The high strain rate response of polycarbonate (PC) and polymethyl methacrylate (PMMA) are measured using a split Hopkinson torsion bar for shear strain rates Ẏ from 500 s-1 to 2200 s-1, and temperatures in the range —100°C to 200°C. The yield and fracture behaviours are compared with previous data and existing theories for Ẏ < I s-1. We find that PC yields in accordance with the Eyring theory of viscous flow, for temperatures between the beta transition temperature Tβ ≈ — 100°C and the glass transition temperature Tg = 147°C. At lower temperatures, T < Tβ , backbone chain motion becomes frozen and the shear yield stress is greater than the Eyring prediction. Strain softening is an essential feature of yield of PC at all strain rates employed. Poly methyl methacrylate fractures before yield in the high strain rate tests for T < 80°C, which is close to the glass transition temperature Tg120°C. It is found that the fracture stress for both materials obeys a thermal activation rate theory of Eyring type. Fracture is thought to be nucleation controlled, and is due to the initiation and break down of a craze at the fracture stress τf. Examination of the fracture surfaces reveals that failure is by the nucleation and propagation of inclined mode I microcracks which link to form a stepped fracture surface. This reveals that failure is by tensile cracking and not by a thermal instability in the material. The process of shear localization is fundamentally different from that shown by steel and titanium alloys.
{"title":"High strain-rate shear response of polycarbonate and polymethyl methacrylate","authors":"N. Fleck, W. Stronge, J. Liu","doi":"10.1098/rspa.1990.0069","DOIUrl":"https://doi.org/10.1098/rspa.1990.0069","url":null,"abstract":"The high strain rate response of polycarbonate (PC) and polymethyl methacrylate (PMMA) are measured using a split Hopkinson torsion bar for shear strain rates Ẏ from 500 s-1 to 2200 s-1, and temperatures in the range —100°C to 200°C. The yield and fracture behaviours are compared with previous data and existing theories for Ẏ < I s-1. We find that PC yields in accordance with the Eyring theory of viscous flow, for temperatures between the beta transition temperature Tβ ≈ — 100°C and the glass transition temperature Tg = 147°C. At lower temperatures, T < Tβ , backbone chain motion becomes frozen and the shear yield stress is greater than the Eyring prediction. Strain softening is an essential feature of yield of PC at all strain rates employed. Poly methyl methacrylate fractures before yield in the high strain rate tests for T < 80°C, which is close to the glass transition temperature Tg120°C. It is found that the fracture stress for both materials obeys a thermal activation rate theory of Eyring type. Fracture is thought to be nucleation controlled, and is due to the initiation and break down of a craze at the fracture stress τf. Examination of the fracture surfaces reveals that failure is by the nucleation and propagation of inclined mode I microcracks which link to form a stepped fracture surface. This reveals that failure is by tensile cracking and not by a thermal instability in the material. The process of shear localization is fundamentally different from that shown by steel and titanium alloys.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"1 1","pages":"459 - 479"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73248214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U*, dispersivity dyadic ͞D*, and apparent volumetric reactivity coefficient ͞K*. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.
{"title":"Convective-diffusive-reactive Taylor dispersion processes in particulate multiphase systems","authors":"S. Dungan, M. Shapiro, H. Brenner","doi":"10.1098/rspa.1990.0077","DOIUrl":"https://doi.org/10.1098/rspa.1990.0077","url":null,"abstract":"Convective-diffusive transport of a chemically reactive solute is studied analytically for a general model of a multiphase system composed of ordered or disordered particles of arbitrary shapes and sizes. Use of spatially periodic boundary conditions permits analysis of particulate multiphase systems of effectively infinite size. Solute transport occurs in both the continuous and discontinuous bulk phases, as well as within and across the interfacial phase boundaries separating them. Additionally, the solute is allowed to undergo generally inhomogeneous first-order irreversible chemical reactions occurring in both the continuous and discontinuous volumetric phases, as well as within the interfacial surface phase. Our object is that of globally describing the solute transport and reaction processes at a macro- or Darcy-scale level, wherein the resulting, coarse-grained particulate system is viewed as a continuum possessing homogeneous material transport and reactive properties. At this level the asymptotic long-time solute macrotransport process is shown to be governed by three Darcy-scale phenomenological coefficients: the mean solute velocity vector ͞U*, dispersivity dyadic ͞D*, and apparent volumetric reactivity coefficient ͞K*. A variant of a Taylor-Aris method-of-moments scheme (Brenner & Adler 1982), modified to include solute disappearance via chemical reactions, is used to express these three macroscale phenomenological coefficients in terms of the given microscale phenomenological data and geometry. The general solution technique, illustrated here for a simple, ordered geometrical realization of a two-phase system, reveals the competitive influences of the respective volumetric/surface-excess transport and reaction processes, as well as the solute adsorptivity, upon the three macroscale transport coefficients.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"52 1","pages":"639 - 671"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85875249","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A one-dimensional diffusion-convection-reaction model is formulated to account for natural convection effects on thermal ignition in an open system consisting of a porous medium. Various limiting cases of the model are considered. A detailed analysis of the Semenov (lumped) model is presented. Explicit relations are derived for the dependence of the critical Semenov number (ψc) on the Rayleigh number (R*). It is shown that for R* → 0, ψc approaches the classical (conduction) limit e-1, while for R* ≫ 1, the ignition locus is given by the convection asymptote ψc/R* = 4 e-2. Inclusion of reactant consumption shows that the conduction asymptote disappears at B = 4 while the convection asymptote ceases to exist for B Ls < 3 + 2√2, where Ls is a modified Lewis number and B is the heat of reaction parameter. It is shown that the Semenov model has five different types of bifurcation diagrams of temperature against Rayleigh number (particle size), (single-valued, inverse S, isola, inverse S + isola and mushroom). This behaviour is found to be qualitatively identical to that of the forced convection problem investigated by Zeldovich & Zysin.
{"title":"Natural convection effects on thermal ignition in a porous medium. I. Semenov model","authors":"V. Balakotaiah, P. Pourtalet","doi":"10.1098/rspa.1990.0072","DOIUrl":"https://doi.org/10.1098/rspa.1990.0072","url":null,"abstract":"A one-dimensional diffusion-convection-reaction model is formulated to account for natural convection effects on thermal ignition in an open system consisting of a porous medium. Various limiting cases of the model are considered. A detailed analysis of the Semenov (lumped) model is presented. Explicit relations are derived for the dependence of the critical Semenov number (ψc) on the Rayleigh number (R*). It is shown that for R* → 0, ψc approaches the classical (conduction) limit e-1, while for R* ≫ 1, the ignition locus is given by the convection asymptote ψc/R* = 4 e-2. Inclusion of reactant consumption shows that the conduction asymptote disappears at B = 4 while the convection asymptote ceases to exist for B Ls < 3 + 2√2, where Ls is a modified Lewis number and B is the heat of reaction parameter. It is shown that the Semenov model has five different types of bifurcation diagrams of temperature against Rayleigh number (particle size), (single-valued, inverse S, isola, inverse S + isola and mushroom). This behaviour is found to be qualitatively identical to that of the forced convection problem investigated by Zeldovich & Zysin.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"15 1","pages":"533 - 554"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91365201","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
O. Zienkiewicz, A. Chan, M. Pastor, D. K. Paul, T. Shiomi
The behaviour of all geomaterials, and in particular of soils, is governed by their interaction with the pore fluid. The mechanical model of this interaction when combined with suitable constitutive discription of the solid phase and with efficient, discrete, computation procedures, allows most transient and static problems involving deformations to be solved. This paper describes the basic procedures and the development of a general purpose computer program (SWANDYNE-X). The results of the computations are validated by comparison with experimental results obtained on physical models tested in the Cambridge Centrifuge.
{"title":"Static and dynamic behaviour of soils : a rational approach to quantitative solutions. I. Fully saturated problems","authors":"O. Zienkiewicz, A. Chan, M. Pastor, D. K. Paul, T. Shiomi","doi":"10.1098/rspa.1990.0061","DOIUrl":"https://doi.org/10.1098/rspa.1990.0061","url":null,"abstract":"The behaviour of all geomaterials, and in particular of soils, is governed by their interaction with the pore fluid. The mechanical model of this interaction when combined with suitable constitutive discription of the solid phase and with efficient, discrete, computation procedures, allows most transient and static problems involving deformations to be solved. This paper describes the basic procedures and the development of a general purpose computer program (SWANDYNE-X). The results of the computations are validated by comparison with experimental results obtained on physical models tested in the Cambridge Centrifuge.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"80 5 1","pages":"285 - 309"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87984205","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The combustion of a liquid droplet adjacent to a cold surface was studied experimentally. To isolate the effect of the proximity of the droplet to the surface, the ambient pressure (0.101 MPa), liquid composition (n-heptane), initial liquid volume (7 x 10-4 ml), surface material (quartz) and ambient temperature (20 ± 2°C) were held constant. A range of distances L from the surface were studied (1 mm < L < ∞). Both horizontal and vertical surface orientations were examined. A more limited set of experiments were carried out in a low gravity (i. e. low buoyancy) environment to provide a basis of comparison with relevant theoretical analyses. The flame shape, soot formation, fuel condensation, and droplet burning rate were all found to be strongly affected by the proximity of the droplet to the surface. For sufficiently large L the flame was observed to be closed around the droplet throughout burning. As L decreased, the flame was truncated. The droplet burning rate decreased as the droplet was brought progressively closer to the surface (in qualitative agreement with a relevant closed form potential flow solution to the analogous problem of a droplet burning adjacent to an adiabatic surface) and the burning rate of a droplet adjacent to a vertical surface was larger than for a horizontal surface. Surface orientation effects were observed to be absent for burning at low gravity. The extent of sooting as revealed by the flame colour was decreased, and fuel vapours condensed in a lens-like shape on the surface, as L was sufficiently reduced.
实验研究了靠近冷表面的液滴的燃烧。为了分离液滴接近表面的影响，环境压力(0.101 MPa)、液体成分(正庚烷)、初始液体体积(7 × 10-4 ml)、表面材料(石英)和环境温度(20±2℃)保持不变。研究了距离表面L的距离范围(1 mm < L <∞)。水平和垂直表面方向都进行了检测。在低重力(即低浮力)环境下进行了一组更有限的实验，以提供与相关理论分析比较的基础。火焰形状、烟尘形成、燃料凝结和液滴燃烧速度都受到液滴接近表面的强烈影响。对于足够大的L，在整个燃烧过程中，火焰在液滴周围是封闭的。随着L的减小，火焰被截断。液滴燃烧速率随着液滴逐渐靠近表面而降低(定性地与液滴在绝热表面附近燃烧的类似问题的相关封闭形式势流解一致)，并且液滴在垂直表面附近的燃烧速率大于水平表面。在低重力下燃烧时，表面取向效应不存在。通过火焰颜色显示出的烟熏程度减少了，并且燃料蒸汽在表面上凝结成透镜状，因为L被充分减少了。
{"title":"Droplet combustion near a cold surface","authors":"S. Chandra, C. Avedisian","doi":"10.1098/rspa.1990.0070","DOIUrl":"https://doi.org/10.1098/rspa.1990.0070","url":null,"abstract":"The combustion of a liquid droplet adjacent to a cold surface was studied experimentally. To isolate the effect of the proximity of the droplet to the surface, the ambient pressure (0.101 MPa), liquid composition (n-heptane), initial liquid volume (7 x 10-4 ml), surface material (quartz) and ambient temperature (20 ± 2°C) were held constant. A range of distances L from the surface were studied (1 mm < L < ∞). Both horizontal and vertical surface orientations were examined. A more limited set of experiments were carried out in a low gravity (i. e. low buoyancy) environment to provide a basis of comparison with relevant theoretical analyses. The flame shape, soot formation, fuel condensation, and droplet burning rate were all found to be strongly affected by the proximity of the droplet to the surface. For sufficiently large L the flame was observed to be closed around the droplet throughout burning. As L decreased, the flame was truncated. The droplet burning rate decreased as the droplet was brought progressively closer to the surface (in qualitative agreement with a relevant closed form potential flow solution to the analogous problem of a droplet burning adjacent to an adiabatic surface) and the burning rate of a droplet adjacent to a vertical surface was larger than for a horizontal surface. Surface orientation effects were observed to be absent for burning at low gravity. The extent of sooting as revealed by the flame colour was decreased, and fuel vapours condensed in a lens-like shape on the surface, as L was sufficiently reduced.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"429 1","pages":"481 - 503"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86001743","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The sources of disturbance (vibrators, small jets, vortices, sound waves) in a boundary layer are considered, emphasizing their ability to provoke the onset of eigenoscillations with exponentially growing amplitude. Harmonic sources give rise to the Tollmien–Schlichting waves, whereas impulsive sources excite wave packets. General requirements are stated for the temporal and spatial characteristics of the signals emitted by the devices causing disturbance, as well as for obstacles met by signals when propagating. To scale the frequencies and wavenumbers in terms of the Reynolds number taking on indefinitely large values, the asymptotic theory of an interacting boundary layer with the triple-deck structure is used. The conclusions from the asymptotic analysis are in line with the results of measurements in wind tunnels when the Reynolds numbers were moderate.
{"title":"Receptivity of boundary layers: asymptotic theory and experiment","authors":"V. Kozlov, O. Ryzhov","doi":"10.1098/rspa.1990.0064","DOIUrl":"https://doi.org/10.1098/rspa.1990.0064","url":null,"abstract":"The sources of disturbance (vibrators, small jets, vortices, sound waves) in a boundary layer are considered, emphasizing their ability to provoke the onset of eigenoscillations with exponentially growing amplitude. Harmonic sources give rise to the Tollmien–Schlichting waves, whereas impulsive sources excite wave packets. General requirements are stated for the temporal and spatial characteristics of the signals emitted by the devices causing disturbance, as well as for obstacles met by signals when propagating. To scale the frequencies and wavenumbers in terms of the Reynolds number taking on indefinitely large values, the asymptotic theory of an interacting boundary layer with the triple-deck structure is used. The conclusions from the asymptotic analysis are in line with the results of measurements in wind tunnels when the Reynolds numbers were moderate.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"2004 1","pages":"341 - 373"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82936802","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
J. F. Clarke, D. Kassoy, N. E. Meharzi, N. Riley, R. Vasantha
Numerical solutions of the Navier–Stokes equations for the plane one-dimensional unsteady motion of a compressible, combustible gas mixture are used to follow the history of events that are initiated by addition of large heat power through a solid surface bounding an effectively semi-infinite domain occupied by the gas. Plane Zel’dovich–von Neumann–Doring detonations eventually appear either at the precursor shock (which exists in every set of circumstances) or in the regions, occupied by an unsteady induction-domain and an initially quasi-steady fast-flame, that lie behind the precursor shock.
{"title":"On the evolution of plane detonations","authors":"J. F. Clarke, D. Kassoy, N. E. Meharzi, N. Riley, R. Vasantha","doi":"10.1098/rspa.1990.0060","DOIUrl":"https://doi.org/10.1098/rspa.1990.0060","url":null,"abstract":"Numerical solutions of the Navier–Stokes equations for the plane one-dimensional unsteady motion of a compressible, combustible gas mixture are used to follow the history of events that are initiated by addition of large heat power through a solid surface bounding an effectively semi-infinite domain occupied by the gas. Plane Zel’dovich–von Neumann–Doring detonations eventually appear either at the precursor shock (which exists in every set of circumstances) or in the regions, occupied by an unsteady induction-domain and an initially quasi-steady fast-flame, that lie behind the precursor shock.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"104 1","pages":"259 - 283"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75021431","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In regular heterogeneous catalytic reactions, evaluation of the adsorption behaviour of the ephemeral intermediates that participate kinetically in the main reaction pathway is often inaccessible experimentally. In electrocatalysis, on the other hand, electrochemical transient methods can provide such information. In the present paper, potential-relaxation transients are used to derive information on the electroactive, kinetically significant adsorbed intermediate states that are involved in the anodic O2 evolution reaction (OER) at Pt electrodes. By means of such transients, digitally recorded over 5–6 decades of time from microseconds to seconds, the adsorption capacitance of the intermediate states in the reaction is evaluated as a function of potential over a range corresponding to appreciable current densities for O2 evolution. Anodic O2 evolution takes place at Pt, as at all other metal anodes, on an oxide film. A well-defined state of such a film must be established by a pre-conditioning programme to make meaningful and reproducible kinetic studies on the OER. The state of the oxide film is conveniently characterized by means of cyclic-voltammetry. The intermediate surface states in the reaction can be two or more oxidation states of Pt atoms in the oxide and OH or O species at the oxide’s surface. Two distinct types of adsorption behaviour are distinguished for potentials above and below ca. 1.85 V against the reversible H2 electrode (RHE), and are related to the observed kinetics of the OER.
{"title":"Examination of electrocatalysis in the anodic O2 evolution reaction at Pt through evaluation of the adsorption behaviour of kinetically involved intermediate states","authors":"B. Conway, T. Liu","doi":"10.1098/rspa.1990.0065","DOIUrl":"https://doi.org/10.1098/rspa.1990.0065","url":null,"abstract":"In regular heterogeneous catalytic reactions, evaluation of the adsorption behaviour of the ephemeral intermediates that participate kinetically in the main reaction pathway is often inaccessible experimentally. In electrocatalysis, on the other hand, electrochemical transient methods can provide such information. In the present paper, potential-relaxation transients are used to derive information on the electroactive, kinetically significant adsorbed intermediate states that are involved in the anodic O2 evolution reaction (OER) at Pt electrodes. By means of such transients, digitally recorded over 5–6 decades of time from microseconds to seconds, the adsorption capacitance of the intermediate states in the reaction is evaluated as a function of potential over a range corresponding to appreciable current densities for O2 evolution. Anodic O2 evolution takes place at Pt, as at all other metal anodes, on an oxide film. A well-defined state of such a film must be established by a pre-conditioning programme to make meaningful and reproducible kinetic studies on the OER. The state of the oxide film is conveniently characterized by means of cyclic-voltammetry. The intermediate surface states in the reaction can be two or more oxidation states of Pt atoms in the oxide and OH or O species at the oxide’s surface. Two distinct types of adsorption behaviour are distinguished for potentials above and below ca. 1.85 V against the reversible H2 electrode (RHE), and are related to the observed kinetics of the OER.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"37 1","pages":"375 - 397"},"PeriodicalIF":0.0,"publicationDate":"1990-06-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87272944","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
High-resolution 11B magic-angle-spinning (MAS) NMR investigations of boric oxide and alkali borate glasses have been carried out. The chemical shift of the trigonal boron shows anomalous behaviour around 10 mol. % alkali oxide. In an attempt to explain this unusual feature, we have carefully examined the structural model for B2O3 glass. The study suggests that around 66% of the boron atoms is likely to be present in the boroxol units, the rest being present in loose BO3/2 units. This model is not only consistent with the earlier literature but also shows that stringent topochemical factors are involved in the formation of the tetraborate and the diborate units in alkali borate glasses. It seems plausible that the remarkable tendency of B2O3 to vitrify may itself have a structural origin.
{"title":"11B NMR spectra and structure of boric oxide and alkali borate glasses","authors":"S. Prabakar, K. Rao, C. Rao","doi":"10.1098/rspa.1990.0048","DOIUrl":"https://doi.org/10.1098/rspa.1990.0048","url":null,"abstract":"High-resolution 11B magic-angle-spinning (MAS) NMR investigations of boric oxide and alkali borate glasses have been carried out. The chemical shift of the trigonal boron shows anomalous behaviour around 10 mol. % alkali oxide. In an attempt to explain this unusual feature, we have carefully examined the structural model for B2O3 glass. The study suggests that around 66% of the boron atoms is likely to be present in the boroxol units, the rest being present in loose BO3/2 units. This model is not only consistent with the earlier literature but also shows that stringent topochemical factors are involved in the formation of the tetraborate and the diborate units in alkali borate glasses. It seems plausible that the remarkable tendency of B2O3 to vitrify may itself have a structural origin.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"16 1","pages":"1 - 15"},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77059301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The way in which the transition amplitude to an initially unoccupied state increases to its exponentially small final value is studied in detail in the adiabatic approximation, for a 2-state quantum system. By transforming to a series of superadiabatic bases, clinging ever closer to the exact evolving state, it is shown that transition histories renormalize onto a universal one, in which the amplitude grows to its final value as an error function (rather than via large oscillations as in the ordinary adiabatic basis). The time for the universal transition is of order √ (ћ/δ) where δ is the small adiabatic (slowness) parameter. In perturbation theory the pre-exponential factor of the final amplitude renormalizes superadiabatically from the incorrect value ⅓π (for the ordinary adiabatic basis) to the correct value unity. The various histories could be observed in spin experiments.
{"title":"Histories of adiabatic quantum transitions","authors":"M. Berry","doi":"10.1098/rspa.1990.0051","DOIUrl":"https://doi.org/10.1098/rspa.1990.0051","url":null,"abstract":"The way in which the transition amplitude to an initially unoccupied state increases to its exponentially small final value is studied in detail in the adiabatic approximation, for a 2-state quantum system. By transforming to a series of superadiabatic bases, clinging ever closer to the exact evolving state, it is shown that transition histories renormalize onto a universal one, in which the amplitude grows to its final value as an error function (rather than via large oscillations as in the ordinary adiabatic basis). The time for the universal transition is of order √ (ћ/δ) where δ is the small adiabatic (slowness) parameter. In perturbation theory the pre-exponential factor of the final amplitude renormalizes superadiabatically from the incorrect value ⅓π (for the ordinary adiabatic basis) to the correct value unity. The various histories could be observed in spin experiments.","PeriodicalId":20605,"journal":{"name":"Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences","volume":"14 1","pages":"61 - 72"},"PeriodicalIF":0.0,"publicationDate":"1990-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86581666","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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