Thermal expansion of anatase and rutile between 300 and 575 K using synchrotron powder X-ray diffraction

Abstract

High-precision unit-cell parameters for the TiO 2 polymorphs anatase and rutile at temperatures between 300 and 575 K have been determined using Rietveld analysis of synchrotron powder XRD data. Polynomial models were used to express the tetragonal unit-cell parameters as a function of absolute temperature, with a (anatase)=1.759 37×10 −8 × T 2 +6.418 16×10 −6 × T +3.779 84, c (anatase)=6.6545×10 −8 × T 2 +4.0464×10 −5 × T +9.4910, V (anatase)=2.237 58×10 −6 × T 2 +1.027 77×10 −3 × T +135.602, a (rutile)=−6.636 42×10 −11 × T 3 +1.005 01×10 −7 × T 2 −1.009 9310 −5 × T +4.586 34, c (rutile)=−4.115 50×10 −11 × T 3 +6.405 94×10 −8 × T 2 +4.675 61×10 −7 T +2.951 81, and V (rutile)=−2.7790×10 −9 × T 3 +4.2386×10 −6 × T 2 −3.3551×10 −4 × T +62.100. The polynomial expressions were used to calculate linear ( α ) and volume ( β ) thermal expansion coefficients of anatase and rutile between 300 and 575 K. At 298.15 K, these values were α a =4.46943×10 −6 K −1 , α c =8.4283×10 −6 K −1 , and β =17.3542×10 −6 K −1 for anatase, and α a =6.99953×10 −6 K −1 , α c =9.36625×10 −6 K −1 , and β =28.680×10 −6 K −1 for rutile.