Ab initio determination of the bulk modulus of the chromium nitride CrN

Abstract

Through ab initio calculations carried out at the hybrid HF/DFT level, we calculate the static energies and the vibrational frequencies of CrN at different cell volumes, in both cubic and orthorhombic geometries.The paramagnetic cubic phase is studied in different magnetic arrangements, whereas the orthorhombic one is studied in the antiferromagnetic configuration. The resulting static energies are fitted by appropriate equations of state to get the static cell volume (V 0 ), static bulk modulus (K 0 ) and its pressure derivative (K9). We obtain a static K 0 for the cubic phase ranging from 282 GPa to 302.1 GPa, with a value of K9 that varies from 2.87 to 3.63 and a conventional V 0 oscillating from 73.074 Å 3 to 73.277 Å 3 . At ambient conditions the bulk modulus is reduced by about 6 GPa and the cell volume is increased by about 0.45 Å 3 . For the orthorhombic phase we obtain a value of K 0 ranging from 452.5 GPa to 476 GPa, whose K9 varies from 3.09 to 3.38 and its conventional V 0 oscillates from 73.074 Å 3 to 73.277 Å 3 . At 300 K, K 0 is reduced by about 6 GPa and the V 0 is increased by about 0.45 Å 3 . The computational results here obtained for the orthorhombic phase, although consistent within the methodology used, differ from the very few experimental results on the same phase, and such a difference cannot be explained at the moment. They have to be confirmed by experimental measures in the future.

Structural, magnetic, and vibrational properties of stoichiometric clusters of CrN

“…Our predicted ground-state structure for (CrN) 6 looks like two interpenetrating cubes. It has a binding energy of 4.086 Figure 2.…”

“…The lowest-energy structures so predicted are shown in Figure 4, and in Figure 5 we compare the energies of the nonmagnetic (CrN) 5 , (CrN) 6 , and (CrN) 9 clusters with those of magnetic isomers with the same geometries as the ground states and various total magnetic moments. The geometries of (CrN) 2 and (CrN) 3 are quite different from those of the corresponding ground-state magnetic clusters.…”

“…Thus magnetism generally does affect cluster structure. Detailed structural analysis of the magnetic clusters (CrN) 5 , (CrN) 6 , and (CrN) 9 with energies represented in Figure 5 reveals that as the total magnetic moment is increased CrACr distances are shortened by up to 10%, while CrAN bond lengths remain largely unmodified. Though small, such Figure 4.…”

“…In the dimer, 0.80 e are transferred from the Cr atom to the N atom, the lowest value among all the systems studied. Already in (CrN) 2 the average absolute charge transfer per atom is 1.06 e. The same variable takes the values 1:23 e; 1:39 e; 1:20 e; 1:25 e, and 1.31e for the ground states of (CrN) [3][4][5][6]9 . The last element in the series is remarkably close to the 61:3 e Bader charges of Cr and N in bulk CrN.…”

“…The "electronic temperature" for Gaussian smearing was 10 meV, which proved small enough to ensure the prediction of total 3 ; rectangular, octahedral, cubic and anticubic structures for (CrN) 4 ; rectangular, octahedral and cubic structures for (CrN) 5 ; and rectangular structures with a square basis cell for (CrN) 6 . For the largest cluster (CrN) 9 , we only considered a biplanar structure (a piece of bulk CrN) as starting geometry.…”