Master's Thesis Anders Klang

Anders Klang
3
Introduction
Zeolites
Zeolites were first mentioned by Baron Axel Cronstedt, who noted that they started to bubble as if
they were boiling when heated using a blow pipe flame, zeo means to boil, lithos means stone in
Greek.1-2
Zeolites in nature are found in channels in rock formations close to where lava flows during
volcano eruptions when there is enough lava present to heat the water in these rock formations to
the point that the water starts dissolving the rock and forming zeolites on recrystallisation. Zeolites
can also form as an alternation of volcanic ash in sediments on the bottoms of saline lakes. 3
Zeolites can be synthesized for industrial use. One way to produce zeolites is synthesising a reactive
aluminosilicate gel with high alkalinity that is allowed to react at temperatures starting from room
temperature to around 200°C to form zeolite crystals. 4
A colloidal gel can also be used in zeolite
synthesis. This gel is not homogenous on a molecular scale and gives rise to other zeolites than the
normal gels. 5
Zeolites can also be grown from kaolin that has been heated to remove water from the
structure and mixing the product known as metakaolin with a metal hydroxide solution. 6
Zeolites are porous materials, but differs from active carbons and organic molecular sieves by having
an ordered crystal structure and a narrow span of pore sizes making them useful as molecular sieves
and holders of catalysts when a narrower range of pore span is required. 7
Another type of materials
that is interesting for carrying catalysts in reactions is mesoporous materials. These materials have
pore sizes ranging from 1.5-10 nanometres and can have surface areas of 1200 square metres per
gram. These materials are synthesised by letting the materials building up the framework crystallise
onto rod shaped micelles and then heating up the product removing the micelles. This process is
called liquid crystal templating.8
Zeolites are a type of aluminosilicate. The chemical formula for zeolites can be written
Mx/n[(AlO2)x(SiO2)y] mH2O, where M is a cation of a metal with charge n. Zeolites have
frameworks with net negative charge. The negative charge is proportional to the concentration of
aluminium as aluminium’s positive charge is three while silicon’s charge is 4. Zeolites have three
dimensional framework structures. The tunnels in zeolites have diameters ranging from atomic to
molecular scale repeated throughout the zeolites framework making them useful for industry and
interesting objects for study. The zeolite frameworks have a multitude of tunnels that run parallel
and perpendicular to each other. These tunnels are often called 6-rings and 8-rings from how they
look in 2-dimensional projections of the structure. Where these tunnels intersect, the dimensions are
slightly bigger. These places, known as cages, contain cations balancing the negative charges of the
framework of the structures 9
. The ions situated inside these cages are exchangeable with other ions
making zeolites useful as ion exchangers. For example zeolites can be used to remove hardness from
water in detergents or to remove hazardous ions like radioactive caesium and strontium from reactor
water. Using zeolites to remove these ions reduces the amount of radioactive waste that needs to be
stored 10-11
. The tunnel-sizes in zeolites are of molecular scale making them suitable to be used as
molecular sieves. A molecular sieve lets through molecules of one size or property while others are
trapped or move much slower through the zeolite, and thereby separating the molecules passing
through12
.
JBW-type Zeolite, Na3Al3Si3O12•2H2O
JBW has a framework structure with aluminium and silicon alternating in 3 dimensions with bridges
of oxygen between them Fig 1-2. The strict alteration of silicon and aluminium leads to a doubling of
the b-axis.

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Figure 1 JBW ab-plane unit cell without doubling of a and b axis marked by a rectangle
Figure 2 In this figure there is a single chain marked with a red rectangle and a double chain marked with a blue square.
In this model of the framework structure of JBW seen along the c-axis with yellow representing silicon and black
aluminium, the tubes represent the oxygen bridges situated between these atoms.
When looking at the framework along the a-axis there is an alternation of single and double zigzag
chains Fig 1-3 that have repeat distances of 2 atomic distances 13
.

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Figure 3 This is the model of the zeolite viewed along the a-axis. From here the single and double chains with 2-repeat
can be seen next to each other, the double chain that is marked with a blue rectangle is closer to the camera than the
single chain marked with a red rectangle. This pattern of alternating single and double chains is repeated infinitely in the
direction perpendicular to the chain upwards in the paper plane and the photo is taken in a direction that more or less
hides the repetition into the paper with identical chains lying on top of each other.
When looking along the c-axis Fig4 8-rings, 6-rings and 4-rings can be seen. The 8-rings contain the
exchangeable cations. When looking along the b-axis there are 6-ring tunnels Fig 5. The cavities
formed along these tunnels contain only sodium ions. The fact that potassium ions do not enter
these 6-ring tunnels suggests a lack of space in the cavities rather than the diameter of these tunnels
being too small14
. The smaller channels, 6-rings are interesting as they only contain sodium ions and
no water molecules. This is one of the reasons that the structure is not collapsing when the ions in
the 8-ring channels are exchanged.

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Figure 4 framework structure seen along the c-axis. An 8-ring tunnel is marked by a rectangle. The exchangeable cations
are located in these tunnels.
Figure 5 Zeolite framework structure seen along the a-axis. A 6-ring tunnel is marked with a blue circle. In the 6-ring
tunnels there are sodium ions that are non-exchangeable
When zeolites are produced, methods are needed to verify that what you got really is a zeolite and to
determine what structure it has. Fortunately there are some powerful techniques to do so. The most
common technique that was also used for the zeolite in this paper is X-ray diffraction where X-rays
with a characteristic wavelength are diffracted by the sample, and from the information of these X-
rays the structure of the zeolite can be determined except for hydrogen bonds and position of the
hydrogen atoms as their low electron density compared to the surrounding atoms make their
positions very uncertain. To fully characterize the structure including hydrogen atoms, neutron

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diffraction need to be used in combination with NMR. To detect the positions of the hydrogen atoms
Healy et. Al used neutron diffraction and to see what atoms that interact with hydrogen atoms they
used NMR. Healy et. Al. replaced all hydrogen atoms with deuterium in the synthesis to get a better
data set and higher resolution 15
. The NMR technique they used to determine what atoms participate
in the hydrogen bonds is called magic angle spinning. This method uses the fact that when a crystal is
spun tipped at 54.74° from the magnetic field that is applied in the technique, all dipolar interactions
and chemical shift anisotropy are averaged out giving a clearer picture of the chemical interactions
between all atoms in the sample. 16
Theory
The data in this project was gathered using X-ray diffraction. To increase the understanding of how
the data was collected and how the machines works, Bragg’s law Eq1, and some key concepts like
symmetry and structure factors are explained in the text below.
n n x λ x d x sin θ
Eq 1
Figure 6 Bragg’s Law, Illustration of how X-rays are reflected by the lattice planes with the angle θ
17
From equation 1 and Fig 6 Bragg’s law is described, where λ is the wavelength of the X-rays, θ is the
diffraction angle of the X-rays and d is the distance between two lattice planes, Fig6. 18
Bragg’s law
shows that a given interplanar spacing will give rise to reflections only for distinct values of the angle
θ. For a structure that is well ordered in three dimensions the diffraction will result in a pattern of
sharp diffraction spots that form a lattice. It is clear from Bragg’s law that a short interplanar spacing
gives rise to a large diffraction angle, and hence the term “reciprocal lattice” is used to reflect the
reciprocal nature between the lattice of atoms and the lattice of the diffraction pattern.
The relationship between the structure and the diffraction pattern is given by the expression for the
structure factor in Eq2.
Fhkl = Σj fj e2πi(hx
j
+ ky
j
+lz )
Eq2

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Where hkl is the name of the set of planes reflecting the X-rays.
Symmetry
Crystals, even the ones barely visible to the eye, contain billions of atoms. The good news is that the
positions of the atoms are in most cases regular and can be described in smaller repeating units. In
this way it is possible to describe the average structure of a material with the positions of the atoms
in a small well defined volume that is repeated throughout the crystal. So by knowing the smallest
set of atoms needed to describe the crystal structure, known as the unit cell, one can describe the
whole crystal19
. The edges of the unit cell are defined by three vectors: a, b and c, that may be of
different length. The vectors have the same origin and are separated in space by the angles α, β, and
γ. The symmetry of the structure is used to classify the unit cell. Examples of unit cells are cubic,
hexagonal, and orthorhombic.
Figure 7 The shape of the orthorhombic cell is a box with all sides of different lengths and all angles are 90 °
The unit cell of a crystal can be orthorhombic Fig 7, meaning a unit cell where all angles are
constrained by symmetry to be 90 ° and all sides of the unit cell may have different lengths. 20
When describing crystals and their structures symmetry is a very important concept, with e.g. mirror
planes and glide planes arrangements of atoms can be described in a more comprehensible way.
Figure 8 m is the mirror line, the 5 atoms below are generated by a reflection of those above in m
By using a mirror line m in Fig 8, we only need the 5 atoms above the plane to describe all 10
positions in the picture.

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Figure 9 m is the mirror plane, and being perpendicular to the paper the plane is projected onto the paper as a line. The
atoms that are black are closer to us than the light blue atoms.
In three dimensions Fig 9 the black atoms are not on the same level as the atoms with a light blue
core. In other words the 5 atoms above the plane are reflected and describe the 5 atoms placed
under the mirror plane m.
Figure 10 a is a glide line, the atom below is generated by translation of half a unit cell to the right and than reflected
perpendicular to the b-axis
In finite objects all symmetry operations are rotations, proper or improper, but in periodic objects,
translations are also symmetry operations. Also the combination of translations and rotations are
possible and give rise to glides and screws. Fig 10 The upper atom is moved half a unit cell to the
right (this movement half a unit cell is called a translation) and then reflected in the glide
lineperpendicular to b.

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Figure 11 In an n-glide there is a translation of half a unit cell in the ac-diagonal followed by a reflection in the plane
perpendicular to b, this plane is defined by its normal vector N.
If Fig 11 an n-glide is described, it can be seen as a translation of half a unit cell in the ac-diagonal
followed by a reflection in the plane perpendicular to b. In other words n is a glide plane and this is 3-
dimensional symmetry compared to 2-dimensional with the a-glide.
Figure 12 is a screw-axis in the z-plane, the atom marked with a black fish moves ½ a unit cell out of the paper and
rotates 180° clockwise to its new position marked with a blue fish
In Fig 12 the atom R to the right is situated at the same height as the paper in the x-y plane and it
moves to the blue R to the left is half a unit cell up from the paper. Having a screw-axis in the z-plane,
the atom moves ½ a unit cell out of the paper and are rotated 180°. By using a screw axis the atom
marked with a black fish describes two positions related to each other21-22
. The translational
symmetries described above together with rotational symmetries can only be combined in a limited
number of ways. These combinations together make up the 230 space groups.

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Diffractometry
Figure 13 This is a sketch of the diffractometer. A is the X-ray source and monochromator, B is the sample mounted on a
goniometer, and C is the detector. 1 is the X-rays emitted from A, 2 are X-rays that have been scattered by the sample
and hits the detector C.
Fig 13 shows a schematic picture of a diffractometer. X-rays are produced at the source A and pass
through the monochromator that only lets through X-rays of a certain known wavelength. The X-rays
then hit the sample B, mounted on the goniometer B, to produce diffraction that is recorded on the
detector C. After collecting the data computer programs like CrysAlisPro and Jana 2006 were used to
evaluate the data, meaning that a computer model of the structure is made. The computer model
was compared to the original data and an R-value is given. The R-value gives the difference between
the data collected and the computer model generated. 23
Until the 1970:s all crystals were thought to be periodic, to the point that data indicating aperiodicity
were discarded. A periodic crystal has a well defined unit cell like the one of rutile that consists of
titanium and oxygen atoms arranged so that each titanium atom is surrounded by six oxygen atoms
in an octahedron and each oxygen is surrounded by a square of 4 titanium atoms.
Figure 14 In this figure the unit cell of rutile TiO₂ is shown in ab-projection, where the blue atoms are titanium and the
smaller red ones are oxygen.
The unit cell of rutile is described in Fig 14. in the ab-projection. What happens in the rutile structure
if we replace part of the titanium atoms for another species in an ordered way? In a fully ordered
structure this must lead to a superstructure and in rutile, it is common to generate a longer c-axis of
the unit cell. In tri-rutile Fig 15, there is a tripling of the unit cell along the c axis. It is caused by the
ordering of iron and tantalum cations.24

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Figure 15 Tri-rutile,
25
the tripling of the c-axis due to the ordering of the Ta (light blue) and Fe (grey) cations. All cations
are situated in the centre of the octahedrons and all corners of the octahedrons are oxygen atoms.
A tripling of the c-axis from introducing new atoms to the lattice and thereby increasing the repeat
distance in one direction is easy to envisage and clearly this can be generalised to fourfold, fivefold or
even higher? And can we describe this in a better way than describing it with a huge unit cell. This
problem was addressed and solved by three Dutch scientists, de Wolff, Janner, and Jansen.26
They
introduced a notation where a fourth parameter is added to describe the structure, using the original
three dimensions to describe to conventional small repeating unit cell and the fourth parameter,
called a wavevector or a wavefunction, to describe the deviation away from the average structure by
superstructure arrangement.
Yamamoto found that in CuAl II could be solved using a wavevector with the length that is 1/10 of
the b*-axis giving a repeat distance of 10 b as can be seen in Fig 16.27
Figure 16 The modulation of Cu-Au II can be seen in this figure, Cu is represented with white circles and Au with black.
The real power in the method introduced by de Wolff, Janner and Jansen is that it is not limited to
conventional superstructures but it also works if the superstructure is a non-integer number. How
can this be understood. Consider the structure of CuAu above. The superstructure is already large,
but we can envisage a situation where the anti-phase boundary that causes the superstructure does
not occur after 10 repeats, but after 10.5. In that case, every second block of in-register repeats is 10
atoms wide and every second is 11 atoms wide. The resulting grand total is a super cell 21 times the
original cell. But the model can be pushed further. If the anti-phase boundary happens after an
irrational number of atomic repeats, say 10.456789..., the sequence of 10 and 11 atom blocks that
comes closest to that number will be aperiodic. This is an aperiodic occupancy wave, an
incommensurate structure. It is common in incommensurate structures that the effect of the
superstructure is not only an exchange of two species but also a displacement of atoms is involved.
This is called displacive modulation.28
Fig 17.

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Figure 17 The atoms in this figure are subject to a transversal displacement, they differ from a straight line in such way
that their locations can be fitted onto displacement wave vector with the wavelength λ.
The positions may be somewhat regular differing from a central line in two or three dimensions in a
way that fits well onto a transversal wavefunction. This means that the positions of these atoms may
be accurately described with a regular pattern in the direction of the central line. Another case is
when the atoms/molecules are placed along a line with a variation in distance Fig 18.
Figure 18 Here the atoms are in a straight line, but their placement are not commensurate with the unit cell in the b-
direction. The placements are however well fitted onto a transversal displacement wave vector with wavelength λ.
This way of describing displacements of atoms is called displacive modulation29
. Modulations may
also be used to describe occupation; in this case the wave function shows where to find atoms along
one or more directions. If the modulation wave is positive the position is occupied if the function is
zero the position is vacant. It is also possible to do complimentary modulations where a negative
value of the wavefunction means that the position is taken by an alternative species.30-31
Experimental
Synthesis
A. M. Healy et al. discovered that some ion combinations such as sodium and potassium increased
the yield of JBW type zeolites when equimolar amounts of aluminium and silicon were used in the
reaction. In the year 1999 JBW type zeolite sodium/potassium alumosilicate were fully characterized
using magic angle spinning, X-ray- and neutron diffraction. All hydrogen atoms in the structure were
replaced with deuterium. When making the JBW type zeolite with aluminium and germanium using
the combination of sodium/potassium the result was not a JBW, only when potassium was replaced

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rubidium in the reaction was JBW structure produced in the aluminium germanium reaction [A.M.
Healy et al.32-33
When trying to synthesize NH1 at 200°C using the proportions proposed by Healy et. al. and the
method of Hansen and Fälth the resulting product was mainly sodalite. Crystals were picked and
measured but they proved to be too small to yield single crystal diffraction data.
Analysis
The first step in evaluation of the X-ray diffraction data is to search the exposures for X-ray
reflections above a certain threshold level. After this the program is instructed to find the unit cell of
the crystal. For special cases, (including the caesium and rubidium zeolite crystals in this study) the
reflections are not fully described by a simple unit cell, but an additional vector usually referred to as
the q-vector is used. An estimate of this vector is given by the user,the value is refined and later used
during integration.
The crystals used in this experiment were synthesised by Hansen and Fälth in 1980. Glass with
equimolar ratios of SI:Al was ground and sieved to achieve an even size distribution of the glass
particles. The sieved glass particles were mixed with a solution of NaOH. The mixture was allowed to
react in steel autoclaves at 200°C under autogenic pressure to produce the zeolite crystals. The
original zeolite contained only sodium ions and the aluminosilicate framework, and the other zeolites
were produced by performing ion exchange of the original material with either potassium, rubidium
or caesium.34-35
X-ray diffraction measurement
The zeolite crystals were picked and mounted on goniometer heads and X-ray diffraction
measurements were made using two different single crystal diffractometres: Xcalibur Sapphire 3 and
Xcalibur E, both from Agilent Technologies Ltd. The data collected was evaluated using CrysAlisPro
171.33.5236
and the structure was solved using Superflip37
and refined using Jana 2006 01/07/201138
.
X-ray diffraction interpretation
After importing the data that has been processed by CrysAlisPro the first step is to use Superflip.
Superflip is a function in Jana2006 that allows you to find a good starting model. Superflip works by
Fourier recycling. The data is Fourier-transformed using random phases to produce a starting model
that contains positive and negative electron densities. The positivity criterion is then applied in a
rather harsh way: All negative electron densities are exchanged for the corresponding positive
densities. The phases from the resulting model are used together with the experimental amplitudes
to produce the second-generation structure, and the procedure is repeated until convergence is
reached. The final electron density map is interpreted to yield atomic positions. In some cases the
structure that is generated as the first suggestion does not contain all the atoms needed to refine the
structure. In this case a function called difference Fourier calculation is helpful to locate the missing
atoms. The procedure is similar to the Fourier recycling in Superflip: The Fourier transform of the
experimental amplitudes is calculated using the phase information from the model. The resulting real
space structure is then compared to the model and the difference in electron density between the
two is used to adjust atomic positions or to propose entirely new ones.
When evaluating the data the R-value is of great importance, as it tells you how good the computer
model is compared to the original data. Needless to say, when solving a structure it is a good idea to
keep an eye of the R-value to see if anything goes wrong when solving the structure of the crystal. 39
A computer model is only as good as the data it uses, and therefore it is important to look at the
original data to make sure that no important reflections have been left out in the model describing
the structure. The function for looking at these reflexes is called Unwarp. This function in CrysAlisPro

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is used to generate 2-dimensional structures of crystal planes that contains all data of each plane as
it was collected before any data reduction was made. These planes are used to confirm or discard the
existence of a larger unit cell that describes the crystal. For example hk1 generates a plane with all x
and y coordinates where z equals 1, in other words the x-y plane translated one unit cell up from the
paper, along the z-axis.
In the end of the process the atoms are represented in other shapes than a symmetrical sphere. This
relaxation of shape helps a lot in the end of the refinement process
Results
Sodium
The zeolite that was not ion exchanged had the same structure as obtained by Hansen in 1980. It had
a doubling of b because of the alternation of Si and Al in the framework structure as can be seen in
Fig 19 and as the squares in Fig 20. The reflections marked by circles in the Fig 20 give the doubling of
a Fig 19-20 as a result of the organisation of sodium and water molecules in the 8-ring tunnels where
they are close to the neighbour and far apart in every second tunnel in this direction. The refinement
data from JBW is given in Table 1. The sodium ions in the 6-rings are all bound to the oxygen atoms in
the rings surrounding them, these bindings are left out in Fig 19 to give a clearer picture of the
framework structure of the zeolite.
Figure 19 In this picture the distribution of sodium marked with blue ellipses can be seen in the 8-ring tunnels in the a-b
plane. It is clear that sodium ions are close to each other in every second tunnel blue, and are as far apart as possible in
every second tunnel red. The order of the cations along the a direction can be seen in the chain of 8-rings in this figure.

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This doubling of a and b result in what is called an superstructure. A substructure of this can be
described by the smaller unit cell a, b, c.
Figure 20 Reconstructed reciprocal lattice image of Na JBW. Main reflections are marked with dark blue squares while
those marked with rectangles double b due to the alternation of aluminium and silicon and those marked with circles
double the a-direction. This final doubling of the lattice is caused by the ordering of water and sodium in the channel
system of the zeolite. This image was generated from a twinned specimen, and it is important to note that the split
reflections do not represent a modulation but simply the presence of two different lattices.
Crystal data
Al3H0Na3O13.963Si3 V = 1290.4 (3) Å3
Mr = 457.6 Z = 4
Orthorhombic, Pna21 Mo Kα radiation, λ = 0.7107 Å
a = 16.441 (2) Å μ = 0.75 mm−1
b = 15.0146 (18) Å T = 293 K
c = 5.2273 (5) Å
Data collection
Xcalibur, Eos
diffractometer 3014 independent reflections
Absorption correction: multi-scan
CrysAlis PRO, Oxford Diffraction Ltd., Version
1.171.33.52 (release 06-11-2009 CrysAlis171 .NET)
(compiled Nov 6 2009,16:24:50) Empirical
absorption correction using spherical harmonics,
implemented in SCALE3 ABSPACK scaling
algorithm.
674 reflections with I > 3σ(I)
Tmin = 0.924, Tmax = 1 Rint = 0.096
14576 measured reflections
Refinement
R[F2 > 2σ(F2)] = 0.029 0 restraints
wR(F2) = 0.068 H-atom parameters constrained

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S = 0.59 Δρmax = 0.71 e Å−3
3014 reflections Δρmin = −0.50 e Å−3
143 parameters
Table 1 The data collected from JBW Na3Al3Si3O13.963 H0
The R-value is a bit higher than expected as the crystal used for this measurement had at least 2
twins in the crystal structure. All attempts were made to establish the positions of hydrogen
atoms on the oxygen atoms located in the 8-ring tunnels were unsuccessful on all zeolites in this
report.
Potassium
The zeolite that had been ion-exchanged with potassium had the same structure as the original
zeolite, the same result was obtained by A.M. Healy et al. in 2000.40
The doubling of a was not visible
on measurements made by Hansen in 1984, could be a result of today’s detectors are stronger than
in 1984. The doubling of a and b seen in the reciprocal lattice reconstruction in Fig 21 are analogous
to those in the Na compound. When refining the potassium exchanged crystal, the results got
significantly better when decreasing the occupation of sodium in one position in the 6-ring channels
to 0.9 and increasing the total of potassium occupations in K3 and K4 to 1.1 as noted by Hansen41
. In
the potassium exchanged zeolite the order producing the doubling in the a direction is different from
the sodium zeolites. Rather than having every second tunnel close and far away, the potassium
exchanged zeolite have an alternation between potassium and water along the tunnels. These chains
are placed in a way so when looking in the a-b plane every second tunnel will have a potassium
cation and the other a water molecule. This effect is not visible in Fig 22 as potassium is occupying
the same site as Water in the model and only the biggest molecule occupying the given site is visible
in the model. In Table 2 the refinement data from the potassium ion-exchanged zeolite crystal is
given.
Figure 21 Reciprocal lattice Reconstruction of the a*b*-plane. In congruence with figure 7 main reflections are marked
with dark blue squares, reflections originating from aluminium silicon ordering are marked with rectangles and
reflections originating from water/potassium ordering are marked with circles. This image was generated from a twinned
specimen, and it is important to note that the split reflections do not represent a modulation but simply the presence of
two different lattices.

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Figure 22 The potassium in this zeolite is placed along the 8-ring tunnels, the atoms inside the blue and red elipses are
potassium and Water occupying the same position. The water and potassium are ordered so every second atom along
the tunnels are potassium the other water. Along the a- and b-directions there is also this ordering with every second
tunnel potassium and water.
Crystal data
Al3K1.1Na1.9O12.9Si3 V = 1290.1 (2) Å3
Mr = 458.3 Z = 4
Orthorhombic, Pna21 Mo Kα radiation, λ = 0.7107 Å
a = 16.2855 (4) Å μ = 1.06 mm−1
b = 15.2487 (11) Å T = 293 K
c = 5.1949 (9) Å
Data collection
Oxford Diffraction CCD
diffractometer 1340 reflections with I > 3σ(I)
Rint = 0.028
14530 measured reflections 3064 independent reflections
Refinement
R[F2 > 2σ(F2)] = 0.055 139 parameters
wR(F2) = 0.147 0 restraints
S = 2.72 Δρmax = 1.62 e Å−3
3064 reflections Δρmin = −0.90 e Å−3
Table 2 Refinement data from JBW that has been ion-exchanged with potassium
Rubidium
The zeolite that had been ion-exchanged with rubidium had the same doubling of b as the previous
structures Fig 23. One of the crystals had a strong indication of having the repeat distance of 5 in the
a-direction as Hansen obtained in1984, though the refinement improved when a modulation vector
was used. The crystal structure Pnm21 means that the crystal has an n glide in the a-direction a
mirror plane in the b direction and a 21 screw axis in the c direction. The modulation was in the same
direction as the modulated rubidium, and the same direction as the n-glide. The refinement data of
the rubidium zeolite can be seen in Table 3. The placement of rubidium in the 8-ring channels along
the a direction can also be seen in Fig 25 results in a doubling very close to the 5 of a Fig 26. In order
to get an exact description of the placement of the rubidium ions a q-vector was used. A fuller
description of the structure of the rubidium exchanged zeolite is given together with the caesium
case below.

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Figure 23 Reciprocal lattice Reconstruction of the a*b*-plane. In congruence with F0igure 7 main reflections are marked
reflections originating from water/rubidium ordering are marked with circles. It is because of these satellite reflections
that a q-vector is needed for the characterisation of the rubidium-exchanged zeolite.
Crystal data
Al1.5NaO6.542Rb0.483Si1.5 V = 641.6 (12) Å3
Mr = 251.5 Z = 4
Orthorhombic, Pnm21(α00)0s0† Mo Kα radiation, λ = 0.7107 Å
q = 0.408000a* μ = 4.35 mm−1
a = 8.078 (3) Å T = 293 K
b = 15.35 (2) Å
c = 5.174 (7) Å
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, −x2+1/2, x3+1/2, −x4; (3) x1, −x2, x3, x4+1/2; (4)
−x1,
x2+1/2, x3+1/2, −x4+1/2.
Data collection
Xcalibur, Eos

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algorithm.
Tmin = 0.903, Tmax = 1 Rint = 0.047
Refinement
R[F2 > 2σ(F2)] = 0.051 4261 reflections
wR(F2) = 0.132 119 parameters
S = 1.38 0 restraints
Table 3 Refinement data from JBW ion-exchanged with rubidium
Looking at the formula for the caesium ion-exchanged zeolite in table 4, it is likely that the ion
exchange was close to 100%. As full occupation of rubidium would give Rb 0.5, using the fact
that the electron density equals 0.483 rubidium and knowing the number of electrons in
rubidium and sodium, calculation yields that roughly 95 percent of the sites are occupied by
rubidium cations and 5 % by sodium cations.
Caesium
The zeolite that had been ion-exchanged with caesium had the same doubling of b as the previous
structures. In Table 4 the refinement data of the structure is given. The caesium zeolite also had a
Pmn21unit cell analogous to rubidium. The placement of caesium in the 8-ring channels along the a
direction, as in the rubidium case, Fig 24 results in a doubling very close to the 5 of a Fig 27. A q-
vector was used for the caesium exchanged zeolite to obtain the average distance between two
caesium atoms.
A fuller description of the structure of the rubidium exchanged zeolite is given together with the
caesium case below.
Figure 24 Reciprocal lattice Reconstruction of the a*b*-plane. In congruence with Figure 7 main reflections are marked

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21
reflections originating from water/caesium ordering are marked with circles. As in the rubidium case it is these
reflections that give rise to the modulation in the a-direction and that a q-vector is needed for the characterisation of
the caesium-exchanged zeolite.
Crystal data
Al1.5Cs0.317NaO6.5Si1.5 V = 663.21 Å3
Mr = 251.7 Z = 4
Orthorhombic, Pnm21(α00)0s0† Mo Kα radiation, λ = 0.7107 Å
q = 0.404600a* μ = 2.40 mm−1
a = 8.1969 Å T = 293 K
b = 15.0245 Å
c = 5.3852 Å
† Symmetry operations: (1) x1, x2, x3, x4; (2) −x1, −x2+1/2, x3+1/2, −x4; (3) x1, −x2, x3, x4+1/2; (4)
−x1,
x2+1/2, x3+1/2, −x4+1/2.
Data collection
Xcalibur, Eos
algorithm.
Tmin = 0.876, Tmax = 1 Rint = 0.060
Refinement
R[F2 > 2σ(F2)] = 0.086 4514 reflections
wR(F2) = 0.191 64 parameters
S = 2.49 0 restraints
Table 4 Refinement data from JBW ion-exchanged with caesium
Looking at the formula for the caesium ion-exchanged zeolite in table 4, it is likely that the ion
exchange was about 55 % complete, the formula indicates that roughly 55 percent of the sites
are occupied by caesium cations and 45 % by sodium cations. This value is obtained using the
same calculations described in the rubidium case.
Two types of Modulation
The doubling of the a-axis exhibited by the Na and K zeolites represents the simplest possible type of
modulation. A modulation is a periodic distortion of a simpler structure. A doubling is a modulation
with a period that is exactly twice of that of the original cell repeat. This type of modulation is called
commensurate since the period of the modulation is commensurate with that of the lattice, this
doubling has an effect on the symmetry of the unit cell; the original cell has a mirror plane with a
screw axis while the doubled cell has an a-glide with a screw axis along c.

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22
Figure 25 In this picture the distribution of sodium marked with blue and red ellipses can be seen in the 8-ring tunnels in
the a-b plane. It is clear that sodium ions are close to each other in every second tunnel blue, and are as far apart as
possible in every second tunnel red. This order can be seen in both a- and b-directions.
Modulations may be incommensurate, meaning that the period of the unit cell repeat and that of the
modulation are not reconcilable into any common superstructure, but instead, the structure
becomes aperiodic along the modulation direction. The rubidium- and caesium- exchanged zeolite
crystals did not show the doubling of a as the smaller cations did. The increase in repeat distance
along the a direction is probably an effect of increasing sizes of the cations. In the rubidium and
caesium cases, the sizes of the cations effects the placemnts of cations in more tunnels along the a
direction than the placements in the adjacent tunnels. In order to fully describe the effect of the
larger cations two types of modulation was used. The first and strongest effect is from these atoms
being located in a manner that cannot be described by the original unit cell in (one or more)
directions. To describe the positions a wave function is used that tells us what is found in all positions
Fig 28-29. When the function is above neutral there is a metal ion, caesium, rubidium or sodium
occupying the place, and if the function is below the positions are occupied by water. In the caesium
case a crenel function Fig 30 is used , meaning the function is square shaped changing abruptly from
above to below neutral and vice versa. The other type of modulation is displacive modulation
describes how the positions of atoms diverge compared to the position they would have had without
interaction from neighbouring atoms.42 43

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23
Figure 26 The placement of rubidium in the 8rings, on the top row marked by 5 blue circles it is clear that the rubidium in
the adjacent 8-ring is affected by its neighbour marked by red circles. Along a the sequence with rubidium situated on
the right side in the tunnel followed by left side, two sitting on the right side and finally one the left hand side, this
results in what is very close to a 5-fold superstructure in the a-direction.
Figure 27 The placement of caesium in the 8rings can be seen in this figure, this pattern with the first 2 caesium marked
with blue circles pointing right followed by caesium alternating right and left three times is the repetition distance of
close to 5 displayed in caesium and in rubidium exchanged zeolites of JBW. The average placement of rubidium and
caesium are the same in both figures, the difference along a is too small to bi visualized by this figure.
In the thesis of Hansen, the K exchanged JBW is described as disordered with respect to K and water.
In this study we find that the structure is partially ordered. This may be due to a lower detection limit
for weak reflections or an ordering that has taken place over time as the crystals have been stored.
For the rubidium and caesium exchanged crystals the results are quite similar, both show
modulations of the alkali metal/water ordering and the length of the modulation vector is very
similar for the two; qRb = (0.408 0 0) and qCs = (0.403 0 0). The values are close to commensurate
2/5 0 0, but refinements constraining the structures to commensurate yield considerably worse fits
than incommensurate treatments Both structures must be considered to be effectively

Anders Klang
24
incommensurate. While the Rb structure was reported as a simple 5 fold structure by Hansen, the Cs-
structure deviated more clearly. In Hansen’s report the q vector corresponds to a superstructure
between 4.1 and 4.4 times the a-axis corresponding to q = (0.44-0.49 0 0)
The result of 0.403 (4.962 unit cell repeats) differs significantly from 4.1-4.4 stated by Hansen in
1982. This is probably an effect of diffusion, as the crystals have been stored in room temperature for
30 years, making it possible for the cations to rearrange themselves in the tunnels during this time.
Figure 28 In this picture the combination of displacement modulation and occupation modulation of rubidium can be
seen, rubidium is marked with yellow and water with red in the modulation curve. Change a to q

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Figure 29 In this picture the occupancy of rubidium yellow and occupancy of water red can be seen. Change a to q

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Figure 30 Crenel wave of occupancy of caesium yellow and Water red in caesium exchanged zeolite Change a to q?

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27
References
1
Lesley E. Smart, Elaine A. Moore, Solid State Chemistry: an Introduction, Third ed., Taylor and
Francis, Boca Raton, 2005, pp. 259-266.
2
Donald W. Breck, Zeolite Molecular Sieves: Structure, chemistry, and use, John Wiley & sons, New
York, 1974, pp. 10
3
York, 1974, pp. 187-191
4
York, 1974,pp. 249-250
5
York, 1974, pp. 277
6
York, 1974, pp. 313
7
York, 1974, pp. 3-4
8
9
10
York, 1974, pp. 588
11
S. Hansen, A Structural Study of Nepheline Hydrate I, an Inorganic Ion Exchanger, Inorganic
Chemistry 2, Chemical Center, Lund, 1985, pp. 7
12
13
14
15
A.M. Healy et al. , Micro and Mesoporous Materials 37, 2000, pp. 153-157
16
P.W. Atkins, physical chemistry, 6th
edition, Oxford University Press, New York, 1998 pp. 555-556
17
Picture taken from http://www.amanzi.org/craig/diagrams/ made some modifications to Figure.
Accessed 12 Feb 2013.
18
P.W. Atkins, physical chemistry, 6th
edition, Oxford University Press, New York, 1998 pp. 625-632

Anders Klang
28
19
T. Janssen, G. Chapuis and M. de Boissieu, Aperiodic Crystals from Modulated Phases to
Quasicrystals, Oxford University Press, New York 2007, pp 4
20
C. Giacovazzo, Fundamentals of Crystallography, IUCr, Oxford University press, New York, 1992,
pp. 20-24
21
Christopher Hammond, The Basic of Crystallography and Diffraction, 3rd
edition, IUCr, Oxford
University press, New York, 2009, pp 56-76 (
22
Christopher Hammond, The Basic of Crystallography and Diffraction, 3rd
edition, IUCr, Oxford
University press, New York, 2009, pp 100-109
23
24
www.princeton.edu/~cavalab/tutorials/public/structures/rutiles.html Accessed 16 Jan. 2013
25
http://www.princeton.edu/~cavalab/tutorials/public/structures/pics/FeTa2O6.jpg Accessed 16
Jan. 2013
26
de Wolff, Janner, and Janssen, The Superspace Groups for Incommensurate Crystal Structures with
a One-Dimensional Modddulation, Acta Cryst. 1981, A37, pp 625-636
27
A. Yamamoto, Modulated Structure of CuAu II (One Dimensional Modulation), Acta Cryst. 1982,
B38, pp 1446-1451
28
Quasicrystals, Oxford University Press, New York 2007, pp 49-50
29
30
C. Giacovazzo, Fundamentals of Crystallography, IUCr, Oxford University press, New York, 1992,
pp. 221-224
31
T. Janssen, A. Janner, A. Looijenga-Vos, and de Wolff, Incommensurate and Commensurate
Modulated Structures, International tables for crystallography Volume C: mathematical, physical and
chemical tables, 2004, pp 907-913
32
33
34
Chemistry 2, Chemical Center, Lund, 1985, pp. 9-11
35
5th
International Conference on Zeolites, Napoli, June 2-6, 1980, Recent Progress Reports and
Discussion, Edited by R. Sersale, C. Colella and R Aiello, Giannini- Napoli pp. 45-48
36
CrysAlis PRO, Oxford Diffraction Ltd., Version 1.171.33.52 (release 06-11-2009 CrysAlis171 .NET)
(compiled Nov 6 2009,16:24:50)

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37
L. Palatinus, G. Chapuis, J. Appl. Cryst. 40 (2007) 786-790 (superflip)
38
V. Petricek, M. Dusek, and L. Palatinus, (2006). Jana2006. Structure Determination Software
Programs. Institute of Physics, Praha, Czech Republic.
39
40
41
S. Hansen and L. Fälth, Structure of a Potassium-Ion-Exchanged Nepheline I Hydrate Crystal,
Journal of Solid State Chemistry 55, 1984, pp 225-230 text about this is New
42
43
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