Prediction of possible metastable alloy phases in an equilibrium immiscible Y–Mo system by ab initio calculation L.T. Kong, J.B. Liu, and B.X. Liua) Laboratory of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing 100084, China, and Laboratory of Solid-State Microstructure, Nanjing University, Nanjing 210008, China (Received 14 May 2001; accepted 8 January 2002)

In the equilibrium immiscible Y–Mo system, the total energies of the possible structures for YMo3 and Y3Mo metastable phases were calculated as a function of their lattice constants, by employing the Vienna ab initio simulation package, and the results suggested that the D019, L12, and L60 structures were three possible metastable states in the system. Experimentally, hcp and fcc YMo3 metastable phases were obtained in the Y–Mo multilayers driven far from equilibrium by ion irradiation. Moreover, the lattice constants determined by diffraction analysis were in agreement with the predicted values.

The requirement of new materials of high performance has stimulated an increasing interest in developing novel materials processing methods to produce new metastable alloys as well as in promoting an understanding of the underlying formation mechanism. Since the early 1980s, ion mixing (IM) of multiple metal layers has been employed as a powerful means to produce new metastable materials with either an amorphous or crystalline structure in the binary metal systems.1 From the experimental observations, it is of interest to note that a number of similar metastable crystalline phases obtained by IM have similar alloy compositions near A3B and AB3, where A and B stand for the constituent metals A and B of the system, respectively, and that these phases are frequently of similar crystalline structures (hcp or fcc), when metals A and B are both transition metals. These observations raise a challenging issue for further theoretical investigation to reveal the physical origin responsible for the formation of the metastable crystalline phases. In this regard, some researchers have studied the stability of the nonequilibrium solid phases by calculating their free energies under the framework of Miedema’s model.2,3 Generally speaking, thermodynamic calculation is still at a semiquantitative stage, and to approach a better understanding at a depth of electronic structure, first-principles calculation is necessary. In this study, we conduct a first-principles calculation to reveal the possible nonequilibrium states of A3B and AB3 types in a representative Y–Mo system, which is equilibrium

a)

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immiscible and characterized by a positive heat of formation of +35 kJ/mol, i.e., to predict the possibility of forming new metastable alloys in the Y–Mo system. It is known that there are about 20 possible different structures for the A3B and AB3 phases, i.e., the A15, Ae, D02, D03, D09, D011, D018, D019, D020, D021, D022, D023, D024, D0a, D0b, D0c, D0d, L12, L1a, and L60 structures. First, in the above 20 structures, some are very complicated, such as the D02 and D021 structures containing more than 16 atoms/unit cell. For the L1a structure, it can also be considered as a complicated one, as it has 32 atoms/unit cell,4,5 or 8 atoms per unit cell according to Pearson notation. These phases probably require highly sufficient kinetic conditions to nucleate and grow, e.g., requiring relatively high temperature to enhance the atomic mobility and a long time to enable the atoms to organize themselves into a specific configuration. In other words, if such kinetic conditions are not available, these phases are hardly formed.6 Second, the nonequilibrium crystalline phases that have so far been obtained by IM were only of simple structures like hexagonal-closepacked (hcp) and face-centered-cubic (fcc), probably because of the restricted kinetic conditions involved in the IM process.7 Consequently, in our ab initio calculation, the A15, D019, L60, and L12 structures of A3B and AB3 types were calculated to investigate their relative structural stabilities. The total energies of the Y3Mo and YMo3 phases with four chosen structures were computed on the basis of the well-established Vienna ab initio simulation package (VASP),8 which has been described in detail elsewhere.9,10 Briefly, the development of the VASP code was based on the density functional theory within the © 2002 Materials Research Society

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local-density approximation. In this work, the exchange and correlation items were described by the specially defined functions proposed by Perdew and Zunger,11 in which the nonlocal corrections in the form of the generalized-gradient approximation (GGA) of Perdew and Wang12 were added for improving the computation. The electron-ion interaction was described by pseudopotentials. The method13 used to build the pseudopotentials was derived from Vanderbilt’s recipe14 previously employed for ultrasoft pseudopotentials and from that developed by Kresse et al.13,15 The pseudopotentials allowed the use of a moderate cutoff for the construction of the plane-wave basis for the transition metals. The integration in the Brillouin zone was done on some special points in the reciprocal k-space determined by employing the Monckhorst–Pack scheme. For the possible YMo3 phase, the total energy was calculated as a function of the lattice constant(s) for four different structures, i.e., D019, L12, A15, and L60, respectively. The c/a ratios of the D019 and L60 structures were optimized. To discuss the stability of the alloy phases of interest, a mechanical mixture of pure Y and Mo with a chemical stoichiometry of 1:3 was set as a reference state to compare with that of the predicted YMo3 phase and the total energy of the reference state was calculated to be −9.72 eV/atom. Accordingly, we define the formation energy of an alloy phase to be the total energy difference between the metastable and the reference states and the definition was used for both YMo3 and Y3Mo phases. Figure 1 exhibits the four calculated curves showing the correlation of the formation energy versus the average atomic volume. Apparently, the total energies of the four structures are all higher than that of the reference state, and therefore, they correspond to the possible nonequilibrium states existing in the Y–Mo system. One sees from the figure that the increasing order of the relative

structural stability for the possible YMo3 phase is A15, L12, D019, and L60, and they can be divided into three energetic groups. First, the A15 structure, which is of cubic structure, has the highest energy. Second, the D019 and L12 structures have similar energy and are both much lower than the previous one. The D019 structure has a lower minimum total energy than that for L12 by about 0.04 eV/atom, and the cohesive energy difference between L12 and D019 structures is therefore less than 0.04 eV/atom. Third, the L60 structure has an even lower energy than the former three. Table I lists the calculated minimum cohesive energy and other properties for the four possible YMo3 phases. It can be seen that the difference of the atomic volume between the D019 and L12 structures is less than 0.5%, reflecting the well-known fact that the fcc (L12) and hcp (D019) structures are very much alike. Because of the similarity of the fcc and hcp structures in their atomic configurations, it is of theoretical relevance that the total energies of the fcc and hcp phases are very close. Similar calculations were also conducted for the possible Y3Mo phase, and the four calculated curves are displayed in Fig. 2, showing the correlation of the formation energy versus the average atomic volume. For the case of Y3Mo, a corresponding mechanical mixture of pure Y and Mo was also set as a reference state whose total energy was calculated to be −7.51 eV/atom. The calculated cohesive properties for the four structures are listed in Table II. Similar to the case of YMo3, the four corresponding states are of nonequilibrium. One sees that the increasing order of the relative structural stability for the possible Y3Mo phase is A15, L60, L12, and D019. The four calculated structures of the Y3Mo phase are also divided into three groups. First, the A15 structure has apparently a higher minimum total energy than the D019, L60, and L12 structures, implying that the A15 structure is relatively unstable. Second, the minimum total energies of the L60 (which is tetragonal and can be regarded as tetragonal deformed L12 or superstructure of A6 type) and L12 structures are quite close, and the L12 structure has a lower total energy than that for L60 by about 0.01 eV/atom. Third, the D019 structure, instead of L60 in the case of YMo3, has the lowest total energy. TABLE I. The calculated equilibrium cohesive properties (lattice constants a and c/a, atomic volume V, minimum total energy Emin, and formation energy E f ) of YMo 3 in the D0 19 , L1 2 , A15, and L60 structures.

FIG. 1. Calculated formation energy versus average atomic volume for YMo3 metastable phases with different structures.

a (Å) c/a V (Å3/atom) Emin (eV/atom) Ef (eV/atom)

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D019

L12

A15

L60

2.92 1.69 18.31 −9.00 0.72

4.19 ··· 18.39 −8.96 0.76

5.89 ··· 25.54 −8.16 1.56

4.49 0.79 17.85 −9.25 0.47

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FIG. 2. Calculated formation energy versus average atomic volume for Y3Mo metastable phases with different structures.

It is of interest to compare the above calculation results with the experimental results obtained earlier by the authors’ group.16 First, at the Mo-rich side, two metastable phases were observed in the Y27Mo73 multilayers upon IM and their structures were of fcc and hcp, respectively. The composition of the obtained metastable phases was therefore very close to YMo3. Although the observed fcc phase is not exactly the L12 structure, which is an ordered lattice, they are, at least, both of fcc type. Generally speaking, an ordered lattice possesses lower free energy than its disordered counterpart, which frequently turns out first during the crystal growth process as a precursor. It is therefore believed that the observed fcc phase situates a little higher energetic level than the L12 structure.

TABLE II. The calculated equilibrium cohesive properties (lattice constants a and c/a, atomic volume V, minimum total energy Emin, and formation energy E f ) of Y 3 Mo in the D0 19 , L1 2 , A15, and L60 structures.

a (Å) c/a V (Å3/atom) Emin (eV/atom) Ef (eV/atom)

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D019

L12

A15

L60

3.32 1.61 25.57 −7.20 0.31

4.67 ··· 25.46 −7.15 0.36

5.99 ··· 26.87 −6.00 1.51

4.85 0.89 25.36 −7.14 0.37

In this sense, the experimental observation was in agreement with the calculated result. Moreover, the experimentally determined lattice parameters of the fcc was measured to be afcc ⳱ 4.04 Å, which was also in accordance with the calculated value of aL12 ⳱ 4.19 Å for the L12 structure. The above discussion concerning the structural similarity was also valid for the observed hcp phase. Besides the lattice parameters of the hcp phase were identified to be ahcp ⳱ 2.89 Å and c/a ⳱ 1.62, while the calculation results were aD019 ⳱ 2.92 Å and c/a ⳱ 1.69. In short, the experimental results did confirm the existence of such metastable states located near YMo3 with a structure of either fcc or hcp type in the equilibrium immiscible Y–Mo system. One may notice that, at the Mo-rich side, the calculated minimum total energy of the L60 structure is lower than those of the L12 and D019, yet the L60 did not appear in the previous IM experiments. Instead, fcc and hcp YMo3 metastable phases were obtained. These results were thought to be relevant. From the structural point of view, the L60 structure is relatively complicated in comparison to those of L12 and D019, as mentioned above, it probably requires highly sufficient kinetic conditions for nucleate and grow, e.g., high temperature to enhance atomic movement and a long time for atoms to organize themselves into specific atomic configurations. While in the process of IM, the kinetic condition available for growing an alloy phase is very restricted during the relaxation period (lasting only for about 10−9 s) immediately after atomic collision triggered by ion irradiation and therefore allows forming only those simple structured alloy phases.7 Consequently, it might be the kinetic constraint that prevented the L60 structures from growing in the IM process. An interesting issue is that, on the Y-rich side, the possible D019 is a simple structure having a lower energy than L12. Nonetheless, this structure has not been observed in the previously conducted experiments, and it certainly deserves further investigation. In summary, with employment of the VASP, ab initio calculation results are quite relevant in predicting the existence of some nonequilibrium solid states in the Y–Mo system, and technically, some of the corresponding alloy phases, such as hcp and fcc YMo3 phases, were obtained in the Y27Mo73 multilayers upon ion irradiation, which is a process of far from equilibrium.

ACKNOWLEDGMENTS

The authors gratefully acknowledge the financial aid from the National Natural Science Foundation of China, the Ministry of Science and Technology of China through a Grant No. G2000067207, and the Administration of Tsinghua University.

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