The crystal structure and phase stability of the zeta phase in the group VB transition metal carbides: a computational investigation

The crystal structure and composition of the zeta phase in the group VB transition metal carbides are not completely understood despite decades of experimental studies. As such, the phase rarely appears on phase diagrams of the group VB transition metal carbides. There is currently renewed interest in this phase, as tantalum carbide composites exhibit high fracture toughness in the presence of this phase. This work extends the initial computational study using density functional theory of the phase stability of the zeta phase in the tantalum carbide system, where the tantalum carbide zeta-phase crystal structure and stability were determined, to the niobium and vanadium carbides. It is shown that the zeta phases in the three systems share the same crystal structure and it is an equilibrium phase at low temperatures. The carbon atom ordering in the three different phases is explored and it is demonstrated that the zeta phase in the tantalum carbides prefers to order carbon atoms differently than in the niobium and vanadium carbide zeta phases. Finally, the properties of this crystal are computed, including elastic constants, electronic densities of states and phonon dispersion curves, to illustrate that this crystal structure is similar to other transition metal carbides.

Computing details

(I)

Crystal data

Monoclinic, C2/m	c = 10.31700 Å
a = 5.49100 Å	β = 79.76300°
b = 9.51050 Å

Data collection

h = →	l = →
k = →

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Biso*/Beq
Nb1	0.30706	0.00000	−0.36936
Nb2	0.12367	0.00000	0.12891
Nb3	0.21871	0.17515	0.36902
Nb4	0.37276	0.16650	−0.11967
C1	0.42134	0.00000	0.24165
C2	0.41862	0.33214	0.24163
C3	0.00000	−0.33336	0.50000