2.4.4. Differential Scanning Calorimetry

The differential scanning calorimetry (DSC) measurements were performed using two instruments, a DSC204 (NETZSCH, Selb, Germany) and a DSC8500 (PERKIN-ELMER, Cleveland, OH, USA) using aluminum crucibles. Heating was carried out in a linear way in a temperature range from 25 to 450 ◦C. The standard heating rate was 10 K/min. During DSC, the annealing of deformation-induced defects can be observed by the occurrence of exothermic peaks. The area of a given peak corresponds to the total energy being stored in all defects of a given type, *Ede f ect*, from which its density can be derived. For dislocations, their stored energy *Edisl* is related to their density ρ [36]:

$$E\_{\rm disl} = G b^2 \frac{\rho}{4\pi\kappa} \cdot \ln\left(\left(b\sqrt{\rho}\right)^{-1}\right) \tag{2}$$

where *G* is the shear modulus and b the absolute value of the Burgers vector. κ denotes the arithmetic average of 1 and (1 − ν), with ν = 0.343 as Poisson's ratio, assuming equal parts of edge and screw dislocations. The concentration of vacancies *cv* can be evaluated from the stored energy of vacancies *Evac* divided by the formation enthalpy per vacancy, <sup>Δ</sup>*<sup>H</sup>* (in Mg, <sup>Δ</sup>*<sup>H</sup>* <sup>=</sup> 1.27 <sup>×</sup> <sup>10</sup>−<sup>19</sup> Joule <sup>=</sup> 0.79 eV [37]),

$$\omega\_V = \frac{E\_{\text{vac}}}{\Delta H \times \nu \times N\_a} \,\text{\,\,\,}\tag{3}$$

with ν being the amount of substance and *Na* Avogadro's number. Information on the nature of the defects can be obtained from the annealing peak temperature *Tmax* and the activation (defect's migration) enthalpy *Q*. For the latter, the method of Kissinger [38] was applied by evaluating the shift of *Tmax* with changing heating rate. By plotting

$$\ln\left(\frac{\phi}{T\_{\text{max}}\omega}\right) = -\frac{Q}{R}\frac{1}{T\_{\text{max}}} + \text{const} \tag{4}$$

for various heating rates Φ and absolute peak temperatures *Tmax*, the migration enthalpy *Q* can be determined; *R* is the gas constant.
