A Method to Predict the Adhesion Energy of Nonreactive Ceramic-Metal Wetting Based on Chemical Thermodynamics Considerat
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INTRODUCTION Ceramic-metal interfaces exist in many industrial products. High resolution transmission electron microscopy has revealed the atomic configurations for several ceramic-metal interfaces [1]. Ab initio atomistic modeling and simulation [2, 3, 4] see a fast progress. There is, however, a long way to go before it is possible to predict the interface microstructures and properties for an arbitrary ceramic-metal combination solely based on an ab initio strategy. The study of the atomic configuration at the ceramic-liquid metal interfaces is much more difficult than that of the solid state interfaces due to the inability of high resolution transmission electron microscopy in the case of liquid materials. As a result, very little is known about the atomic arrangement at ceramic-liquid metal interfaces, which makes modeling and simulation difficult. McDonald and Eberhart's pioneering work [5] divided the sites of liquid metal atoms on an alumina surface into two types. Metal atoms on type A sites were assumed to be chemically bonded to the oxide ions with a bond energy comparable to that of the bulk metal oxide. Metal atoms located on the type B sites were assumed to be bonded to the oxide ions by van der Waals forces. Chatain et al. [6] indicated that McDonald and Eberhart's model did not distinguish between reactive and nonreactive wetting; further, this model does not agree well with experimental results. Yu [7] established a model that treats reactive and nonreactive wetting separately. Van der Waals interaction was assumed across the interface in a nonreactive system, while chemical bonds were assumed in a reactive system. This assumption deviates significantly from the real situation in view of the results of first principle simulation [4, 8] that there are chemical bonds even in nonreactive ceramic-metal systems like Nb-sapphire. Based on the models of McDonald and Eberhart [5] and Yu [7], Chatain and co-workers [6] proposed a model with the following assumptions: (1) bonds between metal-oxide cation are taken into account, in addition to the metal-oxide anion interaction; (2) these bonds are chemical in nature, established without reconstruction of the liquid metal; and (3) the bond energy is characterized by the enthalpy instead of the Gibbs energy. Then the adhesion energy is expressed as 12
(Me)
(1)
No' V16 e where C, 0 and Me are the oxide metal, oxygen, and liquid metal, respectively, c is a dimensionless constant for each oxide, VM6 is the molar volume of the liquid metal, n is 363
Mat. Res. Soc. Symp. Proc. Vol. 492 © 1998 Materials Research Society
CLiquid Metal Me Figure 1: Sketch for ceramic-metal wetting. The ceramic ion A- embedded in the ceramic surface layer occupies a region which has approximately i of its total surface area in contact with the liquid metal. the stoichiometric ratio of oxygen to cation in the oxide, and AHjMe and AHI/(Me) are the enthalpies of mixing at infinite dilution of the oxygen 0 and oxide metal C in the liquid metal Me, respectively. Yet, the physical meani
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