Hard Mode IR Spectroscopy is an useful tool for studying microscopic properties of solid solutions. Local distortions due to the relaxations of a structure around different atoms in a given crystallographic site give rise to spectral line broadening, and the autocorrelation function can be used to quantify such line width variation in IR powder absorption spectra. This procedure eliminates the need to use more or less arbitrary fits of individual peaks in complex spectra. Analyses of different frequency ranges of the IR spectra indicate the response of the different parts of a structure to cation substitutions or ordering. As an example of how this method is suited for detecting changes in sequences of samples which differ in composition or structural state, the results of autocorrelation analysis are reviewed for three different systems. The effective line widths of synthetic alumino-silicate garnets in the binary-joins pyrope-almandine, almandine-grossular and pyrope-grossular correlate with the elastic local strains arising from cation substitutions and might be used to quantify the enthalpy of mixing of the solid solutions (T. Boffa Ballaran, M.A. Carpenter, C.A. Geiger and A.M. Koziol, submitted). Cation ordering in omphacites and the non-ideality of the augite-jadeite solid solution can be characterised at a local length scale. In this system, it appears that the tetrahedral chains play an important role in accommodating the local strains due to ordering and substitution (Boffa Ballaran et al., 1998). Mixing, non convergent order and a displacive phase transition, C2/m -> P21/m, in the cummingtonite-grunerite solid solution also give rise to spectral line broadening which can be analysed in the same way.
Boffa Ballaran T, Carpenter MA, Domeneghetti MC, Salje EKH & Tazzoli V, Am. Mineral, 83, 434-443, (1998).
The phonon IR spectra of 35 natural cordierites with XFe values between 0.1 and 0.8 have been measured in the region 1200 to 50 cm-1. The aim is to obtain information about the local structure of cordierite upon Mg2+ Fe2+ exchange on the octahedral site and with incorporation of different components in the channels.
In the MIR region we found a linear decrease of peak positions going from Mg-cordierite to Fe-cordierite. The higher frequency modes between 1200 and 500 cm-1 are related to Si(Al)-O stretching and bending modes. Single-crystal x-ray refinements show a linear change of T-O bond angles and only a slight change of T-O bond distances with increasing XFe (Wallace and Wenk, 1980). This is consistent with the linear behaviour of the MIR phonon frequency shifts, which are coupled to those in the FIR and consequently are an indirect measure of XFe. In the FIR region the interpretation is more difficult. Modes in the region 330 to 200 cm-1 show only slight variations in peak position, on the order of 1 to 5 cm-1. Modes below 200 cm-1 also show a linear decrease of frequencies with increasing XFe. The low frequency modes in the FIR show considerable changes in intensity as a function of composition. Some of these modes are related to motions in the octahedral site, where the Fe-Mg exchange takes place. In order to assign modes in this region, measurements made on cordierite synthezised from 26Mg and 57Fe are planned.
Using the autocorrelation function (Boffa Ballaran et al., in prep.), the variation in the phonon linewidths has been examined. The advantage of this method is its independence of a precise description of the shape and number of phonon modes. The correlation lengths of phonons in the MIR-region can be estimated to be on the order of tens of Å (Boffa Ballaran et al., in prep.). Hence variations in effective linewidths are a measure of local strain fields.
In the region 1200 to 700 cm-1 we found a linear increase of phonon linewidths with increasing XFe. The line broadening of the high frequency modes is also related to the amount of alkali cations, primarily Na+, located in the channels. This can be related to the position of Na+ in the center of the six-membered tetrahedral ring, which influences the internal Si(Al)-O stretching vibrations of the tetrahedra. This result is in agreement with single-crystal Raman measurements of cordierite (Kolesov and Geiger, in prep.). Further investigation in the FIR region is underway, in order to check for strain fields over longer correlation lengths.
Wallace J H, Wenk H R, Am. Min., 65, 96-111, (1980).
It is well known that aluminosilicate minerals develop various degrees of short-range order (SRO) and long-range order (LRO), depending on the composition (Al,Si ratio) and the thermodynamic history of the samples. The development of long-range order can be studied by experimental methods which measure the average LRO parameter and can be successfully modelled using Landau Theory. However, when LRO cannot develop due to compositional or kinetic constraints, the thermodynamic properties are a function of the degree of SRO. The SRO parameter is more difficult to measure, but in many cases 29Si NMR spectroscopy has been successful in providing the populations of local Si distributions. When we introduce SRO we have to change our thermodynamic methodology from the Landau model to the Ising model. In this model the system of interacting Al and Si atoms reduces its configurational free energy by finding a compromise between decreasing the number of unfavourable nearest-neighbour bonds (i.e. Al-O-Al) and keeping the entropy as high as possible. There are two different strategies for reducing the number of Al-O-Al bonds. The first is to increase the degree of local correlation between Al and Si atoms (increase SRO); the second is to develop periodic alternations of site occupancies throughout the lattice (increase LRO). At high Al, Si ratios and at low temperatures the second strategy is most successful (e.g. development of LRO in anorthite), while at low Al,Si ratios and high temperatures the first strategy is more favourable.
The problem of using Ising models to describe SRO and LRO in a structure as complex as plagioclase feldspar is to develop a statistical thermodynamic model in which these parameters, as well as the composition are treated as independent variables. Such a model, termed the Cluster Variation Method (CVM), exists and is very widely used for the description of atomic ordering in alloys. The basic idea is that in the case of SRO the entropy cannot be calculated by an ideal mixing over the Al,Si sites, and must be calculated over large enough clusters to correctly reproduce the topological features of the structure. However, for complex structures the evaluation of the probability distribution of all possible configurations of Al and Si, constrained by the composition and the LRO and SRO parameters, involves introducing a very large number of variables. Using the traditional CVM approach this would not be computationally viable.
Here we demonstrate that using a different approach (Vinograd et al., 1997; Vinograd and Putnis, 1998, 1999), the problem literally disappears and we can construct accurate CVM models for aluminosilicates while avoiding most of the computational difficulties. The validity of the method is demonstrated by the virtually exact correspondence between the equilibrium configurational entropy in the high T plagioclase solid solution obtained from recent Monte Carlo simulations and the CVM method.
The determination of the probability distribution of Al,Si in large clusters (up to 16-point) is the first step to constructing a model for the enthalpy of the solid solution. We show that an electrostatic model containing only one adjustable parameter (the effective charge difference between Si and Al) can consistently explain a large number of experimental data related to the high temperature plagioclase solid solution.
Vinograd VL, Saxena SK & Putnis A, Phys. Rev. B, 56, 11493-11502, (1997).
Vinograd VL & Putnis A, Phys. Chem. Minerals, In press, (1998).
Vinograd VL & Putnis A, Amer. Mineral, In press, (1999).
The partitioning of Fe2+ and Mg on the M1 and M2 sites of orthopyroxenes from the Johnstown meteoritic diogenite has been equilibrated between 1000°C and 700°C in ordering and disordering runs. The method of bivariate high order truncation analysis (Kroll et al., 1997) has been employed to refine the site occupancies from conventional X-ray intensity data. The Fe2+,Mg distribution coefficient varies according to
lnKD = 0.386(102) - 2508(120) / T [K]
From isothermal kinetic ordering and disordering experiments an exceptionally large activation energy was derived. Combining our data with those of Zema et al. (1997) results in the Arrhenius equation for the rate constant:
lnkdis [min-1] = 41.1(±0.9) - 97.8(±1.9) [kcal/mol] / RT
For the first time, non-linear continuous cooling experiments were performed in which the crystals were cooled from 850°C to 250°C at an average rate of 10°C/day. The Fe2+, Mg distributions were determined after the crystals had reached 650°C, 550°C, 450°C, 350°C and 250°C, respectively. Using the Mueller rate equation (Ganguly, 1982) and employing the temperature dependencies of KD and kdis as given above the experimentally delineated ordering path is closely reproduced by the calculated path.
However, due to the large activation energy cooling rates calculated for the untreated crystals turn out to be physically unreasonable: some 10-5 K/My. By contrast, Arrhenius parameters determined in the literature on orthopyroxenes with compositions similar to the Johnstown crystals produce physically reasonable rates of some hundred K/My. At present, we cannot offer a convincing solution to this dilemma, but can only relate it qualitatively - following Zema et al. (1997) - to the intricate exsolution microtexture of the Johnstown orthopyroxenes.
Ganguly J, Advances in Physical Geochemistry, Vol. 2, S.K. Saxena (Ed.), Springer, New York, 58-99, (1982).
Kroll H, Lueder T, Schlenz H, Kirfel A, Vad T, Eur. J. Mineral., 9, 705-733, (1997).
Zema M, Domeneghetti M C, Tazzoli V, EUG 9 Terra Nova, 9, 422, (1997).
We combined X-ray single-crystal structure-refinement (SREF) with EMP analyses for major elements and with SIMS analyses for H and trace elements (REE, HFSE) with the aim of characterising natural and synthetic (sodic, sodic-calcic and calcic) amphiboles crystallised under P,T,X conditions of interest for upper-mantle studies. This approach allowed us:
to unravel and model the crystal-chemical mechanisms balancing for dehydrogenation;
to relate the amount of dehydrogenation and the consequent structural modifications; we can now obtain accurate estimates of the H content solely from SREF results (mainly cation-cation and cation-O distances);
to obtain reliable distributions of Ti among the tetrahedral (T2) and the octahedral (M1, M2, M3) sites on the basis of SREF results (mainly cation-O distances and adp); the occurrence of Ti in each site is related to different crystal-chemical mechanisms and thus depends in different ways on the P, T, X, and fO2 conditions of crystallisation.
to unravel the crystal-chemical mechanisms for REE and HFSE partitioning in amphibole; their site preference strongly varies for different amphibole compositions, and is determined mainly by the relative dimensions of the relevant sites (M4, M4' and M2 in the case of REE; M1, M2, and M3 in the case of HFSE).
This novel crystal-chemical knowledge further contributes to the modelling of solid solutions within the amphibole compositional-space. In particular, modelling of trace-element partitioning on the basis of the lattice-site elastic-strain theory allowed us to put into a close relationship the incorporation of trace elements with the site parameters of the fraction of sites which are actually active (those occupied by major-element constituents with similar ionic-radii and charges, i.e, charge = 1). Under this hypothesis, more correct site-parameters (r0, the ideal cation radius, D0, the "strain-compensated" partition coefficient and the Young's modulus) can be calculated, which could be used to constrain the energetics of solid-solutions processes.
Two points deserve further consideration. The first is that (partial) dehydrogenation occurs in all the amphibole compositions, and is much more frequent than formerly thought; therefore, it has to be taken into account anytime unconvincing EMP analyses are obtained. The second is that the information obtained from long-range averaged techniques such as SREF can be used to decipher fine-scale details of cation partitioning also at the trace-element level.
Pyroxenes are an important group of rock-forming minerals, and occur as stable phases in many igneous rock types. They are also found in many high-grade metamorphic rocks of most compositions. The exact knowledge of ferrous/ferric ratios in minerals is essential for the determination of physico-chemical conditions of crystallization, such as temperature, pressure and oxygen fugacity. In this study we investigate Fe3+/(sum)Fe ratios in clinopyroxenes of the solid solution series acmite-hedenbergite by Mössbauer spectroscopy and electron energy-loss spectroscopy (EELS). The Fe L2,3 electron energy-loss near-edge fine structures (ELNES) show valence specific multiplet structures, e.g. changes of the L3 : L2 white line intensity ratio (L3/L2) and chemical shift. For different minerals, like garnets, spinels, and other oxides and hydroxids, L3/L2 as a function of Fe3+/(sum)Fe results in an universal curve which can be used not only for valence fingerprints but also for the quantitative determination of the Fe3+/(sum)Fe (van Aken et al., 1998).
M2[Ca2+1-xNa+x]M1[Fe2+1-xFe3+x]Si2O6-pyroxenes were synthesized hydrothermally at 4 kbar (Redhammer, 1996). Run products were characterized by scanning electron microscopy and X-ray diffraction. High-resolution Fe L2,3 ELNES recorded in a transmission electron microscope (TEM) are presented for the solid solution series acmite-hedenbergite with various Fe3+/(sum)Fe ratios for which Fe3+/(sum)Fe was determined from L3/L2 using the universal curve. In addition, the Fe3+/(sum)Fe ratio was determined by 57Fe-Mössbauer spectroscopy (Redhammer, 1996) yielding excellent agreement with the Fe L2,3-ELNES results. With this additional set of data, L3/L2 versus Fe3+/(sum)Fe for the pyroxenes, the universal curve described in van Aken et al. (1998) was confirmed and its accuracy was improved.
Therefore, the analysis of the Fe L2,3-ELNES is a powerfull and promising method in quantifying Fe3+/(sum)Fe, and can routinely be performed with high spatial resolution on a scale of a few nm, by a combination with TEM.
Redhammer GJ, Dissertation, Institut für Mineralogie, Universität Salzburg, (1996).
van Aken PA, Liebscher B, Styrsa VJ, Phys. Chem. Minerals, 25, 323-327, (1998).
Simulation methods are able to provide highly detailed and important information on the level of individual atoms and their interactions. They can therefore serve as a supplement to experimental methods to determine, on an atomistic scale, the structural and energetic processes associated with the formation of solid solutions. For modelling of silicate solid-solutions, static lattice energy calculations with empirical potentials are used. This parameterised model has been shown to be a robust method for the prediction of structural properties (Winkler et al., 1991), as well as for the description of mineral behaviour such as phase transition and order/disorder phenomena (Dove et al., 1996). Solid-solutions can be modelled using two different approaches: 1) using mixed potentials or 2) generating many different configurations in a supercell. In the first method it is assumed that there is complete disorder between the different types of cations (A and B) that share a common site (X) in the solid-solution. A mixed potential is then generated according to the occupancy xB of cation B and (1- xB) of cation A on the X-site using a scheme proposed by Winkler et al. (1991). This procedure is a "mean-field" approximation and does not allow for local distortions. The second approach involves the generation of a large number of different arrangements of cations A and B on the X-sites in a large supercell containing a sufficient number of X-sites. The composition of the solid solution is controlled by placing different numbers of A and B cations on the X-sites. This configurational method allows for local distortions and, hence, for a minimisation of local stress caused by different sized cations on crystallographic equivalent sites. In the case of garnet, the structural properties are highly affected by local distortions, which can be seen by a reduction of the volumes and enthalpies of mixing by a factor of three to five compared to those calculated using the method of mixed potentials. As a further issue, the configurational method allows an analysis of the interaction energies of next-nearest neighbours and/or longer-range interactions. This can be used to determine whether short- or long-range order is to be expected and/or to elucidate the driving mechanism behind the ordering process. For example, in the garnet binary pyrope-grossular it was shown that in compositions containing both Ca and Mg, like cations avoid forming pairs in directions parallel to the crystallographic axes (Bosenick et al., in prep.). Such behaviour cannot produce long-range order, but it may produce significant short-range order. These interaction energies can then be used in Monte-Carlo simulations to calculate the thermodynamic properties of the solid-solution taking account of the different degrees of order.
Winkler B, Dove MT & Leslie M, American Mineralogist, 76, 313-331, (1991).
Dove MT, Thayaparam S, Heine V & Hammonds KD, American Mineralogist, 81, 349-362, (1996).
Bosenick A, Dove MT, Hammonds KD, Meyers E & Geiger CA, in preparation
Recent developpements in theoretical chemistry allow studies of compounds of interest for Earth Sciences. Until now, closed-shell spinels compounds, such as MgAl2O4, were studied (D'Arco et al, 1991). New version CRYSTAL95 allows studies of open-shell magnetic systems.
We present here the ab initio study of MnCr2O4-Mn3O4 mixed compounds. Pure cubic spinel MnCr2O4 has been studied elsewhere (Fava et al 1997), we perform calculations on pure Mn3O4, for low-temperature tetragonal spinel phase and high-temperature cubic one's. Three intermediate compounds Mn2+Mn3+2xCr3+2-2xO4 have been studied at x=0.25,0.5,0.75. Structural, electronic and magnetic behaviour are analysed and compared with experimental measurements.
Low-temperature Mn3O4 structural parameters were determined, in good agreement with experimental measurements. Calculated volume 328 Angstrom3 and c/a ratio 1.61 are in fairly well agreement with experimental value 314 and 1.64. The Jahn-Teller distortion is well reproduced, the octahedron is distorted: the 6 Mn-O bonds are splitted in two sets: two long apical and four short equatorial. Calculated (2.287,1.947) and experimental (2.288,1.905) (Boucher et al, 1971) bond-lengths are identical within less than 2%. Calculated net charges (obtained using a Mulliken analysis scheme) are +1.86 and +2.29 |e| for manganese in tetrahedral site (A) and in octahedral site (B) respectively, to be compared with the formal oxidation state +2 and +3. Manganese bonds are described to be more covalent in the octahedron than in the tetrahedron. In the octahedron, long apical Mn-O bonds are less covalent than short one's. The calculated spin population: 3.97 and 4.89 <nu>B for B and A site respectively mimicks fairly well experimental values 3.55 and 4.65 (Boucher et al, 1971). The cubic phase is found to be less stable than the tetragonal one's.
Calculated energies of five ferrimagnetic configurations derived from tetragonal structure have been modelized within an additive Ising-type scheme. Four magnetic interactions are taken into account. Calculated antiferromagnetic A-A interaction is the weakest. B-B interactions are splitted in two sets, one corresponds to the short Mn3+-Mn3+ distance (2.96 Angstrom) along chains parallel to a and b-axis, and the other to long Mn3+-Mn3+ distance (3.13 Anqstrom) corresponding to chains formed by octahedra sharing edge and running along [111] direction. The short B-B interaction is antiferromagnetic and the stronger over all interactions considered. Antiferromagnetic chains along a and b-axis are mainly responsible for the low-temperature magnetic structure of hausmannite. This is in line with experimental measurements (Jensen & Nielsen, 1974).
In mixed compounds, the electronic structure of manganese and chromium are close to those calculated in MnCr2O4 and Mn3O4. Calculated volumes and c/a ratio are overestimated by 4% and 5% respectively with respect to the experimental measurements (Kupricka & Novak, 1982). Geometrical results are in line with those obtained for MnCr2O4 and Mn3O4.
Variations of the structure in function of the chromium content are similar to the experimentally determined one. Spinel containing more than 1.4 Cr3+ are found to be cubic. The transition value agrees fairly well with the experimental compositional limit of 1.2 Cr3+.
Boucher B, Buhl R & Perrin M, J Phys Chem Sol, 32, 2429-2437, (1971).
D'Arco P, Silvi B, Roetti C & Orlando R, J Geophys Res, 96, 6107-6112, (1991).
Freyra Fava F, Bataille I, Larrieu C & Dovesi R, submitted, (1997).
Jensen GB & Nielsen OV, J Phys, C7, 409-424, (1974).
Kupricka S & Novak P, Ferromagnetic Materials, North-Holland Publishing Company, (1982).
On the M4-site in tremolite Ca2Mg5 [Si8O22/(OH)2] Ca2+ can be at least partially replaced by Mg2+ forming tremolite-cummingtonite solid solutions. Synthetic tremolites are never pure but contain small amounts of cummingtonite Mg2Mg5[Si8O22/(OH)2]. The amount of cummingtonite is difficult to access, however. The crystal dimensions of the synthesized tremolites are usually to small for precise microprobe analysis. Based on experiments by Jenkins (1987) tremolite compositions of tr90cum10 have been claimed in many studies without verification. But any insufficiency in knowledge of composition causes errors in derived thermodynamic properties. In addition because pure tremolite had been never obtained experimentally and natural samples always contain impurities the molar volume of tremolite is not precisely known.
In this study tremolites have been synthesized in range of 670-800°C and 200-700 MPa. The tremolite crystals were large enough to be analysed by electron microprobe. In addition the run products were studied by SEM, HRTEM, X-ray diffraction (Rietveld analysis) and IR-spectroscopy. The cummingtonite content within each run as determined by the electron microprobe showed a relative large compositional range of 5%. In tremolite-cummingtonite solid solutions with a composition of tr90cum10 only 4% of the total Mg2+ is located on the M4-site. The analytical error of the microprobe due to counting statistics is in order of 2%. Investigations by HRTEM showed that the synthesized tremolites were highly ordered and chain multiplicity faults were rare. Therefore it was not possible to explain the compositional variations in Mg content with variable concentrations of chain multiplicity faults. The observed compositional ranges were not real but clearly due to analytical difficulties. The electron microprobe seem not to be adequate tool to determine the cummingtonite content with the required precision. Furthermore, despite the lattice constants a, b and ß should be highly dependent on cummingtonite content no such correlations were observed using the electron microprobe derived compositions.
It was possible, however, to determine precisely the cummingtonite content by IR-spectroscopy. Around each proton four M4-sites are located, two at a distance of approximately 5.3 Å and two at 5.8 Å. The location and absorbance of the OH-stretching vibration is a function of M4-site occupancy. At least 3 different bands could be identified: 3674.6 cm-1 for the CaCaCaCa and 3669.3 and 3672.2 cm-1 for the MgCaCaCa and CaCaMgCa configurations. The last two bands differ in the distance between H and Mg. The integral absorbances can be used to derive cummingtonite contents. According to the IR-spectra all synthesized amphiboles had cummingtonite contents lower than 6%. In some cases nearly pure tremolite was synthesized (99%). The derived compositions correlate exellent with the lattice constants. Using these correlations the lattice constants of pure tremolite were extrapolated (a = 9.8354 Å, b = 18.0562 Å, 5.2768 Å, ß = 104.74°, V = 906.3 Å3).
Jenkins DM, Am. Miner., 72, 707-715, (1987).
The Tschermaks substitution Mg2+ + Si4+ = Al3+ + Al3+ has been investigated along the tremolite - tschermakite solid solution series. The amphiboles were synthesised in a hydrothermal (600-800°C; 2-5 kbar) and a piston cylinder (600-850°C; 8-20 kbar) apparatus. Oxide-hydroxide mixtures, plus an excess of a CaBr2-solution, were used as the starting materials. The run products were characterized using optical microscopy, REM, HRTEM, EMS, XRD and FTIR. The synthesised Al-tremolites formed needles and lath shaped crystals of up to 200 x 20 µm. HRTEM-observations showed that the majority of the Al-tremolites are well ordered with no or only sporadic chain multiplicity faults. Microprobe analysis yielded a chemical composition for the synthesised amphiboles between tremolite and tremolite50 tschermakite50. A small cummingtonite component of about 5 mole% was observed. Rietveld refinements of the lattice constants revealed a linear decrease of the cell parameters a and b with increasing Al-content, whereas c and ß increase. Small deviations were caused by small amounts of cummingtonite component which leads to a decrease in the cell dimensions. Following equations can be derived for the ternary system tremolite-tschermakite-cummingtonite:
a = 9.8354 xTr + 9.718 xTs + 9.47 xCum
b = 18.0562 xTr + 18.933 xTs + 17.925 xCum
c = 5.2768 xTr + 5.3000 xTs + 5.27 xCum
ß = 104.74 xTr + 105.48 xTs + 102.18 xCum
The derived cell volume for the tschermakite endmember of 890.2 Å3 is 2 Å3 larger than that of other studies (cf. Smelik et al., 1994) because no correction for the cummingtonite component were considered in these studies. IR-investigations of the Al-tremolites in the OH-streching region showed two absorption band systems in the range between 3676 - 3667 cm-1 (I) and 3649 - 3660 cm-1 (II). Earlier studies attributed the band system (I) to configurations without Al and the band system (II) to configurations with Al around the OH-dipole (e.g. Jenkins et al., 1997). High resolution spectra (0.25 cm-1) from this study did show that the band system (I) is also influenced by the Al incorporation. Three bands at 3675, 3672, 3668 cm-1 were detected in the band system (I). The relative intensities of the bands at 3675 and 3672 cm-1 show a contrary behavior. The absorbance of the 3672 cm-1 band increases with increasing Al content, whereas that of the 3675 cm-1 band decreases. The relative intensities of the bands can be used to determine the tschermakite content because a linear correlation between IR and EMP derived compositional data exists.
Smelik E A, Jenkins D M, Navrotsky A, Amer. Min., 79, 1110-1122, (1994).
Jenkins DM, Sherriff BL, Cramer, J & Zhi, X, Amer. Min, 82, 280-290, (1997).
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