Crystallography Flashcards
What are 3 types of crystal symmetry?
Centre, Axis and Plane
What is Axis of Symmetry
If you rotate a crystal around an axis and it looks the same more than once during the rotation, it has an axis of symmetry
What are the types of Axis of Symmetry?
Diad axis - 2 fold axis
ex) A rectangle has 2 short faces and 2 long faces
Triad axis - 3 fold axis
ex) A triangle has 3 edges repeating around 120 degrees
Tetrad axis - 4 fold axis
ex) A square or cube has 4 edges repeating around 90 degrees
Hexad axis - 6 fold axis
ex) A hexagon has 6 edges repeating around 60 degrees
What is the Plane of Symmetry?
Looks the same on both sides if you were to hold it down the centre; Essentially a mirror image (m)
A crystal can have lots of mirror planes (i.e., hexagonal has 6 m)
What are Axial Ratios?
For any structure or shape with two or more axes, is the ratio of the length (or magnitude) of those axes to each other
Ratios express the relative, not absolute, lengths of the cell edges that correspond to the crystallographic axes
In describing a mineral we utilize the following:
Symmetry
Position of faces (Miller Indices)
Representation of 3D crystals in 2D (on paper)
What are Crystallographic Axes?
Are generally taken as parallel to the intersection edges of major crystal faces (parallel to the edges of the unit cell) Allows us to index crystal faces or planes (i.e., specify their orientation in space) All crystals (except hexagonal) are referred to by 3 crystallographic axes designated a, b, c (or x,y,z)
What are Plane Lattices?
Consider a spot, which could represent a group of atoms. Can be repeated parallel to vector A; a row of dots
Can produce 5 different plane lattices in 2D
Can also be repeated by translating parallel to vector b at an angle γ from the direction
What are Space Lattices?
Same thing with a repeat of planes one above another (3D)
Triclinic system
No principle symmetry, very unsymmetrical
No symmetry constraints
a ≠ b ≠ c
α ≠ β ≠ γ ≠ 90º
Tetragonal system
α = β = γ = 90º
Three perpendicular axes where 2 are equal (a1 = a and a2 = b) and one is a different length; a = b ≠ c
Isometric (cubic) system
a = b = c
α = β = γ = 90º
Three axes of equal length at 90º; a = a1, b = a2, c = a3
Orthorhombic system
b = 2-fold or perpendicular to a mirror; a is inclined towards you
Three perpendicular axes where a < b < c
a ≠ b ≠ c; α = β = γ = 90º
What is the Interfacial Angle?
Is the NORMAL to two faces Section through a six-sided crystal Interfacial angle = i [= 180º - θ] If θ = 120º then i = 60º
In all crystals of the same mineral, the angles between
_______ have a constant value
corresponding faces
What are Miller Indices?
The orientation of any plane (or face) in a crystal lattice can be described in terms of the intercepts of the planes on the coordinate axes of the lattice
A Miller Index has the general form (h,k,l), where h, k, and l are integers related to the a, b and c crystal axes, respectively
Law of Rational Faces
It was discovered that for given faces the indices could always be expressed as simple whole numbers or zero
What are Miller-Bravais Indices?
When describing the orientation of a plane in a hexagonal crystal, four digits are used (h,k,i, l)
A modification was developed by Auguste Bravais
Because the 3 axes are at 120º, it always works out that
h + k + i = 0
What is a Crystal Form?
External shape is denoted by the word habit
The crystal form is a collection of equivalent crystal faces related to each other by the symmetry of the mineral
It is identified by { } around the hkl Miller Index of one of the faces that comprise the form
A form may be either open or closed
What is a Zone Axis?
A collection of crystal faces all of which are parallel to a common line called the zone axis
What are Positive and Negative forms?
Positive and negative varieties of a form such as a tetrahedron differ only in that the negative forms is rotated relative to the positive form
The same crystal may have both a positive and a negative version of the same form
Can there be combined Cystral Forms? Why?
Yes, simple crystals consist of only a single closed-form, such as a cube; more complex crystals may include several different open and/or closed forms
The forms on any given crystal must all be compatible with each other
What is an Epistaxis?
When two compositionally different crystalline substances show a non-random overgrowth
What are some examples of parallel growth?
Sceptre quartz
Asbestiform riebeckite amphibole
Quartz
Olivine in picrite, Isle of Rhum
What are some examples of epitaxial growth?
Haematite crystal on magnetite
Rutile crystals in epitaxial overgrowth on haematite
Euhedral
Minerals that display well-formed crystal faces
Anhedral
Minerals without crystal faces
Subhedral
If crystal faces are present, but not well-formed
What is Crystal Twinning?
A twin is the symmetrical overgrowth of 2 (or more) crystals of the same substance. The 2 individuals are related by a symmetry element (twin element) that is absent in a single crystal
Twinned crystals are usually designated as contact twins or interpenetrant twins
Simple twins
Repeated or multiple twins are made up of 3 or more parts twinned according to the same law
What are the twin elements?
(1) reflection (twin plane); (2) rotation (twin axis); and (3) inversion (twin centre)
What is the surface on which the 2 individuals are united is known?
The composition surface (composition plane)
What does the twinning in lower symmetry groups generally produce?
A resulting aggregate symmetry higher than that of each individual
Albite law
Has {010} as the twin axis and indicates that the twins make a form, the faces are parallel to the mirror plane (010)
i.e. perpendicular to the b-axis
Pericline law
Has [010] as the twin axis. As stated above, pericline twinning occurs as the result of monoclinic orthoclase or sanidine transforming to microcline
The 3 twin laws that occur in the mineral orthoclase: are
Manebach (001), Baveno (021) and Carlsbad twinning [001]
Aragonite Crystallography
Orthorhombic system
In the orthorhombic system, the twin plane is most commonly parallel to a prism face. The contact twin of aragonite and the cyclic twins of aragonite and cerusite are all twinned on {110}
Staurolite Crystallography
The mineral staurolite (monoclinic system; but psuedoorthorhombic) is commonly formed as two types of interpenetrant twins: {031} Maltese cross, {231} (60° Iron cross)
What is Growth twinning?
is the result of an emplacement of atoms, or ions (or groups of atoms or ions) on the outside of a growing crystal in such a way that the regular arrangement of the original crystal structure is interrupted
What is Primary twinning?
Growth twinning reflects ‘accidents’ during free growth (nucleation errors)
What is Transformation twinning?
Occurs in pre-existing crystals and represents secondary twinning
May result when a crystal that formed at a high temp. subsequently rearranges its structure to a different symmetry from the high T form
What is Mechanical (deformation) twinning?
This is an example of secondary twinning
If applied stress produces slippage of atoms on a small scale, a twin may result
Is frequently present in metamorphosed limestone (polysynthetically twinned calcite). [always reflection twins]
What is the Stereographic Projection of crystals?
Most natural crystals differ in size, dimensional proportions, and shape of faces - making a drawing or proving symmetry difficult
However, the angular relations (Interfacial angles), which relate to the crystal axes and atomic structure, remain constant for a given mineral
These relations can be accurately depicted, regardless of distortion, by use of Stereographic Projection
What is a Contact goniometer?
Used for measurement of Interfacial angles in well-formed crystals, similar to a protractor
Spherical Projection
The centre of a crystal is imagined as coincident with the centre of a sphere
From the centre project Normals to each crystal face intersect the surface of the sphere
Each intersection of the Normal and the sphere is the pole to that face
From the sphere project down from the face pole to the S-pole and mark where it intersects the Equatorial plane with a dot
What does (•) mean?
The top half of the crystal (positive C axis)
What does (o) mean?
The bottom half of the crystal (negative C axis)
What is the Primitive Circle?
All faces lying in a zone whose zone axis is parallel to the N-S diameter of the projection will have poles lying on the circumference of the Equatorial plane
Other faces will plot within this primitive circle
What are the Properties of a Stereogram?
- Radius is equivalent to an angle of 90º
- Linear distance between 2 poles on the projection is proportional to interfacial angles between the respective faces - relation is given by simple trig
- Planes passing through the centre of the projection will project on the sphere as Great Circles
To save time in construction we use a prepared Stereographic Net - The Wulff Net
Who was Von Laue and what did he discover?
He showed that if a beam of X-rays passed through a crystal, diffraction would take place and a pattern would be formed on a photographic plate placed at a right angle to the direction of
the rays
Also won a Noble Prize
What is a Continuous spectrum?
Produced when a high-speed electron strikes an atom
and bounces off, losing some of its energy in the
process; radiation covers a wide range of λ
What is a Characteristic spectrum?
Produced when high-speed incident electrons dislodge electrons from inner shells; holes created are filled by electrons from outer shells (high to low energy states), producing characteristic or ‘line’ radiation
What is a Cathode Filament and what is its role?
Is part of an x-ray tube and serves to expel the electrons from the circuit and focus them in a beam on the focal spot of the anode
What is an Anode?
An electrode through which the conventional current enters into a polarized electrical device
The Bragg equation?
nλ = 2dsinθ
We can control the wavelength (λ) and vary and continuously measure the incident angle (θ), leaving only the lattice plane spacing (d-spacing) as a variable
What is Bragg’s law?
When Bragg condition is satisfied, the X‐Rays will constructively interfere
If the Bragg condition is NOT satisfied, then Xrays will be diffracted, but will NOT result in coherent reflections
So whenever we observe a constructive interference, at that point we can calculate what?
The d-spacing for the
unknown mineral
In order to use the Bragg equation to determine d-spacings, we must what?
the X-ray beam must be of a single known wavelength (λ)
Most common to use metal filters placed
in the path of the X-rays, between source and sample
How can we modify this primary radiation so that only a
particular wavelength is used?
We cannot make the radiation entirely monochromatic by this method, but the objective is to allow through one very strong characteristic line (with a specific λ) and to filter out the rest
What is an Absorption curve?
A graph that plots the number of photons of light of different wavelengths absorbed by a photopigment
The _____ will increase rapidly with
the increasing wavelength, then at some point (element dependent), it will drop off sharply
Absorption
The presence of this _______ can be used to eliminate any primary radiation to its low wavelength side, allowing a strong character line to pass
Absorption Edge
What is a Powder photograph?
The powder is fitted to a glass fibre or into a glass capillary. X-ray film mounted like a ring around the sample is used as a detector
What is a Powder diffractometer?
A scintillation counter may be used as
a detector instead of film. Using an automated goniometer step by step intensity may be measured and stored digitally
What is Spectrometer Geometry?
Requires that in order for the angle of θ to be
changed, the sample be rotated and the counter be rotated at twice the rate of the sample
What are the Strengths of X-ray Diffraction?
Is Non-destructive - small amount of sample
Relatively rapid, quite versatile
Identification of compounds/phases - not just
elements
Quantification of concentration of phases -
(sometimes)
Classically for powders, but solids possible too
Gives information regarding structure, cell parameters,
crystallinity, size/strain, orientation, thermal
transformations
