research papers
Structures of the cation-deficient perovskite Nd0.7Ti0.9Al0.1O3 from high-resolution neutron powder diffraction in combination with group-theoretical analysis
aAustralian Nuclear Science and Technology Organisation, Private Mail Bag 1, Menai, NSW 2234, Australia, bISIS Facility, Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, England, cDepartment of Mineralogy, The Natural History Museum, Cromwell Road, London SW7 5BD, England, and dDepartment of Earth Sciences, University of Cambridge, Downing Street, Cambridge CB2 3EQ, England
*Correspondence e-mail: zzx@ansto.gov.au
The crystal structures of Nd0.7Ti0.9Al0.1O3, taken to represent the ideal Nd2/3TiO3, have been elucidated from 4 to 1273 K using high-resolution neutron powder diffraction in combination with group-theoretical analysis. The room-temperature structure is monoclinic in C2/m, on a cell with a = 7.6764 (1), b = 7.6430 (1), c = 7.7114 (1) Å, β = 90.042 (2)°. Pertinent features are the layered ordering of the A-site Nd cations/vacancies along the z axis and out-of-phase tilting of the (Ti/Al)O6 octahedra around both the x and z axes. From about 750 to 1273 K, the octahedra are tilted around just one axis (x axis) perpendicular to the direction of the cation ordering, giving rise to an orthorhombic structure with space-group symmetry Cmmm.
Keywords: cation-deficient perovskites; octahedral tilting; neutron powder diffraction; group theory.
1. Introduction
The crystal structures and cation/vacancy ordering in perovskite systems with A-site vacancies, Ax□(1 − x)BO3, are of interest for potentially attractive properties of dielectric behaviour and magnetic response. Mitchell (2002) surveyed the published structural data for this class of materials and concluded that further studies are required as many of the reported structures are probably incorrect. Nd2/3TiO3 is such a compound with one third of the A sites vacant. The of Nd2/3TiO3 was first reported by Yoshii (2000) as orthorhombic in the Pmmm on a 1 × 1 × 2 cell (referred to the edge of the cubic aristotype). It was suggested by Howard & Zhang (2004a,b) that Nd2/3TiO3 would be isostructural with La2/3TiO3, which has an orthorhombic structure in Cmmm on a 2 × 2 × 2 cell. More recently, Sefat et al. (2005) refined the powder neutron data of Nd0.7TiO3 in both Cmmm (on a 2 × 2 × 2 cell) and Pban (on a 21/2 × 21/2 × 2 cell) and found the Cmmm model to be superior. It is generally accepted that Nd2/3TiO3 is unstable in its pure form. However, the structure can be stabilized at a slight oxygen deficiency (Yoshii, 2000) or by low-level doping with NdTiO3 (Sefat et al., 2005) or NdAlO3 (Lee et al., 2004). Lee et al. (2004) studied the microstructure of the (1 − x)Nd2/3TiO3–xNdAlO3 system using (TEM). They recorded reflections indicative of cell doubling in one direction for x = 0.1–0.7 and attributed this to different ionic populations on successive layers of the perovskite A-site. They also proposed for Nd0.7Ti0.9Al0.1O3 (x = 0.1) both out-of-phase and in-phase tilting of the oxygen octahedra along with A-site cation displacement, based on the observation of reflections indexing, when referred to the cell of the at ½(odd odd odd), ½(odd odd even) and ½(odd even even). However, no space-group symmetry was assigned to their structures.
In this paper, we report a new monoclinic structure for the composition Nd0.7Ti0.9Al0.1O3. The structure has been deduced through a combination of high-resolution neutron powder diffraction and group-theoretical analysis. The structure, in the C2/m on a 2 × 2 × 2 cell, is characterized by a layered ordering of the A-site cations/vacancies, and (Ti/Al)O6 octahedral tilting independently around two axes. Temperature studies of the transition to the orthorhombic structure Cmmm are also reported.
2. Symmetry considerations
Among the room-temperature structures considered for Nd2/3TiO3 (Yoshii, 2000; Howard & Zhang, 2004a,b), Nd0.7TiO3 (Sefat et al., 2005) and Nd0.7Ti0.9Al0.1O3 (Lee et al., 2004), there is a consensus on cell doubling in at least one direction, arising from a layered ordering of Nd such that one layer is rich in the cations, and the next is poorer in cations since it contains a greater number of vacancies. It is also agreed that the room-temperature structure is orthorhombic, however, the detailed driving mechanism for the orthorhombic distortion has been a matter for conjecture. Based on our previous experience, we believe that the room-temperature structure arises from a layered ordering of A-site cations/vacancies in combination with the tilting of corner-linked BX6 octahedral units relative to one another (Howard & Zhang, 2003, 2004a,b). Again a group-theoretical approach was used to enumerate the possible structures. The methodology has been described at greater length in two recent publications by Howard & Stokes (2004, 2005).
The layered ordering of cations (or vacancies) on the perovskite A-site was recognized as transforming according to the irreducible representation X3- (k = 0,0,½) of the and giving rise to a structure in the P4/mmm on a 1 × 1 × 2 cell. The octahedral tilting was represented through the irreducible representations (irreps) R4+ (k = ½,½,½) corresponding to modes with out-of-phase tilting of octahedra in successive layers and M3+ (k = ½,½,0) associated with in-phase octahedral tilting. The different possible structures were obtained using the computer program ISOTROPY,1 with results as summarized here in Fig. 1. For each structure, that figure shows the with the tilt system indicated, described using Glazer's notation (Glazer, 1972, 1975) – briefly, the symbol a#b#c# is used to indicate no tilt, in-phase octahedral tilting or out-of-phase octahedral tilting around the 〈001〉 axes of the parent perovskite by showing the superscript as 0, + or −, respectively. The figure also includes the approximate dimensions of the in terms of the cell edge of the The group–subgroup relationships are also shown in Fig. 1; a dashed line joining a group to its indicates that the corresponding is required by Landau theory to be first order.
It is interesting to re-examine the literature in light of this analysis. The proposed orthorhombic structures at room temperature in Pmmm on a 1 × 1 × 2 cell (Yoshii, 2000) and in Pban on a 21/2 × 21/2 × 2 cell (Sefat et al., 2005) do not appear as possibilities in Fig. 1. The other proposal is that Nd2/3TiO3 is isostructural with La2/3TiO3 (Howard & Zhang, 2004a,b; Sefat et al., 2005) in the Cmmm on a 2 × 2 × 2 cell, a structure that has been shown already (Howard & Zhang, 2004a,b) to be consistent with the symmetry analysis above. This orthorhombic structure (a−b0c0 using Glazer's notation) is characterized by A-site cation/vacancy ordering along the z axis and out-of-phase TiO6 octahedral tilting around an axis (x axis) perpendicular to the ordering direction. However, because of the slightly smaller ionic radius of Nd3+ (Shannon, 1976), hence the lower perovskite tolerance factor {t = (RA + RO)/ [21/2(RB + RO)], where RA, RB and RO are the ionic radii of the A- and B-site ions and the O ion, respectively (Goldschmidt, 1926; Roth, 1957)}, Nd2/3TiO3 is expected to show greater octahedral tilting than La2/3TiO3 and possibly lower symmetry due to tilting around more than one axis (Reaney et al., 1994). In fact, our experiments did indicate that the orthorhombic structure in Cmmm was only observed at high temperatures for Nd0.7Ti0.9Al0.1O3, following a continuous at around 750 K (see §4). Therefore, as can be seen from Fig. 1, the only possibilities for the room-temperature structure are the structures in C2/m (a−b0c− on a 2 × 2 × 2 cell), Pmma (a+b−c0 on a 2 × 2 × 2 cell), Amm2 (a−b0c+ on a 2 × 2 × 2 cell) or P2/m (a−b−c0 on 21/2 × 2 × 21/2 cell) – these are the only subgroups allowing a single, possibly to the structure in Cmmm.
3. Experimental
Nd0.7Ti0.9Al0.1O3 samples were produced by our standard alkoxide/nitrate route (Ringwood et al., 1988). This method involved the mixing of correct molar quantities of titanium isopropoxide and aluminium sec-butoxide in ethanol with aqueous solutions of neodymium nitrate, while continuously stirring. After thorough mixing and stir drying, the materials were calcined in air at 1023 K for 1 h to remove nitrates and alcohol, followed by wet milling for 16 h using zirconia balls. The slurry was then dried at 383 K overnight and the dried clumps were crushed in a mortar and pestle into fine powder. The powder was pelletized and sintered in air at 1723 K for 48 h, then furnace cooled. A polished surface was carbon-coated and characterized by (SEM), using a Jeol 6400 instrument fitted with a Tracor Northern energy-dispersive spectrometer (EDS) operated at 15 kV. A comprehensive set of standards was used for the quantitative work, giving a high degree of accuracy. This verified the sample composition and showed the sample to be homogeneous with a very small amount of Nd2Ti2O7 (the amount of impurity phase was below the by X-ray powder diffraction using a Philips X'Pert Pro Diffractometer with Cu Kα radiation).
Time-of-flight neutron powder diffraction data were recorded using the high-resolution powder diffractometer, HRPD, at the ISIS neutron facility, Rutherford Appleton Laboratories, UK (Ibberson et al., 1992). The temperature range of interest, from 4.2 to 1273 K, necessitated the use of both cryostat and furnace. For measurements in the cryostat at 4.2, 100 and 200 K, the powdered sample was lightly packed into an aluminium can of slab geometry, area 20 × 20 mm, 15 mm thick, with thin neutron-transparent windows front and back. Heat was supplied to the sample through a 100 W cartridge heater inserted in the side wall of the sample can and temperature was monitored using a Rh/Fe sensor located in the opposite wall. A gadolinium, neutron-absorbing mask was attached to the side of the can facing the incident and back-scattering detectors to reduce contaminant Bragg peaks arising from either the body of the sample can, including sensor or heater, or the stainless steel frames supporting the vanadium windows. The assembly was attached to a centre-stick and mounted in an AS Scientific, 50 mm diameter, `Orange' helium cryostat, located at the 1 m position of the diffractometer. The exchange gas was He at 30 mbar. For measurements at room temperature and above, the sample was loaded into an 11 mm diameter vanadium can, which was then either suspended from the standard ISIS candlestick for room-temperature measurements or mounted in the RAL vacuum furnace for temperature runs from 373 to 1273 K in 100 K steps. The furnace has vanadium heating elements and the thermometry is based on type-K thermocouples positioned in contact with the sample can at about 20 mm above the beam centre. The sample temperature was controlled to ± 0.2 K. Diffraction patterns from the sample, whether in cryostat or furnace, were recorded over the time-of-flight range 30–130 ms in both back-scattering and 90° detector banks, corresponding to d-spacings from 0.6 to 2.6 Å (at a resolution of Δd/d ≃ 4 × 10−4) and from 0.9 to 3.7 Å (Δd/d ≃ 2 × 10−3), respectively. The patterns were normalized to the incident-beam spectrum as recorded in the upstream monitor and corrected for detector efficiency according to prior calibration with a vanadium scan. Patterns were recorded to a total incident proton beam of ca 75 µA h at room temperature and above, and 100 µA h below room temperature, corresponding to approximately 2.3 and 3.1 h of data collection, respectively, to allow good structure determinations.
4. Results and discussion
An extract from the neutron diffraction pattern, 1.8 < d < 2.4 Å, recorded from Nd0.7Ti0.9Al0.1O3 at room temperature is shown in Fig. 2. The peaks in the figure are identified by indices based on the 2 × 2 × 2 cell. Peaks with all-even indices correspond to peaks from the ideal cubic The peaks are also indexed on the basis of the 2 × 2 × 2 cell and are marked as the X point (two even, one odd indices), R point (all odd indices) or M point (one even, two odd indices). Intensities at the X points arise from A-site cation/vacancy ordering and those at the R points from out-of-phase (−) octahedral tilting. Intensities at the M points could arise from in-phase (+) octahedral tilting; alternatively, very weak intensities (as observed) could appear at these points due to X- and R-point distortions acting in concert.
The inset of Fig. 2 shows the details of the 131/311/113 R-point reflections. In order to separate the individual components, this region was fitted with three peaks each comprising a Voigt function convolved with a sharp-edged exponential, on a linear background – assuming all peaks have the same widths and shapes.2 The heights of the three vertical lines indicate the individual peak intensities, showing that the intensities are in the order of 131 reflection > 113 reflection > 311 reflection. According to Glazer (1975), a− (out-of-phase tilting around the x axis) produces reflections of approximately equal intensities at odd–odd–odd with k ≠ l (here 131 and 113), b− reflections with h ≠ l (113 and 311) and c− reflections with h ≠ k (131 and 311). Applying the above results from Glazer, we can now rule out three of the possible structures enumerated from group-theoretical analysis (Fig. 1): structures in Amm2 (a−b0c+), Pmma (a+b−c0) and P2/m (a−b−c0). The structures in Amm2 (a−b0c+) and Pmma (a+b−c0) would not have produced any intensity at the observed 311 and 131 reflections, respectively, while the structure in P2/m (a−b−c0) would have resulted in the 113 peak being the strongest (not the 131 reflection as observed). This leaves the structure in C2/m (a−b0c−) as the only possibility. Indeed, such a structure, according to Glazer (1975), does produce the relative intensities as observed [I(131) > I(113) > I(311)]. The elimination of structures in Amm2 (a−b0c+) and Pmma (a+b−c0), both involving in-phase (+) octahedral tilting, is supported by the fact that the observed intensities of all the M-point reflections are either very weak or negligible, consistent with the origin of these peaks as the combination of A-site cation/vacancy ordering (X point) and out-of-phase (−) octahedral tilting (R point), rather than in-phase (+) octahedral tilting. Based on the above arguments, we propose the structure in C2/m, tilt system a−b0c−, as the room-temperature structure for Nd0.7Ti0.9Al0.1O3.
The diffraction pattern has been fitted, and both lattice parameters and atomic coordinates were determined using the GSAS computer program (Larson & von Dreele, 2000; Toby, 2001). Patterns from both the back-scattering and the 90° detector banks were fitted simultaneously, the diffractometer constant for the 90° bank being released to ensure that the lattice parameters were determined in every case by the higher-resolution back-scattering bank. Internal coordinates were refined along with displacement parameters and oxygen displacement parameters were taken to be anisotropic (however, in refinements of the very slightly distorted monoclinic structure, the oxygen displacement parameters were constrained to correspond to orthorhombic Cmmm symmetry). The isotropic displacement parameters for the two B-site cations, Ti4+ and Al3+, were constrained to be equal. The distribution of the Nd3+ ions over the two crystallographically distinct A sites was allowed to vary, with the total occupancy constrained to 1.4. The details of the structure, as refined by the are included in Table 1. This monoclinic structure, along with the structure of the high-temperature orthorhombic phase, is depicted in Fig. 3. Note that a from the room-temperature data was also carried out assuming the Cmmm model; the goodness-of-fit (χ2 = 5.0) was, as expected, worse than for the C2/m model.
as implemented in the
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As shown in Table 1,3 the room-temperature confirms the cation ordering to the extent that the A sites at z ≃ 0 are essentially fully occupied by Nd3+ ions (97% occupancy), while the A sites at z ≃ 1/2 contain nearly all the vacancies (43% occupancy). It can be seen, from the values of z tabulated, that the Ti4+/Al3+ ions move away from the fully occupied layer and the O2− ions move (on average) towards it, as might be expected given the additional positive charge on these layers. Not only do these movements make sense, but also they may well account for the stability of the layered ordering that is observed (Thomas et al., 2006). The distinctive feature of the present model is the movement of O atoms associated with octahedral tilting around both the x and z axes. The angles of tilt can be estimated from the oxygen coordinates as the angle made by the line joining O3 with O4 to the y axis. This tilt angle around the x axis is given by tan−1{[z(O4) − z(O3)]c/(b/2)} and is ∼ 6.8°. Similarly the tilt angle around the z axis is given by tan−1{[x(O3) − x(O4)]a/(b/2)} and is ∼ 5.0°. These angles are bigger than the tilt angle of ∼ 4.7° (around the x axis only) reported for La0.6Sr0.1TiO3 at room temperature (having an orthorhombic structure in Cmmm; Howard & Zhang, 2003), consistent with (see §2) the slightly smaller ionic size of Nd3+ compared with La3+.
Diffraction patterns obtained at high temperatures were inspected closely to look for phase transition(s). In fact, this was done before the room-temperature structure was solved, since that relied upon the correct identification of the high-temperature structure and a consideration of structures derived from it (see §2). As in the case of La0.6Sr0.1TiO3, layered ordering of cations/vacancies is expected to remain in the temperature range of this study (up to 1273 K) due to the low cation mobility (Howard & Zhang, 2003). However, phase transitions due to the disappearance of octahedral tilting are expected upon heating. Again the details of the peaks proved to be pivotal. Fig. 4(a) shows details of the 131/311/113 reflections observed at various temperatures. The same peak-fitting procedure, as that applied to the room-temperature data, was carried out for all the temperature runs. The results at T = 100, 673 and 773 K are shown in Figs. 4(b)–(d), respectively; the vertical lines indicate the intensity of each individual peak. For temperatures up to 673 K, three peaks are necessary to fit the 131/311/113 region satisfactorily. For temperatures ranging from 773 to 1273 K, however, the intensity of the middle 311 peak becomes negligible, i.e. only two peaks are required to fit this region. According to Glazer (1975), the appearance of intensity in R-point reflections with k ≠ l (i.e. 131 and 113), together with the absence of intensity at the corresponding k = l reflection (i.e. 311), implies that only around the x axis does the (out-of-phase) octahedral tilt occur. This is similar to the diffraction pattern obtained at room temperature from La0.6Sr0.1TiO3, which was successfully refined using a structure model in Cmmm, tilt system a−b0c0 (Howard & Zhang, 2003). Therefore, we propose the same orthorhombic structure for the high-temperature phase of Nd0.7Ti0.9Al0.1O3.
Diffraction patterns were also recorded below room temperature at 4.2, 100 and 200 K, to check for a possible low-temperature phase. The details of the 131/311/113 reflections at 4.2, 100 and 200 K are shown in Figs. 4(a) and (b); the presence of the middle 311 peak is more evident at lower temperatures due to the slightly wider spacing between peaks. The diffraction patterns are, however, exceedingly well fitted assuming the same C2/m structure as occurs at room temperature, suggesting that there is no additional phase occurring below room temperature.
Structure refinements were carried out for all the temperature runs, from 4.2 to 1273 K, using the same protocol as described earlier. The results of the . The refinements confirm the cations are still ordered in the high-temperature orthorhombic phase, such that one layer is essentially fully occupied by Nd3+ ions and the next contains nearly all the vacancies. As noted in the monoclinic structure at room temperature, the values of z tabulated for the orthorhombic structure at 873 K also reveal that the Ti4+/Al3+ ions move away from the fully occupied layer, and the O2− ions move (on average) towards it. The driving force for the to orthorhombic is the disappearance of the octahedral tilting around the z axis, leaving only the tilting around the x axis. Again this angle is given by tan−1{[z(O4) − z(O3)]c/(b/2)} and is ∼ 6.2° at 873 K, slightly smaller than that at room temperature.
from the patterns recorded at 873 K, a temperature at which the orthorhombic structure is well established, are also shown in Table 1Lattice parameters obtained from the refinements are recorded in Fig. 5. The cell edges show saturation effects at lower temperatures, and accordingly have been fitted with functions of the form l = l0 + l1θs coth(θs/T) (Salje et al., 1991) with saturation temperature θs at 350 K. At 1273 K, the highest temperature studied, the structure is still clearly orthorhombic. Extrapolating on parameters a and b suggests that a transition to a tetragonal structure might occur at around 1480 K. This would be the structure, P4/mmm, formed by perovskites with layered cation/vacancy ordering on the A sites in the absence of octahedral tilting and adopted, for example, by La0.6Sr0.1TiO3 at elevated temperatures (Howard & Zhang, 2003). However, the possibility of other effects, such as the onset of disorder on the A site due to increased cation mobility at high temperatures, cannot be excluded.
The monoclinic β angle is fitted reasonably well with a function of the form β – 90° ∝ (Tc – T)1/4, with Tc = 690 K, consistent with a continuous but tricritical from the monoclinic to the orthorhombic phase (Salje, 1990). The continuous nature of this is confirmed by directly comparing the diffraction patterns from the monoclinic phase with those from the orthorhombic phase – there are no discernible differences aside from the subtle ones in R-point reflections already discussed. The transition temperature from monoclinic to orthorhombic cannot be determined very accurately due to the coarse (100 K) temperature steps used as well as the difficulty (see β in Fig. 5) in obtaining precise estimates of the small monoclinic distortion. Based on our observations of the R-point reflections (Fig. 4), we believe the transition occurs between 673 and 773 K, so tentatively suggest 750 K for the temperature of this transition.
Finally, it should be mentioned that our model for the room-temperature structure in C2/m was used successfully to generate the (SAED) patterns recorded by Lee et al. (2004) in their TEM study of Nd0.7Ti0.9Al0.1O3. Calculated patterns were obtained using the program EMS On Line (Electron Microscopy Image Simulation4), which includes multiple scattering effects. In addition, a multiple domain effect was taken into consideration as the SAED patterns recorded by Lee et al. (2004) were from at least two different domains due to the small domain size in their sample. It is clear that the reflections indexed at ½(odd odd odd), ½(odd even even) and ½(odd odd even) in their paper (referred to the 1 × 1 × 1 cubic cell of the aristotype) can be accounted for by the out-of-phase octahedral tilting, the layered ordering of the Nd3+ ions and a combination of the two, respectively. The manner in which `concert' reflections can be produced by combinations of distortions is highlighted in recent simulations by Woodward & Reaney (2005). It is not necessary in the present case to invoke in-phase tilting or any particular A-site cation displacement as Lee et al. (2004) proposed.
5. Summary and conclusions
The room-temperature structure of Nd0.7Ti0.9Al0.1O3, which we take to represent the structure of Nd2/3TiO3, has been successfully determined. Symmetry arguments were used to limit the possibilities, then the structure solution completed from a high-resolution neutron powder diffraction study revealed details of the weak reflections that arise from octahedral tilting. The structure, monoclinic in C2/m, has been successfully refined by the It is characterized by a layered ordering of the A-site cations/vacancies along the z axis (alternately occupied and partly occupied layers of Nd cations), and out-of-phase tilting of the (Ti/Al)O6 octahedra independently around two axes (∼ 6.8 and 5.0° around the x and z axes, respectively).
The Cmmm has also been examined, with the transition temperature roughly estimated at around 750 K. The driving force for this is the disappearance of the octahedral tilting around the z axis (parallel to the direction of the cation ordering). Upon further heating (beyond the temperature range of this experiment), the octahedral tilting around the x axis (perpendicular to the direction of the cation ordering) is also expected to disappear, leading to a tetragonal structure in P4/mmm, as observed for La0.6Sr0.1TiO3 (Howard & Zhang, 2003).
to orthorhombic inSupporting information
10.1107/S0108768105041066/bk5024sup1.cif
contains datablocks ND0.7AL0.1TI0.9O3_publ, Sample_Preparation, Instrument, ND0.7AL0.1TI0.9O3_RT_overall, ND0.7AL0.1TI0.9O3_RT, ND0.7AL0.1TI0.9O3_RT_p_01, ND0.7AL0.1TI0.9O3_RT_p_02, ND0.7AL0.1TI0.9O3_600C_overall, ND0.7AL0.1TI0.9O3_600C, ND0.7AL0.1TI0.9O3_600C_p_01, ND0.7AL0.1TI0.9O3_600C_p_02. DOI:data_ND0.7AL0.1TI0.9O3_RT_overall. DOI: 10.1107/S0108768105041066/bk5024sup2.rtv
data_ND0.7AL0.1TI0.9O3_RT_p_02. DOI: 10.1107/S0108768105041066/bk5024sup4.rtv
data_ND0.7AL0.1TI0.9O3_600C_p_01. DOI: 10.1107/S0108768105041066/bk5024sup6.rtv
data_ND0.7AL0.1TI0.9O3_600C_p_02. DOI: 10.1107/S0108768105041066/bk5024sup8.rtv
data_ND0.7AL0.1TI0.9O3_RT_overall. DOI: 10.1107/S0108768105041066/bk5024sup3.hkl
data_ND0.7AL0.1TI0.9O3_RT_p_02. DOI: 10.1107/S0108768105041066/bk5024sup5.hkl
data_ND0.7AL0.1TI0.9O3_600C_p_01. DOI: 10.1107/S0108768105041066/bk5024sup7.hkl
data_ND0.7AL0.1TI0.9O3_600C_p_02. DOI: 10.1107/S0108768105041066/bk5024sup9.hkl
? | β = ?° |
Mr = ? | γ = ?° |
?, ? | V = ? Å3 |
a = ? Å | Z = ? |
b = ? Å | ? radiation, λ = ? Å |
c = ? Å | ?, ? × ? × ? mm |
α = ?° |
Least-squares matrix: full | ? data points |
Rp = 0.053 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1084.6 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 12.72 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0; TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 2262.7 #6 (sig-2) = 243.9 #7 (gam-0) = 0.00 #8 (gam-1) = 12.79 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rwp = 0.057 | 62 parameters |
Rexp = 0.045; 0.017 | 0 restraints |
R(F2) = 0.12475; 0.13144 | (Δ/σ)max = 0.02 |
χ2 = 4.162 | Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.239911 2: -3.948660E-02 3: 1.313250E-02 4: -6.363930E-03 5: -4.017170E-03 6: -4.553510E-03; GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 0.264321 2: -7.504890E-02 3: 1.714960E-02 4: -3.143980E-02 |
Al0.1Nd0.7O3Ti0.9 | β = 90.042 (2)° |
Mr = 194.76 | V = 452.43 (2) Å3 |
Monoclinic, C2/m | Z = 8 |
a = 7.67637 (12) Å | ? radiation, λ = ? Å |
b = 7.64297 (12) Å | ?, ? × ? × ? mm |
c = 7.71137 (12) Å |
Least-squares matrix: full | ? data points |
Rp = 0.053 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1084.6 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 12.72 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rwp = 0.057 | 62 parameters |
Rexp = 0.045 | 0 restraints |
R(F2) = 0.12475 | (Δ/σ)max = 0.02 |
χ2 = 4.162 | Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.239911 2: -3.948660E-02 3: 1.313250E-02 4: -6.363930E-03 5: -4.017170E-03 6: -4.553510E-03 |
Al0.1Nd0.7O3Ti0.9 | β = 90.042 (2)° |
Mr = 194.76 | V = 452.43 (2) Å3 |
Monoclinic, C2/m | Z = 8 |
a = 7.67637 (12) Å | ? radiation, λ = ? Å |
b = 7.64297 (12) Å | ?, ? × ? × ? mm |
c = 7.71137 (12) Å |
Rp = 0.053 | χ2 = 4.162 |
Rwp = 0.057 | ? data points |
Rexp = 0.045 | 62 parameters |
R(F2) = 0.12475 | 0 restraints |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Nd1 | 0.2522 (6) | 0.0 | 0.0021 (8) | 0.0091 (9)* | 0.970 (5) |
Nd2 | 0.2493 (14) | 0.0 | 0.5096 (17) | 0.0097 (18)* | 0.430 (5) |
Ti | 0.0046 (11) | 0.2474 (9) | 0.2606 (5) | 0.0053 (6)* | 0.9 |
O1 | 0.0 | 0.2827 (6) | 0.0 | 0.01449 | |
O2 | 0.0 | 0.2231 (8) | 0.5 | 0.0344 | |
O3 | 0.0135 (7) | 0.0 | 0.2092 (5) | 0.01148 | |
O4 | −0.0297 (8) | 0.5 | 0.2683 (5) | 0.01557 | |
O5 | 0.2536 (8) | 0.2730 (7) | 0.2338 (4) | 0.02488 | |
Al | 0.0046 (11) | 0.2474 (9) | 0.2606 (5) | 0.0053 (6)* | 0.1 |
U11 | U22 | U33 | U12 | U13 | U23 | |
O1 | 0.030 (3) | 0.006 (3) | 0.0080 (17) | 0.0 | 0.0 | 0.0 |
O2 | 0.059 (4) | 0.042 (4) | 0.0023 (18) | 0.0 | 0.0 | 0.0 |
O3 | 0.011 (3) | 0.015 (2) | 0.008 (2) | 0.0 | 0.0 | 0.0 |
O4 | 0.026 (3) | 0.005 (2) | 0.016 (2) | 0.0 | 0.0 | 0.0 |
O5 | 0.0008 (10) | 0.030 (3) | 0.044 (2) | −0.005 (2) | 0.0 | 0.0 |
? | β = ?° |
Mr = ? | γ = ?° |
?, ? | V = ? Å3 |
a = ? Å | Z = ? |
b = ? Å | ? radiation, λ = ? Å |
c = ? Å | ?, ? × ? × ? mm |
α = ?° |
Rp = 0.064 | ? data points |
Rwp = 0.072 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1084.6 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 12.72 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rexp = 0.045 | |
R(F2) = 0.12475 | Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.239911 2: -3.948660E-02 3: 1.313250E-02 4: -6.363930E-03 5: -4.017170E-03 6: -4.553510E-03 |
χ2 = NOT FOUND |
? | β = ?° |
Mr = ? | γ = ?° |
?, ? | V = ? Å3 |
a = ? Å | Z = ? |
b = ? Å | ? radiation, λ = ? Å |
c = ? Å | ?, ? × ? × ? mm |
α = ?° |
Rp = 0.041 | ? data points |
Rwp = 0.050 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 2262.7 #6 (sig-2) = 243.9 #7 (gam-0) = 0.00 #8 (gam-1) = 12.79 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rexp = 0.017 | |
R(F2) = 0.13144 | Background function: GSAS Background function number 1 with 4 terms. Shifted Chebyshev function of 1st kind 1: 0.264321 2: -7.504890E-02 3: 1.714960E-02 4: -3.143980E-02 |
χ2 = NOT FOUND |
? | β = ?° |
Mr = ? | γ = ?° |
?, ? | V = ? Å3 |
a = ? Å | Z = ? |
b = ? Å | ? radiation, λ = ? Å |
c = ? Å | ?, ? × ? × ? mm |
α = ?° |
Least-squares matrix: full | 1632 data points |
Rp = 0.037 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 509.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 11.74 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0; TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1822.8 #6 (sig-2) = 248.4 #7 (gam-0) = 0.00 #8 (gam-1) = 12.55 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rwp = 0.041 | 54 parameters |
Rexp = 0.039; 0.018 | 0 restraints |
R(F2) = 0.27973; 0.06728 | (Δ/σ)max = 0.03 |
χ2 = 2.310 | Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.497571 2: 6.126860E-02 3: 2.448550E-02 4: -1.455740E-02 5: -9.745710E-03 6: -1.060520E-02; GSAS Background function number 4 with 4 terms. Power series in Q**2n/n! 1: 0.500328 2: -1.113600E-02 3: 5.555480E-04 4: 1.833090E-05 |
Al0.1Nd0.7O3Ti0.9 | c = 7.74755 (10) Å |
Mr = 194.76 | V = 459.62 (2) Å3 |
Orthorhombic, Cmmm | Z = 8 |
a = 7.71021 (11) Å | ? radiation, λ = ? Å |
b = 7.69428 (11) Å | ?, ? × ? × ? mm |
Least-squares matrix: full | 1632 data points |
Rp = 0.037 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 509.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 11.74 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rwp = 0.041 | 54 parameters |
Rexp = 0.039 | 0 restraints |
R(F2) = 0.27973 | (Δ/σ)max = 0.03 |
χ2 = 2.310 | Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.497571 2: 6.126860E-02 3: 2.448550E-02 4: -1.455740E-02 5: -9.745710E-03 6: -1.060520E-02 |
Al0.1Nd0.7O3Ti0.9 | c = 7.74755 (10) Å |
Mr = 194.76 | V = 459.62 (2) Å3 |
Orthorhombic, Cmmm | Z = 8 |
a = 7.71021 (11) Å | ? radiation, λ = ? Å |
b = 7.69428 (11) Å | ?, ? × ? × ? mm |
Rp = 0.037 | χ2 = 2.310 |
Rwp = 0.041 | 1632 data points |
Rexp = 0.039 | 54 parameters |
R(F2) = 0.27973 | 0 restraints |
x | y | z | Uiso*/Ueq | Occ. (<1) | |
Nd1 | 0.2503 (8) | 0.0 | 0.0 | 0.0228 (11)* | 0.989 (5) |
Nd2 | 0.2535 (18) | 0.0 | 0.5 | 0.023 (2)* | 0.411 (5) |
Ti | 0.0 | 0.2477 (14) | 0.2623 (4) | 0.0164 (7)* | 0.9 |
O1 | 0.0 | 0.2805 (8) | 0.0 | 0.03371 | |
O2 | 0.0 | 0.2254 (10) | 0.5 | 0.0428 | |
O3 | 0.0 | 0.0 | 0.2111 (6) | 0.02528 | |
O4 | 0.0 | 0.5 | 0.2649 (7) | 0.04457 | |
O5 | 0.25 | 0.25 | 0.2354 (7) | 0.04537 | |
Al | 0.0 | 0.2477 (14) | 0.2623 (4) | 0.0164 (7)* | 0.1 |
U11 | U22 | U33 | U12 | U13 | U23 | |
O1 | 0.063 (4) | 0.019 (3) | 0.020 (2) | 0.0 | 0.0 | 0.0 |
O2 | 0.073 (4) | 0.044 (4) | 0.011 (2) | 0.0 | 0.0 | 0.0 |
O3 | 0.029 (4) | 0.021 (3) | 0.026 (3) | 0.0 | 0.0 | 0.0 |
O4 | 0.091 (6) | 0.007 (3) | 0.035 (3) | 0.0 | 0.0 | 0.0 |
O5 | 0.0179 (14) | 0.054 (2) | 0.064 (3) | 0.002 (4) | 0.0 | 0.0 |
? | β = ?° |
Mr = ? | γ = ?° |
?, ? | V = ? Å3 |
a = ? Å | Z = ? |
b = ? Å | ? radiation, λ = ? Å |
c = ? Å | ?, ? × ? × ? mm |
α = ?° |
Rp = 0.047 | ? data points |
Rwp = 0.054 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 509.3 #6 (sig-2) = 0.0 #7 (gam-0) = 0.00 #8 (gam-1) = 11.74 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rexp = 0.039 | |
R(F2) = 0.27973 | Background function: GSAS Background function number 1 with 6 terms. Shifted Chebyshev function of 1st kind 1: 0.497571 2: 6.126860E-02 3: 2.448550E-02 4: -1.455740E-02 5: -9.745710E-03 6: -1.060520E-02 |
χ2 = NOT FOUND |
? | β = ?° |
Mr = ? | γ = ?° |
?, ? | V = ? Å3 |
a = ? Å | Z = ? |
b = ? Å | ? radiation, λ = ? Å |
c = ? Å | ?, ? × ? × ? mm |
α = ?° |
Rp = 0.025 | 1632 data points |
Rwp = 0.032 | Profile function: TOF Profile function number 3 with 21 terms Profile coefficients for exponential pseudovoigt convolution Von Dreele, 1990 (unpublished) #1 (alp ) = 0.2082 #2 (bet-0) = 0.025465 #3 (bet-1) = 0.010109 #4 (sig-0) = 0.0 #5 (sig-1) = 1822.8 #6 (sig-2) = 248.4 #7 (gam-0) = 0.00 #8 (gam-1) = 12.55 #9 (gam-2) = 0.00 #10(gsf ) = 0.00 #11(g1ec ) = 0.00 #12(g2ec ) = 0.00 #13(rstr ) = 0.000 #14(rsta ) = 0.000 #15(rsca ) = 0.000 #16(L11) = 0.000 #17(L22) = 0.000 #18(L33) = 0.000 #19(L12) = 0.000 #20(L13) = 0.000 #21(L23) = 0.000 Peak tails are ignored where the intensity is below 0.0010 times the peak Aniso. broadening axis 0.0 0.0 1.0 |
Rexp = 0.018 | |
R(F2) = 0.06728 | Background function: GSAS Background function number 4 with 4 terms. Power series in Q**2n/n! 1: 0.500328 2: -1.113600E-02 3: 5.555480E-04 4: 1.833090E-05 |
χ2 = NOT FOUND |
Experimental details
(ND0.7AL0.1TI0.9O3_RT_overall) | (ND0.7AL0.1TI0.9O3_RT) | (ND0.7AL0.1TI0.9O3_RT_p_01) | (ND0.7AL0.1TI0.9O3_RT_p_02) | |
Crystal data | ||||
Chemical formula | ? | Al0.1Nd0.7O3Ti0.9 | ? | ? |
Mr | ? | 194.76 | ? | ? |
Crystal system, space group | ?, ? | Monoclinic, C2/m | ?, ? | ?, ? |
Temperature (K) | ? | ? | ? | ? |
a, b, c (Å) | ?, ?, ? | 7.67637 (12), 7.64297 (12), 7.71137 (12) | ?, ?, ? | ?, ?, ? |
α, β, γ (°) | ?, ?, ? | 90, 90.042 (2), 90 | ?, ?, ? | ?, ?, ? |
V (Å3) | ? | 452.43 (2) | ? | ? |
Z | ? | 8 | ? | ? |
Radiation type | ?, λ = ? Å | ?, λ = ? Å | ?, λ = ? Å | ?, λ = ? Å |
Specimen shape, size (mm) | ?, ? × ? × ? | ?, ? × ? × ? | ?, ? × ? × ? | ?, ? × ? × ? |
Data collection | ||||
Diffractometer | ? | ? | ? | ? |
Specimen mounting | ? | ? | ? | ? |
Data collection mode | ? | ? | ? | ? |
Scan method | ? | ? | ? | ? |
2θ values (°) | 2θmin = ? 2θmax = ? 2θstep = ? | 2θmin = ? 2θmax = ? 2θstep = ? | 2θmin = ? 2θmax = ? 2θstep = ? | 2θmin = ? 2θmax = ? 2θstep = ? |
Refinement | ||||
R factors and goodness of fit | Rp = 0.053, Rwp = 0.057, Rexp = 0.045; 0.017, R(F2) = 0.12475; 0.13144, χ2 = 4.162 | Rp = 0.053, Rwp = 0.057, Rexp = 0.045, R(F2) = 0.12475, χ2 = 4.162 | Rp = 0.064, Rwp = 0.072, Rexp = 0.045, R(F2) = 0.12475, χ2 = NOT FOUND | Rp = 0.041, Rwp = 0.050, Rexp = 0.017, R(F2) = 0.13144, χ2 = NOT FOUND |
No. of data points | ? | ? | ? | ? |
No. of parameters | 62 | 62 | ? | ? |
No. of restraints | 0 | 0 | ? | ? |
(ND0.7AL0.1TI0.9O3_600C_overall) | (ND0.7AL0.1TI0.9O3_600C) | (ND0.7AL0.1TI0.9O3_600C_p_01) | (ND0.7AL0.1TI0.9O3_600C_p_02) | |
Crystal data | ||||
Chemical formula | ? | Al0.1Nd0.7O3Ti0.9 | ? | ? |
Mr | ? | 194.76 | ? | ? |
Crystal system, space group | ?, ? | Orthorhombic, Cmmm | ?, ? | ?, ? |
Temperature (K) | ? | ? | ? | ? |
a, b, c (Å) | ?, ?, ? | 7.71021 (11), 7.69428 (11), 7.74755 (10) | ?, ?, ? | ?, ?, ? |
α, β, γ (°) | ?, ?, ? | 90, 90, 90 | ?, ?, ? | ?, ?, ? |
V (Å3) | ? | 459.62 (2) | ? | ? |
Z | ? | 8 | ? | ? |
Radiation type | ?, λ = ? Å | ?, λ = ? Å | ?, λ = ? Å | ?, λ = ? Å |
Specimen shape, size (mm) | ?, ? × ? × ? | ?, ? × ? × ? | ?, ? × ? × ? | ?, ? × ? × ? |
Data collection | ||||
Diffractometer | ? | ? | ? | ? |
Specimen mounting | ? | ? | ? | ? |
Data collection mode | ? | ? | ? | ? |
Scan method | ? | ? | ? | ? |
2θ values (°) | 2θmin = ? 2θmax = ? 2θstep = ? | 2θmin = ? 2θmax = ? 2θstep = ? | 2θmin = ? 2θmax = ? 2θstep = ? | 2θmin = ? 2θmax = ? 2θstep = ? |
Refinement | ||||
R factors and goodness of fit | Rp = 0.037, Rwp = 0.041, Rexp = 0.039; 0.018, R(F2) = 0.27973; 0.06728, χ2 = 2.310 | Rp = 0.037, Rwp = 0.041, Rexp = 0.039, R(F2) = 0.27973, χ2 = 2.310 | Rp = 0.047, Rwp = 0.054, Rexp = 0.039, R(F2) = 0.27973, χ2 = NOT FOUND | Rp = 0.025, Rwp = 0.032, Rexp = 0.018, R(F2) = 0.06728, χ2 = NOT FOUND |
No. of data points | 1632 | 1632 | ? | 1632 |
No. of parameters | 54 | 54 | ? | ? |
No. of restraints | 0 | 0 | ? | ? |
Computer programs: GSAS.
Footnotes
1ISOTROPY is a software package developed by Stokes and Hatch at Brigham Young University. ISOTROPY is available at https://www.physics.byu.edu/~stokesh/isotropy.html .
2Peak-fitting program due to Devinder Sivia, ISIS Facility.
3Supplementary data for this paper are available from the IUCr electronic archives (Reference: BK5024 ). Services for accessing these data are described at the back of the journal.
4EMS On Line is an internet version of the commercial software package developed by Pierre Stadelmann at the Centre Interdépartemental de Microscopie Electronique (CIME) of the Ecole Polytechnique Fédérale de Lausanne (EPFL) in Switzerland. The interface for this version (https://cimesg1.epfl.ch/CIOL/ems.html ) was developed by Pierre-Henri Jouneau.
Acknowledgements
The authors thank Mr Ian Watson, Ms Melody Carter of the Australian Nuclear Science and Technology Organisation for preparing the sample used in this study. Thanks are also due to Mr Min-Han Kim and Professor Sahn Nahm of the Korea University for their cooperation and efforts to fabricate the sample. The neutron facilities at ISIS are operated by the Council for the Central Laboratory of the Research Councils (CCLRC), with a contribution from the Australian Research Council. Travel funding to ISIS was provided by the Commonwealth of Australia under the Access to Major Research Facilities Program.
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