Precipitation kinetics of W₂B₅ in (Ti_0.4W_0.5Cr_0.1)B₂ solid solutions

Abstract

The isothermal precipitation kinetics of W₂B₅ secondary phase from supersaturated polycrystalline (Ti_0.4W_0.5Cr_0.1)B₂ solid solutions were investigated with X-ray diffractometry and scanning electron microscopy in the temperature range between 1500 and 1700°C. The precipitate formation is described by a modified Johnson–Mehl–Avrami–Kolmogorov (JMAK) model, where W₂B₅ particles nucleate preferentially at grain boundaries and subsequently grow into the volume by a two-dimensional process controlled by volume diffusion of the transition metals. Numerical calculations are used to describe quantitatively the time dependence of the precipitated fraction and to determine a differential JMAK exponent n _diff which gives information on the nucleation and growth modes. n _diff decreases during the precipitation process from 2 to about 0.8 for all temperatures investigated. The first limit corresponds to the classical JMAK model (two-dimensional diffusional growth and constant nucleation rate) and the decrease in n _diff is the consequence of an impingement of the nucleating and growing particles in the late stages of the process. Nucleation and growth rates are determined as functions of reciprocal temperature, where the first quantity shows a non-monotonic behaviour with a maximum at about 1650°C and the second quantity exhibits an Arrhenius behaviour with an activation enthalpy of 3.6 eV. From this it can be concluded that the overall precipitate formation is dominated by the kinetics of atomic motion at low temperatures and by the thermodynamics of nucleation at high temperatures.

Acknowledgements

The authors would like to thank E. Ebeling for the ceramographic preparation of the sample surfaces and B. Mühlhan and S. Lenk for their assistance with SEM analysis. The authors are also grateful to P. Klein for helpful discussions in relation to the numerical calculations. This work was supported by the Deutsche Forschungsgemeinschaft.