Mn基合金相变机制的理论研究
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摘要
金属Mn具有α,β,γ,和6四种结构,其中的面心立方结构γ相只有在温度处于1100-C到1140℃之间才能够稳定,通常可以采用合金化(加入Ni, Pd, Rh, Pt, Cu, Fe, Au等金属元素)来稳定γ相。Mn基合金近年来发展为一种新型的智能材料,可以用做重要的磁性部件。大多数Mn基合金(它们的3d轨道是接近半占据的)具有反铁磁性能,同时具有高的尼尔温度TN,因而可以用做自旋阀钉扎材料、巨磁电阻和隧道磁致电阻设备。MnX (X=Ni, Pd, Rh, Pt和Au)合金的低温反铁磁(AFM)结构是由高温的顺磁(PM)结构通过降温转变得到,过程包含马氏体相变及磁性相变,认识它们相变的理论机制有助于研发性能更加优越的磁性材料。本论文基于密度泛函理论(DFT)采用第一性原理方法对MnX(X=Ni,Pd,Rh,Pt,Au和Ir)合金的马氏体相变进行了系统的物理性质的研究,得到了以下创新性结果：
1.利用投影缀加平面波在广义梯度近似(GGA)和局域密度近似(LDA)下分别计算MnX (X=Ni, Pd, Rh, Pt, Au和Ir)体系的所有低温AFM-L10相的晶格结构,结果表明,GGA方法更适合我们研究的合金。以后的计算都采用PAW-GGA方法。首先,计算了PM-B2/L10相及AFM-L10相的晶格参数(晶格常数,原子内坐标,键角),计算结果与实验值比较接近。我们也首次得到MnIr/Pt的PM-B2相及MnIr的PM-L10相的晶格参数。第一性原理计算的总能大小顺序与实验所发现的相变顺序一致,表明用总能来预测相变是正确的。对于MnRh和MnPd、MnPt和MnAu合金,我们得到的总能能差与实验相变温度随合金的价电子总数变化的趋势基本是一致的,再一次表明我们用总能预测的相变顺序是合适的。
2.我们还用第一性原理方法首次计算了MnX(X=Ni, Pd,Rh,Pt和Au)合金体系的弹性常数、德拜温度、弹性模量、机械各向异性、泊松比和比热容。弹性常数的计算表明PM-B2相的弹性常数不满足稳定性标准,剪切模量C'的软化导致其发生四方畸变,会转变为四方结构,这从微观上首次解释了实验所发生的马氏体相变(PM-B2→PM-L10)的相变机理。AFM-L10目的弹性常数计算结果表明这两相是机械稳定的。低温AFM-L10相的德拜温度的计算结果与实验值符合的很好,说明我们计算的弹性常数是正确的。得到的弹性模量,各向异性及泊松比表明MnX (X=Ni, Rh和Ir)合金是脆性的,所有5种合金具有各向异性,并且在单轴变形时具有大的体积改变。AFM-L10相比热容的计算表明,在低温遵从德拜模型,高温接近杜隆-珀替极限。对于MnIr合金,弹性常数的计算结果也证实了我们对其相变的猜想,说明MnIr合金降温时所发生的相变顺序和其它合金一样。
3.为了了解合金的动力学稳定性,我们首次计算了MnX (X=Ni, Pd, Rh, Pt, Au和Ir)合金体系的声子谱。结果显示高温PM-B2相的声子曲线存在虚频点,表明该相是动力学不稳定的,除MnPt外,其它合金的PM-L10相也是动力学不稳定的。除了MnPt和MnAu,其它所有合金的低温AFM-L10相都具有动力学稳定性。具有动力学不稳定的PM-L10结构也只能转变为顺磁结构,因此反铁磁转变(PM-L10→AFM-L10)是由磁性引起的。磁性Mn原子交换参数的首次计算表明,主要决定反铁磁相变的交换参数为：J1及J1L (MnNi),J1和J2L(MnRh和MnPd), J2(MnPt和MnAu)。
4.为了进一步得到MnX (X=Ni, Pd, Rh, Pt, Au和Ir)合金体系的电子结构,我们用VASP软件计算了它们的总态密度和分波态密度。总态密度计算表明它们的低温AFM-L10是最稳定的,首次得到的分波态密度有助于了解合金结构的轨道占据情况,为进一步的实验和理论研究做基础。
The Mn metal exists with four kinds of structures(α,β,γ and δ), in which the face-centered cubic y phase can be stable only from1100℃to1140℃, so y phase can be stabilized by alloying, such as adding Ni, Pd, Rh, Pt, Cu, Fe, Au and so on. In recent years, Mn-based alloys are developed to be a new type of intelligent materials, and can be used for important magnetic components. Most of Mn-based alloys are antiferromagnetic, whose3d orbit is nearly semi-filled and Neel temperature is high, so that they can be used as spin vale pinning materials, giant magnetoresistance and tunnel magnetoresistance equipments. The antiferromagnetic-MnX (X=Ni, Pd, Rh, Pt and Au) at low temperatures is obtained from paramagnetic structures by cooling, the martensite phase transition and antiferromagnetic phase transition occur during the cooling. Understanding the phase transition mechanism helps to develop magnetic materials with more superior performance. In this paper, we systematically study the martensite phase transition for MnX (X=Ni, Pd, Rh, Pt and Au) using the first principles method based on the density functional theory, and obtain the following results:
1. The lattice constants of all AFM-L1O alloys for MnX (X=Ni, Pd, Rh, Pt, Au and Ir) system are respectively calculated by the projector-augmented-wave pseudopotential in the generalized gradient approximation(GGA) and the local density approximation(LDA), the results show that the GGA method is appropriate for the studied alloys, all the following calculations are performed by PAW-GGA method. We first calculate the lattice parameters (lattice constant, atomic coordinate, band angle) of PM-B2/L10phase and AFM-L10phase, the calculations values are close to the experimental data. The lattice parameters of PM-B2MnIr/Pt and PM-L10Mnlr are first obtained. The total energy order calculated through the first-principles is consistent with the phase transformation order found by experiments, which indicate that it is correct to use total energy to predict the phase transition. For MnRh and MnPd, MnPt and MnAu alloy, the tendency.of energy difference of total energy and experimental phase transition temperature dependence on the total number of valence electron shows that it is suitable to use total energy to predict the phase transition once again.
2. We also first calculate the elastic constant, Debye temperature, elastic module, mechanical anisotropy, Poisson's ratio, specific heat capacity of MnX (X=Ni, Pd, Rh, Pt and Au) alloy system. The elastic constant calculations indicate that the elastic constants of PM-B2phase don't satisfy the stability standard, and the softening of shear module C" induces the PM-B2structure to produce tetragonal distortion and transform to the tetragonal structure, which first explains the martensite phase transition (PM-B2→PM-L10) mechanism. The elastic constants calculations for these phases show that they are mechanically stable. The Debye temperatures calculations for low temperature AFM-Llo phases are accord to experimental data well, indicating that our calculated elastic constants are correct. Obtained elastic module, anisotropy and Poisson's ratio indicate that the MnX (X=Ni, Rh and Ir) alloy is brittle, and all the five kinds of alloys are anisotropic and have a large volume change during uniaxial deformation. The specific heat capacity calculations of AFM-L10phases indicate that it follows the Debye module at low temperatures, and approaches to the Dulong-Petit limit. For Mnir alloy, the elastic constant calculations also confirm our guess about its phase transition, showing that the phase transition order for Mnlr alloy by cooling is the same to other alloys.
3. In order to understand the dynamic stability of alloys, we also first calculate the phonon spectrum for MnX (X=Ni, Pd, Rh, Pt, Au and Ir) alloy system. The results show that phonon curves for the high temperature PM-B2phase has imaginary frequency, indicating that this phase is dynamically unstable. Except for MnPt and Mnir, PM-L10phases of other alloys are also dynamically unstable. Except for MnPt and MnAu, AFM-L10phases of other alloys are dynamically stable. The dynamically unstable PM-L10structure can only transform a new PM structure, so that the antiferromagnetic transition (PM-L10→AFM-L10) is caused by magnetism. The exchange parameters of magnetic atom Mn are first calculated and show that the exchange parameters dominating the antiferromagnetic transition are J1and J1L (MnNi), J1and J2L (MnRh and MnPd) and J2(MnPt and MnAu).
4. To obtain the electronic structures of MnX (X=Ni, Pd, Rh, Pt, Au and Ir) alloy system, we have calculated their total density of states and partial density of states. The total density of states calculated show that their AFM-Llo structures are most stable, and first obtained partial density of states help to understand the orbital occupancy of alloy, which are the foundation for further experiments and theoretical research.
1.利用投影缀加平面波在广义梯度近似(GGA)和局域密度近似(LDA)下分别计算MnX (X=Ni, Pd, Rh, Pt, Au和Ir)体系的所有低温AFM-L10相的晶格结构,结果表明,GGA方法更适合我们研究的合金。以后的计算都采用PAW-GGA方法。首先,计算了PM-B2/L10相及AFM-L10相的晶格参数(晶格常数,原子内坐标,键角),计算结果与实验值比较接近。我们也首次得到MnIr/Pt的PM-B2相及MnIr的PM-L10相的晶格参数。第一性原理计算的总能大小顺序与实验所发现的相变顺序一致,表明用总能来预测相变是正确的。对于MnRh和MnPd、MnPt和MnAu合金,我们得到的总能能差与实验相变温度随合金的价电子总数变化的趋势基本是一致的,再一次表明我们用总能预测的相变顺序是合适的。
2.我们还用第一性原理方法首次计算了MnX(X=Ni, Pd,Rh,Pt和Au)合金体系的弹性常数、德拜温度、弹性模量、机械各向异性、泊松比和比热容。弹性常数的计算表明PM-B2相的弹性常数不满足稳定性标准,剪切模量C'的软化导致其发生四方畸变,会转变为四方结构,这从微观上首次解释了实验所发生的马氏体相变(PM-B2→PM-L10)的相变机理。AFM-L10目的弹性常数计算结果表明这两相是机械稳定的。低温AFM-L10相的德拜温度的计算结果与实验值符合的很好,说明我们计算的弹性常数是正确的。得到的弹性模量,各向异性及泊松比表明MnX (X=Ni, Rh和Ir)合金是脆性的,所有5种合金具有各向异性,并且在单轴变形时具有大的体积改变。AFM-L10相比热容的计算表明,在低温遵从德拜模型,高温接近杜隆-珀替极限。对于MnIr合金,弹性常数的计算结果也证实了我们对其相变的猜想,说明MnIr合金降温时所发生的相变顺序和其它合金一样。
3.为了了解合金的动力学稳定性,我们首次计算了MnX (X=Ni, Pd, Rh, Pt, Au和Ir)合金体系的声子谱。结果显示高温PM-B2相的声子曲线存在虚频点,表明该相是动力学不稳定的,除MnPt外,其它合金的PM-L10相也是动力学不稳定的。除了MnPt和MnAu,其它所有合金的低温AFM-L10相都具有动力学稳定性。具有动力学不稳定的PM-L10结构也只能转变为顺磁结构,因此反铁磁转变(PM-L10→AFM-L10)是由磁性引起的。磁性Mn原子交换参数的首次计算表明,主要决定反铁磁相变的交换参数为：J1及J1L (MnNi),J1和J2L(MnRh和MnPd), J2(MnPt和MnAu)。
4.为了进一步得到MnX (X=Ni, Pd, Rh, Pt, Au和Ir)合金体系的电子结构,我们用VASP软件计算了它们的总态密度和分波态密度。总态密度计算表明它们的低温AFM-L10是最稳定的,首次得到的分波态密度有助于了解合金结构的轨道占据情况,为进一步的实验和理论研究做基础。
The Mn metal exists with four kinds of structures(α,β,γ and δ), in which the face-centered cubic y phase can be stable only from1100℃to1140℃, so y phase can be stabilized by alloying, such as adding Ni, Pd, Rh, Pt, Cu, Fe, Au and so on. In recent years, Mn-based alloys are developed to be a new type of intelligent materials, and can be used for important magnetic components. Most of Mn-based alloys are antiferromagnetic, whose3d orbit is nearly semi-filled and Neel temperature is high, so that they can be used as spin vale pinning materials, giant magnetoresistance and tunnel magnetoresistance equipments. The antiferromagnetic-MnX (X=Ni, Pd, Rh, Pt and Au) at low temperatures is obtained from paramagnetic structures by cooling, the martensite phase transition and antiferromagnetic phase transition occur during the cooling. Understanding the phase transition mechanism helps to develop magnetic materials with more superior performance. In this paper, we systematically study the martensite phase transition for MnX (X=Ni, Pd, Rh, Pt and Au) using the first principles method based on the density functional theory, and obtain the following results:
1. The lattice constants of all AFM-L1O alloys for MnX (X=Ni, Pd, Rh, Pt, Au and Ir) system are respectively calculated by the projector-augmented-wave pseudopotential in the generalized gradient approximation(GGA) and the local density approximation(LDA), the results show that the GGA method is appropriate for the studied alloys, all the following calculations are performed by PAW-GGA method. We first calculate the lattice parameters (lattice constant, atomic coordinate, band angle) of PM-B2/L10phase and AFM-L10phase, the calculations values are close to the experimental data. The lattice parameters of PM-B2MnIr/Pt and PM-L10Mnlr are first obtained. The total energy order calculated through the first-principles is consistent with the phase transformation order found by experiments, which indicate that it is correct to use total energy to predict the phase transition. For MnRh and MnPd, MnPt and MnAu alloy, the tendency.of energy difference of total energy and experimental phase transition temperature dependence on the total number of valence electron shows that it is suitable to use total energy to predict the phase transition once again.
2. We also first calculate the elastic constant, Debye temperature, elastic module, mechanical anisotropy, Poisson's ratio, specific heat capacity of MnX (X=Ni, Pd, Rh, Pt and Au) alloy system. The elastic constant calculations indicate that the elastic constants of PM-B2phase don't satisfy the stability standard, and the softening of shear module C" induces the PM-B2structure to produce tetragonal distortion and transform to the tetragonal structure, which first explains the martensite phase transition (PM-B2→PM-L10) mechanism. The elastic constants calculations for these phases show that they are mechanically stable. The Debye temperatures calculations for low temperature AFM-Llo phases are accord to experimental data well, indicating that our calculated elastic constants are correct. Obtained elastic module, anisotropy and Poisson's ratio indicate that the MnX (X=Ni, Rh and Ir) alloy is brittle, and all the five kinds of alloys are anisotropic and have a large volume change during uniaxial deformation. The specific heat capacity calculations of AFM-L10phases indicate that it follows the Debye module at low temperatures, and approaches to the Dulong-Petit limit. For Mnir alloy, the elastic constant calculations also confirm our guess about its phase transition, showing that the phase transition order for Mnlr alloy by cooling is the same to other alloys.
3. In order to understand the dynamic stability of alloys, we also first calculate the phonon spectrum for MnX (X=Ni, Pd, Rh, Pt, Au and Ir) alloy system. The results show that phonon curves for the high temperature PM-B2phase has imaginary frequency, indicating that this phase is dynamically unstable. Except for MnPt and Mnir, PM-L10phases of other alloys are also dynamically unstable. Except for MnPt and MnAu, AFM-L10phases of other alloys are dynamically stable. The dynamically unstable PM-L10structure can only transform a new PM structure, so that the antiferromagnetic transition (PM-L10→AFM-L10) is caused by magnetism. The exchange parameters of magnetic atom Mn are first calculated and show that the exchange parameters dominating the antiferromagnetic transition are J1and J1L (MnNi), J1and J2L (MnRh and MnPd) and J2(MnPt and MnAu).
4. To obtain the electronic structures of MnX (X=Ni, Pd, Rh, Pt, Au and Ir) alloy system, we have calculated their total density of states and partial density of states. The total density of states calculated show that their AFM-Llo structures are most stable, and first obtained partial density of states help to understand the orbital occupancy of alloy, which are the foundation for further experiments and theoretical research.
引文
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