{"title":"优化作为单一体系的闪锌矿相的热容量,或核物理如何帮助物理化学","authors":"V.P. Vassiliev , A.S. Leonov , S.A. Kulinich","doi":"10.1016/j.calphad.2024.102687","DOIUrl":null,"url":null,"abstract":"<div><p>The correct mathematical description of heat capacities <em>C</em><sub>p</sub> in a wide range of temperatures is still unsolved problem. A fragmental description of some phases is like a vision of one part of a large mosaic picture. A single description of <em>C</em><sub>p</sub> or other property of a phase of any isostructural series does not allow one to see the integrity of the entire ensemble. We propose a special mathematical model to describe <em>C</em><sub>p</sub> in a wide temperature range for a whole large class of isostructural sphalerite phases. In the proposed model, it is believed that an ideal crystal does not have any foreign inclusions, defects, or dislocations. The group IV elements (Si, Ge, α-Sn and diamond-like Pb) were taken as the basis, with flerovium (<sup>114</sup>Fl) closing this group. There should be no other elements in this group according to the fine structure constant (<em>α</em>) (or the Sommerfeld constant). As a consequence, the limiting value of the heat capacities of phases with a sphalerite structure falls on the element 114 (<sup>114</sup>Fl) and has a value of <em>C</em><sub>p</sub> = 30.5 ± 0.3 J · mol-at<sup>−1</sup> · K<sup>−1</sup>. This value was obtained as a maximal virtual point <em>C</em><sub>p</sub> of the last element (<sup>114</sup>Fl) of group IV and corresponds to Ln (<em>C</em><sub>p</sub>/<em>R</em>) = 1.30 ± 0.01 for the isotherms ln (<em>C</em><sub>p</sub>/<em>R</em>) vs Ln(<em>N</em>), where <em>N</em> is an atomic number of an element of group IV or the sum of the atomic numbers of A<sup>III</sup>B<sup>V</sup> or A<sup>II</sup>B<sup>VI</sup> compounds per mole-atom. The common point of heat capacity attributable to flerovium is obtained from the linear equations <em>С</em><sub>р</sub>/<em>R</em> vs Ln(<em>N</em>) at low temperatures from 25 to 35K. For only pure elements of group IV (Si, Ge, α-Sn and diamond-like Pb), flerovium closes this group, and there are no other elements behind it, according to <em>α</em>. The maximum heat capacity of flerovium can be taken as 30.5 J·mol-at<sup>−1</sup>·K<sup>−1</sup> with an accuracy of 1%. As the temperature decreases, this value slowly decreases (within 1%), and then, when it approaches 0 K, it drops sharply to 0 J·mol-at<sup>−1</sup>·K<sup>−1</sup>. To describe the set of the isostructural experimental data <em>C</em><sub>p</sub>(<em>T</em>) for diamond-like phases in solid state as a whole system, here we used a special multi-parameter family of functions. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence <em>C</em><sub>p</sub>(<em>T</em>) and corresponding experimental data. The dependence of the heat capacities for elements of group IV (Si, Ge, α-Sn, diamond-like Pb, Fl) at fixed temperatures on Ln(<em>N</em>), where <em>N</em> is the atomic number or the demi sum of the atomic numbers of phases A<sup>II</sup>B<sup>VI</sup> or A<sup>III</sup>B<sup>V</sup>. In this case, either a break point or an inflection point attributable to germanium is observed for parameter dependencies on Ln(<em>N</em>).</p></div>","PeriodicalId":9436,"journal":{"name":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Optimizing the heat capacities of sphalerite phases as single system, or how nuclear physics can help physical chemistry\",\"authors\":\"V.P. Vassiliev , A.S. Leonov , S.A. Kulinich\",\"doi\":\"10.1016/j.calphad.2024.102687\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>The correct mathematical description of heat capacities <em>C</em><sub>p</sub> in a wide range of temperatures is still unsolved problem. A fragmental description of some phases is like a vision of one part of a large mosaic picture. A single description of <em>C</em><sub>p</sub> or other property of a phase of any isostructural series does not allow one to see the integrity of the entire ensemble. We propose a special mathematical model to describe <em>C</em><sub>p</sub> in a wide temperature range for a whole large class of isostructural sphalerite phases. In the proposed model, it is believed that an ideal crystal does not have any foreign inclusions, defects, or dislocations. The group IV elements (Si, Ge, α-Sn and diamond-like Pb) were taken as the basis, with flerovium (<sup>114</sup>Fl) closing this group. There should be no other elements in this group according to the fine structure constant (<em>α</em>) (or the Sommerfeld constant). As a consequence, the limiting value of the heat capacities of phases with a sphalerite structure falls on the element 114 (<sup>114</sup>Fl) and has a value of <em>C</em><sub>p</sub> = 30.5 ± 0.3 J · mol-at<sup>−1</sup> · K<sup>−1</sup>. This value was obtained as a maximal virtual point <em>C</em><sub>p</sub> of the last element (<sup>114</sup>Fl) of group IV and corresponds to Ln (<em>C</em><sub>p</sub>/<em>R</em>) = 1.30 ± 0.01 for the isotherms ln (<em>C</em><sub>p</sub>/<em>R</em>) vs Ln(<em>N</em>), where <em>N</em> is an atomic number of an element of group IV or the sum of the atomic numbers of A<sup>III</sup>B<sup>V</sup> or A<sup>II</sup>B<sup>VI</sup> compounds per mole-atom. The common point of heat capacity attributable to flerovium is obtained from the linear equations <em>С</em><sub>р</sub>/<em>R</em> vs Ln(<em>N</em>) at low temperatures from 25 to 35K. For only pure elements of group IV (Si, Ge, α-Sn and diamond-like Pb), flerovium closes this group, and there are no other elements behind it, according to <em>α</em>. The maximum heat capacity of flerovium can be taken as 30.5 J·mol-at<sup>−1</sup>·K<sup>−1</sup> with an accuracy of 1%. As the temperature decreases, this value slowly decreases (within 1%), and then, when it approaches 0 K, it drops sharply to 0 J·mol-at<sup>−1</sup>·K<sup>−1</sup>. To describe the set of the isostructural experimental data <em>C</em><sub>p</sub>(<em>T</em>) for diamond-like phases in solid state as a whole system, here we used a special multi-parameter family of functions. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence <em>C</em><sub>p</sub>(<em>T</em>) and corresponding experimental data. The dependence of the heat capacities for elements of group IV (Si, Ge, α-Sn, diamond-like Pb, Fl) at fixed temperatures on Ln(<em>N</em>), where <em>N</em> is the atomic number or the demi sum of the atomic numbers of phases A<sup>II</sup>B<sup>VI</sup> or A<sup>III</sup>B<sup>V</sup>. In this case, either a break point or an inflection point attributable to germanium is observed for parameter dependencies on Ln(<em>N</em>).</p></div>\",\"PeriodicalId\":9436,\"journal\":{\"name\":\"Calphad-computer Coupling of Phase Diagrams and Thermochemistry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-04-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Calphad-computer Coupling of Phase Diagrams and Thermochemistry\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0364591624000294\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"CHEMISTRY, PHYSICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Calphad-computer Coupling of Phase Diagrams and Thermochemistry","FirstCategoryId":"88","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0364591624000294","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"CHEMISTRY, PHYSICAL","Score":null,"Total":0}
引用次数: 0
摘要
在广泛的温度范围内对热容量 Cp 进行正确的数学描述,仍然是一个尚未解决的问题。对某些相的片面描述就像对一幅巨大的马赛克图片中的一个部分的观察。对任何等结构系列中某一相的 Cp 或其他性质的单一描述,并不能让人看到整个集合的完整性。我们提出了一种特殊的数学模型,用于描述整整一大类等结构闪锌矿相在宽温度范围内的 Cp。在提出的模型中,我们认为理想晶体不存在任何外来夹杂物、缺陷或位错。以第四族元素(Si、Ge、α-Sn 和类金刚石铅)为基础,氟铈镧矿(114Fl)结束了这一族群。根据精细结构常数 (α)(或索默费尔德常数),这组元素中不应有其他元素。因此,闪锌矿结构相的热容极限值落在 114 (114Fl) 元素上,其值为 Cp = 30.5 ± 0.3 J - mol-at-1 - K-1。该值是作为第 IV 组最后一种元素 (114Fl) 的最大虚拟点 Cp 得出的,对应于 ln (Cp/R) vs Ln(N) 等温线的 Ln (Cp/R) = 1.30 ± 0.01,其中 N 是第 IV 组元素的原子序数或每摩尔原子 AIIIBV 或 AIIBVI 化合物的原子序数之和。在 25 至 35K 的低温条件下,鈇的热容量共同点可从 Ср/R vs Ln(N) 的线性方程中获得。根据 α,只有纯元素 IV 组(Si、Ge、α-Sn 和类金刚石铅)中的鈇关闭了该组,在它后面没有其他元素。鈇的最大热容量可取为 30.5 J-mol-at-1-K-1,精确度为 1%。随着温度的降低,该值会缓慢减小(在 1%以内),当温度接近 0 K 时,该值会急剧下降至 0 J-mol-at-1-K-1。为了将固态类金刚石相的一组等结构实验数据 Cp(T) 作为一个整体系统来描述,我们在这里使用了一个特殊的多参数函数族。对于每种物质,参数都是通过最小化 Cp(T) 理论依赖性与相应实验数据之间的差异而找到的。第 IV 组元素(Si、Ge、α-Sn、类金刚石铅、Fl)在固定温度下的热容取决于 Ln(N),其中 N 是原子序数或 AIIBVI 相或 AIIIBV 相的原子序数之和。在这种情况下,Ln(N)的参数依赖性要么出现断点,要么出现锗的拐点。
Optimizing the heat capacities of sphalerite phases as single system, or how nuclear physics can help physical chemistry
The correct mathematical description of heat capacities Cp in a wide range of temperatures is still unsolved problem. A fragmental description of some phases is like a vision of one part of a large mosaic picture. A single description of Cp or other property of a phase of any isostructural series does not allow one to see the integrity of the entire ensemble. We propose a special mathematical model to describe Cp in a wide temperature range for a whole large class of isostructural sphalerite phases. In the proposed model, it is believed that an ideal crystal does not have any foreign inclusions, defects, or dislocations. The group IV elements (Si, Ge, α-Sn and diamond-like Pb) were taken as the basis, with flerovium (114Fl) closing this group. There should be no other elements in this group according to the fine structure constant (α) (or the Sommerfeld constant). As a consequence, the limiting value of the heat capacities of phases with a sphalerite structure falls on the element 114 (114Fl) and has a value of Cp = 30.5 ± 0.3 J · mol-at−1 · K−1. This value was obtained as a maximal virtual point Cp of the last element (114Fl) of group IV and corresponds to Ln (Cp/R) = 1.30 ± 0.01 for the isotherms ln (Cp/R) vs Ln(N), where N is an atomic number of an element of group IV or the sum of the atomic numbers of AIIIBV or AIIBVI compounds per mole-atom. The common point of heat capacity attributable to flerovium is obtained from the linear equations Ср/R vs Ln(N) at low temperatures from 25 to 35K. For only pure elements of group IV (Si, Ge, α-Sn and diamond-like Pb), flerovium closes this group, and there are no other elements behind it, according to α. The maximum heat capacity of flerovium can be taken as 30.5 J·mol-at−1·K−1 with an accuracy of 1%. As the temperature decreases, this value slowly decreases (within 1%), and then, when it approaches 0 K, it drops sharply to 0 J·mol-at−1·K−1. To describe the set of the isostructural experimental data Cp(T) for diamond-like phases in solid state as a whole system, here we used a special multi-parameter family of functions. For each substance, the parameters are found by minimizing the discrepancy between the theoretical dependence Cp(T) and corresponding experimental data. The dependence of the heat capacities for elements of group IV (Si, Ge, α-Sn, diamond-like Pb, Fl) at fixed temperatures on Ln(N), where N is the atomic number or the demi sum of the atomic numbers of phases AIIBVI or AIIIBV. In this case, either a break point or an inflection point attributable to germanium is observed for parameter dependencies on Ln(N).
期刊介绍:
The design of industrial processes requires reliable thermodynamic data. CALPHAD (Computer Coupling of Phase Diagrams and Thermochemistry) aims to promote computational thermodynamics through development of models to represent thermodynamic properties for various phases which permit prediction of properties of multicomponent systems from those of binary and ternary subsystems, critical assessment of data and their incorporation into self-consistent databases, development of software to optimize and derive thermodynamic parameters and the development and use of databanks for calculations to improve understanding of various industrial and technological processes. This work is disseminated through the CALPHAD journal and its annual conference.