# Recent Progress in Hybrid Additive Manufacturing of Metallic Materials
## 5 Effect of Heat Treatments in AM Processed Maraging Steels
### Strengthening Mechanisms' Models
#### 5.1.3 Precipitation Strengthening
Additive manufacturing offers a unique platform for producing marging steels with tailored microstructures and mechanical properties [109; 6; 110]. One common approach is to homogenize the material by solution treatment, followed by aging at a lower temperature to promote the precipitation of nanoscale intermetallic phases such as Ni\({}_{3}\)(Mo, Mn, Al) and Ni\({}_{3}\)Ti [111; 112]. The choice of alloying elements plays a critical role in deter mining the mechanical properties by influencing the type of intermetallic phases formed. The nucleation and growth of precipitates are dependent on the segregation energy and the degree of diffusion of the solute atoms involved. The interaction energy associated with the alloying elements is expressed by Equation (20). This formula can be used to determine the tendency of elemental segregation. \[\sigma_{p}=\frac{1}{b}\frac{2S}{\sqrt{\pi}w_{q}}\Big{(}\frac{\gamma\ w_{r}r_{ p}}{S}\Big{)}\frac{\sqrt[3]{f}}{r_{p}} \tag{6}\]6  
where \(E\;(A+B,N-2)\) is the supercell energy for two different solutes located in different nearest neighbor positions and \(N-2\) is the major alloying element atoms (Fe in the case of maraging steels). \(E(N)\) is the supercell energy with N number of Fe atoms. \(E\;(A,N-1)\) and \(E\;(B,N-1)\) are the supercell energies associated with \(A\) and \(B\) solute atoms and \((N-1)\) Fe atoms. As demonstrated in Figure 15, the research of [PERSON] et al. [95] showed the variance of the interaction energy between different solute combinations. The interaction energy between elements that are further away is lower compared to elements in the vicinity. As a result, the interaction energy between Ni and Co at the second nearest neighbor is negative (Figure 15), implying that Ni will be attracted to Co's second nearest neighbor. The interaction energy between Ti and Co is also negative at the first nearest neighbor position (Co), resulting in the mutual attraction of Ti and Co during the aging. In the case of the Ti-Mo and Ni-Mo systems, the nearest atom interaction energies are positive, indicating a tendency for Mo repulsion from the Ni-Ti-rich clusters. Additionally, the third nearest neighbor energy for Ti-Mo is negative, suggesting that Mo atoms will be excluded from the Ni-Ti-rich clusters and, instead, form a separate Mo-rich phase. Due to the relatively low aging temperatures employed in the study (480 \({}^{\circ}\)C), the diffusion of Mo is slow, which explains the absence of a Mo-rich phase in the early stages of aging. However, as the aging process advances, it was observed that a Mo-rich phase started to nucleate at the interface between Ni\({}_{3}\)Ti and the matrix. Due to the low interaction energies between Ni, Ti, and Co, these elements are closely associated with each other. The combination of these elements during aging can be classified into three potential categories (refer to Figure 16):  
1. (a) All three elements form a cluster distribution (cd);
2. (b) Ni and Ti combine to form a cluster distribution in the iron-rich region (cd), resulting in Co being dispersed (dd);
3. (c) Co, in turn, forms clusters with Ni and Ti. \[\sigma_{p}=\frac{1}{b}\frac{2S}{\sqrt{\pi}w_{q}}\Big{(}\frac{\gamma\ w_{r}r_{ p}}{S}\Big{)}\frac{\sqrt[3]{f}}{r_{p}} \tag{6}\]7 Interaction energies of different element combinations. Reprinted with permission from [95]. Copyright 2019 Acta Materialia Inc. The stability of each of these possibilities may be compared to the dispersed distribution of alloying elements, which can be expressed using Equation (21). \[\sigma_{p}=\frac{1}{b}\frac{2S}{\sqrt{\pi}w_{q}}\Big{(}\frac{\gamma\ w_{r}r_{ p}}{S}\Big{)}\frac{\sqrt[3]{f}}{r_{p}} \tag{6}\]8  
where \(E_{x}\) is the distribution energy of the involved elements in this case (Ni, Co, and Ti), \(E_{Fe-Co}\), \(E_{Fe-Co}\), and \(E_{Fe-Ti}\) are the energies associated with the dispersed distribution. The lowest energy state is when all three elements form a cluster together.