A long-standing paradox in the theory of sintering ceramics has been
resolved by Alan W. Searcy of the Materials Sciences Division at the
Ernest Orlando Lawrence Berkeley National Laboratory. Searcy's work,
done in collaboration 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 heat-resistant silicon nitrides.
In sintering, one of the most important processes in ceramics
manufacture, fine-powder compacts are heated to temperatures
only a little lower than their melting points; atoms and molecules are
set in rapid motion, and the particles coalesce, reducing porosity and
increasing the strength of the finished product.
At top, particles of lithium fluoride
retain facets during sintering (at 680 degrees Celsius in vacuum.) In
the bottom image, sintered particles which appear rounded would also
reveal facets if seen at higher magnification. (Shown are lithium
fluoride particles heated to 680 degrees Celsius in argon.)
The "classical" approach to sintering assumes that the initial
particles in the compact are spheres and that movements of
atoms or molecules are driven by differences in curvature. In order to
reduce surface free energy (the work required to form a surface), atoms
supposedly move from particles of smaller radius to particles of larger
radius; the concave regions formed by contact
between particles are filled by atoms from convex surfaces.
In fact, the molecules of crystalline particles sometimes move
in directions the theory forbids -- "Which is not surprising,"
Searcy remarks, "because the classical theory fails what I think of as
the 'single-particle sintering test.' It predicts that an isolated
particle of arbitrary shape will evolve into a sphere. On the contrary,
most single crystals, if grown slowly enough, are faceted." Unlike an
idealized sphere, the surface energies of a crystal depend on the
different orientation of the surfaces to the underlying crystal-lattice
"So here's a theory that says you can't get sintering with
particles that have planar surfaces and edges," Searcy says,
"while in fact many solids, such as magnesium oxide, cobalt
oxide, sodium chloride, and lithium fluoride, keep their
faceted shapes -- or even grow into faceted shapes -- while they are
A clue to the puzzle came when Searcy read a footnote in the
work of Josiah Willard Gibbs, the nineteenth-century founder of
chemical thermodynamics. Gibbs pointed out that molecules at the edges
between crystalline facets would leave and return to their crystal
sites more often than molecules in the facet
surfaces, because the edge molecules are less strongly bonded.
Inspired by what he calls Gibbs's "qualitative description of
dynamic equilibrium," Searcy worked with Bullard and Carter,
both former students at LBNL, to develop equations that explain shape
changes during sintering in terms of energy differences among
differently oriented surfaces and edges -- "rate equations" founded on
Searcy's "statistical thermodynamic description of the
unstable internal equilibrium" in crystals of any shape.
The new equations are based on two governing principles: first,
any change in shape is possible if it reduces total energy --
the change need not minimize energy, merely reduce it. Second, among
all possible shape changes, the one that actually occurs is the one in
which the exchange of atoms or molecules and
vacant crystal lattice sites is easiest -- the one most favored
The new equations make it plain that particles don't grow
faster because they are curved; instead the apparent curves are
produced by the growth of new crystal layers. "Rounded" edges which
appear during sintering are actually small additional facets --
kinetically favored to grow because it is easier to move atoms or
molecules to those sites. As these small, fast-growing facets multiply,
particles begin to appear classically rounded, but become faceted
again in the final stages of sintering.
For example, if two cubic crystals of magnesium oxide are in
contact with each other, the smaller rapidly transforms into a
nearly spherical particle. A rounded neck forms between it and the
larger particle, which is still nearly cubic -- producing a sort of
lopsided dumbbell. Given enough time, a single large cube with slightly
rounded edges will form. At every step the changes serve to balance the
demands of minimum surface energy; only changes which
reduce energy are allowed.
Recently Searcy, Bullard, and Carter used Searcy's model to
solve a puzzle reported by Oak Ridge researchers. Observed in a
transmission electron microscope (TEM), box-like particles of magnesium
oxide slowly grew connecting necks during over two hours of sintering
-- then in 20 minutes the necks
collapsed and disappeared.
Three thermodynamic pathways were
suggested by the new equations, one of which matched the observations
exactly by taking into account the chemical reaction of the magnesium
oxide particles with the supposedly unreactive carbon substrate on
which they were mounted. In the vacuum chamber of the TEM, carbon and
magnesium oxide react to release carbon monoxide and magnesium vapor,
reducing the overall energy of the magnesium-oxygen-carbon system.
Searcy is now extending his model to study the thermodynamics
of films on and between solid surfaces, work which promises to
illuminate production methods and properties of such ceramics as
layered semiconductors and strong, tough, high-temperature engine parts
made with silicon nitride particles separated by
glass films only a billionth of a meter thick.
Searcy and Bullard report confirmation of a prediction of the
new model in the Journal of the American Ceramic
Society, September 1997: cubic particles of lithium fluoride sinter
as readily as spherical particles of other ceramics.
The Berkeley Lab is a U.S. Department of Energy national
laboratory located in Berkeley, California. It conducts
unclassified scientific research and is
managed by the University of California.