{"title":"Calculation of Debye temperature and Grüneisen parameter at low temperatures","authors":"Mahach N. Magomedov","doi":"10.1016/j.ssc.2025.115833","DOIUrl":null,"url":null,"abstract":"<div><div>It is known that for many substances, the experimentally determined Debye temperature (Θ) changes with temperature (<em>T</em>). It is shown that in the presence of a temperature dependence Θ(<em>T</em>), the expression for isochoric heat capacity should include terms with the first and second derivatives of the Θ(<em>T</em>) function in temperature. Therefore, for the feasibility of the third law of thermodynamics, the Θ(<em>T</em>) function for an <em>n</em>-dimensional crystal at low temperatures must change according to the dependence: Θ(<em>T</em>)<sub><em>low</em></sub> = Θ<sub>0</sub>[1 – χ<sub><em>n</em></sub>(<em>T</em>/Θ<sub>0</sub>)<sup><em>n</em>+1</sup>]. It is shown that the Θ<sub>0</sub> value differs from the Θ<sub>0<em>s</em></sub> value, which is determined from the experimental heat capacity values, without taking into account the dependence of Θ(<em>T</em>)<sub><em>low</em></sub>. An expression for the temperature dependence of the Grüneisen parameter (γ) was also obtained. It is shown that at χ<sub><em>n</em></sub> > 0, the Θ(<em>T</em>)<sub><em>low</em></sub> function decreases, and the γ(<em>T</em>)<sub><em>low</em></sub> function increases with increasing temperature from the values Θ<sub>0</sub> > Θ<sub>0<em>s</em></sub> and γ<sub>0</sub> > γ<sub>0<em>s</em></sub>, respectively. At average temperatures at χ<sub><em>n</em></sub> > 0, the Θ(<em>T</em>) function has a minimum, and the γ(<em>T</em>) function has a maximum. When χ<sub><em>n</em></sub> < 0, the picture changes to the opposite: the Θ(<em>T</em>) function increases from Θ<sub>0</sub> < Θ<sub>0<em>s</em></sub> to a maximum, and the γ(<em>T</em>) function decreases from γ<sub>0</sub> < γ<sub>0<em>s</em></sub> to a minimum. In any case, the change in the functions Θ(<em>T</em>)<sub><em>low</em></sub> and γ(<em>T</em>)<sub><em>low</em></sub> should be proportional to the dependence (<em>T</em>/Θ<sub>0</sub>)<sup><em>n</em>+1</sup>.</div></div>","PeriodicalId":430,"journal":{"name":"Solid State Communications","volume":"397 ","pages":"Article 115833"},"PeriodicalIF":2.1000,"publicationDate":"2025-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Solid State Communications","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0038109825000080","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, CONDENSED MATTER","Score":null,"Total":0}
引用次数: 0
Abstract
It is known that for many substances, the experimentally determined Debye temperature (Θ) changes with temperature (T). It is shown that in the presence of a temperature dependence Θ(T), the expression for isochoric heat capacity should include terms with the first and second derivatives of the Θ(T) function in temperature. Therefore, for the feasibility of the third law of thermodynamics, the Θ(T) function for an n-dimensional crystal at low temperatures must change according to the dependence: Θ(T)low = Θ0[1 – χn(T/Θ0)n+1]. It is shown that the Θ0 value differs from the Θ0s value, which is determined from the experimental heat capacity values, without taking into account the dependence of Θ(T)low. An expression for the temperature dependence of the Grüneisen parameter (γ) was also obtained. It is shown that at χn > 0, the Θ(T)low function decreases, and the γ(T)low function increases with increasing temperature from the values Θ0 > Θ0s and γ0 > γ0s, respectively. At average temperatures at χn > 0, the Θ(T) function has a minimum, and the γ(T) function has a maximum. When χn < 0, the picture changes to the opposite: the Θ(T) function increases from Θ0 < Θ0s to a maximum, and the γ(T) function decreases from γ0 < γ0s to a minimum. In any case, the change in the functions Θ(T)low and γ(T)low should be proportional to the dependence (T/Θ0)n+1.
期刊介绍:
Solid State Communications is an international medium for the publication of short communications and original research articles on significant developments in condensed matter science, giving scientists immediate access to important, recently completed work. The journal publishes original experimental and theoretical research on the physical and chemical properties of solids and other condensed systems and also on their preparation. The submission of manuscripts reporting research on the basic physics of materials science and devices, as well as of state-of-the-art microstructures and nanostructures, is encouraged.
A coherent quantitative treatment emphasizing new physics is expected rather than a simple accumulation of experimental data. Consistent with these aims, the short communications should be kept concise and short, usually not longer than six printed pages. The number of figures and tables should also be kept to a minimum. Solid State Communications now also welcomes original research articles without length restrictions.
The Fast-Track section of Solid State Communications is the venue for very rapid publication of short communications on significant developments in condensed matter science. The goal is to offer the broad condensed matter community quick and immediate access to publish recently completed papers in research areas that are rapidly evolving and in which there are developments with great potential impact.