METHOD FOR EVALUATING THE CHANGE IN SPECIFIC VOLUME
OF REFRATORY SUBSTANCES DURING CRYSTALLIZATION
A. A. Frolov,
E. V. Voinich,
and Yu. A. Frolov
Translated from Novye Ogneupory, No. 4, pp. 41 – 46, April 2008.
Original article submitted October 10, 2007.
A method is proposed for quantitative evaluation of the change in specific volume of refractory substance
during a liquid – solid phase transition according to the surface shape of a flat ingot crystallized under
conditions of central symmetrical heating. The accuracy of the estimate is up to 5 – 8%. With certain
limitations the method is applied to a quantitative estimate of the volumetric effect of crystallization and in a
number of cases melt density of the refractory materials themselves, for which obtaining information about
melt density by any other method is impossible. Using the proposed method an estimate is provided for the
density of molten yttrium and erbium oxides close to the melting temperature (for Y
= 2440°C, for
= 2430°C respectively).
Existing methods for determining the density of a melt
are unsuitable for highly refractory systems since a necessary
condition for measuring density is contact of the melt with
the material of measuring device structure. This may be the
wall of a measuring crucible, a device for holding melt in the
sessile droplet method, or capillary material in the method
for maximum gas bubble pressure . In this work a method
is proposed for quantitative evaluation of the change in
specific volume of a substance with phase transition of melts,
i.e. a solid form of an ingot surface crystallized under
conditions of centrally-symmetrical heating. At the basis of
the method is contactless heating by a concentrated light flux
in the focal zone of an optical furnace . In carrying out
crystallization of a flat bath of melt a shrinkage cone forms
(in rare cases it is projecting) in the direction of the boundary
of the molten bath towards the center at the surface of an
ingot. The dimensions and shape of the cone are com
mensurate with the volume of the molten bath and the
volume of the crystallized phase specify the change in
specific volume of the substance during crystallization [3, 4].
For the majority of substances, that decrease in volume
during solidification (specific volume of the melt V
greater than the specific volume of the solid phase V
a shrinkage cone (Fig. 1a). For a small number of materials
with a positive value of the volumetric crystallization effect
) at the center of the surface of an ingot a protruding
cone should form (Fig. 1b). By analyzing the ratio of the
volume of the molten bath and the solid ingot it is possible to
obtain information that provides evaluation of the change in
specific volume of a substance during solidification and in a
number of cases, melt density. This information is most
important for high-temperature material melts for which
known methods of density determination are not suitable.
Unfortunately, during melting of refractory oxides a
strong surface tension effect occurs at the boundary of a
molten bath that contributes considerable error to evaluating
the volumetric effect. If we describe areas of an ingot
distorted by surface tension, and limit ourselves to the central
zone, then this analysis is possible. For these purposes it is
necessary to determine correctly the form and volume of
molten bath from which the corresponding area of an ingot
Refractories and Industrial Ceramics Vol. 49, No. 3, 2008
1083-4877/08/4903-0183 © 2008 Springer Science+Business Media, Inc.
I. N. Frantsevich Institute of Materials Science Problems NANU,
Institute of Magentism NANU, Ukraine.
Fig. 1. Diagram of ingot surface formation during crystallization in
the focal zone of an optical furnace: a) for materials with a negative
volumetric effect; b ) for materials with a positive volumetric effect;
1) starting material; 2) crystallized material; 3) concentrated light
flux; 4) molten bath; 5) shrinkage cone; 6) protruding cone.