The paradox of ceramic production solved
During the manufacture of ceramics, finely powdered compacts are heated to just below the melting point. The processes occurring during this process, known as sintering, have so far been interpreted incorrectly. Electron microscopic investigations show that crystals with corners and edges remain. A long-standing paradox in the theory of sintering of ceramic products has now been resolved by Alan W. Searcy of the Materials Sciences Division of the Ernest Orlando Lawrence Berkeley National Laboratory. Searcy's work, which he carried out with Jeffrey Bullard of the University of Illinois and W. Craig Carter of the National Institute of Standards and Technology, promises to shed light on the properties of many ceramics, including layered semiconductors and refractory silicon nitrides.
During sintering, one of the most important processes in the manufacture of ceramics, finely powdered compacts are heated to temperatures just below their melting point. Atoms and molecules are thus set in rapid motion and the particles fuse with one another. This process reduces porosity and increases the strength of the end product.
The “classical” idea of the process assumes that the particles in the compact are spherical and the movement of the atoms and molecules is caused by differences in surface curvature. It was believed that atoms move from smaller radius particles to larger radius particles in order to reduce the surface free energy (the work required to form the surface). The concave areas formed upon contact between the particles would then be filled with atoms from convex surfaces.
In reality, the molecules of crystalline particles sometimes move in directions that this theory does not allow at all."Which is not surprising," Searcy notes, "because classical theory fails at what I call the single-particle sintering test. According to the theory, an isolated particle of any shape should slowly evolve into a sphere. But in contrast, most single crystals, if given enough time to develop, will have facets." In contrast to the ideal sphere, the surface energies of a crystal depend on the different orientation of the surfaces compared to the underlying crystal lattice structure.
"So we have a theory here," says Searcy, "that sintering cannot occur if the particles have planar surfaces and edges. In truth, however, many solids such as magnesium oxide, cob alt oxide, common s alt, and lithium fluoride retain their faceted shapes when sintered; yes, some even develop them during sintering.”
Searcy found a clue to this puzzle when he read a footnote in the work of Josiah Willard Gibbs, who lived in the 19th century. Century living founder of chemical thermodynamics. Gibbs shows that molecules at the edges between the crystal facets leave and resume their places more often than those molecules located in the middle of the crystal faces. This is because the edge molecules are less strongly bound.
Searcy was inspired by what he calls Gibbs' "qualitative description of dynamic equilibrium," and collaborated with Bullard and Carter, both former students at Lawrence Berkeley National Laboratory, to develop equations that account for shape changes during of sintering by energy differences between the differently oriented surfaces and edges. These equations are based on Searcy's "Statistical Thermodynamic Description of Unstable Internal Equilibrium" in crystals of any shape.
The new equations are based on two main principles: First, any shape change is possible as long as the total energy is reduced. The change does not necessarily have to achieve a minimization of the energy, a reduction is sufficient. Secondly, of all the possible changes in shape, the one in which the exchange of atoms or molecules and free crystal lattice sites is most easily possible from the kinetics point of view will always occur.
The new equations make it clear that particles do not grow faster because they are rounded. Instead, the apparently existing curves are produced by the growth of new crystal layers. "Rounded" corners that occur during sintering are actually small, additional crystal faces. From a kinetic point of view, growth is most likely at these sites because it is easier for atoms and molecules to migrate to these sites. As the small, rapidly growing crystal faces multiply, the particles appear to be classically rounded, but become faceted again in the final stages of sintering.
For example, if two cube-shaped magnesium oxide crystals are in contact with each other, the smaller one quickly assumes an almost spherical shape. A rounded neck forms between the smaller and larger particles, which is still almost cube-shaped. A kind of crooked dumbbell is created. After a long enough time, a single, large cube with slightly rounded edges will form. Throughout this evolution, the changes that take place are consistent with the requirements of minimum surface energy: only changes that result in energy reduction are permitted.
Recently, Searcy, Bullard, and Carter used Searcy's model to solve a mystery reported by Oak-Ridge researchers. Box-shaped particles of magnesium oxide were observed with a transmission electron microscope (TEM), slowly forming compound necks during 2 hours of sintering. Then, after another twenty minutes, the necks collapsed and disappeared.
Three thermodynamic pathways were possible according to the new equations, one of which matched the observations exactly. The chemical reaction of the magnesium oxide particles with the supposedly inert carbon substrate on which the particles were located was taken into account. The carbon and the magnesium oxide react with each other in the vacuum chamber of the TEM. Carbon monoxide and magnesium vapor are released, reducing the overall energy of the magnesium-oxygen-carbon system.
Searcy is currently extending his model to study the thermodynamics of films on and between solid surfaces. This work promises new insights into production methods and properties of ceramic materials. These include layered semiconductors and strong, tough engine parts made with particles of silicon nitride separated by glass films just a billionth of a meter.
Searcy and Bullard report confirmation of the new model in the September 1997 Journal of the American Ceramic Society. According to this report, cubic particles of lithium fluoride sinter as readily as spherical particles of other ceramics.
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