*3.8. Determination of SPD-Induced Defect Densities by DSC and XPA*

With differential scanning calorimetry (DSC), one can distinguish between lattice defects through selected annealing. Defects always show exothermal peaks, while the endotherm ones indicate phase transformations. Defects with low migration enthalpy Q exhibit their annealing peaks at low temperatures while those with high Q are reflected by peaks at higher temperatures. For the case of defects produced by plastic deformation, it is well established [29,30] that for SPD-processed pure metals, up to three annealing peaks emerge which are dominated by the annealing of (i) single and/or double vacancies at approximately T = 0.2 Tm (Tm is the melting temperature in K) in the first peak, of (ii) vacancy agglomerates at about T = 0.3 Tm in the second peak and (iii) of dislocations around T = 0.3–0.4 Tm in the third peak, depending on the stress intensity of their arrangement [29]. These peaks can be shifted by up to 100 K to higher temperatures in alloyed metals because of trapping of defects by the alloying atoms.

As a representative for the DSC scans of all Mg alloys investigated, Figure 20 reveals the results for HPT-processed Mg5Zn0.3Ca. Only two peaks emerged in the DSC scans, a peak I between 100–200 ◦C (T = 0.4–0.5 Tm), and a peak II around 300–370 ◦C (T = 0.6–0.7 Tm). Comparisons with the results mentioned for SPD-processed materials, and especially with those from quenched Mg-alloys only exhibiting vacancy-type peaks [32,33], suggest that peak I indicates the annealing of single and double vacancies, while peak II results from an overlap of the second and third peak indicating the annealing of both vacancy agglomerates and dislocations at very similar temperatures.

**Figure 20.** A typical heat flow curve as function of the temperature, for HPT-processed Mg5Zn0.3Ca (black curve—0.5 rotations, red curve—2 rotations) showing two exothermal peaks I and II. The stored energies Etotal of the HPT-induced defects were evaluated from the areas of the peaks.

For further identification of deformation-induced defects, their migration enthalpies Q (Figure 21) were evaluated by measuring the shift of annealing peak temperatures with different DSC heating rates (Kissinger analysis [38]). Results for activation enthalpies of peak I and peak II were 0.7–1.3 ± 0.1 eV and 1.3–3.8 ± 0.3 eV, respectively, for all alloys Mg5Zn0.3Ca, Mg5Zn, Mg5Zn0.15Ca and Mg5Zn0.15Ca0.15Zr. While peak I remains approximately constant with increasing HPT strain, peak II occasionally does not; for further interpretations, see the discussion section.

**Figure 21.** Typical Kissinger plot referring to Equation (4) comprising the peak temperatures *Tmax* of peak I and peak II measured by DSC, for HPT-processed Mg5Zn0.15Ca at 4 GPa for 0.5 rotation. The full lines represent the regression to the experimental data; the activation enthalpy Q was calculated from their slopes.

Following the procedure described in papers [30], combined DSC and XPA measurements were done in order to find out the concentrations of vacancies/vacancy agglomerates. The temperature ranges of the two DSC peaks I and II were further investigated by XPA. With constant crystallite size, the broadening of Bragg peak line profiles yields dislocation densities (N) which allow one—by means of Equation (2)—to estimate the energy which is stored in those dislocations (and their arrangements) solely (*Edisl*). The procedure is to subtract *Edisl* from the total stored energy Etot of peak I (or peak II, respecticely) in order to obtain *Evac*, the energy which is to be attributed to the vacancies/vacancy agglomerates. *Evac* yields the vacancy concentration *cv* by applying Equation (3). For all the furnace-cooled and HPT-processed alloys investigated, Table 6 (for peak I) and Table 7 (for peak II) list all these values in sequence.

**Table 6.** Measured and calculated data for DSC peak I. ρ is the dislocation density, *cv* the vacancy concentration.


**Table 7.** Measured and calculated data for DSC peak II. ρ is the dislocation density, *cv* the vacancy concentration.

