Comparison of the Vibrational Spectra of Copper Polysilicate , CuSiO 3 , with Those of the Prototypic Copper Polygermanate , CuGeO 3

Orthorhombic copper polysilicate, CuSiO3, is isotypic to the spin-Peierls compound CuGeO3 and represents a further example of a quasi-one-dimensional spin = 1/2 antiferromagnetic Heisenberg chain system. This is a representation of the first Raman and IR/FIR spectra for CuSiO3, measured at room temperature on polycrystalline samples. A comparison of the optical phonons, predicted by a factor group analysis, with those observed for the CuGeO3 prototype, is presented. A mode assignment for the silicate is given. Surface effects due to a very small crystallite size may cause additional broad bands observed in the Raman spectrum of CuSiO3. From the analysis of the Davydov doublet an intralayer-to-interlayer bond strength of about 40 is derived for the silicate, which is about 20% lower than for the isotypic germanate, allowing for different magnetic responses at low temperature.


Introduction
Low-dimensional quantum spin systems are of considerable theoretical and experimental interest.Some years ago a spin dimerization transition (spin-Peierls transition), which is one of the quantum phenomena in a S = 1/2 antiferromagnetic Heisenberg linear chain, was observed in inorganic compounds and extensively studied in quasi-one-dimensional (1D) copper polygermanate, CuGeO 3 [1] [2] respectively α' − NaV 2 O 5 [3].American Journal of Analytical Chemistry The crystal structure of copper polygermanate consists of two types of chains which running down the shortest translation period: einer single chains of GeO 4 tetrahedra are connected by chains of edge-sharing CuO 4+2 "octahedra" [4] [5], which are in reality due to the Jahn-Teller effect strongly elongated and distorted tetragonal dipyramids.Because of this the magnetic chains actually are formed by ladders of CuO 2 squares.
Until now CuGeO 3 was the prototypic compound showing such tetrahedral single chains with a repeat sequence of only one GeO 4 unit.The substitution of Si 4+ for Ge 4+ in copper polygermanate according to CuGe 1−x Si x O 3 was only possible in the limited concentration range x ≤ 0.5 for polycrystals by hydrothermal synthesis [6], and the existence of pure CuSiO 3 was considered non-existent [7] [8].However, we succeeded in the preparation of polycrystalline CuSiO 3 , isotypic to CuGeO 3 , by thermal decomposition of the mineral dioptase, Cu 6 Si 6 O 18 •6H 2 O, and investigated its crystal and magnetic structure [9] [10] [11] [12].Strong bonds in the ac-plane form zigzag layers in the crystal structure (Figure 1), but the layer-like character is less pronounced for the silicate than for the germanate, because its interlayer distance is reduced about 3.6% and the intralayer chain distance enlarged about 3.5% in comparison to the germanate.Lattice parameters and CuO 2 chain separations of both compounds are compared in Table 1 and individual bond lengths summarized in Table 2 to complete the data used for the further analysis [10] [13].
Here we report on a first investigation of the room temperature vibrational spectra of a polycrystalline CuSiO 3 sample and compare these measurements with that for CuGeO 3 using previously reported data as well as our own.While the synthesis of CuGeO 3 can easily be performed as a polycrystalline powder by sintering of equimolar amounts of CuO and GeO 2 at 800˚C [11], or as single crystals by the floating zone method [14], the synthesis of pure CuSiO 3 remains a worthwhile task.This paper is an extended (and corrected) version of a contribution that has been pre-published some years ago [15].Table 1.Lattice parameters, unit-cell volume and separations of CuO 2 chains for isotypic CuSiO 3 [10] [11] [12] and CuGeO 3 [13], respectively.Space group Pmma (No. 51, standard setting).

Experimental
The Raman and IR spectra of CuSiO 3 and CuGeO 3 were measured on polycrystalline samples.The copper polysilicate specimen has been obtained by thermal decomposition of the mineral dioptase, Cu 6 Si 6 O 18 •6H 2 O, as a multi-phase educt containing about 76 wt-% CuSiO 3 , 14 wt-% CuO (tenorite) and 10 wt-% amorphous SiO 2 [10].Single-phase powder of CuGeO 3 has been synthesized by sintering of pellets of a thoroughly homogenized CuO and GeO 2 mixture at 1200 K and a repeated grinding and sintering procedure.
The Raman spectrum of CuSiO 3 was recorded with a DILOR LabRAM spectrometer, using a Nd-YAG-laser with frequency doubler (λ = 532 nm) as an exciting source, and the spectrum of CuGeO 3 with a Raman FRA 106 modul attached to a BRUKER IFS 66v interferometer, using once again a Nd-YAG-laser, but with λ = 1064 nm.Infrared spectra of both compounds were obtained with the above mentioned interferometer using CsI pellets of the powdered samples.
The IR and Raman spectra of the minor phases in the phase mixture (CuO as tenorite and amorphous SiO 2 ) were also recorded with the same experimental equipment in order to estimate the possible distortion of the CuSiO 3 spectra and are given by Meibohm (1999) [11].Only few strong bands were observed (IR: 470 and 1108 cm −1 for amorphous SiO 2 and 530 cm −1 for CuO; Raman: 450 cm −1 for amorphous SiO 2 and 300 cm −1 for CuO) that would be in a position to introduce a marginal distortion of the main phase spectra.Only the background of the Raman spectrum near 300 cm −1 as well as the left (high frequency) shoulder of the IR band near 500 cm −1 may be influenced by the presence of the minor phases.

Crystallographic Data
Relevant crystallographic data such as lattice parameters, bond lengths and chain separations are summarised in Table 1 and Table 2 for both CuSiO 3 and Cu-GeO 3 .The Figures 1-3 illustrate crystal structural details in the standard setting (space group Pmma).

Factor Group Analysis
For the factor group analysis (f.g.a.) the unit-cell, containing two non-translationally equivalent CuSiO 3 units and thus n = 10 atoms, were adapted to the standard setting of the Pmma space group in order to apply the tables given by Rousseau [16] and Adams [17] and to compare with the data already reported for CuGeO 3 [18]- [23].From the total number of vibrations (N T = 3n = 30) the 3 acoustic and 2 silent modes were subtracted, leaving 25 remaining optic modes, 12 of which are Raman-active and 13 IR-active modes.The results are summarized in Figure 4 displaying the active modes in frames.The following are features of the analysis that will make the mode assignment easier: a) the copper atoms do not contribute to the Raman spectrum; b) coupling between the two non-translationally equivalent silicate chains of C 2v site symmetry in the unit-cell with D 2h symmetry leads to Davydov pairs [24]; the chain modes split into crystal modes of type A g − B 1u , B 2g − B 3u and B 3g − B 2u , respectively [19].The obtained doublets involving both Raman-and IR-active modes are indicated in Figure 4 by vertical lines.

Results and Discussion
The room temperature Raman and infrared spectra of both CuSiO 3 and CuGeO 3 are shown in Figure 5 and Figure 6, and the extracted vibrational frequencies are summarized in Table 3 along with their intensities and the mode assignments.At a rough estimate the spectra of the silicate shift on average by a factor of F = F m* •F bl = 1.23 to higher frequencies in comparison to that of the germanate.In this way the mode assignment for the germanate, confirmed by a normal coordinate analysis [13], can be applied to the silicate spectra.In particular is   F m* = (m* germanate /m* silicate ) 1/2 = 1.13 , where m* is the reduced mass, and F bl = <d> germanate /<d> silicate = 1.08; the mean bond lengths (bl) were applied as a measure of the stiffness of the compounds with <d> = 1.747Å for the germanate and <d> = 1.611Å for the silicate (Table 2).

Number of modes Activity
The frequency quotient of silicate to germanate modes versus the germanate frequency affords some information about the source of the vibrations and is displayed in Figure 7.In this drawing three regions of different slope can be made out, beginning with a low frequency region below 250 cm −1 (350 cm −1 for the silicate) originating from Cu and Ge/Si atom vibrations, then a region between 250 cm −1 and 550 cm −1 (350 to 600 cm −1 ) with Cu-O and Ge/Si-O vibrations, and finally the region above 550 cm −1 showing modes with a dominant contribution of oxygen vibrations.For the minimum values of the curve it is allowed to neglect F m* thus obtaining a value, which actually reflects the force constant ratio.In Figure 7 distinction is also made between Raman and IR data in order to demonstrate the difference of their low frequency modes.Because the copper atom does not contribute to the Raman spectrum (Table 3), the large Ge to Si mass ratio is decisive for the large frequency ratio, while for the IR spectrum the contribution of Cu to the reduced mass level out the frequency difference between germanate and silicate.
The number of modes found in the spectra are in agreement with the space group symmetry and f.g.a.taking into account the following points.Three very weak bands in the vibrational spectra of CuGeO 3 , given in Table 3 in squares, which have been observed in polarized single crystal spectra [19], are absent in the spectra of powder samples of both CuGeO Once the correct mode assignment has been found, it is sufficient to apply to the silicate the results of the normal coordinate analysis for the germanate, already given by Popović et al. [19], in order to find out what the origin of an individual vibration is.
With regard to the crystal symmetry, the spectroscopic data as well as X-ray diffraction results are supported by a further experiment.According to NQR measurements of Cu in CuSiO 3 there exists, even down to 4.2 K, only one Cu site [25].
Following Popović et al. [19], we can analyse the chain mode doublets (Davydov pairs) for CuSiO 3 , like that for CuGeO 3 , as the result of the vibration of a pair of weakly coupled identical oscillators by the relation ν ± = (ν 0 2 ± ∆ 2 ) 1/2 , where ν 0 is the frequency of the isolated oscillators and ∆ 2 is proportional to the coupling force constant.Then (ν 0 /∆) 2 gives a measure of the ratio of intralayer-to-interlayer bond strength.Table 4 summarizes the phonon doublet analysis (ν + = ν Raman , ν − = ν IR ), which yields the mean value of (ν 0 /∆) 2 for the silicate about 20 % lower than for the germanate [18], in accordance with the changed chain separations that have been derived from the crystal structure analysis (Table 1).
The more 3D-like character of the silicate may be responsible for the different spin-phonon coupling in comparison to the germanate leading at low temperature to a long-range antiferromagnetic Néel state order instead of a spin-Peierls order.

Conclusions
The vibrational spectra of orthorhombic CuSiO 3 from powder samples are presented.The observed Raman respectively IR modes are assigned based on single crystal results for CuGeO 3 previously given.A chain mode analysis of Davydov

Figure 1 .
Figure 1.Crystal structure projection of CuSiO 3 along [010].Zigzag layers along a in the ac plane are depicted by the red line.

Figure 2 .
Figure 2. Polyhedral representation of the CuSiO 3 crystal structure.The unit cell was outlined in margenta color, silicate tetrahedral chains in yellow color, copper oxide octahedral chains in blue color, respectively.

Figure 3 .
Figure 3. Projection of the crystal structure of CuSiO 3 along the b-axis in the displacement ellipsoid representation [12].Oxygen atoms red, Cu atoms blue, Si atoms yellow, respectively.The strongly anisotropic displacement of the oxygen atom O(2) is noticeable.

Figure 4 .
Figure 4. Factor group analysis for orthorhombic CuSiO 3 (space group D 2h −Pmma, No. 51).Mode numbers: N T total number, N A acoustic branch, N O optic branch, R y chain librations, N C coupled vibrations of two chains, O t = terminal oxygen atom, O br = bridging oxygen atom.

Figure 7 .
Figure 7. Frequency ratio of silicate to germanate modes versus the germanate frequency.Raman data are depicted as empty squares, IR data as filled circles, respectively.Davydov pairs are indicated by elliptical frames.