*2.1. Melt Pool Calculations*

First, calculations of the LPBF melt pool dimensions were carried out using the analytical model of a semi-infinite solid with a moving Gaussian heat source [19]. This model has been successfully used for the determination of the LPBF processing parameters for pure iron [18] and Ti-Zr-Nb alloy [20]. The Gaussian model involves a symmetrical distribution of laser irradiance across the beam. The energy from the laser is assumed to be applied on the powder bed surface for a time interval defined by the scanning speed and the laser spot size. In this case, for a Gaussian beam moving with a given velocity, the temperature distribution *T*(*x*·*y*·*z*) in the powder bed is calculated by Equations (1)–(3):

$$T(\mathbf{x} \cdot \mathbf{y} \cdot \mathbf{z}) = T\_0 + \frac{AP}{k r\_f \pi^{\frac{3}{2}}} \int\_{\infty}^{0} \frac{1}{1 + \pi^2} \exp(\mathbf{C}) d\tau \tag{1}$$

*JMMP* **2019**, *3*, 21

$$C = -\frac{\tau^2}{1+\tau^2} \left[ \left( \zeta - \frac{P\_c}{2\tau^2} \right)^2 + \eta^2 \right] - \tau^2 \zeta^2 \tag{2}$$

$$\chi^x = \sqrt{2} \frac{\mathbf{x}}{r\_f} \cdot \eta = \sqrt{2} \frac{\mathbf{y}}{r\_f} \cdot \zeta = \sqrt{2} \frac{\mathbf{z}}{r\_f} \cdot \text{Pe} = \frac{r\_f \mathbf{v}}{2\sqrt{2}a} \cdot \text{\textdegree } \mathbf{r} = \frac{r\_f}{2\sqrt{2at}} \tag{3}$$

where *T*<sup>0</sup> is the powder bed temperature (◦C); *A,* the absorptivity; *P,* the laser power (W); *k,* the thermal conductivity (W/(m·K)); *rf*, the laser beam radius (m); *Pe*, the Peclet number; *ν*, the scanning speed (m/s); *<sup>α</sup>,* the thermal diffusivity (m2/s); *<sup>ρ</sup>*, the material density (kg/m3); *cp*, the specific heat (J/(kg·K)), and *t*, time (s).

The laser energy absorptivity *A* is estimated using Equation (4) from the Drude's theory [19,21]:

$$A \approx 0.365(\lambda \sigma\_0)^{-0.5} = 0.365 \left(\frac{\rho\_0}{\lambda}\right)^{0.5} \tag{4}$$

where *λ* is the laser wavelength (μm), *σ*0, the electrical conductivity (S/m), and *ρ*0, the electrical resistivity of the irradiated material (Ohm·m).
