Theory of Microwave Effects on Atomic Diffusion in Sintering: Basic Considerations of The Phenomenon of Thermal Runaway
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THEORY OF MICROWAVE EFFECTS ON ATOMIC DIFFUSION IN SINTERING: BASIC CONSIDERATIONS OF THE PHENOMENON OF THERMAL RUNAWAY V. M. KENKRE*, *
L.
SKALA*,
M. W. WEISER"" and J. D. KATZ***
Center for Micro-Engineered
Ceramics and Department of Physics, University of New Mexico, Albuquerque, NM 87131 ** Center for Micro-Engineered Ceramics and Mechanical Engineering Department, University of New Mexico, Albuquerque, NM 87131 Alamos National Laboratory, Los Alamos, NM 87475
"***Los
ABSTRACT We present the results of our recent studies of the possible origin of the reported increase in sintering efficiency brought about by the application of microwaves. We study the phenomenon of thermal runaway in ceramic materials undergoing microwave heating and present a theory on the basis of a simple temperature-time equation. The nonlinear evolution inherent in the equation arises naturally from physical considerations. The theory is applied to experimental observations reported on several different materials including silica, alumina, strontium titanate, zinc oxide and iron oxide, and shown to be in good agreement with the data.
INTRODUCTION 3
Recently, several investigators'- have reported substantial effects of microwave heating on the sintering of several materials. The effects have included the lowering of the sintering temperature as well as of the sintering time. Motivated by these findings, we have begun a thorough investigation of the interaction of microwaves with ceramic materials in general. Results we have obtained regarding one of the aspects of this interaction, viz. the 4 5 phenomenon of "thermal runaway",1. . are described below. The phenomenon is typified by figure 1. In a number of materials, it is found during microwave heating that the increase of temperature is found to be gentle at first but explosive later when a threshold is reached. The sudden rise of temperature is referred to as thermal runaway. We have carried out extensive studies of the runaway phenomenon both at the microscopic level and the macroscopic level, including details of the process of absorption of microwaves, the possibility of what is termed "chaos" in the modern physics literature, and generally nonequilibrium interaction of electromagnetic fields with matter. A practical as well as natural description of thermal runaway has emerged in terms of a simple nonlinear temperature-time equation. We have applied it to a 4 5 variety of materials', , as shown in figure 1.
THE TEMPERATURE-TIME EQUATION We have encountered several different types of the shape of the timetemperature curve in our study of the data on various materials. They can all be described together by stating that, generally, there is an initial stage in which the temperature rises relatively slowly with time, followed by a second stage in which the rate of rise is enhanced significantly, resulting in a steep increase of temperature, and a final stage in which the temperature saturates to the environmental temperature. There are materials for which only the first stage is
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