Three examples of disorder found in the averaged structures are presented. The crystal structure of high pressure form ZrO₂determined at 5.1 GPa showed the disorder of oxygen positions separated by 1.22Å. The crystal structure of phase E synthesized at 15 GPa and 1000°C and quenched to the ambient condition showed that there exists short-range order between intralayer vacancies and interlayer cations but there does not exist a long-range order. The crystal structure of hydrous wadsleyite synthesized at 15.5 GPa and 1300°C and quenched to the ambient condition showed small but significant Fourier peaks at the site in a normally vacant tetrahedral void adjacent to Mg octahedral site.

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Thermal vibrational parameters of lower temperature phases of tridymite and melanophlogite, and their related quantities were used to characterize their higher temperature phases and phase transitions. The orthorhombic tridymite appearing right above the monoclinic room temperature phase and β-melanophlogite are all subject to atom disorder. Raman spectroscopic data of the orthorhombic tridymite and their simulations in lattice dynamical calculations suggested that the motions causing the disorder are triggered by a low frequency phonon mode via coupling between themselves having the same symmetry. Higher-order thermal motion tensor analysis of β-melanophlogite indicated that the probability density functions of O atoms are strongly distorted from ellipsoidal ones, directly proving atom disorder, which were further analyzed in terms of 12 α-domains.

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A review is given on the recent developments in the study of magnetic short-range order in disordered and ordered Pt-Mn alloys. We describe the study of the correlation between atomic arrangements and magnetic fluctuations in the alloys by using X-ray and neutron diffraction scattering techniques. The study casts new light in the understanding of the magnetic properties of the disordered and ordered alloys containing 3d-metals.

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Crystals of LiMn₂O₄undergo a first order structural phase transition near the room temperature. The high temperature (HT) form adopts a normal spinel-type structure (cubic, Fd3m) with the octahedral sites populated statistically with heterovalent Mn^IIIand Mn^IVin the equal ratio. The low temperature (LT) form adopts a 3×3×1 superstructure (orthorhombic, Fddd) with respect to the HT form, containing Mn1^III, Mn3^III, Mn4^IV, Mn5^IVand intervalent Mn2 atoms. The synchrotron X-ray single-crystal electron-density analysis revealed a bond-length fluctuation along the pseudo-tetragonal Jahn-Teller distortion parallel to the a axis in the heterocubane Mn2₄O9₄cluster which presumably shares three electrons among foure-parentage orbitals of Mn2 and behaves as a core of Zener polaron. The heterocubane Mn2₄O9₄clusters are isolated with each other and embedded in an ordered way in the charge-ordered matrix containing Mn1^III, Mn3^III, Mn4^IVand Mn5^IV. The transition between the LT and HT forms of LiMn₂O₄can thus be regarded as an order-disorder transition of the Zener polarons. The molecular dynamics (MD) studies revealed that a periodical random switching of Mn valences, reflecting the e-parentage electron hopping model, greatly facilitates the Li-ion self-diffusion. Two distinct but coexistent processes have been proposed for the diffusion of Li atoms in the HT form of LiMn₂O₄.

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We review our recent works on the positional disorder and diffusion path of mobile ions in fast ionic conductors Bi_1.4Yb_0.6O₃and La_0.67Li_0.16TiO₃. These were studied through the nuclear density distribution obtained by a combined technique including the Rietveld refinement, the maximum-entropy method (MEM) and MEM-based pattern fitting of neutron powder diffraction data. The oxide ions in the fluorite-structured Bi_1.4Yb_0.6O₃have a complicated disorder spreading over a wide area, shift to the ‹111› directions from the ideal fluorite position and diffuse along the ‹100› directions. At 77 K, the Li cations in the La_0.62Li_0.16TiO₃perovskite are located at the 2csite (Wycoff notation of theCmmmspace group) on the (002) La deficient layer, while at room temperature, they spread over a wide area and migrate following the 2c-4f-2cor 2c-2d-2ctie line on the (002) layer.

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The Debye-Waller factors determined by diffraction and XAFS experiments provide important information about the thermal vibration and disordered structure. The statistical distribution of Ag in α-AgI and supersonic conduction mechanism have been discussed based on the effective one-particle potential, probability density function and effective pair potential. The disordered nature of α-AgI is due to the thermal motion and the probability of finding mobile Ag ions at saddle point is a few percent in α-AgI.

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Thermodynamic studies of disordered sructure by heat capacity measurements are reviewed, and the important role of thermodynamic properties is explained. The heat capacity anomaly and the excess entropy due to the formation of short-range order in relaxor ferroelectrics are discussed. The excess heat capacity at low temperatures is analyzed on the basis of the disorder structures for glasses and disordered crystals. The lattice vibration spectrum in stabilized zirconia is discussed in terms of disorder in the crystal.

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Structure refinement method using the data from a twinned crystal is reviewed. For twins whose reciprocal lattices coincide in position, three-dimensional twin operations are used to transform the indices. For twins in which only a part of diffractions from two domains coincide in position, a six-dimensional twin refinement technique is illustrated with a few examples.

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By using synchrotron light source, X-ray anomalous dispersion effects have been recently applied for structure determination and local structure analysis of complicated materials. In the present report, we overview validities of the method by introducing examples of superstructure determination of PbZrO₃and long-periodic structure analysis of Te_0.4Se_0.6. In addition, application of the method for small angle scattering measurement will be described as a new approach of macro-structure analysis.

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Four-dimensional approach for incommensurate structures was briefly reviewed. Recent developments of the method using discontinuous modulation functions were explained, which enabled us to get the 4-dimensional description of structures forming the homologous series such as intergrowth compounds and crystallographic shear (CS) structures. An example of the incommensurate CS structure was given, in which domain boundaries were aperiodically inserted in contrast to the usual CS structures.

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High resolution X-ray structure analyses revealed the condition for the charge ordering (CO) observed in the quasi one-dimensional compounds (TMTTF) ₂X. The size and orientational ordering of the counter anion X control the dimerization and tetramerization of TMTTF molecules. The molecular dimerization suppresses the 4kF CO, while the tetramerization assists the 2kF CO. The phase diagram of the electronic states including 2kF and 4kF CO has been proposed associated with magnitudes of the molecular dimerization and tetramerization.

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Inelastic X-ray and neutron scattering experiments are powerful tools on studying atomic dynamics in a liquid. These are complemental technique for liquid dynamics due to their different characters. As an example of structurally disordered materials, we report the atomic dynamics on liquid Ge by means of the inelastic X-ray and neutron scattering experiments. The acoustic phonon dispersion and the quasielastic scattering spectrum due to the structural relaxations are discussed in association with the anomaly in the static structure.

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Neutron diffraction is a powerful tool to elucidate the atomic arrangement of amorphous alloys because of characteristic scattering lengths of constituent elements. For hydrogen absorption amorphous alloys HID isotopic substitution was employed to observe the location of deuterium atoms because the neutron coherent scattering length of deuterium is large enough to observe in comparison with those of the constituent atoms. Moreover, Reverse Monte Carlo (RMC) modeling has been recognized to be an excellent method for visualizing the threedimensional atomic arrangement of amorphous alloys, based on the results of neutron and X-ray diffraction experiments. Therefore, the combination of neutron, X-ray diffraction experiments and the RMC modeling was used to clarify the topological characteristics of the structure of amorphous alloys.

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Small angle X-ray scattering (SAXS) measurements for expanded fluid Hg have been carried out in wide density region including the metal-non-metal (M-NM) transition region at 9.0g cm^-3and the liquid-vapor critical region at 5.8g cm^-3using synchrotron radiation at SPring-8. We could observe the liquid-vapor critical scattering intensity in fluid Hg with good statistics and also SAXS intensity in the M-NM transition region. The latter result suggests that characteristic fluctuations are induced in the M-NM transition in expanded fluid Hg.

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The anomalous X-ray scattering (AXS) coupled with model calculation using reverse Monte Carlo (RMC) simulation, has recently received much attention for analyzing the middlerange ordering for non-crystalline materials. The usefulness of this new method was demonstrated with some selected examples of a Bi₃₀Ga₇₀high temperature liquid alloy and an amorphous ZrO₂.

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Local structures around germanium in liquid germanate have been investigated byin-situX-ray absorption measurements up to 9 GPa at 1000°C. Liquid germanate consisting of tetrahedrally coordinated germanium contracts with increasing pressure without significant changes in the local structure up to 2.5 GPa and then shows an abrupt fourfold-sixfold coordination change around 3 GPa. The coordination change is completed below 4 GPa and a high-density liquid consisting of octahedrally coordinated germanium is stable to 9 GPa. GeO₆octahedron in the high-density liquid is more compressible than that in solids, suggesting the possibility of a density inversion between liquid and solid at higher pressure. By considering the analogy of germanates to silicates, these results give some far-reaching implications for the evolution and dynamics of the Earth's deep interior.

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