## 2 Microstructure  
In general, in a DED process the thermal history of a deposited component has a significant influence on the microstructural features (such as morphology and grain size), in particular due to high heating/cooling rates, significant temperature gradients, and bulk temperature increment. Notwithstanding this, the prediction of the microstructural characteristics of a DED component using the knowledge of many process variables/parameters is still an important challenge [42; 53]. The best mechanical properties of the final component can be achieved by addressing this main challenge. A large and growing body of literature investigated the correlation between some specific process parameters, microstructure, and mechanical properties of the final components. Although, the relationship between these findings and the fabrication of complicated components with different shapes is not still clear [54; 55; 56; 57; 58; 59; 60; 61]. Generally speaking, the solidification rate of the melt pool, the ratio between the cooling rate and the gradient of temperature (R), and the thermal gradient at the interface solid-liquid (G) define the microstructure of a deposited part after solidification. Two main critical parameters of solidification can be identified: the ratio G/R affects the shape of the solidification front and cooling rate, whereas the product G \(\times\) R affects the microstructure dimensions [42; 53]. Inside DEDed titanium-based components three main microstructures can be observed: in particular, columnar, mix of columnar, and equiaxed and equiaxed microstructures are formed at different \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{3}{c}{**Material (S/pound)**} \\ \cline{2-4}  & **Steel** & **Aluminum** & **Titanium** \\ \hline Ore & 0.02 & 0.01 & 0.22 \\ Metal & 0.10 & 1.10 & 5.44 \\ Ingot & 0.15 & 1.15 & 9.07 \\ Sheet & 0.30–0.60 & 1.00–5.00 & 15.00–50.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Cost of different metals in different forms [51]. G and R values [47]. It is found that by increasing the ratio G/R the columnar structure is the predominant morphology of grains, while low G/R values promote the equiaxed morphology of grains [42]. For instance, according to the literature, the appropriate range of G and G \(\times\) R for the fabrication of thin walls by means of LENS are 100-200 K/mm and 200-6000 K/s, respectively [62; 63]. However, the optimum values of G and R are strongly affected by several factors such as machine condition, material features, part geometry, and other process parameters. In addition, it is reported that by increasing the solidification rate the microstructure of a component is altered from columnar to equiaxed grains and a cooling rate increment results in a finer microstructure [42]. Considering the direct laser deposition of titanium alloys, a considerable amount of literature has focused on the attention on production of critical structural parts for aircraft applications, to produce near net shaping components with superior mechanical properties [64]. Prior beta grain structure is one of the vital structural factors which have a direct effect on the mechanical properties of as-deposited components produced by the layer-by-layer AM process. In recent years, there has been an increasing amount of literature focused on the correlation of the as-deposited grain size and morphology, post heat treatment, and mechanical properties of titanium parts [65; 66; 67; 68; 69]. It has been found that in the DED of titanium alloys large prior \(\beta\) grains grow epitaxially in the building direction from the parent grains in the melt pool, as a consequence of the rapid solidification due to the high thermal gradient [13; 27; 58; 70; 71; 72]. This kind of epitaxial growth results in a strong solidification texture and in anisotropic properties. In fact, the tensile ductility and toughness of components in the building direction are higher than the transversal ones [71; 73; 74].