Creation Of Cation Vacancies Research Articles

Enhancing photocatalytic H2O2 production through the improvement of water oxidation via a novel lattice-oxygen-involved pathway

Bi-vacancy-rich BiPO4 nanocrystals (VBi-BIP) have achieved high H2O2 production, providing an in-situ source for UV/H2O2 degradation. These nanocrystals produce H2O2 at 26.7 mM·g−1·h−1, surpassing most inorganic and organic photocatalysts, and have an AQY of 43.4% and ECE of 10.7% at 254 ± 10 nm. The Bi vacancies enhance activity by enabling a new lattice-oxygen-involved pathway for H2O2 formation, with a potential 0.34 V lower than conventional water oxidation reactions. Using in-situ generated H2O2 on VBi-BIP, organic pollutants can be efficiently degraded, achieving a 92% removal rate for ciprofloxacin in a flow reactor operated at 2.4 L/h for 400 hours. The energy cost per unit of treated water (EE/O) in this in-situ degradation device is 0.58 kWh/m3, half of that in traditional UV/H2O2 treatment. The creation of cation vacancies and their function elucidation for H2O2 generation paves the way for designing more efficient photocatalysts for in-situ H2O2 use in the future.

Novel Red Phosphor of Gd3+, Sm3+ co-Activated AgxGd((2-x)/3)-0.3-ySmyEu3+0.30☐(1-2x-2y)/3WO4 Scheelites for LED Lighting.

Gd3+ and Sm3+ co-activation, the effect of cation substitutions and the creation of cation vacancies in the scheelite-type framework are investigated as factors influencing luminescence properties. AgxGd((2-x)/3)-0.3-ySmyEu3+0.3☐(1-2x)/3WO4 (x = 0.50, 0.286, 0.20; y = 0.01, 0.02, 0.03, 0.3) scheelite-type phases (AxGSyE) have been synthesized by a solid-state method. A powder X-ray diffraction study of AxGSyE (x = 0.286, 0.2; y = 0.01, 0.02, 0.03) shows that the crystal structures have an incommensurately modulated character similar to other cation-deficient scheelite-related phases. Luminescence properties have been evaluated under near-ultraviolet (n-UV) light. The photoluminescence excitation spectra of AxGSyE demonstrate the strongest absorption at 395 nm, which matches well with commercially available UV-emitting GaN-based LED chips. Gd3+ and Sm3+ co-activation leads to a notable decreasing intensity of the charge transfer band in comparison with Gd3+ single-doped phases. The main absorption is the 7F0 → 5L6 transition of Eu3+ at 395 nm and the 6H5/2 → 4F7/2 transition of Sm3+ at 405 nm. The photoluminescence emission spectra of all the samples indicate intense red emission due to the 5D0 → 7F2 transition of Eu3+. The intensity of the 5D0 → 7F2 emission increases from ~2 times (x = 0.2, y = 0.01 and x = 0.286, y = 0.02) to ~4 times (x = 0.5, y = 0.01) in the Gd3+ and Sm3+ co-doped samples. The integral emission intensity of Ag0.20Gd0.29Sm0.01Eu0.30WO4 in the red visible spectral range (the 5D0 → 7F2 transition) is higher by ~20% than that of the commercially used red phosphor of Gd2O2S:Eu3+. A thermal quenching study of the luminescence of the Eu3+ emission reveals the influence of the structure of compounds and the Sm3+ concentration on the temperature dependence and behavior of the synthesized crystals. Ag0.286Gd0.252Sm0.02Eu0.30WO4 and Ag0.20Gd0.29Sm0.01Eu0.30WO4, with the incommensurately modulated (3 + 1)D monoclinic structure, are very attractive as near-UV converting phosphors applied as red-emitting phosphors for LEDs.

Interactions between bare and protonated Mg vacancies and dislocation cores in MgO

Water can be incorporated into the lattice of mantle minerals in the form of protons charge-balanced by the creation of cation vacancies. These protonated vacancies, when they interact with dislocations, influence strain rates by affecting dislocation climb, pinning the dislocation, and, potentially, by altering the Peierls barrier to glide. We use atomic scale simulations to investigate segregation of Mg vacancies to atomic sites within the core regions of dislocations in MgO. Energies are computed for bare and $$V_{{{\text{Mg}}}}^{\prime \prime }$$ protonated Mg vacancies occupying atomic sites close to ½ 〈110〉 screw dislocations, and ½ 〈110〉 {100} and ½ 〈110〉 {110} edge dislocations. These are compared with energies for equivalent defects in the bulk lattice to determine segregation energies for each defect. Mg vacancies preferentially bind to ½ 〈110〉 {100} edge dislocations, with calculated minimum segregation energies of − 3.54 eV for and − 4.56 eV for $${\text{2H}}_{{{\text{Mg}}}}^{{\text{x}}}$$ . The magnitudes of the minimum segregation energies calculated for defects binding to ½ 〈110〉 {110} edge or ½ 〈110〉 screw dislocations are considerably lower. Interactions with the dislocation strain field lift the threefold energy degeneracy of the $${\text{2H}}_{{{\text{Mg}}}}^{{\text{x}}}$$ defect in MgO. These calculations show that Mg vacancies interact strongly with dislocations in MgO, and may be present in sufficiently high concentrations to affect dislocation mobility in both the glide- and climb-controlled creep regimes.

Thermally-driven unequal cation vacancy formation and its effect on the dielectric properties in K0.5Na0.5NbO3 ceramics

The formation of cation vacancies can be useful for electro-chemical devices. In this regard, an understanding of vacancy formation is an important subject for enhancing current electrochemical devices and for developing next generation energy devices. In this work, we chose the well-known lead-free ferroelectric (K0.5Na0.5)NbO3 (KNN) as a model system to understand both the formation of cation vacancies and the relationship between cation vacancies and the physical properties. We studied sintering-duration dependence of the dielectric properties and the cation contents of KNN ceramics at the temperatures near the melting point of KNN. The difference in sintering duration led to a drastic change in the dielectric property, as well as to the creation of cation vacancies. Interestingly, we observed unequal evaporation of cations during the sintering process, which was confirmed by the data obtained from laser-induced breakdown spectroscopy. In addition, we found more drastic changes in the imaginary dielectric constant, which were likely due to a decrease in ionic conducting species, such as K and Na, in KNN.

Incommensurate modulated structures and luminescence in scheelites

Scheelite (CaWO4) related compounds (A',A'')n[(B',B'')O4]m with B', B''=W and/or Mo are promising new materials for red phosphors in pc-WLEDs (phosphor-converted white-light-emitting-diode) and solid-state lasers. Scheelites can be prepared with a large concentration of vacancies in the A sublattice, giving compositions characterized by a (A'+A''):(B'O4+B''O4) ratio different from 1:1. The creation of cation vacancies in the scheelite-type framework and the ordering of A cations and vacancies are a new factor in controlling the scheelite-type structure and properties. Very often the substitution of Ca2+ by M+ and R3+ (R3+ = rare earth elements) in the scheelite-type structure leads to switching the structure from 3D to (3+n)D (n = 1,2) regime. The creation and ordering of A-cation vacancies and the effect of cation substitutions in the scheelite-type framework are investigated as a factor controlling the scheelite-type structure and luminescent properties of CaGd2(1-x)Eu2x(MoO4)4(1-y)(WO4)4y (0≤x≤1, 0≤y≤1) solid solutions. Within this series all complex molybdenum oxides have (3+2)D incommensurately modulated structures with superspace group I41/a(α,β,0)00(-β,α,0)00, while the structures of all tungstates are (3+1)D incommensurately modulated with superspace group I2/b(αβ0)00. In both cases the modulation arises due to cation-vacancy ordering at the A site. The replacement of the smaller Gd3+ by the larger Eu3+ at the A-sublattice does not affect the nature of the incommensurate modulation, but an increasing replacement of Mo6+ by W6+ switches the modulation from (3+2)D to (3+1)D regime. Acknowledgement. This research was supported by FWO (project G039211N, Flanders Research Foundation) and Russian Foundation for Basic Research (Grants 11-03-01164, and 12-03-00124).

Electrochemical behavior of CoCrMo implant in Ringer's solution

CoCrMo has been successfully employed as an orthopedic and orthodontic material because of its excellent corrosion resistant and suitable biocompatibility. The purpose of this research was to investigate the susceptibility of CoCrMo in Ringer's solution at three different temperatures: 22 °C, 37 °C, and 60 °C. The corrosion behavior of CoCrMo was carried out by using common electrochemical methods such as open circuit potential, potentiodynamic measurement, electrochemical impedance spectroscopy (EIS), and Mott–Schottky measurements. CoCrMo was passivated by the air, forming a passive film, which was not destroyed during the immersion in electrolytes under different temperatures. Results from potentiodynamic tests showed that at high anodic potentials, the passive film did not demonstrate significant localized corrosion and rather exhibited overall passive film degradation corresponding to the general corrosion of the alloy in Ringer's solution at the three temperatures. EIS measurements showed the presence of the stable passive film on the alloy surface when tested at open circuit potential. Mott–Schottky test indicated that the preformed passive film is an n‐type semiconductor due to the presence of a donor species. This is implied by the existence of oxygen vacancies and interstitial metallic cations. As the potential increased, the Cr3+ oxidized and produced soluble Cr4+ species. This resulted in the film changing to a p‐type semiconductor owing to the dissolution and creation of cation vacancies (acceptor species). The passive film rupture was not due to p‐type characteristics but rather was a result of the considerable oxidative dissolution of the film at high anodic potential. Copyright © 2013 John Wiley & Sons, Ltd.

Spectroscopy of Yb3+ in the disordered Na2/7Gd4/7MoO4 crystal with a scheelite‐type cation‐deficient structure

AbstractThe creation of cation vacancies in the scheelite‐type framework leads to the formation of Na2/7Gd4/7MoO4 compound, where cationic sites are shared by Na+, Gd3+, and vacancies. The spectroscopic properties at ∼1 µm of this novel disordered Yb3+‐doped crystal, grown by the Czochralski method, have been investigated. The absorption and fluorescence spectra at 10 and 300 K provide the important information on the absorption and emission cross‐sections as well as the Stark energy‐level positions of Yb3+ ions in the crystal. The wavelength dependence of the gain cross‐section has been determined, which predicts a broad tuning range and potential sub‐100‐fs laser pulse generation. The laser parameters βmin, Isat, and Imin have been calculated, and the perspectives for applications as a laser‐active material have been discussed.

Na2/7Gd4/7MoO4: a Modulated Scheelite-Type Structure and Conductivity Properties

Scheelite-type compounds with the general formula (A1,A2)(n)[(B1,B2)O(4)](m) (2/3 ≤ n/m ≤ 3/2) are the subject of large interest owing to their stability, relatively simple preparation, and optical properties. The creation of cation vacancies (□) in the scheelite-type framework and the ordering of A cations and vacancies can be a new factor in controlling the scheelite-type structure and properties. For a long time, cation-deficient Nd(3+):M(2/7)Gd(4/7)□(1/7)MoO(4) (M = Li, Na) compounds were considered as potential lasers with diode pumping. They have a defect scheelite-type 3D structure (space group I4(1)/a) with a random distribution of Li(+)(Na(+)), Gd(3+), and vacancies in the crystal. A Na(2/7)Gd(4/7)MoO(4) single crystal with scheelite-type structure has been grown by the Czochralski method. Transmission electron microscopy revealed that Na(2/7)Gd(4/7)MoO(4) has a (3 + 2)D incommensurately modulated structure. The (3 + 2)D incommensurately modulated scheelite-type cation-deficient structure of Na(2/7)Gd(4/7)MoO(4) [super space group I4 (α-β0,βα0)00] has been solved from single-crystal diffraction data. The solution of the (3 + 2)D incommensurately modulated structure revealed the partially disordered distribution of vacancies and Na and Gd cations. High-temperature conductivity measurements performed along the [100] and [001] orientation of the single crystal revealed that the conductivity of Na(2/7)Gd(4/7)MoO(4) at T = 973 K equals σ = 1.13 × 10(-5) Ω(-1) cm(-1).

Synthesis and Dielectric Properties of Novel BaBixTi1-xO3-δ Ceramics

Novel polycrystalline materials of bismuth substituted barium titanate, namely, BaBixTi1-xO3-δ , (x = 0.025, 0.075, 0.125 and 0.175) was prepared by sol-gel chemical route and characterized by X-ray diffraction and scanning electron microscopy. Bismuth ion was added in place of titanium of B-site of ABO3 perovskite structure and both the site-balance as well as charge-balance was considered. The substitution of bismuth for Ti-site is clearly seen in both the XRD as well as IR spectroscopic data. Dielectric and impedance analysis were also made on the present novel ceramics. The above mentioned substitution involves ionic compensation, through creation of cation vacancies and is explained by proposing the defect dynamics. The results were corroborated with dielectric and complex impedance analysis for further understanding of ionic motion in this kind of disordered diffused materials.

The effect of TiO2 on the magnetic power losses and electrical resistivity of polycrystalline MnZn-ferrites

In this paper the mechanism through which TiO2 affects the magnetic power losses of iron excess polycrystalline MnZn-ferrites is investigated. It has been found that TiO2, on being diluted in the bulk of the grains, promotes the homogeneous accumulation of calcium and silicon along the grain boundaries, by providing high specific resistivity properties to the resulting microstructure. This calcium and silicon segregation enhancement is attributed to the increased cation vacancy concentrations associated with the incorporation of tetravalent Ti in the spinel lattice. The creation of cation vacancies through a dopant such as Ti does not have the same effect as the creation of cation vacancies through control of the partial pressure of oxygen during firing. The latter is believed to promote calcium and silicon accumulation at the pores and the triple points rather than along the grain boundaries, resulting thus in microstructures with reduced specific resistivity.

Microstructural characterization of sol–gel derived Pb 1− xLa xTiO 3 ferroelectrics

The ferroelectrics Pb 1− x La x TiO 3 with good stoichiometry were prepared by a sol–gel route in the composition range from x = 0.0 up to 0.4 in 0.05 increment. The compounds were indexed in a tetragonal phase for 0.0 ≤ x < 0.25, and in a cubic phase for 0.25 ≤ x < 0.4. A tiny amount of pyrochlore phase La 2Ti 2O 7 was detected at x = 0.4. The ion oxidation states of solid solution compounds were characterized by X-ray photoelectric spectroscopy (XPS) and electron spin resonance (ESR). For the compounds Pb 1− x La x TiO 3 prepared in the atmosphere, the electrical neutrality is kept not by the reduction from Ti 4+ to Ti 3+, but by the creation of cation vacancies in the A- and B-sites. The grain size of Pb 1− x La x TiO 3 increases with increasing La content.

Promotion of piezoelectric properties of lead zirconate titanate ceramics with (Zr,Ti) partially replaced by Nb2O5

This study investigated the correlation of sintering effects on piezoelectric properties of Nb modified lead zirconate titanate (PZT) piezoceramics produced by the conventional solid reaction sintering. Samples were prepared at a composition Zr/Ti=53/47, contiguous to a morphotropic phase boundary (MPB) for 1 mol% Nb2O5. Replacement of Ti+4 by Nb+5 in such perovskite type solid solutions was accomplished by the creation of cation vacancies. These created vacancies seemed to facilitate material transport and benefit sintering. Calcined at 850 °C/2 h and sintered at 1250 °C/2 h, the PZT ceramics yielded a minimum value of the mechanical quality factor (Qm) 50, and exhibited a maximum electromechanical coupling factor κp 0.62, in accordance with the relationship between the mechanical quality factor and electromechanical coupling factor. In addition, during the sintering process a piezoelectric charge constant at d33 was found to be of 385 pC/N. It was noted that the fundamental resonance frequency was around 200 kHz, which was suitable for piezoelectric nebulizer (fluid atomizer), ultrasonic cleaning transducer applications.

Variability of impurity doping in the modified Pb(Zr,Ti)O3 ceramics of type ABO3

The influence of sintering effects on microstructure, mechanical quality factor Qm and electromechanical coupling factor κ of 1mol% Nb-doped lead zirconate titanate (PZT) piezoceramics with a composition Zr/Ti=53/47 prepared by the conventional ceramic technology were investigated. Replacement of Ti+4 by Nb+5 in such perovskite type solid solutions was accomplished by the creation of cation vacancies. These created vacancies seemed to facilitate material transport and benefit from sintering. Calcined at 850 °C/2 h and sintered at 1250 °C/2 h, the PZT ceramics had the minimum value of Qm 50 and exhibited maximum electromechanical coupling factor κp 0.62 in accordance with the relationship between mechanical quality factor and electromechanical coupling factor. The measured P–E hysteresis loop illustrated that the remanent polarization (Pr) and coercive field (Ec) were 8.63 μC/cm2 and 17.2 kV/cm, respectively. The fundamental resonance frequency was around 200 kHz, which was suitable for piezoelectric resonator and filter applications.

Oxygen stoichiometry, ferromagnetism, and transport properties ofLa2−xNiMnO6+δ

Nominal La 2 NiMnO 6 prepared by solid-state reaction in air in accordance with earlier reports is shown to contain excess oxygen as well as the coexistence of two ferromagnetic phases of comparable Curie temperatures, onemonoclinic and the other rhombohedral. As originally predicted, ordering of Ni 2 + and Mn 4 + ions gives ferromagnetic Ni 2 + -O-Mn 4 + interactions and transforms the orthorhombic Pbnm space group to monoclinic P2 1 In with β90° and the rhombohedral R3c space group to R3m or R3. Synthesis by the Pechini method in Ar, air, and O 2 atmospheres under different thermal treatments also consistently gave O 6 + δ ; the lowest δ=0.05(1) was attained for a single P2 1 /n phase reacted under Ar at 1350°C. Lowering the mean A-site atomic radius in La 2 - x □ x NiMnO 6 and Nd 2 NiMnO 6 also stabilizes the monoclinic phase, and near oxygen stoichiometry was attained in La 2 - x □ x NiMnO 6 for x0.09. Excess oxygen is accommodated in the perovskite structure by the creation of cation vacancies, and it is shown that lanthanum vacancies create deep three-hole acceptor traps. Comparison with the double perovskite La 2 CoMnO 6 and La 2 NiRuO 6 + δ versus La 2 CoRuO 6 signals that stabilization of lanthanum vacancies is associated with a Ni 3 + /Ni 2 + redox couple that is stabilized by a counter octahedral-site cation M having a strong covalent component to its M-O bonding. It is therefore proposed that in the presence of Ni 2 + , but not Co 2 + , a lanthanum vacancy is stabilized by the formation of two holes trapped deeply in molecular orbitals of an O 1 2 cluster of the oxygen atoms that neighbor a lanthanum vacancy. Transport data also indicate a lowering of the separation of the Mn 4 + /Mn 3 + and Ni 3 + /Ni 2 + redox couples from E g ≥0.8 eV to E g 0.3 eV in the ordered Ni 2 + , Mn 4 + array. This lowering and a motional enthalpy ΔH m n 0.1 eV of electrons is attributed to locally cooperative Jahn-Teller deformations of low-spin Ni 3 + and high-spin Mn 3 + octahedral sites. The magnetization M(5 K, 50 kOe) is lowered by both local atomic disorder and the formation of antiphase boundaries. It is shown that a prolonged anneal at 800 °C reduces the local atomic disorder, but it does not remove the antiphase boundaries. Synthetic strategies to increase the magnetization must be designed to reduce the concentration of antiphase boundaries and cation vacancies as well as the atomic disorder.

Crystallization kinetics and mechanism of the Li xNi 2− xO 2 (0< x⩽1) from Li 2CO 3 and NiO

LiNiO 2 is known to be the potential material to replace expensive LiCoO 2 cathode in lithium-secondary battery. Kinetics and mechanism of the Li x Ni 2− x O 2 (0< x⩽1) reacted from Li 2CO 3 and NiO were investigated by X-ray diffraction (XRD), SEM in this study. The formation of Li x Ni 2− x O 2 was found to be a thermally activated process, which can be represented as the Jander model [1−(1− α) 1/3] 2= kt and the reaction activation energy is estimated to be about 190 kJ/mol. The formation of Li x Ni 2− x O 2 can be viewed as the combination of two reactions: (1) the oxidation of nickel (II) to nickel (III) accompanied by the creation of cation vacancies and followed by (2) the filling of lithium ions into the cation vacancies created. Based on the result of kinetics study in this work, the rate-determining step is considered to be the creation of nickel vacancies and can be described as 1/2 O 2 → NiO V Ni ″+2 h + O 0 x

Cerium, iron and bismuth-containing molybdovanadate solid solutions with scheelite-type structure

Bi 1− x /3 Ø x /3 (V 1− x Mo x )O 4 ( x from 0 to 0.75 in steps of 0.15), Bi (1− x /3)+ y Ø ( x /3)− y (V 1− x Mo x − y Fe y )O 4 ( x =0.45; 0.00≤ y ≤0.15 in steps of 0.05), Bi 1− x /3 Ø ( x /3)− y Fe y (V 1− x Mo x − y Fe y )O 4 ( x =0.45; 0.00≤ y ≤0.15 in steps of 0.05), Bi 1− x /3 Ø ( x /3)− y Ce y (V 1− x Mo x − y Fe y )O 4 ( x =0.45 and 0.60; 0.00≤ y ≤ x /3, in steps of 0.05), and Ce 1− x /3 Ø x /3 (V 1− x Mo x )O 4 ( x from 0 to 0.60 in steps of 0.15) solid solution systems (Ø=cation vacancy in the eight-coordinated sites, tetrahedrally coordinated cations in parenthesis) have been prepared by coprecipitation and final firing at 873 K. Structural characterization has been performed by lattice parameter measurements. Optical and magnetic properties have also been investigated. The X-ray analysis showed that the great majority of materials are monophasic with tetragonal scheelite-type structure. The correlation between unit cell volume and metal composition shows the effect of the cation and vacancy substitution on the unit cell lattice, which is interpreted in terms of the different ionic radii of the interchanging metal ions and of filling up or creation of cation vacancies.

Trivalent cation substitution of pulverulent cobalt—iron molybdates Co 1 − xFe xMoO 4

Different mixed cobalt—iron molybdates Co 1 − x Fe x MoO 4 (0 ≤ x ≤ 1) have been prepared by means of a ceramic process. The oxidation of pulverulent samples leads to ferric molybdate Fe 2(MoO 4) 3, spinelle Co 3O 4 and cobalt molybdate CoMoO 4. After a strong grinding which reduces the grain size (about 0.1 μm) and induces crystallographic defects in the grains, the cobalt—iron molybdates can be partially oxidized into cation-deficient phases. This oxidation corresponds to an isostructural substitution of part of the Fe 2+ and Co 2+ ions by Fe 3+ and Co 3+ ions and the creation of cation vacancies. The concomitant presence of trivalent cations and associated cation vacancies in the lattice stabilizes the highest-temperature variety of the cobalt or iron molybdates, i.e., the a variety.

Texture Studies on Chromium Oxide Doped Catalysts

Physisorption of N2 gas at 77 K has been used to determine the surface area (SBET) and porosity of Cr2O3 impregnated with Li2O in molar ratios extending from 0.25 to 50 mol %. Calcination of catalysts was affected in air flow in temperature range of 473-773 K. Variation of the SBET-calcination temperature relationship was interpreted according to the possible lattice rearrangements via a solid-state reaction leading to Li2CrO4 phase formation for Li2O rich samples and by creation of cation vacancies in case of Li2O trace samples. The cumulative calculations together with Va-t plots showed a mesoporous surface nature of samples.

Studies on Lead Titanate Ceramics Containing Niobium or Tantalum

Dielectric, lattice constant, and thermal‐expansion measurements have been made on solid solution ceramics in the systems PbTiO3Pb0.5NbO3 and PbTiO3‐Pbo.5TaO3. The ferro‐electric Curie temperature is lowered to 465OC. at the solubility limit (2 to 5% Nb or Ta). Replacement of Ti4+ by Nb5+ or Ta5+ in these perovskite‐type solid solutions is accompanied by the creation of cation vacancies. These vacancies seem to facilitate material transport and aid sintering. Thus ceramics were obtained with up to 91% of theoretical density. These compositions have peak dielectric constants of the order of 10,000 with tan δ less than 0.1 in the interval 25° to 525°C.

Studies on the Oxidation of Ferrous Sulfide

Abstract The rate and mechanism of oxidation of ferrous sulfide was studied by means of a spring balance and X-ray diffraction analysis over the temperature range from 500°C to 700°C. The conclusion reached is as follows : (1) Complete oxidation, in which only the formation of oxides proceeds, begins at 600°C. (2) At the initial stage of oxidation, a slight increase of weight is found. It was observed by X-ray that the deficiency of cation in ferrous sulfide occurs in this stage. This may be due to the formation of oxide on the surface rather than to chemisorption, which is accompanied by creation of cation vacancies in ferrous sulfide crystal. (3) Above 600°C, the rate of oxidation does not change with temperature, so the rate-determining factor is diffusion of gas. Since the observed rate of oxidation depends upon the quantity of the sample, the diffusion in the bed of sample may determine the rate.