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1.
 The structures of Ca2CoSi2O7, Ca2MgSi2O7, and Ca2(Mg0.55Fe0.45)Si2O7 have been determined in the temperature range between 297 and 773 K with arbitrary intervals. The structures of the incommensurate phase of the three compounds are characterized by the presence of the six-, seven-, and eight-coordinated Ca–O polyhedra and of the bundles along the c-axes consisting of four arrays of the six-coordinated Ca–O polyhedra and an array of T1O4 (T1: Co, Mg, or Mg–Fe) tetrahedra in the structures. The number of bundles in each material decreases at elevated temperatures. The incommensurate phase undergoes a phase transition into the normal phase at 493 K in Ca2CoSi2O7, at 360 K in Ca2MgSi2O7, and at 510 K in Ca2(Mg0.55Fe0.45)Si2O7. The features of the structures of the normal phase are almost the same as those found in the basic structures (the averaged structures of the incommensurate structures), and this fact implies that the characteristics of the structures, such as the six-coordinated Ca–O polyhedra or fragments of the bundles, should be partially preserved at higher temperatures both in the incommensurate structures and also in the structures of the normal phase. Analyses of anisotropic displacement parameters clarified that disorder of the modulation waves is developed in the structures at higher temperatures. The evolution of a disorder in the structures was ascertained by observation of the circular diffuse streaks in the vicinity of the transition temperature between the incommensurate and normal phases. Received: 3 July 2000 / Accepted: 26 October 2000  相似文献   

2.
 The spinel solid solution was found to exist in the whole range between Fe3O4 and γ-Fe2SiO4 at over 10 GPa. The resistivity of Fe3− x Si x O4 (0.0<x<0.288) was measured in the temperature range of 80∼300 K by the AC impedance method. Electron hopping between Fe3+ and Fe2+ in the octahedral site of iron-rich phases gives a large electric conductivity at room temperature. The activation energy of the electron hopping becomes larger with increasing γ-Fe2SiO4 component. A nonlinear change in electric conductivity is not simply caused by the statistical probability of Fe3+–Fe2+ electron hopping with increasing the total Si content. This is probably because a large number of Si4+ ions occupies the octahedral site and the adjacent Fe2+ keeping the local electric neutrality around Si4+ makes a cluster, which generates a local deformation by Si substitution. The temperature dependence of the conductivity of solid solutions indicates the Verwey transition temperature, which decreases from 124(±2) K at x=0 (Fe3O4) to 102(±5) K at x=0.288, and the electric conductivity gap at the transition temperature decreases with Si4+ substitution. Received: 15 March 2000 / Accepted: 4 September 2000  相似文献   

3.
Experimental observations using transmission electron microscopy (TEM) indicate that Fe3+-rich grossular–andradite solid solutions with oscillatory zoning tend to occur as separate lamellae of andradite and intermediate compositions (Hirai and Nakazawa 1986; Pollok et?al. 2001). From one lamella to the next, the Fe3+ concentration can change significantly within a few nm. In order to understand the Fe3+ and Al content of each phase and the thermodynamics, chemistry, structure, and stability at the interfaces, Monte Carlo simulations were performed. According to our calculations, there is an ordered structure with a 1:1 ratio of Al and Fe3+ with alternating Al and Fe octahedra along the main cubic crystallographic axes. Even though this ordered grandite is more energetically favorable than a 1:1 mixture of the end members grossular and andradite [by ≈1.6?kJ (mol exchangeable cations)?1], this structure is stable only at temperatures below ≈500?K. Enthalpies, free energies, configurational and vibrational entropies of mixing, and the long-range order parameter are influenced by the formation of ordered grandite below 500?K. These data also explain why interfaces are stable only between grossular and grandite or between andradite and grandite but not between the end members. The interface energies between the end members and ordered grandite are comparably low [0.16?meV?Å?2∥(1?0?0), 0.55?meV?Å?2∥(1?1?0), 0.63?meV?Å?2∥(1?1?1)] and, therefore, do not hinder the formation of lamellae. Our calculations on the free energies of mixing indicate that there are miscibility gaps between grossular and grandite and between grandite and andradite only below ≈430?K. Since most of these solid solutions are formed at higher temperatures for which we did not find evidence of a miscibility gap, the formation of compositional oscillations is probably due to kinetic hindering of thermodynamically stable complete solid solutions. ?A new methodological aspect is the incorporation of zero-point energies of vibrations and the vibrational entropies into the calculation of the free energy of mixing. In case of the grossular–andradite solid solution, these vibrational effects change the free energy of mixing by only a few percent.  相似文献   

4.
 An ab initio Hartree–Fock calculation on beryl structure has been performed and the wave function has been used for an analysis of the electron density. The equilibrium geometry, determined by minimizing the energy with respect to cell parameters and fractional coordinates, is in good agreement with structural experimental measurements; small differences in length between the various Si–O bonds of the structure are well reproduced by the calculation. The two non-equivalent oxygen atoms (O1 and O2) of beryl show different electron distributions. In particular, the valence shell charge concentration (VSCC) of O1 (the bridge between two Si ions) has a torus-like shape, showing a bulge on the external side of the Si–O–Si angle and a thinning on the internal side of it; by contrast O2 has two lone pairs which are approximately located on the line for O2, normal to the plane passing, on average, through the atoms O2, Si, Be and Al. The electron density of each oxygen is strongly polarized toward the Si ions and much less polarized towards the other cations. Such features of the VSCC of the oxygens can be recast in terms of the valence bond theory, to explain the observed differences in bond lengths. By calculating the potential inside the channels of the beryl structure, predictions could be made about the positions occupied by alkali cations, which are often found in natural minerals belonging to the beryl group: results agree in general with experimental findings, but foresee a shift of such cations off the central positions located on the six fold symmetry axis. Additionally, calculations of position and orientation of H2O inside the channel, in the alkali-free beryl, locate the molecule close to the basal plane, with the H⋯H axis parallel to [001] or oriented at 40 from it. Received: 12 December 2001 / Accepted: 6 April 2002  相似文献   

5.
Static lattice energy calculations (SLEC), based on empirical interatomic potentials, have been performed for a set of 800 different structures in a 2 × 2 × 4 supercell of C2/c diopside with compositions between diopside and jadeite, and with different states of order of the exchangeable Na/Ca and Mg/Al cations. Excess static energies of these structures have been cluster expanded in a basis set of 37 pair-interaction parameters. These parameters have been used to constrain Monte Carlo simulations of temperature-dependent properties in the range of 273–2,023 K and to calculate a temperature–composition phase diagram. The simulations predict the order–disorder transition in omphacite at 1,150 ± 20°C in good agreement with the experimental data of Carpenter (Mineral Petrol 78:433–440, 1981). The stronger ordering of Mg/Al within the M1 site than of Ca/Na in the M2 site is attributed to the shorter M1–M1 nearest-neighbor distance, and, consequently, the stronger ordering force. The comparison of the simulated relationship between the order parameters corresponding to M1 and M2 sites with the X-ray refinement data on natural omphacites (Boffa Ballaran et al. in Am Mineral 83:419–433, 1998) suggests that the cation ordering becomes kinetically ineffective at about 600°C.  相似文献   

6.
 Thermodynamic properties of the barite–celestite solid solution were calculated using molecular principles. Cation–cation (Ba–Ba, Sr–Sr, and Ba–Sr) interaction energies were derived from a number of random and ordered cation distributions which were energy-optimized using force potentials as incorporated in the program package GULP. With these interaction energies, diagrams for the enthalpy and free energy of mixing could be computed for the entire range of the solid solution between the barite and celestite end members and for a number of annealing temperatures. These thermodynamic data show that the solid solution is nonideal. The system has a tendency for Ba2+ and Sr2+ cations to order onto alternating layers ||(100). However, this ordering scheme is thermodynamically only relevant for annealing temperatures below approximately 500 K and systems that are kinetically inhibited during crystal growth. For sufficiently long annealing times at room temperature, the solid solution tends to exsolve with barite–celestite interfaces ||(100). The cell parameters a and c were calculated to have almost linear behavior for the whole solid solution, suggesting close to ideal behavior according to Vegard's law. In contrast, b tends to deviate positively from linearity, in agreement with experimental values. Received: 6 April 1999 / Revised, accepted: 29 September 1999  相似文献   

7.
The kinetics of monodomain order-disorder processes in monoclinic (I2/c) BaAl2Ge2O8-feldspar have been investigated by X-ray powder diffraction, Hard Mode IR Spectroscopy, and TEM darkfield imaging on quenched samples. Compared to the behaviour predicted by the TDGL approximation ordering kinetics observed at low temperatures slow down significantly when equilibrium is approached. Such a delay is not observed in disordering experiments starting from essentially ordered cation distributions. The deviation from TDGL behaviour is interpreted in terms of partial order parameter conservation in a non-uniformly ordered phase. Modifications to the uniform TDGL rate equation are tested against the available data. An activation energy of 352 ± 28 kJ/mol is obtained for Al,Ge ordering. The mixing coefficient ξc 22, which describes the degree of order parameter conservation, is obtained as a function of temperature. While this coefficient vanishes in the vicinity of the transformation temperature T tr, it saturates towards a level of ξc 22≈0.4 for T→0. ξ c 22 determines the kinetic stability of ordered clusters quenched from TT tr. Received: 21 April 1999 / Revised, accepted: 19 July 1999  相似文献   

8.
 The nature of Al–Si ordering across the tetrahedral sites in muscovite, K2Al4(Si6Al2O20)(OH)4, was investigated using various computational techniques. Values of the atomic exchange interaction parameters J l were obtained. From these parameters, a two-dimensional Al–Si ordering scheme was deduced. The transition temperature T c for this two-dimensional ordering is 1900 K. There are several possible ordering schemes in three dimensions, based on different stacking sequences of ordered sheets of tetrahedral sites. Monte Carlo simulations of both two-dimensional and three-dimensional ordering were performed, but in the three-dimensional simulation only the two-dimensional ordering is seen, implying that three-dimensional ordering is too slow to be attained during the timescale of the simulation. The effect of the three-dimensional interactions is to raise the two-dimensional ordering temperature to 2140 K. From the three-dimensional Monte Carlo simulation, the frequency of occurrence of 4Si0Al, 3Si1Al, 2Si2Al and 1Si3Al clusters was determined, which match those inferred by 29Si MAS–NMR measurements reasonably well. In fact, the match suggests that the cation ordering seen in experiments corresponds to a configuration with considerable short-range order but no long-range order, similar to a state that is at a temperature just above an ordering phase transition. Received: 28 August 2000 / Accepted: 12 March 2001  相似文献   

9.
 Synthetic (SiGe)-pyroxenoids are often observed to have superperiods. Whether or not these superperiods grow in connection with Si-Ge ordering is a fundamental question. The size difference between Ge and Si tetrahedra leads to CdGeO3 having the pyroxmangite structure, whereas CdSiO3 has the wollastonite structure. Consequently, considerable strain is expected for a pyroxenoid with a disordered Ge-Si distribution. A 29Si MAS-NMR study of a Cd-pyroxmangite of nominal composition Cd7[Ge6Si]O7 points to considerable Si clustering, probably as GeSiSiSiGe triples corresponding to the wollastonite-like units of the siebener chain. It is proposed that such ordering relieves strain within the tetrahedral chain. Residual strain is also relieved by insertion of an extra pair of GeO4 tetrahedra into the pyroxene-like component of the siebener-chain units, leading to single neuner-chain units which terminate the superperiods. This growth pattern is cyclic. The presence of several types of superperiod may reflect similar energetics for different Ge-Si-ordering patterns within the siebener chains. Ordering of Si-rich unit cells and of unit cells having no Si is proposed as the reason for the occurrence of the superperiods in Cd-pyroxmangite. Received: 25 August 1999 / Accepted: 19 May 2000  相似文献   

10.
BaAl2Ge2O8-Feldspar undergoes an order-disorder phase transition I2/c↔C2/m at T tr ≈1690 K. The thermodynamics of the Al,Ge cation ordering process is described in terms of the compressible Ising model in mean field approximation. The mean field potential predicts a first order character of the phase transition. This is compared to antiferromagnetic ordering in a two-dimensional square Ising model with NN-pair interactions and four-spin interactions on alternating squares. Calculated order parameters and short range ordering are in good agreement with the corresponding properties observed in BaAl2Ge2O8-feldspar by means of X-ray diffraction, hard mode infrared spectroscopy and TEM. Using known calorimetric data a similar model is postulated for Al,Si ordering in anorthite, CaAl2Si2O8, for which the derived potential describes a transition with slightly stronger first order character at T tr ≈1928 K. Received: 30 January 1998 / Revised, accepted: 29 August 1998  相似文献   

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