A simple relationship between the temperature dependence of the density of liquid metals and their boiling temperatures
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has been known for nearly 100 y e a r s that elemental metals and semimetals tend to follow a simple relationship between the coefficient of volume thermal expansion at 293 K, So, and the absolute melting temperature, TM. This relationship, otoTM ~- 0.06,
-
[1]
is valid for metals and semimetals to • pct. However, if Eq. [1] is restricted to FCC, BCC, and HCP s t r u c t u r e s only, then the total e r r o r is reduced to • pct. 1 The burden of this paper is to show that a nearly analogous relationship holds in the liquid state for elemental metals, excepting those in Groups VIH and IIB. Table I lists the values of D M (the density of the liquid at TM in g/cc), and A [=(~}D/OT)p] (the temperature dependence of the density in the liquid state at constant p r e s s u r e in units of -104 g / c c . K ) . In choosing a p r e f e r r e d value of A from an often large and conflicting body of data, the author was influenced primarily by the size of the temperature range over which liquid density measurements were made. The wider the range, the more accurate should be the determination of A. In addition, wherever possible, only data taken since 1960 were used. The column labeled " R a n g e " contains the extremes of modern experimental values for A which the author considers reasonable. The complete range of all data is usually much larger. F o r example, Co, Ni, and Fe would range from 7.1 to 16.5, 6.8 to 13.4 and 6.2 to 14.8, respectively, if all data from just the last 10 y e a r s were considered. The range is given to illustrate the difficulty in measuring A. Even the best known temperature derivatives' (e.g., alkali metals, Sn, Ag) show a spread of approximately 10 pct. To keep the list of references to a minimum, review articles have been cited as the source of most of the data. In particular, these are Refs. 6 (a general review), 2 (Ag, Cu, Pb, Sn, Se), 15 (Co, Ni, Fe) and 10 (Bi, Zn). (Unfortunately, the data quoted in the
D. J. STEINBERG is Senior Physicist, Lawrence Livermore Laboratory, Livermore, Calif. 94550. Manuscript submitted November 19, 1973. METALLURGICAL TRANSACTIONS
last reference does not always agree with the values given in the original sources.) F o r A1, Ga, and Sb, there is sufficient data to indicate that A is not constant over the whole liquid range. In these cases, Table I gives an average A. DM - D B T B _ TM ,
[2]
where DB is the density at the absolute boiling temperature, T B . D B has been determined experimentally for Sb and estimated for A1 and Ga by linearly extrapolating the highest temperature data to T B . The range given for these three elements is for A at TM and T B , respectively. The data for Au are so old and limited that no p r e f e r r e d value is listed. The data for A have been correlated with TB in the following way: It was assumed that the fractional change in density between 0 K and T B is the same for all elements; that is, zXD/Doo is constant. Doo is a scale factor defined by the relationship Doo = D M - ATM, and AD = - A T B . Doo is the density det
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