Phase transition in the countdown problem

We present a combinatorial decision problem, inspired by the celebrated quiz show called Countdown, that involves the computation of a given target number T from a set of k randomly chosen integers along with a set of arithmetic operations. We find that the probability of winning the game evidences a threshold phenomenon that can be understood in the terms of an algorithmic phase transition as a function of the set size k. Numerical simulations show that such probability sharply transitions from zero to one at some critical value of the control parameter, hence separating the algorithm's parameter space in different phases. We also find that the system is maximally efficient close to the critical point. We derive analytical expressions that match the numerical results for finite size and permit us to extrapolate the behavior in the thermodynamic limit.

A critical force constant of the structural phase transition in quartz

Long wavelength optical phonons of quartz were analyzed by a Born-Von Karman model not previously used. It was found that only one force constant associated with the turning of the Si-O bonds has a critical effect on the soft-mode frequency and the α-β transition in quartz. The square of the soft-mode frequency was found to depend linearly on this force constant which has the temperature dependence K(T)= -5.33+225.3x10-4(851-T)2/3 in units of 104 dyn/cm2.

Phase transitions in number theory: from the birthday problem to Sidon sets

In this work, we show how number theoretical problems can be fruitfully approached with the tools of statistical physics. We focus on g-Sidon sets, which describe sequences of integers whose pairwise sums are different, and propose a random decision problem which addresses the probability of a random set of k integers to be g-Sidon. First, we provide numerical evidence showing that there is a crossover between satisfiable and unsatisfiable phases which converts to an abrupt phase transition in a properly defined thermodynamic limit. Initially assuming independence, we then develop a mean-field theory for the g-Sidon decision problem. We further improve the mean-field theory, which is only qualitatively correct, by incorporating deviations from independence, yielding results in good quantitative agreement with the numerics for both finite systems and in the thermodynamic limit. Connections between the generalized birthday problem in probability theory, the number theory of Sidon sets and the properties of q-Potts models in condensed matter physics are briefly discussed

Electrostatic plasma instabilities excited by a high‐frequency electric field

The electrostatic plasma waves excited by a uniform, alternating electric field of arbitrary intensity are studied on the basis of the Vlasov equation; their dispersion relation, which involves the determinant of either of two infinite matrices, is derived. For ω0 ≫ ωpi (ω0 being the applied frequency and ωpi the ion plasma frequency) the waves may be classified in two groups, each satisfying a simple condition; this allows writing the dispersion relation in closed form. Both groups coalesce (resonance) if (a) ω0  ≈  ωpe/r (r any integer) and (b) the wavenumber k is small. A nonoscillatory instability is found; its distinction from the DuBois‐Goldman instability and its physical origin are discussed. Conditions for its excitation (in particular, upper limits to ω0,k, and k⋅vE,vE being the field‐induced electron velocity), and simple equations for the growth rate are given off‐resonance and at ω0  ≈  ωpi. The dependence of both threshold and maximum growth rate on various parameters is discussed, and the results are compared with those of Silin and Nishikawa. The threshold at ω0  ≈  ωpi/r,r  ≠  1, is studied.

Calculation of the spatial distribution of photovoltaic field by arbitrary 2D ilumination patterns en LiNbO3; application to photovoltaic particle trapping.

Patterns of evanescent photovoltaic field induced by illumination on a surface of lithium niobate (LN) have been calculated and compared with the experimental patterns of nano- and microparticles trapped by dielectrophoretic forces. A tool for this calculation has been developed. Calculo de distribución espacial de campo por efecto fotovoltaico con patrones arbitrarios de iluminación, en LiNbO3

Análisis y simulación numérica de problemas electrohidrodinámicos relacionados con el electrospray

La presente tesis es un estudio analítico y numérico del electrospray. En la configuración más sencilla, un caudal constante del líquido a atomizar, que debe tener una cierta conductividad eléctrica, se inyecta en un medio dieléctrico (un gas u otro líquido inmiscible con el primero) a través de un tubo capilar metálico. Entre este tubo y un electrodo lejano se aplica un voltaje continuo que origina un campo eléctrico en el líquido conductor y en el espacio que lo rodea. El campo eléctrico induce una corriente eléctrica en el líquido, que acumula carga en su superficie, y da lugar a un esfuerzo eléctrico sobre la superficie, que tiende a alargarla en la dirección del campo eléctrico. El líquido forma un menisco en el extremo del tubo capilar cuando el campo eléctrico es suficientemente intenso y el caudal suficientemente pequeño. Las variaciones de presión y los esfuerzos viscosos asociados al movimiento del líquido son despreciables en la mayor parte de este menisco, siendo dominantes los esfuerzos eléctrico y de tensión superficial que actúan sobre la superficie del líquido. En el modo de funcionamiento llamado de conochorro, el balance de estos esfuerzos hace que el menisco adopte una forma cónica (el cono de Taylor) en una región intermedia entre el extremo del tubo y la punta del menisco. La velocidad del líquido aumenta al acercarse al vértice del cono, lo cual propicia que las variaciones de la presión en el líquido generadas por la inercia o por la viscosidad entren en juego, desequilibrando el balance de esfuerzos mencionado antes. Como consecuencia, del vértice del cono sale un delgado chorro de líquido, que transporta la carga eléctrica que se acumula en la superficie. La acción del campo eléctrico tangente a la superficie sobre esta carga origina una tracción eléctrica que tiende a alargar el chorro. Esta tracción no es relevante en el menisco, donde el campo eléctrico tangente a la superficie es muy pequeño, pero se hace importante en el chorro, donde es la causa del movimiento del líquido. Lejos del cono, el chorro puede o bien desarrollar una inestabilidad asimétrica que lo transforma en una espiral (whipping) o bien romperse en un spray de gotas prácticamente monodispersas cargadas eléctricamente. La corriente eléctrica transportada por el líquido es la suma de la corriente de conducción en el interior del líquido y la corriente debida a la convección de la carga acumulada en su superficie. La primera domina en el menisco y la segunda en el chorro lejano, mientras que las dos son comparables en una región intermedia de transferencia de corriente situada al comienzo del chorro aunque aguas abajo de la región de transición cono-chorro, en la que el menisco deja de ser un cono de Taylor. Para un campo exterior dado, la acumulación de carga eléctrica en la superficie del líquido reduce el campo eléctrico en el interior del mismo, que llega a anularse cuando la carga alcanza un estado final de equilibrio. El tiempo característico de este proceso es el tiempo de relajación dieléctrica, que es una propiedad del líquido. Cuando el tiempo de residencia del líquido en la región de transición cono-chorro (o en otra región del campo fluido) es grande frente al tiempo de relajación dieléctrica, la carga superficial sigue una sucesión de estados de equilibrio y apantalla al líquido del campo exterior. Cuando esta condición deja de cumplirse, aparecen efectos de relajación de carga, que se traducen en que el campo exterior penetra en el líquido, a no ser que su constante dieléctrica sea muy alta, en cuyo caso el campo inducido por la carga de polarización evita la entrada del campo exterior en el menisco y en una cierta región del chorro. La carga eléctrica en equilibrio en la superficie de un menisco cónico intensifica el campo eléctrico y determina su variación espacial hasta distancias aguas abajo del menisco del orden de su tamaño. Este campo, calculado por Taylor, es independiente del voltaje aplicado, por lo que las condiciones locales del flujo y el valor de la corriente eléctrica son también independientes del voltaje en tanto los tamaños de las regiones que determinan estas propiedades sean pequeños frente al tamaño del menisco. Los resultados experimentales publicados en la literatura muestran que existe un caudal mínimo para el que el modo cono-chorro que acabamos de describir deja de existir. El valor medio y la desviación típica de la distribución de tamaños de las gotas generadas por un electrospray son mínimos cuando se opera cerca del caudal mínimo. A pesar de que los mecanismos responsables del caudal mínimo han sido muy estudiados, no hay aún una teoría completa del mismo, si bien su existencia parece estar ligada a la aparición de efectos de relajación de carga en la región de transición cono-chorro. En esta tesis, se presentan estimaciones de orden de magnitud, algunas existentes y otras nuevas, que muestran los balances dominantes responsables de las distintas regiones de la estructura asintótica de la solución en varios casos de interés. Cuando la inercia del líquido juega un papel en la transición cono-chorro, los resultados muestran que la región de transferencia de corriente, donde la mayor parte de la corriente pasa a la superficie, está en el chorro aguas abajo de la región de transición cono-chorro. Los efectos de relajación de carga aparecen de forma simultánea en el chorro y la región de transición cuando el caudal se disminuye hasta valores de un cierto orden. Para caudales aún menores, los efectos de relajación de carga se notan en el menisco, en una región grande comparada con la de transición cono-chorro. Cuando el efecto de las fuerzas de viscosidad es dominante en la región de transición, la región de transferencia de corriente está en el chorro pero muy próxima a la región de transición cono-chorro. Al ir disminuyendo el caudal, los efectos de relajación de carga aparecen progresivamente en el chorro, en la región de transición y por último en el menisco. Cuando el caudal es mucho mayor que el mínimo del modo cono-chorro, el menisco deja de ser cónico. El campo eléctrico debido al voltaje aplicado domina en la región de transferencia de corriente, y tanto la corriente eléctrica como el tamaño de las diferentes regiones del problema pasan a depender del voltaje aplicado. Como resultado de esta dependencia, el plano caudal-voltaje se divide en diferentes regiones que se analizan separadamente. Para caudales suficientemente grandes, la inercia del líquido termina dominando frente a las fuerzas de la viscosidad. Estos resultados teóricos se han validado con simulaciones numéricas. Para ello se ha formulado un modelo simplificado del flujo, el campo eléctrico y el transporte de carga en el menisco y el chorro del electrospray. El movimiento del líquido se supone casi unidireccional y se describe usando la aproximación de Cosserat para un chorro esbelto. Esta aproximación, ampliamente usada en la literatura, permite simular con relativa facilidad múltiples casos y cubrir amplios rangos de valores de los parámetros reteniendo los efectos de la viscosidad y la inercia del líquido. Los campos eléctricos dentro y fuera del liquido están acoplados y se calculan sin simplificación alguna usando un método de elementos de contorno. La solución estacionaria del problema se calcula mediante un método iterativo. Para explorar el espacio de los parámetros, se comienza calculando una solución para valores fijos de las propiedades del líquido, el voltaje aplicado y el caudal. A continuación, se usa un método de continuación que permite delinear la frontera del dominio de existencia del modo cono-chorro, donde el método iterativo deja de converger. Cuando el efecto de la inercia del líquido domina en la región de transición cono-chorro, el caudal mínimo para el cual el método iterativo deja de converger es del orden del valor estimado del caudal para el que comienza a haber efectos de relajación de carga en el chorro y el cono. Aunque las simulaciones no convergen por debajo de dicho caudal, el valor de la corriente eléctrica para valores del caudal ligeramente mayores parece ajustarse a las estimaciones para caudales menores, reflejando un posible cambio en los balances aplicables. Por el contrario, cuando las fuerzas viscosas dominan en la región de transición, se pueden obtener soluciones estacionarias para caudales bastante menores que aquel para el que aparecen efectos de relajación de carga en la región de transición cono-chorro. Los resultados numéricos obtenidos para estos pequeños caudales se ajustan perfectamente a las estimaciones de orden de magnitud que se describen en la memoria. Por último, se incluyen como anexos dos estudios teóricos que han surgido de forma natural durante el desarrollo de la tesis. El primero hace referencia a la singularidad en el campo eléctrico que aparece en la línea de contacto entre el líquido y el tubo capilar en la mayoría de las simulaciones. Primero se estudia en qué situaciones el campo eléctrico tiende a infinito en la línea de contacto. Después, se comprueba que dicha singularidad no supone un fallo en la descripción del problema y que además no afecta a la solución lejos de la línea de contacto. También se analiza si los esfuerzos eléctricos infinitamente grandes a los que da lugar dicha singularidad pueden ser compensados por el resto de esfuerzos que actúan en la superficie del líquido. El segundo estudio busca determinar el tamaño de la región de apantallamiento en un chorro de líquido dieléctrico sin carga superficial. En esta región, el campo exterior es compensado parcialmente por el campo que induce la carga de polarización en la superficie del líquido, de forma que en el interior del líquido el campo eléctrico es mucho menor que en el exterior. Una región como ésta aparece en las estimaciones cuando los efectos de relajación de carga son importantes en la región de transferencia de corriente en el chorro. ABSTRACT This aim of this dissertation is a theoretical and numerical analysis of an electrospray. In its most simple configuration, a constant flow rate of the liquid to be atomized, which has to be an electrical conductor, is injected into a dielectric medium (a gas or another inmiscible fluid) through a metallic capillary tube. A constant voltage is applied between this tube and a distant electrode that produces an electric field in the liquid and the surrounding medium. This electric field induces an electric current in the liquid that accumulates charge at its surface and leads to electric stresses that stretch the surface in the direction of the electric field. A meniscus appears on the end of the capillary tube when the electric field is sufficiently high and the flow rate is small. Pressure variations and viscous stresses due to the motion of the liquid are negligible in most of the meniscus, where normal electric and surface tension stresses acting on the surface are dominant. In the so-called cone-jet mode, the balance of these stresses forces the surface to adopt a conical shape -Taylor cone- in a intermediate region between the end of the tube and the tip of the meniscus. When approaching the cone apex, the velocity of the liquid increases and leads to pressure variations that eventually disturb the balance of surfaces tension and electric stresses. A thin jet emerges then from the tip of the meniscus that transports the charge accumulated at its surface. The electric field tangent to the surface of the jet acts on this charge and continuously stretches the jet. This electric force is negligible in the meniscus, where the component of the electric field tangent to the surface is small, but becomes very important in the jet. Far from the cone, the jet can either develop an asymmetrical instability named “whipping”, whereby the jet winds into a spiral, or break into a spray of small, nearly monodisperse, charged droplets. The electric current transported by the liquid has two components, the conduction current in the bulk of the liquid and the convection current due to the transport of the surface charge by the flow. The first component dominates in the meniscus, the second one in the far jet, and both are comparable in a current transfer region located in the jet downstream of the cone-jet transition region where the meniscus ceases to be a Taylor cone. Given an external electric field, the charge that accumulates at the surface of the liquid reduces the electric field inside the liquid, until an equilibrium is reached in which the electric field induced by the surface charge counters the external electric field and shields the liquid from this field. The characteristic time of this process is the electric relaxation time, which is a property of the liquid. When the residence time of the liquid in the cone-jet transition region (or in other region of the flow) is greater than the electric relaxation time, the surface charge follows a succession of equilibrium states and continuously shield the liquid from the external field. When this condition is not satisfied, charge relaxation effects appear and the external field penetrates into the liquid unless the liquid permittivity is large. For very polar liquids, the field due to the polarization charge at the surface prevents the external field from entering the liquid in the cone and in certain region of the jet. The charge at the surface of a conical meniscus intensifies the electric field around the cone, determining its spatial variation up to distances downstream of the apex of the order of the size of the meniscus. This electric field, first computed by Taylor, is independent of the applied voltage. Therefore local flow characteristics and the electric current carried by the jet are also independent of the applied voltage provided the size of the regions that determine these magnitudes are small compared with the size of the meniscus. Many experiments in the literature show the existence of a minimum flow rate below which the cone-jet mode cannot be established. The mean value and the standard deviation of the electrospray droplet size distribution are minimum when the device is operated near the minimum flow rate. There is no complete explanation of the minimum flow rate, even though possible mechanisms have been extensively studied. The existence of a minimum flow rate seems to be connected with the appearance of charge relaxation effects in the transition region. In this dissertation, order of magnitude estimations are worked out that show the dominant balances in the different regions of the asymptotic structure of the solution for different conditions of interest. When the inertia of the liquid plays a role in the cone-jet transition region, the region where most of the electric current is transfered to the surface lies in the jet downstream the cone-jet transition region. When the flow rate decreases to a certain value, charge relaxation effects appear simultaneously in the jet and in the transition region. For smaller values of the flow rate, charge relaxation effects are important in a region of the meniscus larger than the transition region. When viscous forces dominate in the flow in the cone-jet transition region, the current transfer region is located in the jet immediately after the transition region. When flow rate is decreased, charge relaxation effects appears gradually, first in the jet, then in the transition region, and finally in the meniscus. When flow rate is much larger than the cone-jet mode minimum, the meniscus ceases to be a cone. The electric current and the structure of the solution begin to depend on the applied voltage. The flow rate-voltage plane splits into different regions that are analyzed separately. For sufficiently large flow rates, the effect of the inertia of the liquid always becomes greater than the effect of the viscous forces. A set of numerical simulations have been carried out in order to validate the theoretical results. A simplified model of the problem has been devised to compute the flow, the electric field and the surface charge in the meniscus and the jet of an electrospray. The motion of the liquid is assumed to be quasi-unidirectional and described by Cosserat’s approximation for a slender jet. This widely used approximation allows to easily compute multiple configurations and to explore wide ranges of values of the governing parameters, retaining the effects of the viscosity and the inertia of the liquid. Electric fields inside and outside the liquid are coupled and are computed without any simplification using a boundary elements method. The stationary solution of the problem is obtained by means of an iterative method. To explore the parameter space, a solution is first computed for a set of values of the liquid properties, the flow rate and the applied voltage, an then a continuation method is used to find the boundaries of the cone-jet mode domain of existence, where the iterative method ceases to converge. When the inertia of the liquid dominates in the cone-jet transition region, the iterative method ceases to converge for values of the flow rate for which order-of-magnitude estimates first predict charge relaxation effects to be important in the cone and the jet. The electric current computed for values of the flow rate slightly above the minimum for which convergence is obtained seems to agree with estimates worked out for lower flow rates. When viscous forces dominate in the transition region, stationary solutions can be obtained for flow rates significantly smaller than the one for which charge relaxation effects first appear in the transition region. Numerical results obtained for those small values of the flow rate agree with our order of magnitude estimates. Theoretical analyses of two issues that have arisen naturally during the thesis are summarized in two appendices. The first appendix contains a study of the singularity of the electric field that most of the simulations show at the contact line between the liquid and the capillary tube. The electric field near the contact line is analyzed to determine the ranges of geometrical configurations and liquid permittivity where a singularity appears. Further estimates show that this singularity does not entail a failure in the description of the problem and does not affect the solution far from the contact line. The infinite electric stresses that appear at the contact line can be effectively balanced by surface tension. The second appendix contains an analysis of the size and slenderness of the shielded region of a dielectric liquid in the absence of free surface charge. In this region, the external electric field is partially offset by the polarization charge so that the inner electric field is much lower than the outer one. A similar region appears in the estimates when charge relaxation effects are important in the current transfer region.

Vortex pinning vs superconducting wire network: origin of periodic oscillations induced by applied magnetic fields in superconducting films with arrays of nanomagnets

Hybrid magnetic arrays embedded in superconducting films are ideal systems to study the competition between different physical (such as the coherence length) and structural length scales such as are available in artificially produced structures. This interplay leads to oscillation in many magnetically dependent superconducting properties such as the critical currents, resistivity and magnetization. These effects are generally analyzed using two distinct models based on vortex pinning or wire network. In this work, we show that for magnetic dot arrays, as opposed to antidot (i.e. holes) arrays, vortex pinning is the main mechanism for field induced oscillations in resistance R(H), critical current Ic(H), magnetization M(H) and ac-susceptibility χ ac(H) in a broad temperature range. Due to the coherence length divergence at Tc, a crossover to wire network behaviour is experimentally found. While pinning occurs in a wide temperature range up to Tc, wire network behaviour is only present in a very narrow temperature window close to Tc. In this temperature interval, contributions from both mechanisms are operational but can be experimentally distinguished.

Determination of the crystal and magnetic structure of the DyCrO4-scheelite polymorph by neutron diffraction

Neutron diffraction data of DyCrO4 oxide, prepared at 4 GPa and 833 K from the ambient pressure zircon-type, reveal that crystallize with the scheelite-type structure, space group I41/a. Accompanying this structural phase transition induced by pressure the magnetic properties change dramatically from ferromagnetism in the case of zircon to antiferromagnetism for the scheelite polymorph with a T N= 19 K. The analysis of the neutron diffraction data obtained at 1.2 K has been used to determine the magnetic structure of this DyCrO4-scheelite oxide which can be described with a k = [0, 0, 0] as propagation vector, where the Dy and Cr moments are lying in the ab-plane of the scheelite structure. The ordered magnetic moments are 10 µB and 1 µB for Dy+3 and Cr+5 respectively

Contribution to the Analysis, Design and Assessment of Compact Antenna Test Ranges At Millimeter Wavelengths - Contribución al Análisis, Diseño y Caracterización de Sistemas de Medida de Antenas en Rango Compacto para Frecuencias Milimétricas

This Doctoral Thesis entitled Contribution to the analysis, design and assessment of compact antenna test ranges at millimeter wavelengths aims to deepen the knowledge of a particular antenna measurement system: the compact range, operating in the frequency bands of millimeter wavelengths. The thesis has been developed at Radiation Group (GR), an antenna laboratory which belongs to the Signals, Systems and Radiocommunications department (SSR), from Technical University of Madrid (UPM). The Radiation Group owns an extensive experience on antenna measurements, running at present four facilities which operate in different configurations: Gregorian compact antenna test range, spherical near field, planar near field and semianechoic arch system. The research work performed in line with this thesis contributes the knowledge of the first measurement configuration at higher frequencies, beyond the microwaves region where Radiation Group features customer-level performance. To reach this high level purpose, a set of scientific tasks were sequentially carried out. Those are succinctly described in the subsequent paragraphs. A first step dealed with the State of Art review. The study of scientific literature dealed with the analysis of measurement practices in compact antenna test ranges in addition with the particularities of millimeter wavelength technologies. Joint study of both fields of knowledge converged, when this measurement facilities are of interest, in a series of technological challenges which become serious bottlenecks at different stages: analysis, design and assessment. Thirdly after the overview study, focus was set on Electromagnetic analysis algorithms. These formulations allow to approach certain electromagnetic features of interest, such as field distribution phase or stray signal analysis of particular structures when they interact with electromagnetic waves sources. Properly operated, a CATR facility features electromagnetic waves collimation optics which are large, in terms of wavelengths. Accordingly, the electromagnetic analysis tasks introduce an extense number of mathematic unknowns which grow with frequency, following different polynomic order laws depending on the used algorithmia. In particular, the optics configuration which was of our interest consisted on the reflection type serrated edge collimator. The analysis of these devices requires a flexible handling of almost arbitrary scattering geometries, becoming this flexibility the nucleus of the algorithmia’s ability to perform the subsequent design tasks. This thesis’ contribution to this field of knowledge consisted on reaching a formulation which was powerful at the same time when dealing with various analysis geometries and computationally speaking. Two algorithmia were developed. While based on the same principle of hybridization, they reached different order Physics performance at the cost of the computational efficiency. Inter-comparison of their CATR design capabilities was performed, reaching both qualitative as well as quantitative conclusions on their scope. In third place, interest was shifted from analysis - design tasks towards range assessment. Millimetre wavelengths imply strict mechanical tolerances and fine setup adjustment. In addition, the large number of unknowns issue already faced in the analysis stage appears as well in the on chamber field probing stage. Natural decrease of dynamic range available by semiconductor millimeter waves sources requires in addition larger integration times at each probing point. These peculiarities increase exponentially the difficulty of performing assessment processes in CATR facilities beyond microwaves. The bottleneck becomes so tight that it compromises the range characterization beyond a certain limit frequency which typically lies on the lowest segment of millimeter wavelength frequencies. However the value of range assessment moves, on the contrary, towards the highest segment. This thesis contributes this technological scenario developing quiet zone probing techniques which achieves substantial data reduction ratii. Collaterally, it increases the robustness of the results to noise, which is a virtual rise of the setup’s available dynamic range. In fourth place, the environmental sensitivity of millimeter wavelengths issue was approached. It is well known the drifts of electromagnetic experiments due to the dependance of the re sults with respect to the surrounding environment. This feature relegates many industrial practices of microwave frequencies to the experimental stage, at millimeter wavelengths. In particular, evolution of the atmosphere within acceptable conditioning bounds redounds in drift phenomena which completely mask the experimental results. The contribution of this thesis on this aspect consists on modeling electrically the indoor atmosphere existing in a CATR, as a function of environmental variables which affect the range’s performance. A simple model was developed, being able to handle high level phenomena, such as feed - probe phase drift as a function of low level magnitudes easy to be sampled: relative humidity and temperature. With this model, environmental compensation can be performed and chamber conditioning is automatically extended towards higher frequencies. Therefore, the purpose of this thesis is to go further into the knowledge of millimetre wavelengths involving compact antenna test ranges. This knowledge is dosified through the sequential stages of a CATR conception, form early low level electromagnetic analysis towards the assessment of an operative facility, stages for each one of which nowadays bottleneck phenomena exist and seriously compromise the antenna measurement practices at millimeter wavelengths.

Self-assembled MgxZn1−xO quantum dots (0 ≤ x ≤ 1) on different substrates using spray pyrolysis methodology

By using the spray pyrolysis methodology in its classical configuration we have grown self-assembled MgxZn1−xO quantum dots (size [similar]4–6 nm) in the overall range of compositions 0 ≤ x ≤ 1 on c-sapphire, Si (100) and quartz substrates. Composition of the quantum dots was determined by means of transmission electron microscopy-energy dispersive X-ray analysis (TEM-EDAX) and X-ray photoelectron spectroscopy. Selected area electron diffraction reveals the growth of single phase hexagonal MgxZn1−xO quantum dots with composition 0 ≤ x ≤ 0.32 by using a nominal concentration of Mg in the range 0 to 45%. Onset of Mg concentration about 50% (nominal) forces the hexagonal lattice to undergo a phase transition from hexagonal to a cubic structure which resulted in the growth of hexagonal and cubic phases of MgxZn1−xO in the intermediate range of Mg concentrations 50 to 85% (0.39 ≤ x ≤ 0.77), whereas higher nominal concentration of Mg ≥ 90% (0.81 ≤ x ≤ 1) leads to the growth of single phase cubic MgxZn1−xO quantum dots. High resolution transmission electron microscopy and fast Fourier transform confirm the results and show clearly distinguishable hexagonal and cubic crystal structures of the respective quantum dots. A difference of 0.24 eV was detected between the core levels (Zn 2p and Mg 1s) measured in quantum dots with hexagonal and cubic structures by X-ray photoemission. The shift of these core levels can be explained in the frame of the different coordination of cations in the hexagonal and cubic configurations. Finally, the optical absorption measurements performed on single phase hexagonal MgxZn1−xO QDs exhibited a clear shift in optical energy gap on increasing the Mg concentration from 0 to 40%, which is explained as an effect of substitution of Zn2+ by Mg2+ in the ZnO lattice.

Perturbed angular correlation study of Ta-181-doped PbTi1-xHfxO3 compounds

In this work, the hyperfine quadrupole interaction at Ta-doped PbTi1-xHfxO3 polycrystalline samples is studied for the first time. Powders with x=0.25, 0.50 and 0.75 were prepared and characterized by X-ray diffraction analysis. Perturbed Angular Correlation (PAC) analyses were done as a function of temperature, using low concentration Ta-181 nuclei as probes. In the ferroelectric and paraelectric phases of these compounds two sites were occupied by the probes. For each site the quadrupole frequency, asymmetry and relative distribution width parameters were obtained as a function of temperature above and below the Curie temperature (T-C). One of these sites was assigned to the regular Ti-Hf site, while the other one was assigned to some kind of defect. The behavior of the hyperfine parameters as a function of temperature was analyzed in terms of a recent published phase diagram and the presence of disorder below and above T-C. For the three compositions measured, the obtained hyperfine parameters present discontinuities which correspond to the ferroelectric-paraelectric phase transition. In both phases it was found broad frequency distributed interactions. The disorder in the electronic distribution would be responsible for the broad line width of the hyperfine interaction. (C) 2012 Elsevier B.V. All rights reserved.

Crack mechanical failure in lithium niobate crystal under ion irradiation; novel simulation by extended finite elements

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion-generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Crack mechanical failure in ceramic materials under ion irradiation: case of lithium niobate crystal

Swift heavy ion irradiation (ions with mass heavier than 15 and energy exceeding MeV/amu) transfer their energy mainly to the electronic system with small momentum transfer per collision. Therefore, they produce linear regions (columnar nano-tracks) around the straight ion trajectory, with marked modifications with respect to the virgin material, e.g., phase transition, amorphization, compaction, changes in physical or chemical properties. In the case of crystalline materials the most distinctive feature of swift heavy ion irradiation is the production of amorphous tracks embedded in the crystal. Lithium niobate is a relevant optical material that presents birefringence due to its anysotropic trigonal structure. The amorphous phase is certainly isotropic. In addition, its refractive index exhibits high contrast with those of the crystalline phase. This allows one to fabricate waveguides by swift ion irradiation with important technological relevance. From the mechanical point of view, the inclusion of an amorphous nano-track (with a density 15% lower than that of the crystal) leads to the generation of important stress/strain fields around the track. Eventually these fields are the origin of crack formation with fatal consequences for the integrity of the samples and the viability of the method for nano-track formation. For certain crystal cuts (X and Y), these fields are clearly anisotropic due to the crystal anisotropy. We have used finite element methods to calculate the stress/strain fields that appear around the ion- generated amorphous nano-tracks for a variety of ion energies and doses. A very remarkable feature for X cut-samples is that the maximum shear stress appears on preferential planes that form +/-45º with respect to the crystallographic planes. This leads to the generation of oriented surface cracks when the dose increases. The growth of the cracks along the anisotropic crystal has been studied by means of novel extended finite element methods, which include cracks as discontinuities. In this way we can study how the length and depth of a crack evolves as function of the ion dose. In this work we will show how the simulations compare with experiments and their application in materials modification by ion irradiation.

Multi-fluid Eulerian model of an electrospray in a host gas.

An Eulerian multifluid model is used to describe the evolution of an electrospray plume and the flow induced in the surrounding gas by the drag of the electrically charged spray droplets in the space between an injection electrode containing the electrospray source and a collector electrode. The spray is driven by the voltage applied between the two electrodes. Numerical computations and order-of-magnitude estimates for a quiescent gas show that the droplets begin to fly back toward the injection electrode at a certain critical value of the flux of droplets in the spray, which depends very much on the electrical conditions at the injection electrode. As the flux is increased toward its critical value, the electric field induced by the charge of the droplets partially balances the field due to the applied voltage in the vicinity of the injection electrode, leading to a spray that rapidly broadens at a distance from its origin of the order of the stopping distance at which the droplets lose their initial momentum and the effect of their inertia becomes negligible. The axial component of the electric field first changes sign in this region, causing the fly back. The flow induced in the gas significantly changes this picture in the conditions of typical experiments. A gas plume is induced by the drag of the droplets whose entrainment makes the radius of the spray away from the injection electrode smaller than in a quiescent gas, and convects the droplets across the region of negative axial electric field that appears around the origin of the spray when the flux of droplets is increased. This suppresses fly back and allows much higher fluxes to be reached than are possible in a quiescent gas. The limit of large droplet-to-gas mass ratio is discussed. Migration of satellite droplets to the shroud of the spray is reproduced by the Eulerian model, but this process is also affected by the motion of the gas. The gas flow preferentially pushes satellite droplets from the shroud to the core of the spray when the effect of the inertia of the droplets becomes negligible, and thus opposes the well-established electrostatic/inertial mechanism of segregation and may end up concentrating satellite droplets in an intermediate radial region of the spray.

Plausibility of a subglacial lake under Amundsenisen Icefield (Svalbard): spatially variable water content and sensitivity to thermal effect of snow and firn layers

Within our study of the plausibility of a subglacial lake under the Amundsenisen Icefield in Southern Spitzbergen, Svalbard achipelago (Glowacki et al., 2007), here we focus on the sensitivity of the system to the thermal effect of the firn and snow layers. Rough heat balance analysis shows that the firn layer plays an important role by driving the heat release to the atmosphere, so that its influence on the ice-water phase transition cannot be neglected (Bucchignani et al., 2012).