Alloy phase diagram of Cu-Ni Eutectic Phase Diagram Critical Opalescence Fe-C Phase Diagram Proposed Nuclear Matter phase diagram
Cravotta, Nicholas, Contributing Technical Editor has reference to this Academic Journal, PHwiki organized this Journal From J.R. WaldramThe Theory of ThermodynamicsAlloy phase diagram of Cu-Nihttp://people.virginia.edu/~lz2n/mse209/Chapter9-p1.pdfEutectic Phase Diagramhttp://www.tulane.edu/~sanelson/geol212/2compphasdiag.htmlNOTE: at a given overall composition (say: X), both the relative amounts of the two phases (a,b or c,d) AND the composition of one (or possibly both) depend on the temperature
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Critical OpalescenceA somewhat more dramatic, but less useful version of the same thing may be seen at the site:http://www.youtube.com/watchv=2xyiqPgZVyw&feature=relatedAt the critical point in a fluid, you get large fluctuations in the density (because the energy cost of creating density changes goes to zero). Consequently, the fluid scatters light very well right at the transition. A goo example of this can be seen in the You-tube video:http://www.youtube.com/watchv=OgfxOl0eoJ0A demonstration with a clearer explanation (by Martin Poliokoff of U. Nottingham) of what is happening, but less compelling video, may be seen at:http://www.youtube.com/watchv=yBRdBrnIlTQ&feature=fvwFe-C Phase DiagramAustenite: gFerrite: dMartensite: metastable phase as long as med by quenching g into the 2-phase region.From T. B. MassalskiAtlas of Binary Phase DiagramsSolid lines show Fe-C equilibrium Phase Diagram, Dashed lines show metastableFe-Fe3C diagram
Quenching Al-Zn alloys into metastable (left ) or unstable (middle) areas of the phase diagram. Notice the different morphology of the phase separated regions as the alloy is allowed to approach equilibrium. Nucleation in addition to growth (left, see HW11) vs. spinodal decompositionProposed Nuclear Matter phase diagramhttp://www.kfa-juelich.de/nic/Publikationen/Broschuere/Elementarteilchenphysik/hadron.jpgQuark Gluon plasma (RHIC)http://www.google.com/imgresimgurl=http://gruppo3.ca.infn.it/usai/cmsimple3-0/images/PhaseDiagram.png&imgrefurl=http://gruppo3.ca.infn.it/usai/%3FResearch:Phase-Transition&h=771&w=1042&sz=200&tbnid=0xQaMFwZufgtxM:&tbnh=111&tbnw=150&prev=/images%3Fq%3DQuark%2Bgluon%2Bplasma%2Bphase%2Bdiagram&usg=-OGqEE-0lIz0fOUddpDFtuCIgeG8=&ei=4HXMS8GkBILw9AS-uoTCBg&sa=X&oi=image-result&resnum=3&ct=image&ved=0CAoQ9QEwAg
Spinodal Decomposition (unstable part of a binary phase diagram)http://en.wikipedia.org/wiki/Spinodal-decompositionSee the wikipedia article on this as long as a nice movie of how the microstructure evolves.From Zemansky Heat in addition to Thermodynamics From Chaikin in addition to Lubensky:Principles of Condensed Matter Physics 1995.MFT
From Kadanoff et al. Rev. Mod. Phys. 35, 395 (1967)NOTE: similar b values as long as magnetismAnd gases!Superfluid Transition: 4HeThe above figure is taken from:http://hyperphysics.phy-astr.gsu.edu/Hbase/lhel.html c2Interesting video of the properties of superfluid He is available at:http://www.youtube.com/watchv=2Z6UJbwxBZIFerromagnetic Iron
Ferromagnetic MaterialsIf the sample is small enough, or the specific magnetization big enough, the domains may be arranged is a less-that-r in addition to om arrangement that leads to zero net magnetization as long as the sample (thereby minimizing the energy associated with the stray field). The above figure from the text demonstrates the typical pattern as long as a small needle (whisker) of material.Critical ExponentsFrom P. Chaikin in addition to T LubenskyPrinciples of Condensed Matter PhysicsNotice that convention allows as long as different exponents on either side of the transition, but often these are found to be the same. Universality ClassesFrom P. Chaikin in addition to T Lubensky Principles of Condensed Matter PhysicsTheory suggests that the class (i.e. set of exponents) depends on spatial dimensionality, symmetry of the order parameter in addition to interaction ( in addition to range of the latter as well) but not on the detailed as long as m or strength of the interactions
Ising ModelConsider a lattice on which each site is occupied by either a + or a (up or down spin to model magnetism, A or B element to model a binary alloy etc.).Label each such state as si ( as long as site I, two possible values).We assume ONLY nearest-neighbor interactions, in addition to describe that interaction with a single energy scale J.The total configurational energy is then: E = -J Snn(si sj)In this model J>0 suggests like neighbors are preferred (lower energy if si in addition to sj are of the same sign)Exact solutions have been found as long as 1 in addition to 2 dimensions, not yet as long as 3 dimensions.Applications:Magnetism (both ferromagnetism in addition to antiferromagnetism)Binary alloys while assuming r in addition to om arrangements of atoms (Bragg-Williams model) shows phase separation as long as J>0.Binary alloys with correlations between bonding in addition to configuration treated via the law of mass action (i.e. bonds as long as ming in addition to breaking; the Quasi-chemical approximation) can show order-disorder transitions as well as phase separation etc.
Cravotta, Nicholas Contributing Technical Editor
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