The first-principle method based on the density functional theory is used to calculate the energy does change with the tetragonal distortions, the lattice constant, the magnetic moment, the electronic density of states and the bulk modulus of Hg2CuTi-type Mn2NiAl. The results show: i) In the process of the tetragonal distortions, there are two stable states near c/a≈1 and c/a≈1.24, corresponding to a austenitic phase and a martensitic phase, respectively.ii) In the austenitic phase and martensitic phase, Mn atoms are the main providers to the magnetism in Mn2NiAl, it shows ferrimagnetic structure for Mn atoms of A lattice position and B lattice position. iii) In the austenitic phase and martensitic phase, the Mn (A) atom or Mn (B) atom can produce more magnetic moment, it derives from a more spin-splitting between the majority-spin and minority-spin states. The direct d-d exchange interaction are weak between Mn atoms of different lattice position, so can hold the antiferromagnetic coupling between them, and that the ferromagnetic coupling is sustained by the indirect exchange interaction by way of s electron of Al atom between Mn atoms of identical lattice position, it is the cause of the Mn2NiAl alloys show ferrimagnetism. ⅳ) The resistance to compression of Mn2NiAl are smaller than Ni2MnGe, Ni2MnGa and Ni2MnB.%基于密度泛函理论架构下的第一性原理方法,对Hg2CuTi型Mn2NiAl的能量随四方变形的变化、晶格常数、磁矩、电子态密度、体弹模量等进行了计算.结果表明:i)在四方变形过程中,在c/a接近1及1.24附近各存在一个稳定的状态,分别对应于奥氏体态和马氏体态.ii)在奥氏体和马氏体两态下,Mn2NiAl的总磁矩主要是由Mn原子提供,A、B晶位Mn原子的磁矩呈现为亚铁磁结构.iii)在奥氏体和马氏体两态下,Mn(A)或Mn(B)原子自旋向上和自旋向下的态密度形成较大的自旋劈裂,产生较大的磁矩.处于不同晶位的两个Mn原子之间的d-d直接交换作用较弱,维持了它们之间的反铁磁耦合,而处于同一晶位的Mn原子之间的铁磁耦合是由Al原子的s电子为媒介的间接交换作用来维持,此即为Mn2NiAl亚铁磁结构形成的机制.iv)Mn2NiAl的抗压缩性比Ni2MnGe,Ni2MnGa和Ni2MnB的均小.
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