A structural phase-transition in K(Mg1?xCux)F3 perovskite

Phys Chem Minerals (1996) 23:141-150

9 Springer-Verlag 1996

E C . B u r n s 9 F.C. H a w t h o r n e 9 A . M . H o f m e i s t e r S.L. Moret

A structural phase-transition in K (Mgl_xCUx)F3 perovskite

Received July 26, 1995/Revised, accepted September 19, 1995

A complete solid-solution series between cubic (Pro3 m) KMgF3 and tetragonal (14/mcm) KCuF3 was synthesized at 730-735 ~ in an inert atmosphere. X-ray powder-diffraction at room temperature shows that the transition between the cubic and tetragonal perovskite structures in the series K (Mgl_~Cux) F3 occurs at x ~ 0.6. Rietveld structure-refinements were done for selected compositions, in the cubic phase, all parameters are linear with composition up to the transition point. At the transition point, there is a strong discontinuity in the cell volume; this is strongly anisotropic with expansion along the a axes and contraction along the c axis due to a pronounced axial elongation of the (Mg, Cu)F6 octahedron that increases with increasing Cu content. The phase transition is first-order, with a discontinuity of ~2% in the symmetry-breaking strain at x~. It is proposed that the phase transition in K (Mg, Cu)F3 is due to the onset of the cooperative Jahn-Teller effect. Compositional relationships for lattice vibrations in this solid solution were established using thin-film infrared spectroscopy. A phase transition occurring above 60 mole % KCuF3 is indicated by the appearance of one of the two modes expected for the tetragonal phase; the weaker mode is not resolved below 80 mole % KCuF3. Modes common to both structures vary smoothly and continuously across the binary; however, frequencies do Abstract

Peter C. Burns (~)~ 9Frank C. Hawthorne Department of Geological Sciences, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2 Anne M. Hofmeister Department of Earth and Planetary Sciences, Washington Universityin St. Louis, Campus Box 1169, St. Louis, MO 63130-4899, U.S.A. Stephanie L. Moret Department of Geosciences, Oregon State University,Corvallis, OR 97331-5506, U.S.A.

Present Address: J Department of Earth and Planetary Sciences, University of New Mexico, Albuquerque, NM 87131-1116, U.S.A.

not depend linearly on composition, nor is mode-softening discernable. Two-mode behaviour is observed only for the bending motion of the cubic phase, because this peak alone has non-overlapping end-member components.

Introduction The properties and structures of fluoride perovskite, AI+M2+F3, have been extensively studied (i.e., Rodriguez et al. 1991; Hofmeister and Billips 1991; Watson etal. 1992; Baldochi and Gesland 1992; Katrusiak and Ratuszna 1992; Bellafrouh etal. 1992; Zhao etal. 1993a, b; Maslen etal. 1993; Boumriche etal. 1994; Baldochi eta/. 1994; Fowler etal. 1995). The system K(Mg, Cu)F3 is of interest because it exhibits a phase transition between two types of perovskite structures and because the phase transition may be driven by the Jahn-Teller effect. Structures which contain octahedrally coordinated r6JCu2+ are highly susceptible to Jahn-Teller instability associated with the d 9 metal in an octahedral ligand-field. Almost invariably, The Cu2+~6 (~0=unspecified ligand) octahedron is distorted such that there are four short Cu2+-(~ equatorial bonds and two long Cua+-(~ apical bonds, a (4+2) distortion (Eby and Hawthorne 1993). An example of this occurs in the K (Mg, Cu 2+) F~ system. Schmitz-Dumont and Grimm (I 967) synthesized five samples of intermediate composition in this series, and reported X-ray diffraction and optical spectra for each composition. The KMgF3 structure crystallizes with the cubic perovskite arrangement, space group Pm 3 m; Mg occupies J the 1 a position with point symmetry m 3m, and is surrounded by six ligands in a holosymmetric octahedral i arrangement. Two modifications of the KCuF3 structure ~ ' are known (type a and type d; Okazaki 1969 a, b) but the j type-a structure is the most common (Tanaka e t a l . 1979); only thetype-a structure was encountered in this ) study. The type-a structure is tetragonal, space group }

142

14/mcm, and is a distorted derivative o f the c u b i c per-

100~20. The powder patterns indicated K (Mg~_ xCu~) F3 to be the dominant phase in each product, with very minor tenorite (CuO) and/or cuprite (Cu20) present in the copper-rich products as surface oxidation on the pellets. Unit-cell parameters were obtained using the Appleman and Evans (1973) least-squares refinement program (Table 1). The transition from the cubic structure to the tetragonal structure occurs at xc~0.6, based upon diffractionpeak splitting. The first synthesis product at x=0.65 appears cubic but with distinct peak-broadening. A second product synthesized at the same composition contains both cubic and tetragonal phases (dominantly tetragonal), suggesting that the transition occurs at xc~0.6. Samples were prepared for Rietveld data-collection by gently back-pressing the powders into an aluminum sample-holder. The top surface of the sample was serrated with a razor blade to minimize preferred-orientation effects. Step-scan data were collected using the experimental conditions given above. A step size of 0.05~ and a count time of 5 s/step was used over the range 20-135~ The X-ray powder diffraction patterns for samples with x ranging from 1.00 to 0.50 are shown in Fig. 1.

ovskite a r r a n g e m e n t ; C u 2§ o c c u p i e s the 4 d p o s i t i o n with p o i n t s y m m e t r y mmm, and is s u r r o u n d e d b y six ligands in an e l o n g a t e d o c t a h e d r a l a r r a n g e m e n t , a ( 4 + 2 ) distortion. Here we r e p o r t the synthesis, s t r u c t u r a l and s p e c t r o s c o p ic c h a r a c t e r i z a t i o n o f the series K(Mg~_~Cu~)F3, 0--0.65 are tetragonal. At 100 cm ~, the),-axis intercept for each spectrum is 0.1 absorbance units. Overtones or LO components are indicated by LO. Assignments are indicated for KCuF3

146 Table3 Variation in infrared band frequency (cm-') for K (Mg I_xCUx)F3 perovskites x cubic 0.000 0.100 0.200 0.300 0.400 0.500 0.575

v3 471.2 471.4 477.6 481.4 481.6 483.9 485.6

tetragonal 0.650 492.6 0.700 491.8 0.750 494.1 0.800 494.1 0.850 496.7 0.900 497.9 0.950 494.4 1.000 495.0

(vo+T) v4-(Mg) V4-(CILI ) V6

357.2

301.9 300.7 300.6 301.9 298.2 294.2 286.4

R

T

% KCuF3

168.2 166.2 165.6 164.0 160.6 156.7 153.1

254.9 256.0 252.2 252.3 251.9 247.6

280.9 277.8 275.0 275.7 276.4 273.8

247.6 247.2 245.8 245.5 247.1 249.7 249.8 251.6

211.7 211.2 207.5 207.6 207.6 202.6 201.5

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reflectivity spectra (Perry and Young 1967; Nakagawa 1973; Barker etal. 1968; Hofmeister and Billips 1991) which have three modes with longitudinal and transverse components at 562-455, 362-298 and 196-164 cm 1. Three strong IR fundamentals dominate the spectrum and several weaker modes occur near positions compatible with overtones or combination modes. In the absorbance spectrum, additional weak modes occur near 250 and 400 c m - J , which are attributed to the forbidden inactive mode, v 6 and an overtone v6+T. Frequency differences between absorption (Table 3) and reflection data can be large, up to 20 cm 1 for the intense modes. This is due to the fact that the absorptivity is related to both the i m a g i n a r y part of the dielectric function e2 and to the real part, n, of the optical function: a (v) = 2 row2 (v)/n (v)

(1)

(Wooten 1972), and that the TO positions are at the maxima in ~2 but lie on the sides of the m a x i m a in n. Differences are small for weak or sharp modes because maxima in e2 and m i n i m a in n are close together, yielding similar m o d e positions in the absorptivity. The absorption spectrum for KCuF 3 (Fig. 5, top) resembles those observed for tetragonal K C a F 3 and K C d F 3 (Karamyan 1979), excepted that there is an additional weak m o d e at 160 cm -1 on the flank of the translational mode. Such a feature would have been difficult to detect in previous low-resolution powder spectra. It's existence is consistent with low-temperature reflectance measurements of tetragonal K M n F 3 (Stobel and Geick 1979). IR thin-film spectra of the solid solutions (Fig. 5, middle) have intensity patterns and frequencies transitional with those of the end-members. Modes are distinct, although often broader, and weak combinations (e.g. v6+T) and overtones can be traced partially across the series. The high-frequency octahedral stretch and the low-frequency translation associated with the cubic

Fig. 6 Powder-dispersion infrared spectra of samples near the transition. The mode condensed from F2u is visible in the least-distorted tetragonal sample

structure change little in either position or intensity across the series. However, the deformation v 4 clearly follows t w o - m o d e behaviour due to the large mass difference between Cu and Mg. This behaviour is limited to v 4 because, unlike the other modes, its e n d - m e m b e r frequencies do not overlap (see Chang and Mitra (1968) for discussion of theoretical behaviour of vibrational modes with composition). The same behaviour is observed for solid solutions of KMgF3 and cubic KNiF3 (Perry and Young 1967; Barker etal. 1968). As the transition is approached, the two modes associated with the tetragonal phase show little change in frequency but decrease rapidly in intensity. In the thinfilm spectra, these two modes could not be detected for low distortions. To examine these weak modes, powder spectra (Fig. 6) were collected for samples from 6 5 85 mole % K C u F 3. This technique enhances weak modes owing to the variety of sample thicknesses present (Hofmeister 1995). Even in concentrated powder dispersions, the weaker R m o d e is only resolved for high distortions near the Cu e n d - m e m b e r (a very weak shoulder appears near 1 6 0 c m -1 > 8 5 m o l e % KCuF3, Fig. 6), whereas the stronger v 6 mode is seen for all samples indicated to be tetragonal by X-ray diffraction. The disappearance of the R m o d e is likely due to simultaneous loss of intensity and broadening due to solid solution. Mode positions for K(Mg1_xCUx)F ~ are shown as a function of composition in Fig, 7. Most of the trends are fairly flat, but each m o d e behaves differently. The stretching frequency is the only m o d e which increases with K C u F 3 content; slight deviations f r o m linearity are within the experimental uncertainty of the position for

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X Fig. 7 Thin-film infrared frequency as a function of composition along the K(Mgj ~Cux)F3 join. For modes with two-mode behaviour, the trends to not extend fully across the compositional axis. Filled circle: v3; triangle: v4; open circle: translations of the K + cation; square: LO component of v4; diamond: v 6 which is present in the cubic phase but IR inactive; hexagon: the weaker tretragonal mode originating from folding in of the R point of the cubic phase

this broad and intense mode. In contrast, the translation decreases monotonically with KCuF 3 content, in accord with the interaction between K and F decreasing as the unit cell expands; this trend is linear above 20 mole% KCuF 3 . The most interesting behaviour occurs for the v4 deformation. The frequency of the component associated with Mg has a sigmoidal trend, being constant near the end-members with a smooth decrease from 30 to 75 mole % KCuF 3. The region of decreasing frequency spans the phase transition. The frequency of the Cu component seems to decrease as the Cu content increases, but may increase slightly above 75% KCuF 3, and the minimum in the curve does not occur at the cubic-tetragonal phase transition as determined by X-ray diffraction. The frequency o f the tetragonal mode, which condenses from the R point of the cubic structure, is constant, whereas v 6 increases slightly but linearly towards the Mg end-member. The stronger v 6 mode decreases in intensity towards the transition point (Figs. 5, 6), and ceases by 65 mole% KCuF 3 (note, however, that the overtone (v6+T) is observed at 65 mole % and possibly at 57.5%). This relationship could not be quantified because Fourier self-deconvolution did not adequately resolve these two modes, and the narrow range of composition over which the weaker R mode can be traced is insufficient to observe any structurally associated changes.

0.8

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X The volume strain as a function of composition for K(Mg 1 • Circles: Vs; triangles: V~

Fig. 8

Discussion Phase-transition mechanism

14/mcm is an isotropy subgroup o f P m 3 m, satisfying the criteria for a continuous transition. The basis functions of the active irreducible representation ( R f in the nomenclature of Stokes and Hatch 1988) do not transform as the components of the spontaneous strain, and thus the strain does not couple linearly to the order parameter. Hence, this transition is an improper ferroelastic (Toledano and Toledano 1987). In addition, the Icentered cell of the tetragonal phase has four times the cell volume of the parent cubic phase. This doubling of the primitive cell indicates that a zone-boundary distortion must be active in the transition. The unit-cell volume of K (Mg, Cu) F3 varies linearly with composition in the cubic phase, with a discontinuity at the transition point, followed by non-linear variation with composition in the tetragonal phase (Fig. 2). A useful guide to the behaviour of the macroscopic order parameter is given by the volume strain: Vs-

V-V9 v9

(2)

where V is the volume of the tetragonal phase at a given : composition, and V9 is that of the cubic phase extrapolat- : ed to the same composition (Fig. 2). In general, Vs is l expected to vary linearly with Q2 (Carpenter 1992). The l variation of both Vs and V 2 is non-linear with composition i (Fig. 8), and discontinuities in Vs and Vasare observed at Xc. ! For the tetragonal phase, the spontaneous strain corn- : ponents e11, e22 and e33 are given by: a-a el 1=e22

-

a9

o (3)

148 C--

e33--

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(4)

Co

where a o and Co are the a and c unit-cell parameters extrapolated from the cubic phase (Fig. 2). The symmetrybreaking strain for the cubic-to-tetragonal transition is then given by: e,-

(2e33--el 1--e22)

~/~

(5)

Figure 9 shows the variation of e t and e 2 with composition for K (Mg I_xCG) F3. Neither e, nor e 2 are linear with composition, and there is a marked discontinuity in e t at x=xo. Thus, this is a first-order transition, with a discontinuity in et at the transition point of ~2%. As noted above, the Rietveld refinement has shown that K(Mgl_xCG)F3, with x=0.575 is cubic at room temperature. However, examination of Fig. 8 shows that the volume strain has a tail which extends past xo to at least x=0.575. Also, examination of Fig. 7 shows that some of the vibrational modes in the infrared spectra for intermediate compositions also vary significantly in the cubic phase prior to the phase transition. This effect is the most pronounced for the v4 mode at ~ 300 c m 1. The overtone v6+T is present at x=0.575, but not in any of the other cubic samples, suggesting some relaxation of selection rules attributable to distortions of the Cu octahedra. The value of the symmetry-breaking strain et for endmember KCuF3 is ~4.5% and the volume strain is ~2.5% (Figs. 2, 9). These spontaneous strains are very large compared to many improper ferroelastic transitions, similar to the P2/c--~P 1 transition in (Zn, Cu)WO4 (sanmartinite-cuproscheelite) (Schofield and Redfern 1992). We have found similar large spontaneous strains associated with the P 42/mnm-+ P 21/n transition

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in (Mg, Cu)F2 (unpublished). These three examples suggest that such large spontaneous strains are associated with transitions in crystals containing octahedrally coordinated Cu 2+. Substitution of small quantities of Cu 2+ into the cubic KMgF3 perovskite structure results in local distortion centres associated with each CuF6 (4+2)-distorted octabedron. Supporting evidence has been obtained through electron paramagnetic resonance spectroscopy, which shows that very dilute concentrations of Cu 2+ in octahedral coordination in a host structure result in local distortions due to the Jahn-Teller effect (i.e., Rubins and Drumheller 1987; Rubins etal. 1984). When a (4+2)distorted CuF6 octahedron is embedded in the cubic perovskite structure, there are three choices of distortion direction. The octahedron may be elongated in any of the three symmetrically equivalent octahedral directions in the cubic structure. For values of 0--