*2.2. Model Calibration*

In order to parameterize the temperature dependent hardness *H*(*T*) as expressed in Equation (**??**), the main attention turns to the determination of *H*0(*T*), ¯ *h*∗(*T*) and *m*(*T*) for *H*n(*T*), given the experimental data or theoretical expression for *H*f(*T*) is generally known for the concerned materials. In the following, the calibration process is briefly introduced, that is,

(1) First, conduct nano-indentation tests for single crystals at different temperatures to obtain the hardness-depth relationships, that is, the *<sup>H</sup>*˜ (*T*) <sup>−</sup> *<sup>h</sup>* curves [**?** ]. Hereafter, the symbol <sup>∼</sup> denotes the experimental data. It then follows from Equation (**??**) that the *<sup>H</sup>*˜ <sup>n</sup>(*T*) <sup>−</sup> *<sup>h</sup>* relationships are obtained by subtracting *H*˜ (*T*) from *H*f(*T*).

