Electron Transfer and Thermal Vibration Parameters in Titanium Nitride: An X‐Ray Diffraction Study

Abstract

An X-ray diffraction study of titanium nitride powder of composition TiN0.89 is carried out at room temperature. The electron transfer from the Ti atom to the non-metal sites is found to be (1.5 f 0.3) electronic charges. The values of the r.m.s. vibration amplitudes of the atoms are U T~ = = (7.12 f 0.04) pm, uN = (6.1Rontgen-Beugungsuntersuchungen an Titannitridpulver der Zusammensctzung TiNo.89 werden bei Raumtemperatur durchgefiihrt. Der Elektronentransport vom Titanatom zu den nichtmetallischcn Platzen wird zu (1,5 0,3) Elektronenladungen gefunden. Die quadratischen Mittelwerte der Schwingungsamplituden der Atome sind UTi = (7,12 f 0,04) pm, U N =

ANALYTIC PRO-p-GROUPS OF RANK 3 AND CLOSED PRO-p-GROUPS OF TYPE (3,4)

“…Here, Rws is the upper limit of the radial integration and we have summed over the radial function and its energy derivative. The resulting charge transfer from the Ti atom to the N atom is in reasonable agreement with x-ray diffraction data by Field (1984). Figure 7 shows the central (100) and (110) sections through the Fermi surface of TiN.…”

Equation of State of TiN at High Pressures and Temperatures: A Possible Host for Nitrogen in Planetary Mantles

“…The parameter q was fixed at 1, a common approximation (e.g., Fischer et al., 2018) that was necessary to reduce the number of fitted parameters. We used a Debye temperature of 579 K based on a computational study (Dong et al., 2009), in agreement with previous experimental work (Field, 1984). A higher value of over 900 K was reported by Y. Yang et al.…”

“…Other experimental work has found evidence for a possible isostructural phase transition at pressures below 10 GPa (Jing‐Geng et al., 2005). Computational work on TiN has been conducted up to higher pressures using ab initio techniques and density functional theory (Abavare et al., 2017; Ahuja et al., 1996; Dong et al., 2009; Field, 1984; Gubanov et al., 2005; Kroll, 2004; Lazar et al., 2007; Liu et al., 2012; Marlo & Milman, 2000; Srivastava et al., 2011; Wang et al., 2010; R. Yang et al., 2016; Y. Yang et al., 2009; Zhang & Veprek, 2008; Zhukov et al., 1988), finding evidence for a phase transition at pressures near 300 GPa. However, to our knowledge no studies have explored the behavior of TiN in situ at the high pressures ( P ) and simultaneous high temperatures ( T ) present in Earth's mantle.…”

“…Other experimental work has found evidence for a possible isostructural phase transition at pressures below 10 GPa (Jing-Geng et al, 2005). Computational work on TiN has been conducted up to higher pressures using ab initio techniques and density functional theory (Abavare et al, 2017;Ahuja et al, 1996;Dong et al, 2009;Field, 1984;Gubanov et al, 2005;Kroll, 2004;Lazar et al, 2007;Liu et al, 2012;Marlo & Milman, 2000;Srivastava et al, 2011;Wang et al, 2010;R. Yang et al, 2016;Y.…”