Large single crystals of rare-earth calcium oxoborates $R{\mathrm{Ca}}_4\mathrm{O}{({\mathrm{BO}}_3)}_3$ with $R=\mathrm{Er}$, Y, Dy, Gd, Sm, Nd, La ($RCOB$) were grown by the Czochralski method. Complete sets of dielectric, piezoelectric stress, and elastic stiffness coefficients of the $RCOB$ crystal species were determined at ambient conditions using a combination of resonant ultrasound spectroscopy and the substitution method. The results are inherently consistent and reveal clear crystal chemical trends, with the size of the trivalent cation playing an important role. In particular, the longitudinal and shear aggregate elastic stiffnesses, $c_{11}^{\mathrm{iso}}$ and $c_{44}^{\mathrm{iso}}$, decrease from about 165 to 154 GPa and, respectively, 45 to 41 GPa from the smallest to the largest $R^{3+}$ cation of the investigated crystal species, while the dielectric coefficients ${ϵ}_{22}$ and ${ϵ}_{33}$ increase. However, the maximum longitudinal piezoelectric effect peaks with $8.6{\mathrm{pCN}}^{-1}$ at $NdCOB$, the species where the radius of $R^{3+}$ best matches the one of ${\mathrm{Ca}}^{2+}$. Increasing differences in the size of $R^{3+}$ and ${\mathrm{Ca}}^{2+}$ lead to anisotropic stresses in the crystal lattice, which are partially relaxed by an increasing degree of cation disorder.

中文翻译：

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稀土硼酸钙RCa4O(BO3)3(R= Er, Y, Dy, Gd, Sm, Nd, La)的弹性、压电和介电特性

稀土硼酸钙的大单晶 $\mathrm{电阻}{\mathrm{钙}}_4\mathrm{哦}{({\mathrm{博}}_3)}_3$ 和 $\mathrm{电阻}=\mathrm{尔}$, Y, Dy, Gd, Sm, Nd, La ($\mathrm{电阻}C哦乙$) 是通过 Czochralski 方法生长的。成套的介电、压电应力和弹性刚度系数$\mathrm{电阻}C哦乙$使用共振超声光谱和置换方法的组合在环境条件下确定晶体种类。结果本质上是一致的，并揭示了清晰的晶体化学趋势，其中三价阳离子的大小起着重要作用。特别是纵向和剪切聚合弹性刚度，$C_{11}^{\mathrm{异}}$ 和 $C_{44}^{\mathrm{异}}$, 分别从约 165 GPa 减少到 154 GPa，从最小到最大分别减少 45 到 41 GPa ${\mathrm{电阻}}^{3+}$ 所研究晶体种类的阳离子，而介电系数 ${\epsilon }_{22}$ 和 ${\epsilon }_{33}$增加。然而，最大纵向压电效应峰值为$8.6{\mathrm{pCN}}^{-1}$ 在 $NdC哦乙$, 半径为 ${\mathrm{电阻}}^{3+}$ 最匹配的一个 ${\mathrm{钙}}^{2+}$. 规模差异越来越大${\mathrm{电阻}}^{3+}$ 和 ${\mathrm{钙}}^{2+}$ 导致晶格中的各向异性应力，随着阳离子无序程度的增加而部分松弛。