I. INTRODUCTION
In the pseudo-binary system AlN-Al2O3, there are six-types of aluminum oxynitride (AlON) compounds established so far (Tabary and Servant, Reference Tabary and Servant1998, Reference Tabary and Servant1999a, Reference Tabary and Servant1999b); there are three types of stoichiometric polytypes 27R (Al9O3N7), 21R (Al7O3N5), and 12H (Al6O3N4) in the AlN-rich region, and three types of spinel phases γ (Lejus, Reference Lejus1964), φ′ (Michel, Reference Michel1972), and δ (Lejus, Reference Lejus1964) in the Al2O3-rich region. In the notation of Ramsdell (Parthé, Reference Parthé1964), the polytypes with the chemical formula AlnO3Nn−2 were denoted as 2nH (n even) or 3nR (n odd). Sakai (Reference Sakai1978) has reported the 16H polytype (Al8O3N6) in addition to 27R, 21R, and 12H. Bartram and Slack (Reference Bartram and Slack1979) have found 20H polytype (Al10O3N8) together with 27R. The phase stability of these two polytypes 16H and 20H therefore remains equivocal in the pseudo-binary system. Although the polytype compounds of 27R, 21R, and 12H are established in the latest AlN–Al2O3 phase diagram (Tabary and Servant, Reference Tabary and Servant1998), their crystal structures are not yet completely characterized.
Recent advances in the field of crystal-structure analysis from X-ray powder diffraction (XRPD) data have enabled us to investigate unknown structures as well as complex structures, including positional disordering of atoms. To begin with, initial structural models are required, which may be determined by, for example, the powder charge-flipping method (Oszlányi and Süto, Reference Oszlányi and Süto2004). The structural parameters are subsequently refined using the Rietveld method (Rietveld, Reference Rietveld1967). A combined use of the Rietveld method, the maximum-entropy method (MEM) (Takata et al., Reference Takata, Nishibori and Sakata2001), and the MEM-based pattern fitting (MPF) method (Izumi, Reference Izumi2004) has enabled us to disclose new structural details. MEM is capable of estimating structural factors of unobserved reflections and improving those of overlapped reflections, which give MEM advantages over the classical Fourier method. However, the Rietveld method and MEM have a drawback in determining the electron-density distributions (EDD) because the observed structure factors, F o(Rietveld), are biased toward the structural model assuming intensity partitioning. On the other hand, the MPF method can minimize structural bias. Thus, the MEM and MPF analyses are alternately repeated (REMEDY cycle) until the reliability indices reach minima (Izumi et al., Reference Izumi, Kumazawa, Ikeda, Hu, Yamamoto and Oikawa2001). Crystal structures can be seen clearly from EDD determined by MPF.
In the present study, we have for the first time determined the crystal structure of 21R-AlON from XRPD data. The initial structural model has been derived using the powder charge-flipping method and further modified into the split-atom model. The validity of the structural model has been confirmed by the three-dimensional EDD determined by the MPF method.
II. EXPERIMENTAL
The reagent-grade chemicals of AlN (Tokuyama Co., Tokyo, Japan) and Al2O3 (Taimei Chemicals Co. Ltd, Nagano, Japan) were mixed in molar ratios of [AlN:Al2O3] = [5:1], corresponding to [Al:O:N] = [7:3:5]. The well-mixed chemicals were heated under a nitrogen pressure of 1.0 MPa at 2273 K for 2 h, followed by cooling to ambient temperature by cutting furnace power. The reaction product was a slightly sintered polycrystalline material, mainly consisting of Al7O3N5 together with small amounts of unreacted Al2O3 and AlN.
The sintered material was finely ground to obtain powder specimen and introduced into a glass capillary tube of internal diameter ca. 0.4 mm. The XRPD intensities were collected on a diffractometer (SmartLab, Rigaku Co., Tokyo, Japan), equipped with an incident-beam Ge(111) Johansson monochromator to obtain CuKα 1 radiation and a high-speed detector (Rigaku D/teX), was used in the Debye–Scherrer geometry. The X-ray generator was operated at 45 kV and 200 mA. Other experimental conditions were: continuous scan, experimental 2θ range from 2.50 to 158.00° with a step size 0.01° and a scan speed 0.2° min−1, 15 551 total data points, and 13.0 h total experimental time. No preferred orientation could be seen in the diffraction pattern that was collected with the specimen rotating. We corrected the X-ray absorption using the μr value (μ, linear absorption coefficient; r, sample radius) of the sample and the capillary tube, which was determined by the transmittance of a direct incident beam. The structural data were standardized according to the rules formulated by Parthé and Gelato (Parthé and Gelato, Reference Parthé and Gelato1984) using the computer program STRUCTURE TIDY (Gelato and Parthé, Reference Gelato and Parthé1987). The crystal-structure models, equidensity isosurfaces of EDD, and two-dimensional EDD map were visualized with the computer program VESTA (Momma and Izumi, Reference Momma and Izumi2008).
The powder specimen was also examined using transmission electron microscope (TEM, JEM 2100F, JEOL Ltd, Tokyo, Japan) operated at 200 kV. The powder particles were deposited with ethyl alcohol on a copper grid. Selected area electron diffraction (SAED) patterns and corresponding lattice images were obtained.
III. RESULTS AND DISCUSSION
A. Crystal structure determination and refinement
The XRPD pattern in Figure 1 showed the presence of weak diffraction intensities peculiar to Al2O3 and AlN. All of the other diffraction peaks were successfully indexed with a rhombohedral unit cell with hexagonal axes of a ≈ 0.305 nm and c ≈ 5.722 nm. The SAED pattern of Al7O3N5 was successfully indexed with the hexagonal unit cell (Figure 2). The corresponding lattice image strongly suggests that the crystal is characterized by a layered structure with the periodicity of ca. 5.7 nm along the c-axis. The unit-cell parameters and integrated intensities were refined by the Pawley method (Pawley, Reference Pawley1981) using the computer program PDXL (Rigaku Co., Tokyo, Japan). The observed diffraction peaks were examined to confirm the presence or absence of reflections. Systematic absences in the h − k + l ≠ 3n class of reflections were found, which implies that possible space groups are R3, R 3, R32, R3m, and R 3m.
Comparison of the observed diffraction patterns of Al7O3N5, Al2O3, and AlN (symbol: +) with the corresponding calculated pattern (upper solid line). The difference curve is shown in the lower part of the diagram. Vertical bars indicate the positions of possible Bragg reflections.
Selected-area electron diffraction pattern and corresponding lattice image. Incident beam is almost parallel to the hexagonal a-axis.
All the possible space groups were tested by the powder charge-flipping method (Oszlányi and Süto, Reference Oszlányi and Süto2004) using the computer program Superflip (Palatinus and Chapuis, Reference Palatinus and Chapuis2007) for crystal structure determination. Since the atomic scattering factors for O and N are nearly the same, a unit-cell content of [21Al 24N] was used as input data for search of an initial structure model. A promising structural model was successfully obtained for the space group R 3m. There are ten independent sites in the unit cell; six Al sites at Wyckoff positions 3a (Al1) and 6c (Al2a, Al2b, Al3a, Al3b, and Al4) and four O/N sites at 6c. Owing to the unusually short distances of Al2a–Al2b (ca. 0.089 nm) and Al3a–Al3b (ca. 0.092 nm), these 6c sites (point symmetry 3m) can be regarded as the split sites of the same symmetry sites of 6c.
The structural parameters of all atoms were refined by the Rietveld method using the computer program RIETAN-FP (Izumi and Momma, Reference Izumi and Momma2007). The structural models of Al2O3 and AlN were included in the refinement as the coexisting phases. A Legendre polynomial was fitted to background intensities with 12 adjustable parameters. The split pseudo-Voigt function (Toraya, Reference Toraya1990) was used to fit the peak profile. The O and N atoms were assumed to be randomly distributed over the same sites in the crystal structure, although there might be site preference of these atoms; the occupancies (g) of O and N atoms in each O/N site were fixed at g(O) = 0.375 and g(N) = 0.625. The isotropic displacement (B) parameters for O/N sites were constrained to be equal. The distribution of Al atoms between Al2a and Al2b sites, and that between Al3a and Al3b sites were determined by imposing the linear constraints of g(Al2a) + g(Al2b) = 1 and g(Al3a) + g(Al3b) = 1. The parameters B(Al2a) and B(Al2b) were constrained to be equal, and so were the parameters B(Al3a) and B(Al3b). Since the g values and corresponding B parameters were strongly correlated, they were refined alternately in successive least-squares cycles. The subsequent Rietveld refinement resulted in satisfactory B parameters for all the sites with R indices (Young, Reference Young and Young1993) of R wp = 4.92% (S = 1.36), R p = 3.67%, R B = 2.70%, and R F = 2.54%, indicating that the disordered arrangements of both Al2 and Al3 sites can be represented adequately with the split-atom model in Figure 3. The separation distances of these split sites are 0.0887(9) nm for Al2a–Al2b and 0.0917(5) nm for Al3a–Al3b. Crystal data are given in Table I, and the final atomic positional and B parameters are given in Table II. It should be noted that the g values of Al2a, Al2b, Al3a, and Al3b are, respectively, nearly equal to 5/6, 1/6, 1/3, and 2/3. Selected interatomic distances, together with their standard deviations, are listed in Table III. Quantitative X-ray analysis with correction for microabsorption according to Brindley's procedure (Brindley, Reference Brindley1949) was implemented in the program RIETAN-FP. The crystalline phase composition of the sample was found to be 92.9 mol% Al7O3N5, 1.0 mol% α-Al2O3, and 6.1 mol% AlN, on the assumption that the effective particle radii of these phases were 5.00 µm.
A crystal structure of Al7O3N5. All the atoms are expressed as solid spheres. Since the occupancies of Al2a, Al2b, Al3a, and Al3b sites are less than unity, the Al atoms occupying them are displayed as blue circle graphs for occupancies. Red and yellow bicolor balls are for oxygen (red) and nitrogen (yellow) sites. Atom numbering corresponds to that given in Table II.
Crystal data for Al7O3N5.
Structural parameters and isotropic atomic displacement parameters (100 × B/nm2) for Al7O3N5.
Selected bond lengths (nm) for Al7O3N5.
The MPF method was subsequently used to confirm the validity of the split-atom model. An EDD with 32 × 32 × 576 pixels in the unit cell, whose spatial resolution is ca. 0.010 nm was obtained from the MPF method using the computer programs RIETAN-FP and Dysnomia (Izumi and Momma, Reference Izumi and Momma2011). After one REMEDY cycle, R B and R F further decreased to 1.73% and 1.63%, respectively (R wp = 4.87%, S = 1.34, and R p = 3.64%). Subtle EDD changes as revealed by MPF significantly improve the R B and R F indices. The decreases in R indices demonstrate that the crystal structure can be seen more clearly from EDD instead of from the conventional structural parameters reported in Table II. Observed, calculated, and difference XRPD patterns for the final MPF are plotted in Figure 1. The EDD determined by MPF are in reasonably good agreement with the atom arrangements (Figure 4). For example, the three-dimensional EDD at the Al2 and Al3 sites were elongated along the c-axis, whose equidensity isosurfaces are in harmony with the atom arrangements. The 2D EDD map at the height of Al2 and Al3 sites shows that the positions of split Al sites are successfully disclosed by the EDD (Figure 5). We found the peak positions of EDD from the 3D pixel data and compared them with the coordinates of all atoms that were determined by the Rietveld method. The positional deviations of all atoms in the unit cell were found to be necessarily less than 0.008 nm, which is within the resolution limit of the 3D EDD. We therefore concluded that, as long as the crystal structure was expressed by a ball-and-stick model, the present split-atom model would be satisfactory.
Three-dimensional electron-density distributions of Al7O3N5 determined by MPF with the structural model. Isosurfaces expressed in smooth shading style for an equidensity level of 0.001 nm−3.
A bird's eye view of electron densities up to 50% (0.057 nm−3) of the maximum on the plane parallel to (110) (lower part) with the corresponding atomic arrangements (upper part). Atom numbering corresponds to that given in Table II.
B. Structure description
The coordination elements of the structure are five types of [Al(O,N)4] tetrahedra and one [Al(O,N)6] octahedron. The Al–N distance of [AlN4] tetrahedron is 0.187 nm for AlN (Jack, Reference Jack1978). With [AlO4] tetrahedron, the ionic radii of Al3+ in the fourfold coordination [r(Al3+(4)) = 0.039 nm and r(O2−(4)) = 0.138 nm] (Shannon, Reference Shannon1976) predicts the interatomic distance of 0.177 nm. Thus, the average interatomic distances of [Al(O,N)4] tetrahedra in Al7O3N5, ranging from 0.182 to 0.189 nm (Table III), indicate that the O/N sites would be actually occupied by both O and N atoms. The ionic radii of Al3+ in the sixfold coordination [r(Al3+(6)) = 0.0535 nm and r(O2−(4)) = 0.138 nm] (Shannon, Reference Shannon1976) predicts the interatomic distance of 0.1915 nm. Since the Al–(O,N) distance of the [Al(O,N)]6 octahedron (= 0.2029 nm in Table III) is longer than the Al–O distance in [AlO6] octahedron, both O and N atoms would actually occupy the octahedral apices. There is a possibility of site preference of O and N in the O/N sites. However, the information available at present on atom distances is insufficient for significant results.
In our previous studies on the layered oxycarbides and oxycarbonitrides, these compounds have been found to be made up of several domains, which are related by pseudo-symmetrical inversion (Iwata et al., Reference Iwata, Kaga, Nakano and Fukuda2009; Inuzuka et al., Reference Inuzuka, Kaga, Urushihara, Nakano, Asaka and Fukuda2010; Kaga et al., Reference Kaga, Iwata, Nakano and Fukuda2010a, Reference Kaga, Urushihara, Iwata, Sugiura, Nakano and Fukuda2010b; Urushihara et al., Reference Urushihara, Kaga, Asaka, Nakano and Fukuda2011). One of the most plausible explanations to interpret the disordered crystal structure of Al7O3N5 is to, in a similar manner, consider the structure to be a statistical average of several structural configurations. We have successfully extracted five types of ordered atom arrangements, which are termed I, II, III, VI, and V (Figure 6), from the parent disordered structural model (Figure 3). All of the ordered models are free from the neighboring cations of Al2b and Al3b, because the interatomic distance of Al2b–Al3b (= 0.2395 nm) is unusually short as compared with those of Al2a–Al3b (= 0.3064 nm), Al2a–Al3a (= 0.3851 nm), and Al2b–Al3a (= 0.3091 nm). The atom arrangement in the unit cell of model I is centrosymmetric with the space group R 3m; the number of each Al atom in the unit cell (N) is N(Al1) = 3, N(Al2a) = 6, N(Al3b) = 6, and N(Al4) = 6 (Table IV). This model is characterized by the absence of Al2b and Al3a sites. On the other hand, the atom arrangements of the remaining four models (II, III, VI, and V) are non-centrosymmetric with the space group R3m. When the center of symmetry is removed from the space group R 3m, the resulting space group is R3m. The two structural configurations of II and III and those of VI and V (Figure 6) are therefore related by a pseudo-symmetry inversion. Both the atomic configurational models of II and III are free from the Al2b site. With the models IV and V, the N(Al2a) –, N(Al2b) –, N(Al3a) –, and N(Al3b) – values are all equal to three. The number of each Al site in the unit cell of the ordered models is summarized in Table IV.
Five types of ordered atom arrangements viewed along [110]. Atomic configurational model I with the space group R 3m. The four models II, III, VI, and V with the space group R3m. The two atomic configurations of II and III, and that of VI and V are related by the pseudo-symmetrical inversion.
Details of the ordered atom-arrangement models.
The five types of atom arrangements as mentioned above are made up of three types of basic building elements: (i) the sheet of [Al1(O,N)6] octahedra (the octahedral sheet), (ii) the sheets of [M(O,N)4] tetrahedra (the tetrahedral sheet), where M = Al2a, Al2b, Al3a, Al3b, and Al4, and (iii) the vacant cation sheet, in which the available tetrahedral positions for Al atoms are necessarily vacant. The octahedral sheet, denoted by O Al1, is made up of an array of edge sharing octahedra with (O,N)1 atoms at the corners. In the tetrahedral sheet each [M(O,N)4] tetrahedron shares three corners, forming a continuous sheet. The unbonded tetrahedral apices of the tetrahedral sheets all point in the same direction; the tetrahedral sheets pointing up along [001] are denoted by U M, and those pointing down are denoted by D M. The vacant cation sheet, which is practically composed of two oxygen layers, is denoted by V. For example, with model I, the sheet stacking sequence along the c-axis between the two O Al1 sheets is 〈O Al1D Al4D Al2aD Al3bVU Al3bU Al2aU Al4O Al1〉 (Figure 6). The stacking sequences of the four other models are given in Table IV.
We speculate that the Al7O3N5 compound with the disordered crystal structure is made up of five types of domains with the ordered models (Figure 6 and Table IV). Since the g values of the disordered structural model are characterized by g(Al2a) = 5/6, g(Al2b) = 1/6, g(Al3a) = 1/3, and g(Al3b) = 2/3, we can estimate the abundance (A) of each domain within the Al7O3N5 compound. The numbers of cation M in the unit cell of each domain dm (m = I, II, III, VI, and V) are summarized in Table IV. Thus, the total number of cations M in the unit cell of the disordered structural model is given by Σ{A(dm) × N(M)m}, where N(M)m is the number of cations M in the unit cell of the ordered model m. The most simple and plausible A(dm)–values (ΣA(dm) = 1) which satisfy both equations of [Σ{A(dm) × N(Al2a)m}:Σ{A(dm) × N(Al2b)m}] = [5/6:1/6] and [Σ{A(dm) × N(Al3a)m}:Σ{A(dm) × N(Al3b)m}] = [1/3:2/3] are A(dI) = 1/3 and A(dII) = A(dIII) = A(dIV) = A(dV) = 1/6. This implies that the formation abundance of domain I is twice that of the other domains.
The five types of domains, with the size distribution probably ranging from the unit-cell size to the coherence range of X-rays, would be combined randomly so as to form the whole disordered structure. In the resultant structure, there are vacant sites between the two oxygen layers, which correspond to the vacant cation sheet of the ordered models. The present domain structure could be formed during crystal growth or high-low phase transformation during cooling. The unequal abundance among the five types of domains still remains enigmatic. A more detailed examination would be necessary to clarify the formation mechanism of the disordered structure.
IV. CONCLUSION
We clarified the disordered crystal structure of 21R-AlON (Al7O3N5), which was satisfactorily represented by the split-atom model with the space group R 3m. The validity of the structural model was confirmed by the EDD determined by MPF. The disordered crystal structure was interpreted to be a statistical average of the five types of ordered atom arrangements. One of them was centrosymmetric with the space group R 3m, and the four others were non-centrosymmetric with the space group R3m.
ACKNOWLEDGMENTS
We thank Drs T. Iwata and H. Toraya, Rigaku Co. Japan, for their technical assistance in XRPD. We also thank Mr T. Horie, National Institute for Materials Science, for sample preparation.
