Size-dependent phase transitions in nanostructured zirconia-scandia solid solutions

The dependences of phase stability and solid state phase transitions on the crystallite size in ZrO2-10, 12 and 14 mol% Sc2O3 nanopowders are investigated by X-ray powder diffraction using a synchrotron source (S-XPD). The average crystallite sizes lie within the range of 35 to 100 nm, approximately. At room temperature these solid solutions were previously characterised as mixtures of a cubic phase and one or two rhombohedral phases, beta and gamma, with their fractions depending on composition and average crystallite sizes. In this study, it is shown that at high temperatures these solid solutions become cubic single-phased. The size-dependent temperatures of the transitions from the rhombohedral phases to the cubic phase at high temperature are determined through the analyses of a number of S-XPD patterns. These transitions were studied on cooling and on heating, exhibiting hysteresis effects whose relevant features are size and composition dependent.

Size-dependent phase transitions in nanostructured zirconia-scandia solid solutions.

Size effects on phase stability and phase transitions in technologically relevant materials have received growing attention. Several works reported that metastable phases can be retained at room temperature in nanomaterials, these phases generally corresponding to the high-temperature polymorph of the same material in bulk state. Additionally, size-dependent shifts in solubility limits and/or in the transition temperatures for on heating or on cooling cycles have been observed. ZrO2-Sc2O3 (zirconia-scandia) solid solutions are known to exhibit very high oxygen ion conductivity provided their structure is composed of cubic and/or pseudocubic tetragonal phases. Unfortunately, for solid zirconia-scandia polycrystalline samples with typical micrometrical average crystal sizes, the high-conductivity cubic phase is only stable above 600°C. Depending on composition, three low-conductivity rhombo-hedral phases (β, γ and δ) are stable below 600°C down to room temperature, within the compositional range of interest for SOFCs. In previous investigations, we showed that the rhombohedral phases can be avoided in nanopowders with average crystallite size lower than 35 nm.

Sequential partitioning: an alternative to understanding size distributions of avalanches in first-order phase transitions

We study the problem of the partition of a system of initial size V into a sequence of fragments s1,s2,s3 . . . . By assuming a scaling hypothesis for the probability p(s;V) of obtaining a fragment of a given size, we deduce that the final distribution of fragment sizes exhibits power-law behavior. This minimal model is useful to understanding the distribution of avalanche sizes in first-order phase transitions at low temperatures.

Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat

A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.

The Becker-Döring equations with exponentially size-dependent rate coefficients

This paper is concerned with an analysis of the Becker-Döring equations which lie at the heart of a number of descriptions of non-equilibrium phase transitions and related complex dynamical processes. The Becker-Döring theory describes growth and fragmentation in terms of stepwise addition or removal of single particles to or from clusters of similar particles and has been applied to a wide range of problems of physicochemical and biological interest within recent years. Here we consider the case where the aggregation and fragmentation rates depend exponentially on cluster size. These choices of rate coefficients at least qualitatively correspond to physically realistic molecular clustering scenarios such as occur in, for example, simulations of simple fluids. New similarity solutions for the constant monomer Becker-Döring system are identified, and shown to be generic in the case of aggregation and fragmentation rates that depend exponentially on cluster size.

Crystallite size-dependent phases in nanocrystalline ZrO(2)-Sc(2)O(3)

ZrO(2)-10, 12 and 14 mol% Sc(2)O(3) nanopowders were prepared by using a nitrate-lysine gel-combustion synthesis. These materials were studied by synchrotron X-ray powder diffraction (SXPD) and Raman spectroscopy after calcination at different temperatures from 650 to 1200 degrees C, which led to samples with different average crystallite sizes, up to about 100 nm. The results from SXPD and Raman analyses indicate that, depending on Sc(2)O(3) content, the metastable t ''-form of the tetragonal phase or the cubic phase are fully retained at room temperature in nanocrystalline powders, provided an average crystallite sizes lower than similar to 30 nm. By contrast, powders with larger average crystallite sizes exhibit the stable rhombohedral, beta and gamma, phases and do not retain or very partially retain the metastable t '' and cubic ones.

A pore-size-dependent equation of state for multilayer adsorption in cylindrical mesopores

The chemical potential of adsorbed film inside cylindrical mesopores is dependent on the attractive interactions between the adsorbed molecules and adsorbent, the curvature of gas/adsorbed phase interface, and surface tension. A state equation of the adsorbed film is proposed to take into account the above factors. Nitrogen adsorption on model adsorbents, MCM-41, which exhibit uniform cylindrical channels, are used to verify the theoretical analysis. The proposed theory is capable of describing the important features of adsorption processes in cylindrical mesopores. According to this theory, at a given relative pressure, the smaller the pore radius is, the thicker the adsorbed film will be. The thickening of adsorbed films in the pores as the vapor pressure increases inevitably causes an increase in the interface curvature, which consequently leads to capillary condensation. Besides, this study confirmed that the interface tension depends substantially on the interface curvature in small mesopores. A quantitative relationship between the condensation pressure and the pore radius can be derived from the state equation and used to predict the pore radius from a condensation pressure, or vice versa.

Size-dependent recombination dynamics in ZnO nanowires.

A deep understanding of the recombination dynamics of ZnO nanowires NWs is a natural step for a precise design of on-demand nanostructures based on this material system. In this work we investigate the influence of finite-size on the recombination dynamics of the neutral bound exciton around 3.365 eV for ZnO NWs with different diameters. We demonstrate that the lifetime of this excitonic transition decreases with increasing the surface-to-volume ratio due to a surface induced recombination process. Furthermore, we have observed two broad transitions around 3.341 and 3.314 eV, which were identified as surface states by studying the dependence of their life time and intensitiy with the NWs dimensions.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Universality in models for disorder induced phase transitions

We have systematically analyzed six different reticular models with quenched disorder and no thermal fluctuations exhibiting a field-driven first-order phase transition. We have studied the nonequilibrium transition, appearing when varying the amount of disorder, characterized by the change from a discontinuous hysteresis cycle (with one or more large avalanches) to a smooth one (with only tiny avalanches). We have computed critical exponents using finite size scaling techniques and shown that they are consistent with universal values depending only on the space dimensionality d.

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

Photopyroelectric study of thermal properties and phase transitions in selected solids

This thesis presents in detail. the theoretical developments and calculations which are used for the simultaneous determination of thermal parameters, namely thermal diffusivity (a). thermal effusivity (e), thermal conductivity (K) and heat capacity (cr ) employing photopyroelectric technique. In our calculations. we have assumed that the pyroelectric detector is supported on a copper backing. so that there will be sufficient heat exchange between the heated pyroelectric detector and the backing so that the signal fluctuations are reduced to a minimum. Since the PPE signal depends on the properties of the detector that are also temperature dependent. a careful temperature calibration of the system need to be carried out. APPE cell has been fabricated for the measurements that can be used to measure the thermal properties of solid samples from ~ 90 K to ~ 350 K. The cell has been calibrated using standard samples and the accuracy of the technique is found to be of the order of± 1%.In this thesis, we have taken up work n photopyroelectric investigation of thermal parameters of ferroelectric crystals such as Glycine phosphite (NH3CH2COOH3P03), Triglycine sulfate and Thiourea as well as mixed valence perovskites samples such as Lead doped Lanthanum Manganate (Lal_xPb~Mn03) Calcium doped (Lal_xCaxMnOJ) and Nickel doped Lanthanum Stroncium Cobaltate (Lao~Sro5Ni,Col_x03).The three ferroelectric crystals are prepared by the slow evaporation technique and the mixed valence perovskites by solid state reaction technique.Mixed valence perovskites, with the general formula RI_xA~Mn03 (R = La. Nd or Pr and A = Ba, Ca, Sr or Pb) have been materials of intense experimental and theoretical studies over the past few years. These materials show . colossal magneloresis/ance' (CMR) in samples with 0.2 < x < 0.5 in such a doping region, resistivity exhibits a peak at T = T p' the metal - insulator transition temperature. The system exhibits metallic characteristics with d %T > Oabove Tp (wherep is the resistivity) and insulating characteristics with d % T < 0 above T p. Despite intensive investigations on the CMR phenomena and associated electrical properties. not much work has been done on the variation of thermal properties of these samples. We have been quite successful in finding out the nature of anomaly associated with thermal properties when the sample undergoes M-I transition.The ferroelectric crystal showing para-ferroelectric phase transitions - Glycine phosphite. Thiourea and Triglycine sulfate - are studied in detail in order to see how well the PPE technique enables one to measure the thermal parameters during phase transitions. It is seen that the phase transition gets clearly reflected in the variation of thermal parameters. The anisotropy in thermal transport along different crystallographic directions are explained in terms of the elastic anisotropy and lattice contribution to the thermal conductivity. Interesting new results have been obtained on the above samples and are presented in three different chapters of the thesis.In summary. we have carried investigations of the variations of the thermal parameters during phase transitions employing photopyroelectric technique. The results obtained on different systems are important not only in understanding the physics behind the transitions but also in establishing the potentiality of the PPE tool. The full potential of PPE technique for the investigation of optical and thermal properties of materials still remains to be taken advantage of by workers in this field.

Critical behavior in nonequilibrium phase transitions

The nonequilibrium phase transitions occurring in a fast-ionic-conductor model and in a reaction-diffusion Ising model are studied by Monte Carlo finite-size scaling to reveal nonclassical critical behavior; our results are compared with those in related models.

Optimal growth strategies when mortality and production rates are size-dependent

Pontryagin's maximum principle from optimal control theory is used to find the optimal allocation of energy between growth and reproduction when lifespan may be finite and the trade-off between growth and reproduction is linear. Analyses of the optimal allocation problem to date have generally yielded bang-bang solutions, i.e. determinate growth: life-histories in which growth is followed by reproduction, with no intermediate phase of simultaneous reproduction and growth. Here we show that an intermediate strategy (indeterminate growth) can be selected for if the rates of production and mortality either both increase or both decrease with increasing body size, this arises as a singular solution to the problem. Our conclusion is that indeterminate growth is optimal in more cases than was previously realized. The relevance of our results to natural situations is discussed.

Bootstrap percolation on homogeneous trees has 2 phase transitions

We study the threshold theta bootstrap percolation model on the homogeneous tree with degree b + 1, 2 <= theta <= b, and initial density p. It is known that there exists a nontrivial critical value for p, which we call p(f), such that a) for p > p(f), the final bootstrapped configuration is fully occupied for almost every initial configuration, and b) if p < p(f) , then for almost every initial configuration, the final bootstrapped configuration has density of occupied vertices less than 1. In this paper, we establish the existence of a distinct critical value for p, p(c), such that 0 < p(c) < p(f), with the following properties: 1) if p <= p(c), then for almost every initial configuration there is no infinite cluster of occupied vertices in the final bootstrapped configuration; 2) if p > p(c), then for almost every initial configuration there are infinite clusters of occupied vertices in the final bootstrapped configuration. Moreover, we show that 3) for p < p(c), the distribution of the occupied cluster size in the final bootstrapped configuration has an exponential tail; 4) at p = p(c), the expected occupied cluster size in the final bootstrapped configuration is infinite; 5) the probability of percolation of occupied vertices in the final bootstrapped configuration is continuous on [0, p(f)] and analytic on (p(c), p(f) ), admitting an analytic continuation from the right at p (c) and, only in the case theta = b, also from the left at p(f).