Applications of q - Deformed Fermi - Dirac statistics and statistical moment method to study thermodynamic properties, magnetic properties of metals and metallic thin films

According to Fig. 4.7 to Fig. 4.9, at the same thickness when the temperature increases, isothermal compressibility of thin films increases non-linearly and strongly in high temperature. At the same temperature, isothermal compressibility decreases with the increasing of the thickness. When the thickness increases from 10 to 70 layers, the isothermal compressibility strongly decreases. When the thickneses is larger than 70 layers, the isothermal compressibility slightly decreases and approaches the value of the bulk.

The temperature and thickness dependence of the thermal expansion coefficient are presented in figures from Fig. 4.10 to Fig. 4.12. According to these figures, at the same thickness, the thermal expansion coefficient increases with the absolute temperature T. At the same temperature, when the thickness increases, the thermal expansion coefficient of thin film increases and approaches the value of the bulk. This result is in consistent with the experimental study of Al thin film on the substrate. When the thickness increases to about 50 nm, the thermal expansion coefficient of thin films approaches the value of the bulk. At room temperature, the coefficient of thermal expansion of the Al and Pb thin films increase with the increasing of thickness. These results are in good agreement with our calculations.

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