Lee O Case's "Elements of the Phase Rule", Introduction and Explanation

This out of print 1939 manuscript, updated, is added to the literature with slight additions

Phase behavior and far-from-equilibrium gelation in charged attractive colloids

In this Rapid Communication we demonstrate the applicability of an augmented Gibbs ensemble Monte Carlo approach for the phase behavior determination of model colloidal systems with short-ranged depletion attraction and long-ranged repulsion. This technique allows for a quantitative determination of the phase boundaries and ground states in such systems. We demonstrate that gelation may occur in systems of this type as the result of arrested microphase separation, even when the equilibrium state of the system is characterized by compact microphase structures.

Phase coexistence of cluster crystals: beyond the Gibbs phase rule

We report a study of the phase behavior of multiple-occupancy crystals through simulation. We argue that in order to reproduce the equilibrium behavior of such crystals it is essential to treat the number of lattice sites as a constraining thermodynamic variable. The resulting free-energy calculations thus differ considerably from schemes used for single-occupancy lattices. Using our approach, we obtain the phase diagram and the bulk modulus for a generalized exponential model that forms cluster crystals at high densities. We compare the simulation results with existing theoretical predictions. We also identify two types of density fluctuations that can lead to two sound modes and evaluate the corresponding elastic constants.

Phase equilibria and surface tension of pure fluids using a molecular layer structure theory (MLST) model

This paper presents a new model based on thermodynamic and molecular interaction between molecules to describe the vapour-liquid phase equilibria and surface tension of pure component. The model assumes that the bulk fluid can be characterised as set of parallel layers. Because of this molecular structure, we coin the model as the molecular layer structure theory (MLST). Each layer has two energetic components. One is the interaction energy of one molecule of that layer with all surrounding layers. The other component is the intra-layer Helmholtz free energy, which accounts for the internal energy and the entropy of that layer. The equilibrium between two separating phases is derived from the minimum of the grand potential, and the surface tension is calculated as the excess of the Helmholtz energy of the system. We test this model with a number of components, argon, krypton, ethane, n-butane, iso-butane, ethylene and sulphur hexafluoride, and the results are very satisfactory. (C) 2002 Elsevier Science B.V. All rights reserved.

European Union emissions trading scheme impact on the Spanish electricity price during phase II and phase III implementation

The European Union Emissions Trading Scheme (EU ETS) is a cornerstone of the European Union's policy to combat climate change and its key tool for reducing industrial greenhouse gas emissions cost-effectively. The purpose of the present work is to evaluate the influence of CO2 opportunity cost on the Spanish wholesale electricity price. Our sample includes all Phase II of the EU ETS and the first year of Phase III implementation, from January 2008 to December 2013. A vector error correction model (VECM) is applied to estimate not only long-run equilibrium relations, but also short-run interactions between the electricity price and the fuel (natural gas and coal) and carbon prices. The four commodities prices are modeled as joint endogenous variables with air temperature and renewable energy as exogenous variables. We found a long-run relationship (cointegration) between electricity price, carbon price, and fuel prices. By estimating the dynamic pass-through of carbon price into electricity price for different periods of our sample, it is possible to observe the weakening of the link between carbon and electricity prices as a result from the collapse on CO2 prices, therefore compromising the efficacy of the system to reach proposed environmental goals. This conclusion is in line with the need to shape new policies within the framework of the EU ETS that prevent excessive low prices for carbon over extended periods of time.

Pseudo Phase Plane and Fractional Calculus Modelling of Western Global Economic Downturn

This paper applies Pseudo Phase Plane (PPP) and Fractional Calculus (FC) mathematical tools for modeling world economies. A challenging global rivalry among the largest international economies began in the early 1970s, when the post-war prosperity declined. It went on, up to now. If some worrying threatens may exist actually in terms of possible ambitious military aggression, invasion, or hegemony, countries’ PPP relative positions can tell something on the current global peaceful equilibrium. A global political downturn of the USA on global hegemony in favor of Asian partners is possible, but can still be not accomplished in the next decades. If the 1973 oil chock has represented the beginning of a long-run recession, the PPP analysis of the last four decades (1972–2012) does not conclude for other partners’ global dominance (Russian, Brazil, Japan, and Germany) in reaching high degrees of similarity with the most developed world countries. The synergies of the proposed mathematical tools lead to a better understanding of the dynamics underlying world economies and point towards the estimation of future states based on the memory of each time series.

Kinetics of crystal growth and equilibrium domains in eclogite of the Sesia Zone, Western Alps

Kinetics of crystal growth and equilibrium domains in eclogite of the Sesia Zone, Western Alps Darbellay Bastien Institut de Minéralogie et Géochimie Résumé grand public Comme toute matière, la roche est sensible à son environnement et cherche à s'adapter pour acquérir un état stable (état d'équilibre). Les changements des conditions physiques (température et pression) vont ainsi impliquer des modifications dans la roche. Le métamorphisme est l'étude de ces changements. Les minéraux qui constituent la roche peuvent modifier, leur structure, leur chimie ou être remplacer par d'autres minéraux plus stables. Il est ainsi crucial de déterminer les processus responsables et limitant de la croissance minérale. Trois processus permettent la croissance ; (1) la dissolution des éléments du réactant, (2) le transport de ces éléments vers le site de croissance, (3) l'incorporation de ces éléments dans la nouvelle structure. Cette thèse se focalise sur les structures des minéraux de haute pression (forme, zonation chimique, structure interne) pour essayer de déterminer les facteurs importants à l'origine de leur état final. Les zones d'étude se situent dans la zone de Sésia. La première partie traite de la problématique liée à l'incorporation d'un élément dans une structure minérale. A l'image de la croissance humaine, les irrégularités minéralogiques permettent de mettre en lumière un dysfonctionnement de la croissance due à un excès ou à une carence d'un élément. Bien dosé, cet élément est cependant essentiel à la croissance. Les zoisites (épidotes) des métabasites de la région de Cima di Bonze montrent une zonation chimique en sablier. Dans cette zonation la teneur en fer excède la capacité maximum que peut contenir la structure orthorhombique de la zoisite. Des défauts de structure permettent l'accommodation de cet excès. La zoisite peut ainsi adapter sa structure pour permettre l'incorporation d'une relativement grande quantité de fer. Les études précédentes montraient, pour des conditions similaires, la formation de deux épidotes distinctes. La deuxième partie se penche sur la compétition entre le minéral qui fait sa croissance et les minéraux (réactants) qui l'entourent. Les métapélites de la région du Monte Mucrone contiennent des grenats atollaires. Des études détaillées de la texture et de la zonation chimique du grenat ainsi qu'une modélisation thermodynamique ont permis de mieux cerner les facteurs importants responsables de la forme atollaire. Cette structure est obtenue par un changement du comportement de la croissance du grenat le long d'un chemin P-T hercynien. Dans un premier stade, le grenat croît rapidement et consume peu le quartz de la matrice. La croissance se fait ainsi le long des jointures des grains de quartz. Dans un second temps, les changements de conditions PT donnent une croissance lente du grenat et une forte consommation du quartz. Le grenat peut ainsi développer sa forme dodécaédrale classique. La troisième partie s'intéresse aux distances de transport par diffusion d'un élément (ici l'argon) durant la haute pression. Pour ce faire, un profile d'âges 40Ar/39Ar sur biotite a été mesuré depuis un veine de haute pression riche en argon jusque dans son encaissant (granitoïd du Monte Mucrone). Le profile montre une répartition des âges suivant une courbe de diffusion. Le transport se fait sur une longueur de deux centimètre avec l'aide d'un fluide. Il est réduit à une échelle millimétrique quand la phase fluide disparaît. Cette étude montre ainsi les difficultés de transport des éléments durant la haute pression ne permettant pas un rééquilibrage de la roche à grande échelle. Kinetics of crystal growth and equilibrium domains in eclogite of the Sesia Zone, Western Alps Darbellay Bastien Institut de Minéralogie et Géochimie Résumé de thèse Les processus de croissance (diffusion des éléments et les réactions d'interface) et les conditions dans lesquelles les minéraux grandissent (température, pression, fluide, composition chimique de la roche), déterminent la texture ainsi que la zonation des minéraux. Cette thèse se focalise, par le biais de textures peu communes, sur trois différents processus impliqués dans la croissance minérale à haute pression (Zone de Sésia, Alpes de l'Ouest, Italie). L'incorporation d'un élément dans une structure minérale ne peut se faire que dans des sites en accord avec la taille et la charge ionique de l'élément. De plus, la balance de charge doit être maintenue dans le minéral. La régularité de la structure cristalline fixe ainsi une limite maximum de concentration d'un élément donné. Les zoisites provenant des métabasites de la région de Cima di Bonze montrent des zonations en sablier caractérisées par une concentration anormale en fer. La zonation se marque par une différente teinte de biréfringence et par un plus grand angle d'extinction que le reste de la zoisite. Une inter-croissance de clinozoisite à l'intérieur de la structure orthorhombique de la zoisite peut ainsi être suspectée. Les analyses XRD (diffraction des rayons x) ainsi que les analyses Raman ne confirment pas cette suspicion. Seules les analyses TEM (microscope à électrons transmis) montrent des défauts de structure pouvant être interprétés comme des modules de clinozoisite. Ils ne peuvent cependant pas être considérés comme une phase thermodynamique. Un nouveau trou d'immiscibilité entre deux zoisite (X ep= 0.1 and Xep = 0.15) a ainsi pu être établi. Dans les métapélites la région du Monte Mucrone, des grenats fortement zonés montrent une évolution texturale singulière. Ils présentent une forme initiale de `champignon' qui se développe pour former une structure atollaire finale. L'étude conjuguée de la structure 3D et des zonations, ainsi que l'établissement d'un model thermodynamique, indiquent que ces structures proviennent de deux épisodes de croissances : (1) La croissance du grenat durant un chemin prograde hercynien (de 525 °C et 6.2 kbar à 640 °C et 9 kbar) permet la formation des textures atollaires. Elles sont le résultat d'une croissance poecilitique initiale suivie d'une croissance idiomorphique du grenat. (2) La structure est rendue plus complexe par la cristallisation d'un grenat homogène tout autour ainsi qu'à l'intérieur du grenat hercynien durant la haute pression alpine (550 °C and 20 kbar). L'arrivée de l'eau durant la haute pression facilite le transport d'éléments et permet une cristallisation rapide du grenat. La diffusion peut être un facteur limitant de la croissance minéralogique. Elle a aussi une grande importance pour la géochronologie. Une veine de haute pression à l'intérieur du granitoïde du Monte Mucrone a été étudiée dans le but de déterminer la distance de diffusion de l'argon. Le profile d'âges 40Ar/39Ar sur biotites, établi de la veine vers le métagranitoïde, suit une courbe de diffusion. Les âges sont élevés proche de la veine (800 Ma) puis décroissent jusqu'à des âges homogènes (170-150 Ma) à deux centimètres de la veine. La présence de fluide, marqué par de hautes concentrations en chlore, permet une diffusion centimétrique. Cependant, la distance est réduite à une échelle millimétrique quand le fluide est absent. Les très faibles distances de diffusion préservent les âges pré-alpins et impliquent un événement géologique pour les âges de 170-150 Ma. Kinetics of crystal growth and equilibrium domains in eclogite of the Sesia Zone, Western Alps Darbellay Bastien Institut de Minéralogie et Géochimie Thesis abstract Rock textures and zonings are the consequence of growth processes (element diffusion and interface reaction) steered by the environment in which they grew (pressure, differential stress, temperature, fluid and rock composition). The thesis presented here focuses on three different topics, each of it dealing with aspects of mineral growth processes during subduction, in a high-pressure environment. All studies were conducted in the Sesia Zone of the Western European Alps, Italy. The first study addresses the crystallography and geochemistry of element incorporation in zoisite, one of the major hydrous minerals found in subduction zone rocks. Elements can be incorporated into a mineral structure only on crystallographic sites that offer enough space for the ion and the overall charge balance has to be maintained. Element concentrations are hence limited. Incorporation of some elements produces complex zoning, including hourglass like patterns, which are the focus of the first contribution. Zoisites from Cima di Bonze (Sesia Zone) show spectacular hourglass zoning defined by Fe-content variations. The hourglass zones have a distinct birefringence and a different extinction angle than the regular part of the zoisite. We show by detailed XRD (X-ray diffraction) and confocal Raman analyses that the high Fe-zones are nevertheless zoisite, and not clinozoisite as one might expect. High resolution TEM (transmission electron microscopy) analyses show planar defects on (100) that can be interpreted as small-scale clinozoisite modules. However, these clinozoisites cannot be interpreted as a distinctive thermodynamic phase and the entire mineral has to be considered as zoisite. The miscibility gap between two zoisites (Xep = 0.1 and Xep = 0.15) can be then definite at 550 ± 50°C and 14 to 20 Kbar. Strongly zoned garnets in quartz rich metapelite from the Monte Mucrone area (Sesia Zone) show evolution form 3D mushroom to atoll structure. The second contribution presents textural investigations, garnet zoning and thermodynamic modeling that demonstrate that atoll garnets are the result of two distinctive growth events. (1) Garnet atoll structure is already formed during a prograde Hercynian path from 525 °C and 6.2 kbar to 640 °C and 9 kbar. It results in an initial poikilitic growth followed by a final idiomorphic growth event. (2) Alpine HP garnet are homogenous (550 °C and 20 kbar) and grew around and also inside the Hercynian garnet. Lack of prograde Alpine garnet and fast growth of the HP garnet is explained by the absence of water during much of the prograde path. Water saturation was only observed towards the end, close towards the peak metamorphic conditions. Diffusion could be a limiting factor for crystal growth. It has also a great importance in geochronology. HP vein inside the metagranitoide of the Monte Mucrone (~300 Ma) was investigated to determine argon diffusion scales during high-pressure metamorphism. 40Ar/39Ar biotite ages profile from the vein toward the metagranodiorite show a diffusion curve: old ages (800 Ma) located close to the vein decrease until homogenous 170-150 Ma ages are obtained, two centimeter away from the vein. Centimeter-scale diffusion occurs with help of a fluid phase marked by high chlorine concentrations. Argon diffusion is reduced to a millimeter scale when free fluid is absent. Very short diffusion distance permits to preserve pre-Alpine ages. The 170-150 Ma ages are considered to be geologic meaningful, probably resulting from the extensional tectonics linked to opening of the Tethian ocean.

Quantification of magmatic and hydrothermal processes in a peralkaline syenite-alkali granite complex based on textures, phase equilibria, and stable and radiogenic isotopes

The Puklen complex of the Mid-Proterozoic Gardar Province, South Greenland, consists of various silica-saturated to quartz-bearing syenites, which are intruded by a peralkaline granite. The primary mafic minerals in the syenites are augite +/- olivine + Fe-Ti oxide + amphibole. Ternary feldspar thermometry and phase equilibria among mafic silicates yield T = 950-750degreesC, a(SiO2) = 0.7-1 and an f(O2) of 1-3 log units below the fayalite-magnetite-quartz (FMQ) buffer at 1 kbar. In the granites, the primary mafic minerals are ilmenite and Li-bearing arfvedsonite, which crystallized at temperatures below 750degreesC and at f(O2) values around the FMQ buffer. In both rock types, a secondary post-magmatic assemblage overprints the primary magmatic phases. In syenites, primary Ca-bearing minerals are replaced by Na-rich minerals such as aegirine-augite and albite, resulting in the release of Ca. Accordingly, secondary minerals include ferro-actinolite, (calcite-siderite)(ss), titanite and andradite in equilibrium with the Na-rich minerals. Phase equilibria indicate that formation of these minerals took place over a long temperature interval from near-magmatic temperatures down to similar to300degreesC. In the course of this cooling, oxygen fugacity rose in most samples. For example, late-stage aegirine in granites formed at the expense of arfvedsonite at temperatures below 300degreesC and at an oxygen fugacity above the haematite-magnetite (HM) buffer. The calculated delta(18)O(melt) value for the syenites (+5.9 to +6.3parts per thousand) implies a mantle origin, whereas the inferred delta(18)O(melt) value of <+5.1parts per thousand for the granitic melts is significantly lower. Thus, the granites require an additional low-delta(18)O contaminant, which was not involved in the genesis of the syenites. Rb/Sr data for minerals of both rock types indicate open-system behaviour for Rb and Sr during post-magmatic metasomatism. Neodymium isotope compositions (epsilonNd(1170 Ma) = -3.8 to -6.4) of primary minerals in syenites are highly variable, and suggest that assimilation of crustal rocks occurred to variable extents. Homogeneous epsilon(Nd) values of -5.9 and -6.0 for magmatic amphibole in the granites lie within the range of the syenites. Because of the very similar neodymium isotopic compositions of magmatic and late- to post-magmatic minerals from the same syenite samples a principally closed-system behaviour during cooling is implied. In contrast, for the granites an externally derived fluid phase is required to explain the extremely low epsilon(Nd) values of about -10 and low delta(18)O between +2.0 and +0.5parts per thousand for late-stage aegirine, indicating an open system in the late-stage history. In this study we show that the combination of phase equilibria constraints with stable and radiogenic isotope data on mineral separates can provide much better constraints on magma evolution during emplacement and crystallization than conventional whole-rock studies.

(E)-2-Nonenal determination in brazilian beers using headspace solid-phase microextraction and gas chromatographic coupled mass spectrometry (HS-SPME-GC-MS)

(E)-2-nonenal is considered an important off-flavor of beer, related to the flavor of beer staling. In this study, a new method for determination of (E)-2-nonenal in beer using headspace solid-phase microextraction and gas chromatographic coupled mass spectrometry (HS-SPME-GC-MS) was developed and applied in Brazilian beer samples. The extractions were carried out in CAR-PDMS (carboxen-polydimethylsiloxane) fiber and the best results were found with 15 minutes of equilibrium and 90 minutes of extraction at 50 °C. The method was linear in the range from 0.02 to 4.0 μg.L-1 with correlation coefficient of 0.9994. The limits of detection and quantification were 0.01 and 0.02 μg.L-1, respectively. 96.5% of recovery and 4% precision (RSD) were obtained in the fortification of beer samples with 2.0 μg.L-1 of (E)-2-nonenal. The developed method proved to be simple, efficient and highly sensitive to the determination of this analyte being easily applied in the quality control of the brewery. (E)-2-nonenal was found in all beer samples analyzed with levels between 0.17 and 0.42 μg.L-1.

Phase separation and surface segregation in ceria-zirconia solid solutions

Using a combination of density functional theory calculations and statistical mechanics, we show that a wide range of intermediate compositions of ceria – zirconia solid solutions are thermodynamically metastable with respect to phase separation into Ce-rich and Zr-rich oxides. We estimate that the maximum equilibrium concentration of Zr in CeO2 at 1373 K is ~2%, and therefore equilibrated samples with higher Zr content are expected to exhibit heterogeneity at the atomic scale. We also demonstrate that in the vicinity of the (111) surface, cation redistribution at high temperatures will occur with significant Ce enrichment of the surface, which we attribute to the more covalent character of Zr-O bonds compared to Ce-O bonds. Although the kinetic barriers for cation diffusion normally prevent the decomposition/segregation of ceria-zirconia solid solutions in typical catalytic applications, the separation behaviour described here can be expected to occur in modern three-way catalytic converters, where very high temperatures are reached.

First-Principles Study of Pressure-Induced Phase Transitions and Electronic Properties of Ag2MoO4

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Solid-phase Microextraction and Detection of Organophosphate Triesters in Indoor air

In the work underlying this thesis solid-phase microextraction (SPME) was evaluated as a passive sampling technique for organophosphate triesters in indoor air. These compounds are used on a large scale as flame-retarding and plastizicing additives in a variety of materials and products, and have proven to be common pollutants in indoor air. The main objective of this work was to develop an accurate method for measuring the volatile fraction. Such a method can be used in combination with active sampling to obtain information regarding the vapour/particulate distribution in different indoor environments. SPME was investigated under both equilibrium and non-equilibrium conditions and parameters associated with these different conditions were estimated. In Paper I, time-weighted average (TWA) SPME under dynamic conditions was investigated in order to obtain a fast air sampling method for organophosphate triesters. Among the investigated SPME coatings, the absorptive PDMS polymer had the highest affinity for the organophosphate triesters and was consequently used in all further work. Since the sampling rate is dependent on the agitation conditions, the linear airflow rates had to be carefully considered. Sampling periods as short as 1 hour were shown to be sufficient for measurements in the ng-μg m-3 range when using a PDMS 100-μm fibre and a linear flow rate above 7 cm s-1 over the fibre. SPME under equilibrium conditions is rather time-consuming, even under dynamic conditions, for slowly partitioning compounds such as organophosphate triesters. Nevertheless, this method has some significant advantages. For instance, the limit of detection is much lower compared to 1 h TWA sampling. Furthermore, the sampling time can be ignored as long as equilibrium has been attained. In Paper II, SPME under equilibrium conditions was investigated and evaluated for organophosphate triester vapours. Since temperature and humidity are closely associated with the distribution constant a simple study of the effect of these parameters was performed. The obtained distribution constants were used to determine the air levels in a common indoor environment. SPME and parallel active sampling on filters yielded similar results, indicating that the detected compounds were almost entirely associated with the vapour phase To apply dynamic SPME method in the field a sampler device, which enables controlled linear airflow rates to be applied, was constructed and evaluated (Paper III). This device was developed for application of SPME and active sampling in parallel. A GC/PICI-MS/MS method was developed and used in combination with active sampling of organophosphate triesters in indoor air (Paper IV). The combination of MS/MS and the soft ionization achieved with methanol as reagent gas yielded high selectivity and detection limits comparable to those provided by GC with nitrogen-phosphorus detection (NPD). The method limit of detection, when sampling 1.5 m3 of air, was in the range 0.1-1.4 ng m-3. In Paper V, the developed MS method was used in combination with SPME for indoor air measurements. The levels detected in the investigated indoor environments range from a few ng to μg m-3. Tris(2-chloropropyl) phosphate was detected at a concentration as high as 7 μg m-3 in a newly rebuilt lecture room.

Lee O Case's "Elements of the Phase Rule", Chapter 3

This is the last (third) chapter of the phase rule text, again altered by the author, addressing 3 and 4 compnent systems.

(Table 3) Run conditions and phase relations and proportions during cooling rate experiments on ODP Interval 163-989B-10R-7,55-59

Equilibrium melting and controlled cooling experiments were undertaken to constrain the crystallization and cooling histories of tholeiitic basalts recovered by the Ocean Drilling Program drilling of Site 989 on the Southeast Greenland continental margin. Isothermal experiments conducted at 1 atm. and at the fayalite-magnetite-quartz buffer using lava sample Section 163-989B-10R-7 yielded the equilibrium appearance sequence with decreasing temperature: olivine at 1184 ± 2ºC; plagioclase at 1177ºC ± 5ºC; augite at 1167 ± 5ºC; and pigeonite at 1113 ± 12ºC. In controlled cooling experiments using the same starting composition and cooling rates between 10ºC/hr and 2000ºC/hr, we find a significant temperature delay in the crystallization of olivine, plagioclase, and augite (relative to the equilibrium appearance temperature); pigeonite does not form under any dynamic crystallization conditions. Olivine exhibits the largest suppression in appearance temperature (e.g., 30º for 10ºC/hr and >190º at 100ºC/hr), while plagioclase shows the smallest (~10ºC at 10ºC/hr; 30ºC at 100ºC/hr, and ~80ºC at 1000ºC/hr). These results are in marked contrast to those obtained on lunar basalts, which generally show a large suppression of plagioclase crystallization and modest suppression of olivine crystallization with an increased cooling rate. The results we report agree well with the petrography of lavas recovered from Site 989. Furthermore, the textural analysis of run products, representing a large range of cooling rates and quench temperatures (1150ºC to 1000ºC), provide a framework for evaluating cooling conditions necessary for glass formation, rates of plagioclase growth, and kinetic factors governing plagioclase growth morphology. Specifically, we use these insights to interpret the textural and mineralogical features of the unusual compound flow recovered at Site 989. We concluded from the analysis that this flow most likely records multiple breakouts from a distal tube at an abrupt break in slope, possibly a fault scarp, resulting in the formation of a lava fan delta. This interpretation implies that normal faulting of the oldest lava sequences (lower and, possibly, middle series) preceded eruption of Site 989 lavas.