*3.4. Hardness and Modulus*

The corresponding hardness and elastic modulus were measured using an indentation tester for these coatings. It can be seen from Figure 7a that hardness and elastic modulus both reach the maximum value under the sputtering condition of 400 ◦C-100 W, 9 GPa, and 157 GPa, respectively. In general, the high hardness of coatings is usually attributed to their dense structure and small grain size. As shown in Figure 4, the Ta coating at 400 ◦C-100 W exhibits the densest structure with a minimal grain gap. On the other hand, this is concerned with the grain size that has an effect on mechanical properties of coatings due to the Hall– Petch (H-P) effect [27]. On the basis of the dislocation theory, grain boundaries are obstacles in the movement of dislocations, and refining grains can produce more grain boundaries. If the grain boundary structure does not change, a larger external force is required to generate dislocation plugging, thereby strengthening the material.

**Figure 7.** (**a**) H and E, (**b**) H/E and H3/E2, (**c**) load–depth curves, and (**d**) elastic recovery ratio of Ta coatings.

Furthermore, the enhanced hardness H is not a single important property of the hard coating. For many applications, H/E (elastic strain failure strength) [28] and H3/E2 (plastic deformation strength) [17] calculated by hardness and modulus are more important than their extremely high hardness. H/E and H3/E2 are important parameters of coating materials in the field of wear, which are positively related to the toughness of coatings and play a vital role in the crack resistance process [29]. Figure 7b shows the change in H/E and H3/E2 calculated from hardness (H) and elastic modulus (E). It can be seen that H/E and H3/E2 show similar variation trends, and both reach their highest at 400 ◦C-100 W, which are 0.057 and 0.030 GPa, respectively. It also demonstrates that the Ta coating at 400 ◦C-100 W has better crack resistance and toughness, with abilities to endure mechanical damage in abrasive wear applications and withstand impact energy from deformation to fracture [28].

The load–depth curves of Ta coatings at various sputtering conditions are illustrated in Figure 7c. The coatings were complied with an elastoplastic deformation according to the curves. In the nanoindentation test, some of the total energy (WT) was recovered as reversible elastic energy (WE), while some was lost as irreversible plastic deformation energy (WP). The elastic recovery ratio (ηw), which can be defined as η<sup>w</sup> = WE/WT, is a measure to express the response of a material to indentation [30,31]. Take the coating prepared at 300 ◦C-150 W as an example; WE and WT are given by the areas under the loading and unloading curves, respectively, as shown in Figure 7c. The coating prepared at 400 ◦C-100 W has a higher η<sup>w</sup> value of 0.39 in Figure 7d, indicating better resilience.

Figure 8 shows the comparison of the H/E and H3/E2 of α-Ta coatings prepared in this work with other literatures. In previous studies, the H/E and H3/E2 varied within a range of 0.0275–0.055 and 0.0058–0.031 GPa, respectively. Compared with other studies, the α-Ta coating at 400 ◦C-100 W in our work has higher H/E and comparable H3/E2 in contrast to G. Abadias et al. [21], which can be attributed to its high densification and homogeneous structure.

**Figure 8.** Comparison of the H/E and H3/E2 of α-Ta coatings with other literatures [15,21,32–34].
