Thanks, Ethan,
For your third point- I realized (after sending) that the distribution
would be stretched along the long axis- but actually I'm having
a hard time coming to grips with that conceptually- if there
are n atoms in the cell, they will necessarily be distributed
more sparsely in projection along the long cell axis than the
short axes, and you can't add more atoms along the long axis
to increase it's density without increasing density along the other two.
As for the rest, I think it is semantics or a question how precisely
we want to say something. Yes, what I was describing was a randomly
chosen sample from a uniform probability distribution, but it is this
sample that the OP is requesting- so I would rephrase your question:
does he want _a random sampling from_ a uniform probability distribution
throughout the lattice, or ...
Ed
Ethan Merritt wrote:
On Monday 01 December 2008 10:28:34 Edward A. Berry wrote:
Ethan A Merritt wrote:
On Friday 28 November 2008, Mueller, Juergen-Joachim wrote:
Dear all,
does anybody know a program to
fill an unit cell a,b,c randomly by an arbitrary number
of spheres (atoms)?
First you would need to define "random".
Uniform density throughout the lattice?
Uniform distribution of neighbor-neighbor distances?
Uniform fractional coodinates?
Must the placement conform to space group symmetry?
Although I am sure it was not intended, this might suggest
to some that uniform is equivalent to random-
actually they are the opposite: a random distribution would
have large areas with nothing and other places where two or
three spheres are almost on top of each other.
A uniform distribution is, well, uniform.
I fear you are muddying the waters rather than clarifying.
What you refer to as "random distribution" is better described
as random sampling from a uniform distribution.
Most programming languages have a function to generate a random
number evenly distributed between 0 and 1.
My point was that simple random sampling is not correct in the
context of crystallographic symmetry. If you use this procedure to
"fill the unit cell", as originally requested, you will violate
the crystal symmetry. If you use it to fill the asymmetric unit,
then the distribution that describes placement within the full
unit cell is no longer the same distribution as you sampled from,
since it is now perturbed by the additional placements generated
by crystallographic symmetric rather than by random sampling.
That may be acceptable, or it may not, depending on the
intended application.
Decide how many atoms
you want, get three random numbers for each atom, and those are
your fractional coordinates of your random spheres. Coordconv will
convert to orthogonal angstroms given your cell parameters.
That was the "uniform fractional coordinates" case that I listed.
It is unlikely to be the correct choice (although as always it depends
on the question). This problem is that since it is based on fractional
coordinates rather than the true cartesian coordinates, the resulting
density of atomic centers will be strongly anisotropic. The density
along each axis will be inversely proportional to the cell edge.
You would do better to define a cartesian coordinate grid that fills
the region of interest, and then assign an atom to each grid point with
probability 1/N. This produces artifacts of its own, of course, since
the distribution of interatomic distances is now discrete rather than
continuous.
The question "what is random?" is very deep, and the answer
depends strongly on the intended application.
