Constant-pressure specific heat to hemispherical total emissivity ratio for undercooled liquid nickel, Zirconium, and Si
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I.
INTRODUCTION
D A T A on both constant-pressure specific heat cp and hemispherical total emissivity er of undercooled liquids are important parameters for studies of phase transformation into various solid phases that exhibit a range of physical and chemical properties. The constant-pressure specific heat is defined as the first derivative of specific enthalpy, h, with respect to temperature at constant pressure; i.e., cp =
[11 p
The temperature dependence of cp is needed to calculate the thermodynamic state functions such as enthalpy, entropy, Gibbs free energy, etc. For example, cp through its influence on the Gibb's free energy determines the depth of undercooling reached before the onset of solid phase nucleation. The depth of undercooling allows us to control the phases and microstructure of the solid product.tu The total hemispherical emissivity of a sample, er, is defined as the ratio of its hemispherical total emissive power, H, to that of a black body; i.e.,
er =
H o-T 4
[2]
where cr is the Stefan-Boltzmann constant (5.670 • 10 -8 W m -2 K -a) and T is the absolute temperature, t21 Data on er are needed to calculate radiant heat fluxes. For example, er determines the thermal environment during crystal growth in the floating zone growth system. It also plays an important role in determining the cooling rate of atomized droplets in rapid solidification processing. In addition, er data may serve as a bridge to other materials properties. The relationship between er AARON J. RULISON, Research Associate, formerly with JPL, Pasadena, CA, is with the Department of Chemical Engineering, Johns Hopkins University, Baltimore, MD 21218. WON-KYU RHIM, Member of Technical Staff, is with Jet Propulsion Laboratory, Pasadena, CA 91109. Manuscript submitted July 12, 1994. METALLURGICAL AND MATERIALS TRANSACTIONS B
and the electrical resistivity, re, in metals has been explored by a number of researchers, t3J Data on both er and re at a given temperature should, in principle, allow calculation of the electronic transport properties of the metals, i.e., the effective number of free electrons per unit volume, Neff, and the electronic relaxation time, r. These two quantities determine much of the behavior and properties of a metal. In spite of their importance, cp and er are known for very few high-temperature liquids. This is due to the difficulties of maintaining pure liquids at high temperatures. Data is particularly scarce for undercooled liquids since they immediately solidify when placed in contact with most crucibles. These problems are avoided, however, using the recently developed high-temperature, highvacuum electrostatic levitator (HTHVESL) subsequently described, taj The HTHVESL allows accurate determination of Cp/er in a simple heat transfer environment while the levitated melt cools to a deeply undercooled state. In the HTHVESL, levitated materials can be melted, undercooled, and solidified in vacuum. Under such conditions, deeply undercooled liquids can be maintained for significant periods of time. Th
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