Lattice vibrational property in the transition-metal diboride ZrB2

Lattice vibrational property has been determined in ZrB2 system using the temperature-dependent extended X-ray-absorption fine-structure (EXAFS) technique from room temperature to 28 K. The smooth behavior of Debye–Waller factor curve with temperature is slightly abnormal for the first pair Zr–B. In order to reproduce this curve, an improved Einstein mode with two Einstein frequencies has been used. The quantitative analysis of temperature-dependent Debye–Waller factor of Zr–B pair shows one Einstein frequency is very high and the other is small. These frequencies correspond to the vibration of boron layer atoms and transition-metal layer atoms, respectively. Based on the Einstein mode with one frequency, the vibrational frequency for Zr–Zr pair has been also obtained. Zirconium diboride has two types of Zr–Zr interaction. One is in-plane and the other is out-of-plane along the high symmetry axis. Our analysis shows there is a little difference between in-plane Zr–Zr vibration and out-of-plane one. And the smaller Einstein vibrational frequency for the Zr–B shell is just between the two ones of the Zr–Zr shells. Our results show that the lattice vibrational behavior in ZrB2 presents obvious particularity and anisotropy.