Solidification
In order to melt a metallic solid a certain amount of heat must be expended, the heat of melting. Different metals melt at different temperatures. This is related to the binding forces between the atoms. At the melting temperature, T m , the thermal energ
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Solidification
8.1 The liquid state In order to melt a metallic solid a certain amount of heat must be expended, the heat of melting. Different metals melt at different temperatures. This is related to the binding forces between the atoms. At the melting temperature, T m , the thermal energy per mole (RTm) has to be of the same order of magnitude as the binding energy (heat of melting per mole, Hm): Hm ~ RTm (Richards rule). At the melting temperature the liquid and solid state coexist in thermal equilibrium, which requires (for constant pressure) that they have the same Gibbs free energy: • •
Gliq'Uid = G solid Hliq'Uid - Tm ·8liq'Uid = Hsolid - Tm ·8solid
• •
HHq'Uid - Hsolid = T m (8Hq'Uid - 8 sol i d) H m =Tm ·8m
where Hm denotes the heat of melting, and 8 m is the melting entropy. The quantities Hm and Tm can be measured (Table 8.1). For most metals the increase of entropy during melting is about 2 cal/mol/K (= 8.37 J /mole/K) ~ R (R - gas constant). Most metals crystallize in close-packed crystal structures (fcc and hcp). During melting the crystalline state breaks down and, therefore, the average packing density becomes smaller than in the solid state. Correspondingly, the volume increases during melting, as shown in Fig. 8.1 for Cu. This volume change is reversible and, therefore, restored during solidification by a volume contraction during solidification. In non-close packed crystalline materials the crystalline state has a low density because of special bonding arrangements. In this case the volume decreases upon melting, for instance for silicon, which crystallizes in the diamond cubic (dc) structure to satisfy the oriented covalent bonds. The dc crystal structure is "open" and has a lower density than
G. Gottstein, Physical Foundations of Materials Science © Springer-Verlag Berlin Heidelberg 2004
358
8 Solidification
Table 8.1. Heat of melting and melting entropy of several metals. Element
Heat of melting
Melting temperature
Melting entropy
[J/molJ
[K]
[J/mol· KJ
8422 11523 2640 2353 7333 4860 11187 9344 10685 15880 5782 33730 13282 9679 7123 22207 7123 9972 19567
1517 1812 371 337 923 600 1356 1118 1233 1725 594 3683 1336 933 692 2046 505 544 903
5.45 6.29 7.12 7.12 7.96 7.96 8.25 8.38 8.80 9.22 9.64 9.22 10.06 10.48 10.48 10.89 14.25 18.44 23.88
Mn Fe Na K Mg Pb Cu Ca Ag Ni Cd W Au Al Zn Pt Sn Bi Sb
0.130
/
0.125
(J)
>
0.120
0-
0.115 0-
0.110
--- -- -- -200
400
.-o~
600
.....--0-
800
1000
1200
temperature 1°C]
Fig. 8.1. Volume change due to thermal expansion and volume increase during melting of copper.
fcc and hcp (Table 8.2). The atomic arrangement of atoms in a melt is not entirely random. Rather the interatomic forces keep trying to establish a locally dense arrangement, which is counteracted, however, by the thermal motion of the atoms. Therefore, liquid atomic arrangements are not as densely packed as in a close-packed crystalline solid. This becomes obvious from Fig. 8.2 in terms of the scattered X-ray intensity of liquid zinc at a temperature of 460°C,
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