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intense have I/ꢅI = 2.5 and 1.4. An n glide plane perpendicular
to b is possible; of 17 h0`, h + ` 2n re¯ections only the 001
re¯ection is present (I/ꢅI = 8.3). The strong 103 re¯ection
(I/ꢅI = 27) seems to rule out the possibility of an a or c glide
perpendicular to b. A 21 axis parallel a is likely; none of the
three h00, h 2n re¯ections has I/ꢅI > 0.6.5
3. Packing considerations
The crystal packing of ME2C7O4 is determined by the con¯ict
between the packing preferences of the two regions of the
molecule. The planar, polar, O-rich end (hereafter, the head)
of the molecule and the tetrahedral, apolar, Me-rich end
(hereafter, the tail) are so different electronically that inter-
molecular interactions between them should be minimized.6 A
packing arrangement in which the molecular heads and tails
are segregated is expected.
Because the Me-rich tail of the molecule is about as thick as
two of the O-rich heads, and because those heads are planar,
the basic packing unit is a double stack of molecules (see Figs.
3 and 5) with methyl groups on the outside and the O-rich
heads interleaved in the center. The observation that the c axis
is the direction of fastest crystal growth supports the identi-
®cation of the double stacks as the basic packing unit.
Attractions within the stacks are stronger than attractions
between stacks.
The cross section of a stack (see Fig. 2) is an approximate
rhombus. The stacks are then rhombic prisms, which would be
predicted to crystallize in the C-centered arrangement that is
found for the subcell. The mirror planes relating the C O and
CÐOH groups are retained in the crystal because the differ-
ences between the groups are too small to matter (see foot-
note 1) and because the mirror is consistent with the C-
centered packing.
The observation that two of the {110} faces of the pseudocell
[e.g. (110) and (1 10)] are large while the other two are small
or ill-formed indicates that crystal growth is relatively rapid in
two of the pseudocell directions h110i (e.g. [110] and [110]),
but slow in the other two. The crystal habit seemed at ®rst to
be inconsistent with the symmetry of the unit cell, but the
habit can be understood if the contacts of the stack faces
across (110) are generally favorable, but if the speci®c
CMe2Á Á ÁCMe2 contacts along b are not. Crystal faces {110}
pass through all the unfavorable CMe2Á Á ÁCMe2 contacts, but
also separate interacting stacks. It seems likely that crystals
nucleate from a small number of layers that include the
directions [001] and (e.g.) [110], along which growth is rapid;
such a group of layers would include many interacting stacks,
but relatively few CMe2Á Á ÁCMe2 contacts. Growth perpendi-
cular to those ®rst layers would require the addition of layers
(e.g. along [110], [110], [010] or [010]); such growth would be
We investigated packing arrangements and tried re®ne-
ments in a number of primitive orthorhombic space groups; a
successful model was eventually found in Pmnb (#62; an
alternate setting of Pnma). The alternate setting was retained
so that the axis labels could be the same as in the RT (Cmc21)
structure. The asymmetric unit of the Pmnb structure contains
two independent molecules that are related by a local twofold
pseudorotation around a at y = 0.3751 (2) ' (3/8) and z =
1
2
0.515 (3) ' . Layers separated by a/2 are related by the
approximate translation 0, 14, 0. There is a local c glide, as well
as the true n glide, perpendicular to b.
The very low ꢃmax value and the location of so many atoms
on mirror planes meant that the Pmnb re®nement had to be
highly constrained. In the end we decided to treat the two half-
molecules as rigid groups and to re®ne nine Uiso values, i.e. one
for each of the chemically different non-H atoms. The rigid
groups (including H atoms) were based on the ordered
molecule C of the full RT Cmc21 re®nement. The various
measures of the ®t of the model (see Table 1) are satisfactory.
The ratio Nobs/Nvar is 482/20, but the restraints effectively
reduce the number of variables even further (to 16; only one
rigid-group rotation per molecule allowed to vary). The Uiso
2
Ê
values (0.015±0.030 A ) show no unusual patterns; values are
smallest for C1, C4 and C7, and largest for atoms C8, C9, O1
and O3. The peaks in the ®nal difference map (see Table 1) are
associated with atoms O3, C4, O1 and C1 and are located out
of the molecular plane (see also below). We conclude that the
basic features of the packing arrangement have been deter-
mined (see Fig. 5). It was possible to perform an acceptable, if
restrained, anisotropic re®nement (R1 = 0.062, wR2 = 0.178 for
79 parameters and 42 restraints), but the resulting ellipsoids,
although not exceptionally eccentric, are neither pleasing nor
informative. Allowing variation of the molecular conforma-
tions did not improve the ®t.
It is possible that the true structure at 130 K is actually
monoclinic, in which case the crystal we studied was a non-
merohedral twin. The shattering of the crystal during data
collection would be consistent with twinning, although the
usual strains associated with cell contraction or chemical
reaction are also a possible explanation.
6 The segregation of electronically different parts of molecules into different
regions of crystal structures is related to short-range order in solutions. The
ÁH term for interactions of unlike molecules in solutions or unlike regions of
molecules in crystals is in¯uenced in part by the dispersion interactions, which
are proportional to the products of the polarizabilities of the interacting units.
If PA PB, then P2A PB2 is greater than 2PAPB and ÁH will be positive for
mixing. If stronger (e.g. dipolar) interactions are possible, the ÁH term for
mixing is expected to be even more positive. Note that positive deviations
from Raoult's Law are much more common than negative deviations; it is
much more common for the activities of solution components to be greater
than their mole fractions than less than their mole fractions. Most solutions
form only because the ꢁTÁSmix term is large enough to offset the positive
ÁHmix term. For ordered solid phases, in which ÁSmix = 0, segregation of
different molecules into different crystals (i.e. fractional crystallization) or of
different parts of a single molecule into different regions of a single crystal is
the rule.
5 At the time the orientation matrix for data collection was determined we had
no reason to think that the symmetry of the crystal might be lower than
orthorhombic [ꢂ = 90.05 (3), ꢇ = 90.03 (2), ꢈ = 89.96 (3)ꢂ]. Two octants of data
(+h, +k, Æ`) were collected, but unfortunately these do not allow testing for
the equivalence of re¯ections that would be different (+h, +k, +` and ꢁh, ꢁk,
`) if c were the unique monoclinic axis. In any event the data do not average
well (Rint = 0.13) even in P11m, perhaps partly because the re¯ections are
generally weak (Rsig = 0.11).
ꢀ
Acta Cryst. (2002). B58, 502±511
Duncan et al.
Two phases of C9H12O4 507