Cohesive simple metals

The mobilities of dislocations are determined by interactions between the atoms (molecules) within the cores of the dislocations. In pure simple metals, the interactions between groups of adjacent atoms depend very weakly on the configuration of the group, since the cohesive forces depend almost entirely on the local electron density, and are of long range. 

Strongly for the ionic crystals, yet the bulk modulus for the alkali halides varies as d. The cl trend for the bulk modulus will show up in the study of simple metals, and in terms of the pseudopotentials that will be used in the study of simple metals, d" -dependence takes on a particularly fundamental role. In Problem 15-3, the simple metal theory is used to give a good account of the bulk modulus in C, Si, and Gc. It should be noted also that the simple metal theory docs not give a good account of cohesive energy itself there is much cancellation between terms for that property, and there are important contributions (for example, that do not vary as... 

The cohesive energy (energy of atomization) of the simple metals, in cV. Values of some semiconductors and scmimctals are also included. 

As in the other solid types, the entire range of structural, elastic, and vibrational properties arc determined by the electronic structure. Likewise, as in other systems, the density, bulk modulus, and cohesion arc considcfed together as a separate problem and, for the metals, were treated in Chapter 15. We have given a reasonably simple description of the electronic structure of simple metals in Chapter 16, and can now use it to treat the more detailed aspects of the bonding properties. 

Binding energy, simple metals, 355. See also Cohesive energy... 

We consider a homogenous gas that consists of free electrons in Chapter 5. Notions of exchange energy and correlation energy of electrons are introduced. The theory enables one to calculate some macroscopic properties of simple metals, which have the ns external electronic shell. The calculated cohesive energy of simple metals turns out to fit the experimental values satisfactorily. 

A most important test of the theory is to compare their data with the bonding energy of real metals. This comparison has been performed. It turned out that the cohesive energy of simple metals could be explained by the theory described in Sections 5.2-5.4. Simple metals are those without d electrons in the electron shells. 

Potassium is a typical simple metal. The model of the electronic gas (Chapter 5, Table 5.2) describes the cohesive energy of the bulk potassium well. The completely delocalized s electrons ensure the interatomic bond in potassium. 

Hafner (1985) applies to binary alloys formed by s and p elements the same approach already used by Heine Weaire (1970) in the evaluation of the cohesion energy of simple metals (sp-bonded metals). 

As with the simple metals, a theoretical treatment of the cohesive energies of the transition metals requires a more sophisticated quantum mechanical treatment. A few trends can be observed, however. Unlike the simple metals, the strongest bonds occur... 

Table 2.1 lists a number of DFT and experimental values for a simple metal Al, two noble metals Cu and Ag, and a transition metal with an unfilled d shell Pd. One example from each of the first four generations of exchange-correlation functional is given so as to provide a flavor of the current state of DFT for the cohesive properties of metals. In addition to the LDA, we show results from the PBE (GGA), TPSS (meta-GGA), and PBEO (hybrid) functionals. Let us consider each functional in turn and see what general conclusions can be drawn ... 

In Fig. 7 the results of the model for the cohesive energy are given, and compared with the experimental values and with the results of band calculations. The agreement is satisfactory (at least of the same order as for similar models for d-transition metals). For americium, the simple model yields too low a value, and one needs spin-polarized full band calculations (dashed curve in Fig. 7) to have agreement with the experimental value. 

The cohesive energy, equilibrium atomic volume, and bulk modulus across a transition metal series may now be evaluated by choosing the following simple exponential forms for ( and h(R), namely... 

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