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The thermal expansion coefficients of DyScO3 and GdScO3 have been determined earlier from 25 to 1000°C using XRD [26]. The calculated volumetric thermal expansion coefficients of DyScO3 and GdScO3 are V,DSO = 2.42 x 10-5 K-1 and V, GSO = 3.07 x 10-5 K-1, respectively. We have seen in the previous section that the frequency of all Raman modes decreases to a good approximation linearly with temperature from room temperature to 1200 °C. Such a linear temperature dependence makes the Raman modes themselves in principle suitable for the determination of the thermal expansion, assuming that changes in the volume V and thus in bond distancesd, induce changes in force constants and thus in vibrational frequencies. The Grüneisen model assumes that the Grüneisen constant correlates the temperature dependence of vibrational frequencies with the unit cell volume. At constant pressure the Grüneisen constant is defined by where is the frequency of a vibrational mode, V the unit cell volume and V the volumetric thermal expansion given by (2) As a consequence, when the temperature dependence of vibrational modes is known, the Grüneisen parameter can be determined from the known thermal expansion (or vice-versa). The so-calculated Grüneisen parameters are given in Table 1 under the assumption that the same volumetric thermal expansion V can be used for every mode. As expected the Grüneisen parameters vary significantly from one mode to the other. |
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ll921(金币+50, 翻译EPI+1): 2011-03-25 06:54:00
| 早先利用XRD确定了从25到1000°C温度范围内DyScO3和GdScO3的热膨胀系数[26]。计算的DyScO3和GdScO3的体积热膨胀系数分别为V,DSO = 2.42 x 10-5 K-1 和V, GSO = 3.07 x 10-5 K-1。从前面的讨论部分我们看到从室温到1200°C内所有拉曼模式频率随温度呈现很好的近似线性的降低趋势。 此线性的温度相关性使得拉曼模式本身原则上适合于热膨胀的测定，假设体积V变化引起键长d的变化，进而引起力常数变化而最终导致振动频率变化。Grüneisen模型认为Grüneisen常数可将与温度有关的伸缩频率和晶胞体积相关联。在固定压力下，Grüneisen常数通过公式（2）中给出的振动模式频率位置，晶胞体积V以及体积热膨胀量所定义。因此，当已知振动模式的温度相关性时，Grüneisen参数可由已知的热膨胀来确定，反之亦然。在相同的体积热膨胀V适用于每个模式的假设前提下，如此计算出的Grüneisen参数列于表1。这如所预见的一样，从一种模式转到另一种模式时Grüneisen参数发生显著的变化。 |
2楼2011-03-25 00:20:59
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