Through an extensive data analysis of powder X-ray diffraction data obtained at pressures up to at least 78 GPa, we report the experimental equations of state for all lanthanide nitrides between NdN and LuN, excluding the radioactive Pm. By fitting the obtained unit cell volumes as a function of pressure with the third order Birch–Murnaghan equation of state, we find that the bulk modulus increases with an increasing lanthanide number from K0 = 146(12) GPa for NdN to 182(7) GPa in EuN. Hereafter, the bulk modulus reaches a plateau for the rest of the series except for TmN which has a lower bulk modulus. We find that the first derivative of the bulk modulus is around 4 for all compounds except TbN, which displays a significantly different compression behavior. In addition, we find a B1 to B10 pressure-induced phase transition in NdN, SmN, EuN, and GdN at increasingly higher pressures. In fact, we observe that the onset pressure of the phase transition increases linearly with Ln atomic number. From TbN and onwards, we do not observe any sign of a B1 to B10 transition indicating that the transition pressure exceeds the studied pressure range. Therefore, we believe that, for the heavier lanthanides, the linear relationship between the onset pressure and the lanthanide number does not hold and even higher pressures are needed to observe the transition. This coherent study of the series of lanthanide nitrides offers a unique opportunity for benchmark studies of computational methods applied to compounds with 4f electrons.
Emma Ehrenreich-Petersen, Morten B. Nielsen, Martin Bremholma, “Experimental equation of state of 11 lanthanide nitrides (NdN to LuN) and pressure induced phase transitions in NdN, SmN, EuN, and GdN,” J. Appl. Phys. 128 (13), 135902 (2020). DOI: 10.1063/5.0021591 abstract
Waterfall plot of diffraction data as a function of pressure from low pressures at the back to higher pressure in the front (not to scale) for GdN and TbN using Si-oil as PTM. The pressure increases from 0.046(9) GPa to 95.4(9) GPa for GdN, and from 3.16(9) GPa to 87.3(9) GPa in TbN. A B1 to B10 transition is clearly observed in GdN, especially around 6.5° and 9°. The red tick marks indicate the B10 phase. In TbN, a B1 to B10 transition is not observed in the studied pressure range.