Determination of density changes during melting by X-ray absorption
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where I = transmitted intensity, I0 = incident intenC. ERNEST BIRCHENALL is Distinguished Professor of Metallurgy, Department of Chemical Engineering, University of Delaware, Newark, DE 19711. ANDREW J. HARRISON, formerly Postdoctoral Fellow, University of Delaware, is now at the Thornton Research Centre, Shell Research Ltd., P.O. Box No. I, Chester CH 1 3SH, England. SILVIA N. BALART, formerly Graduate Student, University of Delaware, is now at Depto de Metalurgia, Comisi6n Noc. de Energia At6mica, Centro Atdmica Constituyentes, Buenos Aires, Argentina. Manuscript submitted July 16, 1979.
sity, P./O = mass absorption coefficient, 0 = density and t = sample thickness or X-ray path length. The mass absorption coefficient/x/0 is a constant for a particular wavelength of X-ray radiation and for a particular absorbing element; it is independent of the chemical or physical state of the element and orientation of crystals. Consequently, for an alloy, the average mass absorption coefficient is given by the mass weighted average for all the constituents. I f f i is the mass fraction of component i in the alloy,
During congruent melting or eutectic transformation all components undergo the same proportionate change in spatial density even if some individual solid phases increase in density while others decrease, provided that no porosity develops. Combining Eqs. [1] and [2], and subtracting the logarithm of the intensity transmitted through the solid from that transmitted through the liquid
Equation [3] can be solved for the density change on transformation in terms of the change in transmitted X-ray intensity. To find the volume change on transformation requires that, in addition to the density difference Os either the density of the solid or of the liquid at the melting point be known. AVtransf - 1/pl - 1/O~ Vs
=
1/p,
P,-
-
0~,
Pl
[4]
Pt
The solid density at the melting point can be obtained from the same experiment if the alloy is free of voids, its density at room temperature is known, and the sample deforms on expansion so that it maintains a thickness defined precisely by the rigid cell walls. An analog of Eq. [3], including a correction for the thermal expansion of the cell from room temperature to the melting point, permits evaluation of the linear coefficient k c of thermal expansion of the material. lOge(/~/L) =
{p,t,
--Pm[r [1 + (~)
k~(T m -
T,)] }
[51
~/fi i
ISSN 0360-2133/8010711-1213500.75/0 METALLURGICAL TRANSACTIONS A 9 1980 AMERICAN SOCIETY FOR METALS AND THE METALLURGICAL SOCIETY OF AIME
VOLUME 11A, JULY 1980--1213
The subscripts r and m denote room temperature and melting temperature, respectively. Above the melting temperature, the volumetric expansion coefficient of the liquid metal can be obtained in a similar way. S E L E C T I O N OF M A T E R I A L S A N D C O N D I T I O N S Using the equations presented above, the tabulated mass absorption coefficients (Table I) and densities, the feasibility of using this method for the determination of volume changes on transformation of th
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