Re: What is the unit cell for Nd2Fe14B magnets?

This is an interesting question and it is believed that the positions of
the atoms within the unit cell is what gives rise to the magnetic
properties of NdFeB magnets.  You're on a good track, but there's a trick.
 The unit cell in this case consists of more than just one repeat of Nd2Fe14B!

The short story is the unit cell is the P4_2/mnm space group (also listed
as structure #136).  In english, that is a tetragonal unit cell containing
68 atoms, or equivalently, 4 repeats of the Nd2Fe14B.  The arrangement
looks like two nearly cubical blocks, with one stacked on top of the other.
 On the bottom face, the top face, and the middle plane (where the two cube
faces meet), are the Nd, B, 4Fe atoms.  Between those planes are hexagonal
nets of Fe atoms.  The Nd and boron atoms swap place between the bottom and
middle planes (and then again from middle to top).  Well, swap isn't quite
right as they're not moving into exactly the same positions.  However, on
the bottom and top faces the Nd atoms surround the Boron atoms while in the
middle plane the boron atoms are outside the Nd atoms.  This structure was
first determined by neutron scattering experiments about 20 years ago [*1].

A view of the unit cell can be seen at :
 http://cst-www.nrl.navy.mil/lattice/struk/d8_b.html

However, this merely shows you the lattice positions and doesn't actually
tell you where the particular atoms are in the Nd2Fe14B metal.  A picture
is given in reference [*1] should you be able to obtain a copy.


In any case, the shape of the electron clouds from the surrounding Fe atoms
causes the spins of the Nd atoms to align in a preferential direction.  The
f-orbital electron distribution clouds (the regions where it is likely to
find the electrons) of the iron atoms are not symmetric in shape, AND their
orientation is set by their position in the crystal structure of the unit
cell.  The magnetic moments of the Nd atoms then prefer to align in the
direction that will minimize energy due to the interaction of the spins
with the different arrangement of electric fields from the Fe atoms.  In
this case the Nd atoms will favor an alignment that points along the
(parallel or anti-parallel) to the long direction of the unit cell.

This is still not completely understood and many scientists are still
trying to understand the exact nature of this phenomena.  However, the
basic idea is this: Most of the actual magnetization is actually due to the
iron atoms in the system.  The iron dominates by a factor of 5 (or so) over
the Nd atoms.  However, the Nd atoms play a beautiful role by only favoring
directions along or opposed to the unit-cell.  Thus, even though most of
the magnetization is coming from the iron atoms, the Nd atoms stick
themselves in one of two directions and the rest of the irons atoms will
follow suit and end up pointed along the same axis to minimize the energy
of the material.

People are continuing to try and understand the role of the crystal unit
cell and it's effects on the magnetic properties in Rare-Earth Fe B systems
such as Nd2Fe14B.  Scientists at the building across the campus from me are
attempting to do just that with powerful x-ray scattering experiments. 
They are trying to probe the relative strength of the different Nd
positions within the crystal by scattering light through the system in a
clever way.  [*2]

These two references do require a subscription to the American Physical
Society to download.  However, these are the most widely, frequently (ie
popular!) physics journals and if you live close to a university or
college, you can probably gain access there for free.

[*1] Herbst etal, Physical Review B, Vol 29, page 4176, 1984.
[*2] Haskel D. etal, Physical Review Letters, Vol 95, 217207, 2005.

Some material may also be found at : http://www.aps.anl.gov/Sector4/home/