Semiconducting cubic titanium nitride in the ${\mathrm{Th}}_3{\mathrm{P}}_4$ structure

We report the discovery of a long-sought-after phase of titanium nitride with stoichiometry ${\mathrm{Ti}}_3{\mathrm{N}}_4$ using diamond anvil cell experiments combined with in situ high-resolution x-ray diffraction and Raman spectroscopy techniques, supported by ab initio calculations. ${\mathrm{Ti}}_3{\mathrm{N}}_4$ crystallizes in the cubic ${\mathrm{Th}}_3{\mathrm{P}}_4$ structure [space group $I\overline{4}3d$ (220)] from a mixture of TiN and ${\mathrm{N}}_2$ above $\approx 75$ GPa and $\approx 2400$ K. The density ($\approx 5.22$ g/cc) and bulk modulus ($K_0=290$ GPa) of cubic-${\mathrm{Ti}}_3{\mathrm{N}}_4$ ($c-{\mathrm{Ti}}_3{\mathrm{N}}_4$) at 1 atm, estimated from the pressure-volume equation of state, are comparable to rocksalt TiN. Ab initio calculations based on the GW approximation and using hybrid functionals indicate that $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ is a semiconductor with a direct band gap between 0.8 and 0.9 eV, which is larger than the previously predicted values. The $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ phase is not recoverable to ambient pressure due to dynamic instabilities, but recovery of ${\mathrm{Ti}}_3{\mathrm{N}}_4$ in the defect rocksalt (or related) structure may be feasible.

Figure 1

(a) Synchrotron XRD pattern of $\mathrm{TiN}+{\mathrm{N}}_2$ mixture before and after laser heating inside the DAC. The inset shows the corresponding diffraction rings on the 2D image plate after laser heating. The tick marks indicate the Bragg peaks from $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ and $rs$-TiN phases. The black dotted curve represents the calculated pattern of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$. (b) Ball-and-stick model of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$. The coordination polyhedron of (c) Ti and (d) N.

Figure 2

(a) P-V data for $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$. The colored dashed-dotted lines represent the calculated P-V relations using different functionals. The estimated standard deviations (e.s.d.) in experimental volume are much smaller than the size of the data symbols (black circles). The inset shows the thermodynamic stability at 0 K of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ as a function of pressure (calculated using the PBE functional). (b) Calculated phonon dispersion of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ at ambient pressure (1 atm). Phonon dispersion at 70 GPa is shown in Fig. S4 [29].

Figure 3

Raman spectra of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ collected from the laser-heated spot on the sample during decompression run. All the Raman modes at 1 atm match with that of ${\mathrm{TiO}}_2$ (anatase/rutile), indicating the oxidation of the sample after the Raman measurement in air. The solid vertical lines represent the calculated Raman modes of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ at 70 GPa. The inset shows the optical micrograph of the sample chamber inside the DAC.

Figure 4

(a) Band structure of $c-{\mathrm{Ti}}_3{\mathrm{N}}_4$ around the band edges along the high-symmetry lines of BCC. The selected high-symmetry points in the first Brillouin zone are $\mathrm{\Gamma }\left[0,0,0\right]$, $N\left[0.0,0.5,0.0\right]$, $H\left[-0.5,0.5,0.5\right]$, and $P\left[0.25,0.25,0.25\right]$. The $G_0{W}_0$ calculation from the PBE wave function (black dots) reveals a 0.87 eV direct band gap at Γ, while $G_0{W}_0$ calculation from the HSE06 wave function (green dots) shows a 0.91 eV band gap. (b) Comparison of experimental XRD pattern (gray circles and line) of the recovered sample at ambient conditions with the corresponding calculated XRD patterns of disordered $rs-{\mathrm{Ti}}_3{\mathrm{N}}_4$ (blue line), ordered $m-{\mathrm{Ti}}_3{\mathrm{N}}_4$ (green line), and $rs$-TiN (pink line) phases.