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First principles study on relaxor-type ferroelectric behavior without chemical inhomogeneity in BaTaO2N and SrTaO2N Yoyo Hinuma, Hiroki Moriwake, Ya-Ru Zhang, Teruki Motohashi, Shinichi Kikkawa, and Isao Tanaka Chem. Mater., Just Accepted Manuscript • Publication Date (Web): 22 Oct 2012 Downloaded from http://pubs.acs.org on October 23, 2012
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Chemistry of Materials
First principles study on relaxor-type ferroelectric behavior without chemical inhomogeneity in BaTaO2N and SrTaO2N Yoyo Hinuma1*, Hiroki Moriwake2, Ya-Ru Zhang3, Teruki Motohashi3, Shinichi Kikkawa3, Isao 1,2 Tanaka . 1
Department of Materials Science and Engineering, Kyoto University, Kyoto 606-8501, Japan
2
Nanostructures Research Laboratory, Japan Fine Ceramics Center, Nagoya 456-8587, Japan
3
Faculty of Engineering, Hokkaido University, Sapporo 060-8628, Japan
. KEYWORDS oxynitrides, perovskite, first principles calculations, relaxors, ferroelectricity
ABSTRACT: The wide range of applications attracts interest to oxynitride perovskites. BaTaO2N and SrTaO2N have relaxor-type high dielectric permittivities, and are promising candidates in many applications especially because Pb is not included unlike in many relaxor ferroelectrics. There is an urgent need to understand the relation between the anion ordering and the permittivity to facilitate screening and designing materials with higher permittivity, and the chemistry that result in relaxor-type behavior without chemical inhomogeneity. We show using systematic first principles calculations that stable anion orderings in BaTaO2N and SrTaO2N have two kinds of similar, 3D –Ta–N– coiled chain motifs that can switch to each other, forming a mechanism to break long range order and increasing the diversity of anion orderings around the pentavalent Ta. Both materials have two sets of low-energy displacements forming opposite polarization directions that can be easily alternated at the picosecond scale. This explanation of the origin of relaxor-type behavior without chemical inhomogeneity currently found only in these two materials will fuel further searching of similar materials.
Introduction 1
Oxynitride perovskites have wide range of applications . BaTaO2N and SrTaO2N are Pb-free oxynitrides showing remarkable relaxor-type2-4 high dielectric permittivities of about 10,0005, 6 over a range of the order of a few hundred kelvins. BaTaO2N is typically refined in a cubic space group with one perovskite unit, or formula unit (FU)5, 7, 8, whereas the low temperature phase of SrTaO2N is refined in a tetragonal space group with 2 × 2 × 2 = 4 perovskite units5, 9-11. The relation between the perovskite unit and the tetragonal SrTaO2N cell is shown in Fig. 1a. On the basis of electron diffraction experiments, Withers et al.8 proposed formation of structurally frustrated one-dimensional polar nanoregions (1D PNRs)2 along the axis as the reason for the relaxor-type ferroelectric behavior in BaTaO2N. They also claimed that random local strain fields from chemical disorder suppresses transverse correlations of chain dipoles and the development of a long range ordered ferroelectric state8. However, there is clearly local anion ordering in BaTaO2N because preference for “cis-type” TaO4N2 octahedra with 90degree N-Ta-N bonds as opposed to “trans-type” octahe-
dra with 180-degree N-Ta-N bonds has been experimentally and theoretically proposed in BaTaO2N7, 12, 13. This means that the simplest 1-FU model by Günther et al.14, where all 4a sites (1/3 of anion sites: pink balls in Fig. 1a) are occupied by N and all 8h sites (remaining anion sites: orange balls in Fig. 1a) by O in Fig. 1a, is an inappropriate model because this is the only 1-FU model without partial occupancies and has 3D periodic boundaries, however the N-Ta-N bonds must be trans-type. Hence, –Ta–N– chains that bend at Ta should form in BaTaO2N, and the formation of such chains has been suggested for SrTaO2N11. Two anion sites with different O:N occupancy ratios were reported in SrTaO2N: neutron diffraction experiments on tetragonal SrTaO2N found that the O:N ratios at the two anion sites are approximately 1:1 in the axial sites and 3:1 in the equatorial sites respectively9-11. The high temperature, pseudo-cubic phase of SrTaO2N is reported to contain no N in 1/3 of the anion sites and to have 1:1 O:N occupancy in the remaining sites, which resulted in the recent suggestion of disorder of – Ta–N– chains in 2D as the mechanism for statistical anion distribution in this phase11. Yang et al. also pointed out that the anion order is coupled with tilt order of octahe-
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dra11, while ice-type disorder on square and cubic lattices was shown to result in “subextensive entropy with open order”, which was claimed to exist in some perovskite oxynitrides 15.
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all of the five two-FU unit cells were calculated as well as 40 four-FU unit cells. The four-FU unit cells were either
1× 1× 4 ,
2 × 2 × 2 , or 2 × 2 × 1 supercells of the
perovskite unit and had 1:1 O:N occupancy in axial sites and 3:1 occupancy in equatorial sites, which is the occupancies that were observed using neutron diffraction in tetragonal SrTaO2N9-11. There are 40 such anion ordering patterns, and all of them were calculated. Nine of the 46 calculated structures have cis-TaO4N2 octahedra, whereas the remaining 37 do not. The lowest energy unit cell with cis-TaO4N2 octahedra was stable by 19 meV/FU in BaTaO2N and 8 meV/FU in SrTaO2N relative to the lowest energy unit cell without cis-TaO4N2 octahedra. Three spatial configurations of cis-TaO4N2 octahedra sharing a common axial N are possible: namely the “0-deg”, “90deg”, and “180-deg” configurations (Figs 1(b,e), 1(c,f), 1(d,g) respectively). Among the nine unit cells with cis-TaO4N2 octahedra, the lowest energy structure with the “90-deg” configuration was stable compared to structures with either “0-deg” or “180-deg” by at least 14 meV/FU in BaTaO2N and 17 meV/FU in SrTaO2N. The 1-FU model by Günther et al.14 was unstable by more than 300 meV/FU compared to the 4-FU unit cell with lowest energy.
Here we show through systematic first principles calculations that the dual coiled chain motif, where the anion ordering is a coexistence of two types of 3D –Ta–N– coiled chain motifs similar to each other, is stable in both BaTaO2N and SrTaO2N. The chains should be able to switch to each other with relative ease because of the similarity; therefore, this is a mechanism to break long range order that increases the diversity of anion ordering around the pentavalent Ta. Both materials have two sets of lowenergy displacements with opposite polarization directions that can be easily alternated at the picosecond scale. The breaking of long-range order and the ability to undergo polarization reversal are necessary conditions of relaxor-type ferroelectricity. Computational procedure First-principles calculations were performed using the generalized gradient approximation (GGA) to density functional theory. Core electron states were represented by the projector augmented-wave method16 with the Perdew-Burke-Ernzerhof (PBE) exchange correlation17, and a plane-wave representation for the wave function with a cutoff of 420 eV was used as implemented in the VASP code 18-20. The first-order method of Methfessel and Paxton21 with an energy level broadening of 0.05 eV was used. Structural optimization was carried out using gamma-centered k-meshes of approximately one point per 0.007Å-3 to sample the reciprocal lattice. Spin polarization was allowed, and all lattice parameters and atomic coordinates were fully relaxed within the highest symmetry space group possible for each anion ordering.
Next, we performed additional calculations for larger unit cells with different 3D –Ta–N– chain configurations. We focused on anion orderings with cis-TaO4N2 octahedra with “90-deg” configuration at axial N. A total of 45 anion orderings commensurate with a 2 × 2 × 4 = 16 -FU supercell were calculated. These unit cells had anion orderings with cis-TaO4N2 octahedra having “90-deg” configuration at axial N. The stacking of cis-TaO4N2 octahedra along the axis was restricted to either a helical pattern in Fig. 2(a,c), which was proposed in Reference 10, or the pattern in Fig. 2(b,d), where one pair of O and N is flipped from Fig. 2(a,c), or both. All 45 anion orderings that satisfy the above conditions were calculated. This investigation allows us to model more complex chains within a larger repeat unit instead of stacking simple 4-FU cell, improving the description of longer-range order or disorder.
Molecular dynamics simulations in the NVT ensemble were conducted as implemented in the VASP code using a
2 × 2 × 4 supercell of the perovskite unit (80 atoms) with the anion ordering of BaTaO2N_A for BaTaO2N and the lowest energy structure for SrTaO2N. Gamma-centered kmeshes of approximately one point per 0.007Å-3 were used to sample the reciprocal lattice. A time step of 5.0 fs was used with a Nose-Hoover thermostat, and simulations were conducted for 500 steps (2.5 ps) with the first 100 steps (0.5 ps) discarded as equilibration steps. The temperature of the MD during the sampling steps was fluctuating within ±50K of the target temperature.
The two most stable BaTaO2N structures among those calculated are two non-centrosymmetric structures, i.e., BaTaO2N_A and BaTaO2N_B, whose lattice parameters and Wyckoff positions are given in Tables 1 and 2 in Supporting Information. Preference for TaO4N2 octahedra formation means that Ta–N bonds form chains (or rings) where straight Ta–N–Ta edges bend 90 degrees at Ta. Description of all N sites uniquely determines the anion ordering; therefore, showing the –Ta–N– chains is sufficient in describing the anion ordering. The –Ta–N– chains of BaTaO2N_A are shown in Fig. 3, and the chains in BaTaO2N_B in Fig. 4. Although the anion arrangements of these two structures are sensibly different, their formation energies are different only by 1 meV/FU, i.e. they are al-
Favored anion orderings in BaTaO2N and SrTaO2N We first investigated the stability of cis-TaO4N2 octahedra in BaTaO2N and SrTaO2N using first principles calculations. The formation energies of a total of 46 anion orderings were calculated here: the one-FU unit cell14 and
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most degenerate accidentally. The next stable structure is centrosymmetric and the formation energy is 9 meV/FU above the lowest energy structure, which is about an order of magnitude larger difference than that between the two lowest energy structures. Next we look at the energetics of SrTaO2N. The lattice parameters and Wyckoff positions of the most stable structure is given in Table 3 in Supporting Information, and the anion ordering in Fig. 5. Its formation energy was 5 meV/FU lower than that of the second most stable structure, and there were seven additional structures within 10 meV/FU from this lowest energy structure. All of these nine structures are noncentrosymmetric. In summary, non-centrosymmetric anion ordering was favored, and multiple structures were found within 10 meV/FU of the lowest energy structure in both BaTaO2N and SrTaO2N.
represent the two distinct 3D chain motifs, which will hereafter be called “coiled chains”, that exist in BaTaO2N_A. These coiled chains have a periodicity of eight Ta–N–Ta edges. The red coiled chains extend in the [100] direction, and the repeat unit of the motif can be ex-
→ − ↑ + → + ↓ − using the symbols →←↑↓ + − for Ta–N–Ta edges proceeding in the [100],
pressed
as
[-100], [010], [0-10], [001], and [00-1] directions respectively. The brown coiled chains have the motif
→ − ↓ + → + ↓ − and extend in the [1-10] direction. These two motifs differ by only one symbol (3rd symbol from the left), thus are very similar. Such dual coiled chain motifs cannot appear in small 4-FU unit cells but is only possible to capture in larger unit cells, which in this case is a 16-FU cell.
The –Ta-N- chains for the most stable anion ordering in SrTaO2N (Fig. 5) is 3D, which is different from the 2D chain model proposed by Yang et al.11. Their model is consistent with the experimentally observed anion occupation ratios for both the low temperature, tetragonal 4-FU phase 5, 9-11 and the high temperature, pseudocubic 1-FU phase of SrTaO2N11. One of the three anion sites in the pseudocubic 1-FU unit cell is occupied by O only and the other two sites has an O:N occupancy ratio of 1:1 11, hence these occupancy ratios oblige –Ta-N- chains to be 2D in the high temperature phase. The ordering pattern in Fig. 5 is thus inconsistent with the experimental data collected at high temperature. However,3D –Ta-N- chains can be consistent with the occupancy ratios for the low temperature phase. Any model with -Ta-N- chains that have one unique axis, including models with 3D chains as proposed in the present study, would be consistent with the low temperature, tetragonal phase of SrTaO2N.
Fig. 6a shows a schematic of how the long range order is broken in BaTaO2N. The small colored blocks each represent different orientations of coiled chains. Fig. 6b shows an example of coiled chains in two different blocks and how the chains connect at the boundary between adjacent blocks. The red and brown coiled chains extend in the [001] and [1-10] directions in the left blue block, but extend in the [001] and [110] directions in the right orange box respectively. The red chains switch into brown chains and vice versa at the boundary between these boxes. Switching of chains can act as a disorder source that breaks the long range ordering, and a statistical distribution between the switching points would result in a random field because each Ta at the center of the TaO4N2 octahedra has a different view of the anion ordering, or the boxes and the boundaries. The direction that the chains extend can change at the boundaries, resulting in further non-uniformity. There is a degree of freedom on where to switch the chains and in what direction, and results in an effectively “random” view of the anion ordering and, in consequence, a random local electric field around each Ta.
Origin of relaxor-type high dielectric permittivity in BaTaO2N and SrTaO2N The most intriguing property of BaTaO2N and SrTaO2N is the relaxor-type high dielectric permittivity. Existence of polar nanoregions are essential for relaxor behavior22, 23. The random field Ising ferromagnet model (RFIM) has been proposed as a model of PNRs in the relaxor Sr0.61Ba0.39Nb2O6 (SBN)24, 25, which involves quenched local charges (randomly distributed cation vacancies as well as Ce3+ on Sr2+ sites for Ce-doped SBN) that give rise to random electric fields at the ferroelectrically active offcentral Nb5+ ions26-28. The Ising ferromagnet part is satisfied by the ability to undergo polarization reversal.
Fig. 7a shows the displacement of atoms from their respective high symmetry positions in BaTaO2N_A. Large displacements along the c-axis are seen in half of Ta and all 4a site N. Here, polarization points to the c-axis only because there are two-fold rotation axes parallel to the caxis. The direction of polarization is mainly determined by displacements of Ta and 4a N, and can be reversed by changing the displacements of Ta and 4a N into a “metastable” displacement (Fig. 7b). Focusing on the bond lengths in the Ta–N(4a)–Ta triplets along the c-axis, the long Ta–N(4a) bonds in Fig. 7a become short bonds in Fig. 7b and vice versa. Such displacements of Ta along the c-axis are consistent with the electron diffraction results by Withers et al.8 The formation energies for displacements in Fig. 7a and Fig. 7b are almost the same within 0.1 meV/FU, therefore both states are equally stable and the
In BaTaO2N and SrTaO2N, each –Ta–N– chain in the 16FU unit cells has a periodic spatial configuration; hence the chains can be distinguished by the repeat unit, or motif. BaTaO2N_A (Fig. 3) has two chains with different motifs, and BaTaO2N_B (Fig. 4) consists of a chain motif and a ring motif. The Ta–N bonds of BaTaO2N_A are highlighted by thick lines, and the two colors (red and brown)
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preferred displacement, or polarization, is strongly influenced by an external electric field. Note that although BaTaO2N is typically refined in a cubic space group with neutron diffraction 5, 7, 8, electron diffraction showed diffuse streaks normal to one axis8, indicating that one axis must be distinguishable from the other two at the microscopic electron diffraction scale but not at the macroscopic neutron diffraction scale. The c-axis is distinguished from the other two axes in this computational work because layers of 4a sites and 8h sites alternate along the caxis.
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trimers instead of a trivial fluctuation around a single energy well. Displacements from high symmetry sites change collectively with polarization reversal, which is also found in SrTaO2N as will be discussed later. SrTaO2N is in a similar but different situation. The two coiled chain motifs in the calculated lowest energy structure of SrTaO2N (Fig. 5) have repeat units of
↓+→+↑+←+
(orange) and ↑ + → + ↑ + ← + (purple). The motifs differ by one symbol; therefore, existence of disorder from switching of motifs is expected as in BaTaO2N_A. An example of motif switching in SrTaO2N analogous to the example for BaTaO2N in Fig. 6 is shown in Fig. 10. One notable characteristic of the chain motifs in SrTaO2N is that both chains proceed in a unique direction, namely the [001] direction in Fig. 10. In other words, a unique axis must exist, at least locally, in this model. Fig. 7c shows the tilting of TaO4N2 octahedra along the caxis in the calculated lowest energy structure of SrTaO2N, in perfect agreement with the large anisotropic displacement at the anion sites as observed in neutron diffraction10. Polarization exists only along the a-axis because two-fold rotation axes exist parallel to the a-axis, which is in sharp contrast to the c-axis polarization in BaTaO2N. The metastable displacement (Fig. 7d), which has 1 meV/FU higher energy and has polarization in the opposite direction compared to the stable displacement in Fig. 7c, is obtained by “phase reversal”, or rotation of the octahedra around the c axis by changing the direction of displacement of equatorial anions along the a or b axis, which has been observed in neutron diffraction10.
Molecular dynamics (MD) simulations were conducted to investigate whether polarization reversal could indeed happen at room temperature, and if possible, at which time scale. Fig. 8 shows the change in polarization in a 2 ps MD simulation. The thick green, blue, and red lines indicate the polarization in the a, b, and c directions respectively at 300K. The c-direction polarization is negative at about 1 ps but positive at 0 ps and 2 ps, showing that polarization reversal is possible in the MD simulation timescale. The thin orange line in Fig. 8 shows the polarization in the c direction in an MD simulation at 77K. Reversal of polarization is unlikely at this temperature, at least at THz frequencies. The polarization in Fig. 8 was calculated by taking the weighted average displacement of internal coordinates from high symmetry sites, i.e. internal coordinates in
2× 2× 4
supercell of a perovskite unit with space group Pm-3m. The nominal charges are used as weights, namely +2 for Ba or Sr, +5 for Ta, -2 for O and -3 for N, and the sum of displacements multiplied by weights is divided by the number of perovskite units (16 in this work). This vector quantity is not necessarily proportional to the actual polarization. However, this qualitatively reflects the polarization, is easy to calculate, is not affected by any drift of atoms, and is independent of the supercell size and shape. We are aware that use of the nominal charge instead of the Born effective charge underestimates the polarization by about one-half in ABO3 perovskites29, 30. However, we are only interested in whether collective movement of atoms that is necessary for reversal of polarization can happen or not at room temperature rather than what the absolute value of the polarization is; therefore nominal charges are used in this work as weights to obtain the weighted average of the atom positions.
Fig. 11 shows the polarization in a SrTaO2N MD simulation similar to what was carried out in BaTaO2N at 300K. The thick green, blue, and red lines indicate the polarization in the a, b, and c directions respectively, which were calculated using the method that was used in BaTaO2N. The polarization in all directions can become positive and negative; however it is necessary to look at the tilting of Ta octahedra to observe whether the system is fluctuating between distinct states. Fig. 12 shows the tilting of octahedra at (a) 0.925 ps and (b) 1.385 ps. The octahedra are tilted more or less in-phase along the c-direction in Fig. 12a but is aligned out-of-phase in Fig. 12b, indicating that the tilting of octahedra can change at room temperature in SrTaO2N. Therefore, rotation of cis-TaO4N2 octahedra at the picosecond scale was observed in this MD simulation, implying that SrTaO2N can also respond to external electric fields alternating at THz frequencies. The rotation of the octahedra occurred in a plane, corroborating the existence of a unique axis in SrTaO2N.
Fig. 9 shows the displacements from high symmetry sites in the (a) 0.925 ps snapshot and (b) 1.370 ps snapshot for BaTaO2N. The timings of the snapshots are given as vertical lines in Fig. 8. The positions of the short Ta–N(4a) bonds (blue vertical bonds) are different, indicating that at 300K the changes in bond lengths in Ta–N(4a)–Ta trimers happen at the picosecond scale, or at THz frequencies, and that the polarization reversal arises from the switching between the two stable states of Ta–N(4a)–Ta
Conclusions In conclusion, we showed that BaTaO2N and SrTaO2N both have mechanisms to generate a random field and to
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accommodate reversal of polarization, which explains the relaxor-type behavior through the RFIM model. The random field is speculated to originate from having a variety of chain motifs that can switch to each other, breaking the long-range ordering of anions while retaining the local cis-TaO4N2 octahedra configuration. This is a new mechanism for disorder because chemical inhomogeneity is not necessary unlike in solid solution relaxor systems such as SBN, Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT), Pb(Ni1/3Nb2/3)O3-PbTiO3 (PNN-PT), or (Pb,La)(Zr,Tr)O3 (PLZT) 2. The Ising model part is realized by the existence of stable and metastable states, which have the same anion ordering and are essentially degenerate, but have different displacements with opposite polarization directions. MD simulations showed that reversal of polarization can happen at THz frequencies in both SrTaO2N and BaTaO2N, in agreement with the weak frequency dependence of dielectric permittivity in these materials5. We have therefore found a new mechanism for the onset of relaxor-type behaviors in systems without chemical inhomogeneity, and searching of new relaxor materials through finding systems where the new mechanisms can apply is expected to attract further attention.
Fig. 2. (a,b) Top view and (c,d) side view of two allowed stackings of cis-TaO4N2 octahedra along the c-axis in 16 FU calculations. Legend: green balls = Ta, purple balls = O, blue balls = N.
Fig. 3. –Ta–N– chains in BaTaO2N_A as observed from two directions. Red and brown lines correspond to two types of chains. Fig. 1. (a) Sites of atoms in SrTaO2N. Thin lines indicate the perovskite unit, thick lines indicate the conventional tetragonal cell of SrTaO2N. (b-d) Top view and (e-g) side view of (b,e) “0-deg”, (c,f) “90-deg”, and (d,g) “180-deg” configuration of two cis-TaO4N2 octahedra sharing an axial N. Legend: brown balls = Sr, green balls = Ta, pink balls = 4a anion sites, orange balls = 8h anion sites, purple balls = O, blue balls = N.
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Fig. 7. Two sets of displacements each in (a,b) BaTaO2N and (c,d) SrTaO2N with opposite polarization. Orange arrows indicate the direction of polarization. Legend: (a,b) brown balls = Ba, green balls = Ta, purple balls = O, blue balls = N. (c,d) TaO4N2 octahedra are shown as brown octahedra that are tilting out-of-phase along the c axis. Displacements from high symmetry sites are exaggerated three-fold for clarity.
Fig. 4. –Ta–N– chains in BaTaO2N_B as observed from two directions. Red and blue lines correspond to two types of chains.
Fig. 5. –Ta–N– chains in the lowest energy structure of SrTaO2N as observed from two directions. Orange and purple lines correspond to two types of chains.
Fig. 8. Changes in polarization during a MD simulation of BaTaO2N. The thick green, blue, and red lines indicate the polarization in the a, b, and c directions at 300K, the thin orange line shows the polarization in the c direction at 77K.
Fig. 6. (a) A schematic of long range order breaking in BaTaO2N. Each colored box represents a block of BaTaO2N where the chains do not switch, and the chains extend in the same direction in boxes with the same color. (b) One example of chain switching at the boundary of blocks (blue plane). Here, red and brown lines show –Ta–N– chains, and red lines become brown lines and vice versa at the boundary.
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Fig. 9. Snapshots of atom positions during a MD simulation of BaTaO2N at 300K, a) at 0.925 ps, b) at 1.370 ps. Legend: brown balls = Ba, green balls = Ta, purple balls = O, blue balls = N. Displacements from high symmetry sites are exaggerated three-fold for clarity.
Fig. 11. Changes in polarization during a MD simulation of SrTaO2N. The thick green, blue, and red lines indicate the polarization in the a, b, and c directions at 300K.
Fig. 12. Snapshots of tilting of octahedra as observed from the c direction during a MD simulation of SrTaO2N at 300K, a) at 0.925 ps, b) at 1.385 ps. TaO4N2 octahedra are shown as brown octahedra. Displacements from high symmetry sites are exaggerated three-fold for clarity.
ASSOCIATED CONTENT Supporting Information Available: Three tables showing the lattice parameters and Wyckoff positions of calculated structures of BaTaO2N and SrTaO2N. This material is available free of charge via the Internet at http://pubs.acs.org. Fig. 10. Example of coiled chain switching based on two chains found in the lowest energy structure of SrTaO2N. The same 3D structure is observed from two directions. Orange and purple lines correspond to two types of –Ta–N– coiled chains, and extend in the same direction in each colored box. The –Ta–N– coiled chain motifs switch and change directions at the blue planes at the boundaries of two boxes.
AUTHOR INFORMATION Corresponding Author *E-mail
[email protected] .
ACKNOWLEDGMENT
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This study is supported by a Grant-in-Aid for Scientific Research (A). This work was supported by JSPS KAKENHI Grant Number 23246111.
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