The crystal structure of rutile as a function of temperature up to 1600° C

Abstract

The crystal structure of rutile (Ti0 2 ) has been studied at high temperatures up to about 1600°C based on sets of single crystal X-ray diffraction intensities collected on a four-circle diffractometer. The thermal expansion coefficients for the a-and c-axes in the measured temperature range were a" = 8.9(1) χ 10" 6 °C _I and ot c = 11.1(1) χ 10~6 °C _1 , respectively. The thermal response of the octahedra about Ti is such that the thermal coefficient for the four short equatorial Ti -Ο bonds was 8.4(3) χ 10 " 6 ° C " 1 and for the two long apical Ti -Ο bonds 11.5(3) χ 10 " 6 °C _1 . The rate of thermal expansion of the octahedral shared edge is relatively large under ~ 1200°C, while it becomes small above ~ 1200°C. An / to l 0 ratio, which we denote shrinkage index, however, decreases with the raise of temperature (/ = the length of the shared edge at a temperature; l 0 = the edge length of a regular octahedron having the same volume as the Ti octahedron has at the same temperature).

Conversion Efficiency of Alkoxide Precursor to Oxide Films Grown by an Ultrasonic‐Assisted, Pulsed Liquid Injection, Metalorganic Chemical Vapor Deposition (Pulsed‐CVD) Process

“…Some degree of texture is evident upon comparing the XRD pattern obtained from the coating with the powder diffraction pattern for the rutile phase. 8 We invariably Fig. 2.…”

Thermal Stability of α Phase of Titanium by Using X-Ray Diffraction

“…Moreover, the combination and formation of several phases in this range have been predicted by the theory of reconstructive phase transitions [21,22] and also in the phase diagram schematic mentioned earlier. In addition, it has been observed that the stability of the a phase is maintained between room temperature up to 923 K (650°C), because with an increase in temperature, the aforementioned phase would gradually disappear and lead to the formation of titanium oxide (TiO 2 ) with the mineralogical name of rutile and the unit cell parameters a = 4.6001 Å and c = 2.9654 Å , [23] which is clearly observable at the temperature of 1003 K (730°C) and is completed at 1183 K (910°C). This result is, in fact, in good agreement with the theoretical predictions of References 9, 12, and 21.…”

Pressure–temperature dependence of thermodynamic properties of rutile (TiO2): A first-principles study

“…Temperature dependence of the unit cell volume and coefficient of volume thermal expansion (CVTE) curves at zero pressure are shown in figures 1a and 1b. It can be seen from figure 1b, that at all temperatures, the results of Debye-Grüneisen calculations are lower and are in better agreement with the experimental data[16,17]. Infigure 1(c), the values of the bulk modulus obtained from two models are compared.…”

“…Phase transitions from and to rutile have been investigated by many researchers [7][8][9][10][11][12][13][14][15]. The coefficient of thermal expansion (CTE) have been reported by Krishna Rao et al [16], Sugiyama and Takéuchi [17] and Henderson et al [18]. Ligny et al [19] and Yong et al [20] reported the heat capacities and Fritz [21] measured the pressure and temperature dependences of the elastic properties of rutile.…”