## 3 Results and Discussion  
The schematic diagram in Figure 1 illustrates a brief process of the new step annealing method for synthesizing the (211) Ti\({}_{2}\)AlN MAX phase beginning from the precursors. This is comprehensively explained in the experimental section. Generally, MAX phase ceramics are synthesized at high temperatures [49], and it is very difficult to obtain relative purity at lower temperatures. As illustrated in the schematic diagram, the 3D ceramic MAX phase of Ti\({}_{2}\)AlN was prepared using a unique step annealing method in an argon environment after pelletizing the precursors. In this particular method, a temperature soaking step at 600 \({}^{\circ}\)C for 1 h was maintained in step 1 because the melting point of Al is relatively low compared to other precursors, that is, 660 \({}^{\circ}\)C, which causes inevitable weight loss at higher temperatures [47]. The desorption of Al occurs at temperatures greater than 600 \({}^{\circ}\)C because of its high vapor pressure [50]. The absence of Al at high temperatures can change the composition of the reaction system. To overcome this phenomenon, the precursor ratio was initially adjusted and excess of Al was added to the composition. The increased formation of TiN phase impurities occurs in the temperature range of 900 \({}^{\circ}\)C to 1000 \({}^{\circ}\)C [50]. Therefore, from step 1 to step 2 of annealing, a higher step rate of 20\({}^{\circ}\) min\({}^{-1}\) was used to inhibit TiN formation. In step 2, the temperature soaking step was maintained at 1100 \({}^{\circ}\)C for 3 h to complete the MAX phase synthesis. The XRD pattern of the as-synthesized Ti\({}_{2}\)AlN MAX phase was recorded in the range of 10\({}^{\circ}\)\(-\)80\({}^{\circ}\) within 20 angle using CuK\(\alpha\) radiation (\(\lambda\) = 1.54 A) with a step size of 0.01\({}^{\circ}\), as shown in Figure 2a. The Ti\({}_{2}\)AlN MAX phase synthesized by the step annealing method with the optimized precursor ratio, indicated by the black profile in Figure 2a, contains most of the diffraction peaks of Ti\({}_{2}\)AlN and small amounts of TiAl with a peak position at 38.9\({}^{\circ}\) as an impurity. The prominent peaks in the pattern were observed at 12.9\({}^{\circ}\), 34.6\({}^{\circ}\), 35.2\({}^{\circ}\), 39.6\({}^{\circ}\), 40.0\({}^{\circ}\), 43.9\({}^{\circ}\), 53.6\({}^{\circ}\), 59.4\({}^{\circ}\), 62.0\({}^{\circ}\), 72.3\({}^{\circ}\), 76.1\({}^{\circ}\) and 76.4\({}^{\circ}\) 20 degree angles. All the diffraction peaks of the as-synthesized max phase can be indexed to the Ti\({}_{2}\)AlN reflections from JCPDS card no. 00-055-0434, which indicates the high purity of the as-synthesized Ti\({}_{2}\)AlN MAX phase. This is consistent with previously reported XRD results [10; 51]. The c-lattice parameter (c-LP) of the two-step annealed Ti\({}_{2}\)AlN presented in Table 1 was calculated to be 13.59 A using \"unit cell\" software from the XRD patterns explained in Figure 2a, and it closely matches with the reported Ti\({}_{2}\)AlN c-LP value [21]. This is strong evidence of high purity of the as-synthesized MAX phase. For comparison, Ti\({}_{2}\)AlN was also synthesized by a typical annealing process at 1100 \({}^{\circ}\)C without any step; its XRD pattern (red profile) is also shown in Figure 2a, which contains a prominent TiN peak at 42.6\({}^{\circ}\) and other impurities such as Ti\({}_{2}\)Al\({}_{5}\) at 43.3\({}^{\circ}\) along with many unspecified peaks. This comparative study of the  
Figure 1: Schematic illustration of Ti\({}_{2}\)AlN MAX phase synthesis by step annealing method. XRD patterns clearly shows the improvement of the step annealing method over the normal annealing method. The FE-SEM image shown in Figure 2b depicts the layered compact structure, which is a typical signature of the MAX phases [4], confirming the successful synthesis of the 3D MAX phase using the unique step annealing method.