Diffusion-controlled Solid-state Reactions Research Articles

Evidence for suboceanic small-scale convection from a “garnet”-bearing lherzolite xenolith from Aitutaki Island, Cook Islands

Garnet peridotite xenoliths have been rarely reported from suboceanic mantle. Petrographic and geochemical characteristics of garnet-bearing oceanic peridotite xenoliths provide precious information on dynamics of the suboceanic lithosphere and asthenosphere interaction. We examined a lherzolite xenolith included in olivine nephelinite lava from Aitutaki Island, a member of the Cook-Austral volcanic chain. The lherzolite xenolith contains reddish fine-grained (< 5 µm in size) mineral aggregates (FMAs) with size range of 0.5–6 mm, consisting of olivine, calcic and sodic plagioclases, aluminous spinel, native iron, and nepheline. Microstructural observations and chemical data corroborate that the FMA is a decomposed pyrope-rich garnet including chromian spinel grains with an irregular highly indented morphology in the center. The FMA is surrounded by pyroxene-poor and olivine-rich aureole. The spatial and morphological relationships of FMA and chromian spinel with pyroxene-depleted margin suggest a reaction of aluminous spinel + pyroxenes → pyrope-rich garnet + olivine, which requires a compression before decomposition of the garnet to FMA. An orthopyroxene grain shows slight but clear chemical zoning characterized by increase in Al, Ca, and Cr from the grain center to the rim. The zoning patterns of Al and Ca in the orthopyroxene grain can be modeled by diffusion-controlled solid-state reactions induced by pressure and temperature changes, keeping surface concentrations in equilibrium with the other coexisting mineral phases. The results indicate that the mantle, from which the lherzolite xenolith was derived, underwent isothermal decompression followed by a weak heating on a time scale of a few tenths of million years before the xenolith extraction. From the deduced compression and decompression histories, we hypothesize that the mantle beneath Aitutaki Island was once dragged down to a garnet-stable deep mantle region and brought up later by small-scale sublithospheric convection.

Self-Limiting Sub-5 nm Nanodiamonds by Geochemistry-Inspired Synthesis.

Controlling diamond structures with nanometer precision is fundamentally challenging owing to their extreme and far-from-equilibrium synthetic conditions. State-of-the-art techniques, including detonation, chemical vapor deposition, mechanical grinding, and high-pressure-high-temperature synthesis, yield nanodiamond particles with a broad distribution of sizes. Despite many efforts, the direct synthesis of nanodiamonds with precisely controlled diameters remains elusive. Here the geochemistry-inspired synthesis of sub-5 nm nanodiamonds with sub-nanometer size deviation is described. High-pressure-high-temperature treatment of uniform iron carbide nanoparticles embedded in iron oxide matrices yields nanodiamonds with tunable diameters down to 2.13 and 0.22nm standard deviation. A self-limiting, redox-driven, and diffusion-controlled solid-state reaction mechanism is proposed and supported by in situ X-ray diffraction, ex situ characterizations, and computational modeling. This work provides a unique mechanism for the precise control of nanostructured diamonds under extreme conditions and paves the road for the full realization of their potential in emerging technologies.

Boosting exciton dissociation and charge transfer by regulating dielectric constant in polymer carbon nitride for CO2 photoreduction

The high binding energy of excitons and their slow charge transfer due to a low dielectric constant greatly limits the further improvement of photocatalytic efficiency in polymer carbon nitride (PCN). Herein, PCN samples with uniformly doped phosphorus (P-PCN) with stable and efficient CO2 photoreduction performance were prepared by the solid-state chemical reaction of PCN with sodium hypophosphite (NaH2PO2). With NaH2PO2 as both the molten salt and dopant precursor, this doping approach ensures that P is doped from the surface into the bulk, resulting in intimate P-OH bonds at the in-planar interstitial sites of the PCN melon. After polarization by the P-OH sites with high dipole moments, 0.7 at% P-PCN shows a significantly increased dielectric constant. Thus, a low exciton binding energy is achieved compared with pure PCN. This enhances the spatial separation and transport efficiency of photogenerated charge carriers over the optimal 0.7 at% P-PCN sample, leading to better selectivity for CO2-to-CO photoreduction with a three-fold higher yield compared to that of pure PCN without any cocatalysts or sacrificial agents. The controllable P doping method utilizing a thermodynamically feasible diffusion-controlled solid-state reaction reported in this work can be adopted to design other cost-effective photocatalytic systems.

Effect of bastnaesite as reductant on hematite reduction during in-situ suspension magnetization roasting of refractory iron ore under neutral atmosphere

The iron tailings of Bayan Obo mines are solid waste, which occupies land area and also causes environmental pollution; however, this waste can be recycled. In this study, based on the characteristics of iron minerals and fluorocarbonate contained in Bayan Obo iron tailings, clean magnetization roasting of iron minerals by bastnaesite from iron tailings during in-situ suspension magnetization roasting in a neutral atmosphere was explored. The results show that for iron tailings with a mass of 12 g, a N 2 gas flow rate of 600 mL/min, and roasting for 5 min at 800 °C, iron concentrate with a 60.44% iron grade at an iron recovery of 76.04% could be obtained. X-ray diffraction analysis showed that the weak magnetic hematite was reduced to strong magnetic magnetite in the neutral atmosphere, without additional reductant. The kinetics of the magnetization roasting of mineral mixtures (bastnaesite and hematite) in a neutral atmosphere showed that the optimal reaction mechanism function was the three-dimensional diffusion model with activation energy of 161.8838 kJ·mol −1 ; this indicates that the reaction was a heterogeneous, diffusion-controlled solid-state reaction.

Kinetics and mechanism of formation of MoO2 by solid state reaction between MoS2 and MoO3

ABSTRACTThe kinetics and mechanism of the solid state reaction between MoS2 and MoO3 to form MoO2 under nitrogen atmosphere between 723 and 973 K were studied using bulk mixed samples, mixed compressed pellets and pure MoS2 and MoO3 pellets with one face in contact. The results show that for the bulk samples, the reaction reaches a maximum conversion of 67.3% at 923 K in 75 min, while for compressed samples conversion under similar conditions reaches 96.1% in 75 min, which reflects the effect of the physical conditions of both types of experiments on the reaction kinetics. The calculated activation energy values for both experimental conditions are consistent, with an average value of −44.2 ± 1.9 kJ, which is in the range of diffusion-controlled solid state reactions. For the samples with one face in contact, above 923 K the results appear to indicate that solid state molecular diffusion of both MoS2 and MoO3 in opposite directions in the newly formed MoO2 crystal structure could take place, with estimated diffusion coefficients of MoS2 in MoO2 and MoO3 in MoO2 at 923 K of 1.08 × 10−6 and 7.78 × 10−6cm2 s−1, and at 973 K of 10−5 and 1.13 × 10−5 cm2 s−1, respectively.

Transmission electron microscopy study of the epitaxial association of hedenbergite whiskers with babingtonite

ABSTRACTOvergrowths of whiskers of hedenbergite (Ca(Fe2+,Mg)Si2O6) on the hydrous pyroxenoid babingtonite (Ca2Fe2+Fe3+[Si5O14(OH)]) have been observed at Arvigo in Switzerland and Kreimbach/Kaulbach in Germany, and we have studied them with transmission electron microscopy in order to understand their structural relationships and formation. The boundaries between babingtonite and hedenbergite are sharply defined, and the two minerals are in direct contact with no additional phases present. The relationships of babingtonite (Bab) and hedenbergite (Hd) were determined as Bab[100]//Hd[112] in the Arvigo specimen and Bab[$\bar 1$00]//Hd[1$\bar 1$2] in the Kreimbach/Kaulbach specimen. Diffraction derived from Bab(031) and Hd(02$\bar 1$) in the Arvigo samples and Bab(031) and Hd(021) in the Kreimbach/Kaulbach samples were observed in identical positions. The reciprocity between the babingtonite and hedenbergite structures is governed by the direction of the SiO4-tetrahedral chains, and the related configuration of octahedra. Thus, hedenbergite is apparently an epitaxial phase grown on a base of {010} plates of babingtonite. The defined orientation relationship is also consistent with that shown in topotaxial intergrowths of other clinopyroxenes and pyroxenoids. The topotaxial intergrowths may result from diffusion-controlled solid-state reactions, whereas rapid whisker growth is characteristic of supersaturated solutions or a vapour medium. The epitaxial growth of hedenbergite whiskers on babingtonite with an abrupt but coherent change of structure at the interface represents an ideal example where the similar chemical compositions of host and guest contribute strongly to the close structural relationship.

Reaction path in formation of Ti1−xWxC solid solution by combustion synthesis

Ti1−xWxC solid solution powders have been prepared by combustion synthesis in two reaction modes of self-propagating high-temperature synthesis (SHS) and thermal explosion (TE). The reaction mechanism in combustion synthesis is investigated and the effects of processing parameters are discussed. Two reaction paths are proposed for the formation of the Ti1−xWxC solid solution. In path 1, Ti1−xWxC crystals are directly precipitated from Ti-W-C melt, and in path 2 the Ti1−xWxC phase is formed by solid-state reaction between TiC and WC. The availability of the two reaction paths depends on the x value and reaction temperature. For smaller x values and higher temperatures, the reaction path 1 dominates and almost full conversion is achieved. For larger x values and lower temperatures, however, path 2 becomes dominant. In path 2, the rate-limiting step is the formation of WC by slow diffusion-controlled solid-state reaction between W and C, which is unable to be completed during the short reaction period and results in the presence of W2C and unreacted W in the products. The reaction between W and C cannot be improved by the addition of excessive C, but can be promoted by using carbon black instead of graphite powder as C source or carrying out the synthesis in a high-pressure N2 atmosphere instead of vacuum. In the fast combustion reaction with high heating/cooling rates, a non-equilibrium state is likely to be created because the mass transfer and energy exchange are limited. The non-equilibrium condition has a strong influence on the reaction kinetics, where the decomposition of W2C is avoided, a localized compositional heterogeneity is caused, and ultrafine grains on a submicron scale are obtained in the products.

Crystal Structure, Magnetism, 89Y Solid State NMR, and 121Sb Mössbauer Spectroscopic Investigations of YIrSb

The ternary antimonide YIrSb was synthesized from the binary precursor YIr and elemental antimony by a diffusion controlled solid‐state reaction. Single crystals were obtained by a flux technique with elemental bismuth as an inert solvent. The YIrSb structure (TiNiSi type, space group Pnma) was refined from single‐crystal X‐ray diffractometer data: a = 711.06(9), b = 447.74(5), c = 784.20(8) pm, wR2 = 0.0455, 535 F2 values, 20 variables. 89Y solid state MAS NMR and 121Sb Mössbauer spectra show single resonance lines in agreement with single‐crystal X‐ray data. YIrSb is a Pauli paramagnet.

Removal of methylene blue from aqueous solution by fibrous clay minerals

Kinetics and equilibrium processes of the methylene blue (MB) retention from aqueous solution by a mixture of fibrous clay minerals, which was isolated from a naturally occurring clay, were investigated. For these purposes, the effects of contact time, initial adsorbate concentration, adsorbent content, pH and ionic strength were determined. The results show that the MB retention obeys a pseudo-first order equation and the process is a diffusion controlled solid-state reaction. Moreover, the isotherm data fitted the Langmuir equation and the MB binding process became more energetic with the increase of the adsorbent concentration. In addition, the augmentation of the clay content or the initial MB concentration reduced the adsorption capacity, presumably because of the clay particles microaggregation and/or the occurrence of MB deriving species. On the other hand, it is observed that the MB uptake limit is reduced in low acid pH, particularly below the PZC, as well as in ionic strengthen solutions. These facts are linked to the silanol group protonation and to the reduction of the electrostatic forces induced by the clay particles, respectively.

Diffusion-Controlled Solid-State Reactions of Spherical Particles, A General Model for Multiphase Binary Systems

The formal treatment of the diffusion-controlled growth of n binary compounds with narrow homogeneity range during the reaction of a sphere of reactant A immersed in reactant B is presented and discussed. Both constituents are assumed to be mobile. The reaction products are assumed to grow simultaneously as uniform and compact concentric layers with ideal contact at the interfaces as well as at the external surface of the sphere. The kinetic equations follow from the coupling between chemical reactions and partitioning of the diffusion flux at phase boundaries. The results for the formation of two and three compounds are presented. The influence of the initial radius of the sphere, of the relative magnitude of the kinetic constants, and of the volume variation is discussed in detail.

Numerical simulation of diffusion-controlled solid-state reactions in spherical particles

The three-dimensional time-dependent diffusion equation, subjected to a chemical reaction at the interface of the reacted layer and unreacted core, used for simulating diffusion-controlled solid-state reactions is solved by a finite volume method in a body fitted curvilinear co-ordinate system. The simulated reaction zone is seen to advance towards the center of a spherical particle. The concentrations of reactants and product are also predicted. Within the reacted zone, the simulated diffusion rates at different spherical cross sections reveal a clear picture of the unsteady diffusion process. The predicted kinetic curves at different conversion constants help to understand the kinetics of diffusion controlled solid-state reactions in spherical particles.

Numerical exploration of diffusion-controlled solid-state reactions in cubic particles

The characteristics of diffusion-controlled solid-state reactions in cubic particles are explored in this study. In order to capture the three-dimensional reaction front, the diffusion equation, subject to an interfacial chemical reaction in cubic particles, is solved in a transient form using the finite volume method. How the unreacted core is shrunk with time is clearly revealed. In addition, the concentration distributions of reactants and products are numerically predicted. A comparison of reacted zones advancing along different directions from the particle surface to the center is also made. The simulated kinetic curves at different conversion constants are shown to be useful to evaluate the conversion kinetics of diffusion-controlled solid-state reactions in cubic particles.

Studies on reactions between aluminium/aluminium alloy and molten sodium

Abstract In this research, reactions between pure aluminium/its alloy and molten sodium at 350∼450°C have been investigated. Optical microscopy and X-ray diffraction analysis were used to observe and analyze the morphology, the distribution and the growth kinetic mechanism of corrosion products. Experiments showed that corrosion severity of specimens from molten sodium was related to the content of silicon in aluminium, and that corrosion of aluminium–silicon alloys in molten sodium was a diffusion-controlled solid-state reaction.

Development of a diffusion-controlled solid-state reaction from an initial nucleus

A mathematical model for the growth of a nucleus of a solid-state reaction product is analyzed that takes into account explicitly stresses and strains. Different regimes of the reaction course are found. The solid-state diffusion equation derived for slow reactions can be useful for describing more complex processes.

Kinetic aspects of the formation of lead zirconium titanate

The kinetics of the second calcination step in the formation of PZT solid solution (with perovskite ABO 3 lattice) has been investigated by using two different particle sizes of the B-site precursor (1.91 and 5.08 μm), the finer size being obtained by prolonged milling. In-situ analysis performed by high-temperature X-ray diffractometry in a non-isothermal mode (20–800 °C) revealed a reduction of the calcination temperature by 100 °C with a decrease in particle size of the precursor. In order to clarify the mechanism of the solid-state reaction to PZT, isothermal heat treatment of the mixtures was performed in the temperature range 540–700 °C. The activation energies for the fine and the coarse powders were estimated as 150 and 210 kJ mol −1 respectively, and the reaction was found to follow the Jander model for diffusion-controlled solid-state reaction kinetics.

Solid state reactions and morphology

The morphology of solid/gas interfaces and interfaces between crystalline solids during diffusion-controlled solid state reactions is investigated experimentally and theoretically. Three types of model experiments with oxides and halides are discussed where externally applied chemical and electrical potential gradients act as driving forces for the fluxes of defects in the crystals by which the interfaces are driven. Using linear stability analysis of the transport equations we analyze the stability of the interfaces on a macroscopic scale while the microscopic behavior is studied by applying Monte Carlo methods for defect diffusion in the crystal lattice.

いん石中の非平衡組織の解析： 不可逆過程の熱力学からのアプローチ

The methods based on thermodynamics of irreversible processes are discussed in order to analyze non-equilibrium textures formed via diffusion-controlled solid-state reactions in meteorites. Simple expressions for rate constants of reaction between enstatite and metallic iron and internal reduction of olivine are presented.

Determination of energy yield of mechanochemical reactions

The main characteristic of mechanochemical conversions is their energy yield, G M ( mol MJ ), and its value was determined for various processes. In investigations of heterogeneous reactions on the friction surface of oxides, e.g., of mechanically activated chemisorption, G M is usually 10 −3–10 −1 smaller energy yield (10 −3–10 −2 mol MJ ) is characteristic of the formation of mechanical paramagnetic defects. In solid-solid reactions the energy yield reaches 0.1–1 mol MJ , whereas a value of 10 2 mol MJ was found for polymorphous transformations. An attempt was made to calculate G M for diffusion-controlled solid-state reactions.

Expanding spherical shell kinetic model for diffusion-controlled solid-state reactions

A reaction kinetic model has been derived for a solid-state diffusion-controlled reaction in a system of spherical particles of A isolated in a matrix of B. This model is analogous to the Ginstling-Brounsthein model except that the diffusion of A is the rate-controlling step. The model, therefore, resulting in an expanding spherical shell of product AB, is ▪ where t = time, x = fraction reaction, K = reaction rate constant.

Determination of the Self-diffusion Coefficient of Nickel Atoms in Nickel Sulfide

Abstract The self-diffusion coefficient of ions or atoms in such crystals as halides, oxides and sulfides can be determined from the rate of the diffusion-controlled solid-state reaction as well as by the tracer method. In the present study, the self-diffusion coefficient of nickel atoms in nickel sulfide was determined from the rates of the sulfidation and desulfidation of nickel sulfide in H2S-H2gas mixtures. The results agreed well with the data obtained by the previous investigators employing the tracer technique.