From: hybl@umbc4.umbc.edu (Dr. Albert Hybl (UMAB-BIOPHYS))
Newsgroups: bionet.info-theory
Subject: What is a "perfect" crystal?
Summary: You all eat too much LITE chowder?
Keywords: X-ray_Diffraction Single_Crystals Disorder Twinning Entropy
Date: 15 Nov 92 21:08:17 GMT
Organization: Univ. of MD, Baltimore County

In message <Bxqnnx.9vy@ncifcrf.gov> dated Sun, 15 Nov 1992 03:43:09 GMT
from toms@fcs260c2.ncifcrf.gov, Tom Schneider writes: "HUNH?" and
>In article <1992Nov12.171556.15938@umbc3.umbc.edu> hybl@umbc4.umbc.edu
>(Dr. Albert Hybl (UMAB-BIOPHYS)) writes:
>>Is the entropy disordered crystal more "perfect" than the
>>hypothetical untwinned crystal?  Who or what defines "perfect?"  
>
>Whoa!  Sorry, the chemistry jargon is getting in my way.
>3.  What was the experiment you did, and what were the results?
The experiment was an X-ray diffraction crystal_structure
determination of "1,3-Diglyceride of 11-Bromoundecanoic Acid."
The results were reported by D. Dorset & A. Hybl (1971)
in Acta Crystallographica Vol. B27, Part 5 May 1971 pages 977-986.
Fractional atomic coordinates and thermal parameters with standard
deviations are published for all of the non-hydrogen atoms.
The abstract says:
  The symmetric diglyceride of 11-bromoundecanoic acid,
  C25H46Br2O5 (DBU), was crystallized from chloroform showing
  a tabular monoclinic aspect and having space group C2/c, with
  unit-cell dimensions a=9.36, b=5.58, c=54.53 A, beta=90.40 degrees
  and with Z=4.  The structure was determined by a three-dimensional
  X-ray diffraction analysis.  Data were collected with a General
  Electric XRD-6 manual diffractometer and nickel-filtered Cu
  Kalpha radiation.  The structure was solved by the heavy atom
  method.  Block-diagonal least-squares refinement led to an R
  of 0.09.  A pseudo twofold axis of molecular symmetry is
  utilized as a statistical axis of symmetry by the space group.
  The two hydrocarbon chain tails in the molecule point in 
  opposite directions and are packed in layers with the chain
  axis parallel.  The direction of the chain tilt, however,
  alternates in successive layers.

There are several figures of the molecule and its crystal structure
included in the paper.  Do you have a library at the Fort?

>1.  What is the molecular system being proposed here?  A crystal
>with two forms of phospholipid?  Do they interconvert in short
>time scales?  Are they a mixture?
  There is ONLY ONE KIND OF MOLECULE IN ONLY ONE CONFIGURATION
in the crystals.  It does NOT contain any Phosphorus.  The
rotational isomers do NOT interconvert; not in the solution nor
in the crystal during the time scale of the experiment.
They are not a mixture--they are a single crystal.  THE MOLECULE
DOES NOT CONTAIN A TWOFOLD AXIS OF SYMMETRY!

>2.  What do you mean by "entropy twinning"?
  Assume that the birth of a crystal nucleus has occurred and
molecules are being deposited at the crystal face with release
of heat energy.  Either of the two rotational orientations of
the molecule are deposited at RANDOM.  X-ray diffractions sees
only a space averaged structure.  During the analysis, we found
the oxygen atom attached to the middle carbon atom of the
glycerol group appearing ambiguously as two peaks related by a
pseudo-symmetry axis.
  We also saw "(1) a very evident twofold axis of molecular
symmetry; (2) that the disorder does not perturb the packing lattice
energy; (3) the free energy of the crystal is probably lower in
the disordered form by a residual entropy contribution of
(k ln 2^N) = R ln 2 = 1.38 cal/mole degree; (4) by placing the
twofold axis of pseudo molecular symmetry coincident to a
twofold axis in the space group C2/c, only half as many
independent parameters are needed to describe the structure."
  I hope that explains the entropy.  Twinning is a crystal-
lographic term related to growth.  F.C. Phillips [(1956).
in "An Introduction to Crystallography," Longmans, Green and
Co., London . New York . Toronto, on page 166] says "The
reasons for the formation of twin-crystals, as for many other
features of crystal habit, are not yet completely understood.  ...
The most important factor, however, is believed to lie in
the geometry of the internal structure of the particular
substance, the substance being by chance almost symmetrical
about the direction of the twin-axis (axis of pseudo-symmetry)
or almost symmetrical over a twin-plane (plane of
pseudo-symmetry).  ... when a portion of the structure is in
twinned orientation this pseuodo-unit extends almost without
deviation over the two orientations in relationship to the
details of the internal structural pattern ..."  Ok, now you
have the reason for the use of the term entropy twinning.
 
>Thanks for your patience.
  You should add some FAT to you chowder, after all, every living cell
contains some lipids.  I intended this to be an example for
something being discused--I forgot what.  Oh, well--just toss
it into chowder pot.
 
>
>      CH2OR               CH2OR          (below plane)
>      .                   .
>      .                   .
>   HO-C-H     and       H-C-OH
>      .                   .
>      .                   .
>      CH2OR               CH2OR          (below plane)
>  (a)                 (b)

                   O  H   H
             R =  -C-(C)9-C-Br
                      H   H
>
>The disorder results from the competitive occupancy for each
>site by rotational isomers (a) and (b). 

Albert Hybl (hybl@umbc3.umbc.edu)