Effect of Elevated Pressure on the Heat Transfer and Power Requirements During Bridgman Growth of PMN-PT Crystals

Performance of the furnace during Bridgman growth of the lead magnesium niobate-lead titanate crystal (PMN-PT) is analyzed. PMN-PT is electrostrictive ceramic that has near ideal strain-voltage function. Furthermore piezoelectric (2000 to 2300 pC/N) and coupling (92 to 95%) constants are exceptionally good. Due to these properties PMN-PT has wide range of applications - from sonars to transducers in a high precision optical systems. In this research first attempt to crystallize PMN-PT in a Mellen type vertical Bridgman furnace was not successful, as melting temperature of precursor materials was not achieved. At this point choice was between building a new more powerful facility or finding ways to enhance performance of the existing furnace. Besides adjusting power supply to the individual heating elements, redesigning ampoule holding cartridge and improving furnace insulation one more radical improvement was proposed. The entire furnace was placed into the high pressure chamber. Further experiments confirmed that temperature inside the furnace was increased sufficiently to melt precursor materials to obtain PMN-PT. Numerical modeling is undertaken to find limitations of this technique and to predict temperature distribution inside the ampoule. It is of interest also to account for main factors contributing to a higher temperatures achieved in the furnace under the higher pressure (up to 10 atm.). Numerical model of the furnace is based on general purpose finite - element code FIDAP and on previous efforts to model Bridgman type furnace with multiply heaters. In order to account for all heat transfer mechanism involved - conduction, convection and radiation - different parts of the furnace are modeled in accordance with expected dominant mode of heat transfer - conduction in the solid parts, conduction and radiation in the ampoule, gas convection and conduction in the furnace openings complemented with wall-to-wall radiation. Because of these complicating factors, dimensional rather than non-dimensional modeling is performed using steady-state 2-D and 3-D models. Particular attention is paid to the modeling of radiation in a semitransparent material of ampoule 7 sapphire. The radiation model is validated by solving realistic test problem - conduction and radiation heat transfer in the fused quartz. Results are in agreement with both experimental and analytical data.