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ll921

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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 distancesd, 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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1楼 2011-03-24 21:06:27

已阅回复此楼关注TA 给TA发消息送TA红花 TA的回帖

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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。

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