*3.1. Quantitative Evaluation*

Let us introduce the width of the laser-treated band *B*n where non-dimensional parameter *γ* for quantitative evaluation of the laser beam profile characterizes the relative temperature range of the laser treatment [43]:

$$\gamma = \frac{T\_{\rm min} - T\_{\rm a}}{T\_{\rm max} - T\_{\rm a}}.\tag{17}$$

The definitions of *B*1/2 and *B*0.9 are shown in Figure 5. Band *B*1/2 approximately corresponds to laser powder bed fusion of metals and alloys such as CoCr at the ambient temperature *T*a with *T*max equal to the boiling/decomposition point (~2800–3300 ◦C) and *T*min equal to the melting point (~1250–1650 ◦C) [48]:

$$
\gamma\_{CoCr} = \frac{1458 \text{ } ^\circ \text{C} - 20 \text{ } ^\circ \text{C}}{3000 \text{ } ^\circ \text{C} - 20 \text{ } ^\circ \text{C}} \approx 0.4826. \tag{18}
$$

The main properties of the cobalt-chromium alloy are shown in Table 2. The data presented in the table are taken from [49,50].



Band *B*0.9 corresponds to laser-additive manufacturing of oxide ceramics at the ambient temperature *T*a with *T*max equal to the temperature of chemical decomposition (~2900 ◦C) [51–55]. *T*min should be chosen as high as possible because of the Arrhenius temperature dependence of the powder consolidation rate [56].

The calculated values of *B*1/2 and *B*0.9 versus Péclet's number for the laser beam profiles are shown in Table 3 and Figure 6. In the considered range of Péclet's numbers (Pe = 0–2.86), the conventional Gaussian profile of TEM00 seems to be the most effective for the wide temperature range of laser treatment of 12 (alloys, metals) when the flattop profile can be significantly more advantageous for the narrow temperature range of 0.9 (mostly oxide ceramics). For *B*1/2, profile TEM01\* seems to be the least effective one, and the flat-top is intermediate. For *B*0.9, profile TEM00 seems to be the least effective one, and TEM01\*is intermediate.

**Table 3.** Calculated widths of the laser-treated band *<sup>B</sup>*1/2 and *B*0.9 versus Péclet's number.


**Figure 6.** Widths of the laser treated band *<sup>B</sup>*1/2 and *B*0.9 versus Péclet's number.
