Structural states of Mg cordierite III: Infrared spectroscopy and the nature of the hexagonal-modulated transition

The time evolution of the Al, Si ordering and the ferroelastic distortion of the Mg-cordierite structure are quantified on a local length scale by Hard Mode Infrared Spectroscopy (HMIS). The line profiles of various absorption peaks were measured at room temperature and at 80 K. Their integrated intensities, frequencies and half width are correlated with the interacting order parameters Q _od (Al, Si ordering), Q (displacive orthorhombic distortion) and their equivalent short-range analogs. It is shown that the phase transition between hexagonal and modulated cordierite is stepwise, as predicted earlier. The local structural state of quenched, modulated cordierite is essentially equivalent to that of the orthorhombic phase. A general concept is outlined which allows, in general, the independent determination of various interacting order parameters using HMIS.     

Infrared vibrational spectra of Beta-Phase Mg2SiO4 and Co2SiO4 to Pressures of 27 GPa

Infrared absorption spectra of the high-pressure polymorphs β-Mg₂SiO₄ and β-Co₂SiO₄ have been measured between 0 and 27 GPa at room temperature. Grüneisen parameters determined for 11 modes of β-Mg₂SiO₄ (frequencies of 300 to 1,050 cm^?1) and 5 modes of β-Co₂SiO₄ (490 to 1,050 cm^?1) range between 0.8 and 1.9. Averaging the mid-infrared spectroscopic data for β-Mg₂SiO₄ yields an average Grüneisen parameter of 1.3 (±0.1), in good agreement with the high-temperature thermodynamic value of 1.35. Similarly, we find a value of 1.05 (±0.2) for the average spectroscopic Grüneisen parameter of β-Co₂SiO₄.     

Xitieshanite—A new ferric sulphate mineral

Xitieshanite is a new ferric sulfate mineral discovered in the oxidation zone of a Pb-Zn deposit at Xitieshan, Qinghai Province, China. The typical crystal of xitieshanite is a rhombic rectangle. It is bright green in colour with a light yellow tint. Luster vitrous Translucent to almost transparent. Streak yellow. Cleavage imperfect. Fracture uneven or conchoidal. H. (Vickers)=62.6kg/mm². Specific gravity=1.99_obs(2.02_calc,) Pleochroism strong, and axial colours: X=colourless to pale yellow, Y=pale yellow, Z=light yellow with greenish tint. It is optically positive, biaxial, 2V=77°,r v. Refractive indices:N _x =1.536,N _y =1.570,N _z =1.628. Extinction parallel and inclined. Elongation positive and negative. X-ray single-crystal study shows it is monoclinic. Space groupP2₁/a. Unit cell parameters:a=14.102,b=6.908,c=10.673 Å, β=111.266°,V=968.9, ų,Z=4. The powder pattern of xitieshanite gave the strongest lines: 6.67(6)(201), 6.09(5)(110), 5.69(5)(011), 4.96(10)(002), 4.81(10)(211), 4.21(5)(112), and 3.90(9)(211). Chemical analysis gave Al₂O₃ 0.01, Fe₂O₃ 26.15, FeO 0.18, MgO 0.03, CaO 0.09, K₂O 0.03, Na₂O 0.07, SO₃ 27.69, H₂O 45.02, total 99.27%, corresponding to the chemical formula: Fe²⁺ (SO₄)(OH) · 7H₂O. The DTA curve shows respectively three strong endothermic peaks at 85°, 170°, and 735°C, and a weak peak at 460°C. The TGA curve shows a loss of weight in three different steps. The infrared spectral curve of xitieshanite demonstrates that it has two principal absorption bands at 3,350 and 1,225–1,003 cm^?1 and two subordinate bands at 1,620 and 603 cm^?1.     

Determination of the degree of Al,Si order Q od in kinetically disordered albite using hard mode infrared spectroscopy

Hard Mode Infrared Spectroscopy (HMIS) is used to correlate the line shifts Δω, the intensity changes ΔA and the variations of spectral line widths Γ of infrared absorption bands with the degree of Al, Si ordering, Q _od, in kinetically disordered Na-feldspar. A simple relationship Δω∝ΔA∝ΔΓ∝Q _od ² was found with the phonon band around 650 cm^?1 being particularly sensitive to small changes of the degree of Al, Si ordering. It is shown that the average degree of Al, Si order can be determined from HMIS with an accuracy of ca. 8 percent using 50 mg of Na-feldspar. The experimental results agree well with recent X-ray determinations using identical samples. The significance of HMIS for the study of kinetic processes in minerals is explained.     

Synthetic Mn3+-kyanite and viridine, (Al2-xMn x 3+ ) SiO5, in the system Al2O3-MnO-MnO2-SiO2

Experiments on the join Al₂SiO₅-“Mn₂SiO₅” of the system Al₂O₃-SiO₂-MnO-MnO₂ in the pressure/temperature range 10–20 kb/900–1050° C with gem quality andalusite, Mn₂O₃, and high purity SiO₂ as starting materials and using /_O2-buffer techniques to preserve the Mn³⁺ oxidation state had following results: At 20 kb/1000°C orange-yellow kyanite mixed crystals are formed. The kyanite solid solubility is limited at about (Al_1.88Mn _0.12 ³⁺ )SiO₅ and, thus, equals approximately that on the join Al₂SiO₅-“Fe₂SiO₅” (Langer and Frentrup, 1973) indicating that there is no Jahn-Teller stabilisation of Mn³⁺ in the kyanite matrix. 5 mole % substitution causes the kyanite lattice constants a _o, b _o, c _o, and V _o to increase by 0.015, 0.009, 0.014 Å, and 1.6 ų, resp., while α, β, γ, remain unchanged. Between 10 and 18 kb/900°C, Mn³⁺-substituted, strongly pleochroitic (emeraldgreen-yellow) andalusite_ss (viridine) was obtained. At 15 kb/900°C, the viridine compositional range is about (Al_1.86Mn _0.14 ³⁺ )SiO₅-(Al_1.56Mn _0,44 ³⁺ )SiO₅. Thus, Al→Mn³⁺ substitutional degrees are appreciably higher in andalusite than in kyanite, proving a strong Jahn-Teller effect of Mn³⁺ in the andalusite structure, which stabilises this structure type at the expense of kyanite and sillimanite and, thus, enlarges its PT-stability range extremely. 17 mole % substitution cause the andalusite constants a _o, b _o, c _o, and V _o to increase by 0.118, 0.029, 0.047 Å and 9.4 ų, resp. At “Mn₂SiO₅”-contents smaller than about 7 mole %, viridine coexists with Mn-poor kyanite. At “Mn₂SiO₅”-concentrations higher than the maximum kyanite or viridine miscibility, braunite (tetragonal, ideal formula Mn²⁺Mn³⁺[O₈/Si0₄]), pyrolusite and SiO₂ were found to coexist with the Mn³⁺-saturated ky _ss or and _ss, respectively. In both cases, braunites were Al-substituted (about 1 Al for 1 Mn³⁺). Pure synthetic braunites had the lattice constants a _o 9.425, c _o, 18.700 Å, V _o 1661.1 ų (ideal compn.) and a _o 9.374, c _o 18.593 ų, V _o 1633.6 ų (1 Al for 1 Mn³⁺). Stable coexistence of the Mn²⁺-bearing phase braunite with the Mn⁴⁺-bearing phase pyrolusite was proved by runs in the limiting system MnO-MnO₂-SiO₂.     

Synthesis and physical properties of piemontite Ca2Al3-pMn p 3+ (Si2O7/SiO4/O/OH)

Mn³⁺-bearing piemontites and orthozoisites, Ca₂(Al_3-pMn³⁺ _p)-(Si₂O₇/SiO₄/O/OH), have been synthesized on the join Cz (p = 0.0)-Pm (p = 3.0) of the system CaO-Al₂O₃-(MnO·MnO₂)-SiO₂-H₂O atP = 15 kb,T= 800 °C, and \(f_{O_2 } \) of the Mn₂O₃/MnO₂ buffer. Pure Al-Mn³⁺-piemontites were obtained with 0.5≦p≦1.75, whereas atp=0.25 Mn³⁺-bearing orthozoisite (thulite) formed as single phase product. The limit of piemontite solid solubility is found near p=1.9 at the above conditions. Withp>1.9, the maximum piemontite coexisted with a new high pressure phase CMS-X1, a Ca-bearing braunite (Mn _0.2 ²⁺ Ca_0.8)Mn ₆ ³⁺ O₈(SiO₄), and quartz. Al-Mn³⁺-piemontite lattice constants (LC),b ₀,c ₀,V ₀, increase with increasingp:

The lattice energy of forsterite. Charge distribution and formation enthalpy of the SiO 4 4− ion

In the lattice energy expression of forsterite, based on a Born-Mayer (electrostatic+repulsive+dispersive) potential, the oxygen charge z _o, the hardness parameter ρ and the repulsive radii r _Mg and r _Si appear as unknown parameters. These were determined by calculating the first and second partial derivatives of the energy with respect to the cell edges, and equalizing them to quantities related to the crystal elastic constants; the overdetermined system of equations was solved numerically, minimizing the root-mean-square deviation. To test the results obtained, the SiO ₄ ^4? ion was assumed to move in the unit-cell, and the least-energy configuration was sought and compared with the experimental one. By combining the two methods, the optimum set of parameters was: z _o=?1.34, ρ=0.27 Å, r _Mg=0.72 Å, r _Si=0.64 Å. The values ?8565.12 and ?8927.28 kJ mol^?1 were obtained, respectively, for the lattice energy E _Land for its ionic component E _L ⁰ ,which accounts for interactions between Mg²⁺ and SiO ₄ ^4? ions only. The charge distribution calculated on the SiO ₄ ^4? ion was discussed and compared with other results. Using appropriate thermochemical cycles, the formation enthalpy and the binding energy of SiO ₄ ^4? were estimated to be: ΔH _f(SiO ₄ ^4? )=2117.6 and E(SiO ₄ ^4? )=708.6 kJ mol^?1, respectively.     

A Stucture—mineralogical Study of Ringwoodite

The powder XRD analysis of ringwoodite(γ-Fe2SiO4),which was synthesized in a II-stage anvil high-pressure capsule,was made,Its unit-cell parameter was calculated:a=8.219A,After the refinements,for several cycles,of the oxygen parameter x and the occupancy rate of Si in octahedron site,i.e.,the iversion degree u,the final result is R=0.077,when x=0.379A and u=27.5%,with the structural formula (Fe1.725 Si0.275)VI(Si0.725Fe0.275)IV O4 and atomic distances(Fe,Si)VI-O=2.022 A and (Si,Fe)IV-O=1.836A,Meanwhile,the Moessbauer spectroscopic analysis of the sample was conducted and the results obtained are in good agreement with those of X-ray structural analysis ,This paper focuses on the phase transformation and the properties of bonds of α－Fe2SiO4→γ-Fe2SiO4.     

Refinement of the parameters of the binary pulsar B0655+64 based on 111 MHz observations

An analysis of monitoring observations for the pulsar PSR B0655+64, which is located in a binary system, at 111 MHz during 2002–2015 are presented. The Keplerian parameters of the pulsar have been refived: the longitude of periastron ω = 276_.^°5785 ± 0_.^°0005 and the orbital semi-major axis is a_p sin i = 4.124976± 0.000003 s. The parameters of the perturbed motion have been determined: the motion of periastron ω = 0_.^°315 ± 0_.^°005/ year, and the derivative of the period of the binary system ? = (-1.66 ± 0.11) × 10^-14 s/s = (-0.524 ± 0.038) µs/year. The estimated time scale for the decay of the PSR 0655+64 system is (1.7 ± 0.1) × 10¹¹ yrs.     

Kinetic rate laws derived from order parameter theory IV: Kinetics of Al,Si disordering in Na-feldspars

The kinetic rate laws of Al-Si disordering under dry conditions (T = 1353K, 1253 K, 1223 K, 1183 K) and in the presence of water (p = 1 kbar, T = 1023 K, 1073 K, 1103 K) were studied both experimentally and theoretically. A gradual change of the degree of order was found under dry conditions. For intermediate degrees of order broad distributions of the order parameter Q _od occur. The variations of Q _od are correlated with structural modulations as observed in the transmission electron microscope. The time evolution of the mean value of Q _od can be well described by the rate law: $$\frac{{dQ_{od} }}{{dt}} = - \frac{\gamma }{{RT}}\exp \sum\limits_{i = 1}^n {X_i^2 } \left[ {\frac{{ - (G_a^0 + \varepsilon (\Delta Q_{od} )^2 )}}{{RT}}} \right]\frac{{dG}}{{dQ_{od} }}$$ with the excess Gibbs energy G and G _a ⁰ = 433.8 kJ/mol, ?= -27.4 kJ/mol, γ = 1.687 · 10¹⁴ h ^?1. Under wet conditions, two processes were found which occur simultaneously. Firstly, some material renucleated with the equilibrium degree of order. Secondly, the bulk of the material transformed following the same rate law as under dry conditions but with the reduced activation energy G _a ⁰ = 332.0 kJ/mol and ? = -43.0 kJ/ mol, γ = 1.047 · 10¹³ h^?1. The applicability of the kinetic theory is discussed and some ideas for the analysis of geological observations are evolved.     

Thermal expansion of single-crystal forsterite to 1023 K by Fizeau interferometry

Using a Fizeau interferometry technique, we have measured the coefficients of linear thermal expansion of single-crystal forsterite (Mg₂SiO₄) along three axial directions to 1023 K during heating and cooling cycles. Overall, the present data are consistent in magnitude (within 1 to 2%) with those previously reported but have less scatter. We used the Grüneisen statistical mechanical approach in analzying the data. The least-squares method was applied to evaluate thermal parameters (?, Q ₀, k and a) in two cases. The expansion coefficients in wider temperature ranges were extrapolated by using the parameters of solution 2 (i.e., solution by fixing ? and k). In contrast to earlier findings, our results show that for forsterite the Grüneisen parameter decreases with temperature, implying that it does not behave too differently from fayalite (Fe₂SiO₄) and periclase (MgO).     

High-pressure single-crystal X-ray diffraction study of jadeite and kosmochlor

The crystal structures of natural jadeite, NaAlSi₂O₆, and synthetic kosmochlor, NaCrSi₂O₆, were studied at room temperature, under hydrostatic conditions, up to pressures of 30.4 (1) and 40.2 (1) GPa, respectively, using single-crystal synchrotron X-ray diffraction. Pressure–volume data have been fit to a third-order Birch–Murnaghan equation of state yielding V ₀ = 402.5 (4) Å³, K ₀ = 136 (3) GPa, and K ₀ ^′  = 3.3 (2) for jadeite and V ₀ = 420.0 (3) Å³, K ₀ = 123 (2) GPa and K ₀ ^′  = 3.61 (9) for kosmochlor. Both phases exhibit anisotropic compression with unit-strain axial ratios of 1.00:1.95:2.09 for jadeite at 30.4 (1) GPa and 1:00:2.15:2.43 for kosmochlor at 40.2 (1) GPa. Analysis of procrystal electron density distribution shows that the coordination of Na changes from 6 to 8 between 9.28 (Origlieri et al. in Am Mineral 88:1025–1032, 2003) and 18.5 (1) GPa in kosmochlor, which is also marked by a decrease in unit-strain anisotropy. Na in jadeite remains six-coordinated at 21.5 (1) GPa. Structure refinements indicate a change in the compression mechanism of kosmochlor at about 31 GPa in both the kinking of SiO₄ tetrahedral chains and rate of tetrahedral compression. Below 31 GPa, the O3–O3–O3 chain extension angle and Si tetrahedral volume in kosmochlor decrease linearly with pressure, whereas above 31 GPa the kinking ceases and the rate of Si tetrahedral compression increases by greater than a factor of two. No evidence of phase transitions was observed over the studied pressure ranges.     

Energy gap and density in SiO2 polymorphs

A relationship between the energy gap (E _G) and density (ρ) for pure SiO₂ polymorphs is derived from atomic weights and first ionization potentials of free silicon and oxygen atoms. Theoretical considerations are based on the Lorentz electron theory of solids. The eigenfrequency v₀ of elementary electron oscillators, in energy units h v₀, is identified with the energy gap of a solid. The numerical relation is expressed as \(E_G = \sqrt {139.24 - 13.8327\rho } \) is in eV. For low-quartz with a density of 2.65 g/cm³ and also for stishovite with a density of 4.28 g/cm³, the energy gap E _G=10.1 eV and 8.9 eV, respectively. From laboratory measurements for low-quartz E _G=10.2 eV. The energy gap-density relation suggests a critical density value of ρ_x ≈ 10.1 g/cm³ for an SiO₂ phase when the energy gap vanishes (E _G=0), which is consistent with estimated densities for a high pressure silica polymorph with the fluorite structure.     

Coda <Emphasis Type="Italic">Q</Emphasis> in Qeshm Island,south of Iran,using aftershocks of the Qeshm earthquake of November 27, 2005

Coda wave attenuation is estimated for Qeshm Island which is located in the southeastern part of Zagros. For this purpose, the aftershocks of Qeshm earthquake in November 27, 2005, recorded within an epicentral distance less than 100 km, have been used. More than 829 earthquakes were recorded by a local temporary network consisting of 16 short period stations installed after a week after the main shock for ～10 weeks. The coda quality factor, Q _c, was estimated using the single-backscattering model in frequency bands of 0.5–24 Hz. In this research, lateral and vertical variations of coda Q in Qeshm Island are explored. In Qeshm Island, absence of significant lateral variation of coda Q is observed. To investigate the attenuation variation with depth, the coda Q value was calculated for coda time windows with different lengths (5, 10, 15, 20, 25, and 30 s). It is observed that coda Q increases with depth. However, in our study area, the rate of increase of coda Q with depth is not uniform. Beneath Qeshm Island, the rate of increase of coda Q is greater at depths less than ～40 km compared with those of larger depths. This is indicating the existence of a low attenuation anomalous structure under the ～40-km depth which may be correlated with the Moho depth in this region. The average frequency relation for this region is Q _c = 36 ± 1.2f ^{0.94 ± 0.039} at a 5 s-lapse time window length and Q _c = 110 ± 1.8f ^{0.88 ± 0.09} at a 30-s lapse time window length.     

Crystal structure of xinganite

Xinganite is a new REE-Be-rich silicate discovered in China. Its ideal formula is: (Y, Ce)Be SiO₄ OH. The mineral is of monoclinic system. The intensity data were collected with a single-crystal four-circle diffractometer. The lattice parameters are: a=4.7681 (± 0.00263) Å,b=7.7657 (± 0.00686) Å, c=9.9301 (± 0.00639) Å; α =90°, β=90.171° (±0.0053°), γ=90° space group p2¹/c;,Z=4. The crystal structure has been determined by direct methods and electron density synthesis methods. The least squares refinement gave a final discrepancy indexR=0.086. The crystal structural analysis shows that xinganite is of datolite-type structure.     

Surface destabilization and laboratory-induced non-stoichiometry in San Carlos olivine

Annealing experiments on natural olivine (Mg_1-x Fe _x )₂SiO₄ (with x≈0.11) crystals (San Carlos, Arizona, spinel-lherzolite context) have been performed between T=1,100° C and 1,500° C for oxygen partial pressures pO₂=10^?3 to 10^?13 bar and times of 1 to 140 h in CO/CO₂ or H₂/H₂O gas mixtures. Even specimens annealed within the T-pO₂ theoretical stability field (TSF) calculated for stoichiometric olivine (Nitsan 1974) show systematic alterations developed within the first few microns of the surface of the crystals. Pyroxene crystals or melt form on the original olivine surface even at T=1,100° C, with preference of pyroxene when T<1,350° C and SiO₂-rich glass if T>1,350° C. This glass (rhyolite-like) can concentrate calcium from the starting olivine, and aluminum when Cr-Al spinels are present as inclusions. These observations are in contradiction with the TSF. They are obviously due to the presence of platinum used as a container of our samples, even if the contact between olivine and platinum is very weak. Rapid surficial diffusion of iron toward platinum (or via the gas phase) induces a Fe-depleted surface. According to the TSF, this more forsteritic surface should have a wider pO₂ range of stability. This is not the case, just because this situation is largely out of equilibrium. This iron loss induces a departure from cationic stoichiometry: (Mg, Fe)_2(1?δ), SiO₄ with δ small and positive. We extended the model that Nakamura and Schmalzried (1983) (N.S.) developed for fayalite (x=1) to our natural olivine composition, under the assumption that the majority defects are magnesium vacancies, Fe³⁺ occupying octahedral and tetrahedral sites, and the more complex neutral defect corresponding to Coulombic attraction between neighboring Fe³⁺ ions. We have recalculated the olivine stability field in pO₂ vs. δ space at T=1,300° C using this model for x≈0.1 (its extreme limit of validity) and conclude that olivine is stable only in a very narrow range in pO₂ which depends on δ. The calculation shows also that when olivine has nearly cationic stoichiometry (δ=0) as we believe for our starting material, the pO₂ range of stability is narrower than indicated by the TSF. In particular, it explains why Fe precipitates from the olivine (δ=0) (in absence of any other precipitation of SiO₂-rich phases) between 10^?11 and 10^?13 bar at 1,300° C; this was not predicted by the TSF. Magnetite or iron precipitates also coexist with SiO₂-rich exsolutions or pyroxene when pO₂ is close to the upper or lower boundaries of the TSF, respectively. The N.S. model may have important implications for the interpretation of the existence of partial melting and/or the low-viscosity/low velocity zone in the upper mantle.     

Exoelectron spectroscopy of traps in surface layers of phenakite and quartz

The possibilities of exoelectron spectroscopy to investigate defects in dielectrics are demonstrated for phenakite Be₂SiO₄, its structural analogs Zn₂ SiO₄, Be₂GeO₄, solid solutions Be₂Si_1?x Ge _x O₄ (x=0÷1) and α-quartz. Emission maxima at 330 and 670 K in phenakite have been found to be due to [GeO₄]^5? andE' centers, respectively. Structural disturbances in the silicon and oxygen positions have been shown to control the exoemission activity of the crystals. Radiation induced decrease of exoemission activity connected with generation ofE' centers by neutron irradiation has been discovered. The energy level scheme of active centers in the subsurface region of Be₂SiO₄ has been established.     

The solution behavior of H2O in peralkaline aluminosilicate melts at high pressure with implications for properties of hydrous melts

Solubility and solution mechanisms of H₂O in depolymerized melts in the system Na₂O-Al₂O₃-SiO₂ were deduced from spectroscopic data of glasses quenched from melts at 1100 °C at 0.8-2.0 GPa. Data were obtained along a join with fixed nominal NBO/T = 0.5 of the anhydrous materials [Na₂Si₄O₉-Na₂(NaAl)₄O₉] with Al/(Al+Si) = 0.00-0.25. The H₂O solubility was fitted to the expression, X_H2O=0.20+0.0020f_H2O-0.7X_Al+0.9(X_Al)², where X_H2O is the mole fraction of H₂O (calculated with O = 1), f_H2O the fugacity of H₂O, and X_Al = Al/(Al+Si). Partial molar volume of H₂O in the melts, , calculated from the H₂O-solulbility data assuming ideal mixing of melt-H₂O solutions, is 12.5 cm³/mol for Al-free melts and decreases linearly to 8.9 cm³/mol for melts with Al/(Al+Si) ∼ 0.25. However, if recent suggestion that is composition-independent is applied to constrain activity-composition relations of the hydrous melts, the activity coefficient of H₂O, , increases with Al/(Al+Si).Solution mechanisms of H₂O were obtained by combining Raman and ²⁹Si NMR spectroscopic data. Degree of melt depolymerization, NBO/T, increases with H₂O content. The rate of NBO/T-change with H₂O is negatively correlated with H₂O and positively correlated with Al/(Al+Si). The main depolymerization reaction involves breakage of oxygen bridges in Q⁴-species to form Q² species. Steric hindrance appears to restrict bonding of H⁺ with nonbridging oxygen in Q³ species. The presence of Al³⁺ does not affect the water solution mechanisms significantly.     

Tracing quartz through the environment

Quartz, SiO₂, a pure mineral with tight crystal structure, is widespread in rocks and soil. Cosmic rays produce¹⁰Be (t _1/2=1·5×10⁶, yr) and²⁶Al (t _1/2=7·05×10⁵ yr) in quartz exposed at or near the earth’s surface. The use of accelerator mass spectrometry permits measurement of these nuclides in samples exposed at sea level for typical periods.In situ production makes interpretation relatively straightforward. Potential applications include age determination, measurement of erosion and deposition rates, and use as a tracer for continental weathering processes.     

Charge distribution from least-energy structure in Ca - Mg orthosilicates

Calcium-olivine, γ-Ca₂SiO₄, larnite, β-Ca₂SiO₄, merwinite, Ca₃Mg(SiO₄)₂, and monticellite, CaMgSiO₄, are considered. According to a rigid oxyanion scheme, eulerian orientation angles of the SiO₄ tetrahedra and translation coordinates of Ca and Si atoms are specified as structural variables τk. All derivatives of the static energy (Born model) contain atomic charges and repulsive parameters as unknowns; the minimum energy conditions ?E _L/?τ_k=0 yield 34 equations which are solved by a least-squares method. The set of energy parameters fitting structural properties of all four phases together is: z _Ca=1.50, z _o=?1.10 e, r _Ca=1.05, ρ=0.25 Å; the Mg charge was fixed at 1.38 e, from a previous study on forsterite. An average shift of 0.04 Å is observed between experimental and least-energy calculated atomic positions. Results are compared with those of Mg₂SiO₄, where the fit was based both on thermoelastic and on structural properties. If no charge values were fixed “a priori”, just ratios between charges could be determined by fitting them to structural data only.