Dynamic and structural stability of cubic vanadium nitride

Structural phase transitions in epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$ thin films are investigated using temperature-dependent synchrotron x-ray diffraction (XRD), selected-area electron diffraction (SAED), resistivity measurements, high-resolution cross-sectional transmission electron microscopy, and ab initio molecular dynamics (AIMD). At room temperature, VN has the B1 NaCl structure. However, below $T_c=250\mathrm{K}$, XRD and SAED results reveal forbidden $\left(00l\right)$ reflections of mixed parity associated with a noncentrosymmetric tetragonal structure. The intensities of the forbidden reflections increase with decreasing temperature following the scaling behavior $I\propto {(T_c-T)}^{1/2}$. Resistivity measurements between 300 and 4 K consist of two linear regimes resulting from different electron/phonon coupling strengths in the cubic and tetragonal-VN phases. The VN transport Eliashberg spectral function ${\alpha }_{\mathrm{tr}}^{2}F\left(\hslash \omega \right)$, the product of the phonon density of states $F\left(\hslash \omega \right)$ and the transport electron/phonon coupling strength ${\alpha }_{\mathrm{tr}}^2\left(\hslash \omega \right)$, is determined and used in combination with AIMD renormalized phonon dispersion relations to show that anharmonic vibrations stabilize the NaCl structure at $T>T_c$. Free-energy contributions due to vibrational entropy, often neglected in theoretical modeling, are essential for understanding the room-temperature stability of NaCl-structure VN, and of strongly anharmonic systems in general.

Figure 1

θ-2θ XRD scan, acquired using $\mathrm{Cu}K\alpha$ radiation, from a 300-nm-thick epitaxial $\mathrm{VN}/\mathrm{MgO}(011)$ layer grown at $T_s=430{}^{\circ }\mathrm{C}$ by reactive magnetron sputter deposition.

Figure 2

Synchrotron x-ray diffraction VN and MgO (a) $\left\{111\right\}$ and (b) $\left\{002\right\}$ pole figures acquired from 300-nm-thick epitaxial $\mathrm{VN}/\mathrm{MgO}(011)$ layers grown at $T_s=430{}^{\circ }\mathrm{C}$ by reactive magnetron sputter deposition.

Figure 3

High-resolution cross-sectional TEM image acquired along the $\left[0\overline{1}1\right]$ zone axis from a 300-nm-thick epitaxial VN layer grown on MgO(011) at $T_s=430{}^{\circ }\mathrm{C}$ by reactive magnetron sputter deposition.

Figure 4

High-resolution reciprocal-space x-ray diffraction map, acquired with $\mathrm{Cu}K\alpha$ radiation, about the symmetric 022 reflection from a 300-nm-thick epitaxial VN layer grown on MgO(011) at $T_s=430{}^{\circ }\mathrm{C}$ by reactive magnetron sputter deposition.

Figure 5

High-resolution reciprocal-space x-ray diffraction map, acquired with $\mathrm{Cu}K\alpha$ radiation, about an asymmetric 311 reflection from a 300-nm-thick epitaxial VN layer grown on MgO(011) at $T_s=430{}^{\circ }\mathrm{C}$ by reactive magnetron sputter deposition.

Figure 6

Typical temperature-dependent selected-area electron diffraction patterns, acquired along the $\left[0\overline{1}1\right]$ zone axis, from epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$ at (a) room temperature and (b) 97 K with the selected-area aperture sampling the upper 200 nm of the film. The VN(011) film was grown at $T_s=430{}^{\circ }\mathrm{C}$ by reactive magnetron sputter deposition.

Figure 7

Temperature-dependent synchrotron x-ray diffraction intensities, acquired along high-symmetry reciprocal-space directions, from a 300-nm-thick epitaxial $\mathrm{VN}/\mathrm{MgO}(011)$ layer grown at $T_s=450{}^{\circ }\mathrm{C}$. Γ, $X,K$, and $L$ points correspond to [222], [322], [2.75 2.75 2], [222], and [2.5 2.5 2.5] positions in reciprocal $\left[hkl\right]$ space.

Figure 8

Typical temperature-dependent high-resolution reciprocal-space synchrotron x-ray diffraction maps, plotted as a function of reciprocal-lattice vectors $k_{100}$ and $k_{010}$, about the asymmetric 003 reflection from a 300-nm-thick epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$ layer grown at $T_s=430{}^{\circ }\mathrm{C}$. The maps are acquired at temperatures of (a) 275, (b) 250, (c) 200, and (d) 100 K. Scale bars correspond to $0.05\mathrm{n}{\mathrm{m}}^{-1}$.

Figure 9

Synchrotron XRD VN(011) forbidden 003 reflection intensities squared, plotted as a function of temperature. Data points correspond to integrated 003 VN peak intensities obtained from HR-RSM measurements carried out on 300-nm-thick epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$ layers, including those shown in Fig. 8.

Figure 10

Renormalized VN phonon dispersion relations, at temperatures between 400 and 200 K, obtained using ab initio molecular dynamics with temperature-dependent effective potentials.

Figure 11

Temperature-dependent $(4<T<300\mathrm{K})$ resistivity $\rho \left(T\right)$ of epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$. Orange lines highlight the regions $250\lesssim T\lesssim 300\mathrm{K}$ and $100\lesssim T\lesssim 150\mathrm{K}$ for which $\rho \propto T$.

Figure 12

(a) Measured temperature-dependent resistivity $\rho \left(T\right)$ of epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$. $\rho \left(T\right)$ is multiplied by a factor of $1/T$ (circles) to highlight contributions due to defect scattering ${\rho }_o$ (dashed orange line) and phonon scattering ${\rho }_{\mathrm{ph}}\left(T\right)$ (dashed blue line). The solid red curve is the calculated total normalized VN resistivity $\rho \left(T\right)/T$, for which $\rho \left(T\right)={\rho }_o+{\rho }_{\mathrm{ph}}\left(T\right)$. (b) Residuals $R$, the difference between measured and calculated resistivities, as a function of temperature $T$.

Figure 13

Acoustic contributions to the tetragonal-VN transport Eliashberg spectral function ${\alpha }_{\mathrm{tr}}^{2}F\left(\hslash \omega \right)$, obtained using an Einstein inversion procedure [15] from temperature-dependent $(10<T<125\mathrm{K})$ resistivity measurements of epitaxial stoichiometric $\mathrm{VN}/\mathrm{MgO}(011)$ (blue circles). For comparison, room-temperature cubic-VN acoustic-phonon density of states $F\left(\hslash \omega \right)$ (gray squares), obtained from inelastic neutron-scattering measurements carried out with bulk samples [9].