TAILIEUCHUNG - Coefficients of thermal expansion of metallic thin films with body centered cubic structure

Numerical calculations of the quantities were performed for Fe and W thin films and found to be in good and reasonable agreement with other theoretical results and experimental data. This research proves that thermal expansion coefficients of thin films approach the values of bulk when thin film is about 70 nm thick. | JOURNAL OF SCIENCE OF HNUE DOI Mathematical and Physical Sci. 2016 Vol. 61 No. 7 pp. 112-121 This paper is available online at http COEFFICIENTS OF THERMAL EXPANSION OF METALLIC THIN FILMS WITH BODY-CENTERED CUBIC STRUCTURE Duong Dai Phuong1 Nguyen Xuan Viet1 Nguyen Thi Hoa2 and Doan Thi Van3 1 Tank Armour Officers Training School Tam Duong Vinh Phuc 2 Hanoi University of Transport and Communications 3 Faculty of Nursing Hanoi Medical Colleges Abstract. The coefficients of thermal expansion of metallic thin films with body-centered cubic BCC structure at ambient conditions were investigated using the statistical moment method SMM including the anharmonicity effects of thermal lattice vibrations. The analytical expressions of Helmholtz free energy lattice constant and linear thermal expansion coefficients were derived in terms of the power moments of the atomic displacements. Numerical calculations of the quantities were performed for Fe and W thin films and found to be in good and reasonable agreement with other theoretical results and experimental data. This research proves that thermal expansion coefficients of thin films approach the values of bulk when thin film is about 70 nm thick. Keywords Metallic thin film statistical moment method thermodynamic properties anharmonicity. 1. Introduction Knowledge of thermodynamic properties of metallic thin film such as heat capacity and coeffcient of thermal expansion are of great importance when determining parameters for the stability and reliability of manufactured devices. In many cases the thermodynamic properties of metallic thin film are not well known or differ from the values for corresponding bulk materials. A large number of experimental and theoretical studies have been carried out on the thermodynamic properties of metal and nonmetal thin film 1-4 . Most of them describe the method used for measuring the thermodynamic properties of crystalline thin films on the .

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