Interface Effect in Ir-Nb-Zr Alloy

Abstract

The mechanical properties of Ir-Nb alloy have been significantly enhanced by the addition of solute Zr, yet there has been no quantitative explanation for this improvement. To address this issue, we investigated it from the perspective of Zr segregation to the Ir/Ir₃Nb interface. The atomic-scale microstructures of three interfaces, namely Ir (100)/Ir₃Nb(100), Ir(110)/Ir₃Nb(110), and Ir(111)/Ir₃Nb(111), were elucidated, along with the precise calculation of their interface energies using an unconventional method. This compensates for the deficiencies of the inaccurate results in calculating the interface energies of earlier prediction. Solute Zr prefers to segregate to the Ir/Ir₃Nb interface by occupying Nb sites on the Ir matrix side, thereby improving the interface adhesion to some extent. High strength of interface region contributes to enhance the mechanical properties of Ir-Nb alloy, which is in agreement with the experimental observation as reported.

1. Introduction

Ir-Nb based superalloy, known for its excellent performance of the high melting temperature and high temperature strength, has become an important high temperature structural material in aerospace field [1,2,3,4,5,6]. However, its application was limited due to poor processability at room temperature, which is caused by its intrinsic brittleness.

Improving this weakness has been an urgent issue that has garnered the attention of the researchers for many decades. It has been found that adding B and C elements to Ir-Nb alloy provides limited improvement in ductility, while also transforming the fracture mode from intergranular to transcrystalline [7,8]. Additionally, experiments have shown that adding Ni and Al significantly enhances the ductility of the alloy. However, the presence of various L1₂ phases in Ir-Nb-Ni-Al alloy can lead to high creep [9,10].

Huang et al. developed an Ir-Nb-Pt-Al alloy, which, compared to Ir-Nb-Ni-Al alloy, contains only one type of L1₂ precipitate and exhibits good ductility and strength [9]. The Ir-Nb-Zr alloy has also been experimentally prepared, and the results suggest that it has a stable microstructure and excellent high-temperature mechanical properties [11,12,13]. More interestingly, adding 8% Zr to Ir-Nb alloy results in an Ir-Nb-Zr alloy with a hardness higher than that of either L1₂-Ir₃Nb or Ir₃Zr. Gyurko et al. attributed this effect to microstructural changes or some degree of solid-solution hardening [11]. However, no qualitative research has been conducted in this regard. In light of the above, we believe that significant attention should be focused on the solute segregation effect of added Zr at the Ir/Ir₃Nb interface. This may provide a more comprehensive interpretation of the improved performance of Ir-Nb-Zr alloy from different perspectives.

As is well known, the uniform distribution of coherent interfaces between the face-centered cubic (FCC) Al matrix and L1₂-phase precipitates (such as Al₃Li, Al₃Sc, and Al₃Zr) plays a crucial role in significantly improving the yield and creep strength of corresponding Al alloys [14,15,16,17,18]. These L1₂-phase precipitates form through heat treatments in the Al matrix and act as obstacles to the movement of dislocations and grain boundaries. More specifically, further alloying with element, such as Zr in Al-Sc alloys, tends to form ternary L1₂-phase nanoprecipitates, namely Al₃(Sc_xZr_1−x). These ternary nanoprecipitates exhibit high lattice coherency with the Al matrix and possess both thermodynamic and kinetic tendencies to form a core–shell structure. This structure provides sufficient resistance against recrystallization and creep, even at higher temperatures [19,20,21]. The formation mechanism of these coherent L1₂-phase nanoprecipitates, Al₃(Sc_xZr_1−x), in dilute Al-Sc-Zr alloys has been theoretically resolved using interface thermodynamics [22].

The ordered L1₂ interface structures in Ir-Nb-Zr alloy are strikingly similar to those in Al-Sc-Zr alloy. Given this similarity, whether the added solute Zr contributes to the enhanced hardness of the Ir-Nb-Zr alloy should be investigated on the basis of analyzing the segregation of Zr at the FCC (Ir)/L1₂-Ir₃Nb interface. However, no reports addressing this topic have been found to date. Also, accurate calculation of the interface energies, rooted in the construction of the rational interface model, for Ir/L1₂-Ir₃Nb interface is necessary to perform subsequent research. Yet virtually microstructures of the Ir/L1₂-Ir₃Nb interface have not been fully characterized either experimentally or theoretically. Although Gong et al. investigated the stability of the Ir/Ir₃Nb interface using first-principles calculations [23,24], they predicted a negative value for the interface energy of Ir(100)/Ir₃Nb(100) and Ir(110)/Ir₃Nb(110) interface. Also, their calculations exist an obvious contradiction between the calculated interface energies and the separate work. All these problems suggest that the calculation method and interface models they employed may not be appropriate.

In light of these unresolved issues, we also employed first-principles calculations to provide clarity. Initially, we modeled three low-index Ir/L1₂-Ir₃Nb interfaces at the atomic scale. Subsequently, we recalculated the interface energies using a different method compared to previous studies. Following this, we explored the segregation effect of solute Zr at the Ir/L1₂-Ir₃Nb interface, with the goal of revealing the underlying mechanisms that contribute to the enhanced mechanical properties of the Ir-Nb-Zr alloy at the microscopic level.

2. Calculation Methods

We performed this work using the DFT code VASP [25] with periodic conditions and the plane-wave basis sets. The electron–ion interactions were described by the projector augmented wave method within the frozen-core approximation (PAW) [26]. The exchange-correlation energy was treated in the generalized gradient approximation (GGA) with the Perdew-Burke-Ernzerhof (PBE) functionals [27]. The energy cut-off of 450 eV of plane waves basis was set for all calculations, and the total energy was converged to 10⁻⁵ eV in the self-consistent iteration loop and the force criterion on each atom was set to within 0.01 eV/Å. The Brillouin zone was sampled with Monkhorst−Pack scheme using the k-points grid of 20 × 10 × 1, 10 × 7 × 1, and 7 × 4 × 1 for Ir (100)/Ir3Nb(100), Ir (110)/Ir3Nb(110), and Ir (111)/Ir₃Nb(111) interface supercell, respectively.

3. Results and Discussion

3.1. Interface Structure and Stability

To model a heterogeneous interface, several factors need to be considered, such as interface orientation relationship (OR), surface termination, interfacial coordination or stacking, and interfacial misfit strains. Based on the experimental OR [5], we constructed the Ir/Ir₃Nb/Ir sandwich interface supercells using different contacting facets, i.e., the low-index (100), (110), and (111) for both Ir and Ir₃Nb. Specially, we stacked 5 layers of Ir on the top and bottom, respectively, and 6–8 layers for L1₂-Ir₃Nb at the center. To ensure a homogeneous interface, stretching strains of ~+1.45% were applied to Ir, while compressive strains of ~−1.45% were applied to L1₂-Ir₃Nb. It should be noted that, unlike the interface supercells constructed by Gong and Bai [23,24], no vacuum region was included here. After fully relaxing the structure of all the modeled supercells, we obtained the most stable coordination relations of the three interfaces, as shown in Figure 1.

Interface energy with two symmetrical interfaces can be defined as

$$\gamma ={\displaystyle \frac{1}{2A}}(E_{\mathrm{int}}-N_{Ir}\times {\mu }_{Ir}^{\mathrm{int}}-N_{Nb}\times {\mu }_{Nb}^{\mathrm{int}}+P\Delta V-T\Delta S)$$

(1)

where $E_{\mathrm{int}}$ is the total energy of a fully relaxed interface supercell, $N_{Ir/Nb}$ is the sum of the corresponding Ir/Nb atoms in interface supercell, ${\mu }_{Ir/Nb}^{\mathrm{int}}$ is the chemical potential of Ir/Nb atom in interface state, and $A$ is the surface area. $\Delta V$ denotes the volume change resulting from interface relaxation. $\Delta S$ represents the vibrational entropy difference between the interface and the alloy matrix; they have very weak impacts on the interface energies and are generally ignored in calculation.

As known, when the interface is in equilibrium, the sum of the elemental chemical potentials for all atoms is equal to that to form the corresponding compound in bulk state; thus,

$$3{\mu }_{Ir}^{\mathrm{int}}+{\mu }_{Nb}^{\mathrm{int}}={\mu }_{I{r}_{3}Nb}^{\mathrm{int}}={\mu }_{I{r}_{3}Nb}^{bulk}$$

(2)

Combined with Equations (1) and (2), we have

$$\gamma ={\displaystyle \frac{1}{2A}}\left[E_{\mathrm{int}}-N_{Nb}\times {\mu }_{I{r}_{3}Nb}^{bulk}+(3N_{Nb}-N_{Ir}){\mu }_{Ir}^{\mathrm{int}}\right]$$

(3)

In terms of forming L1₂-Ir₃Nb compound, the elemental chemical potentials of Ir and Nb in the bulk state must meet Equation (4):

$$3{\mu }_{Ir}^{bulk}+{\mu }_{Nb}^{bulk}+\Delta H={\mu }_{I{r}_{3}Nb}^{bulk}$$

(4)

where $\Delta H$ is the formation enthalpy, which is a negative value, and usually applied to assess the thermodynamic stability for a formed compound.

According to Equations (2) and (4), one has

$$3{\mu }_{Ir}^{bulk}+{\mu }_{Nb}^{bulk}+\Delta H=3{\mu }_{Ir}^{\mathrm{int}}+{\mu }_{Nb}^{\mathrm{int}}$$

(5)

That is

$$\Delta H=3({\mu }_{Ir}^{\mathrm{int}}-{\mu }_{Ir}^{bulk})+({\mu }_{Nb}^{\mathrm{int}}-{\mu }_{Nb}^{bulk})$$

(6)

In order to ensure a stable interface, the chemical potential of Ir/Nb in interface state should be less than that in its bulk state (${\mu }_{Ir}^{\mathrm{int}}-{\mu }_{Ir}^{bulk}<0$ and ${\mu }_{Nb}^{\mathrm{int}}-{\mu }_{Nb}^{bulk}<0$). We here defined the term $\Delta \mu ={\mu }_{Ir}^{\mathrm{int}}-{\mu }_{Ir}^{bulk}$.

In this way, the formular to calculate the interface energy is derived as follows:

$$\gamma ={\displaystyle \frac{1}{2A}}\left[E_{\mathrm{int}}-N_{Nb}\times {\mu }_{I{r}_{3}Nb}^{bulk}+(3N_{Nb}-N_{Ir})({\mu }_{Ir}^{bulk}+\Delta \mu )\right]$$

(7)

It is generally believed that, for the precipitation-strengthened alloys (such as Al alloys), the chemical potential of Al in interface state is almost the same as that in bulk state [28]. Similarly, we here infer the outcome ${\mu }_{Ir}^{\mathrm{int}}$$\approx$${\mu }_{Ir}^{bulk}$. Even though there are some differences between them, these values should be very small. Therefore, the varying range for $|\Delta \mu |$ is given as $0\le |\Delta \mu |\le 0.04$. Based on this, we present the correlation between interface energies and the $\Delta \mu$, as shown in Figure 2.

It can be observed that as $\Delta \mu$ increases, the interface energies for all three interfaces decrease simultaneously. When the value of $\Delta \mu$ is around −0.01 eV, the (100) interface exhibits the smallest interface energy, which is approximately 0.25 J/m². This finding is accordant with the experimental observation [5]. Additionally, the stability of the three interfaces follows the order of $(100)>(110)>(111)$, which, as shown in

Table 1. Calculated interfacial energies of Ir/L1₂-Ir₃Nb interface, extracted as $\Delta \mu$ = −0.01eV, and Al/L1₂-Al₃X (X = Sc, Li) interfaces (1 0 0), (1 1 0), and (1 1 1), using the same method of GGA exchange correlations (J/m²) [29].

	Ir/Ir3Nb				Al/Al3X
	100	110	111		100	110	111
Present	0.25	0.27	0.30	Al3Sc [29]	0.165	0.178	0.189
Others [22]	−0.25	−0.09	1.07	Al3Li [29]	0.012	0.017	0.022

, aligns with the trends observed in other similar L1₂-Al₃X (X = Sc and Li) interface structures [29]. However, the variation in interface energies deviates from the experimental results when $|\Delta \mu |$ exceeds 0.015 eV or falls below 0.002 eV. This deviation, in turn, confirms the rationality of the $|\Delta \mu |$ range we proposed.

3.2. Interface Segregation

We first take the Ir(100)/Ir₃Nb(100) interface as an example, as shown in Figure 3, to illustrate the possible occupied sites of the solute Zr segregating at the interface area. Subsequently, the segregation energy ($\Delta E$), as defined in Equation (8), was used to examine the potential segregation effect of Zr from the Ir matrix to the equilibrium Ir/Ir₃Nb interface. A negative value indicates the possibility of Zr replacing the Ir or Nb atoms in the interface.

$$\Delta E=(E_{\mathrm{int}}^{Zr}-E_{\mathrm{int}}^0)+({\mu }_{Zr}-{\mu }_{Ir/Nb})$$

(8)

Here, $E_{\mathrm{int}}^0$ and $E_{\mathrm{int}}^{Zr}$ denote the total energies of the interface supercell before and after Zr segregation, respectively. ${\mu }_{Zr/Ir/Nb}$ is the chemical potential of a single Zr/Ir/Nb atom.

As shown in Figure 4, Zr is forbidden to replace any Ir atom in the L1₂-Ir₃Nb bulk due to the positive value for $\Delta E$. Nevertheless, it exhibits the possibility to substitute the Nb atom of the Ir-Nb layer within the bulk interior for all three interfaces. In contrast, solute Zr is more likely to segregate to various substitutive sites of the Ir matrix side. More specifically, the Nb sites in the first layer for the (100) and (110) interfaces, as well as the “0” layer for the (111) interface, are particularly attractive for the segregated Zr atom, with the segregation energies of −2.6eV, −5.2eV, and −3.2eV, respectively. Meanwhile, Ir atoms of the matrix side are likely to be replaced as well, but this trend is weaker compared to that of Nb atoms.

3.3. Interface Strength

Segregated solutes have a stronger impact on the interface strength. The work of separation (W_sep) is usually used to evaluate this effect and is defined as

$$W_{sep}={\displaystyle \frac{E_a+E_b-E_{total}}{2A}}$$

(9)

where $E_{total}$ is the total energy of one of the calculated Ir/Ir₃Nb interface supercells. $E_a$ and $E_b$ represent the static energies of the part a and b after the interface supercell was divided into two halves, respectively. $A$ is the bottom area.

The calculated results are shown in Figure 5, where three atomic layers were considered as the whole interface region for the (100), (110), and (111) interfaces. The values of interface sites for the three pure interfaces were found to be 6.62 J/m² for (100), 6.59 J/m² for (110), and 4.90 J/m² for (111). These values are close to those reported earlier [23]: 6.35 J/m², 6.39 J/m², and 4.54 J/m², respectively. However, unlike the earlier reports where the (110) interface had the highest value [23], our calculations are consistent with the change trend given by the calculated interface energies.

Zr segregation significantly improves the strength between the interfacial Ir and the L1₂-Ir₃Nb layers. Specifically, the increase is more pronounced for the (110) interface, with a value of 5%, compared to the other two interfaces. This enhancement is likely associated with the interface coverage of the solute Zr. As seen in Figure 3 and Figure 4, the coverage of solute Zr occupying Nb sites is 50% for the (100) and (111) interfaces, but it reaches 100% for the (110) interface. The higher coverage of segregated solutes at the (110) interface contributes to the remarkable improvement in interface strength [30]. By contrast, the enhancement at other layers is relatively minor, with added values not exceeding 2%. Clearly, increased interface adhesion, caused by the segregated solute Zr, between L1₂-Ir₃Nb and Ir matrix contribute to interfere with the movement of the dislocations in Ir-Nb alloy, improving the mechanical performance as observed in existing experiments [11].

4. Conclusions

The atomic-level structures, interface energies, and solute Zr segregation effects of the Ir(100)/L1₂-Ir₃Nb(100), Ir(110)/L1₂-Ir₃Nb(110), and Ir(111)/L1₂-Ir₃Nb(111) interfaces were explored using first-principles calculations. It was found that the lowest-energy structure among the three interfaces is the one where the atomic arrangement on the Ir matrix side of the interface is coincident with the L1₂-Ir₃Nb phase. The difference in chemical potential for Ir atoms between the interface and bulk states significantly impacts the interface energies of all three interfaces. The added Zr in the Ir-Nb alloy tends to occupy Nb sites on the matrix side of the Ir/L1₂-Ir₃Nb interface region, having significant impact on the interface adhesion. This helps to improve the mechanical properties of Ir-Nb alloy effectively.