The 5d Transition Metals
As shown in the total energy plots the ground state of the 5d elements follow the same trend as in the 3d and 4d elements of the same columns of the periodic table. There are two exceptions La (which we have in the section of f-electron metals) that has t
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The 5d Transition Metals
As shown in the total energy plots the ground state of the 5d elements follow the same trend as in the 3d and 4d elements of the same columns of the periodic table. There are two exceptions La (which we have in the section of f-electron metals) that has the dhcp structure and Hg which crystallizes in a rhombohedral structure. It is interesting to note that while in La the f-states are just above the Fermi level in the other 5d elements the f-states are fully occupied and lie deep below the valence bands. Hf is an exception having its f-states close to the valence bands but still below them. The reader should also keep in mind that in this series, as in other heavy elements, the spin-orbit coupling, which is not included in these calculations, may introduce significant changes to the band structure. The main characteristics of the energy bands and DOS found in the 3d and 4d elements are present in the 5d-series when crystal structure and number of valence electrons are taken into account. Again, as in the 3d-4d comparison, a close comparison of the 4d and 5d elements show that a further widening of the d bands occurs in the 5d metals. A comparison of Ir with Rh and Pt with Pd reveals a change in the ordering of levels at L. Also, Au appears to have a band structure much closer to that of Cu than that of Ag.
© Springer Science+Business Media New York 2015 D.A. Papaconstantopoulos, Handbook of the Band Structure of Elemental Solids, DOI 10.1007/978-1-4419-8264-3_6
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6.1
6 The 5d Transition Metals
Hafnium
Fig. 6.1 Total energy of Hf
Table 6.1 Lattice constants of bulk modulus
a (Bohr) bcc 6.507 fcc 8.275 hcp 5.909 exp 6.028 ΔE ¼ 3.5 mRy
c (Bohr)
B (Mbar)
9.277 9.543
1.119 1.138 2.224 1.09
Table 6.2 Birch fit coefficients
bcc fcc hcp
A1
A2
A3
A4
3.16794 2.82450 5.63387
221.55125 196.72527 392.15107
5070.12559 4435.03874 8848.05911
37618.31312 31923.76295 63976.78690
6.1 Hafnium
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Table 6.3 Hafnium hcp Z ¼ 72 lattice constants 6.0409 a.u. 9.5579 a.u Slater-Koster 3-center parameters Orthogonal Energy integrals (Ry) On site s, s (0) x, x (0) z, z (0) xy, xy (0) yz, yz (0) d2, d2 (0) s, d2 (0) x, xy (0)
0.74947 1.24833 1.09764 0.83209 0.80941 0.73246 0.06073 0.01229
First neighbor s, s (R) s, x (R) s, y (R) s, xy (R) s, d1 (R) s, d2 (R) x, x (R) y, y (R) x, y (R) x, xy (R) y, d1 (R) x, d1 (R) y, xy (R) y, d2 (R) x, d2 (R) z, z (R) z, yz (R) z, xz (R) xy, xy (R) d1, d1 (R) xy, d1 (R) d1, d2 (R) xy, d2 (R) yz, yz (R) xz, xz (R) yz, xz (R) d2, d2 (R)
0.04654 0.07301 0.02961 0.02653 0.06421 0.03015 0.11449 0.00863 0.03410 0.02444 0.02017 0.10353 0.00212 0.00543 0.05597 0.03309 0.01053 0.01696 0.01734 0.05554 0.00860 0.03978 0.00295 0.00105 0.01848 0.01734 0.01717
Energy integrals (Ry)
s, s (T) s, y (T) s, z (T) s, d1 (T) s, yz (T) s, d2 (T) x, x (T) y, y (T) y, z (T) x, xy (T) y, d1 (T) x, xz (T) y, yz (T) y, d2 (T) z, z (T) z, d1 (T) z, yz (T) z, d2 (T) xy, xy (T) d1, d1 (T) xy, yz (T) yz, d1 (T) d1, d2 (T) yz, yz (T) xz, xz (T) yz, d2 (T)
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