Theoretical study of negative thermal expansion mechanism of ZnF2

ZnF2 is reported to exhibit negative thermal expansion (NTE) at lower temperatures very recently. In this article, we present the electronic and NTE properties of ZnF2 using a first-principles calculation. Our results show that ZnF2 is an insulator with a direct band gap and a strong hybridization occurs between Zn-3p, 4s and F-2p states. The related calculations on NTE properties are obtained within the quasi-harmonic approximation. The resulting relationship between volume and temperature confirms the NTE properties. Besides, we discuss the NTE mechanism in accordance to phonon vibrational modes. The phonon vibrational modes contributing to the NTE are singled out by Grüneisen parameters and all these modes are low-frequency optical phonons. The lowest frequency rigid unit mode (RUM) of ZnF6 causes a rotary coupling between two adjacent octahedrons and makes the Zn–Zn distance shorter, which is most responsible for the NTE properties of ZnF2.

Graphical abstractZnF2 owns open-framework structure and its negative thermal expansion (NTE) properties have been confirmed using a first-principles calculation. According to the phonon eigenvectors and group theory analysis, the lowest frequency (48.9 cm−1, B1g mode) rigid unit mode (RUM) of ZnF6 causes a rotary coupling between two adjacent octahedrons and makes the Zn–Zn distance shorter, which is considered to be most responsible for the NTE properties of ZnF2.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► The NTE properties of ZnF2 are confirmed using a first-principles calculation. ► Phonon mode classification and Grüneisen parameters are systematically presented. ► The rigid unit mode causes a rotary coupling and makes the Zn–Zn distance shorter. ► The optical branch with the lowest frequency is most responsible for the NTE.