**4. Discussion**

The mechanism of cementite formation was mainly determined by the diffusion of carbon atoms in the long range or short range. Chen [23] and Li [29] have studied the diffusion behavior of interstitial atoms in α-Fe under the strain field and they find that with the increase of tensile stress, the diffusion barrier decreases and atom diffusion gradually becomes easier. In this study, when external tensile stress is applied, the cubic crystal produces a weak elastic deformation along the tensile direction, then the diffusion barrier and atomic transition distance changes, which affects the diffusion rate of the carbon atoms. As a consequence, the applied tensile stress will exert a significant influence on the migration of carbon atoms and the formation of cementite.

It is reported by Kim [30] that the extra lattice energy arose from the presence of defect (including dislocations, grain boundaries, twins, etc.) in the matrix could lead to a reduction of nucleation energy barrier of cementite. In the present work, according to the first law of thermodynamics, the change of internal energy of the lattice can be expressed as follows:

$$d\,d\,I = d\underline{Q} - d\mathcal{W} \tag{6}$$

where *dQ* and *dW* is the heat absorption and energy dissipation of the lattice, respectively. Assuming that the elastic strain of lattice (Δl) occurs along the tensile direction when tensile stress (*f*) is applied, the heat absorption and energy dissipation are obtained based on the second law of thermodynamics [31]:

$$dQ = TdS\tag{7}$$

$$dW = PdV - f\Delta l \tag{8}$$

where *T* and *S* is the temperature and surface area of the lattice, respectively; *P* and *dV* is the pressure and the volume change, respectively. By substituting Equations (7) and (8) into Equation (6), the modified internal energy change in the lattice (Equation (6)) can be expressed as:

$$d\,dl = TdS - PdV + f\Delta l\tag{9}$$

For crystals, *PdV* = 0, So Equation (9) can be simplified as:

$$d\Omega I = TdS + f\Delta l \tag{10}$$

It should be noted that for the non-isothermal process, the lattice must be in the endothermic state, so the value of heat absorption will be positive (*TdS* > 0). Moreover, since the value of tensile stress is positive ( *f* > <sup>0</sup>), the change of internal energy in the lattice (*dU*) will increase compared with those without applied tensile stress under the same temperature. Therefore, it can be inferred that the applied tensile stress favors the increase of internal energy in the lattice, thereby leading to a reduction of the nucleation of the energy barrier for the crystal core with a same size. This is also the reason for the obvious decrease in activation energy of cementite formation when the tensile stress is applied.
