Eur. J. Mineral. 2011, 23, 425–435 Published online March 2011
K2Ca3Si3O10, a novel trisilicate: high-pressure synthesis, structural, spectroscopic and computational studies ¨ BBENS, REINHARD KAINDL and VOLKER KAHLENBERG* ERIK ARROYABE, FELIX PRECHTEL, DANIEL M. TO
Institut fu¨r Mineralogie und Petrographie, Universita¨t Innsbruck, Innrain, 52, 6020 Innsbruck, Austria *Corresponding author, e-mail:
[email protected]
Abstract: Single crystals of K2Ca3Si3O10 have been obtained in a multi-anvil high-pressure synthesis experiment performed at 10 GPa and 1000 C. The compound adopts the monoclinic space group C2/c with four formula units per cell and the following lattice ˚ , b ¼ 10.6013(16) A ˚ , c ¼ 9.8221(19) A ˚ , b ¼ 118.079(13) , V ¼ 951.2(3) A ˚ 3. The crystal parameters (at 25 C): a ¼ 10.3539(19) A structure was determined from single-crystal X-ray diffraction data using direct methods (Mo-Ka radiation, 2ymax ¼ 59.53 , Rint ¼ 5.90 %) and refined to R(|F|) ¼ 5.64 % using 1042 observed reflections with I . 2s(I). The structure belongs to the group of oligosilicates consisting of [Si3O10] groups. The trimers of the anion complex are located in layers parallel to (001) at about z ¼ and 3 /4, respectively. Ca(1)-octahedra provide linkage between (1) the Si3O10 groups of a single layer by corner sharing of the equatorial oxygen atoms of the terminal tetrahedra and (2) the trimers belonging to adjacent sheets by corner sharing of the apical O-atoms. To ˚ , the remaining two crystallographically independent non-tetrahedral cation sites Ca(2) and K(1) are an upper limit of 3.3 A coordinated by 8 and 10 oxygen atoms, respectively. From a topological point of view the crystal structure of K2Ca3Si3O10 can be classified as a new type of mixed tetrahedral-octahedral framework. The thermal expansion of K2Ca3Si3O10 has been determined in the temperature range between 25 and 750 C. The temperature dependence of the cell volume can be described with a second-order polynomial: V(T) ¼ 0.00002(3)T2 þ 0.026(2)T þ 949.36(34). Structural investigations were completed by Raman spectroscopic studies. The assignment of the bands to certain vibrational species was aided by density functional theory (DFT) calculations. Key-words: crystal structure, high-pressure phase, potassium calcium silicate, thermal expansion, Raman spectroscopy, density functional theory computation.
1. Introduction Alkali–alkaline-earth silicates are of great interest for certain areas of technical mineralogy and industrial inorganic chemistry. The system Na2O-CaO-SiO2, for example, is of fundamental importance for the production of commercial soda-lime-glasses (Morey & Bowen, 1925; Varshneya, 1994). On the other hand, a constantly growing number of studies on the re-processing of residual materials like ashes and slags led to a revival of interest in the phase relationships among potassium calcium silicates. Within this context it is interesting to note that the detailed structural characterization of the ternary phases of this system started only recently (Kahlenberg et al., 2006; Arroyabe et al., 2009a, c) although the only comprehensive phase equilibrium study of the system K2O-CaO-SiO2 system was published 80 years ago by Morey et al. (1930). Compared to the number of investigations at ambient pressure, information concerning the formation and the stability of high-pressure alkali–alkaline-earth silicate phases is much more limited. In the field of Earth sciences a few studies focussed on the synthesis of Mg-bearing Na- and K-silicates as potential mineral phases of the Earth’s interior. The so-called phase-X, for example,
has the general formula A2-xM2Si2O7Hx (A ¼ K, Na, Ca, & (vacancies); M ¼ Mg; x ¼ 0–1) and has been discussed as a possible sink for Na and K in the mantle (Yang et al., 2001; Bindi et al., 2007; Mookherjee & Steinle-Neumann, 2009). Anhydrous as well as hydrous samples of phase-X have been prepared at 1250–1300 C and 10–16 GPa. The structure contains brucite-like layers (containing edge sharing MgO6-octahedra) that are connected by Si2O7-dimers and additional Na/K cations. Ringwood & Major (1971) as well as Gasparik (1989) synthesized sodium garnets with composition Na2CaSi5O12 and Na2MgSi5O12, respectively, at pressures of 15–18 GPa, which are structurally characterized by the simultaneous occurrence of [4]Si and [6]Si. Fourand six-fold coordinated silicon has been also observed in the crystal structure of a sodium calcium silicate with idealized composition Na2CaSi6O14 (Gasparik et al., 1995). The compound is built from [Si5O14] sheets. Linkage between adjacent layers is provided by [SiO6]-octahedra as well as Na/Ca atoms residing on an eight-fold coordinated site. In the course of an ongoing research project on the crystal chemistry of potassium calcium silicates we became interested in the high-pressure behaviour of K2Ca2Si2O7. Actually, we wanted to answer the question whether the ambient pressure form of this compound that 0935-1221/11/0023-2096 $ 4.95
DOI: 10.1127/0935-1221/2011/0023-2096
# 2011 E. Schweizerbart’sche Verlagsbuchhandlung, D-70176 Stuttgart
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has been found and structurally characterized in our laboratory only recently (Arroyabe & Kahlenberg, 2011) can be transformed into a phase-X type structure. The present manuscript reports the results of a crystallographic and spectroscopic characterization of a previously unknown silicate with a slightly different composition that was obtained in an exploratory experiment performed at 10 GPa and 1200 C.
integration as well as reduction of the data. A numerical absorption correction using 11 indexed faces has been applied using the program X-Shape (STOE & Cie GmbH, 2005b). Structure solution and consecutive least squares refinement calculations were carried out with the programs SIR2004 (Burla et al., 2005) and SHELXL97 (Sheldrick, 2008), respectively, both embedded in the WinGX program suite (Farrugia, 1999). Structure determination
2. Experimental details
Table 1. Crystal data, measuring conditions and refinement parameters for K2Ca3Si3O10.
2.1. Synthesis Half a gram of stoichiometric K2Ca2Si2O7 served as starting material. Therefore, dried K2CO3 (AlfaAesar, puratronic), CaCO3 (AlfaAesar, 99.995 %) and SiO2 (AlfaAesar, 99.995 %) in the ratio of 1:2:2 were homogenized in a planetary mill under ethanol, subsequently transferred to a platinum crucible covered with a lid and fired from 300 to 900 C within 10 h. The specimen was then isothermed at the target temperature for 2.5 days and finally quenched in air. Approximately 25 mg of the material were sealed into a platinum capsule with an outer (inner) diameter of 2.0 (1.8) mm and a length of about 3.5 mm. The high-pressure experiment was performed in a 1000 t press, equipped with a Walker-type multi-anvil module (both from Voggenreiter, Mainleus, Germany) using 18/ 11 assemblies. Experimental and calibration conditions were similar to those described by Walker et al. (1990) as well as Keppler & Frost (2005), respectively. The temperature was measured with a W3Re97-W25Re75 thermocouple. Both, pressure and temperature were computer-controlled during the entire experiment which was performed at 10 GPa and 1200 C. The temperature was raised within 40 minutes followed by a dwell-time of 47 h. The run was terminated via turning off the power, which quenched the specimen within less than 10 s below 200 C, and releasing the pressure over night. After the experiment, the Pt-capsule was embedded in epoxy resin and polished to recover the sample. The extracted run product was immediately covered with Paratone-N inert Oil for the sake of preventing possible interactions with moisture. A very first examination using a polarization microscope revealed the sample to consist of small birefringent crystals with cubical habit as well as a glassy matrix. 2.2. X-ray data collection and structure analysis at ambient temperature A single crystal (0.092 0.052 0.024 mm) of the highpressure run with good optical quality was selected for the X-ray diffraction experiment and mounted on the tip of a glass fibre using nail hardener. Data were collected at ambient conditions on a STOE IPDS-II single-crystal diffractometer (Table 1). The X-Area software package (STOE & Cie GmbH, 2005a) was employed for collection,
Crystal data Unit cell dimensions
Volume Chemical formula Space Group Z Dcalc m Crystal form, size Data collection Diffractometer Radiation X-ray power Collimator Monochromator Temperature Detector to sample distance Rotation width in o No. of frames measured Time of exposure per frame 2y-range Reflection ranges Reflections measured Absorption correction R(int) Refinement Unique reflections Observed unique reflections (I . 2s(I)) Final R indices (I . 2s(I)) R indices (all data) Goodness-of-fit on F2 Refined parameters Extinction coefficient Final Drmin; Drmax Data collection (HT-series) Diffractometer Radiation X-ray power Collimator Monochromator Temperatures Detector to sample distance Rotation width in o No. of frames measured Time of exposure per frame
˚ a ¼ 10.3539(19) A ˚ b ¼ 10.6013(16) A ˚ c ¼ 9.8221(19) A b ¼ 118.079(13) ˚3 951.2(3) A K2Ca3Si3O10 C 2/c 4 3.091 g/cm3 3.038 mm1 Fragment, 0.092 0.052 0.024 mm STOE IPDS-II ˚ MoKa, l ¼ 0.71073 A 50 kV, 40 mA 0.5 mm Graphite 25 C 100.0 mm 1.0 180 10.0 min 2.29–59.53 14 h 14, 14 k 13, 13 l 13 4434 Analytical, using 11 indexed faces 0.0590 1228 1042 R1 ¼ 0.0564, wR2 ¼ 0.0984 R1 ¼ 0.0705, wR2 ¼ 0.1021 1.299 84 0.0013(3) ˚ –3 0.549; 0.693 e A STOE IPDS-II ˚ MoKa, l ¼ 0.71073 A 50 kV, 40 mA 0.5 mm Graphite 25, 150, 300, 450, 600, 750 C 100.0 mm 1.0 180 5.0 min
K2Ca3Si3O10 – a novel trisilicate
Table 2. Atomic coordinates and equivalent isotropic displacement ˚ 2] for K2Ca3Si3O10. parameters [A Wyckoff-site Ca(1) Ca(2) K(1) Si(1) Si(2) O(1) O(2) O(3) O(4) O(5)
4e 8f 8f 8f 4e 8f 8f 8f 8f 8f
x
y
z
U(eq)
0 0.8922(1) 0.1465(1) 0.7840(1) 0 0.8113(4) 0.1295(4) 0.8570(4) 0.1180(4) 0.9409(4)
0.3692(1) 0.1185(1) 0.3754(1) 0.3631(1) 0.1601(2) 0.5031(3) 0.2542(3) 0.3565(3) 0.1867(3) 0.0848(3)
0.7500 0.5149(1) 0.5111(1) 0.2915(1) 0.2500 0.7307(4) 0.2584(4) 0.4797(4) 0.7242(4) 0.0921(4)
0.011(1) 0.013(1) 0.015(1) 0.010(1) 0.009(1) 0.015(1) 0.017(1) 0.015(1) 0.015(1) 0.014(1)
revealed that the crystals correspond to a previously unknown potassium calcium silicate phase with composition K2Ca3Si3O10. Final full-matrix least-squares refinement cycles including fractional coordinates as well as anisotropic displacement parameters for all atoms converged to a residual of R1 ¼ 0.0564 for 84 parameters and 1042 reflections with I . 2s(I) (Table 1). The final difference electron density map turned out to be featureless, with maxima and minima ˚ 3. of 0.693 and 0.549 eA Refined atomic coordinates, anisotropic displacement parameters as well as selected interatomic distances and angles are given in Tables 2–4, respectively. Figures showing structural details were prepared using the program ATOMS5.1 (Dowty, 2000). 2.3. High-temperature X-ray data collection In order to study the high-temperature evolution of the crystal structure, data at elevated temperatures were recorded from the same single crystal that was used for the acquisition at ambient conditions. For this purpose, the crystal was dissolved from the glass fibre with acetone and subsequently clamped in the constricting part of an especially thinned-out 0.1 mm quartz-glass capillary. A Heatstream device (as provided by Stoe) was used for the high-temperature single-crystal diffraction experiment.
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This furnace (mounted underneath the sample on the omega axis) supplied a vertical flow of hot nitrogen gas to heat the sample. More details concerning the experimental setup can be found in the paper of Kru¨ger & Breil (2009). Data were collected at temperatures of 25, 150, 300, 450, 600 as well as 750 C. Experimental parameters, equally set for all runs, are summarized in Table 1. No indications for the existence of a phase transformation could be detected. The unit-cell volumes as well as all lattice parameters depend almost linearly on temperature. For example, the increase of the cell volume as a function of temperature can be approximated by the following second-order polynomial: V(T) ¼ 0.00002(3)T2 þ 0.026(2)T þ 949.36(34) (Fig. 1). 2.4. Raman-spectroscopy Confocal Raman spectra of the same single crystal that was used for the X-ray diffraction experiment were obtained with a HORIBA JOBIN YVON LabRam-HR 800 Raman micro-spectrometer. The sample was excited using the 532 nm emission line of a 30 mW Nd-YAG-laser and an OLYMPUS 100 objective (N.A. ¼ 0.9). Size and power of the laser spot on the surface were approximately 1 mm and 5 mW. The spectral resolution, determined by measuring the Rayleigh line, was about 2 cm1. The dispersed light was collected by a 1024 256 open electrode CCD detector. Confocal pinhole was set to 1000 mm. Spectra were recorded unpolarized. The data were corrected assuming second-order polynomial background and fitted to Gauss-Lorentz functions. Accuracy of Raman line shifts, checked by regular measuring a Ne spectral calibration lamp, was in the order of 0.5 cm1. A Raman spectrum of the present compound is given in Fig. 2.
3. Description of the structure K2Ca3Si3O10 belongs to the group of oligosilicates with trimeric basic building units. The central Si(2)O4-tetrahedron of the trisilicate group shares two symmetrically equivalent O(2) ligands with the neighbouring two
˚ 2] for K2Ca3Si3O10. The anisotropic displacement factor exponent takes the form: 2p2 Table 3. Anisotropic displacement parameters [A 2 2 [h a* U11 þ . . . þ 2hka*b*U12].
Ca(1) Ca(2) K(1) Si(1) Si(2) O(1) O(2) O(3) O(4) O(5)
U11
U22
U33
0.011(1) 0.012(1) 0.014(1) 0.011(1) 0.010(1) 0.018(2) 0.016(2) 0.017(2) 0.012(2) 0.015(2)
0.011(1) 0.012(1) 0.017(1) 0.009(1) 0.008(1) 0.013(2) 0.017(2) 0.018(2) 0.017(2) 0.016(2)
0.010(1) 0.016(1) 0.014(1) 0.010(1) 0.009(1) 0.015(2) 0.021(2) 0.013(2) 0.017(2) 0.013(2)
U23 0 0.002(1) 0.002(1) 0.000(1) 0 0.000(1) 0.002(1) 0.001(1) 0.001(1) 0.002(1)
U13
U12
0.005(1) 0.007(1) 0.007(1) 0.006(1) 0.005(1) 0.008(2) 0.010(2) 0.008(1) 0.007(2) 0.007(1)
0 0.001(1) 0.000(1) 0.001(1) 0 0.004(1) 0.004(1) 0.001(1) 0.002(1) 0.001(1)
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˚ ] up to 3.3 A ˚ and selected angles Table 4. Interatomic distances [A [ ] for K2Ca3Si3O10. The calculated values refer to the results of the DFT calculations. Atoms
Observed
Calculated
Deviation
Ca(1)-O(1) (2x) Ca(1)-O(3) (2x) Ca(1)-O(4) (2x) Ca(2)-O(5) Ca(2)-O(4) Ca(2)-O(5) Ca(2)-O(3) Ca(2)-O(3) Ca(2)-O(1) Ca(2)-O(4) Ca(2)-O(2) K(1)-O(1) K(1)-O(2) K(1)-O(2) K(1)-O(5) K(1)-O(3) K(1)-O(3) K(1)-O(1) K(1)-O(4) K(1)-O(2) K(1)-O(5) Si(1)-O(4) Si(1)-O(1) Si(1)-O(3) Si(1)-O(2) Si(2)-O(5) (2x) Si(2)-O(2) (2x) O(4)-Si(1)-O(2) O(3)-Si(1)-O(2) O(4)-Si(1)-O(3) O(1)-Si(1)-O(2) O(1)-Si(1)-O(3) O(4)-Si(1)-O(1) O(2)-Si(2)-O(2) O(5)-Si(2)-O(2) (2x) O(5)-Si(2)-O(2) (2x) O(5)-Si(2)-O(5) Si(2)-O(2)-Si(1)
2.349(3) 2.357(3) 2.365(3) 2.261(3) 2.385(4) 2.435(3) 2.550(3) 2.619(3) 2.671(4) 2.712(4) 2.960(4) 2.722(3) 2.726(4) 2.729(4) 2.797(3) 2.844(3) 2.872(4) 2.910(3) 3.008(4) 3.115(4) 3.237(3) 1.613(3) 1.615(3) 1.637(3) 1.669(3) 1.589(3) 1.642(3) 105.58(18) 106.03(18) 106.60(18) 106.71(18) 112.76(18) 118.31(18) 105.2(3) 106.53(17) 109.05(17) 119.6(3) 160.6(3)
2.335 2.357 2.386 2.267 2.371 2.407 2.532 2.679 2.742 2.609 3.067 2.708 2.683 2.695 2.831 2.842 2.856 2.897 3.084 3.215 3.273 1.618 1.621 1.648 1.674 1.598 1.654 105.700 106.970 105.530 106.620 112.900 118.410 106.130 106.130 107.140 120.510 155.430
0.014 0.000 0.021 0.006 0.014 0.028 0.018 0.060 0.071 0.103 0.107 0.014 0.043 0.034 0.034 0.002 0.016 0.013 0.076 0.100 0.036 0.005 0.006 0.011 0.005 0.009 0.012 0.120 0.940 1.070 0.090 0.140 0.100 0.930 0.400 1.910 0.910 5.170
Si(1)O4-tetrahedra. Although the maximum symmetry of a T3O10 group is mm2, the Si3O10 moiety in K2Ca3Si3O10 shows only point symmetry 2. Amongst silicates made up of trimers, two principal types can be distinguished: (a) linearly or slightly bent moieties and (b) strongly bent or horseshoe-like arrangements (Wierzbicka-Wieczorek et al., 2010). In our case (Fig. 3), the Si-Si-Si angle exhibits a value of 97.54 . Hence, the present compound can be allocated to type (b). The Si-O distances within each trimer follow the ˚ for expected trend (Liebau, 1985) with 1.613–1.669 A ˚ for Si(2). More precisely, two Si(1) and 1.589–1.642 A groups of Si-O bond lengths can be distinguished. The average distance between Si and the bridging O(2)-atoms ˚ , i.e. considerably longer than the of the trimer is 1.656 A ˚ ). The O-Si-O angles range remaining eight bonds (1.614 A from 105.6 to 118.3 for Si(1) and from 105.2 to 119.6 for
Fig. 1. Evolution of the unit cell volume of K2Ca3Si3O10 as a function of temperature. Standard uncertainties are within the size of the symbols.
Fig. 2. Raman spectrum of a K2Ca3Si3O10 single crystal. Vertical bars represent wave numbers of experimentally determined band positions (top) and calculated vibrational modes (bottom).
Si(2). A quantitative measure of the polyhedral distortion can be expressed by the quadratic elongation l and the angle variance s2 (Robinson et al., 1971). The corresponding values for these parameters are l ¼ 1.006 and s2 ¼ 26.67 for Si(1) and l ¼ 1.006 and s2 ¼ 27.44 for Si(2). These values are comparable with those obtained in other silicates containing [Si3O10]-moieties. The trimers of the anion complex are located in layers parallel to (001) at about z ¼ and 3/4, respectively. Neighbouring layers are related by centres of inversion resulting in an . . . ABABA . . . stacking sequence (Fig. 4). Within a single layer the trimers are arranged in a zigzag pattern as shown in Fig. 5, where a single sheet is shown in a projection perpendicular to (001). The M(1)-octahedron provides linkage between (a) the Si3O10 groups of a single layer by corner sharing of the equatorial oxygen atoms O(1) and O(4) of the terminal
K2Ca3Si3O10 – a novel trisilicate
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Fig. 3. Side view of a single [Si3O10]-group in K2Ca3Si3O10. Thermal displacement ellipsoids are drawn at the 50 % probability level.
Fig. 4. The trimers of the anion complex are located in layers parallel to (001) stacked in an . . . ABABA . . . sequence.
tetrahedra and (b) the trimers belonging to adjacent sheets by corner sharing of the apical O(3)-atoms. To an upper ˚ , the remaining two crystallographically limit of 3.3 A independent non-tetrahedral cation sites M(2) and M(3) are coordinated by 8 to 10 oxygen atoms.
To a certain extent, the assignment of the 8 potassium and 12 calcium atoms within the unit cell to the three different M-sites is ambiguous. Since Kþ and Ca2þ are isoelectronic ions, site occupancy refinements using X-rays are not suitable for the discrimination between
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Fig. 5. Projection of a single layer containing trimeric units and Ca(1)-octahedra perpendicular to (001). The trimeric units of the anion complex are interlinked via equatorial oxygen atoms of the Ca(1)-octahedra.
these two species. Finally, bond distance considerations indicated that the sites M(1) and M(2) are preferentially occupied by calcium, whereas potassium is enriched on the M(3) position. Bond valence sum calculations using the bond valence parameter set of Brese & O’Keeffe (1991) corroborated this assumption. A calculation where the Mpositions were treated as pure Ca and K sites, respectively, resulted in the following values: M(1) ¼ Ca(1), 2.09 v.u.; M(2) ¼ Ca(2), 1.79 v.u.; M(3) ¼ K(1), 1.39 v.u. The slight under- as well as over-bonding of the last two sites may point to minor K $ Ca substitutions. The arrangement of the atoms in the cationic sub-structure can be described as follows. The Si atoms in the tetrahedral centres of adjacent layers are located near six corners of imaginary distorted cubes with mean edge ˚ centred about the Ca(2) and K(1) lengths of about 4 A cations, respectively. The remaining two vertices of each cube are occupied by two of the octahedrally coordinated Ca(1) ions. A different understanding of the structure can be obtained from a description as a three-dimensional mixed tetrahedral-octahedral framework with a specific [TO4]:[MO6] ratio of 3:1. The method to analyze these so-called ‘‘MT’’-frameworks by topological methods has been successfully applied by Ilyushin & Blatov (2002) to the large group of natural and synthetic zirconosilicates and their analogues.
Principally, topologically ideal MT frameworks with exclusively bridging O-atoms have to be distinguished from MT frameworks with O gaps where terminal oxygens can occur as well. Actually, the MT framework of K2Ca3Si3O10 can be allocated to the second group. According to the topological approach the structures can be classified using the following concepts: the primary structural units (MO6 octahedra and TO4 tetrahedra) are linked into larger clusters or polyhedral micro ensembles (PME) by sharing common vertices. For the MT6 ensembles, for example, from a topological point of view, 12 different types have to be distinguished. K2Ca3Si3O10 belongs to the so-called type A (Fig. 6), i.e. the six tetrahedra, which are directly linked to a central CaO6-polyhedron, do not share any common oxygen ligands. The topological representation of the whole crystal structure is accomplished by a graph composed of the vertices (sites of M, T and O atoms) and edges (bonds) between them. The coordination sequence in turn is a set of integers {Nk}, k ¼ 1, . . . ,n, where Nk is the number of sites in the kth coordination sphere of the M, T or O-atom which has been selected to be the central one. The corresponding coordination sequences for Ca(1) and the two silicon sites up to n ¼ 12 have been determined using the program TOPOS (Blatov, 2006) and are listed in Table 5. The comparison with the tables given by Ilyushin & Blatov
K2Ca3Si3O10 – a novel trisilicate
Fig. 6. Side view of a single polyhedral micro ensemble (PME) of the MT-framework. The six tetrahedra which are interlinked with the octahedron around Ca(1) via common corners do not share any common oxygen ligands.
Table 5. Coordination sequences of the octahedrally (Ca(1)) and tetrahedrally (Si(1), Si(2)) coordinated nodes of the MT-framework in K2Ca3Si3O10. Coordination sequences Nk (k ¼ 1–12) Atom Ca(1) Si(1) Si(2)
1 6 4 4
2 3 4 6 18 13 4 18 13 2 6 5
5 50 36 24
6 7 32 88 26 100 20 56
8 9 49 164 54 136 35 126
10 11 84 214 76 252 68 174
12 111 119 91
(2002) reveals that K2Ca3Si3O10 represents a new MTframework type. Figure 7 shows the whole MT framework as well as the more irregularly coordinated cation sites that are located within tunnels of the framework running parallel to [110].
4. DFT-calculations and Raman modelling The vibrational frequencies of K2Ca3Si3O10 have been computed from first principles. The program CRYSTAL06 (Dovesi et al., 2006) was employed, using Gaussian basis sets and calculating frequencies from numerically computed second derivatives of the energy at a stationary point on the potential energy surface (Pascale et al., 2004). Basis sets were selected as follows: for silicon the 86311G(1) contraction (Pascale et al., 2005), for oxygen a 8411G(1) contraction based on the 8-411G contraction
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given by Towler et al. (1994), for potassium a 86511G(21) contraction based on the 86-511G(3) contraction used by Dovesi et al. (1991) and for calcium the 86511G(21) contraction used for grossular (ZicovichWilson et al., 2008). The same combination of basis sets has been applied successfully in previous studies (Arroyabe et al., 2009b, c). For all basis sets the exponents of the two most diffuse sp shells and of the one most diffuse d shell have been reoptimized to the following values: sp(Si) ¼ 0.344, 0.13, d(Si) ¼ 0.677, sp(O) ¼ 0.466, 0.195, d(O) ¼ 0.538, sp(K) ¼ 0.389, 0.243, d(K) ¼ 0.35, sp(Ca) ¼ 0.453, 0.294, d(Ca) ¼ 0.310. A Pack-Monkhorst k net with 6 6 6 points in the Brillouin zone was used. The level of numerical accuracy was increased over the default settings of the software as described by Noel et al. (2006), selecting tolerances for coulomb and exchange sums (keyword TOLINTEG 7 7 7 7 15), thresholds of the SCF energy of 108 Ha for the geometry optimizations and of 109 Ha for the frequency calculations as well as a (75,974)p (keyword XLGRID) grid for the numerical integration of the DFT exchangecorrelation contribution. Following our previous experiences (Kaindl et al., 2011) we initially calculated the Raman frequencies using the local density approximation. This approach enabled an unequivocal assignment of observed and calculated frequencies in the high-frequency range of the Raman spectrum. However, the density of modes was too high in the low-frequency range of the spectrum to allow meaningful assignments. Therefore, a re-calculation with the PBE0 hybrid functional (Adamo & Barone, 1999) was performed. This functional is known to give very good values for the geometry of the crystal (Demichelis et al., 2010). This is confirmed here; a comparison between the calculated and observed geometrical parameters of the structure (Table 4) shows that only small deviations remain: lattice parameters were reproduced within 0.3 % or 0.3 , respectively, interatomic distances and bond angles within the ˚ and 1.1 , respecSiO4 tetrahedra are correct within 0.1 A tively. The largest negative deviation (5.2 ) occurred for the Si-O-Si angle. However, the PBE0 functional overestimates the vibrational frequencies (Demichelis et al., 2010). In our case the unequivocal frequencies in the highfrequency range showed a very good proportional relation of Freq(Obs) ¼ 0.977 * Freq(PBE0). We used this value as an experimental scaling factor to correct the frequencies for all modes. While this approach may seem to be crude, it has been used successfully by Scott & Radom (1996). In our case the intended result of the calculations was the assignment of vibrational modes, their symmetry and the associated movements of atoms to the experimentally observed lines. Since it was possible to derive an unequivocal allocation of all frequencies after scaling – limited only by the experimental resolution – the abovementioned approach is justified. After scaling the Raman shifts agree with the experimental spectrum within a maximum deviation of 7 cm1 and a standard deviation of 3 cm1 (Table 6). This agreement is better than those obtained with any of the other tested Hamiltonians.
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Fig. 7. Side view of the MT-framework. The more irregularly coordinated cationic sites are located in tunnels of the network running parallel to [110]. Larger grey spheres represent the K(1) positions. The Ca(2) sites are shown as smaller spheres.
Factor group analysis resulted in the following set of irreducible representations that characterize all the vibrational modes at the Brillouin centre of the monoclinic unit cell of K2Ca3Si3O10 (point group 2/m or C2h): Vib ¼
26Ag þ26 Au þ28 Bg þ28 Bu
Ag and Bg modes are Raman-active, Au and Bu modes are IR-active. The 52 theoretical Raman modes face 37 observed lines in the experimental Raman spectrum (Fig. 2); 33 of them could be assigned to one or several theoretical modes, depending on the experimental resolution. Four experimental lines could not be assigned to any theoretical mode. These very broad bands (60–100 cm1) probably originate from glue-residuals, used to fix the single crystal for the X-ray diffraction experiment. All theoretical modes could be assigned to experimental lines. Two are at low frequencies, outside of the experimentally accessible range. The mode at 694 cm1 has a signal-to-noise ratio of about 2. This is below the generally accepted detection limit of 3 (McCreery, 2000). Nevertheless, it is listed in Table 6 because it is predicted by the calculations. As usual for silicates, Raman modes with shifts .800 cm1 are all associated with Si-O stretching modes. For detailed assignments see Table 6. The gap in the spectrum is both typical and interesting in terms of taxonomy amongst oligosilicates. Confirming this general trend for dimer-based structures, vibrational spectra of yttrium silicates (Kaindl et al., 2011) exhibit that prominent gap in the Raman spectrum between 700 and 850 cm1. According to Kaindl et al. (2011), the trimer-based structures a- and Z-Y2Si2O7 on the other hand show a strong
characteristic mode of bs(Y-Si-O)-type at about 730 cm1 and weak ones at about 680 cm1. The calculation of the spectra of a-Y2Si2O7 gave an unequivocal assignment for these two isolated lines observed at 728 and 685 cm1, respectively. The one at 728 cm1 is a Si-O-Si bending mode, in which the atomic displacements are dominated by a joint movement of the two connecting oxygen atoms normal to the long axis of the trimer. The second line is associated with a Si-O stretching mode. The bridging Si-O bonds in the two outer tetrahedra stretch in counter-tact, which results in a rotation of the central tetrahedron. Both mechanisms obviously have no counterpart in the dimer based structures. In the spectrum of K2Ca3Si3O10 the same two patterns of atomic movements appear. However, their relative frequency is inversed. The second, weak line is at nearly unchanged frequencies, but is even weaker. The strong first line, which is characteristic for trimers, appears here at 614 cm1. This might be due to the nearly linearly arranged trimeric units of the yttrium silicates with Si-Si-Si angles of 154.6 that are obviously opposing the afore described horseshoe-like arrangement in K2Ca3Si3O10. The region from 350–650 cm1 is dominated by O-Si-O bending modes. Vibrations in this region of the spectrum involve no significant movement of the Kþ and Ca2þ cations. In contrast, modes with Raman shifts below 350 cm1 are all dominated by characteristic movements of the cations.
5. Discussion, comparison with related structures and conclusion Compared to the large number of silicates reported in the literature (a search in the recent volume of the
K2Ca3Si3O10 – a novel trisilicate
433
Table 6. Observed and calculated Raman modes. The calculated values refer to the results of the DFT-calculations. Obs [cm1] – – 103 113 117 – – – – 147 165 171 176 – – 200 212 232 253 280 312 331 – 360 – 402 423 450 458 478 506 522 550 569 614 694 791 845 864 897 920 945 963 993 1023 1078 1090 a
Calca [cm1]
Difference [cm1]
Symmetry mode
85 95 102 113 118 124 129 139 140 147 166 174 177 182 190 198 199 203 216 217 231 234 237 252 277 282 284 310 316 334 351 364 368 400 427 443 456 475 504 521 522 551 – 620 693 – 847 865 898 914 – 965 970 990 992 1025 1078 –
– – 1 0 1 – – – – 0 1 3 1 – – 2 1 3 4 5 1 2 5 1 3 2 4 2 4 3 – 4 – 2 4 7 2 3 2 1 0 1 – 6 1 – 2 1 1 6 – 2 7 3 1 2 0 –
BG BG AG AG BG BG AG AG BG AG BG BG AG BG AG AG BG BG BG AG BG AG BG AG BG AG BG AG AG BG BG BG AG AG AG AG BG BG AG BG AG BG – AG BG – BG AG AG BG – AG BG BG AG AG BG –
Calculated Raman shifts are given after a scaling correction with the factor 0.977.
Type (S) stretching (B) bending (?) K1-K1-K1 (?) Ca2-Ca2-Ca2 (B) K1-K1-K1; Ca2-Ca2-Ca2 (B) K1-K1-K1; Ca2-Ca2-Ca2 (B) K1-K1-K1 (B) Ca2-Ca2-Ca2 (S) K1-K1; (B) Ca2-Ca2-Ca2 (B) K1-K1-K1 (S) K1-O5; (B) K1-K1-K1 (B) K1-K1-K1 (S) K1-O5 (B) K1-K1-K1; Ca2-Ca2-Ca2, K1-Ca2-K1 (S) K1-K1-K1; Ca2-Ca2-Ca2, K1-Ca2-K1 (B) Ca2-Ca2-Ca2 (S) Ca2-O3 (S) K1-O1 (S) K1-K1 (B) O4-Ca1-O3 (B) O1-Ca1-O3 (S) K1-O2; K1-O3 (S) Ca2-O5; K1-O1 (S) Ca2-O4 (B) Ca2-Ca2-Ca2 (S) Ca2-Ca2 (S) Ca2-Ca2 (S) Ca1-O4 (S) Ca1-O1 (B) O5-Ca2-O4 (B) O3-Ca1-O4 (B) O4-Ca1-O4 (B) O2-Si1-O4 (S) K1-O1 (S) Ca2-O5 (B) O2-Si1-O4; O2-Si1-O2 (B) O5-Si2-O2 (B) O5-Si2-O5 (B) O2-Si1-O1, O3, O4 (B) O1-Si1-O3 (B) Si1-O2-Si1 (B) O3-Si1-O4 (B) O3-Si1 O4 (B) O2-Si2-O5 Glue (B) O2-Si1-O1, O3 (B) K1-Si1-O2 Glue (S) Si1-O3 (S) Si1-O3 (S) Si1-O1 (S) Si1-O4 Glue (S) Si2-O5 (S) Si1-O1 (S) Si2-O2 (S) Si1-O4 (S) Si1-O2; Si2-O2 (S) Si2-O5 Glue
434
E. Arroyabe, F. Prechtel, D.M. To¨bbens, R. Kaindl, V. Kahlenberg
Inorganic Crystal Structure Database (ICSD-Web, Version 1.2.1) for the term ‘‘silicate’’ resulted in about 9000 hits), the group of oligosilicates built of triple tetrahedral units is rather limited. A first study by Povarennykh et al. (1976) reported 17 natural as well as synthetic phases. However, this already small number was subsequently reduced because some of the quoted compounds were proved not to consist of [Si3O10]-units. Several years later, another review has been given by Simonov (1988). The most recent contribution to this field has been published by Wierzbicka-Wieczorek et al. (2010). In this study, the authors reported detailed information on five new trisilicates plus a general summary of geometrical aspects of this group of compounds. In order to find structurally related materials one may be tempted to start with other silicates having the same general formula A2þ1B3þ2Si3O10. Actually, Na2Ca3Si3O10 (Treushnikov et al., 1971) and Na2Cd3Si3O10 (Simonov et al., 1968) belong to this group and contain [Si3O10] moieties. However, the trimeric units in these two compounds show an almost linear arrangement (160.3 for Na2Ca3Si3O10 and 152.1 for Na2Cd3Si3O10) and, therefore, exhibit completely different topologies. Strongly bent, horseshoe-like trimers have been observed for a group of REE-silicates with composition BaREE2Si3O10 (REE ¼ Gd, Er, Yb, Sc) (Wierzbicka-Wieczorek et al., 2010). Nevertheless, there is a pronounced difference compared to the present compound, since the linkage between the terminal tetrahedra of the [Si3O10]-unit is provided by octahedral zigzag chains comprising corner and edge sharing BaO6-polyhedra. One characteristic structural feature of K2Ca3Si3O10 is the existence of the layers given in Fig. 5. Sheets with principally the same type of arrangement of octahedra and trimers have been described for the following mixed anion silicates: kilchoanite or Ca6(Si3O10)(SiO4) (Taylor, 1971), Na4Ca4(Si3O10)(SiO4) (Kahlenberg & Ho¨sch, 2002), Ba8(Al3O10)(AlO4) (Kahlenberg, 2001) and Sr8(Ga3O10)(GaO4) (Kahlenberg et al., 2005). However, in the latter four phases the trimer-containing layers are separated by slabs of insular TO4-groups (T: Si, Al, Ga), whereas in K2Ca3Si3O10 the corresponding layers are directly connected to each other. Concerning the starting point of our investigation it has to be stated that – so far – an anhydrous phase-X type high-pressure modification of K2Ca2Si2O7 could not be prepared. However, the pressure of 10 GPa that was used for our first synthesis experiment may have been too low to obtain this specific structure type. Actually, this pressure value represents the lower boundary of the pressure regime where phase-X like compounds have been obtained in chemically comparable systems (see Section 1). In the course of this project we will continue with a larger series of synthesis runs to chart the P-T-diagram in the range up to 20 GPa and temperatures between 1000 and 1300 C.
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Received 19 October 2010 Modified version received 9 January 2011 Accepted 3 February 2011
