The relationship between chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice

The theoretical model developed by Lidiard was extended to describe the relationship between the chemical and tracer diffusion coefficients of aliovalent ions in an ionic lattice.It is shown that the relationship between the chemical diffusion coefficient, D, and the tracer diffusion coefficient, D¹, is D = 2D¹ if the migration of dimers is the principal mechanism of transport and for the migration of trimers D = 3D¹ if the concentration of impurity ion is relatively small. These relationships are valid regardless of the charge of the aliovalent or lattice ions.The chemical diffusion coefficients of Cr³⁺ in Cr-doped MgO were determined for three different temperatures, 1656, 1717 and 1768K, and for the concentration region 2.5×10^?2?2.8×10^?1 mole% Cr₂O₃. Using previously determined values for the tracer diffusion coefficient of ⁵¹Cr in Cr-doped MgO it was found that for the temperature and concentration region investigated D = (2.00±0.17)D¹ which indicates that diffusion proceeds primarily by the migration of dimers.     

Similarity law for kinetic coefficients of hot electrons in atomic liquids with molecular impurities

A straightforward similarity law is proposed in the framework of the Lekner-Cohen theory which makes it possible to estimate the effect of the impurities on the kinetic coefficients of electrons in liquids with molecular additions.     

The relationship between viscosity and glass forming ability of Al-(Ni)-Yb alloy systems

The dynamic viscosity of Al-Yb and Al-Ni-Yb superheated melts was measured using a torsional oscillation viscometer. The results show that the temperature dependence of viscosity fits the Arrhenius law well and the fitting factors are calculated. The amorphous ribbons of these alloys were produced by the melt spinning technique and the thermal properties were characterized by using a differential scanning calorimetry (DSC). E (the activation energy for viscous flow), which reflects the change rate of viscosity, has a good negative relation with the GFA in both Al-Yb and Al-Ni-Yb systems. However, there is no direct relation between liquidus viscosity (ηL) and GFA. The superheated fragility M can predict GFA in Al-Yb or Al-Ni-Yb alloy system.     

Tracer diffusion in glassforming liquids

In the last decades, a wide collection of experimental evidence has been found in the study of supercooled glassformers on the existence of a crossover between two dynamical regimes at a temperature T_c. We discuss the validity of the Vogel-Fulcher-Tammann in both regions. The breakdown of the Stokes-Einstein relation below T_c is presented, indicating that the diffusion coefficient of a tracer becomes decoupled from the viscosity through an exponent ξ, and the diffusion process is intensified. We verify that a temperature shift on the diffusion coefficient introduces the same effect as the Stokes-Einstein breakdown equation. We present the dependence of this exponent on the ratio between the radii of the tracer and the host liquid molecule.     

Reproducibility of dynamical heterogeneities and metabasin dynamics in glass forming liquids: the influence of structure on dynamics

The discovery that the propensity for particle motion in a supercooled liquid is completely determined by the initial structure pointed to the existence of a causal link between structure and dynamics in glassy systems. Here we demonstrate that this underlying influence of structure is only local in time, fading out beyond the metabasin lifetime much before the relaxation time. Thus, our results reveal the irreproducibility of metabasin dynamics and support the scenario of a random walk on metabasins for the long time diffusion.     

A quantum field theory of the liquid-glass transition in multi-component liquids

An established unified theory of the liquid-glass transition in one-component liquids is extended to multi-component liquids. The universal features such as the Kauzmann paradox, the Vogel-Tamman-Fulcher (VTF) law on the relaxation times and the transport coefficients, the jump of the specific heat at the glass transition temperature and the Boson peaks are elucidated. The Kauzmann entropy in a form of a Curie law with a negative sign comes from the mixing between the sound and the intra-band fluctuation entropies, where the critical temperature corresponds to the sound instability temperature at a reciprocal particle distance. The VTF law is constructed from the Einstein relation on entropy and probability so that the Kauzmann entropy is included as a normal form in exponent of the VTF law. The Kauzmann entropy explains the Kauzmann paradox and the jump of the specific heat so that the universal features of the glass transition are elucidated consistently.     

The relationship between kinetic and thermodynamic fragilities in metallic glass-forming liquids

The correlation between the temperature dependence of the kinetic and thermodynamic properties of a series of metallic glass-forming liquids is investigated using the concept of fragility. The results indicate a correlation between the kinetic fragility and thermodynamic fragility in these liquids. The correlation depends critically on the approach used to evaluate the thermodynamic fragility. Two distinct correlation lines are found for the metal–metalloid and for the all-metallic-constituents glass-forming liquids. For the same thermodynamic fragility the metal–metalloid liquids exhibit a distinctively larger kinetic fragility than the pure-metallic liquids. From the evaluation of the Gibbs free-energy difference between the undercooled liquid and the crystalline phase mixture, a correlation between the kinetic fragility and the driving force for nucleation is found, showing that for glass formation in metallic alloys the thermodynamic and kinetic contributions act together.     

Radiation-enhanced diffusion in ion-implanted glass

The Rutherford backscattering technique was used to characterize the purposedly added cesium impurities in soda-lime glass. The impurities were introduced into the glass matrix by an ion-exchange diffusion process at room temperature. The diffusion coefficient of cesium was determined from the measured depth profiles. The diffusion of the cesium impurities stimulated by 280 keV Kr⁺-ion beam irradiation was also studied. The depth distributions obtained are discussed using the model of radiation enhanced diffusion. Results are compared with theoretical values based on transport of ions in matter calculations and other experimental work.On sabbatical leave at Applied Science University, Physics Department, P. O. Box 926296, Amman, Jordan     

Correlation between liquid structure and glass forming ability in glassy Ag-based binary alloys

The atomic structures of liquid Ag-based binary alloys have been investigated in the solidification process by means of X-ray diffraction. The results of liquid structure show that there is a break point in the mean nearest neighbor distance r1 and the coordination number Nmin for glass-forming liquid, while the correlation radius rc and the coordination number Nmin display a monotone variational trend above the break point. It means glass-forming liquids have a steady changing in structure above liquidus a...     

多分量胶体悬浮系统转动扩散张量的反射理论

研究多分量胶体悬浮系统的反射理论,给出用反射理论推导转动扩散张量的方法.计算了流体力学相互作用对转动扩散张量的二体贡献和首项三体贡献. 关键词： 反射理论 扩散 胶体悬浮系统 流体力学作用     

The mathematical relationship between Zipf’s law and the hierarchical scaling law

The empirical studies of city-size distribution show that Zipf’s law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their relationship has never been revealed by strict mathematical proof. In this paper, the Zipf’s distribution of cities is abstracted as a q$q$-sequence. Based on this sequence, a self-similar hierarchy consisting of many levels is defined and the numbers of cities in different levels form a geometric sequence. An exponential distribution of the average size of cities is derived from the hierarchy. Thus we have two exponential functions, from which follows a hierarchical scaling equation. The results can be statistically verified by simple mathematical experiments and observational data of cities. A theoretical foundation is then laid for the conversion from Zipf’s law to the hierarchical scaling law, and the latter can show more information about city development than the former. Moreover, the self-similar hierarchy provides a new perspective for studying networks of cities as complex systems. A series of mathematical rules applied to cities such as the allometric growth law, the 2ⁿ$2^n$ principle and Pareto’s law can be associated with one another by the hierarchical organization.     

Biexponential apparent diffusion coefficients in prostate cancer

Purpose

The purpose of this study was to investigate the need for biexponential signal decay modeling for prostate cancer diffusion signal decays with b-factor over an extended b-factor range.

Materials and Methods

Ten healthy volunteers and 12 patients with a bulky prostate cancer underwent line scan diffusion-weighted MR imaging in which b-factors from 0 to 3000 s/mm² in 16 steps were sampled. The acquired signal decay curves were fit with both monoexponential and biexponential signal decay functions and a statistical comparison between the two fits was performed.

Results

The biexponential model provided a statistically better fit over the monoexponential model on the peripheral zone (PZ), transitional zone (TZ) and prostate cancer. The fast and slow apparent diffusion coefficients (ADCs) in the PZ, TZ and cancer were 2.9±0.2, 0.7±0.2×10⁻³ mm²/ms (PZ); 2.9±0.4, 0.7±0.2×10⁻³ mm²/ms (TZ); and 1.7±0.4, 0.3±0.1×10⁻³ mm²/ms (cancer), respectively. The apparent fractions of the fast diffusion component in the PZ, TZ and cancer were 70±10%, 60±10% and 50±10%, respectively. The fast and slow ADCs of cancer were significantly lower than those of TZ and PZ, and the apparent fraction of the fast diffusion component was significantly smaller in cancer than in PZ.

Conclusions

Biexponential diffusion decay functions are required for prostate cancer diffusion signal decay curves when sampled over an extended b-factor range, providing additional, unique tissue characterization parameters for prostate cancer.     

Phenomenological equations of the glass transition in liquids

The paper presents a theoretical analysis of the glass transition. It is demonstrated that the kinetics of glass transition is described by the following equations: the Maxwell equation of a viscoelastic medium; the equation of elastic relaxation, which, in addition to the usual Debye term, involves a nonlinear term due to the positive feedback between the strain field and temperature; and the equation of specific heat continuity, in which the entropy term includes the contribution of elastic fields and the heat flux contains a term related to external cooling. These equations are analogous to the Lorenz synergetic system, in which the strain plays the role of an order parameter, the conjugate field reduces to elastic stresses, and the temperature is a controlling parameter.     

Copper diffusion in ion-exchanged soda-lime glass

Cu-alkali ion exchange in silicate glasses gives rise to a peculiar copper distribution, with the presence of both the Cu²⁺ and Cu⁺ oxidation states. Grazing incidence X-ray absorption near-edge structure spectroscopy and secondary ion mass spectrometry were performed on different ion-exchanged samples. The results show that the Cu²⁺/Cu⁺ ratio is strongly depth-dependent. The relative presence of the two species throughout the exchanged region turns out to be governed by their different diffusion regimes, while the chemistry of the red-ox process is shown to play a minor role. A phenomenological model is proposed to describe the diffusion process. PACS 61.10.Ht; 61.43.Fs; 82.65.+r; 67.80.Mg     

Structure and diffusion in mixtures of ionic liquids

The properties of ionic mixtures of LiBr-KBr are investigated on the basis of molecular dynamics calculations, using the Tosi-Fumi pair-potentials. The determination of the excess internal energy of mixing indicates the predominant negative contribution of the coulomb energy. The position of the first peak of the anion-cation radial distribution function depends strongly on the size of the ions and its height is much influenced by the strength of the coulomb forces. It is shown that the equivalent coordination numbers vary from about 4 for the Li-Br pair to 6 for the K-Br pair. These numbers do not change very much when the composition is varied.

The ionic dynamics is analysed through the brownian-like formalism which gives a useful connection between the structure and the particle motion. Two mechanisms are involved in the diffusion process: an oscillation of the particle in the force field of the neighbouring particles and a collective mode of motion which has a longer relaxation time. The strong anion-cation correlation, which mainly affects the smallest cation, dominates when the charge ordering (quasi-lattice structure) vanishes.     

Fragile-strong transitions and polyamorphism in glass forming fluids

A simple model of a glass forming fluid, consisting of a bidisperse mixture of penetrable spheres, is studied numerically by Monte Carlo simulation. The model shows a transition from fragile to strong behaviour as the temperature is reduced. This transition is driven by the competition between the two mechanisms that contribute to diffusivity in the model: collective rearrangement of particles (responsible for the fragile behaviour), and individual particle motion (which gives rise to the strong behaviour at low temperatures). Also observed is a maximum of diffusivity as a function of pressure that can be interpreted within the same framework. The connection between this behaviour and polyamorphism is addressed.