Calculations of Electronic Structure

Fig. 4.6 presents calculated plots of the densities of states (DOS) and crystal-orbital Hamilton population (COHP) for a detailed investigation of the electronic structure and bonding properties.

Calculated model ‘Hf6Cu16Al8’ was established using crystal data of Hf6Cu16Al7.58 with the Al2 position designed to be fully occupied. There is no observable band gap about the Fermi level, indicating the compound to be metallic. A maximum occurs between ca. -4 and -2 eV, which pertains mainly to 3d orbitals of copper. The contributions of electronic states about the Fermi level were mainly from 4d orbitals of Hf atoms, 3p orbitals of Al atoms and 4s orbitals of Cu atom, indicating regular interactions between these atoms. Individual and total –ICOHP values for

bonding interactions are listed in Table 4. Consistent with the result of the bond distance, the calculation reveals a weak interaction in the Hf–Cu bond with –ICOHP = 0.43, smaller than that for a homoatomic Cu–Cu bond, 0.61. The Cu–Al interaction was strong (0.99) with a large bonding contribution per cell, marking the dominance of the Cu–Al bond in the contribution to structural bonding (53.40 %). The COHP curves reveal a strong Hf–Al interaction (–ICOHP value: 1.21) with a sharp maximum near the Fermi level. The corresponding electronic structure of hypothetical model ‘Hf6Cu16Al7’ (with an empty 4b site) is marked with a dot line in the figure, indicating that the strength of the Hf–Al bond was determined by the composition of the Al atom in the 4b site. As a result, the partial occupancy of Al2 atom is not only attributed to an unfavorable coordination environment, but also in seeking an optimal bonding strength of the Hf–Al interaction.

Fig. 4.6 Calculated densities of states (DOS) and crystal-orbital Hamiltonian-population (COHP) curves for theoretical model Hf6Cu16Al8.

Table 4.1 Individual and total -ICOHP values for bonding interactions for Hf6Cu16Al7.58

bond Hf-Cu Hf-Al Cu-Cu Cu-Al

number of bonds/cell 64 48 48 128

-ICOHP/bond (avg.) 0.43 1.12 0.61 0.99

-COHP/cell 27.52 53.76 29.28 126.72

contribution /% 11.60 22.66 12.34 53.40

Chapter 5

Synthesis and Characterization of Hf

Al

Sb

(x = 0.70, 1.44, 2.14)

Results and Discussion

5.1 Synthesis

The title compounds were obtained from reactions with general formula "Hf5Al3–xSbx", in which x was varied from 0 to 3 in step 0.5. It performed a survey of ternary phase through the concentration line between two binary compounds Hf5Al3 [153] and Hf5Sb3 [154] . To the best of our knowledge, these new compounds were the first examples of ternary phase in the Hf-Al-Sb system. In attempts to find new ternary phases, similar trials, such as reactions HfAl1–xSbx and HfAl2–xSbx, were not successful. According to the powder XRD measurements (Fig. 5.1), the product of Hf5Al3-xSbx

remained within the Mn5Si3 type in the range 0 < x < 1.0. The signals shifted to smaller 2 theta angle, indicating an extension of the cell volume, as Sb atoms gradually replaced Al atoms. The pattern exhibited a two-phase feature (Mn5Si3 and W5Si3 structural types) when x = 1.5, and showed single-phase product of W5Si3 type within the range 2 < x < 2.5. Finally, the pattern for Hf5Sb3 (x = 3) revealed air-sensitive product of Y5Bi3 structural type. 

Fig. 5.1 Experimental X-ray powder patterns for Hf5Al3–xSbx.

5.2 Crystal structure

Hf5Al2.30Sb0.70 crystallized in hexagonal space group P63/mcm with structure of Mn5Si3-type as shown in Fig. 5.2. It implied a condensation of two distinct octahedra which condensed by sharing basal faces along the [001] direction. One of octahedral was centered by Hf1 atom, which was surrounded by six M(Al/Sb) atoms with a distorted form (Fig. 5.2b) on the threefold axes; the other was established by six Hf2 atoms with regular coordination around the origin of unit cell (Fig. 5.2c).

Relative to the isostructural compound Hf5Al3, Sb substitution caused an increase of the unit cell volume of the ternaries. The a axis of HfAl2.30Sb0.70 increased from 8.07 Å to 8.14 Å for Sb substitution ~23 %; the M-M distances expanded from 3.19 Å to 3.32 Å. The Hf1-M bonds were consistent at distance 2.88 Å, and those for Hf2-M varied from 2.89 Å to 3.09 Å. The Hf1 atoms were separated vertically with distance 2.83 Å, indicative of Hf-Hf interaction for it was significantly smaller than that in structure of Hf metal (3.13 Å).

Fig. 5.2 (a) Structure of HfAl2.30Sb0.70 in a projection along the c-axis. (b) Hf1-centered trigonal antiprism composed by mixtures of metals (Al/Sb) with vertical Hf-Hf bond. (c) Trigonal antiprism composed by Hf2 atoms.

Fig. 5.3 displayed W5Si3 structure adopted by Hf5Al1.56Sb1.44 and Hf5Al0.86Sb2.14, which contains four crystallographically unique positions for two Hf atoms (4b and 16k) and two mixtures of Al and Sb atoms (4a and 8h). It consisted of polyhedra of two types, which were a M2-based tetrahedron and a Hf2-based square antiprism, stacking along the c direction through edge-sharing and face-sharing, respectively. The Hf1 atom was distant from the M2 sites by 2.88 Å in Hf5Al1.56Sb1.44, which was near that of 2.89 Å in Hf5Al0.86Sb2.14. The Hf2-M bonds were nearly

identical in these two compounds within the range 2.87 – 2.92 Å. Similar to the Hf5Al2.30Sb0.70

(Mn5Si3 structure type), the Hf1 atoms and M1(Al/Sb) atoms were adjacent to themselves vertically with half-length 2.76 Å of the c-axis. This distance was smaller than the bond length within the elements aluminium (2.86 Å), antimony (2.90 Å) and hafnium (3.13 Å).

Fig. 5.3 (a) Structure of HfAl1.56Sb1.44 and HfAl0.86Sb2.14 in a projection along the c-axis. (b) Tetrahedron composed by mixtures of metals (Al/Sb) with vertical Hf-Hf bond. (c) Square antiprism composed by Hf2 atoms with vertical M-M bond.

Based on the crystallographic data, the smaller Al atoms preferred to locate in the 4a site with coordinated environment CN:10, whereas the larger Sb atoms mostly situated in the 8h site with fewer neighbor atoms, CN: 6. This behavior was also observed in many intermetallics, in which the 4a site was occupied by the smaller transitional-metal atoms [108, 109] . Brewer-Engel rules interpret the conflict of the size factor, such that the cohesive energy was supposed to be the result of d-electron interactions, which leads to maximal number of bonding between early and late transition-metal atoms [155] . The short bonds to adjacent atoms in the vertical direction are unfavorable for the larger atoms. We verified the result that Sb atoms were disadvantageous to place in the 4a site for the adverse bonding characters of a Sb-Sb interaction, relative to Al-Al and Al-Sb interactions, considering the phase-width behavior as specified in the theoretical calculation below.

Fig. 5.4 presented the resistivities of the pure samples of reaction Hf5Al3–xSbx, in which x = 0.5, 1.0 and 2.0. The resistivities 0.63, 0.78 and 0.90 mΩ·cm, respectively, at 323 K, gradually increased with temperature, indicating metallic properties as revealed in the calculations of electronic structure.

Fig. 5.4 Temperature dependence of the resistivities of Hf5Al3–xSbx species (x = 0.5, 1.0 and 2.0), which are presented as blue (triangle), red (circle) and black (square) dots, respectively.

5.3 Calculations of electronic structure

To understand the electronic structure and bonding properties, we undertook quantum-chemical calculations with model ‘Hf5Al1.5Sb1.5’ of Mn5Si3 and W5Si3 types. These models were constructed by reducing the symmetry of Mn5Si3 and W5Si3 types to P31m and P4, respectively. The resulting models contained split metal sites from 6g of Mn5Si3 type and (4a, 8h) of W5Si3 type, which were assigned to match the designed formula to simulate the mixed Al/Sb site occupancies. Densities of states (DOS) and crystal-orbital Hamilton populations (COHP) calculated for model Hf5Al1.5Sb1.5 of Mn5Si3 type were plotted in Fig. 5.5. The Fermi energy (EF) was located in a continuous band characterizing a metal property. The local minimum of the conduction band

composed mainly of the Hf d-orbitals with small contributions from Al 3s/3p and Sb 5p orbitals.

The calculated band structure was similar to that of Hf5Al3 (not shown) except Sb orbitals narrowly lying below –10 eV, indicating Sb 5s states to be localized and considered as core orbitals.

The integrated COHP values of Hf-Hf, Hf-Al, and Hf-Sb were listed in Table 5.1. The average –ICOHP for Hf-Hf and Hf-Sb were similar at value 1.13, which is more substantial than Hf-Al (0.84). The overall –ICOHP contributions per cell in Hf5Al1.5Sb1.5 were 50.1 % and 37.3 % from Hf-Sb and Hf-Al bonding, respectively, but 12.6 % for Hf-Hf, which indicated the Hf-M interactions to be mainly constructing the framework of the structure; the strong Hf-Sb bonding indicated that Sb replacements from Hf5Al3 would be stable within structure of Mn5Si3 type. Further substitutions of Al atoms from Hf5Al1.5Sb1.5 were unfavorable for the bond strength of Hf-Sb contacts decreased as strongly affected by the anti-bonding.

Table 5.1 Individual and total -ICOHP values for bonding interactions for Hf5Al1.5Sb1.5 model of Mn5Si3 type

bond Hf-Hf Hf-Al Hf-Sb

number of bonds/cell 2 8 8

-ICOHP/bond (avg.) 1.14 0.84 1.13

-COHP/cell 2.28 6.72 9.04

contribution /% 12.6 37.3 50.1

Fig. 5.5 Calculated densities of states (DOS) and crystal-orbital Hamiltonian-population (COHP) curves for theoretical model Hf5Al1.5Sb1.5 of Mn5Si3 type.

Fig. 5.6a displayed a DOS plot calculated for model Hf5Al1.5Sb1.5 of W5Si3 type. The curves were expected to show a metallic property for the Fermi level located near the local energy minimum. The most prominent features in the DOS were the broad Hf 5d bands distributed above ~ –7.5 eV and the split Sb 5s bands from ~ –9 eV to ~ –12 eV. The partial DOS revealed that the Sb 5s states at the M2 site concentrated as core orbitals, whereas those at M1 site contributed to the Sb-Sb bond located at lower energy. To better compare the site preference in the square antiprism environment, Al and Sb atoms were assigned in two P4 symmetry models to establish Al-Al, Sb-Sb (model1) and Al-Sb bonds (model2). Individual and total –ICOHP values for bonding interactions

were listed in Table 5.2. In both models, the average –ICOHP for Hf-Hf (0.88) was smaller than that in the Mn5Si3-type model (1.14), likely because of the bond length decreased from 2.83 Å to 2.76 Å, and the Hf-Sb bonding was still substantial and contributed the greatest bond populations relative to other metal interactions. The Hf–Al and Hf-Sb bonds were essentially optimized at the Fermi level with largest –ICOHP values 0.98 and 1.27 eV/bond, which showed strong bonding interactions. Fig. 5.6c displayed bonding characteristics of Al-Al, Sb-Sb and Al-Sb bonds, which revealed essentially nonbonding near the Fermi level, indicating a result of the phase width as observed in experiments. Despite the COHP calculations indicating strong Sb-Sb interactions (–

ICOHP values: Sb-Sb, 1.15; Al-Al, 1.00; Al-Sb, 1.07), the feature of Sb-Sb anti-bonding was more evident beyond the Fermi level compared to Al-Al and Al-Sb interactions, i.e. the Sb-Sb bond was unfavorable as the Sb composition increased or decreased in the corresponding phase. Considering the experimental observation to phase width, the W5Si3-type structure hence preferred Al atoms to occupy the 4a site to prevent the formation of linear Sb-Sb bonds, consistent with previous discussions about the preference of a smaller occupied atom [108, 109].

Fig. 5.6 Calculated densities of states (DOS) and crystal-orbital Hamiltonian-population (COHP) curves for theoretical model Hf5Al1.5Sb1.5 of W5Si3 type.

Table 5.2 Individual and total -ICOHP values for bonding interactions for Hf5Al1.5Sb1.5 model of W5Si3 type

model1 model2

bond Hf-Hf Hf-Al Hf-Sb Al-Al Sb-Sb Al-Sb

number of bonds/cell 2 10 10 2 2 4

-ICOHP/bond (avg.) 0.88 0.98 1.27 1.00 1.15 1.07

-COHP/cell 1.76 9.80 12.70 2 2.30 4.28

Chapter 6