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Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma). The molecules in a solid are closely packed together and contain the least amount of kinetic energy. A solid is characterized by structural rigidity (as in rigid bodies) and resistance to a force applied to the surface. Unlike a liquid, a solid object does not flow to take on the shape of its container, nor does it expand to fill the entire available volume like a gas. The atoms in a solid are bound to each other, either in a regular geometric lattice (crystalline solids, which include metals and ordinary ice), or irregularly (an amorphous solid such as common window glass). Solids cannot be compressed with little pressure whereas gases can be compressed with little pressure because the molecules in a gas are loosely packed. The branch of physics that deals with solids is called solid-state physics, and is the main branch of condensed matter physics (which also includes liquids). Materi

Phase-field modeling of micropore formation in a solidifying alloy

Hossein Meidani

This thesis is focused on the study of the morphology of micropores formed during solidification of metallic alloys. Micropores constrained to form in well-developed dendritic solid network adopt complex non-spherical shapes. Previous studies using X-ray tomography (XRT) have shown that the local mean curvature of micropores can be as large as 0.2μm−1. Such a high curvature induces an overpressure of 400 kPa in the pore with respect to the surrounding liquid and thus highly affects its volume fraction. While trying to predict pore formation at the macro-scale using average equations, the effect of this curvature is usually introduced using simple mathematical relationships, i.e., pinching model, describing the pore curvature as a function of the volume fraction and a typical length scale (e.g., the secondary dendrite arm spacing or DAS) of the primary phase. Such relationships, however, are based on simplifications of the pore morphology that are not generally backed up with an extensive study of the pore shape and its evolution during solidification. On the other hand, direct observations using XRT offer valuable information about micropore morphologies after solidification, but unfortunately their limited spatial resolution does not allow yet for a detailed study of the curvature of micropores during their formation. In this work, a multiphase-field model has been developed in order to study and better understand the formation of micropores constrained to grow in a solid network (i.e., pinching effect). The model accounts for the pressure difference due to capillarity forces between liquid and gas and the mechanical equilibrium condition at triple (solid-liquid-pore) lines. The partitioning and diffusion of dissolved gases such as hydrogen in aluminum alloys are also incorporated into the model by solving together Sievert’s law, the perfect gas law and Fick’s equation. The model was first implemented in 2-D, and then was extended to 3-D by developing a program for parallel Distributed Memory Processor (DMP) machines. The model was used to study the influence of the DAS, primary phase solid fraction and gas content on the morphology of micropores. After validating the multiphase-field approach for a spherical micropore growing freely in a supersaturated liquid, the calculations show that a pore constrained to grow in a narrow liquid channel exhibits a substantially higher mean curvature, a larger pressure and a smaller volume than an unconstrained pore. The morphology of pores at steady state, obtained with the model for different solid morphologies and initial gas concentrations, was also analyzed. From their predicted 3-D morphologies, entities such as the Interfacial Shape Distribution (ISD) were plotted and analyzed. As expected, it was verified that the mean curvature of the pore-liquid interface, and thus also the pressure inside the pore, is uniform. The local morphology of the pore, however, varies depending on the position of the pore-liquid interface with respect to the primary solid: In between two parallel dendrite arms, the pore adopts a cylindrical-type shape with one principal curvature being almost nil and the other being about twice the mean curvature of the pore-liquid interface growing with a spherical-type tip in between four parallel dendrite arms. The results were then compared with analytical pinching models. While predicting a similar trend, analytical models tend to underestimate the pore curvature at high solid fraction and gas concentration. For pores spanning over distances larger than the average DAS, the simulations showed that the mean curvature varies between two limits: a minimum curvature given by the largest sphere that can be fitted in the interdendritic liquid, and a maximum curvature given by the size of the narrowest section that the pore needs to pass in order to expand. The pore curvature is therefore a complex non-monotonic function of the DAS, solid fraction, gas content and statistical variations of the liquid channel widths. Based on this and considering the complex morphology of pores reconstructed using high-resolution XRT, the present phase-field results suggest that a simple pinching model based on a spherical tip growing in between remaining liquid channels is a fairly good approximation. This model was further validated by performing phase-field calculations for a pore growing in a representative volume element taken from XRT. For such condition, it was observed that as the pore grows and penetrates thin liquid channels, the fraction of cylindrical-type pore-liquid interfaces increases and becomes dominant over spherical-type ones, a feature already observed in XRT observations of as-solidified micropores. Finally, in-situ XRT observations were also performed on Al-Cu samples directionally viii solidified in a Bridgman furnace and then quenched. Macroscopic calculations of porosity formation using the software ProCast showed that a high fraction of pores can form during the quench itself, and not so much during directional solidification. After solidification, small specimens were analyzed by XRT on the TomCat beamline of the Paul Scherrer Institute in Villigen, during isothermal holding at a temperature slightly above the eutectic temperature. It was shown that the volume fraction of primary solid increases during holding time, as a result of solid state diffusion of copper, while coalescence of secondary dendrite arms simultaneously modifies the topology of the remaining liquid from continuous films to isolated droplets. This topology change is shown to modify substantially the average hydrogen diffusion coefficient in the mushy zone. In parallel to the evolution of the solid-liquid interface, the number of micropores and their volume fraction change over time. This evolution is analyzed in terms of a local mass balance of hydrogen and of diffusion of hydrogen toward the ambient atmosphere.

EPFL2013

Porosity in Aluminum Alloys

Milan Felberbaum

Porosity is one of the major defects in castings because it reduces the mechanical properties of a cast piece [1]. Porosity formation results from the effect of two concomitant mechanisms, namely solidification shrinkage and segregation/precipitation of gases [1]. A model for the prediction of microporosity, macroporosity and pipe shrinkage during the solidification of alloys has been developed at the Computational Materials Laboratory (LSMX-EPFL) [2]. This model has then been improved by taking into account the effect of various alloying elements and gases on porosity formation [3, 4, 5]. However, the modeling of two physical phenomena still needed to be improved: (i) the curvature influence and (ii) the hydrogen diffusion influence on the growth of pores. The effect of pinching, i.e. the pores are forced by the growing solid network to adopt a complex non spherical shape, induces curvature restriction to the pores. This pinching effect can be a limiting factor for the growth of pores and is too simply modeled in the model of Péquet et al. [2]. Several other pinching models exist, but a rigorous experimental study to validate either one of these models is needed. Additionally, Carlson et al. [6] have recently shown that hydrogen diffusion might also be a limiting factor for the growth of pores. In the model of Péquet et al. [2], this effect was not taken into account. This thesis is mainly aimed to (i) provide experimental results that specifically validate the pinching model developed by Couturier et al. [4], (ii) investigate the influence of hydrogen diffusion on the growth of pores and (iii) provide a new model that takes into account the pinching effect and the hydrogen diffusion influence on the growth of pores. At first, pores formed in aluminum-copper (Al-Cu) samples (cast under controlled conditions) have been analyzed using high resolution X-ray tomography. The influence of the alloy inoculant, copper content, cooling rate and initial hydrogen content on the morphology of pores has been investigated. The results show that the curvature of micropores pinched in either non-inoculated or inoculated Al-4.5wt%Cu alloys can be fairly well approximated to that of cylinders. The results also show that the pinching model must be function of (i) the volume fraction of the primary phase gα and (ii) the secondary dendrite arm spacing λ2. However, the influence of the initial hydrogen content appears to be negligible. The pinching model developed by Couturier et al. [4] accounts for these observations and their relation fits fairly well the average mean curvature value of our experimental data. A new model has been developed to calculate an effective hydrogen diffusion coefficient De(gs), that is a function of the volume fraction of solid only. For that purpose, in-situ X-ray tomography has been performed on Al-Cu alloys. For each volume fraction of solid 0.6 ≤ gs ≤ 0.9, a representative volume element of the microstructure has been obtained from the tomography data. Solid and liquid voxels being assimilated to solid and liquid nodes respectively, a hydrogen diffusion equation has then been solved numerically. Calculations have been run until steady-state was reached in order to deduce De(gs) and the simulation results were successfully compared with a new theory based on effective-medium approximations. Both approaches lead to the main conclusion that hydrogen diffusion through the solid phase cannot be neglected, unlike it is assumed in the model of Carlson et al. [6]. Next, using the pinching model of Couturier et al. [4] and the obtained De(gs), a new volume-averaged model has been developed in order to simulate the growth of pores limited by (i) the curvature of the pore phase and (ii) the diffusion of hydrogen. The results show that, although hydrogen diffusion can be a limiting factor for the growth of pores, the pinching effect has a much larger influence. Accordingly, any model for porosity prediction should carefully take into account the influence of curvature and hydrogen diffusion on the growth of pores. In order to ripen this study at a refined scale, a 2D phase-field model has been developed to describe the complex shape of a pore formed within interdendritic liquid channels [7]. The influence of the solid, which can force the pore to adopt a non-spherical shape, is taken into account through the geometry of the domain and appropriate boundary conditions. This model accounts for curvature influence and hydrogen diffusion in the liquid, two of the main aspects governing the growth kinetics of a pore. However, the model still needs to be combined with a description of the liquid flow induced by the pore growth. Basically, this model should serve as a sound basis for further developments that might lead to more sophisticated pinching models. Finally, an experimental study has been conducted in order to track the inoculant influence on the shape of pipe shrinkage. Simultaneously, pipe shrinkage calculations (using the model of Péquet et al. [2]) were performed in order to track the influence of the gs,c parameter on the shape of the pipe shrinkage. This gs,c parameter corresponds to the critical volume fraction of solid at which mass feeding stops. Comparisons between experimental and simulation results show that the gs,c parameter should be set equal to 0.6 or 0.1 for a casting simulation of an inoculated or non-inoculated alloy, respectively.

EPFL2010

Dynamics of Electronic and Ionic Charges in Cyanine Organic Semiconductor Devices

Sandra Christina Jenatsch

Organic semiconductor materials have been widely applied in optoelectronic devices to replace their inorganic counterparts and explore new fields of applications. Due to their high extinction coefficients, chemical tunability and solubility, cyanine dyes are an interesting class of molecules to be employed in organic semiconductor devices. Their beneficial properties have been demonstrated in organic solar cells (OSC), photodetectors and recently in organic light-emitting electrochemical cells (OLEC). The focus of this thesis is to analyse different aspects regarding the dynamics of electronic and ionic charges in cyanine based devices. Models and conclusions are not restricted to cyanine based devices but can potentially be applied in various systems where combined ionic and electronic charges are present. In order to focus on electronic processes in OSCs, a combination of steady-state, transient and impedance analysis is used. It is resolved that trapped charges can be introduced at the dye/hole extracting layer interface by using specific solvents for the cyanine layer fabrication. These measurements also reveal the low hole mobility of cyanine films which in turn limits the possible upper layer thickness in OSCs. A frequently used way to enhance the conductivity of organic semiconductors is the addition of extra charges by chemical doping. This concept is employed for a near-infrared absorbing dye which is used as donor in a bilayer solar cell. The dependence of all figures of merit versus doping concentration and layer thickness is studied in detail. It is found that the performance of the optimised cell is not further improved by doping, but that it presents a good option if thicker layers are required, e.g. on rough substrates. Furthermore, the stability and degradation pathway of the p-doped species is analysed. This information is of general relevance as they also occur after charge transfer at the heterojunction interface of an OSC and during operation of OLECs. The dynamics of ionic charge carriers is separated into two contributions. In a first step, the steady-state diffusion profile of the counter ion within a cyanine/fullerene bilayer structure is scrutinised using different profiling techniques. An unexpected constant ion profile is found throughout the C60 layer. Simultaneously, the potential within the acceptor is measured by the Kelvin probe technique. A mechanism of combined electron and ion transfer from the C60 to the dye and vice versa is proposed which is in agreement with the experimental results. A prerequisite for OLEC operation is the mobility of ionic charge carriers. Their dynamics in cyanine salts under the effect of an external field is therefore studied in such devices. Several methods are developed and applied to characterise the dynamic p-i-n structure in detail, i.e. the position and width of the intrinsic region as well as the doping concentrations in p- and n-doped regions. The combination of all these methods helps to understand the transient behaviour of these cyanine devices but can also be adapted to other OLEC systems. A major drawback of cyanine dyes as emissive material is their low fluorescence quantum yield in solid films. To overcome this restriction and improve the OLEC efficiency, host-guest systems with various visibly emitting dyes are studied. The gain in fluorescence quantum yield in the film can directly be transferred to an increase in external quantum efficiency of the device.

EPFL2017