和XA结构之间的能量差为–0.11 eV/f.u., 与前面的讨论一致. 在此基础上, 掺杂的Zn原子进入D位的总能量始终低于进入C位的情况, 表明这是一种更稳定的结构, 也说明Ni2FeGa1–xZnx在整个研究范围内都保持了L21结构. 之前有文献报道, Zn在Heusler合金中表现出了类主族元素的行为[16], 本研究中Zn对D晶位的择优占位支持了这一结论, 这主要与Zn具有全满的闭合3d壳层有关(3d104s2). 图 1 计算得到的Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1)合金总能量与晶格常数的关系曲线, 其中Zn(C)和Zn(D)分别表示Zn进入C和D晶位 Figure1. Calculated total energies of Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1) as functions of lattice constant. Here Zn (C) and Zn (D) indicate that Zn enters the C and D sites, respectively.
Heusler合金原子占位与晶格中各原子之间的价电子杂化和成键特性密切相关. 为了进一步讨论Zn的择优占位及其原因, 计算比较了XA和L21型Ni2FeZn在(110)面上的差分电荷密度(charge density difference, CDD)[24], 结果在图2中给出. 图 2 Ni2FeZn合金XA(左)和L21(右)结构在(110)面上的差分电荷密度 Figure2. The charge density difference on the (110) plane of Ni2FeZn alloy with XA (left) and L21 (right) structures.
表1计算得到的Ni2FeGa1–xZnx(x = 0, 0.25, 0.5, 0.75, 1)合金立方奥氏体相的平衡晶格常数a, 形成能Ef和磁性参数 Table1.The calculated equilibrium lattice constant a, formation energy Ef and magnetic properties of Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1) alloys in cubic austenitic state.
Heusler合金中的马氏体相变可以通过四方畸变后Heusler合金的基态总能量变化来预测[28]. 为了简化计算, 这里假设相变前后奥氏体和马氏体相的晶胞体积保持不变, 这也是Heusler型磁性形状记忆合金计算中常用的手段[29]. 关于计算的更多详细信息可以见参考文献[30, 31]. 当晶格四方畸变(c/a ≠ 1)后, 总能量将随c/a比值的变化而改变, 可以此确定四方马氏体的能量最小值和平衡晶格常数并得到马氏体和奥氏体相之间的能量差ΔEM, 用来预测Heusler合金中可能的马氏体相变[32,33]. 当ΔEM为负值时, 表明马氏体相的能量低于奥氏体且更稳定, 从而可能发生立方到四方相的转变. 在具有相似成分的一系列合金中, ΔEM的绝对值越大, 则马氏相具有越高的稳定性, 也将具有更高的马氏体相变温度TM. 图3给出了Ni2FeGa1–xZnx(x = 0, 0.25, 0.5, 0.75, 1)合金马氏体与奥氏体相能量差ΔEM随c/a值的变化. 计算得到的ΔEM等具体数据在表2中列出. 在Ni2FeGa1–xZnx合金的ΔEM-c/a曲线中, c/a > 1和c/a < 1时, 都存在一个能量的极小值, 而能量的最小值位于c/a > 1一侧, 这表明Ni2FeGa1–xZnx晶胞在马氏体相变后倾向于c轴伸长而a, b轴收缩. 随着Zn含量的增大, Ni2FeGa1–xZnx的ΔEM的绝对值呈现出单调增加的趋势. 当x = 0时, Ni2FeGa的ΔEM为–0.11 eV/f.u., 而x = 1时Ni2FeZn的ΔEM变为–0.15 eV. 这表明Zn的掺杂有利于增加马氏体相的稳定性并提高相变温度TM, 这与之前文献报道的Zn在Ni2MnGa和Mn2NiGa中所起作用是一致的[16], 也表明Zn取代主族元素作为一种提高Heusler型MSMA相变温度的“广谱”手段, 值得进一步深入研究. 图 3 Ni2FeGa1–xZnx中马氏体和奥氏体相能量差ΔEM随c/a比值的变化关系. 在图中, 零点对应于每种合金的立方奥氏体能量(c/a = 1) Figure3. Variation of the energy difference ΔEM between the martensitic and austenitic phase with the c/a ratio in Ni2FeGa1–xZnx. Here the zero point corresponds to the cubic austenite (c/a = 1) of each alloy.
x
0.00
0.25
0.5
0.75
1.00
ΔEM/(eV·f.u.–1)
–0.110
–0.119
–0.128
–0.144
–0.151
c/a
1.36
1.36
1.34
1.33
1.32
Mt/(μB·f.u.–1)
3.38
3.48
3.63
3.73
3.85
MNi/μB
0.28
0.32
0.35
0.38
0.41
MFe/μB
2.92
3.00
3.02
3.06
3.11
MGa/μB
–0.11
–0.10
–0.08
–0.07
—
MZn/μB
—
–0.13
–0.11
–0.10
–0.09
表2计算得到的Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1)合金在马氏体状态下的马氏体与奥氏体之间能量差ΔEM, c/a比值和磁性参数 Table2.The calculated energy difference ΔEM between the martensite and austenite, c/a ratio and magnetic properties of Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1) alloys in tetragonal martensitic state.
在参考文献[30, 32]中, 已经发现对于成分相近的一系列Heusler型磁性形状记忆合金, 其马氏体相变温度TM与两相能量差ΔEM之间存在近似正比关系, 因此可以通过ΔEM的计算结果对材料的TM进行大致的推算. 在参考文献[18]中, 同样发现Zn掺杂后材料ΔEM的增加与实验观察到的TM的升高存在对应关系. 对于本文中的Ni2FeGa1–xZnx, 在x = 0.25时ΔEM相比x = 0时增加了约8%, 因此TM相比掺杂前的142 K可能有12 K左右的提高, 而当Ga全部取代Zn时, TM有可能达到195 K左右. 但是对于更具体的情况, 还需要后续开展实验研究加以确定. 为了深入讨论Zn掺杂影响合金马氏体相变的物理机理, 分别计算了Ni2FeGa1–xZnx (x = 0, 0.25, 0.5, 0.75, 1)在奥氏体和马氏体状态下的态密度(density of states, DOS), 并在图4中进行了比较. 图 4 Ni2FeGa1–xZnx奥氏体和马氏体相总态密度的对比 Figure4. Comparison between the total DOS of austenitic and martensitic type Ni2FeGa1–xZnx.