The solid-state reactions occurring in the system Pb0-Ti02-Zr02 were investigated using constant heating rates up to 1000°C. DTA, dilatometric length changes, and XRD analysis were used for characterization. PbO and T i 0 2 reacted exothermally to form the product PbTi03 with a large volume expansion between 450' and 600'C. Formation of PbZrO, from PbO and Zr02 occurred endothermally with a large volume expansion between 700° and 800'C. The expansion was due to reaction topology, differential molar volumes of products and reactants, and the pellet microstructure. In the formation of PZT from ternary powder mixtures, PT formed between 450' and 6OO0C, followed by PZT formation at >7OO0C with no measurable amounts of PbZr03 formed as determined by XRD analysis. The analysis of the mechanisms indicates that the overall kinetics of homogeneous PZT solid-solution formation are determined by either the ionic transport within the perovskite lattice or the phase-boundary reactions leading to perovskite formation and not by the diffusion of Ti across PbO, which is relatively rapid.

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A theoretical analysis was carried out to estimate the quasisteady-state external mass transport by lattice, surface and gaseous diffusion in terms of the stereologically measurable microstructural parameters of a mixed powder compact. It was shown that the gaseous transport can be described by a single dimensionless quantity termed "sublimation transport modulus." Using these equations, the relative importance of the alternate external transport modes can be evaluated.Based on the above analysis, "shrinking core" and "grain models" were modified whereby the microstructural parameters appeared explicitly in the kinetic expressions. Conditions under which the mixed powder reactions assume a gas-solid type of kinetic behavior were established. "Contact-Maintenance theory" based on the volumetric changes on a particulate level was developed to explain the abrupt changes observed in the reaction mechanism. Accordiniy, it becomes possible to predict the conditions under which a contact between the reactant particles can I "=ak leading to the gaseous external mass transport as a new and possibly a rate limiting step.The "Macroscopic Expansion Model" was developed to correlate the particulate volume changes to the pellet dimensional changes for a mixture of powders of arbitrary size distributions and fixed shapes. Shrinking Core Model for Nonporous SolidsThe shrinking core (also called 'unreacted core' or 'topochemical reaction ) model has the advantage of physical and mathematical simplicity. Reaction is assumed to proceed by diffusion of one reactant through the nonporous product to a sharp interface of nonporous second reactant. Nucleation occurs instantaneously over the entire reactant surface and therefore does not pose a kinetic barrier. Gas-solid reaction models based on this geometry were developed by St. Clair/ 4 ' Lu and Bitsianes^5' and Spitzer et al.' 6^ which took into account a variety of factors such as reversibility of reactions, pressure drop across the product layer, etc. Conditions under which both the chemical reaction and the diffusion are of comparable magnitude were modeled by Lu and multiplicity of (81 reactions was incorporated into analysis by others. Shrinking (9) core model as modified by Shen and Smith/ further included effects of volume differences between products and reactants as well as the effect of external gas-phase mass transfer. Their model therefore represents the most mature form of shrinking-core nodel for reactions between gases and nonporous solids. Shrinking core model indirectly forms the basis of almost all the commonly used solid-solid reaction models in that they usually assume a similar geomptry. A surface of a nonporous component with a product layer on it is assumed to be completely and continually covered by the diffusing component. In practice this condition can be realized only for solid-fluid reactions, and therefore such an assumptions amounts to ignoring the effects of external microstructure on the reaction kinetics. Moreover, almost all models have been devoted ...