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
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
http://www.tulane.edu/~sanelson/geol212/2compphasdiag.html
Critical Opalescence
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 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
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: g
Ferrite: d
Martensite:
metastable phase
formed by
quenching g 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-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)
See the wikipedia article on this for a nice
“movie” of how the microstructure evolves.
http://en.wikipedia.org/wiki/Spinodal_decomposition
From Zemansky “Heat and
Thermodynamics”
MFT
From Chaikin and Lubensky:
“Principles of Condensed Matter
Physics” 1995.
From Kadanoff et
al. Rev. Mod.
Phys. 35, 395
(1967)
NOTE: similar b values for magnetism
And 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 (BraggWilliams 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.