Eutectic Phase Diagram 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

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

Fe-C Phase Diagram Austenite:  Ferrite:  Martensite: metastable phase formed by quenching  into the 2-phase region. From T. B. Massalski Atlas of Binary Phase Diagrams Solid lines show Fe-C equilibrium Phase Diagram, Dashed lines show metastable Fe-Fe 3 C diagram

Al-Zn phase diagram unstable metastable

The pictures on the left show electron micrographs of alloys “Quenched Al-Zn alloys” The samples of different composition (horizontally) wer cooled quickly to lower temperature and then the pictures were taken as a function of time (vertical). The left column is a quench into the metastable portion of the diagram whereas the middle went into an unstable area 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) vs. “spinodal decomposition” (center)

Spinodal Decomposition (unstable part of a binary phase diagram) See the wikipedia article on this for a nice “movie” of how the microstructure evolves.

Proposed Nuclear Matter phase diagram

Quark Gluon plasma (RHIC) 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

Critical Opalescence A somewhat more “dramatic”, but less useful version of the same thing may be seen at the site: 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: A demonstration with a clearer explanation (by Martin Poliokoff of U. Nottingham) of what is happening, but less compelling video, may be seen at:

Ferromagnetism “unmagnetised” Ferromagnet “Magnetised” Ferromagnet

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.

Superfluid Transition: 4 He The above figure is taken from: Interesting video of the properties of superfluid He is available at:

From Zemansky “Heat and Thermodynamics” From Chaikin and Lubensky: “Principles of Condensed Matter Physics” MFT

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.

From Kadanoff et al. Rev. Mod. Phys. 35, 395 (1967) NOTE: similar  values for magnetism And gases!

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  i (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  nn (  i  j ) In this model J>0 suggests like neighbors are preferred (lower energy if  i and  j 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.

Order-Disorder Transition ers/thesebook-chap5.pdf

Order-Disorder Transition ers/thesebook-chap5.pdf In this case, once any site has a slightly higher probability for having Cu (or Zn) rather than the other, the symmetry is broken, new Bragg peaks start to appear, and the order parameter is non-zero. ’’

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 and symmetry of both the order parameter and interaction (and range of the latter as well), but not on the detailed form or strength of the interactions