Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
Introduction to CaRIne: Bravais and Metallic Lattices
His face showed rather the quiet and interested composure of the chemist who
sees the crystals falling into position from his oversaturated solution.
"Remarkable!" said he. "Remarkable!"
Sir Arthur Conan-Doyle, "THE VALLEY OF FEAR"
Introduction
Crystalline solids have an essentially regular structure, often called an ordered structure. A
crystalline solid is formed by the repetition of a small, basic building block throughout the
structure. Amorphous solids have an irregular structure. The positions of the atoms are
random. Usually amorphous solids occur when solids are formed too rapidly to organize into a
crystalline arrangement. In common soot, for example, carbon atoms formed in the gas phase
during combustion condense to a solid form of carbon that has little long-range structure.
Recently it was discovered that soot does contain individual molecular solids with the
remarkable formulae C60 and C70. When these unique compounds are extracted from the soot,
they crystallize. Another type of amorphous solid are those which can be though of as frozen
liquids, preserving the random orientation of the molecules in the liquid state. Glass is a
common and extremely important example of a frozen solution.
We normally think of crystals in terms of their ideal structures, i.e. where every atom or
molecule in the structure is present at its exact position throughout the almost infinite number of
positions within a macroscopic-sized crystal. In reality, small defects are common, and
statistically almost unavoidable. But most crystal structures are robust enough that one missing
or dislocated atom every few thousand or so does not upset the gross structure. Such minor
impurities are extremely important in making many solids useful. For example, the colours of
gemstones are imparted by very small percentages of impurities in otherwise colourless crystals.
There are several distinct types of crystalline solids from the chemical perspective: (i) metals;
(ii) ionic solids; (iii) covalent solids; (iv) molecular solids. The simplest to understand
structurally are metals and ionic solids. In this tutorial you will learn to build your own models
in CaRIne software, including your own models of the Bravais lattices and five of the idealized
structures commonly found for pure metals.
Instructional goals:
(1)
(2)
(3)
(4)
Recognition of the local and long range structure of the 14 Bravais lattices.
Recognition of the local and long range structure of the common metallic lattice types.
Learn build lattice models using CaRIne software.
Use the CaRIne models to examine the structural properties of lattices.
The "metallic" lattices
The basic ordered unit in a crystal structure is called the unit cell. This is defined as the smallest
region of the crystal which can make up the full crystal structure by repetition of that unit and
possesses the full symmetry of the crystal. Consider the following two-dimensional
representation of the choice of a unit cell. By extension, the full 3-dimensional case is similar.
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
Unit cell
Assymmetric unit
Lattice point
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Repeating unit which is not a good unit cell choice
The correct choice of the unit cell is shown at the top left. A variety of smaller units could be
chosen, including the diagonal box which encloses on asymmetric unit shown at the bottom
left. Such smaller units can replicate the full lattice, but they do not have the same symmetry as
the whole lattice, and are therefore rejected. The asymmetric unit in this lattice is defined at the
top right. It consists of a small circle and a large circle. The heavy dots indicate the lattice
points. The lattice can be represented by an abstract collection of points, each of which stands
for a single unit cell. In this particular lattice, there are two asymmetric units (on average) for
each unit cell. We get this by counting ¼ for each corner circle, shared between four boxes, ½
for each edge circle, and a full count for a circle completely contained within the unit cell. Thus
there are 4 × ¼ + 1 = 2 large circles, and 4 × ½ = 2 small circles inside the correct unit cell.
There are altogether 7 crystal systems, depending on the overall symmetry of the lattice. These
are known as the cubic, the hexagonal, the tetragonal, the trigonal, the orthorhombic, the
monoclinic and the triclinic. In this class we will discuss primarily cubic systems, for which the
trigonometry involved in the calculations is simple, and a few hexagonal and tetragonal systems.
The remaining will not be dealt with, but they are extremely important for lower-symmetry
solids, such as many organic solids (e.g. solid benzoic acid, naphthalene, etc.), as well as most
compounds of the non-metals (e.g. elemental sulfur has many polymorphs, including a
monoclinic and a trigonal form. The basic shapes of these systems is shown in the diagram
below, from which the basic structural parameters are easily determined. Thus in the cubic
system, the edge lengths are all equal and represented by a. The angles between the axes are all
90°. Tetragonal has a square base with sides a, but the height c may be either shorter or longer
than a. Angles are still 90°. The last system with all 90° angles is the orthorhombic case, where
the edge lengths are all different (a, b and c). The trigonal system (also called rhombohedral)
can be derived from the cube by making all the angles α < 90°. The hexagonal system is unusual
in that the unit cell is actually one third of the hexagonal prism shown in the picture. This
prismatic cell has a parallelepiped base of edge length a, separated by 120°, and a height c. The
remaining cell types are monoclinic (one non-90° angle, β > 90°) and triclinic (all three angles α,
β and γ are non-90° and > 90°). Detailed discussion of all possible crystal structures, e.g. as
observed in mineralogy, is beyond the scope of this course.
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
Within the unit cell, the atoms are located by specifying their fractional coordinates. Thus an
atom located at a corner is said to have coordinates of x = o, y = 0 and z = 0, or to have
coordinates (0,0,0). An atom located in the dead-centre of the cell has coordinates of (½, ½, ½),
one half way along any edge has two coordinates of 0, and one of ½, while in the centre of any
face has two coordinates of ½ and one of 0. The advantage of this method is that all lattices of
the same type can be specified by the same set of fractional coordinates. The only thing that is
then altered between the structures is the corresponding values for the unit-cell edge lengths, a, b
and c.
Structures adopted by metals
About 80% of the elements are metallic. The vast majority adopt one of four crystalline
structure types, known as the cubic closest packed (alias face-centred cubic), the hexagonal
closest packed, the body-centred cubic, and the diamond structures. These structures belong
to two crystal classes, the cubic and the hexagonal. In addition, there is a single element,
polonium, which exists in the simple cubic form. This is included for completeness, and also
because it is the base lattice type for one of the important ionic lattice types. Thus in all there are
only five structural motifs to cover a very large proportion of the periodic table.
The two closest-packed structures are simply the densest possible packing of equal-sized spheres
that is possible by geometry. Both are built up from the same kind of closest packed layers.
Consider a layer of spheres packed as close as possible (e.g. billiard balls). They naturally fit
together to form a triangle! Geometrically we can describe this layer as consisting of rows of
spheres arranged in straight lines, with each second row offset from the first by one radius unit
(i.e. half the diameter of the sphere). It is this offset that allows the spheres to nudge into the
depressions naturally formed by the previous rows, and this creates the denser packing in closest
packed layers. The layer is shown in figure (a) below.
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
(a) A single close-packed layer
(b) A second layer placed over top of the first
The second layer is of exactly the same type, but it fits over-top of the first layer in such a way
that its spheres fit into the triangular depressions left behind by the first layer, as shown in figure
(b) above. Geometrically it is offset one radius over and one radius down from a corresponding
row of the first layer. This layering of the atoms leaves small gaps in the lattice between the two
layers. Note that some of the spheres of the second layer fit neatly over a triangle of atoms in the
lower layer. The resulting gaps (which are not visible) have four nearest neighbor spheres,
which are tetrahedrally disposed with respect to the dead center of the hole. These are therefore
called tetrahedral holes. There are both downward- and upward-pointing tetrahedral holes, the
latter resulting from a single atom on the lower layer and a triangle of atoms in the upper.
However, at other sites, a triangle of atoms in the top layer fits above a triangle of atoms in the
lower layer, except that the two triangles are rotated 180° from each other. The geometry of the
resulting holes is octahedral (6 nearest neighbors). In the above figure these holes are shown as
the gaps between the spheres near the middle of the picture. There is only a single kind of
octahedral hole.
x
"up"
x
"down"
Tetrahedral hole
Octahedral hole
If we count the layers, we find that there are:
• Tetrahedral holes - twice as many as the number of spheres
• Octahedral holes - exactly as many as the number of spheres.
Note that all the holes above layer A are counted with layer A, since the holes above B belong to
B, etc., and we consider an essentially infinite array to get this count. (Discontinuities at the
edges of the array are small compared to the total number of spheres).
(a) ABA sequence of the HCP structure
Chemistry 4000 Chemical Crystallography
(b) ABC sequence of the CCP structure
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
It is at the point of adding the third (and subsequent) layer to this structure that the distinction
between hexagonal and cubic closest packing is first observed. We now consider these two
structure types for metals, and we will start to refer to the spheres as atoms. Closest packing
occurs in pure metal where all the atoms are of equal type, and hence of equal size.
Hexagonal closest packed
If we place the third layer directly in line with the first layer, and the fourth where the second
was, and so forth, we obtain what is called ABABABA... packing, and this results in what is
known as a hexagonal close packed lattice (HCP
for short). A typical view of this lattice is shown in
figure (a) at the right. The actual unit cell is
actually 1/3rd of this picture. It consists of a
lozenge-shaped prism with a base of equal edge
length a, 120° apart, and a height c identical to the
picture at the right. The coordinates of the two
atoms in the unit cell are:
Atom in layer A: (0, 0, 0)
Atom in layer B: (1/3, 2/3, 1/2)
If we consider the atom in the center of the top
face, there are six surrounding atoms in the same
layer (A). There are three atoms below it in a
triangle in layer (B), and there will be and identical
triangle in the layer (B) above it, which is not
shown in the picture. Thus there are in all 12
nearest neighbors, and trigonometry can show that
all such atoms are equidistant to the first atom.
Thus the coordination number of the HCP structure
is 12.
Cubic closest packed (also known as facecentered cubic)
If instead the third layer is placed over the holes in both layers A and B, i.e. located over the
octahedral sites in the lattice, we obtain a different structure. This is known as ABCABCABC...
packing, and describes the cubic close packed lattice (CCP for short). The unit cell of this
structure is shown in figure (b) above, and this picture immediately explains the synonym of this
structure, which is face-centered cubic, FCC. Indeed, the structure consists of a cubic box with
edge lengths a of equal length, an atom at each corner, and atoms at the center of each face of the
box. In all, four atoms "belong" to a single unit cell of CCP. The coordinates of the atoms are as
follows:
Atom in layer A: (0, 0, 0)
Atom in layer B: (1/2, 1/2, 0) (1/2, 0, 1/2) (0, 1/2, 1/2)
Atom in layer C: not specified, but supplied by lattice symmetry
The relationship between the ABC layers and the cube is seen only by placing the cube vertically
in line with two opposite corners, the so-called body-diagonal vector in the cube. Then the
atom in the lowest corner is in layer (A), the atoms in the center of the three lowest faces and at
the three lowest corners are all in layer (B), the atoms in the three higher corners and faces are in
layer (C), and the very top corner atom belongs to the next layer (A).
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
The coordination number of the atoms in a CCP lattice is also twelve. It is necessary to
construct a considerably larger model (several unit cells) in order to count these accurately. The
density of both the CCP and HCP is identical, and 74% of space is filled by spheres in either
geometry. It is possible to have random metallic structures in which ABAB layering alternates
with ABCABC sequencing. Such structures are still closest packed, and have the same density,
but they have much larger and more complex unit cells that we do not wish to study in detail.
The known examples are found to have overall hexagonal symmetry.
Body-centered cubic
The body-centered cubic, or BCC, structure, is
considerably less dense than the closest-packed
structures. This can be seen by the fact that all
the atoms have a coordination number of 8. This
structure does not have regular Oh or Td holes.
Its shape is quite easily appreciated, consisting
of a cubic box with atoms at each corner and one
at the very center, hence the name. The
structure is shown in the figure at right in both a
realistic space-filling model, and in a "wire-frame" version that allows the lattice arrangement to
be seen more clearly.
Again it is useful to construct models with more than a single unit cell in order to verify that all
the atoms in this structure are identical. Thus the corner atoms themselves could just as well be
center atoms in a lattice where all the current center atoms become corners. Thus all the atoms
have CN = 8. The coordinates that need to be entered in a crystallographic computer program
are:
(0, 0, 0) and (½, ½, ½)
It has equal edge lengths which are again given by the distance a. Metallic sodium is the bestknown example of this lattice type, but many other metals also adopt this structure.
Simple cubic (primitive cubic)
The simple cubic structure is very open, and is
thus not a good way to fill space. It is only known
for the element polonium, and it may be the
intense radioactivity of this unstable element that
keeps the atoms so far apart as they are in the
simple cubic lattice. The structure consists of a
cube with an atom at the corner only. The
coordinates of the atom are (0, 0, 0), and the CN =
6.
Diamond structure
The least dense structure of all is common to the Group 14 elements, including carbon in the
form of diamond, for which the structure is named. This is of course a non-metal, but the
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
metalloids Si and Ge, and the α (low temperature) forms of Sn and Pb all have this same
structure. This structure also belongs to the cubic class of crystal lattices, but has a more
complex arrangement of the atoms than even the FCC structure. The coordinates of the atoms
are as follows:
Corner atoms:
(0, 0, 0)
Face atoms:
(½ , ½, 0)
(½, 0, ½)
(0, ½, ½)
Interior atoms:
(¼, ¼, ¼)
(¼, ¾ , ¾)
(¾, ¼, ¾)
( ¾ , ¾, ¼)
The metalloids have considerable covalent character in their bonding.
They therefore form solid structures that have quite low density, i.e. far
from close-packed. It is this chemical feature which allows them to
adopt the diamond structure, in which each atom is tetrahedrally
configured, and the CN = 4. We can think of each atom being sp3
hybridized, and thus having four bonds at the tetrahedral angles of
109.5°. It is the most open of all the metallic lattices. Note that this is
not the most stable form of carbon, which is graphite. Graphite is not a
general structure type, and belongs to the structures of the non-metallic
elements that we will consider later on.
It is worthwhile to stop and consider just which atoms "belong" to the unit cell and which don't.
Most people are comfortable with unit cell pictures in which there are atoms at each corner of
the "box". However, this can lead to miscounting the contents of the cell. A corner atom only
contributes 1/8th of its volume to that unit cell, the remainder belong to neighbouring cells. This
point is strongly emphasized by the following graphics in which the unique unit cell only is
shown, and the atoms, if necessary have been "sliced" to fit within the cell boundaries:
"Sliced" view of Simple Cubic unit cell
"Sliced" view of BCC
"Sliced" view of FCC
We thus count 8 × 1/8th = 1 for simple cubic, 8 × 1/8th + 1 = 2 for BCC and 8 × 1/8th + 6 × 1/2 =
4 for FCC. For the HCP unit cell, there are 8 × 1/8th corner atoms and one interior atom for a
total of 2. Notice that the coordinates given above correspond directly to these numbers of
atoms. It is thus equivalent to locate a single atom at the origin (0, 0, 0) or to locate 1/8th of this
same atom at each corner. The repetition of the crystal lattice accounts for this dual description
method. Typical crystallographic software programs have the lattice repeats programmed in, and
thus it becomes important to only add each unique atom position a single time into the program.
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
Procedure
You will work individually in this tutorial using your workstation running CaRIne. Physical
models of the lattices may also be available for study. You will submit your Crystal Model files
(.CRY) for grading. Please submit these individually. It is strongly recommended that you store
your models for future use (e.g. onto your personal “P:” drive; on a USB memory stick, etc.; the
files are very small.)
Limited instruction on the actual operation of CaRIne is provided as needed (blue text); your lab
instructor can supply more information on an as-needed basis. As one of the key goals of this
Tutorial is learning to build models and use them, you are encouraged to explore the features of
the software as much as possible.
Exercise 1
Unit Cells of the 14 Bravais Lattices (Pearson nomenclature, see Notes page 4-3)
Models to create:
Parameters
aP_yourname.CRY
a = 7.4, b = 4.6, c = 5.9 Å, α = 94.2, β = 97.5, γ = 103.4˚, col. R1C1
mP_yourname.CRY
a = 3.15, b = 3.4, c = 4.6 Å, β = 98.4˚, colour: R1C2
mC_yourname.CRY
a = 6.3, b = 6.8, c = 4.6 Å, β = 98.4˚, colour: R1C3
oP_yourname.CRY
a = 4.1, b = 3.6, c = 5.8 Å, colour: R1C4
oC_yourname.CRY
a = 8.2, b = 7.2, c = 5.8 Å, colour: R1C5
oI_yourname.CRY
a = 6.1, b = 4.2, c = 7.2 Å, colour: R1C6
oF_yourname.CRY
a = 8.2, b = 7.2, c = 11.6 Å, colour: R1C7
tP_yourname.CRY
a = 4.1, c = 6.2 Å, colour: R1C8
tI_yourname.CRY
a = 5.3, c = 7.4 Å, colour: R2C1
hP_yourname.CRY
a = 3.8, c = 5.4 Å, colour: R2C2
hR_yourname.CRY
a = 4.8, α= 78.4˚, colour: R2C3 (note: this generates primitive R!)
cP_yourname.CRY
a = 3.8 Å, colour: R2C4
cI_yourname.CRY
a = 5.4 Å, colour: R2C5
cF_yourname.CRY
a = 7.2 Å, colour: R2C6
Start the CaRIne program. Under the Window menu, check that all four tools are checked on. A
“floating” Rotations menu should be present somewhere on screen.
• Using the keyboard and mouse, add a number (e.g. 5) in each of the first three white panels.
This will be the amount that rotations of the models are stepped by using the rotation tools.
• Even more useful is the scaling tools which appear as magnifying glasses with (+) for
enlarging and (–) for reducing the size of your models. Note that CaRIne does not
automatically re-scale any model.
• Rotation of the models is also possible with the mouse (click and drag) if you keep the CTRL
key depressed.
• Under the File menu, use the command New Crystal to create a blank (black) window.
Note: In these tutorials we will not be using Cells at any time, so be sure to always open and
save to the Crystal section of the File command.
• Under the Cell menu, select Triclinic, Monoclinic, etc, and then “P”, “C” as needed.
• Enter the unit cell parameters provided above. Use the default “atom” radius of 1 Å. Choose
a colour from the grid as specified.
• Only one window is active at a time.
• If you enter a wrong value, it can be fixed afterwards using Creation/List under Cell menu.
The models may be made dynamic (rotating).
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
• To (re)start rotation, push the number 2 on the numeric keypad of the keyboard.
• To stop rotation, push down the Spacebar.
The models are created with full atomic radii scale (100%).
• You may at times need to scale back to a lower radii scale to “see” within the lattice.
• To do this, in the active window, push CTRL X, and enter a new percentage in place of
100%.
• In a chemically realistic lattice, the atoms touch or even interpenetrate at 100% scale.
• A good compromise for real crystals is to have the atoms scaled to 25% of their actual radii
Once you have created and saved your Bravais lattice models, it is possible to use the power of
CaRIne to enhance your models.
• Optical enhancement is achieved using the CTRL G (graphics) menu command.
• The first tab can be left as it is (or you may remove some of the items.)
• On the Shading tab, click both boxes on (the default entries seem to work o.k.)
Next, it is helpful to replace the thin lines for the unit cell edge lengths with a thicker line.
•
O
O
O
O
Activate the “Modify Links” tool I → Π.
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Click on two adjacent atoms along a unit cell edge. A box opens with a selection of colours
and thickness. Select “4” or “5” as appropriate values for these small unit cells.
• Click on the “Apply changes for same links” box before closing this menu!
• You may also change the colour of the edges (it is best to avoid Black or Blue as these are
used for the cell-edge names and Cartesian coordinate markers).
Always save your crystal models after modifying them, because the special features may well be
removed by subsequent operations. If necessary, save different versions (e.g. a 3×3 unit cell
cluster) under separate .CRY crystal model file names.
Exercise 2
Examples of common metallic lattices
Models to create:
Parameters
Po_yourname.CRY
a = 3.06 Å (use the atomic radius of polonium listed, 1.53 Å)
Na_yourname.CRY
a = 4.29 Å (again, use the atomic radius provided)
Cu_yourname.CRY
a = 3.615 Å (again, use the atomic radius)
Ge_yourname.CRY
a = 7.2665 Å (this is cF, plus additional locations, see for diamond)
Mg_yourname.CRY
a = 3.2904, c = 5.380 Å (this is hP, plus locations, see above)
In the Introduction to this Tutorial, the coordinates for these element (metallic) lattices are
provided, as well as their crystal systems. Thus Po is cP, Na cI and Cu cF, in each case with one
metal atom at a lattice point. However, Ge has the diamond lattice, which is more open, and is
specified as cF with four additional locations for Ge atoms that must be specified. Similarly, Mg
is hP, but has one additional site occupied by atoms that must be specified.
•
To add additional atom sites (Ge and Mg), once the model is created, open it up with the
Creation/List command under Cell.
• Type in the coordinates (simple fractions can be entered directly using “/”, or else you can
use exact decimals, which are not so good for “thirds”!)
• Then push on the Add button, and finally after all are entered, on the Apply button.
The crystal model should now be updated to the desired structure. Proceed as described
previously to improve the look of your model. Be sure to save as a Crystal. You may also save
the Cell files if you wish.
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Tutorial 2
Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
Note that these are true metallic lattices, and the atoms at their 100% “true” radii will touch or
even interpenetrate each other. To get a more “open” view of the lattice, it is usually helpful to
scale back the radii to ~20% (see above for instruction.)
For all five models, check for the direction vector where the spheres touch each other (i.e. along
a cube edge, along a cube face diagonal, or along the body diagonal.) You may wish to create
links between the atoms in fact the directions along which the atoms touch. They should not be
considered to be “bonds” (except perhaps in the case of germanium), but rather visual guides to
help you determine the atom coordination number. You may also use different colours to
distinguish different “sites” of equivalent atoms types. Such colours do not denote a difference
in atom identity.
• To diagnose the full identity of any atom, simply active the Modify Atom tool (z→z), and
click on the atom. Be sure to press Cancel when exiting the informational window that pops
up, or you will modify the atom.)
To add “bonds” to a lattice model, the best procedure is as follows:
• Use the “Distance between atoms” tool (z→z) to discover the shortest contact distance.
• After most recently clicking on the desired distance, press the “Multi link” command on the
Crystal menu. This will insert “bonds” between all atoms linked by the most recently
measured distance. Note these are faint green lines and may be hard to see.
• Use the Modify Links with “Apply changes for the same links” checked to alter the
appearance of the links.
• Note that only rarely will the unit cell edge lengths correspond to such “bonds”.
To gain full control over the model, you may have to do some of the following:
• To temporarily hide any atom, find the “hide atom” tool on the horizontal tool bar: z→{.
• The reverse tool will restore the “hidden” atom (looks like: {→z).
• To rotate the model to any desired position, either click with the mouse on the red arrows on
the rotation bars which give (+x,–x), (+y,–y) and (+z,–z) in the amount entered in the step
sizes (e.g. 1, 2, 5 degrees, as you wish), or gain full motional control bye holding down the
CTRL key while moving the mouse with either the left mouse button or the right mouse
button depressed.
• The sense of rotation is different for each button, and a little bit of practice should allow you
to turn the models in any desired orientation.
• Hint: do not move them too rapidly, or you may become disoriented. Use the blue XYZ
arrows at the center of each model to regain your orientation.
• To obtain the volume of each unit cell, find under the Calcul. menu the command Unit Cell
Volume; a window will open and report the volume in Å3.k Note that the Count atoms in
crystal command does not give the number of atoms in the unit cell, rather the number of
spheres provided by the specific model you are watching. These are definitely not the same
quantity!
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Tutorial 2
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Introduction to CaRIne 3.1 – Bravais and Metallic Lattices
To obtain the atom distances, activate the Distance Between Atoms tool from the toolbar
(z→z).
Click on any two atoms in sequence, and a window pops up displaying the fractional
coordinates of the two atoms, and the distance between them in Å.
To obtain the angle in degrees, activate the Angle Between Two Directions with Mouse tool
(∠). In all, four mouse clicks are required to get an angle.
Two clicks define one vector, two a second vector, and the window pops up to report the
angle between these vectors.
This is a very versatile tool – but note that it only defines a “bond angle” if a common central
atom is used for both “bonds”.
Exercise 3
Additional practice with lattice models
It is often instructive to make lattice models of more than one unit cell. If you make such
modifications, save them under a different .CRY crystal model file name.
To make a multi-cell model, under the Crystal menu, click on “Spread of crystal”. You can
specify integer multiples in a, b and c directions. Note that these can start from a corner (the
“origin”) or from the center of the unit cell.
Under the Calcul menu, there are many options for taking measurements within the lattice, and
some practice with this is recommended.
Other features of the software, such as the XRD (powder Xray), stereo projection, and
Reciprocal lattice modules will be used later in the course.
Evaluation
Submit your models in the way that your instructor wishes to receive them. Email is quite
feasible as the files are very small.
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