ARTICLE pubs.acs.org/JPCC
Vacancy and Oxygen Substitution for Nitrogen-Induced Structural Stability of Ta2N3 Xiang Po Du,†,‡ Yuan Xu Wang,†,‡,* and V. C. Lo‡ † ‡
Institute for Computational Materials Science and Physics Department, Henan University, Kaifeng 475004, People's Republic of China Department of Applied Physics, The Hong Kong Polytechnic University, Hong Kong, China ABSTRACT: First-principles calculations were carried out to investigate the structural stability of synthesized orthorhombic Ta2N3. It is found that the stoichiometric orthorhombic Ta2N3 is unstable below 20 GPa. However, it can be stabilized by a small amount of nitrogen vacancies or oxygen substitution into nitrogen sites. The calculated electron localization function indicates that both the formation of nitrogen vacancy and the substitution of oxygen atom can enhance the Ta-N bonding, which is essential for the structural stability. Furthermore, both oxygen substitution and nitrogen vacancy plays a similar role in stabilizing the orthorhombic lattice of Ta2N3. The results of our calculations show that nitrogen vacancies or oxygen substitution into nitrogen sites can alter the charge distribution over the unit cell, which leads to a new arrangement of atoms and enhanced Ta-N bonds.
I. INTRODUCTION Nitrides synthesized under high pressure and at high temperature conditions have drawn much attention of both theoreticians and experimentalists due to their interesting properties and a wide variety of applications. For example, γ-Si3N4 exhibits a high Vickers microhardness about 30-43 GPa and a high thermal stability in air up to 1673 K.1-3 Cubic-phase Zr3N4 demonstrates a high hardness of 30 GPa,4,5 and can be deposited as thin films with a better wear resistance than that of δ-TiN films, enabling the former as a widely used material in industry.6 Recently synthesized noble transition-metal nitrides such as PtN2, IrN2, OsN27-9 are found to have a high bulk modulus above 350 GPa, indicating their potentially high hardness. Both WN2 and ReN2 have been theoretically predicted to be potentially superhard materials.10,11 In addition to the applications as materials with high hardness, these transition-metal nitrides are also used as diffusion barriers in microelectronics.12,13 A recent first-principles study shows that the synthesized marcasite OsN2 might be a superconductor with Tc = ∼1 K.14 Tantalum nitrides, with their outstanding properties such as chemical stability, high hardness, high melting point, good thermal and electronic conductivity, and superconductivity, are always the focus of attention of scientists.15 Recently, using Kawai-type multianvil apparatuses, Zerr et al. claimed to have synthesized η-Ta2N3 under high pressures and at high temperatures, and noted that it being the first nitride in the U2S3 structure (space group: Pbnm).16 Orthorhombic Ta2N3, exhibiting excellent thermodynamic stability over a wide pressure range (11-20 GPa) at high temperatures (1800-2000 K), high hardness of about 30 GPa, and peculiar texture, is suggested to be the candidate material for hard and fracture-resistant applications. However, r 2011 American Chemical Society
the first-principles calculations suggest that the orthorhombic structure is unstable.17 The investigation of structure and stability of a material is important. Jiang et al.17 used both the ’rounding up the usual suspects’ based on the known crystal structures and random structural searches to predicate a stable tetragonal Ta2N3 (space group: P42), and they also confirmed that the substitution of minor oxygen for nitrogen atoms can stabilize the orthorhombic Ta2N3 lattice. However, tetragonal Ta2N3 will transform into orthorhombic phase at a pressure of 7.7 GPa. In other words, tetragonal Ta2N3 was not observed under high pressures (1120 GPa) as reported in Zerr’s experiment.16 More recently, Nb2N318 with the U2S3 structure was suggested to be both thermodynamically and mechanically stable and can be prepared under moderate pressure conditions. To date, the detailed thermodynamic stability of orthorhombic Ta2N3 against decomposition as well as its mechanical and dynamical stability under high pressure are still unclear. In the synthesis of transition-metal nitrides under high pressure and at high temperature conditions, nitrogen vacancy (or N-vacancy) is easily generated. It is wellknown that transition-metal nitrides can exist in substoichiometric phase and the N-vacancy is the major contribution to the nonstoichiometry.15,19-24 Previous studies have shown that N-vacancy plays a critical role in hardening23 and stabilizing transition-metal nitrides.20-22 However, the study of the effect of N-vacancy on the stability and mechanical properties of Ta2N3 has never been reported in the literature. Herein, first-principles calculations were performed to investigate the thermodynamic, Received: November 15, 2010 Revised: January 11, 2011 Published: February 1, 2011 3129
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Table I. Calculated Lattice Constants for Orthorhombic Ta2N3, d-AC, d-AC0 , o-AC, and o-AC0 Structuresa
Table II. Calculated and Experimental Internal Atomic Coordinates of Orthorhombic Ta2N3
Ta2N3 (Pbnm)
a
Jiang et al.17
this work
exp 16
this work
Jiang et al.17
Exp.16
d-AC
d-AC0
o-AC
o-AC0
atom
x
y
x
y
x
y
a
8.17
8.19
8.19
8.20
8.22
8.26
8.26
Ta1
0.313
0.979
0.313
0.979
0.313
0.980
b
8.23
8.24
8.18
8.19
8.25
8.21
8.23
Ta2
0.505
0.306
0.505
0.306
0.505
0.307
c
2.99
3.00
2.98
5.97
5.95
5.96
5.95
N1
0.875
0.046
0.875
0.046
0.875
0.025
N2
0.549
0.879
0.549
0.879
0.585
0.890
N3
0.200
0.220
0.200
0.220
0.201
0.248
The previous theoretical and experimental data are shown as well.
mechanical, and dynamical stabilities of orthorhombic Ta2N3 under high pressures. Moreover, the enhancement of structural stability for orthorhombic Ta2N3 induced by both N-vacancy and the substitution of oxygen into nitrogen site are comprehensively studied. Our calculations show that stoichiometric orthorhombic Ta2N3 is unstable below 20 GPa and that vacancy or oxygen substituted Ta2N3 can retain orthorhombic lattice and is mechanically and dynamically stable. N-vacancy and oxygen substitution play a similar role in stabilizing the orthorhombic lattice by redistributing the charge over the unit cell. However, higher concentration of N-vacancy or oxygen substitution is unfavorable for structure stability.
II. COMPUTATIONAL DETAILS The calculations in this work were performed based on the density functional theory (DFT) using all-electron projector augmented waves (PAW) method25 within the generalized gradient approximation (GGA) of Perdew, Burke, and Ernzerhof (PBE),26 as implemented in the Vienna ab initio simulation package (VASP).27 The structures were optimized with the conjugate-gradient algorithm method. The plane wave cutoff energy was chosen to be 500 eV, and Brillouin zone sampling was performed using the Monkhorst-Pack grid.28 Dense k-point meshes were used to guarantee that the total energy was less than 5 meV/(unit cell). During the geometrical optimization, all forces on atoms were converged to less than 2 meV/Å. The elastic constants were computed using strain-stress method29 except for those of orthorhombic Ta2N3 under high pressure which were computed using the method described in ref 30. The bulk and shear moduli were derived from the Voigt-Reuss-Hill approximation31 The phonon dispersion curves were obtained based on the harmonic approximation using the frozen phonon technique, as implemented in the fropho code.32 III. RESULTS AND DISCUSSION The calculated lattice constants and atomic coordinates for orthorhombic Ta2N3 are listed in Table I and II, respectively. The structure of Ta2N3 polyhedron is shown in Figure 1. As seen in the two tables, our calculated structural parameters are in excellent agreement with those in ref 17. Both our theoretical results and those of previously reported by Jiang et al.17 also agree with the experimental values,16 except for the z coordinate for the position of the nitrogen atom. The discrepancy in the z coordinate between the theoretical and experimental results is mainly due to the difficulty in accurately determining the positions of N atoms in experiment. The shortest bond length is 2.10 Å for Ta1-N2, which is different from the value of 1.91 Å for Ta1-N3 as reported in ref 16. The largest distance is 2.59 Å for Ta2 and N3. One Ta2 atom and six N atoms form a trigonal
Figure 1. Structure and polyhedral view of orthorhombic Ta2N3. The large and the small spheres represent Ta and N atoms, respectively. The red small balls with the label A, B, C, and D represent N3 atoms.
prism, with one of the three faces of this prism capped by the seventh N atom. Ta2 and surrounding N atoms form a decahedron, a distorted one-face-capped trigonal prism, which is perpendicular to the former. This is also different from the result in ref 16, where only one type of polyhedra of one-face-capped or two-face-capped trigonal prism is formed by considering the different largest Ta-N bond length. Ta2N3 was synthesized under high pressure and at high temperature via the following reaction route: 2Ta3 N5 ¼ 3Ta2 N3 þ 0:5N2
ð1Þ
To study its thermodynamic stability, the formation enthalpies of Ta2N3, including the following possible reaction routes of (i) Ta þ N2, (ii) Ta2N þ N2, (iii) TaN þ N2, (iv) Ta4N5 þ N2, (v) Ta5N6 þ N2, were calculated as functions of pressure and are plotted in Figure 2. Our calculations also show that orthorhombic Ta2N3 is more stable than tetragonal Ta2N3 above 6.3 GPa, which is consistent with the result in ref 17. Consequently, we do not show the formation enthalpy of tetragonal Ta2N3 in this figure. At ambient pressure, the total energy of N2 molecule of a unit cell of size 10 10 10 Å3 was calculated. The calculated N-N triple bond length is 1.10 Å, in excellent agreement with the experimental value of 1.09 Å. We have also calculated the total energies of TaN in P-6m2, P-62m, P6/mmm, and FM-3m phases, and found that TaN in the P-62m phase is more energetically stable at ambient pressure, in agreement with previous calculations.33 Therefore, P-62m was chosen as the reference phase of ground state for TaN. For Ta2N, Ta4N5, Ta5N6, and Ta3N5, P-31m, I4/m, P63/cm, and Cmcm phases were chosen as their reference phases, respectively. Under high pressure, R-nitrogen34 is chosen as the reference phase. Our calculations also suggest that above 5 GPa, the P-6m2 structure, instead of the P-62m phase, is the most stable phase among the considered TaN phases and is thus chosen as the reference phase at high pressure. Ta3N5 in Pnma phase is chosen as the reference phase in light of our calculations for pressure above 9 GPa. As seen from Figure 2, orthorhombic Ta2N3 is thermodynamically stable against decomposition into Ta, Ta2N, TaN, Ta4N5, or Ta5N6 þ N2 during the whole considered pressure range. 3130
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Figure 2. Calculated formation enthalpy of orthorhombic Ta2N3 via different reaction routes.
Table III. Calculated Elastic Constants cij (in GPa), Bulk Modulus B (in GPa), Shear Modulus G (in GPa) of Orthorhombic Ta2N3 and Its Various Vacancy Structures c11 c22 c33 c44 c55
c66
c12 c13 c23
this work
460 635 655 170 198 -57 261 222 190
ref 17
456 610 639 165 193 -54 248 203 176
B
G
under 20 GPa
628 836 828 233 266 124 344 299 259 453 245
Ta8N11
524 651 475 187 162 160 166 210 192 313 197
d-AC
473 561 638 161 151 147 233 200 182 321 179
d-AC0
464 499 632 149 155 171 216 193 180 307 177
o-AC o-AC0
494 603 664 161 174 156 245 207 181 335 192 502 557 666 162 195 178 240 207 177 330 198
Ta16N22O2-I17 487 531 649 153 188 175 230 193 166 315 173 Ta16N22O2-II17 481 581 646 153 176 147 235 194 170 322 167
At ambient conditions, orthorhombic Ta3N5 becomes thermodynamically stable against decomposition into Ta2N3 þ N2. Orthorhombic Ta2N3 becomes favorable for pressure above 5 GPa. The formation enthalpy reaches a minimum of -0.043 eV/atom at 10 GPa, and increases monotonously throughout the pressure range of 10-25 GPa with the value of nearly zero at 25 GPa, suggesting that orthorhombic Ta3N5 may again become thermodynamically favorable at higher pressure (above 25 GPa). However, orthorhombic Ta2N3 is thermodynamically stable and can not be converted to any other stoichiometric tantalum nitrides throughout the range of 10-25 GPa, in accordance with the claim made by Zerr et al. that orthorhombic Ta2N3 is thermodynamic stable over a broad pressure range.16 It seems from Figure 2 that orthorhombic Ta2N3 might be synthesized from Ta, Ta2N, TaN, Ta4N5, or Ta5N6 and nitrogen, but it should be noted that the pressure should be high enough to overcome the large energy barrier of nitrogen molecules. For a structure to be mechanically stable, its elastic constants should satisfy the following stability criteria:35 c11 > 0,c22 > 0,c33 > 0,c44 > 0,c55 > 0, c66 > 0,c11 þ c22 þ c33 þ 2ðc12 þ c13 þ c23 Þ > 0, ð2Þ c11 þ c22 -2c12 > 0,c11 þ c33 - 2c13 > 0,c22 þ c33 - 2c23 > 0:
Orthorhombic Ta2N3 is unstable at ambient conditions due to the negative shear modulus c66 (Table III). Because Zerr et al.16 suggested that orthorhombic Ta2N3 is thermodynamically stable over a broad pressure range (from 11 to 20 GPa), it is desirable to calculate elastic constants under high pressure to investigate its stability. We computed the elastic constants of orthorhombic Ta2N3 under 10 and 20 GPa respectively and list them in Table III. As seen from Table III, all the elastic constants cij increase monotonously with elevated pressure. The value of c66
Figure 3. Calculated phonon dispersion curves of orthorhombic Ta2N3 under (a), 0 GPa; (b), 10 GPa; and (c), 20 GPa.
becomes positive at 10 GPa. Apparently, the computed elastic constants now satisfy the above equations. The pronounced change is that the calculated c66 value at 20 GPa is almost 100 GPa larger than that at 10 GPa, suggesting that the structure would be more mechanical stable at higher pressure. A rigid criteria has been used to determine the structural stability of orthorhombic Ta2N3. Phonon dispersion curves of orthorhombic Ta2N3 under 0, 10, and 20 GPa respectively were calculated and are plotted in Figure 3. As seen from part a of Figure 3, imaginary frequencies appear in the Brillouin zone, indicating that orthorhombic Ta2N3 is unstable, consistent with the result derived from the analysis of the calculated elastic constants. However, we also note that under 10 GPa, although the calculated elastic constants obey the stability criteria,30 phonon anomalies still exist, suggesting that the structural instability is mainly driven by the softening of the phonon which might be weakly coupled to the negative elastic shear modulus c66. Orthorhombic Ta2N3 is not dynamically stable until at or above 20 GPa. From the above analysis, we can now conclude that orthorhombic Ta2N3 is unstable over the pressure range of 11-20 GPa. Furthermore, the effect of temperature on structure stability22 was not taken into account. To study the influence of N-vacancy on the stability of orthorhombic Ta2N3, calculations were carried out on the orthorhombic unit cell with one N vacancy (Ta8N11), corresponding to about 5% vacancy concentration. It is found that when the vacancy occupies one of the equivalent N sites, the system has the same total energy, and that when vacancy occupies one of the N3 sites, the total energy keeps the lowest value. Therefore, we focus on N-vacancy being at N3 sites. Using the structure with one N vacancy on the N3 site (0.70, 0.28, 0.25) as a representative, the elastic constants of Ta8N11 based on the optimized structure were calculated and their results are listed in Table III. From this table, c66, being negative in the normal orthorhombic Ta2N3, now becomes positive, indicating that the defective Ta2N3 is mechanical stable. Moreover, the estimated high bulk and shear moduli (in Table III) are so high that they can be categorized into the class of materials with high hardness. It can also be noted that vacancy plays an important role on stabilizing the structure and enhancing 3131
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Figure 4. Left: orthorhombic Ta2N3 with double cell along the c direction. Large and small balls represent Ta and N atoms, respectively. Red small balls represent N atoms on N3 sites, and large green and large gray balls represent Ta atoms, which would move out of the cell when introducing vacancy or oxygen on some of the N3 sites. Right: o-AC structure. Large and small balls represent Ta and N atoms, respectively. Red small balls represent oxygen atoms, large green balls represent Ta atoms, which moved into the cell from its nearest cell.
the mechanical properties of a material. However, the optimized structure of Ta8N11 is monoclinic (space group: Pm). To maintain orthorhombic lattice, a supercell with double unit cells along c direction was constructed, in which two vacancies were induced among eight available N3 sites. All the cases that vacancies randomly occupy two of the eight available N3 sites were taken into account. It is convenient to label the four N3 sites in one of the two unit cells as A, B, C, and D respectively, and, correspondingly, in the other unit cell, as A0 , B0 , C0 , and D0 , respectively (Figure 4). Thus, we use d-AB to represent the structure in which vacancies occupy respectively the N3 sites labeled A and B, and use d-AB0 to denote the structure in which vacancies occupy respectively the N3 sites labeled A and B0 , and so on. The total number of the considered defective Ta2N3 is 28. The AA0 , BB0 , CC0 , or DD0 structure (referred to as AA0 structure) are in fact a double Ta8N11 in which a single vacancy occupied one of the N3 sites. After a series of structural optimizations on the considered defective Ta2N3, to our surprise, we found when vacancies occupy AC, AC0 , A0 C, A0 C0 , BD, BD0 , B0 D, or B0 D0 sites, the structure can maintain orthorhombic lattice. Our calculations show that the d-AC, d-A0 C0 , d-BD, and d-B0 D0 structures have the same lattice constants, total energy, volume, and crystal symmetry. The other four orthorhombic structures also yield the same results. Therefore, we put the eight structures into two classes denoted as d-AC and d-AC0 , respectively. The calculated lattice constants of d-AC and d-AC0 types are shown in Table I. All the atoms in both d-AC and d-AC0 types deviate from their original positions due to breaking the force equilibrium between atoms by introducing N vacancies. They are no longer strictly confined in a series of planes perpendicularing to the z direction. It is interesting to note that the two Ta atoms (large green balls in Figure 4) on the Ta2 sites in the d-AC, d-AC0 , d-A0 C, d-A0 C0 structures move against the x direction into their neighboring cell and another two Ta atoms (large gray balls in Figure 4) on the same sites in the other four orthorhombic structures move along the x direction into their neighboring ones. The AC structure possesses Pmc21 symmetry (No. 26). In this type of structure, all Ta atoms around the vacancy slightly move outward except one Ta atom. The lattice a increases by 0.38%, whereas b and c decrease by about 0.41% and 0.35% respectively from the nondefective double Ta2N3 unit cell. The calculated equilibrium volume of the AC type structure is 401.19 Å3, slightly smaller than that of the nondefective double Ta2N3 unit cell (402.76 Å3). In AC0 structures (space group: Pmn21, No. 31), metal atoms surrounding the vacancy relax outward, similar to the case in TiCx, NbCx, and TiCx.38 The calculated equilibrium
Figure 5. Calculated phonon dispersion curves of d-AC and o-Ac structures.
volume of this type is 403.12 Å3, larger than that of the nondefective double Ta2N3 unit cell, indicating that the presence of vacancies expands the orthorhombic lattice. However, the calculated total energy of AC0 type is about 0.25 eV lower than that of AC type. Our calculations also show that when vacancies occupy the AB, AB0 , A0 B, A0 B0 , CD, CD0 , C0 D, or C0 D0 sites, the system energy is the lowest, but when they occupy the AD, AD0 , A0 D, A0 D0 , BC, BC0 , B0 C, or B0 C0 sites, the system energy is the highest instead. All the structures in lowest energy have the same crystal symmetry and volume, and were referred to as d-AB type. The d-AB type belongs to triclinic system (space group: No. 2). It is found that all the highest energy structures also have the same crystal symmetry and volume, and were referred to as d-AD type. The d-AD type belongs to the monoclinic system with the space group of P21 (No. 4). In this work, however, we do not make further study on these two types of structures. In order to investigate the stability of d-AC and d-AC0 types, we have calculated the elastic constants of the two types using the d-AC and d-AC0 structure respectively as a representative and the results are listed in Table III. From this table, the calculated elastic constants evidently meet the structural stability requirements. We further calculated the phonon dispersion curves of the d-AC structure, as shown in Figure 5. No imaginary frequency are observed throughout the whole Brillouin zone, indicating that it is stable.39 The larger calculated polycrystalline bulk modulus of the d-AC type is attributed to its smaller equilibrium volume compared with that of the d-AC0 type. To investigate the origin of vacancy-induced structural stability, we calculated the electron localization function (ELF) for the d-AC structure as well as for the nondefective Ta2N3. Their projection on (001) plane are 3132
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Figure 6. Calculated ELF for nondefective Ta2N3 (left) and d-AC structure (right). The large and small balls represent Ta and N atoms, respectively.
plotted, as shown in Figure 6. ELF is based on the Hartree-Fock pair probability of parallel spin electrons and can be calculated in VASP. It is widely used to describe and visualize chemical bonding in molecules and solids.40 The value of ELF is scaled between 0 and 1. ELF maxima in the region of the valence electrons indicate either lone pairs or covalent bonds. It is well-known that electrons are transferred from metal to nonmetal atoms in the formation of transition-metal nitrides. When the nonmetal atoms are removed, the electrons would return to the metal atoms. However, during the formation of N-vacancy, not all the electrons that have been transferred from the tantalum atoms to the nitrogen atoms before the introduction of vacancy completely return to the metal atoms because there is a localization of electrons on the vacancy site, as can be seen from Figure 6. The localized vacancy state makes the vacancy negatively charged and forms a weak bonding with surrounding atoms. Previous studies have pointed out that the weak bonding has a minor effect on the shear stiffness.19 It is significant to note that there is an enhanced localization of electrons between metal and nonmetal atoms compared to that in the nondefective Ta2N3, reflecting a stronger Ta-N covalent bond forming between metal and nonmetal atoms. Therefore, we infer that the presence of vacancy changes the charge distribution in the unit cell and thus breaks the force equilibrium between the atoms which leads to the atomic rearrangement. The atomic movement in turn redistributes the charge in the unit cell and consequently results in an enhanced bonding between Ta and N atoms. The enhanced Ta-N covalent interaction are helpful to resist shear strain and responsible for its large positive c66. From this point of view, vacancy can strengthen the mechanical property of Ta2N3 through acting as pinning centers which inhibit dislocation motion and enhancing covalent bonding between Ta and N atoms. This idea will be pursued through the following calculations. Zerr et al. have pointed out that experimentally synthesized Ta2N3 is slightly contaminated by oxygen.16 It is worthwhile to investigate the role of the oxygen substitution for nitrogen in stabilizing the orthorhombic Ta2N3 lattice. The calculations for the case of the substitution of nitrogen atom by an oxygen atom in the unit cell was carried out to locate the preferable site that oxygen might take up. Our result shows that when oxygen occupies one of the N3 sites, the total energy keeps the lowest value, consistent with the previous calculations.17 However, this structure belongs to the monoclinic system with space group of Pm, similar to Ta8N11. To search potential orthorhombic structures, we constructed a supercell with two oxygens randomly occupying two of the eight N3 sites, similar to the case of
Figure 7. Similarities of structure type, total energy trend, and crystal symmetry between nitrogen vacancy and oxygen substitution Ta2N3. The labels near the circle in the figure represent the different space group.
N vacancy. Similarly, o-AB, o-AC, and so on, are used to represent structures in which oxygens take up the corresponding N3 sites. For comparison, we also show the similarities of total energy, crystal symmetry, and structure type between nitrogen vacancy and oxygen substitution Ta2N3 in Figure 7. Surprisingly, oxygen substitution for nitrogen plays a similar role as nitrogen vacancy in determining the crystal structure. First, the o-AB and o-AD types have the lowest and highest total energy respectively, similar to the case of N vacancy. Moreover, the o-AB type has the same crystal symmetry to the d-AB. Second, the o-AC (Figure 4) and o-AC0 types are also two kinds of orthorhombic structures having the same crystal symmetry to the d-AC and dAC0 types, respectively. Furthermore, we also carefully examined the rearrangement of atoms in all considered structures and found that the movement of atoms due to oxygen substitution is similar to the case of N vacancy. However, unlike the N vacancy, oxygen substitution lead to a slightly increase in volume for all considered structures compared to those nondefective Ta2N3 cases. The volumetric difference between the o-AC and o-AC0 structures (about 0.6 Å3) is also smaller than that between the d-AC and d-AC0 ones (about 2 Å3). We also note that the highest 3133
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Figure 8. Calculated ELF for o-AC structure. The dark large balls represent Ta atoms, whereas the blue and the red small balls represent N and O atoms, respectively.
energy structure o-AD type has a lower crystal symmetry than the d-AD type. The calculated elastic constants for single crystalline orthorhombic o-AC and o-AC0 structures are listed in Table III. Apparently, they are stable by satisfying the stability criterion for orthorhombic structure. The elastic constants of Ta16N22O2-I and Ta16N22O2-II reported by Jiang et al.17 are also listed in Table III for comparison. Apparently, they agree well with each other. Our calculated phonon dispersion curves (see Figure 5) further confirm their stability. In order to study the origin of their stability, we calculated the ELF of the o-AC structure and plotted its projection along (001) plane in Figure 8. As in the case of N vacancy, oxygen substitution induces enhanced localization of electrons and subsequently the enhanced covalent bond between Ta and N atoms. This stronger covalent bond than those in the nondefective Ta2N3 is responsible for their structure stability. From Figure 6 and Figure 8, the electron distributions on the (001) plane in both d-AC and o-AC structures show some similarities, which should be attributed to their similar atom arrangement. Nitrogen is well-known to have a larger electronegativity than oxygen. Oxygen substitution would make extra electrons be transferred from metal atoms to nonmetal atoms and therefore break the original equilibrium state leading to a new atomic arrangement and charge redistribution over a cell. The enhancement of Ta-N covalent bonding is caused by the charge redistribution. It is also noted that oxygen substitution and nitrogen vacancy play a similar role in the structure stability by causing charge redistribution. On the other hand, both d-type and o-type atoms move in such a similar way that the o-type structure can be regarded as the insertion of oxygen atoms into the vacancies in the d- type structures. Even though the insertion of oxygen atoms slightly expands the o-type lattice compared with that of d-type, it increases the density of the o-type lattice with a larger incompressibility than that of d-type, as can be seen from the calculated polycrystalline bulk moduli tabulated in Table III. As discussed above, either oxygen substitution for nitrogen or nitrogen vacancy can stabilize the orthorhombic lattice of Ta2N3 in a similar way in that they can change the charge distribution in the unit cell. However, their formation processes are different. The introduction of N vacancy in the Ta2N3 would draw some electrons back to metal atoms, while oxygen substitution would deprive more electrons from the metal atoms. Consequently, we infer that the manipulation of either vacancy or oxygen concentration could be used in stabilizing the orthorhombic lattice. For
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example, we have tried the calculation on a single unit cell with two N3 sites being substituted by vacancies or oxygens to demonstrate the effect of higher vacancy or oxygen concentrations. Here, we use D- and O- to denote the corresponding structures. There are totally six D-type or O-type structures. D-AB and O-AB respectively represent vacancy and oxygen occupying AB sites (Figure 1), and so on. After a full a relaxation, the D-AC, D-AD, D-BC, D-BD, O-AC, O-AD, O-BC, and O-BD can keep orthorhombic lattice. However, the calculations show that D-AD, D-BC, O-AC, and O-AD are mechanically unstable. This is in accordance with our above analysis. Therefore, the study on D- and O-type structures were omitted. It is noted that the orthorhombic d-AC, d-AC0 , o-AC, and oAC0 structures are not the phases with the lowest energy. However, the computed energy differences between them and those lowest energy phases are less than 0.5 eV/(unit cell). We also calculated the enthalpies of considered N-vacancy structures throughout the pressure range of 0-25 GPa and find that there is no phase transition between these N-vacancy structures. The sequence of their enthalpies does not change under the pressure range 0-25 GPa.
4. CONCLUSIONS In conclusion, using first-principles calculations, we investigated the effect of N-vacancy and oxygen substitution on the structure and stability of orthorhombic Ta2N3. Our calculations suggest that orthorhombic Ta2N3 is unstable below 20 GPa. A small amount of N-vacancy or oxygen atoms (at about 5% concentration) can stabilize the orthorhombic lattice. N-vacancy and oxygen substitution play a similar role in stabilizing the system by charge redistribution in the unit cell. The structure with oxygen substitution are more incompressible than that with N-vacancy due to larger density. Higher concentration of N-vacancy or oxygen substitution is unfavorable to orthorhombic structure stability. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This research was sponsored by the The Hong Kong Polytechnic University through University Research Grant (No. 1-ZV44), the National Natural Science Fundation of China (No. 21071045), and the Fundation of Henan University (No. SBGJ090508). ’ REFERENCES (1) Zerr, A.; Miehe, G.; Serghiou, G.; Schwarz, M.; Kroke, E.; Riedel, R.; Fuesz, H.; Kroll, P.; Boehler, R. Nature (London) 1999, 400, 340. (2) Jiang, J. Z.; Kragh, F.; Frost, D. J.; Stahl, K.; Lindelov, H. J. Phys.: Condens. Matter 2001, 13, L515. (3) Zerr, A.; Kempf, M.; Schwarz, M.; Kroke, E.; G€oken, M.; Riedel, R. J. Am. Ceram. Soc. 2002, 85, 86. (4) Dzivenko, D. A.; Zerr, A.; Bulatov, V. K.; Miehe, G.; Li, J.; Thybusch, B.; Br€otz, J.; Fueβ, H.; Brey, G.; Riedel, R. Adv. Mater. 2007, 19, 1869. (5) Gao, F.; Xu, R.; Liu, K. Phys. Rev. B 2005, 71, 052103. (6) Chhowalla, M.; Unalan, H. E. Nat. Mater. 2005, 4, 317. (7) Gregoryanz, E.; Sanoup, C.; Somayazulu, M.; Badro, J.; Fiquet, G.; Mao, H.-K.; Hemley, R. J. Nat. Mater. 2004, 3, 294. 3134
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