High-Pressure, High-Temperature Single-Crystal Growth, Ab initio Electronic Structure Calculations, and Equation of State of ε-Fe₃N_1+x

Abstract

The high-pressure behavior of the hard material ε-Fe 3 N 1+x was studied up to 33 GPa with in situ X-ray diffraction experiments using diamond anvil cells in combination with synchrotron radiation as well as by ex situ high-temperature, high-pressure treatment at 1600(200) K in a two-stage multianvil device with a Walker-type module. Evaluation of the pressure-volume data up to 10 GPa by fitting a Murnaghan-type equation reveals a bulk modulus of B 0 ) 172( 4) GPa (B′ ) 5.7, fixed). The calculated bulk modulus (220 GPa) on the basis of density-functional theory (GGA-PAW-PBE) is in satisfying agreement with the experimental one. Single crystals of ε-Fe 3 N 1+x as obtained by ex situ high-temperature, high-pressure experiments reveal in X-ray diffraction data refinements a structural model of iron atoms in the motif of a hexagonal close packing with occupation of octahedral voids by nitrogen atoms exhibiting long-range order. The preferred structural model is described in space group P312 (a ) 4.7241(2) Å, c ) 4.3862(2) Å, V ) 84.773(6) Å 3 , Z ) 2, R(F) ) 0.0339, wR(F 2 ) ) 0.0556) and compared to a second model in P6 3 22. This choice of structural description is corroborated by the results of density-functional calculations. These yield a total energy at 0 K, which is 5 kJ/mol lower for the model in space group P312 compared to the second best alternative arrangement. Using micro-and nanoindentation techniques, a Vickers hardness of H V ) 7.4(10) GPa, a nanoindentation hardness of H ) 10.1(8) GPa, as well as a reduced elastic modulus in the amount of E r ) 178(11) GPa were measured for ε-Fe 3 N 1+x single crystals.

Generalization of first-principles thermodynamic model: Application to hexagonal close-packed ε-Fe3N

“…Also notice that the increased. Moreover, the predicted bulk modulus and its derivative with respect to pressure listed in Table 2 are in good agreement with experimental data and provide improvements compared to previous first-principles calculations [5].…”

“…Equilibrium ratio r = c/a is correctly reproduced by the fitted equations of state. provided [1,3,5]. The complete set of equation of state parameters and fitting errors are given in Table 3 for reference.…”

“…In Table 4 unit cell volume and lattice parameter ratio c/a are listed and compared to highpressure experimental data [5]. The sample is prepared at high-temperature and quenched to ambient temperature.…”

“…Fe 2 N 1 − z has been studied experimentally [2,3,4,5,6] and thermodynamic models accounting for long-range order of the nitrogen atoms were developed and fitted to experimental data [1,7,8]. The ground state stability at 0 K was also investigated from first-principles calculations using density functional theory [9,10].…”

Influence of the chemical surface structure on the nanoscale friction in plasma nitrided and post-oxidized ferrous alloy

“…In order to do this, we shall assume the following. First, the sound velocities C T and C L are 3232 and 6081 m s À1 (for nitrides 15,16 ) and 3555 and 7110 m s À1 (for magnetite 17 and considering C T ffi C L /2 for the C T 14 ), respectively. Second, the nitrides are assumed to be formed by a 50% of the constituting nitride phases (c-Fe 4 N þ e-Fe 2-3 N) and both surfaces have the same n a .…”