Silver niobium trioxide, AgNbO₃

The present structure determination of silver niobium trioxide at 291 K was performed on a twinned single crystal with a predominant presence [about 93 (1)%] of one twin domain. The sample contained traces of V (about 1 atomic %). This study confirms that the room-temperature phase of AgNbO₃ is isostructural with the room-temperature phase of NaNbO₃, i.e. it is a tilted perovskite. Structural deviation in AgNbO₃ from centrosymmetry was not detected in this study and its structure was refined in Pbcm, though a previous study indicated ferroelectricity below 350 K, in contrast with NaNbO₃.

S1. Comment

The room-temperature phase of AgNbO₃ belongs to the perovskite family and is closely related to the room-temperature phase of NaNbO₃. Both compounds undergo a number of phase transitions when cooled down from the prototypic cubic phase. The concomitant distortions of the prototypic structure result in the formation of superstructures and symmetry changes which give rise to twins. Some of the phases and the pertinent phase transitions in AgNbO₃ and NaNbO₃ correspond to each other (Kania et al., 1984; Łukaszewski et al., 1983; Paweł czyk, 1987; Glazer & Megaw, 1973; Verwerft et al., 1989).

The room-temperature phase of NaNbO₃ is antiferroelectric (Cross & Nicholson, 1955) and its structure has been determined by a single-crystal experiment on a moderately twinned crystal using film techniques [Sakowski-Cowley et al., 1969; this reference, as well as other related structure determinations, was listed in the Inorganic Structure Database (Bergerhoff et al., 1983)]. The other structure determination of the room-temperature phase of NaNbO₃, from neutron powder data, was carried out by Hewat (1974); c.f. the (+)-variant given in Table II of that article. These two structural models are slightly different, though their tilting scheme is the same.

In both the above descriptions, the structure is orthorhombic (Pbcm), with the lattice parameters a_o ~b_o ~(2a_p)^1/2; c_o ~4a_p (hereafter the subscript `p' denotes the primitive pseudocubic unit cell, while the subscript `o' denotes the orthorhombic unit cell.) The room-temperature phase of AgNbO₃ has the same type of lattice distortion as the room-temperature phase of NaNbO₃ (Verwerft et al., 1988).

AgNbO₃ is reported to be ferroelectric below 350 K, in contrast with NaNbO₃. The transition was detected by X-ray diffraction and dielectric measurements on both single-crystal and polycrystal samples of AgNbO₃, by Łukaszewski et al. (1983). However, Pawełczyk (1987) did not observe a change in distortion of the pseudoperovskite unit cell at 350 K. Similarly, Verwerft et al. (1989), using electron diffraction and imaging techniques, did not observe a transition at about 350 K. Kania (1998) reported that X-ray diffraction experiments (the Bond method) detected no change of the lattice parameters at 350 K, although a broadening of the lines took place. Nor did Raman spectroscopy give clear indications of the ferroelectric phase transition in AgNbO₃ (Kania, 1998). Nevertheless, in ceramic samples of AgNbO₃ a spontaneous polarization below 350 K was measured by Kania et al. (1984). Its value P_s ~0.04 µCcm⁻² at 293 K) is about three orders of magnitude lower than in e.g. KNbO₃, BaTiO₃ or PbTiO₃ (Jona & Shirane, 1962).

Verwerft et al. (1988) suggested two space groups for AgNbO₃, Pbcm or Pbc2₁, as well as a tilt scheme of NbO₆ octahedra, which was determined from high resolution electron microscopy experiments. The tilt scheme transformed into the basis applied in this article is (a_p⁻a_p⁻c_p⁺)₁² (a_p⁻a_p⁻c_p⁻)₂³ (a_p⁻a_p⁻c_p⁺)₃⁴ (for the adopted notation see Glazer, 1972). Verwerft et al. (1988) also pointed out that the crystals of AgNbO₃ contained planar faults perpendicular to [001]_p.

AgNbO₃ tends to form non-stoichiometric phases with a lower content of Ag. This deficiency of Ag is supposed to be accompanied by oxygen reduction (Łukaszewski et al., 1983). The precipitation of Ag was also observed by Verwerft et al. (1989). Matsumoto et al. (1992) observed the deficiency of Ag, as well as the release of O, during heating of sintered powder samples. From the dependence of electronic conductivity on the content of Ag in the bulk, these last authors concluded the existence of some Nb atoms in valences lower than +5.

The principal result of the present study is the confirmation of a model given by Hewat (1974), both for AgNbO₃ and NaNbO₃ (we collected single-crystal data on a sample of NaNbO₃ whose structure is not published here, due to the high proportion of a second domain). The relevant interatomic distances are given in Table 1 and the structure is depicted in Fig. 1. The tilt scheme is the same as that determined for NaNbO₃ by Sakowski-Cowley et al. (1969) and Hewat (1974) and suggested for AgNbO₃ by Verwerft et al. (1988).

This study could not distinguish between the centrosymmetric and non-centrosymmetric space groups Pbcm and Pbc2₁. Refinement in Pbc2₁ was hindered by high correlations, so the structure is reported in Pbcm.

Referring to the reported ferroelectricity in AgNbO₃, it should be remembered that the spontaneous polarization observed in AgNbO₃ is about three orders of magnitude lower than that in KNbO₃ or BaTiO₃ (Jona & Shirane, 1962). The displacements of non-O atoms do not exceed several tenths of Å in the latter compounds (Katz & Megaw, 1967). Consequently, the displacements of non-O atoms in AgNbO₃ should be duly smaller. These small displacements hinder the detection of deviation from centrosymmetry.

S2. Experimental

The preparation of both single crystals and ceramic polycrystal samples of AgNbO₃ is described by Łukaszewski et al. (1983). Single crystals were grown by the molten salt method (solvents 8 A g₂O···5V₂O₅ and Ag₂SO₄). Traces of V observed in the single crystals (concentration ~1 atomic °; Kania, 1998) come from the V₂O₅ in the solvent. The single crystals of AgNbO₃ are usually twinned; the domains in AgNbO₃ can be created by external stress. Among the crystals of AgNbO₃ available for the present work, one crystal was found with only a small fraction of a second domain, and this was used for the present X-ray structure determination.

S3. Refinement

The structure is a twinned fourfold superstructure related to the perovskites. Due to imperfect superposition, reflections were only averaged through inversion. Those reflections which were partially overlapped were discarded from the calculation. The Fourier maps were therefore biased, either because not all reflections were used or because the |F_o| values were not directly available. The deepest electron density minima are ~0.6 Å distant from Ag1, Ag2 and Nb. Being a ferroelastic superstructure, there are pseudosymmetry properties. We attempted to refine the occupancy of Ag under the assumption that the occupancy of Ag1 is equal to that of Ag2. The occupancy of the O atoms was constrained in order to keep the charge balanced. The number of constraints was 15. The indicators of refinement decreased to the values R_obs = 0.0316, Rw_obs = 0.0477, R_all = 0.0357, Rw_all = 0.0357 and S = 2.42, and the composition resulted in Ag_0.9802 (2)Nb_0.99V_0.01O_2.9901 (2). However, trying to include the refinement of the occupation of Nb/V was hindered by high correlations and resulted in unrealistic occupancies for all the heavy atoms. Therefore, the model with the ideal formula AgNbO₃ is reported here. The differences between the pertinent positional parameters which resulted from the refinement assuming the ideal non-stoichiometric compositions were as much as 5 × the respective s.u.s. A full discussion of the treatment of twinning is available in the archived CIF; see the deposition footnote for access details.

Computing details

Data collection: HW (Petříček, 1996); data reduction: JANA98 (Petříček & Dušek, 1998); program(s) used to refine structure: JANA98; molecular graphics: ORTEPIII (Burnett & Johnson, 1996); software used to prepare material for publication: JANA98.

Figures

Fig. 1. %T Fig. 1. A view of the third layer [z$ιn$ (1/2, 3/4)] of AgNbO$_{3}$ along the {ιt c} axis, showing 50° probability displacement ellipsoids ({ιt ORTEP}III; Burnett \& Johnson, 1996).

silver niobate

Crystal data

AgNbO3	Dx = 6.799 Mg m^−3
Mr = 248.77	Mo Kα radiation, λ = 0.71073 Å
Orthorhombic, Pbcm	Cell parameters from 50 reflections
a = 5.5462 (3) Å	θ = 5–33°
b = 5.6028 (4) Å	µ = 12.49 mm^−1
c = 15.6365 (13) Å	T = 292 K
V = 485.90 (6) Å^3	Prism, light brown
Z = 8	0.31 × 0.17 × 0.09 mm
F(000) = 896

Data collection

Hilger & Watts diffractometer	Rint = 0.025
ω/2θ scans	θmax = 30°
Absorption correction: gaussian (Templeton & Templeton, 1978)	h = −7→7
Tmin = 0.130, Tmax = 0.356	k = −7→7
5156 measured reflections	l = −21→22
1689 independent reflections	3 standard reflections every 30 reflections
1497 reflections with I > 3σ(I)	intensity decay: 7.0%

Refinement

Refinement on F	0 constraints
Least-squares matrix: full with fixed elements per cycle	w = (σ^2(Fo) + 0.0001(Fo)^2)^-1
R[F^2 > 2σ(F^2)] = 0.034	(Δ/σ)max = 0.01
wR(F^2) = 0.053	Δρmax = 1.20 e Å^−3
S = 2.69	Δρmin = −3.65 e Å^−3
1689 reflections	Extinction correction: type II (Becker & Coppens, 1974)
52 parameters	Extinction coefficient: 0.000228 (4)

Special details

Refinement. %T The orientation of the domains was visualized on precession photographs of the $hk$0 and $hhl$ nets of AgNbO$_{3}$. The twinning with the domain boundary (1${οverbar 1}$0) $_{o}$ can be described by the following transformation ($\varphi = αrctan(b_{o}/a_{o}$):$$ λeft (µatrix{h_{2} & k_{2} & l_{2} χr} ρight)_o = λeft (µatrix{h_{1} & k_{1} & l_{1} χr} ρight)_o πmatrix {2χos^{{2}\varphi − 1 & 2σin}{2}\varphi & 0 χr 2χos^{{2}\varphi & 1 − 2χos}2 \varphi & 0 χr 0 & 0 & 1 χr}$$

where ($h_{1}k_{1}l_{1})_{o}$ and ($h_{2}k_{2}l_{2})_{o}$ are the coordinates of a selected point with respect to the first and the second reciprocal basis, respectively. This twinning was confirmed for both AgNbO$_{3}$ and NaNbO$_{3}$ on a single-crystal diffractometer. The photograph of the perpendicular $hhl$ net did not reveal any other reflection splitting.

The twinning given by the above matrix corresponds to that observed by Verwerft {ιt et al.} (1989) using electron microscopy and electron diffraction. These authors observed the fourfold superstructure in three perpendicular directions, $a_{p}$, $b_{p}$ and $c_{p}$, while we have detected just one preferred orientation along the {ιt c} axis, both on the samples of AgNbO$_{3}$ and of NaNbO$_{3}$.

The diffraction peaks related by twinning from the two domains are partially overlapped, so the pattern of the systematic absences is obscured. The reflections of the type µbox{$h$0$l$} with $h$ = 2$n$ + 1 and $l$ = 2$n$ + 1, as well as the reflections µbox{0$kl$} with $k$ = 2$n$ + 1 and $l$ = 2$n$ + 1, were systematically absent. These observed systematic absences confirm the space groups {ιt Pbcm} or {ιt Pbc}2$_{1}$.

Reflections belonging to single domains were measured. From the 79 pairs of these reflections with µbox{$I>$9$\s(I)$} the domain fractions were calculated for the sample of AgNbO$_{3}$.

Starting models of AgNbO$_{3}$ for refinement were derived from the cubic prototypic perovskite structure by all possible 5$^{{χirc}$ tilts of the independent O octahedron about the orthorhombic unit-cell axes. The model which converged smoothly to the deepest minimum agreed with the model of NaNbO$_{3}$ determined by Hewat (1974); {ιt c.f.} the (+)-variant given in Table II of that article.}

The partial overlapping of reflections hindered the averaging of reflections except for inversion. The refinement of AgNbO$_{3}$ was carried out on those reflections which were either well superimposed or sufficiently distant from the peak diffracted by the minor domain. The limits of the differences between the respective diffractometer setting angles, $Δelta^{χhi$, $Δeltaοmega$ and $Δeltaτheta$, which decided which of the reflections should be discarded from the refinement due to partial overlapping, were chosen after a series of refinements with these values varying ({ιt CHECKRAN} in {ιt JANA}98; Pet\v r\'ι\v cek \& Du\v sek, 1998). Those reflections with differences in the diffractometer setting angles $µidΔeltaχhiµid$, $µidΔeltaοmegaµid$ and $µidΔeltaτhetaµid$ simultaneously lower than µbox{0.40, 0.20 and 0.20${χirc}$,} respectively, were considered as superimposed; those reflections for which at least one of the differences $µidΔeltaχhiµid$, $µidΔeltaοmegaµid$ or $µidΔeltaτhetaµid$ was greater than µbox{1.60, 0.55 or 0.55${χirc}$,} respectively, were considered as separated. Reflections between these limits were not used in the refinement.}

It should be noted that the learnt-profile method (Clegg, 1981; Pet\v r\'ι\v cek, 1996), which was applied in the evaluation of the net intensities of the measured reflections, tends to suppress those contributions of the minor domain which are scattered out of the peak centroid.

Clegg, W. (1981). Acta Cryst. A37, 22–28.

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ag1	0.75770 (3)	0.22738 (7)	3/4	0.0128 (1)
Ag2	0.75550 (3)	1/4	1/2	0.0128 (1)
Nb	0.74525 (2)	0.72338 (7)	0.625014 (8)	0.0059 (1)
O1	0.6978 (2)	0.7664 (2)	3/4	0.0090 (4)
O2	0.8043 (2)	3/4	1/2	0.0095 (4)
O3	0.4662 (2)	0.5364 (2)	0.61132 (6)	0.0088 (3)
O4	−0.0334 (2)	0.4727 (2)	0.63865 (7)	0.0092 (3)

Atomic displacement parameters (Ų)

	U^11	U^22	U^33	U^12	U^13	U^23
Ag1	0.0128 (2)	0.0123 (2)	0.0133 (2)	−0.00211 (4)	0.0 (1)	0.0 (1)
Ag2	0.0113 (2)	0.0141 (1)	0.0130 (2)	0.0 (1)	0.0 (1)	0.00107 (7)
Nb	0.0051 (2)	0.0040 (2)	0.0085 (2)	−0.00014 (3)	−0.00061 (4)	0.00031 (4)
O1	0.0118 (6)	0.0119 (7)	0.0031 (7)	0.0009 (4)	0.0 (1)	0.0 (1)
O2	0.0100 (6)	0.0127 (6)	0.0059 (7)	0.0 (1)	0.0 (1)	0.0004 (4)
O3	0.0064 (4)	0.0084 (5)	0.0115 (5)	−0.0033 (3)	−0.0013 (3)	0.0014 (3)
O4	0.0086 (4)	0.0077 (5)	0.0114 (5)	0.0030 (3)	0.0010 (3)	0.0013 (3)

Geometric parameters (Å, º)

Nb—O1	1.9866 (3)	Ag1—O1^vii	3.028 (1)
Nb—O2	1.9876 (3)	Ag1—O3	3.211 (1)
Nb—O3	1.8811 (9)	Ag1—O3^viii	3.211 (1)
Nb—O3^i	2.121 (1)	Ag2—O2^iii	2.8144 (1)
Nb—O4^ii	1.878 (1)	Ag2—O2	2.8144 (1)
Nb—O4^i	2.1333 (9)	Ag2—O2^ix	2.442 (1)
Ag1—O1^iii	2.604 (1)	Ag2—O2^x	3.105 (1)
Ag1—O1^iv	2.536 (1)	Ag2—O3	2.8597 (9)
Ag1—O3^iv	2.719 (1)	Ag2—O3^x	2.444 (1)
Ag1—O3^v	2.720 (1)	Ag2—O3^iv	2.444 (1)
Ag1—O4^ii	2.503 (1)	Ag2—O3^xi	2.8597 (9)
Ag1—O4^vi	2.503 (1)	Ag2—O4^ii	2.762 (1)
Ag1—O4^iv	2.721 (1)	Ag2—O4^xii	2.762 (1)
Ag1—O4^v	2.721 (1)	Ag2—O4^x	3.081 (1)
Ag1—O1	3.038 (1)	Ag2—O4^iv	3.081 (1)
O1—Nb—O2	168.59 (4)	O3—Nb—O3^i	89.66 (4)
O1—Nb—O3	94.04 (5)	O3—Nb—O4^ii	97.71 (4)
O1—Nb—O3^i	85.75 (5)	O3—Nb—O4^i	172.94 (4)
O1—Nb—O4^ii	93.76 (5)	O3^i—Nb—O3	89.66 (4)
O1—Nb—O4^i	85.51 (5)	O3^i—Nb—O4^ii	172.63 (4)
O2—Nb—O3	93.74 (4)	O3^i—Nb—O4^i	83.28 (4)
O2—Nb—O3^i	85.97 (4)	O4^ii—Nb—O4^i	89.35 (4)
O2—Nb—O4^ii	93.45 (4)	O4^i—Nb—O4^ii	89.35 (4)
O2—Nb—O4^i	85.74 (4)

Symmetry codes: (i) −x+1, y+1/2, z; (ii) x+1, y, z; (iii) x, y−1, z; (iv) −x+1, y−1/2, z; (v) −x+1, y−1/2, −z+3/2; (vi) x+1, y, −z+3/2; (vii) −x+2, y−1/2, z; (viii) x, y, −z+3/2; (ix) −x+2, −y+1, −z+1; (x) −x+1, −y+1, −z+1; (xi) x, −y+1/2, −z+1; (xii) x+1, −y+1/2, −z+1.