NH4CdF3: Structure of the low temperature phase

Physica B 162 (1990) 231-236 North-Holland

NH,CdF,: STRUCTURE OF THE LOW TEMPERATURE PHASE A. LE BAIL and J.L. FOURQUET Laboratoire

J. RUBIN,

des Fluorures,

UA CNRS 449, Universiti du Maine, Route de Laval, 72017 Le Mans Cedex,

E. PALACIOS

and J. BARTOLOME

Instituto de Ciencia de Materiales de Aragdn, 50009 Zaragoza, Spain

Received 20 December

France

Universidad de Zaragoza-CSIC,

Facultad de Ciencias, E. T.S.I.I.

Z.,

1989

The low temperature crystal structure of the perovskite NH,CdF, is solved from its powder X-ray diffraction pattern, by a modified Rietveld method. The true symmetry is orthorhombic - SG Pnma, Z = 4, a = 6.1791(14) A. b = 8.8786(6) A and c = 6.1655( 14) A, R, = 0.038, R, = 0.084, R,, = 0.103 and R, = 0.030. The final model is consistent with a three tilts scheme of the final quasi-regular CdF, octahedra, around the axis of the primitive cubic cell of the perovskite structure. The results are compared to other fluoro-perovskites and the effect of the presence of the ammonium ion is discussed.

1. Introduction A great amount of work has been devoted to the cubic perovskites NH,MF, (M = divalent cation). The compounds with M = Mg, Zn, Co, Mn and Cd have a cubic high temperature phase (SG Pm3m) and upon cooling undergo a structural first order transition to a phase of lower symmetry. The structural parameters and transition temperatures (T,) were determined from heat capacity measurements [l-4] and neutron and X-ray diffraction experiments [5]. The low temperature form was expected to be similar to other related compounds such as NH,MCl, [6,71, KMnF, PI and RbCaF, [9], where the distortion was accounted for through small tilts of the CdF, octahedra. Though small single crystals of the Mn and Zn ammonium perovskites were obtained and their X-ray diffraction study performed previous to this work, only ambiguous structure determinations could be obtained since the crystals were systematically twinned. So, in spite of the already achieved knowledge of these systems, the actual atomic positions have to be known in order to understand the dynamics of the ammonium ion in the low temperature phase, a problem which is currently under study with neutron techniques [lo].

We have decided to re-examine the crystal structure of the low temperature phase of one member of the series through a profile analysis of its X-ray powder diffraction pattern. For this purpose, NH,CdF, is ideal since it has the highest T, (331.2 K) of the series, thus allowing a room-temperature study of the low symmetry phase. Previous determinations performed with X-ray powder diffraction as a function of temperature showed a strong elongation along the c axis (c/a = 1.014) characteristic of the ammonium trifluoroperovskites [ 111. The cell parameters were determined to be a = 4.390(2) A in the cubic phase, and a = 4.368(l) 8, and c = 4.430(l) 8, in the pseudo-tetragonal low temperature phase.

2. Experimental The sample was prepared by heating a mixture of CdF, and NH,F up to 420 K [12]. The excess of NH,F was removed with methanol and heating the sample at 400 K for several hours. The X-ray powder pattern was recorded at 293 K on a Siemens D501 Daco MP powder diffractometer with graphite monochromatized Cu K, radiation. The step scan was O.O2”(2f3)

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A. Le Bail et al. I Crystal structure of NH,CdF,

232

and the 28 range lo”-135”. The refinement of the structure was performed with a modified Rietveld method [13].

3. Resolution of the structure The diffraction pattern is in quite good agreement with that published by Cousseins and Piiia P&ez [12] who claimed a tetragonal symmetry Table 1 Best set of the adjustable parameters

(a = 4.368 8, and c = 4.447 A), but a careful examination of some split peaks at high-angles clearly revealed that the true symmetry is lower than tetragonal. The diffraction pattern was then indexed in an orthorhombic primitive cell with and c= b = 8.8786(6) 8, a = 6.1791( 14) A, 6.16.55( 14) A. The conditions observed, limiting possible reflections (0 k I with k + I = 2n and h k 0 with h = 2n) are consistent with the centrosymmetric space group Pnma which was

for NH,CdF,.

Atom

Position

X

Y

z

B(A’)

N* Cd Fl F2

4c 4a 8d 4c

OS** 0 0.2848(47) -0.013( 10)

0.25 0 0.0216(16) 0.25

o.o** 0 0.7851(44) 0.0388(34)

2.8(5) 0.66(4) 1.7(2) 1.7(2)

a = 6.1791(14) A, b = 8.8786(6) A, c = 6.1655(14) A, SG Pnma

Vol= 338.25(4) A’ Step scan (” 20) : 0.02 20 range (“): lo-135 *Its nominal number (4) is allowed to refine to simulate NH:, its final value is 4.7(2). **Fixed values (see text). Reliability factors (%): R, = 3.79, R, = 8.37, R,, = 10.34, R, = 2.95.

Fig. 1. Comparison of observed (. .) and calculated (-) intensities for NH,CdF,. same scale.

The difference pattern appears below at the

A. Le Bail et al. I Crystal structure of NH,CdF,

Table 2 Characteristic

interatomic distances (A) and angles (“).

CdF, octahedra

N environment

2 x Cd-F1 :2.211(28) 2 x Cd-F1 : 2.212(27) 2 x Cd-F2:2.234(4) (Cd-F) : 2.219 88.7 < F,-Cd-F, < 91.3

2 x N-F1 :2.76(2) N-+2:2.84(2) N-F2:3.02(6) 2 x N-F1 : 3.06(2) N-F2:3.18(6) 2 x N-F1 : 3.21(2) N-F2: 3.32(2) 2 x N-F1 :3.46(l)

found for RbCaF, [9], and quoted [14] as one of the possible space groups resulting from a simple three tilts scheme of the octahedra. The refinement was started from the following model: N in 4c positions: x, a, z (x = 1 and z i= 0); Cd in 4a positions: 0, 0, 0; Fl in 8d positions X, y, z (x = a, y = 0 and z= i); F2 in 4c positions X, a, z (X = 0 and z = 0). In the course of the resolution, we decided to fix the x and z coordinates of the N atom at $ and 0, respectively, because they refined very near to these ideal values but with quite large esd (0.01). We have checked that this fact did not modify significantly the final results. The presence of a small quantity of CdF, was taken into account by the multipattern option of the Rietveld program. Table 1 presents the best values of the adjustable parmeters. The good agreement obtained between the calculated and observed patterns can be observed in fig. 1. Table 2 shows some characteristic distances and angles.

233

[15] where the distortions in the octahedra were considered to be negligible, while for KCdF, it is at most 0.001 A [16]. As a consequence, the resulting structure is consistent with a system of three coherent tilts of octahedra around the axes of the perovskite cubic cell; this would be denoted by a-b+a-, space group Pnma [14]. The structure resulting from the tilted octahedra is depicted in fig. 2. These rotations of the octahedra, though static of course, are similar to those occurring in the normal modes of the cubic phase that transform as the irreducible representation R,, and M,. Both imply rotations around the four-fold axis, but they differ in the sequence of the sense of rotation of the adjacent octahedra along that axis. In terms of these modes, the space group Pnma corresponds to the condensation of RISx, R25z and MS,, coinciding with the space group found for KCdF, below T, = 471 K. The rotation angles around the [l,O,O] and [O,O,l] pseudocubic axis (R,,, = RzSr), are 4.7”, while around [O,l,O] (M3y) the angle takes the value of 8.6”. This is quite comparable to 5” and 7.7”, respectively, found for KCdF, [16]. The only possible comparison with an ammonium perovskite is to the low temperature phase of NH,MnCl, [6]. There, it is reported to be Cmcm, consisting of slightly distorted octa-

4. Discussion The room temperature structure corresponds to a distorted cubic perovskite since its transition temperature is T, = 331.2 K. The CdF, octahedra which build up the high temperature phase do not seem to distort significantly, since within the standard deviation the Cd-F distances obtained from the fitting procedure are equal. The same feature has been found in TlCdF, and RbCdF,

Fig. 2. Low temperature distorted perovskite structure. The tilted CdF, octahedra are depicted around the NH:, here shown as the central sphere.

A. Le Bail et al. I Crystal structure of NH,CdF,

234

hedra with a rotation of 8.7” around the [O,O,l] axis. Thus, it is different to our determination for NH,CdF,. The N-F distances within the distorted dodecahedral cavity range from 2.76 to 3.46A. The shortest distances are close to 2.90 A, the value found in NH,AlF, 1171 where it clearly indicated the existence of N-H. . * F bonds. Six of them are smaller than the N-F distance in the cubic phase (3.1 A). Moreover, the four F- ions located at the shortest distance form a quasitetrahedral cage (of Cs symmetry), which is highlighted in fig. 3 by connecting the four F- atoms involved with staggered lines. As a consequence, the most probable orientation on the NH: ion would be that, in which the four protons point towards those four F- ions. In fact, for estimation purpose only, we have calculated the electrostatic energy of a regular tetrahedron in the site, rotating it around the different symmetry axes. Just the ratio between barriers can be assessed in this way. However, the absolute barrier values were estimated by scaling in energy with the known activation ener-

NH4CdF3

II

Fig. 3. Surrounding atoms of the NH: ion. The four nearest F- ions, here connected by staggered lines, form a nearly tetrahedral cage of Cs symmetry. Also shown is the orientation of the NH: ion that minimizes the electrostatic potential energy.

gy for stochastical jumps (E,lk, = 1950 + 50 K, [ll]), which was equated to the calculated energy difference between the ground state and the barrier at the saddle point, corrected for zero point energy. As a result, the proposed orientation was found to be 1049 K lower in energy than for any other, thus supporting our hypothesis of a preferential orientation. This energy difference is of the correct order of magnitude with respect to the anomalous enthalpy content AH/ R = 600 K measured by adiabatic calorimetry [4]. This present proposal for the low temperature orientation of the NH: ion is consistent with the site symmetry Cs, deduced from IR spectroscopy on partially deuterated Zn and Mn fluoroperovskites [18]. However, the proposed orientation has no other distinguishable one which is degenerate in energy. Consequently, the entropy content in the reorientational anomaly should be ASIR = In 6 = 1.79 while a value of ASIR = 1.2 has been reported [4]. Revisiting that work we have found the anomalous entropy was probably understimated through the interpolation of a very naive non-anomalous base line. Then, a larger entropy content of rotational origin is probably present well below T,. However, this would imply that the Cd compound is, in this respect, also quite different to the other members of the ammonium fluoroperovskites. This question will have to wait until the solution of the low temperature phases of the Zn or Mn compounds is found. From the comparison of the present results to the other members of the Cd series one notes the following facts. (a) The transition temperature from the cubic phase to a lower symmetry decreases for increasing cubic cell parameter. (b) In the cubic phase, the Cd-F distances are shorter than the expected values calculated from the average ionic R, = 1.285 and R,, = 0.95A [19], i.e. the parameter A = a/2 - (R, + R,,) is negative. Moreover, this apparent contraction decreases for increasing cubic cell parameter. (c) The NH,CdF, low temperature phase symmetry (Pnma) coincides only with the KCdF, at one lowest temperature, in spite of the very different cubic cell parameters. In fact the N-F

A. Le Bail et al. I Crystal structure of NH,CdF,

distances for NH,CdF,, in the Pnma structure, are comparable to the K-F distances in KCdF,, in the phase of coincident symmetry. (d) On the contrary, though the cell parameter for the Tl and Rb fluoroperovskite cubic phases are similar to that of NH,, the low symmetry phase (14/mcm) is different. From these perceptions one may conclude that the NH,’ ion plays a similar role to the other alkaline cations in fluoroperovskites. To argue this, one may first remember the geometrical Goldsmidt tolerance factor [20] R, + R, = tv2(R, + R,,) with X = K, Rb, Tl, Cs, in terms of the ionic radii. This has been used as an empirical rule for the stability of the perovskite structure. For t = 1 the atomic spheres fill the space exactly giving rise to a very stable cubic structure, which would not distort at any temperature, as seen for CsCdF, in the present discussion. If t < 1, the space left for the alkali ion is larger than its size and, as a consequence, structural packing instability sets in. The smaller R, the less stable the structure becomes, thus the phase transition will take place at a higher temperature. Indeed, this is the case for the XCdF, series, except for the NH: case, where its ionic radius depends on the particular compound. However, if one correlates the trend for the Goldsmidt parameter to that of the cell parameter, one could expect the NH,CdF, value to be intermediate between the Tl and K cases and, indeed, its transition temperature is intermediate. One concludes that the NH,CdF, follows the same trend in T, as the rest of the cubic perovskites.

235

The negative value of A = -0.04 8, for NH,CdF, cubic phase implies that the mean Cd-F distance in the NH, compound is slightly shorter than the sum of their atomic radii. This may come either from covalence effects or, more probably, because the F- ions are pushed out of the Cd-Cd line by thermal motion. In fact, to explain the Pm3m + Pnma transition in RbCaF, [9], similar to our case, the motion of the octahedra was assumed to be dominated by precession around the c axis, on one hand, [21] and through the condensation of the R,, and M, phonons to give account of the atomic displacement in the plane perpendicular to the c axis, on the other. The phase transition is then interpreted as having characteristics of both order-disorder (along the c axis) and displacive (in the plane perpendicular to the c axis). This model seems quite adequate in our case because two of the tilt angles are equal, while the third is different. Note that the A parameter in the NH, case is very similar to the Rb and Tl cases, while that for the K compound is larger. Notwithstanding that fact, the low temperature phase of the NH, compound is similar to the K case. We think that it reflects the influence of the NH: ion in the perovskite structure. From the above discussion one concludes that the NH: ion in the perovskite structure neither imposes a peculiar low temperature symmetry nor shows a significantly different degree of distortion, since NH,CdF3 follows the same trends as the other members of the series. However, it is worth noting that NH; has undoubtful in-

Table 3 Comparison of structural transition data for the series of Cd fluoroperovskites. ap: cubic cell parameter; T,: transition temperature; t: Goldsmidt parameter; A: A = a/2 - (R, + R,,); +: indicates the structural transition from high temperature to low temperature phase. The last column indicates the tilting of the octahedra in terms of condensed modes. Compound

-[ref.]

a,(A)

T,(K)

t

AD

Phases

485 471 332 191 124 _

0.925

-0.070

0.944 0.951

-0.040 -0.038 -0.036

Pm3m+ Bmmb + Pm3m -+ Pm3m-+ Pm3m-+

1.001

-0.003

Pm3m

KCdF,

[12,151

4.330

NH,CdF, TICdF, RbCdF, CsCdF,

[ill 1151 1151 1121

4.390 4.395 4.399 4.465

Condensed modes Bmmb Pnma Pnma 14/mcm 14/mcm

Rx, + I%, + R,,, Rx, + M,, + R,,, R 251 R 25r

236

A. Le Bail et al. I Crystal structure of NH,CdF,

fluence on the transition through an enhancement of T, and the different resulting symmetry with respect to the Rb and Tl compounds which have comparable cell parameters. It is also singular in that it distorts directly from the Pm3m symmetry to the Pnma one, without any intermediate phase. To our knowledge this is the first time that the structure of the low temperature phase of a compound of the NH,MF, family has been solved.

Acknowledgements This work was financially supported by a grant from the French-Spanish Committee for scientific cooperation Al 95, the CEE ST2P-0458-C and CICYT MAT 88-0302 Projects.

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