Grain Growth Control of Dielectric and Magnetic Ceramics

The sintering process transported the atoms in the materials by decreasing the total interface energy. The microstructure changes as a result of grain growth and densification under the capillary driving force due to the interface curvature among grains. The grain growth rate is expressed as the product of the interface mobility and the driving force. According to grain growth theories, the mobility of the interface governed by diffusion control is constant but interface mobility is nonlinear when the movement of an interface is governed by interface reaction. As the growth rate is nonlinear for the regime of interface reaction control, the grain growth is nonstationary with annealing time. The microstructure can be controlled by changing the growth rate of an individual grain with the correlation between the maximum driving force and the critical driving force for appreciable growth. The present paper discusses applications of the principle in the fabrication of dielectric and magnetic ceramic materials.

The interfacial energy penalty to crystal growth close to equilibrium

Understanding the origin of rock microstructure is critical for refining models of the geodynamics of the Earth. We use the geometry of compositional growth zoning of a population of garnet porphyroblasts in a mica schist to gain quantitative insight into (1) the relative growth rates of individual crystals, (2) the departure from equilibrium during their growth, and (3) the mobility of the porphyroblast-matrix interface. The driving force for garnet growth in the studied sample was exceedingly small and is comparable in magnitude to the interfacial energy associated with the garnet-matrix interface. This resulted in size-dependent garnet growth at macroscopic length scales, with a decrease in radial growth rates for smaller crystals caused by the penalty effect of the interfacial energy. The difference in growth rate between the largest and the smallest crystal is ~45%, and the interface mobility for garnet growth from ~535 °C, 480 MPa to 565 °C, 560 MPa in the phyllosilicate-dominated rock matrix ranged between ~10–19 and 10–20 m4 J–1 s–1. This is the first estimation of interface mobility in natural rock samples. In addition to the complex structural and chemical reorganization associated with the formation of dodecahedral coordination polyhedra in garnet, the presence of abundant graphite may have exerted drag on the garnet-matrix interface, further decreasing its mobility.

Phase Field Simulation of AA6XXX Aluminium Alloys Heat Treatment

Heat treatment has a significant impact on the microstructure and the mechanical properties of Al-Mg-Si alloys. The present study presents a first Phase-Field modelling approach on the recrystallisation and grain growth mechanism during annealing. It focuses on the precipitate fraction, radius, and Mg-Si concentration in the matrix phase, which are used as input data for the calculation of the yield strength and hardness at the end of different ageing treatments. Annealing and artificial ageing simulations have been conducted on the MultiPhase-Field based MICRESS@ software, while the ThermoCalc@ software has been used to construct the pseudo-binary Al-Mg phase-diagrams and the atomic-mobility databases of MgxSiy precipitates. Recrystallisation simulation estimates the recrystallisation kinetics, the grain growth, and the interface mobility with the presence/absence of secondary particles, selecting as annealing temperature 400 °C and a microstructure previously subjected to cold rolling. The pinning force of secondary particles decelerates the overall recrystallisation time, causing a slight decrease in the final grain radius due to the reduction of interface mobility. The ageing simulation examines different ageing temperatures (180 and 200 °C) for two distinct ternary systems (Al-0.9Mg-0.6Si/Al-1.0Mg-1.1Si wt.%) considering the interface energy and the chemical free energy as the driving force for precipitation. The combination of Phase-Field and the Deschamps–Brechet model predicted the under-ageing condition for the 180 °C ageing treatment and the peak-ageing condition for the 200 °C ageing treatment.

Study of the effect of Sn grain boundaries on IMC morphology in solid state inter-diffusion soldering

This paper reports on 3D phase field simulations of IMC growth in Co/Sn and Cu/Sn solder systems. In agreement with experimental micrographs, we obtain uniform growth of the CoSn3 phase in Co/Sn solder joints and a non-uniform wavy morphology for the Cu6Sn5 phase in Cu/Sn solder joints. Furthermore, simulations were performed to obtain an insight in the impact of Sn grain size, grain boundary versus bulk diffusion, IMC/Sn interface mobility and Sn grain boundary mobility on IMC morphology and growth kinetics. It is found that grain boundary diffusion in the IMC or Sn phase have a limited impact on the IMC evolution. A wavy IMC morphology is obtained in the simulations when the grain boundary mobility in the Sn phase is relatively large compared to the interface mobility for the IMC/Sn interface, while a uniform IMC morphology is obtained when the Sn grain boundary and IMC/Sn interface mobilities are comparable. For the wavy IMC morphology, a clear effect of the Sn grain size is observed, while for uniform IMC growth, the effect of the Sn grain size is negligible.