二元Pb合金结构和性质的分子动力学模拟及真空蒸馏实验研究
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摘要
分子动力学能够准确模拟体系的宏观性质,同时又能存储大量的微观信息,已成为研究液态合金性质的重要方法。合金熔体的微观结构、高温下合金的热力学性质和熔体内部的传输性质均对固态合金的结构和性质产生重要影响,并且决定了冶金中合金的分离、提纯等动力学过程,因此对液态合金的结构、热力学和动力学性质的模拟已成为目前分子动力学研究的热点问题。本文针对在分子动力学领域模拟较少的四种Pb-Cu、Pb-Au、Pb-Ag、Pb-Mg二元合金,模拟高温下合金的熔体结构、熔体内部的团簇情况、合金的热力学性质和扩散性质；模拟四种金属单质Pb、Ag、Cu、Au的扩散性质；同时针对Pb-Cu、Pb-Au、Pb-Ag合金,进行真空蒸馏的实验研究,其目的在于考察合金的熔体结构和扩散性质对合金真空蒸馏产生的影响。本文的主要工作包括以下几点：
首先模拟不同成分下Pb-Cu、Pb-Au、Pb-Ag和Pb-Mg合金的熔化过程,计算不同温度下合金的对相关函数、配位数、相关半径及熔体团簇的原子个数。采用熔体结构参数分析熔体内部不同原子间相互作用的大小,并进行比较；分析合金的配位数和偏配位数随温度和成分的变化规律,并使用配位数分析合金内部同种和异种原子间的成键情况；采用合金的相关半径分析合金内部的团簇情况及无序区与合金成分的关系,采用对相关函数第一峰高度分析合金内部团簇的晶化程度与Pb含量的关系。
计算不同温度下Pb-Cu、Pb-Ag、Pb-Au合金的焓值、结合能和形成能等能量函数,得到的计算值与实验值较为符合,丰富了二元Pb合金的热力学数据库。在相同温度和Pb含量时,比较Pb-Cu,Pb-Au和Pb-Ag三种合金的形成能,可以看出Pb-Ag和Pb-Cu合金为正偏差体系,Pb-Au合金为负偏差体系；在相同温度下Pb-Cu的形成能大于Pb-Ag的形成能,说明Pb-Cu合金的偏离程度大于Pb-Ag的偏离程度；随着温度的升高,合金形成能的绝对值不断降低趋近于0,合金与理想熔体间的偏离程度不断降低,趋近于理想熔体。
然后计算Cu, Ag, Au, Pb四种液态金属扩散性质,并与已有的实验值和其他研究者的计算结果进行比较,通过比较可以发现：本文得到的Ag, Au, Cu, Pb金属单质的自扩散系数在熔点附近的计算值与实验值的误差最大不超过1.9%。计算四种金属单质的自扩散激活能和指前因子,可以看出计算得到的金属自扩散激活与指前因子与实验值符合较好,从而验证了GEAM势对高温下液态金属单质自扩散系数计算的准确性。
采用分子动力学方法结合NRTL方程提出了一种计算合金互扩散系数的新方法,使得采用分子动力学方法模拟二元合金的扩散性质成为可能。该方法首先模拟得到合金中各组分的自扩散系数,然后使用NRTL方程计算合金的热力学因子,进而结合Darken公式得到合金在目标温度下的互扩散系数。本文使用该方法计算Pb-Cu、Pb-Mg、Pb-Au、Pb-Ag合金在目标温度下的互扩散系数。可以看出计算结果与已有的实验值符合较好,互扩散系数的变化趋势与实验值一致,同时从微观熔体结构角度分析了影响合金扩散系数的因素。通过分析可以看出合金中原子的成键情况、原子的团簇情况和晶化程度共同影响合金的扩散系数。计算了合金中两组份的相关性,可以看出,合金中两组份的相关性是由合金中异种原子的成键数目决定的,异种原子的成键数越多合金两组份的相关性越强。
最后采用真空蒸馏的方法对Pb-Cu、Pb-Ag和Pb-Au二元合金进行实验研究,结果表明真空蒸馏可以较好的分离三种合金,并从熔体结构和合金的扩散性质两方面对合金真空蒸馏的实验现象进行了解释。
计算了三种二元Pb-Ag、Pb-Au和Pb-Cu合金在真空蒸馏过程中Pb的挥发速率和Pb在熔体内部的扩散通量,通过比较可以看出,当残留物中Pb的浓度差为1%-5%时,合金中Pb的扩散通量与Pb的挥发速率极为接近,合金熔体内部的扩散速率决定了Pb的挥发速率；当Pb的浓度差在5%-10%时,合金中Pb的扩散通量小于Pb的挥发速率,但两者差值不大,表明此时Pb的挥发受温度和扩散性质共同影响,其中扩散系数的影响较大；当残留物中Pb的浓度差大于10%时,Pb的扩散通量远小于Pb的挥发速率,表明此时Pb的挥发速率受温度的控制。
Molecular dynamics has become one of the key methods in researching the structure of the melt because it can simulate the macroscopic properties and can collective lots of microcosmic information. Microstructure, thermodynamic and transmission properties of the alloy at high temperature are all important parameters for the structure and properties of solid state alloy, and also effect the separation and purification progress of the alloy and become the focus of the present molecular dynamics reserch. Microstructures, clusters, thermodynamic properties, and diffusion properties of Pb-Cu, Pb-Au, Pb-Ag and Pb-Mg alloy were simulated at this research. And also did systemic vacuum distillation experiments for Pb-Cu, Pb-Ag and Pb-Au binary alloy to explore the effcte of Microstructures and diffusion properties on vacuum distillation of binary alloy. The central work and conclusion of this paper includes:
Firstly, we simulate the melting process for Pb-Cu, Pb-Ag, Pb-Au and Pb-Mg binary alloy. The pair correlation function, correlation radius, coordination number and atomic number of the cluster were calculated. With the parameter of the pair correlation function, atmic interaction was analyzed. The vatiations of the coordination number with content of Pb are discussed, and compared the bond of homologous and heterologous atom by coordination number. With the correlation radius the cluster and the vatiations of the disorderd region in binary alloy with content of Pb are discussed. The height of the first peak in the partial pair correlation function was used to analyze the content of Pb dependence of crystallization of Cu cluster.
Enthalpy of formation, cohesive energy and formation energy at different temperature were calculated and agreed well with the experimental value. Formation energy of Pb-Cu, Pb-Au and Pb-Ag alloy at the same temperature and the same lead content was compared, formation energy of Pb-Ag and Pb-Cu alloy are positive so the alloy belong to positive deviation system, the Pb-Au alloy belong to negative deviation system. With the temperature increased, the deviation degree decreased and the alloy approaches to ideal melt. Formation energy of Pb-Cu alloy is higher than that of Pb-Ag alloy at the temperature, namely the deviation degree of Pb-Cu alloy is higher than that of Pb-Ag alloy.
Diffusion properties of liquid pure Cu, Ag, Au and Pb were calculated and compared with the experimental ones, calculation errors of four pure metals are less than 1.9% near the melting point. Activation energy and pre-factor of self diffusion were calculated and agree well with the experimental values, high calculation precision of self diffusion coefficient appears in this paper.
A new method to calculate the mutual diffusion coefficient was proposed based on molecular dynamics and NRTL thermodynamic equation. At first, self diffusion coefficient was calculated with molecular dynamics, then thermodynamic factor was calculated with NRTL equation, mutual diffusion coefficient was obtained with Darken equation. Mutual diffusion coefficients of Pb-Cu, Pb-Mg, Pb-Au and Pb-Ag alloy at different temperature were obtained in this paper and the calculated value agrees well with the experimental one. Influencing factors to diffusion coefficient was analyzed with crystallization, cluster and the bond of atom influence the self and mutual diffusion coefficients. The relevance of the two component was calculated, we can obtian form the result that the relevance of the two component are determined by the number of heterologous atom bond, the more numbers of heterologous atom bond the stronger relevance we have.
Vacuum distillation experiments were carried out with Pb-Cu、Pb-Ag and Pb-Au binary alloy, from the result we can see Pb-Cu、Pb-Ag and Pb-Au binary alloy can separate well with vacuum distillation method, some special experiment phenomena were observed, and analysed with microstructure of melt and diffusion coefficients.
The mass flux and evaporation velocity of Pb in binary alloy were calculated and compared, when the concentration difference of Pb in residuum is 1%-5%, the mass flux and evaporation velocity is similar, the evaporation velocity of Pb in binary alloy was controlled by the mass flux. When the concentration difference of Pb is 5%-10%, the mass flux is less than the evaporation velocity of Pb, but the differences between them are not so significant, so the evaporation velocity of Pb in binary alloy was controlled by the mass flux and the temperature, and the effect of the mass flux makes a big difference compared with that of the temperature. When the concentration difference of Pb is more than 10%, the mass flux is much less than the evaporation velocity of Pb, which means the evaporation velocity of Pb in binary alloy was controlled by the temperature.
首先模拟不同成分下Pb-Cu、Pb-Au、Pb-Ag和Pb-Mg合金的熔化过程,计算不同温度下合金的对相关函数、配位数、相关半径及熔体团簇的原子个数。采用熔体结构参数分析熔体内部不同原子间相互作用的大小,并进行比较；分析合金的配位数和偏配位数随温度和成分的变化规律,并使用配位数分析合金内部同种和异种原子间的成键情况；采用合金的相关半径分析合金内部的团簇情况及无序区与合金成分的关系,采用对相关函数第一峰高度分析合金内部团簇的晶化程度与Pb含量的关系。
计算不同温度下Pb-Cu、Pb-Ag、Pb-Au合金的焓值、结合能和形成能等能量函数,得到的计算值与实验值较为符合,丰富了二元Pb合金的热力学数据库。在相同温度和Pb含量时,比较Pb-Cu,Pb-Au和Pb-Ag三种合金的形成能,可以看出Pb-Ag和Pb-Cu合金为正偏差体系,Pb-Au合金为负偏差体系；在相同温度下Pb-Cu的形成能大于Pb-Ag的形成能,说明Pb-Cu合金的偏离程度大于Pb-Ag的偏离程度；随着温度的升高,合金形成能的绝对值不断降低趋近于0,合金与理想熔体间的偏离程度不断降低,趋近于理想熔体。
然后计算Cu, Ag, Au, Pb四种液态金属扩散性质,并与已有的实验值和其他研究者的计算结果进行比较,通过比较可以发现：本文得到的Ag, Au, Cu, Pb金属单质的自扩散系数在熔点附近的计算值与实验值的误差最大不超过1.9%。计算四种金属单质的自扩散激活能和指前因子,可以看出计算得到的金属自扩散激活与指前因子与实验值符合较好,从而验证了GEAM势对高温下液态金属单质自扩散系数计算的准确性。
采用分子动力学方法结合NRTL方程提出了一种计算合金互扩散系数的新方法,使得采用分子动力学方法模拟二元合金的扩散性质成为可能。该方法首先模拟得到合金中各组分的自扩散系数,然后使用NRTL方程计算合金的热力学因子,进而结合Darken公式得到合金在目标温度下的互扩散系数。本文使用该方法计算Pb-Cu、Pb-Mg、Pb-Au、Pb-Ag合金在目标温度下的互扩散系数。可以看出计算结果与已有的实验值符合较好,互扩散系数的变化趋势与实验值一致,同时从微观熔体结构角度分析了影响合金扩散系数的因素。通过分析可以看出合金中原子的成键情况、原子的团簇情况和晶化程度共同影响合金的扩散系数。计算了合金中两组份的相关性,可以看出,合金中两组份的相关性是由合金中异种原子的成键数目决定的,异种原子的成键数越多合金两组份的相关性越强。
最后采用真空蒸馏的方法对Pb-Cu、Pb-Ag和Pb-Au二元合金进行实验研究,结果表明真空蒸馏可以较好的分离三种合金,并从熔体结构和合金的扩散性质两方面对合金真空蒸馏的实验现象进行了解释。
计算了三种二元Pb-Ag、Pb-Au和Pb-Cu合金在真空蒸馏过程中Pb的挥发速率和Pb在熔体内部的扩散通量,通过比较可以看出,当残留物中Pb的浓度差为1%-5%时,合金中Pb的扩散通量与Pb的挥发速率极为接近,合金熔体内部的扩散速率决定了Pb的挥发速率；当Pb的浓度差在5%-10%时,合金中Pb的扩散通量小于Pb的挥发速率,但两者差值不大,表明此时Pb的挥发受温度和扩散性质共同影响,其中扩散系数的影响较大；当残留物中Pb的浓度差大于10%时,Pb的扩散通量远小于Pb的挥发速率,表明此时Pb的挥发速率受温度的控制。
Molecular dynamics has become one of the key methods in researching the structure of the melt because it can simulate the macroscopic properties and can collective lots of microcosmic information. Microstructure, thermodynamic and transmission properties of the alloy at high temperature are all important parameters for the structure and properties of solid state alloy, and also effect the separation and purification progress of the alloy and become the focus of the present molecular dynamics reserch. Microstructures, clusters, thermodynamic properties, and diffusion properties of Pb-Cu, Pb-Au, Pb-Ag and Pb-Mg alloy were simulated at this research. And also did systemic vacuum distillation experiments for Pb-Cu, Pb-Ag and Pb-Au binary alloy to explore the effcte of Microstructures and diffusion properties on vacuum distillation of binary alloy. The central work and conclusion of this paper includes:
Firstly, we simulate the melting process for Pb-Cu, Pb-Ag, Pb-Au and Pb-Mg binary alloy. The pair correlation function, correlation radius, coordination number and atomic number of the cluster were calculated. With the parameter of the pair correlation function, atmic interaction was analyzed. The vatiations of the coordination number with content of Pb are discussed, and compared the bond of homologous and heterologous atom by coordination number. With the correlation radius the cluster and the vatiations of the disorderd region in binary alloy with content of Pb are discussed. The height of the first peak in the partial pair correlation function was used to analyze the content of Pb dependence of crystallization of Cu cluster.
Enthalpy of formation, cohesive energy and formation energy at different temperature were calculated and agreed well with the experimental value. Formation energy of Pb-Cu, Pb-Au and Pb-Ag alloy at the same temperature and the same lead content was compared, formation energy of Pb-Ag and Pb-Cu alloy are positive so the alloy belong to positive deviation system, the Pb-Au alloy belong to negative deviation system. With the temperature increased, the deviation degree decreased and the alloy approaches to ideal melt. Formation energy of Pb-Cu alloy is higher than that of Pb-Ag alloy at the temperature, namely the deviation degree of Pb-Cu alloy is higher than that of Pb-Ag alloy.
Diffusion properties of liquid pure Cu, Ag, Au and Pb were calculated and compared with the experimental ones, calculation errors of four pure metals are less than 1.9% near the melting point. Activation energy and pre-factor of self diffusion were calculated and agree well with the experimental values, high calculation precision of self diffusion coefficient appears in this paper.
A new method to calculate the mutual diffusion coefficient was proposed based on molecular dynamics and NRTL thermodynamic equation. At first, self diffusion coefficient was calculated with molecular dynamics, then thermodynamic factor was calculated with NRTL equation, mutual diffusion coefficient was obtained with Darken equation. Mutual diffusion coefficients of Pb-Cu, Pb-Mg, Pb-Au and Pb-Ag alloy at different temperature were obtained in this paper and the calculated value agrees well with the experimental one. Influencing factors to diffusion coefficient was analyzed with crystallization, cluster and the bond of atom influence the self and mutual diffusion coefficients. The relevance of the two component was calculated, we can obtian form the result that the relevance of the two component are determined by the number of heterologous atom bond, the more numbers of heterologous atom bond the stronger relevance we have.
Vacuum distillation experiments were carried out with Pb-Cu、Pb-Ag and Pb-Au binary alloy, from the result we can see Pb-Cu、Pb-Ag and Pb-Au binary alloy can separate well with vacuum distillation method, some special experiment phenomena were observed, and analysed with microstructure of melt and diffusion coefficients.
The mass flux and evaporation velocity of Pb in binary alloy were calculated and compared, when the concentration difference of Pb in residuum is 1%-5%, the mass flux and evaporation velocity is similar, the evaporation velocity of Pb in binary alloy was controlled by the mass flux. When the concentration difference of Pb is 5%-10%, the mass flux is less than the evaporation velocity of Pb, but the differences between them are not so significant, so the evaporation velocity of Pb in binary alloy was controlled by the mass flux and the temperature, and the effect of the mass flux makes a big difference compared with that of the temperature. When the concentration difference of Pb is more than 10%, the mass flux is much less than the evaporation velocity of Pb, which means the evaporation velocity of Pb in binary alloy was controlled by the temperature.
引文
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