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Topic: Phase equilibrium

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	ASM Phase Diagrams
		When an intermediate phase of limited (or no) homogeneity range is located at or near a specific ratio of component elements that reflects the normal positioning of the component atoms in the crystal structure of the phase, it is often called a compound (or line compound).
		Phase diagrams to be used by scientists are usually plotted in atomic percentage (or mole fraction), while those to be used by engineers are usually plotted in weight percentage.
		Phase diagrams can be used in a manner similar to that used in the discussion of eutectic and eutectoid reactions to determine the microstructures expected to result from cooling an alloy through any of the other six types of reactions listed in Table 2.
	www.asminternational.org /asmenterprise/apd/help/intro.aspx (8488 words)

	Phase (matter) - Wikipedia, the free encyclopedia
		Liquid crystals are another phase intermediate between solids and liquids; the molecules of such a substance have an orderly orientation and in some cases (that is, for smectic liquid crystals) even an orderly position in one direction, but are free to flow past one another.
		In contrast, in the plasma phase the atoms are dissociated, i.e.
		These phases are of great interest to astrophysics, because these high-pressure conditions are believed to exist inside stars that have used up their nuclear fusion "fuel", such as white dwarves and neutron stars.
	en.wikipedia.org /wiki/Phase_(matter) (2698 words)

	Phase Diagrams
		This phase change is called sublimation (the reverse process is called deposition or desublimation) and the temperature at which it occurs is called the sublimation point (or sublimation temperature).
		Static equilibrium occurs whenever the components of forces and torques acting in one direction are balanced by the components of forces and torques acting in the opposite direction.
		Dynamic equilibrium occurs whenever a change in the statistical behavior of a large group of particles is balanced by an opposite change in the statistical behavior of a similarly large group of different particles.
	hypertextbook.com /physics/thermal/pressure-temperature (1460 words)

	Gibbs' phase rule - Wikipedia, the free encyclopedia
		In chemistry, Gibbs' phase rule describes the possible number of degrees of freedom (F) in a closed system at equilibrium, in terms of the number of separate phases (P) and the number of chemical components (C) in the system.
		The key thermodynamics result is that at equilibrium the Gibbs free energy change for small transfers of mass between phases is zero.
		when two phases are in equilibrium, P = 2, such as along the melting or boiling boundaries, the (intensive) variable pressure is a determined function of (intensive) variable temperature, ie.
	en.wikipedia.org /wiki/Phase_equilibrium (686 words)

	GAS-PHASE EQUILIBRIUM CALCULATIONS
		As the equilibrium concentrations of hydrogen and oxygen are small compared to the concentration of water, setting the initial concentration of water equal to its equilibrium concentration is justified.
		Occasionally, the equilibrium constant is so close to one that simplifying approximations are invalid or accurate data are available and deviations from ideal gas conditions can be properly handled.
		Equilibrium problems in the real world are usually complicated and an algebraic approach is not possible.
	pages.pomona.edu /~wes04747/handout/equil_1.htm (1736 words)

	The Thermodynamic Modeling of Multicomponent Phase Equilibria
		Phase diagrams are visual representations of the state of a material as a function of temperature, pressure, and concentrations of the constituent components and are, therefore, frequently hailed as basic blueprints or roadmaps for alloy design, development, processing, and understanding.
		Thus, all phases are assumed to be in thermodynamic equilibrium at all temperatures during solidification.
		Thermodynamic calculation of the phase equilibria of a multicomponent alloy was interfaced with a micromodel for computing the change of fraction solid and temperature, given a specified change in enthalpy during the liquid-solid transformation.
	www.tms.org /pubs/journals/JOM/9712/Kattner-9712.html (5001 words)

	Lab 5 (Site not responding. Last check: 2007-10-17)
		) with the phase boundaries correspond to the compositions of the phases at that temperature.
		The phase boundaries in the binary equilibrium phase diagram with a terminal solid solutions represent this change in solubility limit with temperature.
		Determine the composition from the quantitative metallography and the equilibrium phase diagram.
	mot.vuse.vanderbilt.edu /mse150/lab_5.htm (1707 words)

	[No title] (Site not responding. Last check: 2007-10-17)
		A vapor-liquid equilibrium ratio (K-value) is defined for a component as the ratio of mole fraction in the vapor to mole fraction in the liquid for that component.
		At equilibrium, the temperature and pressure must be the same in all phases, for thermal and mechanical equilibrium considerations (i.e., no driving forces to cause fluxes of heat or fluid movement).
		Thus, in addition to thermal and mechanical equilibrium, the chemical potential for any given component must be the same in all phases at equilibrium.
	www.che.wsu.edu /~millerrc/301-10.doc (2003 words)

	Phase equilibria menu (Site not responding. Last check: 2007-10-17)
		Explains how to interpret a simple phase diagram for a pure substance, including a look at the special cases of water and carbon dioxide.
		Explains the relationship between the cooling curves for liquid mixtures of tin and lead, and the resulting phase diagram.
		It explains how a phase diagram for such a mixture is built up and how to interpret it.
	www.chemguide.co.uk /physical/phaseeqiamenu.html (274 words)

	Chapter 9. Phase Diagrams
		But the time to achieve equilibrium may be so long (the kinetics is so slow) that a state that is not at an energy minimum may have a long life and appear to be stable.
		Hence, the new layers that solidify on top of the grains have the equilibrium composition at that temperature but once they are solid their composition does not change.
		A terminal phase or terminal solution is one that exists in the extremes of concentration (0 and 100%) of the phase diagram.
	www.virginia.edu /bohr/mse209/chapter9.htm (1145 words)

	Intute sciences - Chemical Sciences: Chemical Equilibrium: Simple Gas-Phase Equilibria (Site not responding. Last check: 2007-10-17)
		When all of the substances which participate in a chemical equilibrium are gases, it is most convenient to express the amounts of substance present per unit volume in terms of the partial pressure of each of the gases.
		The equilibrium partial pressure of chlorine in a container which has a partial pressure of 100 kPa of HCl and 1.00 Pa of hydrogen can be calculated.
		In many studies of chemical equilibria, it is either inconvenient or impractical to measure the equilibrium concentrations, partial pressures, or activities of all of the substances involved in the equilibrium.
	www.intute.ac.uk /sciences/reference/plambeck/chem1/p01111.htm (667 words)

	Gas-Phase Equilibrium
		When this system is at equilibrium, by definition, the rates of the forward and reverse reactions are equal.
		In an equilibrium reaction, even though the reaction proceeds in both directions, the reagents to the left of the arrow are assumed to be the reactants and the reagents to the right of the arrow are assumed to be the products.
		That is, this is basically the equilibrium constant expression, but when the reaction does not necessarily have to be at equilibrium.
	library.thinkquest.org /C006669/data/Chem/equilibrium/gas.html?tqskip1=1 (1626 words)

	Phase
		Its use for the phases of the moon, which repeat in a regular sequence, gave rise to its use for the time sequence of a signal, particularly a sinusoidal signal, where the phase is represented as an angle that steadily increases with time.
		The result is a two-dimensional phase diagram, as for a single substance, where the coordinates are the temperature T and the concentration c.
		A schematic phase diagram for a system in which the constituents are completely miscible in both the liquid and the solid phases is shown at the left.
	www.du.edu /~jcalvert/phys/phase.htm (6901 words)

	Ceramics Division Glossary of Terms for Phase Equilibria Diagrams (Site not responding. Last check: 2007-10-17)
		A eutectic represents an invariant point (unique temperature, pressure, composition) for a system at which the phase reaction on the addition or removal of heat results in an increase or decrease, respectively, of the proportion of liquid to solid phases, without change of temperature.
		At a eutectic point the composition of the liquid phase in equilibrium with the solid phases can always be expressed in terms of positive quantities of the solid phases.
		An invariant point composed solely of crystalline phases, at which the phase reaction on change of heat content at constant temperature results in a change in proportions of the solid phases exactly analogous to that at a eutectic point, in which one of the phases is liquid.
	www.ceramics.nist.gov /webbook/glossary/ped/e.htm (405 words)

	JOM Paper: Thermodynamic Modeling ... (Site not responding. Last check: 2007-10-17)
		Phase diagrams are visual representations of the state of a material as a function of temperature, pressure and concentrations of the constituent components and are, therefore, frequently hailed as basic blueprints or roadmaps for alloy design, development, processing and basic understanding.
		Phase equilibrium calculations can not only give the phases present and their compositions but also provide numerical values of enthalpy contents, temperature and concentration dependence of phase boundaries for coupling of microscopic and macroscopic modeling.
		Figure 5: Phase fraction vs. temperature curves for solidification of an alloy with the composition 0.21 wt.% Si, 0.23 wt.% Fe, 4.44 wt.% Cu, 0.55 wt.% Mn 1.56 wt.% Mg, 0.05 wt.% Zn and the remainder Al.
	www.metallurgy.nist.gov /phase/papers/jom/thermo_model.html (5141 words)

	Gas Phase Chemical Equilibrium (Site not responding. Last check: 2007-10-17)
		Gas phase equilibria is the introductory chapter to the topic of equilibrium.
		Here, you are expected to review the general concept of calculating equilibrium constants for any process involving a gas, a liquid, a solid or combinations of the phases.
		The equilibrium for any reaction may be shifted by external effects such as temperature, pressure, reactant concentrations, etc. You need to be able to identify the nature of such effects and be able to predict the direction of a shift.
	www.dartmouth.edu /~chem/introchem/gaseq.html (352 words)

	Metals (PHASE DIAGRAMS (EQUILIBRIUM DIAGRAMS) FOR METALLIC SYSTEMS)
		he phase diagram for water is plotted in Figure 5-9, with the pressure as ordinate and the temperature as abscissa.
		The number of phases is P = 2 because anywhere along this curve, liquid and solid phases of water coexist in equilibrium.
		Figure 5-10(a) shows a typical phase diagram for two metallic elements, and Figure 5-10(b) shows ceramic materials that are completely soluble in each other in both liquid and solid phases.
	mst-online.nsu.edu /mst/metals/metals3.htm (735 words)

	Petrography
		If the system solid-liquid is at equilibrium and the pressure is increased the phase with the highest density should be favored (that is, it should be thermodynamically stable).
		Consider two unary phase diagrams, one for phase A and one for phase B. If we were interested in the behavior of all possible mixtures between pure a and pure B then we would need three dimensions - Temperature, Pressure, and Composition (see Figure 8.
		The upper most two phase tie line illustrates that the first formed solid solution is enriched in An and that the last liquid to disappear on cooling is enriched in Ab.
	www.uh.edu /~jbutler/petrography/phase.html (4113 words)

	Phase Equilibrium and Intermolecular Interactions
		At an applied pressure of 1 atm, the temperature of the phase transition from liquid to gas is the temperature at which the vapor pressure of the liquid is equal to 1 atm.
		The first we will consider is why the pressure of a vapor in equilibrium with its liquid does not depend on the volume of the container into which the liquid evaporates, or on the amount of liquid in the container, or on the amount of vapor in the container.
		The situation is "equilibrium" in that the observable properties of the liquid and gas in the container are not changing, but the situation is "dynamic" in that there is constant movement of molecules between phases.
	cnx.org /content/m12596/latest (3887 words)

	Phase Equilibrium of Water (Site not responding. Last check: 2007-10-17)
		Convective motion tranports latent heat and sensible heat from the surface to the atmosphere to balance the energy both at the surface and the atmophere until the radiative-convective equilibrium is achieved (temperature of each layer does not vary any more).
		The climate equilibrium is not stable unless the phase equilibrium of water is achieved.
		The phase equilibrium is another requirement in addition to the radiative energy balance at the top of the atmosphere and the convective stable state of the lower atmosphere.
	asd-www.larc.nasa.gov /~yhu/paper/thesisall/node62.html (161 words)

	LearnSeq3W51
		The phase diagram is a type of map that allows us to predict what will happen when we change the temperature or the overall composition of the material.
		LEVER RULE: The relative fraction of material present in a particular phase is equal to the ratio of the tie line portion which lies between the overall composition and the phase boundary curve away from the phase of interest, to the total tie line length.
		What are the compositions of the phases in equilibrium when the overall composition of the solid is 40% MgO (and 60% NiO) at 2300° C. Same question for 20% MgO, and 80% MgO.
	www.mrl.ucsb.edu /~edkramer/LectureVGsMat100B/99Lecture13VGs/LearnSeqPhaseDiagrams.html (2633 words)

	Phases of Matter
		The liquid / vapor equilibrium curve follows a simple relation, because the amount of heat needed to vaporize the gas (molecular stickiness) determines the vapor pressure.
		The equation governing the pressure of a gas in equilibrium with a solid or a liquid can be derived from the postulates of Thermodynamics and is a milestone in the fundamental understanding of Phase Equilibria.
		At POINT C and POINT D on the diagram, two phases are in equilibrium and off the line entirely there is only one stable phase of the substance.
	itl.chem.ufl.edu /2045_s00/lectures/lec_f.html (1197 words)

	Gibbs Phase Rule :: Computational Thermodynamics
		In other words, the number of degrees of freedom for a system at equilibrium is the number of intensive variables (often taken as the pressure, temperature, and composition fraction) that may be arbitrarily specified without changing the number of phases.
		In a region with M stable phases, the values of N-M+2 state variables can be changed independently and preserving the same set of stable phases.
		The sum of each of the stable phases multiplied by the amount of that phase is equal to the Gibbs energy of the whole system.
	www.calphad.com /gibbs_phase_rule.html (302 words)

	Gas-Vapor Phase Equilibrium
		The (saturation) condition for the simultaneous existence of the liquid and gas phases is, in general, a consequence of the equality of the chemical potentials of the condensable substance in each phase (or equivalently in this case, the equality of their fugacities).
		, f is the fugacity, g denotes the gas phase, liq denotes the liquid phase and y is the mole fraction of the condensable component, A, in the gas.
		Assuming that the exit gas stream is in equilibrium with the condensed (n-hexane) liquid stream, the n-hexane partial pressure in the exit stream is the saturation pressure corresponding to the exit temperature.
	www.mathtrek.com /contents/gvtut.html (2209 words)

	[No title]
		A phase diagram is a plot of P vs. T and is composed of lines that indicate the points at which two or more phases are in equilibrium with each other and therefore will coexist.
		If there is a potential difference between the two like phases across a membrane and the solute is ionic, both the concentration difference and the overall electrical potential difference influence the transition across the membrane.
		At low temperature both the surface, hydrophilic portion and the hydrophobic phase of the bilayer are fairly rigid.
	faculty.css.edu /pstein/CHM3460/Tinoco5.doc (1197 words)

	[No title]
		By definition, the kinetic region is the period during which the concentrations of the components of the reaction are constantly changing.
		The equilibrium region is the period after which the reaction seems to stop, when there is no further change in the concentrations of the components of the reaction.
		Reversible reactions that reach equilibrium are indicated by a pair of arrows between the two sides of the equation.
	chemed.chem.purdue.edu /genchem/topicreview/bp/ch16/gasframe.html (913 words)

	Two Phase Equilibrium
		Both solid and liquid phases are present and in equilibrium.
		Neither phase is moving, neither is changing into the other, and both phases are at the same temperature, 0 degrees C. The water was originally warmer (20 C, and the ice was originally cooler (5 C).
		Oil and water mixed together and sealed in a jar might be considered two phases in equilibrium, too.
	www.newton.dep.anl.gov /askasci/gen01/gen01744.htm (731 words)

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