Studies on Fracton in Silica Aerogels by Ramman Scattering

在1990财政年度，拉曼散射和中子非弹性散射实验进行。结果报告在Phys. Rev. Letters中，总结如下。在PH 7溶剂（N-样品）和PH 8.5溶剂（B-样品）中制备两种样品。将Ramman散射结果与中子散射结果进行比较，发现存在两种类型的分形子。一个是在交叉频率nue = 10 GHz以上观察到的标度分数，另一个是在nue以下观察到的矢量分数。在N样本下，标度分数d^^=_s的分维数为1.3，矢量分数d^^=_B的分维数为2.2。在B样本中，d^^=_s=0.9且d^^=_B=1.7。分形维数是表征分形动力学行为的一个物理量。结果表明，分形维数依赖于pH值，不是普适的物理量。在1991财政年度，在pH7.03、7.5、8.0和8.5的溶剂中制备了四个样品x-7。为了获得分形子与PH值关系的详细信息，我们进行了拉曼散射实验，很强的弹性散射使我们无法观察到分形子。这是由于北海道大学使用的5光路干涉仪（BurleighRC-110）对比度差造成的。直到我们引进了3+3路串联干涉仪（对比度约为10^<15>），我们才推迟了拉曼散射实验。用β-BiNbO_4晶体的布里渊散射实验代替。在β-BiNbO_4的轴向上测定了圆柱形样品的弹性常数。这一结果在1992年日本物理学会年会上发表。

In 1990 fiscal year, Ramman scattering and neutron inelastic scattering experiments were performed. The results are reported in Phys. Rev. Letters and is summarized as follows. Two samples were prepared in PH7 solvent(N-sample)and in PH8.5 solvent(B-sample). Compared Ramman scattering result with neutron scattering result, we found that there exist two types of fracton. One is scaler fracton observed above crossover frequency nu e=10GHz and the another is vector fraction observed below nu e. In N-sample, fracton dimension of scaler fracton d^^=_s and that of vector fraction d^^=_b are determined to be 1.3 and 2.2, respectively. In B-sample, d^^=_s=0.9 and d^^=_b=1.7. Here fracton dimension is a physical quantity characterizinle, dynamic behavior of fracton. Results show that fractal dimension depends on PH and is not the universal physical quantity. Relation d^^=_s<d^^=_b is, however, hold both in N- and B-sample.In 1991 fiscal year, four samples x-7ere prepared in PH 7.03 7.5, 8.0 and 8.5 solvents. The purpose is to obtain a detailed information about the dependence of fracton on PH. Thouch Ramman scattering experiment was made, the very strong elastic scattering prevented us to observe fracton. This comes from poor contrast of 5 path interferometer(Burleigh RC-110)used in Hokkaido University. Until we introduce the 3+3 path tandem interferometer(contrast is about 10^<15>)we put off Ramman scattering experiment. Brillouin scattering experiment in beta-BiNbO_4 was performed instead. The elastic constants were determined in cylindrical sample alona a^* axis of beta-BiNbO_4. This result was reported at annual meeting of Physical Society of Japan in 1992.