Lattice vibrational property in the transition-metal diboride ZrB2

Lattice vibrational property has been determined in ZrB(2) system using the temperature-dependent extended X-ray-absorption fine-structure (EXAFS) technique from room temperature to 28K. 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 ZrB(2) presents obvious particularity and anisotropy.