From J.R. Waldram “The Theory of Thermodynamics”

From J.R. Waldram“The Theory of Thermodynamics”

Alloy phase diagram of Cu-Ni

http://people.virginia.edu/~lz2n/mse209/Chapter9-p1.pdf

Eutectic Phase Diagram

http://www.tulane.edu/~sanelson/geol212/2compphasdiag.html

NOTE: 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

Critical Opalescence

A somewhat more “dramatic”, but less useful version of the same thing may be seen at the site:http://www.youtube.com/watch?v=2xyiqPgZVyw&feature=related

At 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/watch?v=OgfxOl0eoJ0

A 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/watch?v=yBRdBrnIlTQ&feature=fvw

Fe-C Phase Diagram

Austenite: gFerrite: dMartensite: metastable phase formed by quenching g into the 2-phase region.

From T. B. MassalskiAtlas of Binary Phase Diagrams

Solid 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 and growth (left, see HW11) vs. “spinodal decomposition”

Proposed Nuclear Matter phase diagram

http://www.kfa-juelich.de/nic/Publikationen/Broschuere/Elementarteilchenphysik/hadron.jpg

Quark Gluon plasma (RHIC)

http://www.google.com/imgres?imgurl=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_decomposition

See the wikipedia article on this for a nice “movie” of how the microstructure evolves.

From Zemansky “Heat and Thermodynamics”

From Chaikin and Lubensky:“Principles of Condensed Matter Physics” 1995.

MFT

From Kadanoff et al. Rev. Mod. Phys. 35, 395 (1967)

NOTE: similar b values for magnetismAnd gases!

Superfluid Transition: 4He

The above figure is taken from:http://hyperphysics.phy-astr.gsu.edu/Hbase/lhel.html#c2

Interesting video of the properties of superfluid He is available at:http://www.youtube.com/watch?v=2Z6UJbwxBZI

Ferromagnetic Iron

Ferromagnetic Materials

If the sample is small enough, or the specific magnetization big enough, the domains may be arranged is a less-that-random arrangement that leads to zero net magnetization for the sample (thereby minimizing the energy associated with the stray field). The above figure from the text demonstrates the typical pattern for a small needle (whisker) of material.

Critical Exponents

From P. Chaikin and T Lubensky“Principles of Condensed Matter Physics”

Notice that convention allows for different exponents on either side of the transition, but often these are found to be the same.

Universality Classes

From P. Chaikin and T Lubensky “Principles of Condensed Matter Physics”

Theory suggests that the class (i.e. set of exponents) depends on spatial dimensionality, symmetry of the order parameter and interaction (and range of the latter as well) but not on the detailed form or strength of the interactions

Ising Model• Consider 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 (for site I, two possible values).• We assume ONLY nearest-neighbor interactions, and 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

and sj are of the same sign)• Exact solutions have been found for 1 and 2 dimensions, not yet for 3

dimensions.• Applications:

• Magnetism (both ferromagnetism and antiferromagnetism)• Binary alloys while assuming random arrangements of atoms (Bragg-

Williams model) shows phase separation for J>0.• Binary alloys with correlations between bonding and configuration

treated via the law of mass action (i.e. bonds forming and breaking; the “Quasi-chemical” approximation) can show order-disorder transitions as well as phase separation etc.