## 2 Microstructure
All of the experimental results showed that the formation of a very fine microstructure in DED components is a direct consequence of high cooling rates and the temperature gradient [56; 57]. [PERSON] and [PERSON] found that since the cooling rate significantly influences the primary cellular arm spacing (PCAS), it is possible to evaluate the thermal history and cooling rate of DED parts via PCAS analysis [61]. Therefore, they proposed an equation which describes the correlation between the PCAS and the thermal history of DED samples. Subsequently, several research studies have been conducted to investigate the correlation between the cooling rate (\(\varepsilon\)) and PCAS (\(\lambda\)), and outcomes reveal a linear relationship between log\(\lambda\) and log\(\varepsilon\)[62; 63]. [PERSON] et al. also studied the correlation between dendrite  
Figure 5: The microstructure of the DED thin walls examined at cross-section and longitudinal section in the middle of the thin wall. (**a**) With a constant laser power of 300 W, (**b**) Process control with a constant set-value 0.5 V and (**c**) Process control with a path-dependent set-value 0.3 V (2 mm)–0.5 V (56 mm)–0.3 V (2 mm) [52]. morphology, temperature gradient, and solidification rate during the DED process [27]. Recently, [PERSON] et al. evaluated the PCAS of AISI 316L alloy produced via DED at different distances from the substrate [37]. Thereafter, in their work, the cooling rate is estimated as a function of sample height using the PCAS values. It is found that by increasing the height of the sample up to the last layers, the PCAS values monotonously increase, and thereafter values drop suddenly when close to the previous layers (Figure 6). As can be seen in Figure 6, the estimated cooling rate during DED of AISI 316L lies in the range of \(10^{3}\)-\(10^{4}\) K/s, which is in agreement with the typical cooling rate reported for the DED process [37; 49; 51]. [PERSON] et al. compared the thermal history, cooling rate, and microstructural features of AISI 316L stainless steel produced by DED and laser powder bed fusion (LPBF) [49]. Indeed, in their work, five sets of process parameters are used to produce different cubes. Figure 7 shows the 3D view of the microstructures of the five different cubes; (a) low-power LPBF, (b) high-power LPBF, (c) small-size DED, (d) middle-size DED, and (e) large-size DED (Figure 7). As can be seen, the microstructure of all the samples is almost fully composed of cells, and all the dendrites have transformed into cells. Thereafter, their analyses revealed that the PCAS of each sample gradually increases with increasing the energy density (e) (Figure 8). [PERSON] et al. also found that the solidification behavior of samples produced via DED is slightly different from that of specimens processed by LPBF. This means that by increasing the cooling rate, the solidification behavior is far from representing equilibrium conditions and accordingly results in a non-equilibrium microstructure. Moreover, it is revealed that lower cooling rate and lower supercooling in DED result in the formation of grains with a width and length 2-5 times coarser than those formed in the LPBF process. Figure 6: SEM images of DED AISI 316L at: (**a**) 2 mm, (**b**) 14 mm from the deposition/substrate interface, (**c**) primary cellular arm spacing (PCAS) and cooling rate as a function of the distance from the substrate [37]. Figure 8: The effect of energy density E on the (**a**) PCAS and the (**b**) cooling rate of the as-forming AISI 316 L stainless steel samples at different processing parameters by LPBF and DED [49]. Figure 7: 3D composite view showing the cellular morphologies of the five kinds of typical samples at the processing parameters of (**a**) low-power laser powder bed fusion (LPBF), (**b**) high-power LPBF, (**c**) small-size DED, (**d**) middle-size DED, and (**e**) large-size DED. (**f**) Schematic sketch of measuring PCAS by the three-angle method [49].