Pressure-induced transformations in α- and β-Ge 3N 4: in situ studies by synchrotron X-ray diffraction

Abstract

Metastable high-pressure transformations in germanium nitride ( α- and β-Ge 3N 4 polymorphs) have been studied by energy- and angle-dispersive synchrotron X-ray diffraction at high pressures in a diamond anvil cell. Between P=22 and 25 GPa, the phenacite-structured β-Ge 3N 4 phase ( P6 3/ m) undergoes a 7% reduction in unit-cell volume. The densification is primarily concerned with the a-axis parameter, in a plane normal to the hexagonal c-axis. Based on results of previous LDA calculations and Raman spectroscopic studies, we propose that the structural collapse is due to transformation into a new metastable polymorph ( δ-Ge 3N 4) that has a unit-cell symmetry based upon P3, that is related to the low-pressure β-Ge 3N 4 phase by concerted displacements of N atoms away from special symmetry sites in the plane normal to the c-axis. No such transformation occurs for α-Ge 3N 4, due to the different stacking of linked GeN 4 layers. All three polymorphs ( α-, β- and δ-Ge 3N 4) are based on tetrahedrally coordinated Ge atoms, unlike the spinel-structured γ-Ge 3N 4 phase, that contains octahedrally coordinated Ge 4+. Experimentally determined bulk modulus values for α-Ge 3N 4 ( K 0=165(10) GPa, K 0′=3.7(4)) and β-Ge 3N 4 ( K 0=185(7) GPa, K 0′=4.4(5)) are in excellent agreement with theoretical predictions. The bulk modulus for the new δ-Ge 3N 4 polymorph is only determined above the β– δ transition pressure ( P=24 GPa); K=161(20) GPa, assuming K′=4. Above 45 GPa, both α- and δ-Ge 3N 4 polymorphs become amorphous, as determined by X-ray diffraction and Raman scattering.