The previously reported resistance heaters for the high-temperature single crystal X-ray diffraction study can be classified into two groups based on the characteristics of heater element employed. The elements which are able to use in the open air constitute one group. Platinum or nicrome wire resistance heaters belong to this group and these heaters are suitable for relatively low temperature experiments below 1100°C. Graphite heater and Tantalum heater constitute the other group and these heater elements are stable only under the vacuum or in the inert gas atmosphere. The elements in this group can generate temperatures higher than 2000°C. Two selected designs of heaters were described from each group. A high-temperature cement and a method for mounting sample crystal are also described.

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A new specimen heating equipment is developed for the four-circle diffractometer and the precession camera. The specimen is heated by a hot gas stream. The temperature can be varied from the room temperature to 1100°C and the atmosphere around the specimen can be controlled by changing the composition of gases for heating. The specimen temperature is stable to ±1°C over the full range of the χ angle. The equipment imposes no significant mechanical restrictions on the angular ranges of the four circles. The absorption of incident and diffracted beam intensities due to the high polymer film, which is used as a heat shield of the specimen, is less than 1%. Installation, adjustment and handling of the equipment are very simple and easy. The use of this equipment has been demonstrated for the high temperature X-ray diffraction experiments of the delafossite-type compound CuAlO₂.

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Gas-flame heating apparatus for X-ray diffraction studies designed by Yamanaka, Takéuchi and Sadanaga (1981) consists of gas flow controller and microburner set on the stand and provides temperatures higher than 2000°C. Control of the temperature of the sample is carried out by varying the mixing ratio of propane, oxygen and nitrogen gases. The last gas plays a role to regulate the heating temperature and to suppress a fluctuation of the gas-flame especially at low temperatures. It has been demanded to improve the microburner for a more applicable usage for the single-crystal X-ray diffraction studies. A newly devised heating system is composed of a joint assembly of gas-flame and electric resistance heater. Since the assembly is set on the χ-circle of a four-circle X-ray diffractometer, measurement of the diffraction intensities can be made throughout the same samplesetting from room temperature to high temperatures up to 2500°C and can be conducted at more stable and highly desired temperatures. The measurement of the sample-temperatures higher than 1500°C is carried out by a thermocouple of Pt-Rh (20-40%) or Ir-Rh (40%) and an optical pyrometer. For the precise temperature measurement during the collection of intensity data, the sample is mounted on the thermocouple attached to the goniometer head. The thermoelectric current is guided to the regulator and recorder through a ring terminal fixed to the goniometer.

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A high-temperature single crystal X-ray diffraction camera has been constructed by modifying an infrared thermal-image furnace. High temperatures (∼1700°C) can be readily attained by focussing radiation from a halogen lamp on a single crystal with a gold-plated internal ellipsoidal reflector. This camera has been used for examining the phase transformation and melting of orthopyroxene and proved to be useful for the study of the phase changes and the structure states of the produced phases in single crystals at high temperatures.

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A new laser-heating system which can provide temperatures above 2000°C has been developed for X-ray single-crystal diffraction studies. The system consists ofa CO₂ gas laser, optical system and power controller having a function of measuring the specimen temperature. As a special care is needed for measuring the specimen temperature during intensity data collection, we adapted an optical pyrometer to measure specimen temperatures. The measurement can be executed with less influence of emissivities by ref ering the ratio of radiation intensities corresponding to two wave lengths, in infrared region, to that theoretically derived. The specimen temperature in 1000°-1800°C range was successfully controlled to ±7°C during a trial examination of the total system with a four-circle diffractomter which worked in usual mode of data collection. An application of the system has been demonstrated to the study of high cristobalite at several temperatures from 1000°C to 1600°C.

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An adiabatic calorimeter has been described for the calorimetric measurement of minerals in the range from room temperature to 600°C. Unlike reported adiabatic calorimeters which generally require samples in the amount of 7—100 g, the new calorimeter has been so designed that very small amount of samples, such as 1—2g, may be used. The main part of the calorimeter is composed of metals, and of sheath heaters and sheath thermocouples to obtain good thermal contact, respons and homogeneity in the sample and the environment. The data acquisition system is automated with a microcomputer. The heat capacity (C_P) of corundum between 30°and 500°C has been determined by the calorimeter in the precision of ±2% using about 2 g of the powder.

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It is stressed that the correction of measured integrated intensities for thermal xdiffuse scattering (abbreviated as TDS) is of increasing importance in structure determinations. Firstly explanations on basic ideas and some methods of TDS-correction provided by many authors are given in section 2 and 3. Then is described in section 4 an example of the application of a fairly analytical method according to Merisalo and Kurittu (1978) to F_odata of ZnO with the wurtzite-type structure. The TDS-correction factors of Zn0 are anisotropic; the values in the c*-direction are slightly smaller than those in the directions perpendicular to c*. The magnitudes of the correction factors attain maximum of 20% of measured integrated intensities at the highest value of sin θ/λ (1.5 Å^-1). Least-squares refinements of the three-cumulant model of Zn0 based on F_o′s corrected for TDS led to negligibly small third cumulants (C¹¹³ and C³³³) except for, C¹¹¹, whereas the values of both C¹¹³ and C³³³ were significant in the refinement using F_o′s without TDS-corrections. This result strongly suggests that least-squares determinations of parameters for anharmonic thermal vibrations should be based on F_o′s (or|F_o|^2′s) corrected for TDS.

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Four theoretical studies on anharmonic thermal vibration by Willis (1969), Matsubara (1975 a, b), Kurki-Suonio, Merisalo and Peltonen (1979), and Johnson (1969) are reviewed and compared with each other. Generalized Willis method by Tanaka and Marumo (1983) is also described. Experimental works are summarized to display the charcteristics of each method. Anharmonic thermal vibration of the Cu atoms in KCuF₃ crystals and the O atoms in α-Al₂O₃ crystals were studied by the authors. The study on KCuF₃ crystals exhibited that the aspherical electron distribution and thermal vibration, which appeared on the deformation density map as superposed peaks, could be seperable. Anharmonic thermal vibration of the O atoms in α-Al₂O₃ crystals suggested possible diffusion paths of the O atoms. The maxima of potential along the paths are a little lower than the observed activation energy of the self-diffusion process of the O atoms.

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Thermal vibrations of atoms of a synthetic spinel MgA1₂O₄ (a=8.0806Å, Z=8, Fd 3m) have been studied based on sets of X-ray single-crystal diffraction intensities collected at high temperatures up to 1700°C. The study was initiated by refining the temperature factor T (Q) of each atom in the form of the second-rankk tensor β, assuming the ellipsoidal model of harmonic vibration. Difference Fourier maps based on the structure factors obtained from the refinements at 1230°C (R=4.13 %), 1390°C (R=4. 32 %), and 1660°C (R=4. 31 %) revealed residual electron densities around the atoms at the tetrahedral site A (point symmetry 4 3 m), octahedral site B (3 m) and even around the oxygen atoms (3 m), the modes of occurrence suggesting anharmonic atomic thermal vibrations. In order to execute subsequent anharmonic refinement, the observed reflection intensities I_obs were then corrected for the intensities of thermal diffuse scattering I_TDS, which is related to I_oba as I_obs=I_Bragg+I_TDS-I_Bragg (1+α₁), where I_Bragg is the true intensity of a Bragg reflection. The values of α₁ were evaluated based on the model of one phonon and first order acoustic vibration and using the elastic constants c_ij. For anisotropic anharmonic refinement, we adopted a cumulant expansion of T (Q) in the form exp [∑n!iⁿμ_pqrs……q_pq_qq_rq_s……](Johnson, 1969) and refined, in addition to β_ij, the coefficients γ_pqr and δ_pqrs of the third-and fourth-rank tensors, respectively. The result of the refinement includes : (1) The higher the heating temperature, the more intensified was the anharmonicity of the atomic thermal vibrations. (2) The oxygen u parameter was significantly shifted compared with the case in which anharmonic refinement was not made, the A-0 distances being contracted, while B-O lengthened. (3) The atom at the A site showed a large value of γ₁₂₃, indicating that the thermal motion may well be represented by the shape of a tetrapod, while that at β showed a relatively large value of δ₁₁₂₂, thermal motion being represented by a set of eight lobes along the lines parallel to the cubic body diagonals. (4) The oxygen atom showed a conspicuous anisotropy particularly at 1660°C. In the difference Fourier map based on F_??_´s, obtained after the anharmonic refinement, the above-mentioned residual electron densities around the cation sites were almost cleared out.

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Diffraction intensities from a crystal at very high temperature, such as those above 1000°C, are not rarely contaminated with those from a binder, such as zirconium cement, with which the crystal is fixed to a rod, thus hindering accurate determination of the crystal structure. Such a disadvantage can be evaded by the use of a crystal sample having the shape of a thin needle, 5-10 mm long. As the crystal in this case is not completely bathed in the X-ray beam, a new formulation is required to correct diffraction intensities for absorption and change in volume seen from the beam. A procedure of these corrections for a cylindrical sample has been described for the geometry of four-circle dif f ractometer. A computer program has been provided for the procedure.

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Abstract In view of the importance of multiple diffraction effects in X-ray and neutron diffractions, which may cause misunderstanding for the space group determinationss or intensity measurements, the geometry of the phenomena has been reviewed in a summarized form. As examples, the Umweganregung peaks for pyroxene and enargite observed for the φ-azimuth were indexed by operative and cooperative reflections.

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The crystal structures of fast ionic conductors are characterized by the statistical distribution and strong anharmonic thermal motion of mobile ions i the lattices. Because of the structural characteristics, even the basically simple structures suchh as α-AgI- and CaF₂-type, have been still in investigation. Diffraction studies by X-rays and neutrons are reviewed on the above two types.

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A review has been presented on the structural analyses of silicate melts and silicate glasses by means of various methods which include infrared spectroscopy, Raman spectroscopy, X-ray diffraction, neutron diffraction, X-ray emission spectroscopy, X-ray photoelectron spectroscopy, EXAFS measurement, direct chemical analysis and molecular-dynamics simulation.

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Vapor species vaporized from inorganic materials at high temperatures are complex mixtures consisting of molecules with the same chemical formulae as solid, decomposed smaller molecules and atom, and their polymers. Obtaining the equilibrium constant for the formation reactions of each species leads to calculations for the vapor pressures and the thermodynamic data for each species. In the decomposition reactions of the vaporization of oxides, oxygen gas is usually evolved, so that oxygen partial pressure in the atmosphere affects largely on the equilibrium. Non-equilibrium vaporization from the specimen in vacuum is called the free vaporization. Results in this free vaporization can not be estimated accurately from the above equilibrium data, because of containing the term of vaporization coefficient which depends on atomic structure of the vaporization surface. It increases with increasing temperatures and tends to unity at the melting point. Vapor pressures over single oxides relate to their melting points, but there are some cases which deviate considerably from them. Vapor pressure and vaporization rate decrease with increasing oxygen partial pressures in the atmosphere. The vaporization rate from Cr₂O₃ decreases at lower p_O2 region with increasing p_O2, but it increases after a minimum value, because of the formation of higher valence oxide species CrO₃ and CrO₂. Partial pressure of water vapor in the atmosphere accelerates the vaporization by formations of hydroxide vapor species, especially from alkali and alkaline earth oxides, as measured by the transpiraton method. Vaporizations from double oxide materials may be estimated from the data of the above mentioned single oxides, but the equilibrium vapor pressure of a predominant vaporizing component includes the term of activity in the compound or solid solution. Rate of the free vaporization from double oxides in vacuum usually decreases with time. One component vaporizes pref ereecially and remained component makes a layer (porous or dense compound and solid solution) on the vaporization surface. So the vaporization rate decreases with time, being controlled by diffusion of vaporizing species or ions through the layer, or it is constant due to non-resistivity of passing of vapor species through the porous layer or the congruent vaporization reaction. Vaporizations of minor impurities containing in materials at high temperature may be understood from the above mentioned knowledge, but there are some examples of impurities much stabilzed in the matrix.

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The development of the cubic anvil type high pressure apparatus made it possible to perform powder X-ray diffraction study under wide range of pressure and temperature. By combining with an energy dispersive type X-ray diffraction system, the exposure time has been reduced considerably and the kinetics of the pressure-induced phase transformation can be studied. Diamond anvil cells contributed a lot to extend the pressure range of high pressure X-ray studies. It is now possible to study the structure and the compressibility of powder materials up to megabar region. Many new phase transformations in simple oxides have been found using diamond anvil cells.

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A new method for determining an unknown structure by analizing powder diffraction pattern has been developed especially for the high pressure X-ray diffraction. The method is an extension of 'graphical method' for two dimensions (down to monoclinic structure). The method has been used successfully for Te(II), iodine, Cs(IV) and some sodium halides.

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There are two different methods for heating sample crystal in the pressurized diamond anvil cell; laser-beam heating method and resistance heater method. The laser beam method is able to heat the -crytal higher than 1500°C but the controlling and the measuring the crystal temperature have less accuracy. This method has many difficulty on the application for the X-ray diffraction experiments. On the resistance heater method, the maximum temperature can be obtained is less than 700°C but the temperature control is easier and has higher accuracy. However, one technical difficulty commonly observed on this method is the gradual decrease of the sample pressure above the temperature of 200°C. This difficulty may be solved by the application of the spring coil or Belleville washer on the pressurizing bolt of the diamond anvil cell.

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The results have been summarized of some of our recent single-crystal diffraction studies of mineral structures at high pressures with the use of a diamond-anvil pressure cell. They include: (1) LiScSiC₄ olivine (up to 36 kb) The structure behaves against pressure in a way which is different from the f orsterite case. The result has been basically interpreted in terms of relatively high compressibility of the M(1) octahedra which are occupied by Li. (2) Covellite, CuS (up to 33 kb) A notable feature has been found that the S-S bond in the structure is lengthened with an increase of pressure in the above range. (3) Helvite, Mn₄ (SiBeO₄)₃S (up to 45 kb) The shrinkage of the framework is characterized not only by rotations of the constituent tetrahedra but also contraction of the BeO₄ tetrahedra. And (4) Synthetic f orsterite, Mg₂SiO₄ (up to 79 kb) A new experimental procedure was tested that two crystal pieces, having different orientations, were put in the same gasket hole to obtain diffraction intensities. This procedure has been proved to be advantageous to increase the number of observed diffraction intensities compared with the ordinary case in which one crystal piece is used. The result of structure analysis has in fact provided structural data which are more reliable than reported data.

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A diamond anvil cell was used to investigate the phase relations between low and high temperature phases of cubanite and also between high pressure polymorph and the above-stated phases. Initial slope of low-high temperature phase boundary is about 200°C/GPa, showing a good coincidence with the reported value. Compressions of both low and high temperature phases produce a high pressure modification isostructural with troilite. The conversion accompanies an increase in density of 23%. This compaction is induced by a change of coordination numbers of anions surrounding cations from 4 to 6. The dense phase reverts to high temperature phase but not to low temperature. No significant difference was seen in heat capacities of low and high temperature phases. This implies the structural resemblance between two phases. The change of enthalpy accompanied with the transformation between low and high temperature phases was mainly attributed to the order-disorder transitions of both magnetic and ionic configurations in the lattice.

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The structures of high-pressure phases of Mg₂SiO₄ and MgSiO₃ are summarized based on the results of X-ray diffraction method using single crystals, and the relationships among their structures are discussed with configurations of polyhedra about cations. The α→β→γ phase transformations of Mg₂SiO₄, which are not accompanied with the change in coordination number of cations, are mainly characterized by the idealization and compression of MgO₆ and _??_O₆. The high-pressure phases of MgSiO₃, ilmenite- and perovskite-types, have. SiO₆ octahedra which show a slight expansion in the high-pressure phase. On the other hand, the coordination of Mg-polyhedra change remarkably in high-pressure phase. A linear correlation is observed between phase-transformation pressure and cation polyhedral volume. The Mg_??_Si disorder is not observed in any high-pressure phases of magnesiumsilicates. Effects of Fe²⁺ on the β- and γ-phase structures are also discussed.

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The phase equilibria of the system MgO-FeO-SiO₂ at pressures higher than 20 GPa studied in our laboratory were summarized. The signs of the phase boundary curves were found to be negative for the transformations of ilmenite-perovskite in MgSiO₃ and spinel-perovskite+periclase in Mg₂SiO₄. The phase boundaries are very close each other. The Fe-component does not affect significantly on these features. The stability fields of spinel, ilmenite and perovskite solutions were specified up to 26 GPa. The stabilization of the perovskite-bearing assemblage was demonstrated to bethe dominant cause of the 670km discontinuity, which is completed within a quite narrow pressure interval, less than 1 GPa. The phase relations including the Fe-Mg partitioning between perovskite and magnesiowustite and the density consideration suggest suggest an assebbage of (Mg_0.96Fe_0.04)SiO₃ perovskite and (Mg_0.76Fe_0.24) O magnesiowustite to be the major constituent of the lower mantle.

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The energy minimization method (WMIN, Busing (1981)) has been successfully applied to predicting the crystal structures of minerals of geological interest at high pressure. The repulsive parameters, ionic radius A and ionic compressibility B of some ions have been revised. The changes of the crystal structures with the increase of pressure are summarized as follows : (1) Degrees of shortening of longer bonds are larger than those of shorter bonds; (2) Unshared edges become shorter at the higher rate than the shared edges; In some cases the shortest shared edge remains almost constant; (3) The shape of polyhedron becomes regular, because unshared edges of cation polyhedra tend to approach the length of shared edges. It is often found that the mean Si-O distance increases when the phase transition; however, the mean Si-O distance of a particular phase in the stability field does not differ very much from that of the phase stable at 1 atm. The inter-diffusion coefficients of four transition metals in the forsterite structure previously obtained have been compared with their self-diffusion coefficients in olivine structures estimated on the basis of the potential energy maps by using the WMIN program. We have also applied the WMIN method to predicting the crystal structures of minerals at high temperature and to examining the cation distribution in olivine. Our studies have laid the foundation of the discussion based on the potential energy function about the crystal structures of minerals and about the rate processes applicable to geological phenomena.

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Melting experiments on pyrope Mg₃Al₂Si₃O₁₂ at pressures up to 10 GPa were carried out. The quenched materials from the pyrope melt varied with increasing pressure; glass + pyroxene→pyroxene→pyrope. The compositions of the glass and the pyroxene were the same with that of the pyrope. By means of X-ray studies, the pyroxene crystals of the quenched material were identified as an aluminous orthoenstatite with the space group Pbca. This aluminous enstatite with a pyrope composition is considered to be a metastable phase produced on quenching because it has no stability field in the P-T ranges examined so far. The slope of the melting curve (dTm/dP) significantly decreases above 7 GPa. This result suggests a pressure-induced structural change took place in the pyrope melt at high pressure.

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A brief review has been presented on the Rietveld method and its recent development. It consists of (1) Introduction, (2) Recent development of the method, (3) Intensity measurements including pulsed neutron and synchroton radiation sources, (4) General principles and formula such as those for profile and preferred-orientation correction functions, (5) Computer programs, (6) Examples of the refinement, (7) Discussion, and (8) Concluding remarks.

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The deformation of quartz in granitic rocks up to 5km from the Median Tectonic Line (MTL) was investigated by X-ray diffraction. The X-ray line broadening of the pulverized quartz grains (5-20μm) is related to the strain distribution arond dislocation in quartz grains. In order to determine dislocation densities, a relation has been derived between X-ray line broadenings and dislocation densities. Using the relation, the magnitude of the differential stress level has been found to vary from 50 to 150 MPa(the corresponding dislocation density ranges in 5.9x10⁷ to 5.1x10⁸ cm^-2). The differential stress near MTL(less than 500m from the MTL) was about 130 MPa, but that away more than 2km from MTL was about 60 MPa. This change of the differential stress as a function of distance from MTL reflects the stress state of the last tectonic event.

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A new method of “in-situ” observation of crystal growth processes has been developed. By this method, it is possible to observe on a TV screen the movement of growth layers with mono-molecular step heights spreading on the surfaces . The method has been applied to in-situ observation of growth processes of CdI₂ and NaCI crystals in aqueous solution by means of two baths flow system, where temperature and flow speed can be varied from 30 to 40°C, and 0 to 30 cm/sec ., respectively. The images of moving growth layers on a crystal face are observed by transmission phase contrast microscopy and are converted to video signals by a TV camera. Depending on the type of purposes, the images can be either directly recorded on a video tape recorder or after digitalization on a floppy disk in a micro-computer. The latter technique is more advantageous for the measurements of step velocities or for improving images by means of image processings. The followings have been observed as a result of preliminary application of this new method to the growth process of CdI₂ crystals from the aqueous solution. 1) Two different saturation temperatures are obtained for the spirals growing on one face of a single crystal. These spirals differ each other in their symmetries or in their step heights and show different dependencies of the advancing rates upon supersaturation. 2) when two types of spirals grow on a crystal, the advancing rate of one type of steps are influenced not only by the supersaturation for these steps but also by the supersaturation for the other type of spiral steps. 3) The process of twin formation due to the introduction of a stacking fault is visualized for the first time. The twin is generated at spiral centre by an accidental mistake in stacking and transmitted through the advancement of spiral layers.

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Growth of NaClO₃ crystals from aqueous solution in a quasi-two-dimensional system was studied to analyse the growth mechanism under a diffusion-limited transport process. Special care was paid to eliminate bulk transport processes such as convection and stirring. Whiskers were used as the seed crystals to control the dislocations. Thus, R-σ curves were experimentally obtained referring to the perfect and imperfect growth interfaces. The growth rate and concentration distribution around the crystals were measured in situ by transmission multiple-beam interferometry, using a special growth cell. From the analysis of experimental data, important parameters in crystal growth were obtained as follows; (1) the critical supersaturation for two-dimensional nucleation: σ*=0.04. (2) the step energy: γ= (10±3)×10^-22 J/ion (3) the area of diffusion field at the steady state growth expanded as thegrowth rate increased.

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Structural changes occurring inside electron microscopes may be classified intofive groups, i. e. phase variation due to heating, crystal growth due to heating, solid state reaction due to heating, phase variation due to cooling and lattice imperfection due to electron irradiation. In-situ observations on these structural changes in oxides or sulfides like VS_{1, 155}, WO_2.9, V₆O₁₃ or 4Nb₂O₅.9WO₃ are demonstrated using 100KV and 1 MV high-resolution transmission electron microscopes (HRTEM). Heating of crystalfragments is achieved by an irradiation of intense electron beam. Technical possibilities for extending the HRTEM method into very low or high temperature range is discussed.

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A model for the Ca/Na positions in the superstructure of labradorite feldspar with approximately 50 mol % anorthite is proposed on the basis of high resolution electron microscopic structure images and a comparison of the electron diffraction patterns with optical diffraction patterns obtained from masks representing the projected Ca and Na atoms. Good agreement in corresponding positions is found between these optical diffraction patterns and the electron diffraction patterns for projections along the four different axes [010], [311], [131] and [511] The model proposed is the only one which does not contradict the images taken along different crystal directions and the average structure of labradorite (An 55) analyzed by X-ray diffraction.

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The models of the modulated structure of the plagioclase feldspar based on X-ray diffraction and electron microscopy have been reviewed. Important models so far presented can be divided into two categories due to difference in evaluation of the second harmonic of the (Ca, Na) modulation wave. The first type (TF***, HTKJ**** and KHNE***** models), where the second harmonic is assumed to be negligible, gives the ordered arrangement of Na and Ca among the neighbouring subcells. On the other hand, in the second type (KM** model) the second harmonic is strong enough to give the alternating bands of the albite-like and anorthite-like structures. Because of the weak intensities of the second satellite reflections corresponding to the second harmonic, the final answer between the model types has not been obtained using only the X-ray diffraction method. However, the fine textures with the antiphase domain boundaries and crystal-chemical considerations of the plagioclase feldspars support the existence of the second harmonic, or, of the alternating bands of the albite-like and anorthite-like structures.

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The theory of satellite reflections based on the modulation of occupation probability is summarized. According to the theory, which can well explain the whole extinction rules of satellite reflections of intermediate plagioclase, the superstructure is interpreted as the periodic antiphase domains, constructed by two structure elements ρ₁ and ρ₂. The structure-factors for main and satellite reflections are expressed as F_main ∝F₁ +F₂ and F_sat∝F₁-F₂, respectively, where F₁ and F₂ are the Fourier transforms of ρ₁ and ρ₂.

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A review has been presented on the HRTEM and electron diffraction studies of the pyrosmalite group of minerals, particularly mcGillite and friedelite. These ‘mineral species’ have been found to basically have the same one-layer monoclinic structure. The rhombohedral cell of the twelve-layer structure originally described for mcGillite (Donnay et al. 1980) corresponds to the cell of a twinned lattice of the monoclinic structure. The stacking disorder chracteristic of this mineral group is in fact interpreted as a twin by TLQS (twin-lattice quasisymmetry) with twin index n=4 and twin-obliquity ω=0. The frequency of twinning in friedelite is much higher than that in mcGillite; the reflections of the former that characterize the manclinic structure are completely diffuse out. The mineral species of ‘friedelite’ may thus be regarded as a disordered equivalent of mcGillite. Possible polytypic structures of this mineral group can be systematically studied in terms of the two kinds of unit layers, P and M, that characterize the pyrosmalite and mcGillite structures, respectively. They are classified into four categories.

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Ordering of two kinds of atoms will occur on a side face of growth step due to the charge balance and the difference in ionic radii. When a crystal grows in a solution with low supersaturation, a three-dimensional lattice is produced by the stacking of two-dimensional lattices. The two-dimensional atomic arrangements exposed on the side planes of the growth steps and their symmetry affect the degree of ordering produced during growth, that is, order-disorder structure is determined by the direction of growth step. Optical method is useful to detect a very small variation of the ordering.

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