DISPLAY OF PERCOLATION IN MELTS IN THE STATE DIAGRAM
S. A. Suvorov
and V. V. Kozlov
Translated from Novye Ogneupory, No. 2, pp. 48 – 48, February, 2010.
Original article submitted September 16, 2010.
Percolation of liquid phase in the system melt – solid phase is considered, and a method of determining the
percolation line of a melt in a simple state diagram is proposed.
Keywords: percolation, state diagram, fusion, caking
Percolation is a structural phenomenon related to the for
mation in the body of a material of a continuous cluster on
the basis of certain phases. The influence which any phase
exerts on the properties of the material is determined not
only by its concentration, but also by its structural state,
whether percolated or isolated. Once the concentration of the
phase attains a critical point, called the percolation threshold,
the structural properties of the material determined by this
phase undergo an abrupt change .
The percolation threshold temperature of the liquid phase
(melt percolation temperature) is an important property for
materials that are used under conditions of high tempera-
tures. Virtually any multicomponent material melts in a
range of temperatures, moreover, the temperature at which a
melt appears may either coincide with, or not coincide with,
the percolation temperature of the liquid phase. The magni
tude of the melt percolation temperature, which may be de
termined by recording a sudden change in the electrical resis
tance of a sample [2, 3], may be found for any material in the
range from the solidus point (inclusively) to the liquidus
point, i.e., complete melting of the material, and is deter
mined by its chemical composition, structure, and its param
eter of wettability by a natural melt.
The percolation condition of the liquid phase in a body
of granular material as it gradually melts is given by the rela
is the volumetric fraction of the melt; V
ric fraction of solid phase; K, a coefficient that depends on
the type of packing of the particles in the material (in the
case of hexagonal densest packing, K = 1.723, and for cubic
densest packing, K = 2.907); and a, angle of wetting by melt
of solid phase.
A pure substance will melt at a fixed temperature, though
upon the addition of an impurity component a temperature
interval of melting arises that generally lies below the fusion
point of the pure substance. Let us consider the simple case
in which the basic component A and the impurity B form a
simple eutectic state diagram (Fig. 1).
If the impurity B is present, the liquid phase in the A – B
system will appear at the eutectic temperature T
over, the quantity of melt for some composition 1 at any tem-
perature is determined by the chemical composition and may
be calculated by the lever rule as the ratio of the two seg
ments b/a, where b is the volumetric fraction of impurity
component B and a the difference between B
concentration of the impurity component) and b. Thus, the
relationship between the liquid and solid phases at point 1 is
Refractories and Industrial Ceramics Vol. 51, No. 1, 2010
1083-4877/10/5101-0050 © 2010 Springer Science+Business Media, Inc.
GOUVPO St. Petersburg State Technical Institute (Technical
University), St. Petersburg, Russia.
Fig. 1. SimpleA–Beutectic state diagram.