Thermodynamics and Densification Kinetics in Solid-state Sintering of Ceramics
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Thermodynamics and densification kinetics in solid-state sintering of ceramics J. L. Shi State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, 1295 Ding-Xi Road, Shanghai, 200050, People’s Republic of China (Received 24 November 1997; accepted 25 October 1998)
Based on the stability analysis of the closed pores in two dimensions which was determined mathematically with their particle coordination number and dihedral angle, the stability of those in three dimensions was determined with a spherical pore model. The model is set up by first excluding the effect of interface tension, so the pore was supposed to be spherical, and then the tensile stress arisen from the interface tension was supposed to act on this hypothesized spherical pore. On the basis of the spherical pore model, microstructure models based on pores, not grains, for the real powder compacts were first established. Densification kinetics were then determined from the models by the densification rate equations, which were derived by relating density to pore size to grain size ratio, for the intermediate and final stages of sintering. The criteria for pore shrinkage were discussed quantitatively. The derived equations can be used to simulate the relation between densification rate and density during heating with a constant rate and for the explanation of the effects of pore size distribution, agglomerates, and green density on sintering.
I. INTRODUCTION A. A brief introduction about the sintering stage
The solid-state sintering theory of ceramics has been a fundamental theme for several decades.1–11 According to Coble,12 solid-state sintering can be divided into three stages. The first or initial stage of sintering involves the interface formation and neck growth between primary particles till an equilibrium configuration is reached. The initial stage of sintering, as indicated by Coble, involves no grain growth. The second or intermediate stage of sintering starts when grain growth begins. During this stage of sintering, the grain boundary forms extensively but pores are still connected with each other and form a continuous pore network. No continuous grain boundary networks are formed in this stage. As pores become isolated the intermediate stage of sintering ends and the third or final stage of sintering starts. Density increases slightly but the microstructure develops very rapidly in this stage of sintering. B. A brief review of the solid-state sintering models and theories 1. Theories for the initial stage of sintering
There have been numerous sintering theories developed by different authors13–18 for describing the densification processes in the initial stage of pressureless sintering. These models are mainly based on a similar two-sphere model and differ with each other only by 1398
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J. Mater. Res., Vol. 14, No. 4, Apr 1999
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assuming different mass transpor
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