相平面价电子结构及其在合金研究中的应用
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摘要
本文以余(瑞璜)氏固体与分子经验电子理论(EET)和程(开甲)氏改进的TFD理论为基础定义了相平面价电子结构的概念,建立了平面价电子结构的计算方法,给出了相界面之间的相对电子密度差△p的数学表达式,为相界面电子密度连续的计算和应用奠定了基础。当合金中存在异相界面且按一定的位向关系相匹配时,对原子的定态除了考虑键距差|△D|的大小以外,同样要考虑△p的大小。综合考虑两种因素的影响,提出了原子状态判定因子w,并用它讨论了Fe-C奥氏体、Fe-C马氏体中铁原子的杂化状态和合金奥氏体Fe-C-Me晶胞中原子的杂化状态。结果表明,Fe-C奥氏体含碳结构单元中,Fe~c原子的杂化状态为乙种杂化第13阶(B13),Fe~f原子的杂化状态为乙种杂化第14阶(B14)。Fe-C马氏体含碳结构单元中,Fe_Ⅰ,Fe_Ⅱ及Fe_Ⅲ的杂化状态分别为甲种杂化第12(A12),10(A10)和9阶(A9)。对于合金奥氏体,Fe~c、Fe~f原子的杂化状态因Me(任一合金元素)原子的不同而发生改变。在Fe-C-Cr晶胞中,Fe~c、Fe~f、Cr的杂化状态分别为B14、B15、A7(或A8)阶;在Fe-C-W晶胞中,Fe~c、Fe~t、W原子的杂化状态分别为B13、B14、C1(或C2)阶;在Fe-C-Si晶胞中,Fe~c、Fe~f、Si原子的杂化状态分别为B15、B16(或B17)、A1(或A2、A3)阶;在Fe-C-Mn晶胞中,Fe~c、Fe~f、Mn原子的杂化状态分别为B14(或B13)、B15、C11阶。应用原子状态判定因子w来确定合金组成元素原子的杂化状态,是将程氏提出的各原子相接触的表面上电子密度必须连续这一电子运动的边界条件运用到余氏理论的计算中,不仅可使余氏确定原子杂化状态时解的多重性问题得以简化,而且在“异相界面电子密度连续”这一结合点上使余氏理论和程氏理论得到了衔接。
分别对A_1,A_2和A_3型晶体结构的部分金属的价电子结构进行了计算,并给出了三种类型结构金属的平面价电子结构分析通式。定义了表征晶体沿晶面发生滑移难易程度的参数F,F值越小,滑移越容易进行;反之则滑移越难进行。通过对A_1,A_2和A_3型晶体结构中更多晶面的F值的计算表明,A_1,A_2和A_3型晶体结构中的F值最小的晶面分别为{111},{110}和{0001}面。由此在价电子结构的层次上解释了A_1,A_2和A_3型晶体发生滑移时的滑移面分别为{111),{110}和{0001}面的原因。
把程氏改进的TFD理论中的电子运动边界条件运用于余氏理论中,计算了Fe-C奥氏体和Fe-C马氏体原子排列较密集的几个低指数晶面电子密度,通过对计算数据的分析,在价电子结构的层次讨论了马氏体相变时的位向关系。奥氏体向马氏体转变时,奥氏体的(111)晶面和马氏体的(110)晶面的相对电子密度差为6.95%,小于10%,即在一级近似下奥氏体的(111)面与马氏体的(110)面是连续的。按程氏理论指出的“固体中原子间的边界条件只是电子密度要连续”的量子力学条件,奥氏体向马氏体的转变其位向关系为:(111)_γ∥(110)_α。
应用键能讨论了合金元素对奥氏体向马氏体转变相变点的影响,计算表明,当Mo、Cr、W、Mn、Ni等合金元素加入到奥氏体中后,合金奥氏体晶胞中共价键键能的最大值都比Fe-C晶胞中最大共价键键能值有不同程度的增加,因而需要更大的能量来打断合金奥氏体晶胞中的主干键以发生奥氏体向马氏体的转变,即这些合金元素的加入影响了奥氏体向马氏体的转变温度,共价键能值增加的越多,则所需的过冷度越大,相变温度就越低。Mn、Cr、Ni、Mo、W等合金元素对奥氏体向马氏体转变相变点影响的规律是:Mn、Cr、Ni降低相变点的作用较强,Mo、W次之,与金属学中的实验规律相吻合。
基于平均晶胞模型和平均原子模型的思想分别给出了Fe基间隙固溶体和置换固溶体,Al-Mg置换固溶体的价电子结构详细的计算方法。在γ-Fe-C固溶体中,含碳晶胞的最强键络的共价电子对数n_A较基体(γ-Fe)的n_A值提高了近两倍;γ-Fe-N固溶体的含N晶胞的n_A值较基体(γ-Fe)的n_A值也提高了近1.4倍。然而在置换固溶体中,如Al-Mg固溶体的含Mg晶胞的n_A值和Fe-Si固溶体含Si晶胞的n_A值以及Fe-Mn固溶体含Mn晶胞的n_A值较基体几乎没有变化。间隙固溶体较置换固溶体强化效果之所以更为明显,可以从n_A值的变化找到答案。从而把固溶强化的机制追溯到固溶体的价电子结构上。
In this paper,based on Yu's empirical electron theory of solid and molecule,i.e.EET and Cheng's improved TFD theory,the conception and the calculation methods of plane valence electron structure is defined and established,and the mathematic expression of relative electron density difference△ρof phase interface is proposed.These lay foundation for the continuous calculation and application of electron density of phase interface.For the definite state of atoms in alloy if exiting biphase interface and arranging by definite phase relationship,the values of bond length difference(BLD)△D and△ρshould be both considered.The effect of two factors is considered simultaneously and atom state ascertainment factor w applied to study on the hybridization state of Fe atom in Fe-C austenite and Fe-C martensite and the hybridization state of atoms of Fe-C-Me unit cell in alloyed austenite is presented.The results indicate that in Fe-C austenite C-contained structure unit,the hybrid levels of Fe~c and Fe~f atoms are B13 and B14,respectively and in Fe-C martensite C-contained structure unit,the hybrid levels of Fe_Ⅰ,Fe_Ⅱand Fe_Ⅲatoms are A12,A10 and A9,respectively.For alloyed austenite,different Me(any alloying elements)atoms make the hybridization states of Fe~c and Fe~f atoms change accordingly. The hybridization states of Fe~c,Fe~f and Cr atoms in Fe-C-Cr unit cell are B14,B15 and A7(or A8),respectively;those of Fe~c,Fe~f and W atoms in Fe-C-W unit cell are B13,B14 and C1(or C2),respectively;those of Fe~c,Fe~f and Si atoms in Fe-C-Si unit cell are B15, B16(or B17)and A1(A2 or A3),respectively;those of Fe~c,Fe~f and Mn atoms in Fe-C-Mn unit cell are B14(or B13),B15 and C11,respectively,w is applied to ascertain the hybridization states of atoms of alloying elements,which made that the electron density of the contacting surface between atoms must be continuous(the boundary condition of the movement of electrons)by Cheng Kaijia applied to the calculation of Yu's theory,which can not only simplify the multiply solution ascertaining the hybridization states of atoms, but also join Yu's theory and Cheng's theory at the bonding point that biphase interface electron density is continuous.
Valence electron structures of some metals of A_1,A_2 and A_3 model crystal structures are respectively calculated and the analytic general formula of plane valence electron structure of three models metal is presented.A new parameter "F" is taken as the difficulty coefficient of slipping along certain face.The smaller the value of F is,the easier the slipping;on the contrary,the slipping is much more difficult.In A_1,A_2 and A_3 model crystal structures,the F values of many other crystal planes are calculated and the results show that the crystal planes with the minimum F are {111},{110} and {0001} respectively.So in the level of valence electron structure,the reason that {111},{110} and {0001} are respective slip plane of A_1,A_2 and A_3 model can be explained.
By applying the boundary condition of the movement of electrons in Cheng's improved TFD theory to Yu's theory,electron density of a few low index crystal face that the atoms arrange more dense in Fe-C austenite and Fe-C martensite is calculated.The calculate data are analyzed and the definite orientation relationship of martensite phase transformation is discussed in the level of valence electron structure.When austenite transformed to martensite,relative electron density difference between the plane of(111) of austenite and the plane of(110)of martensite is 6.95%,which is smaller than 10%,i.e. the plane of(111)of austenite and the plane of(110)of martensite is continuous under the first-order approximation.According to the quantum-mechanical condition that the boundary condition between atoms is only that the electron density must be continuous in solid presented in Cheng's theory,the definite orientation relationship is(111)_γ//(110)_αwhen austenite transforms to martensite,.
The effect of alloying elements on the phase transformation point Ms of austenite is studied according to bond energy.The calculation shows that the maximum value of covalent bond energy of alloyed austenite unit cell is bigger than the one of Fe-C unit cell when the Mo,Cr,W,Mn,Ni etc.alloying elements melt into the austenite.So it needs more energy to break the most powerful bond of alloying austenite unit cell for the sake of the transformation from austenite to martensite,i.e.the alloying elements have affected the transformation temperature from austenite to martensite.The more the value of covalent bond energy is increased,the larger degree of supercooling is needed and the lower the phase transformation tempreture is.The rule that Ms from austenite to martensite is affected by Mn,Cr,Ni,Mo,W etc.alloying elements is that the function of Mn,Cr,Ni decreasing the Ms is stronger,while Mo and W take second place,which is in accord with the experimental rule in metallurgy.
Based on the thought of average cell model and average atom model,the detailed calculation methods of valence electron structure of Fe-interstitial solid-solution and substitution solid-solution and Al-Mg substitution solid-solution are presented,respectively. Inγ-Fe-C solid-solution,the number of covalent electron pairs n_A of the most powerful bond of C-contained unit cell is increased about 2 times than the one of matrix(γ-Fe);the n_A ofγ-Fe-N solid-solution N-contained unit cell is increased about 1.4 times than the one of matrix(γ-Fe).In substitution solid-solution,however,the n_A of Al-Mg solid-solution Mg-contained unit cell,the one of Fe-Si solid-solution Si-contained unit cell and the one of Fe-Mn solid-solution Mn-contained unit cell are almost accord with the one of matrix.The reason interstitial solid-solution strengthening is stronger than substitution solid-solution's obviously is the variation of n_A.So the mechanism of solid-solution strengthening can be presented using the valence electron structures of the solid-solution.
分别对A_1,A_2和A_3型晶体结构的部分金属的价电子结构进行了计算,并给出了三种类型结构金属的平面价电子结构分析通式。定义了表征晶体沿晶面发生滑移难易程度的参数F,F值越小,滑移越容易进行;反之则滑移越难进行。通过对A_1,A_2和A_3型晶体结构中更多晶面的F值的计算表明,A_1,A_2和A_3型晶体结构中的F值最小的晶面分别为{111},{110}和{0001}面。由此在价电子结构的层次上解释了A_1,A_2和A_3型晶体发生滑移时的滑移面分别为{111),{110}和{0001}面的原因。
把程氏改进的TFD理论中的电子运动边界条件运用于余氏理论中,计算了Fe-C奥氏体和Fe-C马氏体原子排列较密集的几个低指数晶面电子密度,通过对计算数据的分析,在价电子结构的层次讨论了马氏体相变时的位向关系。奥氏体向马氏体转变时,奥氏体的(111)晶面和马氏体的(110)晶面的相对电子密度差为6.95%,小于10%,即在一级近似下奥氏体的(111)面与马氏体的(110)面是连续的。按程氏理论指出的“固体中原子间的边界条件只是电子密度要连续”的量子力学条件,奥氏体向马氏体的转变其位向关系为:(111)_γ∥(110)_α。
应用键能讨论了合金元素对奥氏体向马氏体转变相变点的影响,计算表明,当Mo、Cr、W、Mn、Ni等合金元素加入到奥氏体中后,合金奥氏体晶胞中共价键键能的最大值都比Fe-C晶胞中最大共价键键能值有不同程度的增加,因而需要更大的能量来打断合金奥氏体晶胞中的主干键以发生奥氏体向马氏体的转变,即这些合金元素的加入影响了奥氏体向马氏体的转变温度,共价键能值增加的越多,则所需的过冷度越大,相变温度就越低。Mn、Cr、Ni、Mo、W等合金元素对奥氏体向马氏体转变相变点影响的规律是:Mn、Cr、Ni降低相变点的作用较强,Mo、W次之,与金属学中的实验规律相吻合。
基于平均晶胞模型和平均原子模型的思想分别给出了Fe基间隙固溶体和置换固溶体,Al-Mg置换固溶体的价电子结构详细的计算方法。在γ-Fe-C固溶体中,含碳晶胞的最强键络的共价电子对数n_A较基体(γ-Fe)的n_A值提高了近两倍;γ-Fe-N固溶体的含N晶胞的n_A值较基体(γ-Fe)的n_A值也提高了近1.4倍。然而在置换固溶体中,如Al-Mg固溶体的含Mg晶胞的n_A值和Fe-Si固溶体含Si晶胞的n_A值以及Fe-Mn固溶体含Mn晶胞的n_A值较基体几乎没有变化。间隙固溶体较置换固溶体强化效果之所以更为明显,可以从n_A值的变化找到答案。从而把固溶强化的机制追溯到固溶体的价电子结构上。
In this paper,based on Yu's empirical electron theory of solid and molecule,i.e.EET and Cheng's improved TFD theory,the conception and the calculation methods of plane valence electron structure is defined and established,and the mathematic expression of relative electron density difference△ρof phase interface is proposed.These lay foundation for the continuous calculation and application of electron density of phase interface.For the definite state of atoms in alloy if exiting biphase interface and arranging by definite phase relationship,the values of bond length difference(BLD)△D and△ρshould be both considered.The effect of two factors is considered simultaneously and atom state ascertainment factor w applied to study on the hybridization state of Fe atom in Fe-C austenite and Fe-C martensite and the hybridization state of atoms of Fe-C-Me unit cell in alloyed austenite is presented.The results indicate that in Fe-C austenite C-contained structure unit,the hybrid levels of Fe~c and Fe~f atoms are B13 and B14,respectively and in Fe-C martensite C-contained structure unit,the hybrid levels of Fe_Ⅰ,Fe_Ⅱand Fe_Ⅲatoms are A12,A10 and A9,respectively.For alloyed austenite,different Me(any alloying elements)atoms make the hybridization states of Fe~c and Fe~f atoms change accordingly. The hybridization states of Fe~c,Fe~f and Cr atoms in Fe-C-Cr unit cell are B14,B15 and A7(or A8),respectively;those of Fe~c,Fe~f and W atoms in Fe-C-W unit cell are B13,B14 and C1(or C2),respectively;those of Fe~c,Fe~f and Si atoms in Fe-C-Si unit cell are B15, B16(or B17)and A1(A2 or A3),respectively;those of Fe~c,Fe~f and Mn atoms in Fe-C-Mn unit cell are B14(or B13),B15 and C11,respectively,w is applied to ascertain the hybridization states of atoms of alloying elements,which made that the electron density of the contacting surface between atoms must be continuous(the boundary condition of the movement of electrons)by Cheng Kaijia applied to the calculation of Yu's theory,which can not only simplify the multiply solution ascertaining the hybridization states of atoms, but also join Yu's theory and Cheng's theory at the bonding point that biphase interface electron density is continuous.
Valence electron structures of some metals of A_1,A_2 and A_3 model crystal structures are respectively calculated and the analytic general formula of plane valence electron structure of three models metal is presented.A new parameter "F" is taken as the difficulty coefficient of slipping along certain face.The smaller the value of F is,the easier the slipping;on the contrary,the slipping is much more difficult.In A_1,A_2 and A_3 model crystal structures,the F values of many other crystal planes are calculated and the results show that the crystal planes with the minimum F are {111},{110} and {0001} respectively.So in the level of valence electron structure,the reason that {111},{110} and {0001} are respective slip plane of A_1,A_2 and A_3 model can be explained.
By applying the boundary condition of the movement of electrons in Cheng's improved TFD theory to Yu's theory,electron density of a few low index crystal face that the atoms arrange more dense in Fe-C austenite and Fe-C martensite is calculated.The calculate data are analyzed and the definite orientation relationship of martensite phase transformation is discussed in the level of valence electron structure.When austenite transformed to martensite,relative electron density difference between the plane of(111) of austenite and the plane of(110)of martensite is 6.95%,which is smaller than 10%,i.e. the plane of(111)of austenite and the plane of(110)of martensite is continuous under the first-order approximation.According to the quantum-mechanical condition that the boundary condition between atoms is only that the electron density must be continuous in solid presented in Cheng's theory,the definite orientation relationship is(111)_γ//(110)_αwhen austenite transforms to martensite,.
The effect of alloying elements on the phase transformation point Ms of austenite is studied according to bond energy.The calculation shows that the maximum value of covalent bond energy of alloyed austenite unit cell is bigger than the one of Fe-C unit cell when the Mo,Cr,W,Mn,Ni etc.alloying elements melt into the austenite.So it needs more energy to break the most powerful bond of alloying austenite unit cell for the sake of the transformation from austenite to martensite,i.e.the alloying elements have affected the transformation temperature from austenite to martensite.The more the value of covalent bond energy is increased,the larger degree of supercooling is needed and the lower the phase transformation tempreture is.The rule that Ms from austenite to martensite is affected by Mn,Cr,Ni,Mo,W etc.alloying elements is that the function of Mn,Cr,Ni decreasing the Ms is stronger,while Mo and W take second place,which is in accord with the experimental rule in metallurgy.
Based on the thought of average cell model and average atom model,the detailed calculation methods of valence electron structure of Fe-interstitial solid-solution and substitution solid-solution and Al-Mg substitution solid-solution are presented,respectively. Inγ-Fe-C solid-solution,the number of covalent electron pairs n_A of the most powerful bond of C-contained unit cell is increased about 2 times than the one of matrix(γ-Fe);the n_A ofγ-Fe-N solid-solution N-contained unit cell is increased about 1.4 times than the one of matrix(γ-Fe).In substitution solid-solution,however,the n_A of Al-Mg solid-solution Mg-contained unit cell,the one of Fe-Si solid-solution Si-contained unit cell and the one of Fe-Mn solid-solution Mn-contained unit cell are almost accord with the one of matrix.The reason interstitial solid-solution strengthening is stronger than substitution solid-solution's obviously is the variation of n_A.So the mechanism of solid-solution strengthening can be presented using the valence electron structures of the solid-solution.
引文
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