# Dense Pure Tungsten Fabricated by Selective Laser Melting
## 4 Discussion  
Effect of Powder Spheroidization on Densification  
Different forming behavior was witnessed between polyhedral and spherical powders. Under the same laser power, continuous molten tracks are formed with spherical powders, while severe balling occurs with polyhedral powders (see Figure 3). In order to better understand the mechanism, the laser absorptivity was measured for both powders by in situ methods. The temperature evolution curve of the substrate was recorded to calculate the laser absorptivity using the apparatus shown in Figure 2. After laser scanning of a substrate that was pre-deposited with powders, part of the input laser energy was absorbed by the substrate, increasing its temperature. The temperature distribution in the substrate was initially non-uniform, with the central zone being hot and the marginal zone cool, but after a period of time elapsed, this heat was conducted to the marginal zone, and the substrate reached an isothermal state. Once this isothermal state was achieved, the substrate cooled according to the convective heat transfer condition described in [24] as:  
\[hS[T(t)-T_{a}]=-mc_{p}\frac{dT(t)}{dt} \tag{1}\]  
where \(h\) is the heat-transfer coefficient, \(S\) is the exchange surface area, \(T(t)\) is the temperature of the sample at time \(t\), \(T_{a}\) is the ambient temperature, \(m\) is the mass of the substrate, and \(c_{p}\) is the specific heat at constant pressure. The relation between \(h\) and \(T\) could be fitted by:  
\[h=B(T(t)-T)^{1/n} \tag{2}\]  
where \(B\) and \(n\) are two constants, which depend on the cooling conditions. The heat capacity of the substrate can be fitted following [PERSON] et al. [25] by:  
Figure 9: Top face hardness of fabricated tungsten for a range of point distances, with SLM parameters P (power) = 400 W, ET (exposure time) = 100 \(\upmu\)s, and hd = 100 \(\upmu\)m.  
\[c_{p}=385+0.2321T. \tag{3}\]  
From the temperature evolution curve, the relation between the heat-transfer coefficient (_h_) versus time (_t_) can be fitted with Equation (1). The equivalent temperature, \(T_{\tau}\), of the substrate just after laser scanning, can then be determined from the fitted result, and the mean laser absorption can then be represented as:  
\[\beta=\frac{mc_{p}(T_{\tau}-T_{a})}{P\cdot\tau} \tag{4}\]  
The temperature evolution curves recorded using polyhedral powders are shown in Figure 10a, from which it can be seen that the central zone of the substrate was heated immediately at \(t\) = 0 s. Indeed, throughout the laser scanning period, the temperature of the central zone kept increasing. At \(t\) = 4.5 s, the laser was switched off, and the central zone reached its peak temperature of 608 K. Subsequently, the central zone began to cool by the conduction of heat to the marginal zone and, at \(t\) = 15 s, the marginal zone reached its peak temperature. At this moment, the rate of heat lost was equal to the heat supply. At \(t\) = 20 s, the temperature difference between center and edge was less than 3 K, which was defined as an isothermal state. The subsequent cooling process is in accordance with the law of convective heat transfer for the whole substrate, given by Equation (1). Inserting Equations (2) and (3) into this equation, the fitted cooling routine can be determined, which is plotted in Figure 10a with the blue \"*\" symbols. The difference between experimental and computed data is less than 3 K across the whole range, which suggests that our analytic modeling is credible. The equivalent substrate temperature (\(T_{\tau}\)) when the laser was switched off was calculated to be 395 K and, therefore, the temperature rise of the whole substrate was 95 K. According to Equation (3), the heat capacity, \(c_{p}\), of the substrate at \(T_{\tau}\) is 444 J/(kg \({}^{\circ}\)C), and so the absorbed energy is calculated to be 452 J, leading to a laser absorptivity value for polyhedral powders of 50%, calculated according to Equation (4).