## 2 Bulk Crystal Characteristics
### Thermal Characteristics, Laser Damage Threshold and Mechanical Characteristics  
Laser performance and crystal growth are usually affected by thermal expansion, specific heat, and so on [38]. Laser crystals are liable to break during the growth process, usually owing to obvious anisotropic thermal expansion, low thermal conductivity, and low specific heat. Meanwhile, the crystal may have a significant thermal effect during the laser experiment process due to a large temperature gradient. The specific heat capacity was measured and then calculated using a thermal analyzer and software produced by Perkin-Elmer Co., Waltham, MA, USA. The specific heat (\(C_{p}\)) of Yb\({}^{3+}\)-ScBO\({}_{3}\) increased with temperature, and the median was 0.73 J\(\cdot\)g\({}^{-1}\cdot\)K\({}^{-1}\) at 330 K, as shown in Figure 3a [36; 39]. Because of a large specific heat, compared with Yb\({}^{3+}\):YCOB (0.75 J\(\cdot\)g\({}^{-1}\cdot\)K\({}^{-1}\)) and Yb\({}^{3+}\):YVO\({}_{4}\) (0.62 J\(\cdot\)g\({}^{-1}\cdot\)K\({}^{-1}\)), Yb\({}^{3+}\):ScBO\({}_{3}\) will not be extremely influenced by the heat caused during the laser emission action and a very large damage threshold can be forecast. Figure 2: (a) Yb\({}^{3+}\)ScBO\({}_{3}\) crystal grown with a seed of platinum wire, (b) optical-quality Yb\({}^{3+}\):ScBO\({}_{3}\) crystal. Inset: cut and polished laser sample. (Source: [34], © 2015 Optica Publishing Group, Washington, DC, USA). A laser flash apparatus was used to take stock of the thermal diffusivity; the findings are shown in Figure 3b, which shows a plot of the thermal diffusivity (\(\lambda_{ij}\)) of Yb\({}^{3+}\):ScBO\({}_{3}\) at temperatures ranging from 303.15 K to 774.15 K.  
In view of the following equation, the thermal conductivity (\(k\)) was determined:  
\[k=\lambda_{ij}\rho C_{p} \tag{2}\]  
when the temperature increased at above temperatures range, the \(a\)-axis thermal conductivity increased from 3.61 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\) to 3.86 W\(\cdot\)m\({}^{-1}\cdot\)k\({}^{-1}\), and the \(c\)-axis thermal conductivity also increased from 2.98 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\) to 3.36 W\(\cdot\)m\({}^{-1}\cdot\)K\({}^{-1}\) (as presented in Figure 3c). Owing to the tendency of the thermal conductivity to rise with rising temperature, this crystal can be utilized in generating medium lasers. The \(\alpha_{ij}\) of one crystal, which is a meristic second-order tensor, represents the thermal expansion coefficient [40]. Since Yb\({}^{3+}\):ScBO\({}_{3}\) appertain a trigonal system, on account of the principle of Neumann, the thermal expansion coefficient tensor is exhibited to be:  
\[\left( \begin{array}{ccc}\alpha_{11}&0&0\\ 0&\alpha_{22}&0\\ 0&0&\alpha_{33}\end{array} \right) \tag{3}\]  
According to the crystal structure, Yb\({}^{3+}\):ScBO\({}_{3}\) has two thermal expansion coefficients, \(\alpha_{11}\) and \(\alpha_{33}\), which are independent. The measurements of the thermal expansion tensor of this crystal were utilized a thermal mechanical analyzer (Diamond TMA). Moreover, the thermal expansion curves of Yb\({}^{3+}\):ScBO\({}_{3}\), plotted versus temperature, are presented in Figure 3d. The two aforementioned thermal expansions remained virtually linear. Then, the thermal expansion coefficients along these two axes were separately determined to be 1.05 \(\times\) 10\({}^{-6}\) K\({}^{-1}\) for \(\alpha_{11}\) and 10.24 \(\times\) 10\({}^{-6}\) K\({}^{-1}\) for \(\alpha_{33}\). The considerable anisotropy in terms  
Figure 3: Thermal characteristics of Yb\({}^{3+}\):ScBO\({}_{3}\) as a function of temperature: (**a**) specific heat, (**b**) thermal diffusion coefficient, (**c**) thermal conductivity with temperature, and (**d**) thermal expansion coefficient [34]. of thermal expansion may lead to cracking during the crystal growth process.