THERMAL EXPANSION OF SOLIDS BASED ON AN ANHARMONIC OSCILLATOR APPROACH
A.I. Hashimova
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ABSTRACT

The article explains the thermal expansion of solids using a harmonic oscillator model. It assumes atoms oscillate around equilibrium points in a crystal lattice. If oscillations were purely harmonic, thermal expansion would not occur; expansion arises from anharmonicity. Anharmonicity introduces an additional term in the potential energy expression, leading to a non-zero thermal expansion coefficient. The theoretical results agree with experimental data, such as the temperature dependence of copper’s thermal expansion coefficient. At high temperatures, the thermal expansion coefficient becomes nearly constant. At low temperatures, it follows a T³ dependence and approaches zero as temperature approaches absolute zero. Factors affecting thermal expansion differ between metals and semiconductors; in metals, the electron gas plays a significant role. In semiconductors, impurities, defects, and changes in the band gap also influence the expansion coefficient. The Debye temperature can be estimated from experimental values of the thermal expansion coefficient.

Keywords: Thermal expansion, solids, harmonic oscillator model, anharmonicity, potential energy
DOI:10.70784/azip.1.2026111

Received: 24.12.2025
Internet publishing: 21.01.2026    AJP Fizika E 2026 1 en p.11-15

AUTHORS & AFFILIATIONS

Sumgait State University, Sumgait, Azerbaijan
E-mail: hasimovaaynur@gmail.com

Graphics and Images

      

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