Mid-range Order Research Articles

Thermodynamic and structural aspects of the polyamorphic transition in yttrium and other rare-earth aluminate liquids

A first-order transition between two liquids has been reported in yttrium–aluminate liquids close to Y 3Al 5O 12 (YAG) composition. This transition is seen as the nucleation and growth of a low-density phase in a matrix of a higher density liquid when Y 2O 3–Al 2O 3 liquids are cooled below the liquidus. Both liquids are quenched to glass before the transition is complete. Analysis of the resulting composite samples shows that the two glasses are identical in composition although the two glasses differ in density by 4%. There are also mechanical differences between the two glasses; the low-density glass is more resistant to polishing, while the high-density glass becomes highly scratched. Following the initial observation, recent research has focused on establishing the thermodynamic and structural features of Y 2O 3–Al 2O 3 liquids which lead to liquid–liquid transitions. In addition, studies of other rare-earth aluminate compositions have been used to determine what, if anything makes the yttrium-bearing liquids exceptional. Differential scanning calorimetry (DSC) has been used to establish the onset of glass transition and, when combined with the heat capacity of crystalline phases, the jump in heat capacity at the point of glass transition. The DSC data enable the liquid fragility to be established and show the high-density liquid to be characterized by a non-Arrhenian viscosity–temperature relation. DSC studies of La–aluminates also show fragile liquid behavior, although liquid–liquid transitions have not been reported for these compositions. A combination of DSC and solution calorimetry has been used to evaluate the energetic differences between the two liquid phases of yttrium–aluminates and these data can also be used to estimate the changes in entropy. The entropy differences between the two phases also indicate differences in liquid rheology with the high- to low-temperature liquid transition also being a transition from a fragile to strong liquid. The structural differences between the two liquid polymorphs of Y 2O 3–Al 2O 3 are difficult to discern. The stable crystalline phase is garnet-structured YAG but this is difficult to nucleate and a metastable assemblage of a-Al 2O 3 and YAlO 3 perovskite tend to crystallize. This has led to the suggestion that the high temperature liquid is dominated by octahedral aluminum, which is consistent with a higher density. Neutron diffraction studies of Y- and La–aluminate glasses show that the liquid structure is very different from that of the crystalline phases, the aluminate liquids are dominated by a tetrahedral aluminate framework and there is little change in the mean Al–O coordination number either at the liquid–liquid transition or when La(III) is substituted for Y(III). The main differences in structure are seen in the ordering of the rare earth coordination polyhedra and network topology, the La- and the low-density Y–aluminate glasses showing increased rare-earth oxygen distances and more mid-range order. Nuclear magnetic resonance studies also show little change in Al(III) coordination although there are differences in the degree of disorder.

Matrix order indices in statistical mechanics

A new notion of matrix order indices which relates the matrix norm and its trace is introduced. These indices can be defined for any given matrix. They are especially important for matrices describing many-body systems, equilibrium as well as nonequilibrium, for which the indices present a quantitative measure of the level of ordering. They characterize not only the long-range order, but also mid-range order. In the latter case, when order parameters do not exist, the matrix indices are well defined, providing an explicit classification of various mid-range orders. The matrix order indices are suitable for describing phase transitions with both off-diagonal and diagonal orders. Contrary to order parameters whose correct definition requires the thermodynamic limit, the matrix indices do not necessarily need the latter. Because of this, such indices can distinguish between different phases of finite systems, thus, allowing for the classification of crossover phase transitions.

Structural order and clustering in annealedα−SiCandα−SiC:H

We carried out a theoretical investigation of the structural properties of annealed $\ensuremath{\alpha}\ensuremath{-}\mathrm{SiC}$ and $\ensuremath{\alpha}\ensuremath{-}\mathrm{S}\mathrm{i}\mathrm{C}:\mathrm{H}.$ The calculations were performed using the free volume Monte Carlo method combined with interatomic potentials. Our prototype nanoparticle contained as much as 85 000 atoms which allows for a superior statistical sampling of the material. The results show that C atoms segregate, forming small clusters embedded in an extensive Si network. Si atoms are mostly contained in a single extensive network and a few small clusters. Unprecedented detailed ring statistics analysis shows that C clusters do not form strictly C rings and that the introduction of H increases the occurrence of microvoids in the structure. Moreover, the incorporation of H slightly reduces the chemical order in the material and, to a larger extent, reduces the midrange structural order. Hydrogen also relaxes bonding stress around atoms in the network. The results are consistent with the available experimental data.

Behaviour of sodium deposited onto thin silica layers

Sodium has been deposited on silica surfaces in vacuum conditions. It has been shown by X-ray absorption spectroscopy (XAS) that its behaviour depends dramatically on the temperature of the substrate. When evaporated on clean silica surface, sodium diffuses into the bulk of the material with a well defined chemical environment which involves oxygen, sodium and silicon at distances of 2.3, 2.9 and 3.8 Å, respectively. On silica at temperature below 220 K, a metallic sodium film is formed but, upon warming the sample up to room temperature, sodium diffuses readily into the silica substrate. Finally, XAS at the silicon K-edge demonstrates that a strong modification of the mid-range order of the silicon in the silica occurs upon the dissolution of the sodium.

Raman study of fractal voids in hot-pressed SiO 2

The sensitivity of the dynamic (vibrational) properties of fractal nanocracks in hot-pressed silica to the thermal and mechanical prehistory of the material was studied by low-frequency Raman scattering. Samples were prepared from gel-derived and fused powdery products. The Raman data demonstrate the fractality of elementary continuity defects. From the frequency dependence of the Raman intensity, the values of the fracton (spectral) dimension that reflects the mid-range order in glass, and the dimensions of fractals in real space were calculated.

Low-energy excitations in stressed poly(methyl methacrylate)

Raman study of flexure stressed poly(methyl methacrylate) (PMMA) plates at the frequency range of libration mode (80 cm−1), boson peak (14 cm−1), and quasi-elastic light scattering (QLS) (below 20 cm−1) is presented. The reversible changes in the vicinity of the Rayleigh line were attributed to partial disturbance of the midrange order due to stress-induced redistribution of random fluctuations of orientation. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1133–1136, 2000

Low-energy excitations in stressed poly(methyl methacrylate)

Raman study of flexure stressed poly(methyl methacrylate) (PMMA) plates at the frequency range of libration mode (80 cm−1), boson peak (14 cm−1), and quasi-elastic light scattering (QLS) (below 20 cm−1) is presented. The reversible changes in the vicinity of the Rayleigh line were attributed to partial disturbance of the midrange order due to stress-induced redistribution of random fluctuations of orientation. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1133–1136, 2000

Oxidation-reduction mechanism of iron in dioctahedral smectites: II. Crystal chemistry of reduced Garfield nontronite

The crystallochemical structure of reduced Garfield nontronite was studied by X-ray absorption pre-edge and infrared (IR) spectroscopy, powder X-ray diffraction, polarized extended X-ray absorption fine structure (P-EXAFS) spectroscopy, and texture goniometry. Untreated and highly reduced (>99% of total Fe as Fe 2+ ) nontronite samples were analyzed to determine the coordination number and the crystallographic site occupation of Fe 2+ , changes in in-plane and out-of-plane layer structure and mid-range order between Fe centers, and to monitor the changes in structural and adsorbed OH/H 2 O groups in the structure of reduced nontronite. Contrary to earlier models predicting the formation of fivefold coordinated Fe in the structure of nontronites upon reduction, these new results revealed that Fe maintains sixfold coordination after complete reduction. In-plane P-EXAFS evidence indicates that some of the Fe atoms occupy trans-sites in the reduced state, forming small trioctahedral domains within the structure of reduced nontronite. Migration of Fe from cis- to trans sites during the reduction process was corroborated by simulations of X-ray diffraction patterns which revealed that about 28% of Fe 2+ cations exist in trans sites of the reduced nontronite, rather than fully cis occupied, as in oxidized nontronite. Out-of-plane P-EXAFS results indicated that the reduction of Fe suppressed basal oxygen corrugation typical of dioctahedral smectites, and resulted in a flat basal surface which is characteristic of trioctahedral layer silicates. IR spectra of reduced nontronite revealed that the dioctahedral nature of the nontronite was lost and a band near 3623 cm −1 formed, which is thought to be associated with trioctahedral [Fe 2+ ] 3 OH stretching vibrations. On the basis of these results, a structural model for the reduction mechanism of Fe 3+ to Fe 2+ in Garfield nontronite is proposed that satisfies all structural data currently available. The migration of reduced Fe ions from cis-octahedra to adjacent trans-octahedra is accompanied by a dehydroxylation reaction due to the protonation of OH groups initially coordinated to Fe. This structural modification results in the formation of trioctahedral Fe 2+ clusters separated by clusters of vacancies in which the oxygen ligands residing at the boundary between trioctahedral and vacancy domains are greatly coordination undersaturated. The charge of these O atoms is compensated by the incorporation of protons, and by the displacement of Fe 2+ atoms from their ideal octahedral position toward the edges of trioctahedral clusters, thus accounting for the incoherency of the Fe-Fe1 and Fe-Fe2 distances. From these results, the ideal structural formula of reduced Garfield nontronite is Na 1.30 [Si 7.22 Al 0.78 ] [Fe 2+ 3.65 Al 0.32 Mg 0.04 ]O 17.93 (OH) 5 in which the increased layer charge due to reduction of Fe 3+ to Fe 2+ is satisfied by the incorporation of protons and interlayer Na.

Rings in the structure of silicate glasses

In this work infrared absorption spectroscopy was applied to investigate the mid-range order in silicate and aluminosilicate glasses. Ring systems containing various rings can exist in the structure of such glasses. Our previous studies on cyclosilicates have allowed us to determine positions of the bands characteristic of various membered rings [M. Sitarz, W. Mozgawa, M. Handke, J. Mol. Struct. 404 (1997) 193; M. Handke, M. Sitarz, W. Mozgawa, J. Mol. Struct. 450 (1998) 229]. Amorphous and crystalline layered silicates (Li2Si2O5, Na2Si2O5 and K2Si2O5) and framework ones (SiO2 and K[AlSiO4]) were investigated. Analysis of the obtained IR spectra and their mathematical decomposition allow us to identify the bands characteristic of rings systems, both for crystalline and amorphous samples. Appearance of the bands characteristic of pseudolattice vibrations (740–600cm−1 connected with rings) in the IR spectra of the amorphous samples is an evidence of the existence of over-tetrahedral order.

Second-nearest-neighbor effects on the NMR shielding of N in P 3N 5 and hexagonal BN

NMR shieldings calculated at the central N atom in models for solid P 3N 5 and BN are strongly influenced by the presence of additional N atoms in second-nearest-neighbour positions. For P 3N 5 such effects are deshielding while for hexagonal BN they are shielding. This indicates both that accurate calculation of N shieldings in solids will require large cluster models and that such shieldings will give information on mid-range order within the material.

RELATION BETWEEN MICROSCOPIC AND MACROSCOPIC CHARACTERISTICS OF STATISTICAL SYSTEMS

Order parameters of physical systems and order indices of their density matrices are, respectively, macroscopic and microscopic characterisics of a statistical system. We claim that there are situations in which the index provides more information than the parameter. This is proved by the exhibition of an exactly solvable model of a Bose system with mid-range order for which the order parameter is zero but for which an order index changes continuously as the Hamiltonian is varied.

Ti4+ in silicate melts: Energetics from high-temperature calorimetric studies and implications for melt structure

The drop solution calorimetric method was used to determine the enthalpy of solution of rutile (ΔHsol) in silicate melts. High-temperature (1760 K) in situ calorimetric data show that ΔHsol is a strong function of melt composition. For potassium endmember melts, potassium disilicate, and trisilicate, ΔHsol increases (from 28–48 kJ/mol) as TiO2 concentration increases. For calcium disilicate melts ΔHsol is constant (69 kJ/mol). For mixed potassium-calcium compositions, ΔHsol is more exothermic than for the calcium endmember but remains constant at 43.9 kJ/mol. The enthalpy of solution of rutile at 1760 K and the enthalpy of mixing at 978 K derived from lead borate solution calorimetry for Ti-bearing potassium aluminosilicate glasses have been used to model the homogeneous equilibria among Ti species in the potassium-bearing melts. The energetics of Ti speciation were used to predict quantitatively the excess heat capacity of titanium-bearing silicate melts previously observed by Lange and Navrotsky (1993), suggesting that heat capacities, mixing properties, and rutile solubility are all controlled by the temperature and composition dependence of the same set of homogenous equilibria among titanium species in the melts. Though knowing the exact microscopic nature of these species is not necessary for macroscopic thermodynamic modeling, the model is consistent with a gradual variation with composition and temperature in mid-range order involving five-coordinated titanyl groups and alkali atoms as proposed by Farges et al. (1996a,b,c).

UsingNMR shielding calculations to help determine local and midrange order in amorphous materials

Solid-state NMR spectroscopy has become a critically important method for the determination of local order in amorphous materials, both natural (such as silicate glasses) and man-made (such as alkali Si sulfide fast ion conductors). Although assignment of NMR features can sometimes be made by comparison with crystalline analogs, there are often unique structural units in glasses which are not found in crystals. To characterize such units, direct ab initio calculations of NMR shieldings using the RPALORC, method have proven very valuable. In addition to considerations of method choice and basis-set selection which are important in calculating NMR shieldings for gas-phase molecules, calculation of NMR shieldings for species in glasses involves a choice of the model used to characterize the local or midrange environment. There is often fragmentary information on the structure and other spectral properties of such species which can be used in combination with the NMR spectra to obtain a firm characterization. Some example materials discussed will be (1) B2O3 glass, for which boroxol ring and nonring sites NMR properties have recently been determined by dynamic angle spinning techniques, (2) F-containing aluminosilicate glasses, where a 5-coordinate Al complex with both oxygen and fluorine ligands has been established, (3) CO2 saturated aluminosilicate glasses, where 13C-NMR reveals a number of complexes of CO2 with aluminosilicate fragments of both “CO2” and “CO3” type, (4) silicon sulfide glasses, which show both corner and edge-sharing oligomeric units, and (5) Si3N4, where the shielding of a central N is found to be strongly affected by the orientation of the neighboring N lone pairs. © 1995 John Wiley & Sons, Inc.

Energetics of radiation damage in natural zircon (ZrSiO4)

Transposed temperature drop calorimetry at 1000 °C was performed on natural zircons (ZrSiO4) from Sri Lanka that were partially to completely metamict due to α-decay event damage (0.06 to 11.7×1015α-decay events/mg). The enthalpy of annealing at room temperature (ΔHanneal) varies sigmoidally as a function of radiation dose. ΔHanneal reaches a saturation plateau at radiation doses greater than 5×1015α-decay events/mg. The annealing of several samples to a crystalline structure with broadened diffraction peaks does not significantly affect the enthalpy of annealing. The large magnitude of the enthalpy of annealing plateau, −59±3 kJ/mol, suggests that the damage to the structure is pervasive on the scale of Angstroms, consistent with the loss of mid-range order characteristic of a glass. The energetics are consistent with, but do not require, chemical heterogeneity caused by micro-domains of amorphous SiO2-rich and ZrO2-rich regions in the metamict state.

Order indices and ordering in macroscopic systems

In A. J. Coleman and V. I. Yukalov:Mod. Phys. Lett. B,5, 1679 (1991) andNuovo Cimento B, 107, 535 (1992) we introduced order indices of reduced density matrices as a tool to connect macroscopic and microscopic properties of physical systems. In the present paper, we give a definition of order indices which is independent of the representation of the density matrices and is valid for both fermion and boson systems and for all types of order: short, mid and long range. Time-dependent indices are introduced to permit discussion of non-equilibrium processes. Special attention is devoted to the study of mid-range order and the corresponding stability conditions. Mid-range order is examined both in a system at rest and in a system with two-velocity motion.

Order indices for boson density matrices

We study low-temperature properties of boson density matrices when macroscopic occupation of quantum energy levels can occur. An important novelty of our approach is the definition of order indices that characterize the behaviour of largest eigenvalues of density matrices in the thermodynamic limit. Continuous variation of the order indices gives rise to a whole spectrum of possible order types: long-range order, mid-range order and short-range order. A relation between order indices is found. As an illustration of the general scheme a new model exemplifying mid-range order is constructed.

Ammoniation and nitridation of highly disperse silica

Infrared spectroscopy, X-ray scattering intensity measurements and chemical analysis of the N content have been used to study the reaction of flowing NH 3 with highly disperse silica (aerosil) at elevated temperatures. During interaction with flowing NH 3 (ammoniation) at temperatures ≤ 723 K, only SiNH 2 groups were formed by substitution of SiOH groups on aerosil. At temperatures higher than 773 K under flowing NH 3 , both SiNH 2 groups and Si-NH-Si groups (silazane bridges) were formed, which could be identified clearly in the IR spectra. Silazane bridges appear at temperatures ≥ 1073 K, replacing not only surface siloxane bridges but also siloxane bridges in the bulk. With increasing reaction time, nitrogen contents up to 25 mass% were introduced into the SiO 2 lattice by a reaction of aerosil with flowing NH 3 at 1373 K. X-ray scattering intensity measurements have shown that the incorporation of nitrogen in the aerosil structure gives rise to a drastic rearrangement of the amorphous SiO 2 structure. Both the primary structure order and the mid-range order of the aerosil were strongly changed after high temperature ammoniation. The treatment of aerosil in flowing N 2 at 1373 K results in formation of cristobalite.

ORDER INDICES AND MID-RANGE ORDER

We introduce a novel notion, order indices of reduced density matrices, characterizing different types of order, long-range as well as mid-range, occurring in statistical systems. The order indices define the behaviour of the largest eigenvalues of density matrices in the thermodynamic limit. These indices are especially useful for describing mid-range order, where they are directly connected with the large-distance asymptotic forms of off-diagonal density matrices. Several examples illustrate the idea.