Ⅰ、Ⅳ和ⅥB族过渡金属电子结构、物理性质和热力学性质的系统研究
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摘要
本文完善了合金系统科学框架中的纯单质理论，并应用此理论对Ⅰ、Ⅳ和ⅥB族元素fcc，hcp和bcc三种晶体以及液体的电子结构、物理性质和热力学性质随温度的变化关系进行了系统研究，建立了完善的纯单质理论分析系统、纯单质知识库和纯单质数据库。
本文系统地对ⅠB、ⅣB和ⅥB族过渡金属进行了五个方面的研究：(1)计算了过渡金属稳定和亚稳相的电子结构，并在电子结构保持不变条件下计算了从OK到熔点的物理性质(势能曲线、结合能、体弹性模量、Debye温度、晶格振动能、原子体积、原子动能和原子势能)和热力学性质(恒容热容、恒压热容、焓、熵和Gibbs能)；(2)假设液体与熔点之前的固体具有相同的晶体结构，计算了液相的电子结构，并在其电子结构保持不变的条件下计算了液相从OK至沸点的物理性质和热力学性质；(3)对单原子方法(价键理论)和单电子方法(能带理论)的电子结构计算结果进行了比较，并分析了电子结构和晶体结构之间的关系；(4)建立了汇集计算电子结构、晶格常数、势能曲线、物理和热力学性质等公式和计算程序于一体的纯单质知识库；(5)建立了纯单质数据库，主要包括基本原子态的电子结构、结合能和晶格常数数据表，电子结构杂化三角形和每一元素fcc、hcp、bcc晶体和液体的物理性质以及热力学性质随温度变化的数据表和曲线图，为建立元素周期表的fcc，hcp和bcc晶体的电子结构和性质数据库奠定了基础。
本文重点对纯金属相变时的电子结构转变及其对材料性质的影响进行了系统研究，取得了五个方面的创新成果：(1)金属材料力学和输运性质的价电子判据T_c、X_c和T_f中，共价电子线密度X_c比体密度T_c更适合作为材料力学性质判据，自由电子体密度T_f可以作为材料输运性质的普适判据，T_f与最近邻共价键上的电子线密度X_(c，1)可以联合为合金的成份设计提供最佳判据；(2)对ⅠB族元素Cu、Ag和Au稳定相的研究表明：金属的电子密度决定其物理性质，共价电子密度越大，原子结合越强，熔点越高，抗压强度等力学性质越高，但自由电子的输运性能将因共价电子的阻碍而下降；自由电子密度越大，金属的塑性、延性、导电和导热性等输运性质越好，但共价电子的结合性能因共价电子数目的减少而削弱；液相中的S_f电子同时受到d_c和s_c电子的散射及原子核热振动的影响，且液相的s_c电子对s_f电子的输运过程起主要阻碍作用；(3)ⅣB族元素Ti、Zr和Hf稳定相hcp晶体的轴比c／a偏离了理想值，其对称性较低，定义共价电子线密度X_c，并结合自由电子密度T_f和键参数研究了hcp相的电子结构与物理性质之间的关系，结果表明，d_c电子的对称性比s_c电子更低，原子配位的方向性和选择性更强，但其数目比s_c多，使得Ti、Zr和Hf元素最终形成了轴比分别为1.5884，1.5925和1.5821(理想比为1.633)的hcp结构；高温时，d电子向s电子转化，球对称的s电子对晶格稳定性起主要作用，形成对了称性更高的bcc结构；(4)对ⅥB族元素Cr、Mo和W稳定相同时采用T_c、X_c和T_f三个判据进行研究发现，最近邻共价键上的电子线密度X_(c，1)的变化趋势为X_(c，1)(Cr)＜X_(c，1)(Mo)＜X_(c，1)(W)，它与三种元素的熔点、拉伸强度、维氏硬度、体弹性模量和最强键键能等性质变化规律完全一致，自由电子体密度T_f的变化趋势为T_f(Cr)＜T_f(Mo)＜T_f(W)，它与三种元素的自由电子键能、导电和导热等性质变化规律一致；ⅥB族元素有可能由bcc结构向hcp或fcc转变，且电子结构的分析表明bcc将优先向hcp转变，该结果不仅与SGTE数据库一致，并且从电子结构层次上解释了ⅥB族元素晶格稳定性的差异；(5)对Ⅰ、Ⅳ和ⅥB族元素的电子结构研究的总体结果表明：当自然态固相向液相转变时，d_n电子的增加导致了液相原子的成键电子总数下降，d_c电子的减少导致了原子配位方向性和原子之间结合力的削弱，s_c电子的增加导致了d_n电子在总价电子数中的比例，即单键半径公式中的δ值减小，引起了单键半径和原子体积的增大，在s_f电子变化不大或者减少的情况下，液相的自由电子密度将下降，导电和导热等输运性质也将下降，这与实验结果一致。
The theory of pure elements in the framework of systematic scienceof alloys(SSA)has been improved in this paper, the electronic structures, physical properties and thermodynamic properties of fcc, hcp and bcccrystals of transition metals inⅠB、ⅣB andⅣB groups have beenstudied using this theory, and the theoretical analyses system of pureelements, the knowledge database and information database have beenestablished.
In this paper, the following researches on metals inⅠB、ⅣB andⅥB groups have been performed: (1) the electronic structures of stableand metastable phases of transition metals have been calculated, physicalproperties including potential curve, cohesive energy, bulk moduli, Debyetemperature, isometric heat capacity, vibrating energies of lattice, atomicvolume, atomic vibrating energies and atomic potential, andthermodynamic properties including isobaric heat capacity, enthalpy, entropy and Gibbs energy from OK to melting points have been calculatedunder the assumption of the temperature independence of electronicstructure; (2)the electronic structures of liquid phases have beencalculated with the assumption that the liquid phase at melting point havethe same structure with that of solid phase, and the Properties from OK tothe boiling point, have been calculated; (3) the comparison of electronicstructures between one-atom(OA)method of chemical bonding theoryand energy band theory in first principles have been performed and therelationship between electronic structure and crystalline structure hasbeen analyzed; (4) the knowledge database of pure elements includingseries of calculation formulas of various properties such as single bondradius, lattice constants, cohesive energies, bulk moduli and thermalexpansion coefficients have been established; (5) the information databaseof pure elements including data tables of electronic structures, cohesiveenergies and lattice constants of basic atom states, triangles ofhybridization of basic atom states and tables and figures of temperaturedependence of physical and thermodynamic properties of fcc, hcp and bcc crystals and liquids of each elements inⅠ、ⅣandⅥB groups have beenestablished and it provides the basis for the establishment of periodictable of electronic structures and property database of fcc, hcp and bcccrystalls of elements.
This paper is focused on the research of relationships betweenelectronic structures and crystalline structures during phase transitions ofpure metals and their influences on the physical and chemical properties.The results of this paper show that (1) in the three criterions of valentelectron density T_c、X_c and T_f, the linear density X_c is a more superiorcriterion than the bulk one T_c for the assessments of mechamic propertiesof metals, while the bulk density of free electrons T_f can be used as auniversal criterion for the assessment of transporting properties of metals, and the combination of T_f and X_c in the nearest covalent bond, i.e. X_(c.1), can provide the best criterions for composition selection in alloy design; (2) the studies on the elements Cu, Ag and Au inⅠB group show that theelectronic density decides the physical properties of metals, on one hand, the larger the density of covalent electrons, the stronger the cohesion ofatoms, the higher the melting point, and the better the compressionresistivity, but the transporting properties are weakened at the same timedue to the blocking of the covalent electrons, on the other hand, the largerthe density of free electrons, the better the plasticity, elongation, electricaland thermal conductivity, but the cohesive properties are weakened due tothe less number of cohesive electrons; and it is found as well that the freeelectrons in s orbital of atoms are influenced by the scattering of thecovalent electrons in both d orbital and s orbital and the vibrating ofatomic nucleus, and it is the covalent electrons in s orbital that mainlyinfluence the transporting function of free electrons in liquid phase; (3)the axial ratios of c/a of Ti, Zr and Hf inⅣB group deviate from the idealvalue, so the crystalline symmetry is low, and the linear density ofcovalent electrons X_c is defined for its application in the research of therelationship between electronic structures and physical properties of hcpphase with the combination of T_f and other bond parameters, and theresults show that the symmetry of d_c electrons is lower than that of s_celectrons, and not only the direction and selection of atom coordination of d_c electrons is stronger but also the number of d_c electrons is more thanthat of s_c electrons, so the hcp structures of Ti, Zr and Hf with c/a beingrespectively 1.5884, 1.5925 and 1.5821 can be formed at low temperature; at high temperature, the electrons in d orbital are transformed into sorbital, so the s electrons play main role in the lattice stability and the bccstructrue can exist stablely; (4)using the criterions T_c, X_c和T_f to the studyon the elements Cr, Mo and W inⅥB group, it is found that theproperties such as melting points, tensile strength, hardness, bulk moduliand the bonding energy of the strongest bond follow the same rule as thelinear density in the nearest covalent bond X_(c, 1), i.e., X_(c, 1) (Cr)＜X_(c, 1) (Mo)＜X_(c, 1) (W), and the electrical conductivity, thermalconductivity and the bonding energy of the free electrons follow the samerule as the the bulk density of free electrons T_f, i.e., T_f(Cr)＜T_f(Mo)＜T_f(W); the analyses of electronic structures of elements Cr, Mo and W inⅥB group show that bcc structure is probable to betransformed into hcp or fcc structure and bcc is more preferred to betransformed into hcp due to the more covalent electrons with strongerbonding ability in d orbital and the less covalent electrons with weakerbonding ability in s orbital in hcp than fcc phase, which causes lowerpotential and higher stability of hcp structure, this result agrees well withthat of SGTE database and can explain the difference of lattice stability inSGTE database from the level of electronic structure; (5) when the solidphase of transition metals inⅠ,ⅣandⅥB group is transformed intoliquid phase, both the nonbonding electrons in d orbital and the covalentelectrons in s orbital increase, the covalent electrons in d decrease, andthe free electrons in s orbital have no obvious change or decrease, thischange of electronic structures leads to the decrease of bonding electrons, weakening of bonding direction and cohesion of atoms, increase of singlebond radius and atomic volume, decrease of the density of free electronsand corresponding decrease of electrical conductivity of liquid phase.
本文系统地对ⅠB、ⅣB和ⅥB族过渡金属进行了五个方面的研究：(1)计算了过渡金属稳定和亚稳相的电子结构，并在电子结构保持不变条件下计算了从OK到熔点的物理性质(势能曲线、结合能、体弹性模量、Debye温度、晶格振动能、原子体积、原子动能和原子势能)和热力学性质(恒容热容、恒压热容、焓、熵和Gibbs能)；(2)假设液体与熔点之前的固体具有相同的晶体结构，计算了液相的电子结构，并在其电子结构保持不变的条件下计算了液相从OK至沸点的物理性质和热力学性质；(3)对单原子方法(价键理论)和单电子方法(能带理论)的电子结构计算结果进行了比较，并分析了电子结构和晶体结构之间的关系；(4)建立了汇集计算电子结构、晶格常数、势能曲线、物理和热力学性质等公式和计算程序于一体的纯单质知识库；(5)建立了纯单质数据库，主要包括基本原子态的电子结构、结合能和晶格常数数据表，电子结构杂化三角形和每一元素fcc、hcp、bcc晶体和液体的物理性质以及热力学性质随温度变化的数据表和曲线图，为建立元素周期表的fcc，hcp和bcc晶体的电子结构和性质数据库奠定了基础。
本文重点对纯金属相变时的电子结构转变及其对材料性质的影响进行了系统研究，取得了五个方面的创新成果：(1)金属材料力学和输运性质的价电子判据T_c、X_c和T_f中，共价电子线密度X_c比体密度T_c更适合作为材料力学性质判据，自由电子体密度T_f可以作为材料输运性质的普适判据，T_f与最近邻共价键上的电子线密度X_(c，1)可以联合为合金的成份设计提供最佳判据；(2)对ⅠB族元素Cu、Ag和Au稳定相的研究表明：金属的电子密度决定其物理性质，共价电子密度越大，原子结合越强，熔点越高，抗压强度等力学性质越高，但自由电子的输运性能将因共价电子的阻碍而下降；自由电子密度越大，金属的塑性、延性、导电和导热性等输运性质越好，但共价电子的结合性能因共价电子数目的减少而削弱；液相中的S_f电子同时受到d_c和s_c电子的散射及原子核热振动的影响，且液相的s_c电子对s_f电子的输运过程起主要阻碍作用；(3)ⅣB族元素Ti、Zr和Hf稳定相hcp晶体的轴比c／a偏离了理想值，其对称性较低，定义共价电子线密度X_c，并结合自由电子密度T_f和键参数研究了hcp相的电子结构与物理性质之间的关系，结果表明，d_c电子的对称性比s_c电子更低，原子配位的方向性和选择性更强，但其数目比s_c多，使得Ti、Zr和Hf元素最终形成了轴比分别为1.5884，1.5925和1.5821(理想比为1.633)的hcp结构；高温时，d电子向s电子转化，球对称的s电子对晶格稳定性起主要作用，形成对了称性更高的bcc结构；(4)对ⅥB族元素Cr、Mo和W稳定相同时采用T_c、X_c和T_f三个判据进行研究发现，最近邻共价键上的电子线密度X_(c，1)的变化趋势为X_(c，1)(Cr)＜X_(c，1)(Mo)＜X_(c，1)(W)，它与三种元素的熔点、拉伸强度、维氏硬度、体弹性模量和最强键键能等性质变化规律完全一致，自由电子体密度T_f的变化趋势为T_f(Cr)＜T_f(Mo)＜T_f(W)，它与三种元素的自由电子键能、导电和导热等性质变化规律一致；ⅥB族元素有可能由bcc结构向hcp或fcc转变，且电子结构的分析表明bcc将优先向hcp转变，该结果不仅与SGTE数据库一致，并且从电子结构层次上解释了ⅥB族元素晶格稳定性的差异；(5)对Ⅰ、Ⅳ和ⅥB族元素的电子结构研究的总体结果表明：当自然态固相向液相转变时，d_n电子的增加导致了液相原子的成键电子总数下降，d_c电子的减少导致了原子配位方向性和原子之间结合力的削弱，s_c电子的增加导致了d_n电子在总价电子数中的比例，即单键半径公式中的δ值减小，引起了单键半径和原子体积的增大，在s_f电子变化不大或者减少的情况下，液相的自由电子密度将下降，导电和导热等输运性质也将下降，这与实验结果一致。
The theory of pure elements in the framework of systematic scienceof alloys(SSA)has been improved in this paper, the electronic structures, physical properties and thermodynamic properties of fcc, hcp and bcccrystals of transition metals inⅠB、ⅣB andⅣB groups have beenstudied using this theory, and the theoretical analyses system of pureelements, the knowledge database and information database have beenestablished.
In this paper, the following researches on metals inⅠB、ⅣB andⅥB groups have been performed: (1) the electronic structures of stableand metastable phases of transition metals have been calculated, physicalproperties including potential curve, cohesive energy, bulk moduli, Debyetemperature, isometric heat capacity, vibrating energies of lattice, atomicvolume, atomic vibrating energies and atomic potential, andthermodynamic properties including isobaric heat capacity, enthalpy, entropy and Gibbs energy from OK to melting points have been calculatedunder the assumption of the temperature independence of electronicstructure; (2)the electronic structures of liquid phases have beencalculated with the assumption that the liquid phase at melting point havethe same structure with that of solid phase, and the Properties from OK tothe boiling point, have been calculated; (3) the comparison of electronicstructures between one-atom(OA)method of chemical bonding theoryand energy band theory in first principles have been performed and therelationship between electronic structure and crystalline structure hasbeen analyzed; (4) the knowledge database of pure elements includingseries of calculation formulas of various properties such as single bondradius, lattice constants, cohesive energies, bulk moduli and thermalexpansion coefficients have been established; (5) the information databaseof pure elements including data tables of electronic structures, cohesiveenergies and lattice constants of basic atom states, triangles ofhybridization of basic atom states and tables and figures of temperaturedependence of physical and thermodynamic properties of fcc, hcp and bcc crystals and liquids of each elements inⅠ、ⅣandⅥB groups have beenestablished and it provides the basis for the establishment of periodictable of electronic structures and property database of fcc, hcp and bcccrystalls of elements.
This paper is focused on the research of relationships betweenelectronic structures and crystalline structures during phase transitions ofpure metals and their influences on the physical and chemical properties.The results of this paper show that (1) in the three criterions of valentelectron density T_c、X_c and T_f, the linear density X_c is a more superiorcriterion than the bulk one T_c for the assessments of mechamic propertiesof metals, while the bulk density of free electrons T_f can be used as auniversal criterion for the assessment of transporting properties of metals, and the combination of T_f and X_c in the nearest covalent bond, i.e. X_(c.1), can provide the best criterions for composition selection in alloy design; (2) the studies on the elements Cu, Ag and Au inⅠB group show that theelectronic density decides the physical properties of metals, on one hand, the larger the density of covalent electrons, the stronger the cohesion ofatoms, the higher the melting point, and the better the compressionresistivity, but the transporting properties are weakened at the same timedue to the blocking of the covalent electrons, on the other hand, the largerthe density of free electrons, the better the plasticity, elongation, electricaland thermal conductivity, but the cohesive properties are weakened due tothe less number of cohesive electrons; and it is found as well that the freeelectrons in s orbital of atoms are influenced by the scattering of thecovalent electrons in both d orbital and s orbital and the vibrating ofatomic nucleus, and it is the covalent electrons in s orbital that mainlyinfluence the transporting function of free electrons in liquid phase; (3)the axial ratios of c/a of Ti, Zr and Hf inⅣB group deviate from the idealvalue, so the crystalline symmetry is low, and the linear density ofcovalent electrons X_c is defined for its application in the research of therelationship between electronic structures and physical properties of hcpphase with the combination of T_f and other bond parameters, and theresults show that the symmetry of d_c electrons is lower than that of s_celectrons, and not only the direction and selection of atom coordination of d_c electrons is stronger but also the number of d_c electrons is more thanthat of s_c electrons, so the hcp structures of Ti, Zr and Hf with c/a beingrespectively 1.5884, 1.5925 and 1.5821 can be formed at low temperature; at high temperature, the electrons in d orbital are transformed into sorbital, so the s electrons play main role in the lattice stability and the bccstructrue can exist stablely; (4)using the criterions T_c, X_c和T_f to the studyon the elements Cr, Mo and W inⅥB group, it is found that theproperties such as melting points, tensile strength, hardness, bulk moduliand the bonding energy of the strongest bond follow the same rule as thelinear density in the nearest covalent bond X_(c, 1), i.e., X_(c, 1) (Cr)＜X_(c, 1) (Mo)＜X_(c, 1) (W), and the electrical conductivity, thermalconductivity and the bonding energy of the free electrons follow the samerule as the the bulk density of free electrons T_f, i.e., T_f(Cr)＜T_f(Mo)＜T_f(W); the analyses of electronic structures of elements Cr, Mo and W inⅥB group show that bcc structure is probable to betransformed into hcp or fcc structure and bcc is more preferred to betransformed into hcp due to the more covalent electrons with strongerbonding ability in d orbital and the less covalent electrons with weakerbonding ability in s orbital in hcp than fcc phase, which causes lowerpotential and higher stability of hcp structure, this result agrees well withthat of SGTE database and can explain the difference of lattice stability inSGTE database from the level of electronic structure; (5) when the solidphase of transition metals inⅠ,ⅣandⅥB group is transformed intoliquid phase, both the nonbonding electrons in d orbital and the covalentelectrons in s orbital increase, the covalent electrons in d decrease, andthe free electrons in s orbital have no obvious change or decrease, thischange of electronic structures leads to the decrease of bonding electrons, weakening of bonding direction and cohesion of atoms, increase of singlebond radius and atomic volume, decrease of the density of free electronsand corresponding decrease of electrical conductivity of liquid phase.
引文
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