Blake A.J.(ed.) Crystal Structure Analysis

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22 Introduction to symmetry and diffraction

shape, but some trigonal crystal structures have a different (rhombohe-

dral) lattice not discussed here in detail, so there are just seven possible

different metric symmetries.

Some properties of the 32 crystallographic point groups are summa-

rized in Table 2.5. Here, in the last column, an enantiomorphous point

Table 2.5. The 32 crystallographic point groups.

symm along

system,

Laue, centring

point

group

space

group nos. xyz order E/P/C

Triclinic 11 111 1EP

1 P 12 1 1 12C

monoclinic 2 3–5 1 2 1 2 E P

2/mPC m 6–9 1 m 12P

2/m 10–15

12/m 14C

orthorhombic 222 16–24 2 2 2 4 E

mmm P C I F mm2 25–46 mm24P

mmm 47–74 2/m 2/m 2/m 8C

z x,y xy

tetragonal 4 75–80 4 1 1 4 E P

4/mPI

4 81–82 411 4

4/m 83–88 4/m

1 18C

tetragonal 422 89–98 4 2 2 8 E

4/mmm P I 4mm 99–110 4 mm 8P

42m 111–122 42m 8

4m2 4 m 2

4/mmm 123–142 4/m 2/m 2/m 16 C

trigonal 3 143–146 3 1 1 3 E P

3 PR 3 147–148 3 1 16C

trigonal 321 149–155 3 2 1 6 E

3mPR 312 3 1 2

3m1 156–161 3 m 16P

31m 31m

3m1 162–167 32/m 112C

31m 3 12/m

hexagonal 6 168–173 6 1 1 6 E P

6/mP

6 174 611 6

6/m 175–176 6/m

1 112C

hexagonal 622 177–182 6 2 2 12 E

6/mmm P 6mm 183–186 6 mm 12 P

62m 187–190 62m 12

6m2 6 m 2

6/mmm 191–194 6/m 2/m 2/m 24 C

x,y,z xyz xy,yz,zx

cubic 23 195–199 2 3 1 12 E

3 PIF m3 200–206 2/m 3 124C

cubic 432 207–214 4 3 2 24 E

3mPIF 43m 215–220 43m 24

3m 221–230 4/m 32/m 48 C

2.6 Further points 23

group (E) means one available for the crystallization of optically pure

chiral molecules; a polar point group (P) is one in which at least one par-

ticular direction is symmetrically distinct from the opposite direction;

C means a centrosymmetric point group. The order of a point group is

the number of equivalent general positions in each of the related space

groups with P unit cells, and must be multiplied by 2 for A, C and I,by

3 for R, and by 4 for F cells. For some tetragonal, trigonal and hexagonal

point groups, differentarrangements of symmetry elements are possible

for the a- and b-axes and the directions lying between them, leading to

the use of alternative symbols so that different but related space groups

are clearly distinguished; these are shown in adjacent rows.

24 Introduction to symmetry and diffraction

Exercises

1. You are provided in Fig. 2.3 and Fig. 2.4 with four two-

dimensional repeating patterns (Traidcraft gift wrap-

ping paper!). For each one, identify lattice points and

outline a unit cell (possible shapes are oblique, rectan-

gular, square, and hexagonal; a rectangular unit cell can

be primitive or centred). Find the symmetry elements;

for a 2D pattern the following are possible: 2-, 3-, 4- and

6-fold rotations, mirror lines, and glide lines (mirrors

with a half-unit-cell translation component parallel to

the reﬂection line); in 2D inversion symmetry is the same

as a 2-fold rotation. Show what fraction of the unit cell

is the asymmetric unit.

(1)

(2)

Fig. 2.3 Patterns for Exercise 1.

(3)

(4)

Fig. 2.4 Patterns for Exercise 1.

2. The point group of a ferrocene molecule [Fe(C

)

]

is D

, assuming an eclipsed conformation of the two

rings. This point group symmetry is not possible in the

crystalline solid state (no 5-fold rotation axes!). The sym-

metry elements of D

are: a ﬁve-fold rotation axis, 5

two-fold rotation axes perpendicular to this, 5 ‘verti-

cal’ mirror planes each containing Fe and 2 C atoms,

and one ‘horizontal’ mirror plane through Fe and lying

between the two rings (there is also an S

improper rota-

tion axis). Which of these symmetry elements could be

retained in the site symmetry of a ferrocene molecule in

a crystal structure,and what is the highest possible point

Exercises 25

group symmetry for ferrocene in the crystal (the maxi-

mum number of symmetry elements that can be retained

simultaneously)?

3. Why does the list of conventional Bravais lattices not

include any centred unit cells in the triclinic system,

tetragonal C , or cubic C?

4. Work out the point group andthe Laue class correspond-

ing to the following space groups: (a) C2; (b) Pna2

; (c)

3c; (d) I4

cd.

5. From the space group symbols alone, what (if any) spe-

cial positions would you expect to ﬁnd for (a) P

1; (b) C2;

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Crystal growth and

evaluation

Alexander Blake

3.1 Introduction

Whether growing crystals or giving advice to someone else trying to

do so, it is vital to remember that the quality of the crystal from which

diffraction data are acquired is generally the main determinant of the

ﬁnal quality of the structure. The effects of a suboptimal crystal will

propagate through data collection, structure solution and reﬁnement to

affect the quality of the ﬁnal structure, in which unsatisfactorily high

uncertainties may limit useful comparison and discussion. It may be

difﬁcult or impossible to get such a structure published.

3.2 Protect your crystals

Before you start trying to grow crystals you need to think about how

they will be handled. They will need to be extracted from the vessel they

grew in without suffering any damage. Less obviously, some containers

make this easier than others: an oversized one like a 250-ml round-

bottomed ﬂask makes the procedure of ﬁnding and removing a small

crystal unnecessarily difﬁcult. At the other extreme, a container with a

small aperture that will not admit a narrow spatula or pipette is also

troublesome. You should avoid screw-top or other containers that nar-

row near the top, as the ‘shoulders’ prevent easy removal of the crystals:

a small vial with straight walls works best.

Many crystals lose solvent on removal from the solution in which

they have grown (mother liquor). Although the envelope of the crys-

tals may appear intact, even a few per cent solvent loss usually renders

them useless for structural analysis. This is particularly common for

crystals grown from chlorocarbon solvents like dichloromethane and

chloroform,but can affect crystals grown from almost any solvent,water

included. If a crystal loses solvent and then does not behave well on

the diffractometer, there is no way to know whether the original crys-

tal was unsuitable, or whether the poor diffraction was due solely to

28 Crystal growth and evaluation

solvent loss. For this reason you should keep crystals under mother

liquor whenever possible. There are other good reasons for doing this –

see below.

3.3 Crystal growth

The term recrystallization has two related meanings but thereare crucial

differences between these. In the synthesis and puriﬁcation of compounds,

the aim is to maximize purity and yield, although these can be mutually

exclusive.The material is oftenprecipitatedveryrapidly(∼1 s), resulting

in microcrystalline or virtually amorphous products that are useless

for conventional single-crystal work. For diffraction work the object is to

obtain a small number (one may do) of relatively large (∼0.1–0.4 mm)

singlecrystals.Aslongasthis is achieved, yield is irrelevantandpurityis

likelyto be enhanced.Tothisend, crystals shouldbegrown slowly,taking

from minutes to months depending on the system. To understand why

this is important, visualize the process of growth at a crystal surface. The

greater the rate at which molecules arrive at the surface, the less time

they have to orient themselves in relation to molecules already there:

random accretion is more likely, leading to crystals that are twinned or

disordered. Suitable growth conditions include the absence of dust and

vibration: if these are present they can lead to small or non-singular

crystals.

3.4 Survey of methods

3.4.1 Solution methods

These are by far the most ﬂexible and widely used. They are suitable for

use with molecular compounds that are the subject of most crystal struc-

ture determinations. The use of solvents means that crystals can grow

separately from each other. It is therefore important not to let a solu-

tion dry out, as crystals could become encrusted and may not remain

single. When choosing solvents remember the general rule that ‘like dis-

solves like’: look for a solvent that is similar to the compound (in terms

of polarity, functional groups, etc.) and an antisolvent that is dissimi-

lar to it in order to reduce its solubility (see below). Information about

solvents is available from several sources (e.g. Handbook of Physics and

Chemistry, chromatographic elution data), and the process of synthesiz-

ing and purifying a compound will often confer a knowledge of suitable

solvents. Mixing solvents allows manipulation of solubility: a mixture

of solvent A (in which a compound is too soluble) and antisolvent B

(in which it is not sufﬁciently soluble) may be more useful than either

alone. If crystals grown from one solvent are poor in quality, try differ-

ent solvents or mixtures of solvents. Solution methods can be extremely

ﬂexible: a number of crystallizations, differing in the proportions of sol-

vents A and B used, can be set up to run in parallel. If a particular range

3.4 Survey of methods 29

of proportions appears to be more successful in producing crystals it

can be investigated more closely by decreasing the difference between

successive mixtures of A and B.

It is important that any vessels used for crystal growth should be

free of contaminants. Older containers also tend to have a large number

of scratches and other surface defects, providing multiple nucleation

points and tending to give large numbers of small crystals. Two factors

that favour the formation of twinned crystals are the presence of impu-

rities and uneven thermal gradients. Conversely, if the inner surface of

a container is too smooth this may inhibit crystallization. If this appears

to be the case, gently scratching the surface with a metal spatula a few

times may be effective. Some of the possible variations are described

brieﬂy below, and virtually all methods described can be adapted to

accommodate air sensitivity.

Concentration. If the volume of a solution is reduced, for example

by evaporation of a volatile solvent, the concentration of the solute will

rise until it begins to crystallize. When using mixed solvents the poorer

solvent should be the less volatile so that the solubility of the solute

decreases upon evaporation (but see Fig. 3.1). The rate of evaporation

can be controlled in various ways, for example by altering the tempera-

ture of the sample or by adjusting the size of the aperture through which

the solvent vapour can escape. As solvents are frequently ﬂammable or

irritants, it is important to work on the smallest scale possible and ensure

than any vapour released from the solution is safely dealt with. Avoid

obvious hazards such as those that will arise if large volumes of diethyl

ether or other highly volatile solvents are allowed to evaporate in a

closed container such as a refrigerator.

As noted above, it is highly undesirable to let a solution evaporate

to dryness as this will allow otherwise suitable crystals to become

encrusted,grow into an aggregateor be contaminated by impurities. The

crystals may be degraded by loss of solvent of crystallization, especially

ifchlorocarbonsolventssuchasdichloromethane havebeenused.It may

prove impossible to identify good crystals even if these are present, and

extracting them undamaged from a mass of material may prove difﬁcult

or impossible.

Large rubber Subaseal

Small Schlenk tube

Solution in a mixture

of solvents

Fig. 3.1 A method of controlling solubility

by selectively removing the less volatile sol-

vent in which the compound is more solu-

ble. This (chlorocarbon) solvent is absorbed

by the rubber Subaseal, while the antisol-

vent (diethyl ether) is not, leading to a

more concentrated solution and eventually

to crystallization.

Apparently sealed NMR tubes that have been forgotten at the back of

a fume cupboard or fridge for weeks or months are a fruitful source of

good-quality crystals: there is in fact slow evaporation of solvent and

crystals are able to grow undisturbed. As long as the NMR tube is clean

and relatively unscratched the smooth inner surface and narrow bore

provide an excellent environment for crystal growth.

Cooling. Either make up a hot, nearly saturated solution and allow

it to cool slowly towards room temperature or make up such a solu-

tion at room temperature and cool it slowly in a fridge or freezer. The

cooling rate can be reduced by exploiting the fact that the larger and

more massive an object, the longer it will take to lose heat. Thus, a hot

solution in a large vessel (or in a small vessel within a larger one) will

cool relatively slowly (Fig. 3.2, left). Similarly, a sample tube containing

30 Crystal growth and evaluation

Capped vial

Cooling

Solution

Crystals

collect here

Heat

Sample

Crystals

Saturated

solution

Thermal

reservoir

Fig. 3.2 Controlled cooling (left) and an apparatus to exploit convection (right).

a solution will cool at a slower rate if it is contained in a metal block that

was originally at room temperature, or if surrounded by an effective

layer of insulation. Cooling methods are based on the generally valid

assumption that solubility decreases with temperature. There are rare

exceptions to this (e.g. Na

in water) and some solubilities rise so

rapidly with temperature that it can be difﬁcult to control crystalliza-

tion (e.g. of KNO

from water). However, it is usually possible to ﬁnd

a combination of solute and solvent where solubility varies slowly and

controllably with temperature.

Fig. 3.3 Soxhlet apparatus.

Convection. The aim hereis to establish a temperaturegradient across

the solution, so that material dissolves in the warmer area and deposits

in the colder. This gradient can be established by various means, for

example (a) allow sunlight to shine on one part of the vessel; (b) put one

part of the vessel against a cooler surface, such as a window at night;

in some sections (Fig. 3.2 right). A smooth concentration gradient will

give the best results.

One method that combines variation of both concentration and tem-

perature and is especially useful for sparingly soluble compounds is

Soxhlet extraction (Fig. 3.3). The recycling of the solvent is the key fac-

tor here and crystals can even appear in the reﬂuxing solvent. Failing

this, they normally appear after slow cooling of the solution. There are

several other methods available to control concentration. One of these

is based on osmosis, where the solvent passes through a semipermeable

membrane into a concentrated solution of an inert species. The resulting

increase in the concentration of the solute may lead to crystal formation.

Solvent diffusion. This method is based on the fact that a compound

will dissolve well in certain solvents (‘good solvents’) but not in others

(‘poor solvents’ or antisolvents), which must be co-miscible. Dissolve

3.4 Survey of methods 31

the compound in the ‘good solvent’ and place this solution in a narrow

tube. Using a syringe ﬁtted with a ﬁne needle, very slowly inject the

neat antisolvent. If it is lighter than the solution, layer it on top; if it is

denser, inject it slowly into the bottom of the tube to form a layer under

the solution. Injecting the solvent is better than running it down the

side of the tube. If the tube is protected from vibration, these layers will

mix slowly and crystals will grow at the interface (Fig. 3.4). If necessary,

cooling of the tube can be used both to lower the rate of diffusion and

to reduce the solubility.

Fig. 3.4 Solvent diffusion.

Gaps

Inner

vessel

Anti-

solvent

Solution

Outer

vessel

(closed)

Fig. 3.5 Vapour diffusion.

Vapour diffusion. This method is also called isothermal distillation.

The antisolvent diffuses through the vapour phase into a solution of

the compound in the ‘good solvent’, thereby reducing the solubility

(Fig. 3.5). The advantages of this method include the relatively slow

rate of diffusion, its controllability and its adaptability, for example in

combination with Schlenk techniques to grow crystals of air-sensitive

samples. It is usually worth trying vapour diffusion as it frequently

succeeds where other methods have failed. A variant on this is the

hanging-drop method, principally used for the growth of crystals of

proteins and other macromolecules: the precipitant sits in a well and dif-

fuses slowly into a drop of solution suspended on a glass slide covering

the well.

If you are using a needle to make holes in the polythene cap of a

sample vial, take particular care to remove completely any slugs of poly-

thene formed by this procedure. They may be inside the vial or hanging

loosely from the cap. If these slugs get into your sample they can look

remarkably like large single crystals (Fig. 3.6), and even show plausible

optical properties due to the stress of their formation. They can often be

identiﬁed by the presence of a tail-like extension, but this is not always

present, and they are often identiﬁed only by their diffraction pattern

(Fig. 3.7). Making holes from the inside of the cap outwards makes it

easier to check for the presence of slugs, but close scrutiny of vial and

cap is always worthwhile.

Reactant diffusion. It is sometimes possible to combine synthesis and

crystal growth. In favourable cases crystals may simply drop out of the

reaction mixture, but the rate of many reactions means that crystals form

rapidly and are therefore small and of low quality. If the reaction rate

Fig. 3.6 A polythene slug produced by using a needle to make holes in the cap of a vial.