Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness
This paper proposes a model for the dependence of heat capacity of thin metal films on the temperature and on the number of atomic layers in these films directly. Model representations are based on the principles of statistical physics for solids and concepts of the distribution of principal quantum...
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| Format: | Article |
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MDPI AG
2023-05-01
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| Series: | Materials Proceedings |
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| Online Access: | https://www.mdpi.com/2673-4605/14/1/35 |
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| author | Vladimir Syrovatko Yuliya Syrovatko |
| author_facet | Vladimir Syrovatko Yuliya Syrovatko |
| author_sort | Vladimir Syrovatko |
| collection | DOAJ |
| description | This paper proposes a model for the dependence of heat capacity of thin metal films on the temperature and on the number of atomic layers in these films directly. Model representations are based on the principles of statistical physics for solids and concepts of the distribution of principal quantum numbers in the system of oscillators distributed in solids at high temperatures, i.e., Bose–Einstein distribution. The calculations were performed based on the comparison of the Helmholtz free energy values for the various configurations of films and the number of layers in them. The main tool for the model implementation was the formation and further calculation of the partition function, being an expression of the distribution of principal quantum numbers in the complex system of a thin film. Calculations showed the existence of the optimal film thickness at which the maximum heat capacity was achieved. The calculations were performed based on a comparison of the values of the Helmholtz free energy for different film configurations and the number of layers in them. The main tool for implementing the model was the formation and further calculation of the partition function, which was an expression of the distribution of principal quantum numbers in the complex system of a thin film. The calculation results show the presence of a 15–20% increase in the heat capacity of thin films, corresponding to 400–600 atomic layers and the Dulong–Petit law, i.e., the comparison of exceeding heat capacity values with bulk objects for a certain temperature range. The heat capacity reaches the highest values in thin films of 30–50 atomic layers in thickness and exceeds the value of 3R by ~2.0 times. |
| first_indexed | 2024-03-10T22:30:13Z |
| format | Article |
| id | doaj.art-9f1891714f93452581df94ac2db5730c |
| institution | Directory Open Access Journal |
| issn | 2673-4605 |
| language | English |
| last_indexed | 2024-03-10T22:30:13Z |
| publishDate | 2023-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Materials Proceedings |
| spelling | doaj.art-9f1891714f93452581df94ac2db5730c2023-11-19T11:46:47ZengMDPI AGMaterials Proceedings2673-46052023-05-011413510.3390/IOCN2023-14508Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and ThicknessVladimir Syrovatko0Yuliya Syrovatko1Dnipropetrovsk Branch of the State Institution, “Soil Protection Institute of Ukraine”, Doslidne Settlement, 52071 Dnipro, UkraineDnipropetrovsk Branch of the State Institution, “Soil Protection Institute of Ukraine”, Doslidne Settlement, 52071 Dnipro, UkraineThis paper proposes a model for the dependence of heat capacity of thin metal films on the temperature and on the number of atomic layers in these films directly. Model representations are based on the principles of statistical physics for solids and concepts of the distribution of principal quantum numbers in the system of oscillators distributed in solids at high temperatures, i.e., Bose–Einstein distribution. The calculations were performed based on the comparison of the Helmholtz free energy values for the various configurations of films and the number of layers in them. The main tool for the model implementation was the formation and further calculation of the partition function, being an expression of the distribution of principal quantum numbers in the complex system of a thin film. Calculations showed the existence of the optimal film thickness at which the maximum heat capacity was achieved. The calculations were performed based on a comparison of the values of the Helmholtz free energy for different film configurations and the number of layers in them. The main tool for implementing the model was the formation and further calculation of the partition function, which was an expression of the distribution of principal quantum numbers in the complex system of a thin film. The calculation results show the presence of a 15–20% increase in the heat capacity of thin films, corresponding to 400–600 atomic layers and the Dulong–Petit law, i.e., the comparison of exceeding heat capacity values with bulk objects for a certain temperature range. The heat capacity reaches the highest values in thin films of 30–50 atomic layers in thickness and exceeds the value of 3R by ~2.0 times.https://www.mdpi.com/2673-4605/14/1/35thin filmsheat capacitytemperaturethin film thicknessDebye temperaturequantum numbers |
| spellingShingle | Vladimir Syrovatko Yuliya Syrovatko Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness Materials Proceedings thin films heat capacity temperature thin film thickness Debye temperature quantum numbers |
| title | Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness |
| title_full | Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness |
| title_fullStr | Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness |
| title_full_unstemmed | Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness |
| title_short | Modeling the Dependence of the Heat Capacity of Metallic Thin Films on Temperature and Thickness |
| title_sort | modeling the dependence of the heat capacity of metallic thin films on temperature and thickness |
| topic | thin films heat capacity temperature thin film thickness Debye temperature quantum numbers |
| url | https://www.mdpi.com/2673-4605/14/1/35 |
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