浓度和含量的康普顿散射测定原理
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摘要
材料是人类社会的里程碑,是人类社会发展的物质基础。因此发展新材料已成为21世纪最重要、最有发展潜力的领域之一。新材料的发展离不开材料科学的发展。材料学是研究材料成分、组织、结构、加工及性能相互关系的一门科学,其中成分、组织、结构和性能的测定依赖于不断发展的材料分析测试技术。本文的目的在于,利用康普顿散射现象,开发一种新的浓度和含量的分析测试技术。这种测试技术的开发成功,将有重要的应用价值和理论意义。本文从理论上对康普顿散射作了系统整理,在此基础上,结合溶液、粉末混
合物和合金的特点,推导出溶液的浓度(或粉末混合物、合金的含量)与康普顿散射光子数之间的关系式。结果表明,溶液浓度(或粉末混合物、合金的含量)与康普顿散射光子数成线性关系。这一结果为浓度或含量的康普顿散射法测定奠定了理论基础。
酸碱盐的康普顿散射实验证明:用Cs~(137)作放射源(射线能量为661.5kev)的条件下,溶液浓度与康普顿散射光子数之间成线性关系;不同碱金属的盐溶液和碱溶液,不同碱土金属的盐溶液,其线性关系的斜率彼此不同,而且随着金属原子序数的增加,线性关系的斜率减少。理论推证和实验结果都说明,可以用康普顿散射作为溶液浓度测定的方法。
用Cs~(137)作放射源的Cu-Ni、Fe-C粉末混合物的康普顿散射实验说明,随着粉末混合物中Ni(或C)含量的增加,康普顿散射光子数成线性增加,这一方面证明了第二章理论推导公式的正确性,另一方面说明可以用康普顿散射测定粉末混合物中某一成分的含量。原子序数仅相差1的Cu-Ni混合物和原子序数相差20的Fe-C混合物比较说明,后者线性关系的斜率较前者大,这意味着混合物中两成分的原子序数相差越大,用康普顿散射法测定某成分的灵敏度越高。
用Cs~(137)作放射源对一组无限固溶Cu-Ni合金进行康普顿散射实验说明,随着合金中Ni含量的增加,康普顿散射光子数缓慢的增加,而Ni含量与康普顿散射光子数之间仍然成线性关系,但直线的斜率很小。和成分含量完全相同的Cu-Ni粉末混合物相比,用康普顿散射法测定的灵敏度要低一些。两者出现这种差别,与Cu-Ni形成合金后,电子结构发生了变化有关系。一组有限固溶的Fe-Cu合金的康普顿散射实验说明,随着Cu含量的增加,康普顿散射光子数并无明显的变化。这一结果表明,康普顿散射光子数既与散射体的电子密度有关,也与电子所受的束缚有关,而Fe中加入Cu,使两者达到平衡,以致随着Cu含量的增加,散射光子数并无明显变化,显然康普顿散射法不适合测定Fe-Cu合金中的Cu含量。
利用量子化学的密度泛函理论(DFT)方法,计算分析了H_2SO_4、HCl、LiCl、NaCl、KCl、NaOH、KOH、MgCl_2、BaCl_2等溶液的离子水合物的电子结构,对H~+、Li~+、Na~+、K~+阳离子的水合物的电子密度分布进行了分析,得出电子的重叠部分按H~+、Li~+、Na~+、K~+的顺序而越来越少,说明水合离子体系中,电子受到的束缚按H、Li、Na、K的顺序而增强。同理Mg~(2+)、Ba~(2+)形成的水合离子体系中,电子受到的束缚按Mg、Ba的顺序而增强;Cl~-、SO_4~(2-)形成的水合离子体系中,电子受到的束缚按Cl~-、SO_4~(2-)的顺序而增强。水合离子中的电子受到束缚增强的规律与康普顿散射中浓度与散射光子数间线性关系的斜率的变化规律一致。用量子化学的计算结果,合理地解释了不同溶液的康普顿散射中,浓度与散射光子数间线性关系的斜率的变化规律。
利用量子化学的密度泛函理论(DFT)的平面波赝势理论,计算了Cu-Ni和Fe-Cu合金的原子电荷布居数和局域态密度(PDOS)。结果表明Cu-Ni合金中随着Ni含量的增加,由于电子越来越多地由低于费米面处向着(甚至超出)费米面的方向转移,说明合金中的电子越来越自由。得到的这些理论分析结果,合理地解释了Cu-Ni合金中康普顿散射光子数与含Ni量间的依赖关系。Fe-Cu合金中随着Cu含量的增加,合金的电子密度增加,相应的康普顿散射光子数应该增加,但由于电子越来越多地向低于费米面的方向转移,电子越来越不自由,最终使康普顿散射光子数在一个很窄的范围内波动。
综合分析酸碱盐溶液、粉末混合物和合金康普顿散射的规律,得出可用康普顿散射法非接触地测定液体浓度和粉末混合物含量,容易实现自动检测和在线检测。用康普顿散射测定合金含量问题,有待进一步研究。
Material is the milestone and the matter basis for the development of human society. So the development of new material is one of the most important and potential fields. New material’s development depends on that of material science, which focuses on the study of the relations between component, texture, structure, machining and the capability of the material. And the measurement of component, texture, structure, machining and capability relies on the constant development of the analysis and testing technique of material. This thesis is to exploit a new analysis and testing techniques to measure the concentration and the content of the scatterer through the Compton scattering phenomenon. And its success will be of profound theoretical and practical significance.
Through the study of the Compton scattering of acid, alkali, salt solutions, powder mixture and alloy, based on systematically of the Compton scattering, the analysis the author has deduced the expression theoretically between the Compton scattering photon counts and the concentration of solutions, or between the Compton scattering photon counts and the content of powder mixture and alloy. The results show that the relationship is linear between the concentration of solutions (or the content of powder mixture and alloy) and the Compton scattering photon counts. And this has laid a theoretical foundation for the measurement of the concentrations and contents through Compton scattering.
Through the Compton scattering experiments of acid, alkali and salt solutions, it is proved that the relationship is linear between the concentration of solutions and the Compton scattering photon counts on the condition that the radiation source is Cs~(137)(the ray energy is 661.5kev). And the line slope is different for different solutions. But for the different alkali solutions and different salt solutions of the alkali metal, there is something similar: with the increasing of the metal’s atomic number, the line slope is decreasing. It is proved that the Compton scattering method can be used to measure the concentration by theoretical deduction and by the results of the Compton scattering experiments.
The Compton scattering experiments of Cu-Ni powder mixtures and Fe-C powder mixtures when adopting theγray source Cs~(137) as the radiation source show that the Compton scattering photon counts are increasing linearly with the increasing of the Ni (or C) content in the powder mixture scatterer. On the one hand this proves the formula by deduction is theoretically correct, and on the other hand, it also shows that the content of certain component in the powder mixture can be measured with the Compton scattering method. The comparison between Cu-Ni powder mixture (the difference between the two atomic numbers is 1) with Fe-C powder mixture (the difference between the two atomic numbers is 20) displays that the slope of the latter is sharper than that of the former. This means, the larger is the difference between the atomic number of the two components of the mixture,the higher is the sensitivity of the method.
The Compton scattering experiments with Cs~(137) as radiation source of Cu-Ni infinite solid solutions show that the Compton scattering photon counts are increasing linearly slowly with the increasing of Ni content in the infinite solid solutions. Nevertheless, the slope of the line is very small. Comparing the result of the Compton scattering of Cu-Ni infinite solid solutions with those of the Cu-Ni powder mixture, the author finds that the sensitivity of the method is lower. This is related with the change of the electronic structure of the scatterer. The Compton scattering experiments of Fe-Cu finite solid solutions, show that there is no obvious change of the Compton scattering photon counts with the Cu content increasing in the Fe-Cu alloy. The result shows that the Compton scattering photon counts are not only related to the electron density of the scattered, but also are related to the freedom degree of the electrons. With the increasing of Cu content, there is a balance between the electron density and the freedom degree of the electrons, so that there is no obvious change of the scattered photon counts. From this we can see that this method is not fit to measure the Cu content in the scatterer of Fe-Cu alloy.
Through the density functional theory method of the quantum chemistry, the electron structure of ion hydrates of some solutions, including H_2SO_4, HCl, LiCl, NaCl, KCl, NaOH, KOH, MgCl_2and BaCl_2 has been computed and analysized. The analysis of the electronic density distribution of the cation H+, Li+, Na+ and K+ shows that the overlapped electronic density is decreasing in the order of the cation H+, Li+, Na+ and K+. It shows that the bound energy of electron becomes larger in the order of the cation H+, Li+, Na+ and K+. For the same reason, the bound energy of electron becomes larger in the order of the cation Mg~(2+) and Ba~(2+) in the Mg~(2+) and Ba~(2+) hydrates system. And the bound energy of electron becomes larger in the order of the cation Cl~- and SO_4~(2-)in the Cl~- and SO_4~(2-) hydrates system. The law that the bound energy of electron becomes larger for the ion hydrate system agrees with that of the linear slope which demenstrates the relationship between the concentration and the scattered photon counts in the Compton scattering. It can reasonably explain the law of the linear slope which shows the relationship between the concentration and the scattered photon counts in the Compton scattering with the result from the quantum chemistry.
Through the employment of the plane-wave pseudopotential method based on the density functional theory (DFT) in Quantum Chemistry, the author calculates the partial density of states (PDOS) and atomic populations of Cu-Ni alloy and Fe-Cu alloy. The analysis shows that the more is Ni content in the Cu-Ni alloy, the more of the electrons move away the Fermi surface. This indicates that the electrons are becoming freer. And it can explain the experimental phenomena which express the relationship between the Compton scattering photon counts and the Ni content in the alloy. It also shows that the more is Cu content in the Fe-Cu alloy, the more of the electrons move towards the lower energy level from the Fermi surface. This indicates that the electrons are bounded more strongly. And under the condition that the electron density is little changed, the strength of the electron bounded will influence the Compton scattering photon counts in the Compton scattering experiments.
After the comparation of the rule of Compton scattering of the acid, alkali and salt solutions, powder mixtures and alloy, the Compton scattering method is promoted, which can measure the concentration of the solution and the content of powder mixture without touching the scatterer. And then automatic measurement and online measurement can be realized easily of the concentration of the solution and the content of powder mixture. But the method to measure the content of the alloy needs to be studied further.
合物和合金的特点,推导出溶液的浓度(或粉末混合物、合金的含量)与康普顿散射光子数之间的关系式。结果表明,溶液浓度(或粉末混合物、合金的含量)与康普顿散射光子数成线性关系。这一结果为浓度或含量的康普顿散射法测定奠定了理论基础。
酸碱盐的康普顿散射实验证明:用Cs~(137)作放射源(射线能量为661.5kev)的条件下,溶液浓度与康普顿散射光子数之间成线性关系;不同碱金属的盐溶液和碱溶液,不同碱土金属的盐溶液,其线性关系的斜率彼此不同,而且随着金属原子序数的增加,线性关系的斜率减少。理论推证和实验结果都说明,可以用康普顿散射作为溶液浓度测定的方法。
用Cs~(137)作放射源的Cu-Ni、Fe-C粉末混合物的康普顿散射实验说明,随着粉末混合物中Ni(或C)含量的增加,康普顿散射光子数成线性增加,这一方面证明了第二章理论推导公式的正确性,另一方面说明可以用康普顿散射测定粉末混合物中某一成分的含量。原子序数仅相差1的Cu-Ni混合物和原子序数相差20的Fe-C混合物比较说明,后者线性关系的斜率较前者大,这意味着混合物中两成分的原子序数相差越大,用康普顿散射法测定某成分的灵敏度越高。
用Cs~(137)作放射源对一组无限固溶Cu-Ni合金进行康普顿散射实验说明,随着合金中Ni含量的增加,康普顿散射光子数缓慢的增加,而Ni含量与康普顿散射光子数之间仍然成线性关系,但直线的斜率很小。和成分含量完全相同的Cu-Ni粉末混合物相比,用康普顿散射法测定的灵敏度要低一些。两者出现这种差别,与Cu-Ni形成合金后,电子结构发生了变化有关系。一组有限固溶的Fe-Cu合金的康普顿散射实验说明,随着Cu含量的增加,康普顿散射光子数并无明显的变化。这一结果表明,康普顿散射光子数既与散射体的电子密度有关,也与电子所受的束缚有关,而Fe中加入Cu,使两者达到平衡,以致随着Cu含量的增加,散射光子数并无明显变化,显然康普顿散射法不适合测定Fe-Cu合金中的Cu含量。
利用量子化学的密度泛函理论(DFT)方法,计算分析了H_2SO_4、HCl、LiCl、NaCl、KCl、NaOH、KOH、MgCl_2、BaCl_2等溶液的离子水合物的电子结构,对H~+、Li~+、Na~+、K~+阳离子的水合物的电子密度分布进行了分析,得出电子的重叠部分按H~+、Li~+、Na~+、K~+的顺序而越来越少,说明水合离子体系中,电子受到的束缚按H、Li、Na、K的顺序而增强。同理Mg~(2+)、Ba~(2+)形成的水合离子体系中,电子受到的束缚按Mg、Ba的顺序而增强;Cl~-、SO_4~(2-)形成的水合离子体系中,电子受到的束缚按Cl~-、SO_4~(2-)的顺序而增强。水合离子中的电子受到束缚增强的规律与康普顿散射中浓度与散射光子数间线性关系的斜率的变化规律一致。用量子化学的计算结果,合理地解释了不同溶液的康普顿散射中,浓度与散射光子数间线性关系的斜率的变化规律。
利用量子化学的密度泛函理论(DFT)的平面波赝势理论,计算了Cu-Ni和Fe-Cu合金的原子电荷布居数和局域态密度(PDOS)。结果表明Cu-Ni合金中随着Ni含量的增加,由于电子越来越多地由低于费米面处向着(甚至超出)费米面的方向转移,说明合金中的电子越来越自由。得到的这些理论分析结果,合理地解释了Cu-Ni合金中康普顿散射光子数与含Ni量间的依赖关系。Fe-Cu合金中随着Cu含量的增加,合金的电子密度增加,相应的康普顿散射光子数应该增加,但由于电子越来越多地向低于费米面的方向转移,电子越来越不自由,最终使康普顿散射光子数在一个很窄的范围内波动。
综合分析酸碱盐溶液、粉末混合物和合金康普顿散射的规律,得出可用康普顿散射法非接触地测定液体浓度和粉末混合物含量,容易实现自动检测和在线检测。用康普顿散射测定合金含量问题,有待进一步研究。
Material is the milestone and the matter basis for the development of human society. So the development of new material is one of the most important and potential fields. New material’s development depends on that of material science, which focuses on the study of the relations between component, texture, structure, machining and the capability of the material. And the measurement of component, texture, structure, machining and capability relies on the constant development of the analysis and testing technique of material. This thesis is to exploit a new analysis and testing techniques to measure the concentration and the content of the scatterer through the Compton scattering phenomenon. And its success will be of profound theoretical and practical significance.
Through the study of the Compton scattering of acid, alkali, salt solutions, powder mixture and alloy, based on systematically of the Compton scattering, the analysis the author has deduced the expression theoretically between the Compton scattering photon counts and the concentration of solutions, or between the Compton scattering photon counts and the content of powder mixture and alloy. The results show that the relationship is linear between the concentration of solutions (or the content of powder mixture and alloy) and the Compton scattering photon counts. And this has laid a theoretical foundation for the measurement of the concentrations and contents through Compton scattering.
Through the Compton scattering experiments of acid, alkali and salt solutions, it is proved that the relationship is linear between the concentration of solutions and the Compton scattering photon counts on the condition that the radiation source is Cs~(137)(the ray energy is 661.5kev). And the line slope is different for different solutions. But for the different alkali solutions and different salt solutions of the alkali metal, there is something similar: with the increasing of the metal’s atomic number, the line slope is decreasing. It is proved that the Compton scattering method can be used to measure the concentration by theoretical deduction and by the results of the Compton scattering experiments.
The Compton scattering experiments of Cu-Ni powder mixtures and Fe-C powder mixtures when adopting theγray source Cs~(137) as the radiation source show that the Compton scattering photon counts are increasing linearly with the increasing of the Ni (or C) content in the powder mixture scatterer. On the one hand this proves the formula by deduction is theoretically correct, and on the other hand, it also shows that the content of certain component in the powder mixture can be measured with the Compton scattering method. The comparison between Cu-Ni powder mixture (the difference between the two atomic numbers is 1) with Fe-C powder mixture (the difference between the two atomic numbers is 20) displays that the slope of the latter is sharper than that of the former. This means, the larger is the difference between the atomic number of the two components of the mixture,the higher is the sensitivity of the method.
The Compton scattering experiments with Cs~(137) as radiation source of Cu-Ni infinite solid solutions show that the Compton scattering photon counts are increasing linearly slowly with the increasing of Ni content in the infinite solid solutions. Nevertheless, the slope of the line is very small. Comparing the result of the Compton scattering of Cu-Ni infinite solid solutions with those of the Cu-Ni powder mixture, the author finds that the sensitivity of the method is lower. This is related with the change of the electronic structure of the scatterer. The Compton scattering experiments of Fe-Cu finite solid solutions, show that there is no obvious change of the Compton scattering photon counts with the Cu content increasing in the Fe-Cu alloy. The result shows that the Compton scattering photon counts are not only related to the electron density of the scattered, but also are related to the freedom degree of the electrons. With the increasing of Cu content, there is a balance between the electron density and the freedom degree of the electrons, so that there is no obvious change of the scattered photon counts. From this we can see that this method is not fit to measure the Cu content in the scatterer of Fe-Cu alloy.
Through the density functional theory method of the quantum chemistry, the electron structure of ion hydrates of some solutions, including H_2SO_4, HCl, LiCl, NaCl, KCl, NaOH, KOH, MgCl_2and BaCl_2 has been computed and analysized. The analysis of the electronic density distribution of the cation H+, Li+, Na+ and K+ shows that the overlapped electronic density is decreasing in the order of the cation H+, Li+, Na+ and K+. It shows that the bound energy of electron becomes larger in the order of the cation H+, Li+, Na+ and K+. For the same reason, the bound energy of electron becomes larger in the order of the cation Mg~(2+) and Ba~(2+) in the Mg~(2+) and Ba~(2+) hydrates system. And the bound energy of electron becomes larger in the order of the cation Cl~- and SO_4~(2-)in the Cl~- and SO_4~(2-) hydrates system. The law that the bound energy of electron becomes larger for the ion hydrate system agrees with that of the linear slope which demenstrates the relationship between the concentration and the scattered photon counts in the Compton scattering. It can reasonably explain the law of the linear slope which shows the relationship between the concentration and the scattered photon counts in the Compton scattering with the result from the quantum chemistry.
Through the employment of the plane-wave pseudopotential method based on the density functional theory (DFT) in Quantum Chemistry, the author calculates the partial density of states (PDOS) and atomic populations of Cu-Ni alloy and Fe-Cu alloy. The analysis shows that the more is Ni content in the Cu-Ni alloy, the more of the electrons move away the Fermi surface. This indicates that the electrons are becoming freer. And it can explain the experimental phenomena which express the relationship between the Compton scattering photon counts and the Ni content in the alloy. It also shows that the more is Cu content in the Fe-Cu alloy, the more of the electrons move towards the lower energy level from the Fermi surface. This indicates that the electrons are bounded more strongly. And under the condition that the electron density is little changed, the strength of the electron bounded will influence the Compton scattering photon counts in the Compton scattering experiments.
After the comparation of the rule of Compton scattering of the acid, alkali and salt solutions, powder mixtures and alloy, the Compton scattering method is promoted, which can measure the concentration of the solution and the content of powder mixture without touching the scatterer. And then automatic measurement and online measurement can be realized easily of the concentration of the solution and the content of powder mixture. But the method to measure the content of the alloy needs to be studied further.
引文
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