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Magnesite (MgCO3), calcite (CaCO3), dolomite [(Ca, Mg)CO3], and siderite (FeCO3) are among the best-studied carbonate minerals at high pressures and temperatures. Although they all exhibit the calcite-type structure ( $${\text{R}}\bar{3}{\text{c}}$$ ) at ambient conditions, they display very different behavior at mantle pressures. To broaden the knowledge of the high-pressure crystal chemistry of carbonates, we studied spherocobaltite (CoCO3), which contains Co2+ with cation radius in between those of Ca2+ and Mg2+ in calcite and magnesite, respectively. We synthesized single crystals of pure spherocobaltite and studied them using Raman spectroscopy and X-ray diffraction in diamond anvil cells at pressures to over 55 GPa. Based on single crystal diffraction data, we found that the bulk modulus of spherocobaltite is 128 (2) GPa and K′ = 4.28 (17). CoCO3 is stable in the calcite-type structure up to at least 56 GPa and 1200 K. At 57 GPa and after laser heating above 2000 K, CoCO3 partially decomposes and forms CoO. In comparison to previously studied carbonates, our results suggest that at lower mantle conditions carbonates can be stable in the calcite-type structure if the radius of the incorporated cation(s) is equal or smaller than that of Co2+ (i.e., 0.745 A).

The new mineral ferrorhodonite, a Mn2+–Fe2+ ordered analogue of rhodonite with the idealized formula CaMn3Fe[Si5O15], was found in the manganese-rich metamorphic rocks of the Broken Hill Pb–Zn–Ag deposit, Yancowinna Co., New South Wales, Australia. Ferrorhodonite occurs as brownish red coarsely crystalline aggregates in association with galena, chalcopyrite, spessartine, and quartz. The mineral is brittle. Its Mohs hardness is 6. Cleavage is perfect on {201} and good on {021} and {210}. The measured and calculated values of density are 3.71 (2) and 3.701 g cm−3, respectively. Ferrorhodonite is optically biaxial positive, with α = 1.731 (4), β = 1.736 (4), γ = 1.745 (5) and 2 V (meas.) = 80 (10)°. The average chemical composition of ferrorhodonite is (electron-microprobe data, wt%): CaO 7.09, MgO 0.24, MnO 32.32, FeO 14.46, ZnO 0.36, SiO2 46.48, and total 100.95. The empirical formula calculated on 15 O apfu (Z = 2) is Ca0.81Mn2.92Fe1.29Mg0.04Zn0.03Si4.96O15. The Mossbauer and IR spectra are reported. The strongest reflections in the powder X-ray diffraction pattern [(d, A (I, %) (hkl)] are: 3.337 (32) (−1–13), 3.132 (54) (−210), 3.091 (41) (0–23), 2.968 (100) (−2–11), 2.770 (91) (022), 2.223 (34) (−204), 2.173 (30) (−310). Ferrorhodonite is isostructural with rhodonite. The crystal structure was solved based on single-crystal X-ray diffraction data and refined to R 1 = 4.02% [for 3114 reflections with I > 2σ(I)]. The mineral is triclinic, space group P $$\bar{1}$$ , a = 6.6766 (5), b = 7.6754 (6), c = 11.803 (1) A, α = 105.501 (1)°, β = 92.275 (1)°, γ = 93.919 (1)°; V = 580.44 (1). The crystal-chemical formula of ferrorhodonite inferred to be: M5(Ca0.81Mn0.19) M1−3(Mn2.52Fe0.48) M4(Fe 0.81 2+ Mn0.12Mg0.04Zn0.03) [Si5O15]. .

A combined powder and single-crystal X-ray diffraction analysis of dolomite [CaMg(CO3)2] heated to 1,200°C at 3 GPa was made to study the order–disorder–reorder process. The order/disorder transition is inferred to start below 1,100°C, and complete disorder is attained at approximately 1,200°C. Twinned crystals characterized by high internal order were found in samples annealed over 1,100°C, and their fraction was found to increase with temperature. Evidences of twinning domains combined with probable remaining disordered portions of the structure imply that reordering processes occur during the quench. Twin domains are hereby proposed as a witness to thermally induced intra-layer-type cation disordering.

We performed comparative study of phase relations in Fe1−x Ni x (0.10 ≤ x ≤ 0.22 atomic fraction) and Fe0.90Ni0.10−x C x (0.1 ≤ x ≤ 0.5 atomic fraction) systems at pressures to 45 GPa and temperatures to 2,600 K using laser-heated diamond anvil cell and large-volume press (LVP) techniques. We show that laser heating of Fe,Ni alloys in DAC even to relatively low temperatures can lead to the contamination of the sample with the carbon coming from diamond anvils, which results in the decomposition of the alloy into iron- and nickel-rich phases. Based on the results of LVP experiments with Fe–Ni–C system (at pressures up to 20 GPa and temperatures to 2,300 K) we demonstrate decrease of carbon solubility in Fe,Ni alloy with pressure.

Despite a large number of studies of iron spin state in silicate perovskite at high pressure and high temperature, there is still disagreement regarding the type and P–T conditions of the transition, and whether Fe2+ or Fe3+ or both iron cations are involved. Recently, our group published results of a Mossbauer spectroscopy study of the iron behaviour in (Mg,Fe)(Si,Al)O3 perovskite at pressures up to 110 GPa (McCammon et al. 2008), where we suggested stabilization of the intermediate spin state for 8- to 12-fold coordinated ferrous iron ([8–12]Fe2+) in silicate perovskite above 30 GPa. In order to explore the behaviour in related systems, we performed a comparative Mossbauer spectroscopic study of silicate perovskite (Fe0.12Mg0.88SiO3) and majorite (with two compositions—Fe0.18Mg0.82SiO3 and Fe0.11Mg0.88SiO3) at pressures up to 81 GPa in the temperature range 296–800 K, which was mainly motivated by the fact that the oxygen environment of ferrous iron in majorite is quite similar to that in silicate perovskite. The [8–12]Fe2+ component, dominating the Mossbauer spectra of majorites, shows high quadrupole splitting (QS) values, about 3.6 mm s−1, in the entire studied P–T region (pressures to 58 GPa and 296–800 K). Decrease of the QS of this component with temperature at constant pressure can be described by the Huggins model with the energy splitting between low-energy e g levels of [8–12]Fe2+ equal to 1,500 (50) cm−1 for Fe0.18Mg0.82SiO3 and to 1,680 (70) cm−1 for Fe0.11Mg0.88SiO3. In contrast, for the silicate perovskite dominating Mossbauer component associated with [8–12]Fe2+ suggests the gradual change of the electronic properties. Namely, an additional spectral component with central shift close to that for high-spin [8–12]Fe2+ and QS about 3.7 mm s−1 appeared at ~35 (2) GPa, and the amount of the component increases with both pressure and temperature. The temperature dependence of QS of the component cannot be described in the framework of the Huggins model. Observed differences in the high-pressure high-temperature behaviour of [8–12]Fe2+ in the silicate perovskite and majorite phases provide additional arguments in favour of the gradual high-spin—intermediate-spin crossover in lower mantle perovskite, previously reported by McCammon et al. (2008) and Lin et al. (2008).

The high-pressure elastic behaviour and the pressure-induced structural evolution of synthetic magnetite were investigated up to 11.11(5) GPa by means of in situ single-crystal X-ray diffraction with a diamond anvil cell, using the mix methanol:ethanol:water = 16:3:1 as pressure-transmitting medium and the ruby-fluorescence method for pressure-calibration. The evolution of the ruby R1-fluorescence line with P, with a drastic increase of the full-width-at-half-maximum (FWHM) of the Lorentzian profile at P > 9 GPa, shows that the P-medium is not hydrostatic above 9 GPa. Such a condition is well reflected by the drastic increase (by 20–22%) of the FWHM of the diffraction peak profiles of magnetite, by the behaviour of the Eulerian finite strain versus normalized pressures plot (f e –F e plot) and by the slight EoS-misfit. However, the diffraction data collected during decompression showed a reversible/complete restoration of the diffraction profiles and of the elastic behaviour in the f e –F e plot. The reflection conditions dictated by the $$ Fd\bar 3m $$ space group confirm that symmetry of magnetite is maintained within the P-range investigated. The structural refinements performed at 0.0001, 4.99(3) and 9.21(8) GPa show that the evolution of the oxygen u-parameter is almost constant within the P-range investigated. A weighted linear regression through the data points gives only a slight negative slope and no discontinuity is observed within the P-range investigated. A similar continuous behaviour is also observed in the evolution of the T- and M-polyhedral volumes, bond distances and angles with P. On the basis of data reported in this study, it appears that the elastic behaviour and the structural evolution of magnetite is drastically influenced by the experimental conditions (i.e., hydrostatic or non-hydrostatic), and diffraction data of magnetite collected under non-hydrostatic conditions are unusable for a reliable description of the elastic behaviour and for the P-induced structural rearrangements. Comparisons are carried out between the experimental findings of this study and those reported in the previous ones, in which an inverse-to-direct spinel phase transition at P > 8 GPa is suggested.

Combined X-ray powder diffraction, Mossbauer, and XANES spectroscopy in situ experiments revealed the transformation of cubic (Mg0.8Fe0.2)O ferropericlase to a rhombohedrally distorted phase at 35(1) GPa and room temperature. The Mossbauer spectroscopy results show that the rhombohedral distortion does not involve magnetic ordering. Combined with data from the literature, our results imply that the cubic to rhombodedral transition occurs in (Mg,Fe)O under conditions of non-hydrostatic stress over a wide range of composition (0.2≤x Fe≤1).

Examination of schorlomite from ijolite at Magnet Cove (USA) and silicocarbonatite at Afrikanda (Russia), using electron-microprobe and hydrogen analyses, X-ray diffraction and Mossbauer spectroscopy, shows the complexity of substitution mechanisms operating in Ti-rich garnets. These substitutions involve incorporation of Na in the eightfold-coordinated X site, Fe2+ and Mg in the octahedrally coordinated Y site, and Fe3+, Al and Fe2+ in the tetrahedrally coordinated Z site. Substitutions Ti4+Fe3+Fe3+−1Si−1 and Ti4+Al3+Fe3+−1Si−1 are of major significance to the crystal chemistry of schorlomite, whereas Fe2+ enters the Z site in relatively minor quantities (

Germanate garnets are often used as isostructural analogues of silicate garnets to provide insight into the crystal chemistry and symmetry of the less accessible natural garnet solid solutions. We synthesised two series of germanate garnets at 3 GPa along the joinVIIICa 3 VI (CaGe)IVGe3O12–VIIICa 3 VI Fe 2 IV Ge3O12 at 900 °C and 1,100 °C. Samples with compositions close to the CaGeO3 end-member consist of tetragonal garnet with a small amount of triclinic CaGe2O5. Samples with nominal compositions between XFe=0.4 and 1.0 consist of a mixture of tetragonal and cubic garnets; whereas, single-phase cubic garnets were obtained for compositions with XFe>1.2 (XFe gives the iron content expressed in atoms per formula unit, and varies between 0 and 2 along the join). Run products which were primarily single-phase garnet were investigated using Mossbauer spectroscopy. Spectra from samples synthesised at 1,100°C consist of one well-resolved doublet that can be assigned to Fe3+ in the octahedral site of the garnet structure. A second doublet, present primarily in samples synthesised at 900°C, can be assigned to Fe2+ at the octahedral sites of the garnet structure. The relative abundance of Fe2+ decreases with increasing iron content. Transmission electron microscopy analyses confirm this tendency and show that the garnets are essentially defect-free. The unit-cell parameters of tetragonal VIIICa 3 VI (CaGe)IVGe3O3 garnet decrease with increasing synthesis temperature, and the deviation from cubic symmetry becomes smaller. Cubic garnets show a linear decrease of unit-cell parameter with increasing iron content. The results are discussed in the context of iron incorporation into VIIIMg 3 VI (MgSi)IVSi3O3 majorite.

Wadsleyite II is a variably hydrous magnesium-iron silicate phase similar to spinelloid IV and a potential host for H in the Transition Zone of the Earth’s mantle. Two separate samples of wadsleyite II synthesized at 17.5 GPa and 1400°C and at 18 GPa and 1350°C have been characterized by electron microprobe, single-crystal X-ray diffraction, visible, IR, Raman, and Mossbauer spectroscopies, and transmission electron microscopy including electron energy-loss spectroscopy. The two samples have the following chemical formulae: Mg1.71Fe0.18Al0.01H0.33Si0.96O4 and Mg1.60Fe0.22Al0.01 H0.44Si0.97O4. Mossbauer spectroscopy and electron energy loss spectroscopy (EELS) indicate that about half of the iron present is ferric. Refinement of the structures shows them to be essentially the same as spinelloid IV. Calculated X-ray powder diffraction patterns show only subtle differences between wadsleyite and wadsleyite II. The hydration mechanism appears to be protonation of the non-silicate oxygen (O2) and possibly the oxygens surrounding the partially vacant tetrahedral site Si2, charge-balanced by cation vacancies in Si2, M5 and M6. The unit cell volume of this phase and its synthesis conditions indicate that it may be an intermediate phase occurring between the fields of wadsleyite and ringwoodite, if sufficient trivalent cations are available. The unit cell parameters have been refined at pressures up to 10.6 GPa by single-crystal X-ray diffraction in the diamond anvil cell. The refined bulk modulus for the sample containing 2.8 wt% H2O is 145.6 ± 2.8 GPa with a K’ of 6.1 ± 0.7. Similar to wadsleyite and ringwoodite, hydration has a large effect on the bulk modulus. The presence of this phase in the mantle could serve to obscure the seismic expression of the phase boundary between wadsleyite and ringwoodite near 525 km. The large apparent effect of hydration on bulk modulus is consistent with hydration having a larger effect on seismic velocities than temperature in the Transition Zone.

Fifteen samples of (Mg,Fe)SiO3 majorite with varying Fe/Mg composition and one sample of (Mg,Fe)(Si,Al)O3 majorite were synthesized at high pressure and temperature under different conditions of oxygen fugacity using a multianvil press, and examined ex situ using X-ray diffraction and Mossbauer and optical absorption spectroscopy. The relative concentration of Fe3+ increases both with total iron content and increasing oxygen fugacity, but not with Al concentration. Optical absorption spectra indicate the presence of Fe2+–Fe3+ charge transfer, where band intensity increases with increasing Fe3+ concentration. Mossbauer data were used in conjunction with electron microprobe analyses to determine the site distribution of all cations. Both Al and Fe3+ substitute on the octahedral site, and charge balance occurs through the removal of Si. The degree of Mg/Si ordering on the octahedral sites in (Mg,Fe)SiO3 majorite, which affects both the c/a ratio and the unit cell volume, is influenced by the thermal history of the sample. The Fe3+ concentration of (Mg,Fe)(Si,Al)O3 majorite in the mantle will reflect prevailing redox conditions, which are believed to be relatively reducing in the transition zone. Exchange of material across the transition boundary to (Mg,Fe) (Si,Al)O3 perovskite would then require a mechanism to oxidize sufficient iron to satisfy crystal-chemical requirements of the lower-mantle perovskite phase.

The partitioning of Fe and Mn between the large M(4) site and the octahedral sites, M(1,2,3) in the amphibole structure has been investigated in two natural manganogrunerites of compositions Ca0.1Mn1.9 Mg1.25Fe2+ 3.56Fe3+ 0.38Si7.81O22(OH)2 and Ca0.24Mn1.57 Mg2.27 Fe2+ 2.76Fe3+ 0.32Si7.84O22(OH)2. The long-range cation distribution in the two samples has been elucidated by in situ neutron powder diffraction revealing that Mn is preferentially ordered onto M(4) ≫ M(2) >M(1) >M(3) in both samples. Partitioning of Mn from M(4) into the octahedral sites begins at 350 °C, with site exchange energies of −16.6 kJ mol−1 and −14.9 kJ mol−1, in samples containing 1.90 and 1.57 Mn apfu, respectively. Mossbauer and infrared spectroscopy have been used to study the samples at room temperature, and Mossbauer data agree well with the diffraction results, confirming that high-temperature cation distributions are retained during cooling. The fine structure in the hydroxyl-stretching region of the IR absorption spectra has been used to discuss qualitatively the site occupancies of the coordinating M(1)M(3)M(1) triplet, linked by O(3). On the basis of such modelling, we conclude that a degree of local clustering is present in both samples.

We report Mossbauer milliprobe measurements on small single-crystals of a magnesium-rich hedenbergite, approximate composition CaFe0.54Mg0.46 (SiO3)2, in which each of the electric-field gradient and mean-squared displacement tensors for Fe2+ in the M1 site of the crystal are precisely determined. Each tensor has in common, as required of crystal symmetry, the twofold axis of the monoclinic unit cell, but the principal directions of the two tensors in the perpendicular plane are non-coincident. The mean-squared displacements determined in the Mossbauer experiment exceed those determined from the X-ray vibration ellipsoids for Fe2+/M1 by a factor of 1.6; the anisotropy in the mean-squared displacement tensor from the Mossbauer measurements exceeds that from X-ray by a factor of around 5. The ramifications of these differences are discussed.

Mossbauer spectra were recorded at multiple temperatures between 80 and 293 K to study the nature of Fe3+ in Fe0.05Mg0.95SiO3 perovskite that had been synthesised in a multianvil press at 1650 °C and 25 GPa at its mimimum \(\) stability limit. The Mossbauer data were fitted to a model with quadrupole splitting distributions (Fe2+) and Lorentzian lineshapes (Fe3+ and Fen+). The centre shift data were fitted to a Debye model with the following results: ΘM (Fe2+)=365±52 K and ΘM (Fe3+)=476±96 K. Hyperfine parameter data for Fe3+ suggest occupation of the octahedral site only. The average valence seen by the Mossbauer effect in rapid electron exchange that occurs between Fe2+ and Fe3+ is calculated from the hyperfine parameters to be 2.50±0.07. Correction of area fractions for site-dependent recoil-free fractions gives a value for Fe3+/∑Fe of 9.4±1.4%, which is independent of temperature. A perovskite phase of similar composition synthesised in the multianvil press at higher oxygen fugacity gives a value for Fe3+/∑Fe of 16±3%, where Fe3+ appears to occupy both sites in the perovskite structure.

A suite of 14 synthetic Ca-free P2 1 /c low-clinopyroxenes of compositions across the enstatite-ferrosilite (En-Fs) join have been studied by X-ray powder diffraction and Mossbauer spectroscopy. The crystal structure of one sample with composition X Fs=0.39 was determined by single-crystal X-ray diffraction. The powder diffraction data show that there is no significant (

57Fe Mossbauer studies at room temperature and temperature-dependent resistance studies have been performed on a natural specimen of cubanite (CuFe2S3) in a diamond-anvil cell at pressures up to ∼10 GPa. An insulator-metal phase transition occurs in the range 3.4–5.8 GPa coinciding with a previously observed structural transition from an orthorhombic to a hexagonal NiAs (B8) structure. The room temperature data shows that the metallization process concurs with a gradual transition from a magnetically ordered phase at low pressure to a nonmagnetic or paramagnetic phase at high-pressure. The change in magnetic behaviour at the structural transition may be attributed to a reduction of the Fe-S-Fe superexchange angle formed by edge-sharing octahedra occurring in the high-pressure phase. The non-magnetic or paramagnetic metallic phase at high pressure is retained upon decompression to ambient pressure-temperature conditions, indicative of substantial hysteresis associated with the pressure driven orthorhombic→hexagonal structural transition. The pressure evolution of both the 57Fe Mossbauer hyperfine interaction parameters and resistance behaviour is consistent with the transition from mixed-valence character in the low pressure orthorhombic structure to that of extended-electron delocalization in the hexagonal phase at high-pressure.

Majorite of bulk composition Mg0.86Fe0.15SiO3 was synthesized at 19 GPa and 1900 °C at an oxygen fugacity close to the Re/ReO2 buffer. Optical absorption spectra of polycrystalline samples were measured from 4000 to 25000cm−1. The following features were observed: (1) Three bands at 4554, 6005 and 8093 cm−1 due to the 5Eg → 5T2g transition of Fe2+ in a distorted dodecahedral site. (2) A band at 9340 cm−1 due to the transition 5T2g → 5Eg of octahedral Fe2+. (3) A band at 22784 cm−1 resulting from Fe3+, probably in an octahedral site (6A1g → 4A1g, 4Eg). (4) A very intense system of Fe2+ → Fe3+ intervalence charge transfer bands which can be modelled by two Gaussian components centered at 16542 and 20128 cm−1. The existence of two components in the charge transfer spectrum could be related to the fact that the tetragonal majorite structure may contain Fe3+ in two different octahedral sites. The crystal field splitting Δ of Fe2+ in dodecahedral coordination is 5717 cm−1. If a splitting of the ground state in the order of 1000 cm−1 is assumed, this yields a crystal field stabilization energy (CFSE) of 3930 cm−1, comparable to the CFSE of Fe2+ in pyrope-rich garnet. However, the splitting of 5T2g is significantly higher than in pyrope. This would be consistent with Fe2+ preferentially occupying the more distorted one of the two dodecahedral sites in the majorite structure. For octahedral Fe2+, Δ= 9340 cm−1 and CFSE=3736 cm−1, assuming negligible splitting of the ground state.

To study the crystal chemistry of bernalite, Fe(OH)3, and the nature of the octahedral Fe3+ environment, Mossbauer spectra were recorded from 80 to 350 K, optical spectra were recorded at room temperature and a sample was studied using transmission electron microscopy. The Mossbauer spectrum of bernalite consists of a single six-line magnetic spectrum at 80 K. A broadened six-line magnetic spectrum with significantly less intensity is observed at higher temperatures, and is attributed to a small fraction of bernalite occurring as small particles. The variation of hyperfine magnetic field data for bulk bernalite with temperature is well described by the Weiss molecular field model with parameters of H 0 = 55.7±0.3 T and T N = 427±5K. The centre shift data were fitted to the Debye model with parameters δ0=0.482±0.005 mm/s (relative to α-Fe) and ΘM=492±30 K. The quadrupole shift is near zero at 300 K, and does not vary significantly with temperature. Absorption spectra in the visible and near infrared range show three crystal field bands of Fe3+ at 11 300, 16000 and 23 200 cm-1, giving a crystal field splitting of 14 570 cm-1 and Racah parameters of B=629 cm-1 and C=3381 cm-1. Infrared reflection spectra show two distinct OH-stretching frequencies, which could correspond to two structurally different types of OH groups. A band was also observed at 2250 cm-1, suggesting the presence of molecular CO2 in the large cation site. Analytical transmission electron microscopy indicates that Si occurs within the bernalite structure as well as along domain boundaries. Electron diffraction and imaging show that bernalite is polysynthetically twinned along {100} planes with twin domains ranging from 3 to 20 nm in thickness. Results are discussed with respect to the nature of the octahedral Fe3+ site, and compared with values for other iron oxides and hydroxides.

To investigate the equation of state of α-MnS at high pressure and the possibility of a phase transition, the compression curve was measured at 298 K from 0 to 21 GPa using powder x-ray diffraction with a diamond anvil cell. The compression data are fit to a thirdorder Birch-Murnaghan equation of state, with parameters K 0 = 72(2) GPa and K′ 0 = 4.2(13). To compare present results with previous work, the data sets from three previous investigations (Clendenen and Drickamer 1966; Wakabayashi et al. 1968; Kraft and Greuling 1988) are refit to a Birch-Murnaghan equation of state. In the low pressure region (P < 10 GPa), the results of Clendenen and Drickamer (1966) agree with the present data; however the results of Wakbayashi et al. (1968) differ by more than 10%. A greater discrepancy between the present and previous results occurs above 10 GPa. Kraft and Greuling (1988) reported a structure transition at 7 GPa, and Clendenen and Drickamer (1966) observed a structure distortion at approximately 10 GPa; the present data show no evidence of either transition, and are well fit by a single equation of state from 0 to 21 GPa. Nonhydrostatic stress is discussed as one possibility for the discrepancy.

The success of molecular orbital theory in calculating crystal properties such as bond lengths and atomic force constants has been well documented in the literature. Calculations can be extended to crystals under simulated compression and strain to determine elastic moduli and their pressure derivatives. Comparison of the molecular orbital results with both experimental values and results obtained by calculations such as the potential induced breathing model provides insight into the nature of chemical bonding in MgO. In this study, several molecular clusters were investigated as possible models for MgO; the cluster Mg4O4H24 was chosen as the best model. Molecular energies were calculated with respect to bond length for both compression and expansion based on clusters that had been optimized for minimum energy. The resulting energy-volume curve was fitted to a recently derived equation of state (Brown, in preparation) to derive the values of K 0 and dK0/dP and the individual elastic moduli and their pressure derivatives were calculated by applying strain to the molecular cluster at both zero and elevated pressures. Agreement between theory and experiment varies between parameters, but the overall trend is encouraging. Since the molecular orbital model includes only short range interactions, its ability to approximating model the elastic moduli of MgO suggests a strong contribution to the elastic energy from short range interactions.