Continuous distribution of relaxation times during mechanical relaxation of fully-stabilized zirconia

Abstract

The internal friction (IF) was measured for ZrO₂ doped with 10 mol% Y₂O₃ polycrystals and single crystals before aging. The degree of the temperature shift with the frequency change δ(1/T ) was examined in order to determine if one or both parameters in the Arrhenius's equation contribute to the occurrence of the continuous distribution of relaxation times (τ). A continuous distribution is derived only from the continuous distribution of the pre-exponential factor (τ ₀), while the activation energies (H ) for τ are constant in two peaks. The peak fitting was carried out using some conventional distribution functions, i.e., the RCSI model, and some famous functions for dielectric relaxation. The IF curves can be fitted quite well by the Kohlrousch–Williams–Watts (KWW) equation with reasonable parameters. The orientation factor (Γ) dependence of the relaxation of the reciprocal torsional modulus (δG ⁻¹) is a linear function relative to Γ in both peaks. When the H for τ of both peaks of the poly- and single crystals was compared, the polycrystalline results should be considered average values of the single-crystalline results. Therefore, the single-crystalline IF peaks also consist of two peaks and the parameters (the relaxation strength and H ) obtained by the peak fitting are valid. A continuous distribution of τ is derived only from the continuous distribution of τ ₀ and the distribution function is the KWW equation.

Acknowledgements

This work is supported by a grant-in-aid from the Iketani Science and Technology Foundation (No. 0101021). I would like to thank M.D. Kazunori Tsuchino, Dr. Toshihiko Watanabe, Dr. Fuho Suzu, and Mr. Kimio Ito for their obliging consistent encouragement. I would also like to thank Dr. Satoshi Ito, Dr. Masao Kikuchi, Prof. Yoichi Tomii, Prof. Shiomi Kikuchi, and Prof. Yasuhiko Ito for their help in obtaining the experimental data, and Prof. Masahiro Koiwa and Dr. Kan Hachiya for their helpful discussions.