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Single crystals of Ni3Se2 (trinickel diselenide) and NiSe (nickel selenide) with stoichiometric chemical compositions were grown in evacuated silica-glass tubes. The chemical compositions of the single crystals of Ni3Se2 and NiSe were determined by scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM/EDS). The crystal structures of Ni3Se2 [rhombohedral, space group R32, a = 6.02813 (13), c = 7.24883 (16) Å, Z = 3] and NiSe [hexagonal, space group P63/mmc, a = 3.66147 (10), c = 5.35766 (16) Å, Z = 2] were analyzed by single-crystal X-ray diffraction and refined to yield R values of 0.020 and 0.018 for 117 and 85 unique reflections, respectively, with F o > 4σ(F o). R32 is a Sohncke type of space group where enantiomeric structures can exist; the single-domain structure obtained by the refinement was confirmed to be correct by a Flack parameter of −0.05 (2). The existence of Ni—Ni bonds was confirmed in both compounds, in addition to the Ni—Se bonds. The value of the atomic displacement parameter (mean-square displacement) of each atom in NiSe was larger than that in Ni3Se2. The larger amplitude of the atoms in NiSe corresponds to longer Ni—Se and Ni—Ni bond lengths in NiSe than in Ni3Se2. The Debye temperatures, θD, estimated from observed mean-square displacements for Ni and Se in Ni3Se2, were 322 and 298 K, respectively, while those for Ni and Se in NiSe were 246 and 241 K, respectively. The existence of large cavities in the structure and the weak bonding force are likely responsible for the brittle and soft nature of the NiSe crystal.

The stability of hauerite (MnS2) as compared to that of pyrite (FeS2) can be explained by the long Mn–S distance and departure from the typical pyrite-type structures. The structural differences of MnX2 compounds (X=S, Se, and Te) are the result of spin configurations that are different than those of other MX2 compounds; however, the arrangement of d-electrons and the size of the ions in MnX2 compounds do not clearly explain why Mn2+ in MnX2 does not exist as a low spin state. To investigate the structural differences of MnX2 compounds, we synthesized single-crystal MnTe2 and MnSe2 and performed single-crsytal X-ray diffraction experiments. The single-crystal X-ray diffraction experiments were conducted on MnTe2 [a=6.9513(1) Å, u-parameter=0.38554(2), space group Pa3̅, Z=4], MnSe2 [a=6.4275(2) Å, u-parameter=0.39358(2)], MnS2 [hauerite; a=6.1013(1) Å, u-parameter=0.40105(4), obtained from Osorezan, Aomori, Japan], and FeS2 [pyrite; a=5.4190(1) Å, u-parameter 0.38484(5), obtained from Kawarakoba, Nagasaki, Japan]. The X-ray intensity datasets of these compounds do not show any evidence of symmetry reduction. In MnS2, the S–S distance is 2.0915(8) Å, which is significantly shorter than that of FeS2 (2.1618(9) Å), and the mean square displacement of S (U 11=0.00915(9) Å2) is smaller than that of Mn (U 11=0.01137(9) Å2). The thermal vibration characteristics of MnX2 compounds are significantly different than those of FeS2. Based on structural refinement data, we discuss the low spin state of MnX2 compounds and the structural stability of pyrite-type structures.

Single crystals of the vanadate garnet Ca2NaCd2V3O12 (dicalcium sodium dicadmium trivanadate) were synthesized using the floating-zone method and the crystal structure was investigated using single-crystal X-ray diffraction. We considered the effectiveness of substitution of the Y-site cation with reference to previous structural studies of vanadate garnets. The structures of vanadate garnets are subject to geometric constraints similar to those of silicate garnets. These constraints force the tetrahedral–dodecahedral shared edge length in vanadate garnets to become shorter than the unshared dodecahedral edge length, as in ugrandite (uvarovite, grossular and andradite) garnets. However, the vanadate garnet Ca2NaCd2V3O12 exhibits the normal structural feature, similar to pyralspite (pyrope, almandine and spessartine) garnets, namely that the dodecahedral–dodecahedral shared edge length is shorter than the unshared dodecahedral edge length. With increasing ionic radius of the Y-site cation, the atomic coordinates x, y and z of oxygen adopt values which satisfy Pauling's third rule.

The Sr–Ge–O system has an earth-scientific importance as a potentially good low-pressure analog of the Ca–Si–O system, one of the major components in the constituent minerals of the Earth's crust and mantle. However, it is one of the germanate systems that has not yet been fully examined in the phase relations and structural properties. The recent findings that the SrGeO3high-pressure perovskite phase is the first Ge-based transparent electronic conductor make the Sr–Ge–O system interesting in the field of materials science. In the present study, we have revealed the existence of a new high-pressure strontium germanate, SrGe2O5. Single crystals of this compound crystallized as a co-existent phase with SrGeO3perovskite single crystals in the sample recovered in the compression experiment of SrGeO3pseudowollastonite conducted at 6 GPa and 1223 K. The crystal structure consists of germanium–oxygen framework layers stacked along [001], with Sr atoms located at the 12-coordinated cuboctahedral site; the layers are formed by the corner linkages between GeO6octahedra and between GeO6octahedra and GeO4tetrahedra. The present SrGe2O5is thus isostructural with the high-pressure phases of SrSi2O5and BaGe2O5. Comparison of these three compounds leads to the conclusion that the structural responses of the GeO6and GeO4polyhedra to cation substitution at the Sr site are much less than that of the SrO12cuboctahedron to cation substitution at the Ge sites. Such a difference in the structural response is closely related to the bonding nature.

Dehydration behavior of a natural hydrated Ca-chabazite with composition (Ca1.57Na0.49)(Al3.39Si8.55)O24·12.47H2O has been studied by the structure analyses based on the in-situ high-temperature single-crystal X-ray diffraction data at 100, 200 and 250 °C. Among the five water sites (OW1–OW5) and four exchangeable-cation sites (Ca1–Ca4) found previously in the room-temperature (RT) structure, the present structure analyses revealed the presence of OW1, OW4, Ca3 sites at 100 °C and of OW3, Ca3, Ca4 sites at 200 and 250 °C. The presence of the new extraframework sites was also revealed: OW2’ site at 100 °C and Ca5 site at 200 and 250 °C. From the temperature dependence of the occupation for these extraframework sites, the dehydration and cation migration processes are summarized and rationalized as follows. With heating up to 100 °C, OW3 water molecules, having no bonds to exchangeable cations, are completely desorbed. Simultaneously, Ca1 and Ca2 cations lose the large amounts of water molecules as ligands (OW1 and OW5 for Ca1, OW4 for Ca2); this brings about the simultaneous migration of both cations to adjacent Ca3 site, surrounded by more ligands. With further heating up to 250 °C, OW2’ water molecules, having no bonds to exchangeable cations, are completely desorbed. Simultaneously, most of the Ca3 cations migrate to adjacent Ca4 and Ca5 sites by losing the large amounts of water molecules as ligands (OW1, OW4). A part of the water molecules desorbed in the temperature range of 100–250 °C migrate to OW3 site to be bonded to the remaining Ca3 cations. The peculiar temperature dependence of Si/Al−O1, −O2 and −O3 bond lengths in the framework structure can be explained in terms of their bond-valence variations due to such dehydration and cation migration processes. On the other hand, the variation of Si/Al−O4 bond length is dominated by thermal expansion effect rather than the bond valence effect.

Single-crystal X-ray diffraction study of CaGeO3 perovskite has been conducted over the temperature range of 98 to 1048 K. The crystal begins to deteriorate at a temperature above about 900 K and completely amorphizes by 980 K. The diffraction-intensity distribution and the structure refinements indicate that the Pbnm structure is kept until the occurrence of amorphization. The obtained unit-cell parameters, unit-cell volumes, bond lengths, and displacement parameters increase monotonously with increasing temperature. Thus, no evidence for the existence of the Cmcm high-temperature phase, previously suggested above 520 K, is observed. The Ge-O bond lengths show much smaller thermal expansions than the Ca-O bond lengths; the former ranges between 0.42(2) × 10−5 K−1 and 0.57(2) × 10−5 K−1, and the latter between 1.58(4) × 10−5 K−1 and 3.96(6) × 10−5 K−1. The Debye temperatures and static disorder components for each constituent atom were determined by applying the Debye model to the temperature dependence of mean square displacements (MSDs) of the atoms. Consequently, no significant static disorder components can be detected in each atom. The Debye temperatures averaged over all directions, obtained from the Debye model fitting to U eq, yield the harmonic one particle potential coefficients of 4.76(2) eVA−2 for Ca, 11.0(1) eVA−2 for Ge, 5.02(2) eVA−2 for O1, and 5.33(5) eVA−2 for O2. These values become larger in order of Ca < O1 < O2 << Ge, which shows that the one particle potential of Ge is much narrower than that of Ca. This relationship between Ca and Ge is consistent reasonably with bonding stiffness expected from the thermal expansion coefficients of the bond lengths. The anisotropies of MSDs are remarkable in O1 and O2 atoms as a consequence of the strong interaction with adjacent Ge atoms, forming the rigid bonds with these O atoms. In comparison of the three Pbnm orthorhombic perovskites of CaGeO3, CaTiO3, and MgSiO3, all of these have the BO6 octahedra more rigid than the AO12 polyhedra (A = Ca or Mg; B = Ge, Ti, or Si) and the tilt angles of BO6 octahedra are the largest in MgSiO3 perovskite. These observations indicate that if MgSiO3 perovskite under high pressures undergoes the same sequence of the high-temperature phase transitions as CaTiO3 perovskite, the phase boundaries have positive Clapeyron slopes and the phase transition temperatures should become further much higher than those (1512 K for the Pbnm to I 4/ mcm transition and 1635 K for the I 4/ mcm to Pm 3 m transition) observed in CaTiO3 perovskite at ambient pressure. This leads to the conclusion that the high-temperature phase transition to a perovskite phase with different symmetry under high pressures previously suggested in MgSiO3 perovskite is unlikely.

Single crystals of MgAl2–xBxO4 (x = 0.0, 0.11 and 0.13) spinel were synthesized under high pressure (5 and 11 GPa) and high temperature (1873 and 1273 K) using a 1000 ton “6–8” type uniaxial split-sphere apparatus. Single-crystal X-ray diffraction measurements were carried out using a laboratory diffractometer with a Weissenberg-type imaging plate detector and using a four-circle diffractometer with synchrotron radiation at Photon Factory, Japan. The maximum content of boron was about x = 0.13 at 1273K and 11GPa. The smallest boron ion occupies the octahedral site in top priority in the spinel solid solution of the Mg/Al/B systems. The B3+ ions can replace considerably bigger Al3+ ion under pressure. We estimated the cation distribution of each site from the reproduction of the observed average distance using the observed local bond lengths for Mg–O and Al–O and the normal B–O distance. The chemical formula of boron-bearing spinels are estimated as (Mg0.47,Al0.53)[Al1.36,Mg0.53,B0.11]O4 (x = 0.11) and (Mg0.50,Al0.50)[Al1.37,Mg0.50,B0.13]O4 (x = 0.13), respectively. These spinel solid solutions are largely disordered crystals and the inversion parameter grow up to 0.5 in the tetrahedral site. The temperature factor Beq for oxygen site in boron-bearing spinels were significantly larger than that in pure MgAl2O4 spinel. Only the positional shifts of oxygen ions have, therefore, been relaxing the disorder in structure.

Single crystals of CaIrO 3 were prepared via flux growth method. Crystal structure parameters, including the anisotropic displacement parameters, are determined based on a single-crystal X-ray diffraction experiment. The unit-cell dimensions are a = 3.147(2), b = 9.866(6), and c = 7.302(5) A. The structure is a three-dimensional dense structure with small vacant spaces. The CaIrO 3 structure can be described as a pseudo-one-dimensional oxide and is compared with Ca 4 IrO 6 structure. The IrO 6 octahedra are significantly distorted, in contrast to other octahedral Ir 4+ compounds. The O-O distances for faces and edges shared between polyhedra are shorter than other non-shared edge distances. These effects are explained by Pauling’s rules and occur to decrease the repulsion between the cations. Thermal vibrations of Ca and Ir atoms are significantly anisotropic. Thermal vibrations of Ca and Ir atoms are restricted in orientation toward the shared face, shared edges, and shortest cation-cation directions. The single-crystal experiment shows that CaIrO 3 crystals grow fastest along the a axis and that they assume a prism or needle shape. Strongly preferred orientation of such prism shaped CaIrO 3 -type post perovskite MgSiO 3 crystals may develop under the shear flow in the Earth’s mantle.

Locations of water molecules and exchangeable cations in a hydrated natural chabazite with a composition of Ca1.57Na0.49 [Al3.39Si8.55O24] ⋅12.47H [d2] O were successfully determined by single crystal X-ray diffraction. The structure analyses have revealed the presences of five partially occupied water sites (OW1-OW5) and four partially occupied exchangeable-cation sites (Ca1-Ca4), and have showed that fully coordinated exchangeable cations can adopt sixfold or sevenfold coordination. The distances between water sites and framework oxygen sites and between water sites suggest that the hydrogen bonds formed between water molecules and framework oxygen atoms are very weak, whereas strong hydrogen bonds exist between water molecules.

Crystallographic configurations of water molecules and exchangeable cations in a hydrated natural CHA-zeolite (chabazite) with a composition of (Ca 1.57 Na 0.49 )(Al 3.39 Si 8.55 )O 24 · 12.47H 2 O have been examined from the structure analyses based on single-crystal X-ray diffraction data. The structure analyses have revealed the presence of five partially occupied water sites (OW1–OW5) and four partially occupied exchangeable-cation sites (Ca1–Ca4), and the final structure refinement converged to R = 0.0283 and R w = 0.0276 for 1255 reflections. Of these sites, the Ca4 and OW2 sites are located at the center of the [4 6 6 2 ]-ring and the center of the 8-ring window in the [4 12 6 2 8 6 ]-cavity, respectively, and the remaining sites are inside the [4 12 6 2 8 6 ]-cavity. The Ca1 atoms can be coordinated only by water molecules, and fully coordinated Ca1 atoms can adopt an octahedral coordination or a triangular-prismatic coordination depending on configurations of water molecules. The Ca2 and Ca3 atoms can be coordinated by both framework oxygen atoms and water molecules, and fully coordinated Ca2 and Ca3 atoms can adopt a sevenfold coordination and an octahedral coordination, respectively. The Ca4 atoms are coordinated octahedrally by six framework oxygen atoms. Judging from OW⋯O and OW⋯OW distances, the hydrogen bonds formed between water molecules and framework oxygen atoms are expected to be very weak, whereas strong hydrogen bonds can exist between water molecules.

A high-temperature single-crystal X-ray diffraction study of a synthetic PbTiO3perovskite was carried out over the wide temperature range 298–928 K. A transition from a tetragonal (P4mm) to a cubic (Pm \bar 3 m) phase has been revealed near 753 K. In the non-centrosymmetricP4mmsymmetry group, the difference in relative displacement between Pb and O along thec-axis is much larger than that between Ti and O. The Pb and Ti cations contribute sufficiently to polarization being shifted in the opposite direction compared with the shift of O atoms. Deviation from the linear changes in Debye–Waller factors and bonding distances in the tetragonal phases can be interpreted as a precursor phenomenon before the phase transition. Disturbance of the temperature factorUeqfor O is observed in the vicinity of the transition point, whileUeqvalues for Pb and Ti are continuously changing with increasing temperature. The O site includes the clear configurational disorder in the cubic phase. The polar local positional distortions remain in the cubic phase and are regarded as the cause of the paraelectricity. Estimated values of the Debye temperature ΘDfor Pb and Ti are 154 and 467 K in the tetragonal phase and decrease 22% in the high-temperature phase. Effective potentials for Pb and Ti change significantly and become soft after the phase transition.

Single crystals of the SrGeO3 high-pressure phase are prepared by hot pressing of the polycrystalline pseudowollastonite SrGeO3 (BN anvil press, 6 GPa, 1223 K, 1 h).

High-pressure single-crystal X-ray diffraction experiments of MgSiO 3 perovskite have been carried out up to 15 GPa in a diamond-anvil cell using synchrotron radiation. Precise crystal structural parameters, including the anisotropic displacement parameters of every atom in MgSiO 3 , are determined under high pressure. In the pressure range up to 15 GPa, the most important responses of the structure are the compressions of SiO 6 and MgO 8 polyhedra and an increase in tilting of SiO 6 octahedra represented by the decrease in angles between octahedra (both Si-O2-Si angle in the a-b plane and Si-O1-Si angle in the b-c plane decrease). The degree of the change in both angles in the a-b and b-c planes is the same. The amplitude of mean square displacement for the Mg atom has the largest value in the structures and its thermal vibration is significantly anisotropic at ambient pressure. Under high pressure, all atoms in the structure have obvious anisotropy of thermal vibration and the largest amplitudes of thermal vibration for Mg, Si, and O2 atoms are directed toward vacant space in the structure. Anisotropy of the structure increases with pressure.

Synthesis experiments in the system MgAl2O4–MgFe2O4 [MgAl2− x Fe x O4 (0 ≤ x ≤ 2)] were carried out using a PbF2 flux. The crystalline products synthesized in the compositional range of 0.6

The cation-cation repulsions across the shared edges of polyhedra in garnet structure are the most prominent between tetrahedral and dodecahedral cations, and this effect has a significant influence on cation distribution and symmetry change in garnets. Moreover, the shared edge of SiO6 octahedron in stishovite (SiO2), with rutile structure, is more compressible than the unshared edges; this can be explained by Si-Si repulsion across the shared edge. Thus, the cation-cation repulsions across the shared edges of polyhedra cannot be ignored as a significant factor governing the stability of compounds with edge-sharing structures.

It is widely known that CoAl2O4, IV(Co1−xAlx) VI[CoxAl2−x]O4, is a largely normal spinel (0

Crystal chemistry and structure of garnets are reviewed with special attention to the cation-cation repulsion across the shared edges of polyhedra. The cation-cation repulsion plays an important role in the stability of garnet structure, and this effect is the most prominent between tetrahedral and dodecahedral cations. The magnitude of the cation-cation repulsion is closely related to the degree of polyhedral distortion, based on the difference in length between the shared and the unshared edges in polyhedra, due to the structural geometric restriction. Especially, the cation-cation repulsion increases in garnet solid solutions owing to the decrease in the shielding effect when the structural geometric restriction brought by the substitution of the cations with different sizes forcibly stretches the shared edges compared with the unshared ones. This is a factor to destabilize the crystal structure. Both the tendency of cation distribution in Y3Fe5O12 (YIG)-Y3Ga5O12 (YGG) system and the symmetry in Mg3Al2Si3O12-MgSiO3 system change with the compositional variations in these solid solutions. These changes are the good examples of the destabilization of the crystal structures due to the effect of the cation-cation repulsion.

Single-crystal X-ray diffraction study of SrGeO3 perovskite (cubic; space group Pmɜm) synthesized at 6 GPa and 1223 K was conducted at a low temperature of 100 K. The residual electron density revealed the presence of the bonding electron at the center of the Ge–O bond, in accordance with our previous conclusion that the Ge–O bond is strongly covalent. From comparison with our previous structure-refinement result at 296 K, the mean square displacement (MSD) of the O atom in the direction of the Ge–O bond is suggested to exhibit no significant temperature dependence, in contrast to that in the direction perpendicular to the bond. Thus, the strong covalency of the Ge–O bond can have a large influence on the temperature dependence of thermal vibration of the O atom.

The crystal structures of MgAl2–xGaxO4 (0 ≤ x ≤ 2) spinel solid solutions (x = 0.00, 0.38, 0.76, 0.96, 1.52, 2.00) were refined using 27Al MAS NMR measurements and single crystal X-ray diffraction technique. Site preferences of cations were investigated. The inversion parameter (i) of MgAl2O4 (i = 0.206) is slightly larger than given in previous studies. It is considered that the difference of inversion parameter is caused by not only the difference of heat treatment time but also some influence of melting with a flux. The distribution of Ga3+ is little affected by a change of the temperature from 1473 K to 973 K. The degree of order-disorder of Mg2+ or Al3+ between the fourfold- and sixfold-coordinated sites is almost constant against Ga3+ content (x) in the solid solution. A compositional variable of the Ga/(Mg + Ga) ratio in the sixfold-coordinated site has a constant value through the whole compositional range: the ratio is not influenced by the occupancy of Al3+. The occupancy of Al3+ is independent of the occupancy of Ga3+, though it depends on the occupancy of Mg2+ according to thermal history. The local bond lengths were estimated from the refined data of solid solutions. The local bond length between specific cation and oxygen corresponds with that expected from the effective ionic radii except local Al–O bond length in the fourfold-coordinated site and local Mg–O bond length in the sixfold-coordinated site. The local Al–O bond length in the fourfold-coordinated site (1.92 A) is about 0.15 A longer than the expected bond length. This difference is induced by a difference in site symmetry of the fourfold-coordinated site. The nature that Al3+ in spinel structure occupies mainly the sixfold-coordinated site arises from the character of Al3+ itself. The local Mg–O bond length in the sixfold-coordinated site (2.03 A) is about 0.07 A shorter than the expected one. Difference Fourier synthesis for MgGa2O4 shows a residual electron density peak of about 0.17 e/A3 in height on the center of (Ga0.59 Mg0.41)–O bond. This peak indicates the covalent bonding nature of Ga–O bond on the sixfold-coordinated site in the spinel structure. Kationenverteilung und Strukturvarianten von Mischkristallen aus der Spinellreihe MgAl2–xGaxO4 (0 ≤ x ≤ 2) Die Kristallstrukturen von Mischkristallen aus der Spinellreihe MgAl2–xGaxO4 (0 ≤ x ≤ 2) mit x = 0.00, 0.38, 0.76, 0.96, 1.52, 2.00 wurden aus Einkristall-Rontgenbeugungsdaten unter Berucksichtigung von 27Al MAS NMR-Messungen verfeinert. Die Kationenverteilung wurde untersucht. Der Inversionsparameter (i) von MgAl2O4 (i = 0.206) ist etwas groser als bisher berichtet wurde. Wahrscheinlich ist dieser Unterschied nicht nur auf unterschiedliche thermische Behandlung, sondern auch auf die Verwendung von Flusmitteln zuruckzufuhren. Die Verteilung von Ga3+ ist zwischen 973 K und 1473 K wenig temperaturabhangig. Das Ausmas der Ordnung von Mg2+ und Al3+ auf den Tetraeder- bzw. Oktaederlucken ist nahezu unabhangig vom Galliumgehalt. Das Verhaltnis Ga/(Mg + Ga) in der Oktaederlucke ist konstant uber die ganze Mischkristallreihe unabhangig vom Al-Gehalt. Die Besetzung von Al3+ ist unabhangig von derjenigen des Ga3+, sie hangt aber von der durch die Temperaturbehandlung bestimmten Mg2+-Besetzung ab. Die Atomabstande wurden anhand der Verfeinerungen fur die Mischkristalle abgeschatzt. Die lokalen Kation–Anion-Abstande entsprechen der Erwartung anhand von effektiven Ionenradien mit Ausnahme des Al–O-Abstands im Tetraeder und des Mg–O-Abstands im Oktaeder. Der lokale Al–O-Abstand ist im Tetraeder mit 1.92 A um 0.15 A langer als erwartet. Dieser Effekt resultiert aus einer unterschiedlichen Lagesymmetrie des Tetraederzentrums. Der Charakter von Al3+, bedingt, das es vorzugsweise die Oktaederlucke besetzt. Der Mg–O-Abstand im Oktaeder ist mit 2.03 A etwa 0.07 A kurzer als erwartet. Die Differenzfouriersynthese fur MgGa2O4 zeigt ein Restelektronendichtemaximum von 0.17 e/A3 im Zentrum der (Ga0.59 Mg0.41)–O-Bindung. Dieses Maximum spiegelt die kovalente Natur der Ga–O-Bindung um die Oktaederlucke der Spinellstruktur wider.

Six single crystals of Mg 3 (Mg x Si x Al (sub 2-2x) )Si 3 O 12 with x = 0.05, 0.13, 0.24, 0.38, 0.52, and 0.64 (the majorite solid-solution) were synthesized at 20 GPa and 2000 degrees C with a "6-8" type uniaxial split-sphere apparatus. Single-crystal X-ray diffraction studies revealed discontinuities in compositional dependence of the molar volume, equivalent isotropic temperature factors (Be q ), and mean bond lengths between x = 0.24 and 0.38. Single crystals in the compositional range 0 I4 1 /acd --> I4 1 /a, with increasing MgSiO 3 component. The symmetry changes from Ia3d to I4 1 /acd cannot be explained by the cation ordering on the octahedral site. Strong electrostatic interaction between the dodecahedral (Mg (super 2+) ) and tetrahedral (Si (super 4+) ) cations was observed from atomic thermal motion and electron density distribution. Because one of the site symmetries of the two nonequivalent tetrahedral sites in I4 1 /acd structure loses the center of symmetry with the symmetry reduction from Ia3d to I4 1 /acd, the symmetry reduction may be caused by the electronic polarization of the cations due to the neighboring cation-cation interaction.

Five single crystals of Y3Al5−x Ga x O12 (0 ≤ x ≤ 5) garnet solid solutions with the compositions x = 0.0, 1.0, 2.0, 3.0 and 4.0 were synthesized using a flux method. The compositional dependence of the lattice constants of the garnet solid solutions shows a large deviation from Vegard's law. Investigation of the cation distributions of these garnets using single-crystal X-ray diffraction shows that Ga3+, which is larger than Al3+, preferentially occupies the tetrahedral (four-coordinate) site rather than the octahedral (six-coordinate) site. On the basis of the results obtained from structure refinements, geometric analyses of the polyhedral distortions were carried out. The results imply that the cation–cation repulsive force across the polyhedral shared edges decreases with increasing substitution of Ga3+. Moreover, the proportion of covalent bonding in the cation–oxygen bonds was estimated from the bond strength; the results indicate that the covalency of the Ga—O bond is greater than that of the Al—O bond. The peculiar cation distributions observed in the Y3Al5−x Ga x O12 garnet solid solutions are most probably caused by the strong covalency of the Ga—O bond and also simultaneously induced by the need to decrease the cation–cation repulsive force. Crystal data: cubic, Ia3¯d, Z = 8, Mo Kα, λ = 0.71069 Å; at x = 0.0 (triyttrium pentaaluminium dodecaoxide): a 0 = 12.0062 (5) Å, V = 1730.7 (2) Å3, D x = 4.56 Mg m−3, M r = 593.613, μ = 21.21 mm−1, F(000) = 2224, R = 0.029 for 294 reflections; at x = 1.0 (triyttrium tetraaluminium gallium dodecaoxide): a 0 = 12.0432 (7) Å, V = 1746.7 (3) Å3, D x = 4.84 Mg m−3, M r = 636.351, μ = 24.09 mm−1, F(000) = 2368, R = 0.022 for 124 reflections; at x = 2.0 (triyttrium trialuminium digallium dodecaoxide): a 0 = 12.0926 (9) Å, V = 1768.3 (4) Å3, D x = 5.10 Mg m−3, M r = 679.089, μ = 26.85 mm−1, F(000) = 2512, R = 0.018 for 144 reflections; at x = 3.0 (triyttrium dialuminium trigallium dodecaoxide): a 0 = 12.1552 (6) Å, V = 1795.9 (3) Å3, D x = 5.34 Mg m−3, M r = 721.827, μ = 29.43 mm−1, F(000) = 2656, R = 0.018 for 184 reflections; at x = 4.0 (triyttrium aluminium tetragallium dodecaoxide): a 0 = 12.2123 (8) Å, V = 1821.3 (4) Å3, D x = 5.58 Mg m−3, M r = 764.565, μ = 31.97 mm−1, F(000) = 2800, R = 0.014 for 159 reflections.

A single crystal of a birefringent Cr-bearing majorite, Mg 3 (Mg (sub 0.34) Si (sub 0.34) Al (sub 0.18) Cr (sub 0.14) ) 2 Si 3 O 12 , was synthesized at 20 GPa and 2000 degrees C using "6-8" type uniaxial split-sphere apparatus. This garnet is tetragonal with the unit-cell parameters a nearly equal c and deviates slightly from cubic symmetry. The structure refinements using single-crystal X-ray diffraction intensity data were carried out by assuming three space groups (one cubic and two tetragonal) to determine the most probable symmetry. The most probable space group is I4 1 /a (tetragonal). The Cr ions show a disordered distribution between the two nonequivalent octahedral sites in the I4 1 /a structure.

Single crystals of cobalt digallium tetraoxide, CoGa2O4, have been grown by cooling slowly a 1:1 mixture of CoO and Ga2O3 from 1473 K to room temperature under the presence of a PbF2 flux. The compound crystallizes with the cubic spinel structure (space group Fd\overline{3}m). The occupancy refinement based on single-crystal X-ray diffraction data shows CoGa2O4 to be a largely normal spinel with an inversion parameter of 0.575 (4), resulting in a structural formula of IV(Co0.425Ga0.575)VI[Co0.575Ga1.425]O4, where IV() and VI[] represent the tetrahedral and the octahedral sites, respectively.

The crystal structure of the low-temperature (LT) modification of LaBO3 has been redetermined from single-crystal X-ray data; the resulting structure confirms the previous study [Abdullaev, Dzhafarov & Mamedov (1976). Azerbaidzhanskii Khim. Zh. pp. 117–120], but with improved precision. LT-LaBO3 crystallizes in space group Pnma and adopts the aragonite-type structure. Except for one O atom, which is situated on a general position, all other atoms (one La, one B and a second O atom) lie on mirror planes. The structure is composed of LaO9 polyhedra with an average La—O distance of 2.593 Å and trigonal BO3 groups with an average B—O distance of 1.373 Å. Slight anisotropies of the thermal vibrations of La and B atoms suggest that the electrostatic La...La and La...B interactions across the shared edges are weak.

The structure of Sr4Fe6O13is orthorhombic, space groupIba2, with unit cell dimensionsa= 11.278(3) Å,b= 18.953(6) Å,c= 5.546(3) Å,Z= 4. The crystal structure was refined by full-matrix leastsquares toR= 0.010 using 301 reflections measured with an imaging plate using a Weissenberg camera and mono-chromatized synchrotron radiation of wavelength 1.000 Å. The result is essentially the same with the previously reported structure (Yoshiasa, Ueno, Kanamaru, Horiuchi, 1986) but has yielded some details of the structure in which Fe–O bondings are involved. The polyhedral distortions and ionic radii for the five coordinated Fe3+ions in the structure have been discussed in comparison with those of related structures.

Single crystals of LaAlO3 (lanthanum aluminium trioxide) have been synthesized at 4.5 GPa and 1273 K, in the presence of an NaCl + KCl flux. The compound crystallizes with the cubic perovskite structure (space group Pm\overline{3}m). The thermal vibration of the O atom is remarkably suppressed in the directions of the Al—O bonds, and this anisotropy ranks among the largest observed in stoichiometric cubic perovskites.

Single crystals of CaGeO3 garnet were synthesized at 3 GPa and 1000 °C using a cubic anvil type of high pressure apparatus and the crystal structure was refined from single crystal X-ray diffraction data. This garnet is tetragonal with lattice parameters of a = 12.535(2) A, c = 12.370(2) A, V = 1943.5(5) A3 and belongs to space group I 41/ a . Two dodecahedral sites are occupied only by Ca with mean Ca-O bond lengths of 2.480(4) and 2.467(4) A. The Ca and Ge cations are completely ordered at two octahedral sites with mean Ca-O = 2.301(3) A and mean Ge-O = 1.910(3) A. Three tetrahedral sites are occupied only by Ge, and their mean Ge-O bond lengths are 1.753(3), 1.787(4), and 1.764(4) A. Furthermore, the present tetragonal garnet has an unusual feature in that the mean value [2.704(5) A] of the shared edge lengths of GeO6 octahedron is larger than that [2.699(5) A] of the unshared ones, as has also been observed for other tetragonal garnets with I 41/ a .

The crystal structures of Y 3 Fe 5-x Ga x O 12 (0≤ x ≤ 5) solid solutions (x = 0.0, 1.0, 1.6, 2.0, 2.5, 3.0, 3.6, 3.8, 4.6 and 5.0) with garnet structure were refined by single-crystal X-ray diffraction analyses. Site preferences of cations in the crystal structure were examined in detail. The smaller Ga 3+ ion occupies only the four-coordinated site in the composition range x = 0.0-1.6 (region I), whereas the larger Fe 3+ ion occupies only the six-coordinated site from x = 5.0 to 3.8 (region III). Both cations occupy these two sites from x=1.6 to 3.8 (region II). The tendency for site preference of cations changes near x=1.6 and 3.8. When Ga 3+ and Fe 3+ occupy only the four- (region I) and six-coordinated sites (region III), respectively, the enhancement of the cation-cation interaction can be considered as a result of the geometric restriction due to the variation of cation size. The change in tendency for cation site preference is most probably caused by the increased cation-cation interaction. Crystal data: cubic, Ia3d, Z = 8, Mo Kα, λ = 0.71069 A; at x = 0.0: a 0 = 12.375(1)A, V = 1895.3(3)A 3 , D x = 5.17 mg m -3 , m r = 737.938, μ = 26.42 mm -1 , F(000) = 2744, R = 0.020 for 144 reflections; at x = 1.0: a 0 = 12.360(1)A, V = 1888.2(4)A 3 , D x = 5.29 Mg m -3 , M r = 751.811, μ = 27.95 mm -1 , F(000) = 2784, R = 0.019 for 131 reflections; at x = 1.6: a 0 = 12.351(1)A, V = 1883.9(3)A 3 , D x = 5.36 Mg m -3 , M r = 760.135, μ = 28.88 mm -1 , F(000) = 2808, R = 0.021 for 110 reflections; at x = 2.0: a 0 = 12.342(1)A, V = 1880.1(4)A 3 , D x = 5.41 Mg m -3 , M r = 765.684, μ = 29.51 mm -1 , F(000) = 2824, R = 0.018 for 117 reflections; at x = 2.5: a 0 = 12.333(1)A, V = 1875.8(3)A 3 , D x = 5.47 Mg m -3 , M r = 772.621, μ = 30.30 mm -1 , F(000) = 2844, R = 0.015 for 111 reflections; at x = 3.0: a 0 = 12.317(1)A, V = 1868.7(3)A 3 , D x = 5.54 Mg m -3 , M r = 779.557, μ = 31.14 mm -1 , F(000) = 2864, R = 0.017 for 119 reflections; at x = 3.6: a 0 = 12.312(2)A, V = 1866.2(5)A 3 , D x = 5.61 Mg m -3 , M r = 787.881, μ = 32.06 mm -1 , F(000) = 2888, R = 0.016 for 168 reflections; at x = 3.8: a 0 = 12.302(1)A, V = 1861.8(4)A 3 , D x = 5.64 Mg m -3 , M r = 790.655, μ = 32.42 mm -1 , F(000) = 2896, R = 0.020 for 117 reflections; at x = 4.6: a 0 = 12.289(1)A, V = 1856.1(3)A 3 , D x = 5.73 Mg m -3 , M r = 801.754, μ = 33.69 mm -1 , F(000) = 2928, R = 0.013 for 103 reflections; at x = 5.0: a 0 = 12.273(1)A, V = 1848.7(4)A 3 , D x = 5.80 Mg m -3 , M r = 807.303, μ = 34.45 mm -1 , F(000) = 2944, R = 0.021 for 118 reflections.

A variable-temperature single-crystal X-ray diffraction study of a synthetic BaTiO3perovskite has been performed over the temperature range 298–778 K. A transition from a tetragonal (P4mm) to a cubic (Pm \overline 3 m) phase has been revealed near 413 K. In the non-centrosymmetricP4mmsymmetry group, both Ti and O atoms are displaced along thec-axis in opposite directions with regard to the Ba position fixed at the origin, so that Ti4+and Ba2+cations occupy off-center positions in the TiO6and BaO12polyhedra, respectively. Smooth temperature-dependent changes of the atomic coordinates become discontinuous with the phase transition. Our observations imply that the cations remain off-center even in the high-temperature cubic phase. The temperature dependence of the mean-square displacements of Ti in the cubic phase includes a significant static component which means that Ti atoms are statistically distributed in the off-center positions.

High-temperature powder X-ray diffraction measurements for ScAlMgO4 ( in space group) grown by Czochralski method were carried out from 303 to 1473 K. The obtained temperature-dependent unit cell parameters were expressed as for the a-axis and for the c-axis, where T is temperature in kelvin. The axial thermal expansion coefficients for the a-axis estimated from the unit cell parameters were comparable to those of GaN and ZnO. A c-plane ScAlMgO4 substrate can be easily obtained with using cleavage plane along c-plane, which is parallel to a-axis. Thus, ScAlMgO4 is one of the promising substrates for c-plane epitaxial growth of GaN and ZnO. High temperature X-ray single crystal structural analysis of ScAlMgO4 demonstrated the mechanism of the nonlinear variation of the obtained cell parameters as a function of temperature.

Single crystals of strontium cobaltate, SrCoO3−x, have been grown by the floating-zone method in an oxy­gen flow. The compound crystallizes with the cubic perovskite structure, with Pm\overline 3m symmetry, as determined by X-ray diffraction. Refinement of the O-atom site occupancy yields the chemical composition SrCoO2.64 [x = 0.36 (3)]. The anisotropic displacement ellipsoids of the O atoms suggest that their positional disorder occurs in a direction perpendicular to that of the Co—O bonds.

Geiger (2013) argues that the large mean square displacement (MSD) of Mg in the dodecahedral site in pyrope, Mg3Al2Si3O12, originates from the dynamic disorder of Mg due to its large anisotropic thermal vibration, including anharmonic contribution, and refutes our findings that the Mg static disorder is present. His argument is based on the diffraction, spectroscopic, thermodynamic, and computational studies made mainly by him and his co-workers. However, these investigations only suggested the large anisotropy of the Mg thermal vibration, and do not necessarily prove that there is no Mg static disorder. What we must obtain is conclusive experimental proof as to whether the Mg static disorder exists or not. In the present paper, a reply to his comment (Geiger 2013), we discuss the validity of our findings (Nakatsuka et al. 2011). A “direct” method to confirm the Mg static disorder is to observe a splitting of electron density maxima around the Mg site form the structure analysis. As shown in Nakatsuka et al. (2011), we successfully observed the residual electron density maxima around the Mg site (24 c site) in the difference Fourier map at a low temperature of 97 K. In addition, the refinements assigning Mg to these electron density maxima (split-atom model refinements) yielded “the Mg positional parameters deviating significantly from the 24 c site” and provided “the atomic displacement parameters (ADPs) of Mg significantly smaller than the ones in the normal-model refinements,” assigning Mg to the 24 c site, as a consequent of the removal of the static disorder components. These are direct evidence for the presence of the Mg static disorder. In the anharmonic refinements, several of the higher-rank tensor coefficients of Mg, Al, Si, and O atoms deviated significantly from …

Hydrogarnets, represented by hydrogrossular, are produced by the replacement of (ZO4)4- in garnets by (H4O4)4- (Z: tetrahedral cation) and the vacancies of tetrahedral cations are created by this replacement. Most of reported hydrogarnets crystallizes with cubic symmetry (space group Ia-3d). To our knowledge, Ca3Mn2[SiO4]2.07[H4O4]0.93 with space group I41/acd (tetragonal) [1] has been only reported as a low-symmetry hydrogarnet. In the cubic hydrogarnets, all O atoms are crystallographically equivalent, whereas in low-symmetric one, they can be located at non-equivalent sites. Therefore, the investigation of low-symmetry hydrogarnes is important to gain knowledge of the site preference of H atoms. Recently, we have successfully synthesized the single crystal of a new low-symmetry hydrogarnet CaGe0.924O3H0.304 (= Ca3(CaGe)[GeO4]2.696[H4O4]0.304) with tetragonal space group I41/a, at 3 GPa and 1273 K under the presence of H2O component. This tetragonal hydrogarnet is produced by the partial replacement of (GeO4)4- in high-pressure CaGeO3 garnet, Ca3(CaGe)[GeO4]3, by (H4O4)4-. In the present study, we report the single crystal X-ray diffraction study of this hydrogarnet at 98 and 298 K. In the structure refinement at 298 K, the occupancy parameters resulted in 0.393(2) for tetrahedral Z2(Ge) site, coordinated only by O6 atoms, and showed no significant deviation from 1.0 for the remaining cation sites. The bond valence sums of each atom except O6 atom agree with the valences of occupied atoms, whereas that of O6 atom are 1.50, deviating largely from oxygen valence. Thus, the substitution of OH groups for O atoms in the present sample occurs only at O6 site, which indicates that O6 is the most preferential site for the OH substitution. The position of H atom will be examined from the residual electron density distributions at a low temperature of 98 K, and the hydrogen bonding in the crystal structure will be discussed.

The CaGeO3 perovskite and garnet were synthesized in a cubic anvil type apparatus under high pressure. The measurements of Ca and Ge K- edge XAFS spectra were carried out in the transmission mode at temperature up to 700 K. The effective pair potentials V(u)=αu2/2+βu3/3!, for Ca-O bond in various phases of CaGeO3 have been investigated by the temperature dependence of EXAFS Debye-Waller factors. The potential coefficient α for the Ca-O bond in perovskite-type CaGeO3 is small, 4.4 eV/A2 compared with those in garnet (6.0 eV/A2) and wollastonite (6.4 eV/A2). The potential for Ca-O bond in perovskite is broader than those in other CaGeO3 polymorphs, which is one reason for the Clausius-Clapeyron's curve for perovskite-garnet phase boundary having a negative slope. The potential coefficients for the Ca-O in perovskite are significantly smaller than those for the longer Ge-Ge distances as the framework vibration though the potential coefficient decreases usually as a result of the larger bond distance.