Cohesive energy metals, plot

The remarkable result is that a plot of E vs. R is a universal one, in that a single curve fits the data for many metals and covalent molecules. It is also valid for data on adhesion, adsorption and impurity binding energies. It can be used to correlate a number of physical properties of metals, such as surface energies and equations of state. Note that cohesive energies and eompressibility data are needed as input parameters. Also, UBER does not apply to ionic solids, nor to polar molecules. 

Cohesive Energies of Metals. The strength of binding among the atoms in metals can conveniently be measured by the enthalpies of atomization. Fig. 2-13 shows a plot of the energies of atomization of the metallic elements, lithium to bismuth, from their standard states. It is first notable that cohesive... 

Fig. 38. The calculated band contribution to cohesion (full line) for the light actinide metals, evaluated using self-consistent RLMTO calculations. The dashed line is the same quantity evaluated using LMTO calculations. The dash-dotted curve is the band contribution to cohesion evaluated from the experimental cohesive energies after analysis of the free atoms (see text). are the experimental cohesive energies (Ward 1983), which follow a different trend. A value of E for Pa, equal to 7 eV per atom reported by Bradbury (1981), is not plotted.

During the 1980 s a major controversy arose when ab initio cohesive energy calculations for transition metals were confronted with semiempirical data obtained from a so called CALPHAD approach, in which Gibbs energies are constructed to reproduce and predict alloy phase diagrams. The issue is often illustrated with reference to a plot such as in Fig. 3, where the results for the enthalpy difference at 0 K from ab initio calculations (solid line) are shown together with semiempirical data (points). 

One would expect the peak in the cohesive energies to peak in column 7 when the d-shells are half full. This does not quite happen in Figure 3.10. However, if the cohesive energy/volume instead of energy/atom of the transition metals is plotted (Figure 3.15), the curves are seen to be more symmetrical about column 7 than in Figure 3.10. The anomalous behavior of the 3d metals (Cr, Mn, Fe, Co, and Ni) can be explained by the fact that some of their d-electrons are tied up in magnetic interactions and do not overlap to make covalent bonds (see Chapter 25). 

Cohesive energy per volume vs. column number for the 3d, 4d, and 5d transition metals. In this plot, the curves tend to be more symmetrical about column 7 where the number of bonding states should be maximized. 

Figure 10 The experimental cohesive energy E b (data from Refs. 5, 19, and 20 see Table 5) plotted versus the phonon-related energy Es for solids in the NaCl-type crystal structure and in energy units of Ry (1 Ry = 2.18 X 10 J). The straight lines are only guides for the eye. They refer to Ad and 5d transition metals from groups IV (Zr, Hf) and V (Nb, Ta) in the periodic table, respectively, and J>d elements from group V (V) and from group IV (Ti) plus Sc from group II and Cr from group V.

Fig. 3.4 The surface tension, a, of molten salts plotted against their cohesive energy density, ced. Equation (3.3) pertains to the red symbols alkali metal halides ( ), alkaline earth metal halides (A). other alkali metal salts with univalent anions ( ) Eq. (3.4) pertains to the alkali metal salts with divalent anions ( ) outliers from Eq. (3.3) (O), also post-transition metal halides and AgNOs [ ], and lanthanide chlorides ( ) (From Marcus [156] by permission of the publisher (Elsevier))...

Figure 2.1 S (a) Plot of experimental values of the surface free energy (C ). (From Ref. [135]) against the cohesive energy ( ) (From Ref [143]) for more 20 twenty simple, transition, and noble metals. Lines corresponding to proportionality constants of 1/6 and the result of Eq. (2.34), 0.134, are also displayed, (b) Variation of the computed DFT LDA surface energies across the 4d transition metal series and for various close-packed surfaces. Note that in...

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