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Based on the principle of such a polyhedra-type approach, it has been proposed that elastic properties such as thermal expansion or compressibility of perovskites can be estimated through the analysis of particular Raman modes, even without explicit knowledge of the Grüneisen parameters [43-45]. In the following we will test this model by using our temperature-dependent Raman spectra of DyScO3 and GdScO3. The method described in detail in ref. [43] is based on the following assumptions. (i) Changes in the lattice parameter a induce changes in force constants k and consequently in vibrational frequencies (Grüneisen model) and (ii) polyhedron stretching modes involve mainly one type of force constants and the thermal expansion (or compressibility) of the polyhedron is determined by these microscopic force constants. Based on these assumptions, the approximation of a pseudo-cubic structure and that the force constants obey an empiric law for ionic crystals as described in ref. [46], Loridant et al. [43] have proposed that the thermal expansion of a polyhedron can be described by the following empirical equation: |
» 搶金幣啦!回帖就可以得到:
+1/461
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基于多面形方法理論,通過詳細的Raman模型分析在缺少Grüneisen參數(shù)的情況下評價了鈣鈦礦熱脹或收縮的彈性特征。我們使用DyScO3 和GdScO3的依溫(與溫度有關)Raman 范圍對該模型進行了測試。描述在文獻[43]中的方法是居于下面的假設:(1)幾個參數(shù)a的改變導致了力常數(shù)k的改變,進而導致振動頻率的改變 (Grüneisen model) (ii) 通過三個微觀常數(shù)測定多面體拉伸模型(該模型包括一種多面體的力常數(shù)和熱脹(或收縮)類型);谶@些假設,1個假設的立方體結(jié)構(gòu)和力常數(shù)的近似值服從文獻[46]中描述的離子晶體的經(jīng)驗定律 Loridant et al. [43] 已經(jīng)提出多面體的熱膨脹能用下面的經(jīng)驗公式描述: |
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