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
What are the Limits of X-Ray Diffraction?
Bulky technique (generally) - unless a camera is used
Not a “stand-alone” technique - often need chemical
data
Complicated spectra - multiphase materials
(identification / quantification can be difficult)
What are the Advantages of an X-ray Camera?
Very little sample material needed The whole pattern is generally obtained Broad, weak reflections are more easily detected above background Preferred orientation is less enhanced
What is a Sample preparation?
A powdered ‘representative’ sample
Particles represent ‘infinite’ random particle orientations
Watch for preferred orientation (e.g., clay minerals)
What do you do for a Data Analysis?
- Plot the data (2θ vs. Counts)
- Determine the Bragg equation for each
of the peaks - Calculate d for each peak
What is a mineral?
A naturally formed solid with a specific
chemical composition and characteristic
crystal structure
Why do minerals form crystals?
Crystals can form in (from) a solution, a melt or a vapour (gas).
It is the process by which disordered atoms
take on an ordered arrangement, characteristic of the crystalline state
Crystallization occurs in response to what exactly?
Precipitation of salt from seawater during evaporation
of the seawater.
Growth of minerals (e.g., sulphur) around a fumarole
(volcanic vent)
Crystallisation of minerals in a cooling magma (lava)
Crystal growth is related to what?
Nucleation
Critical size
2 competing tendencies for crystals in a magma
Thermal vibrations that tend to destroy the nuclei of
potential minerals.
Attractive forces that aggregate atoms/ions into
crystal structures
Morphology (shape) of zircon as a function of ____ and ____
growth rate, melt chemistry
In describing a mineral we utilize the following
Symmetry
Position of faces (Miller Indices)
Representation of 3D crystals in 2D (on paper)
Monoclinic System
Is a diad
If 2-fold is present: b is parallel to it
If m is present: b is perpendicular to it
a ≠ b ≠ c
a-axis is inclined towards you
a = γ = 90º; β > 90º
Hexagonal System
Three axes of equal length at 120º in one plane
The c-axis is perpendicular to the plane of the others
a1 = a2 = a3 ≠ c
What is a Parametral Plane?
The unique face which intercepts the crystallographic axis in distances that have the same ratio as the lengths of the sides of the unit cell for that particular crystal
What is a Pinacoid?
A form comprising of parallel faces
What is a Prism?
A form comprising of three or more faces that meet in edges that are parallel
What is a Pyramid?
A form comprising of three or more faces intersecting the vertical axis either positively or negatively and also intersecting at least one horizontal crystallographic axis
Twin crystals may originate through:
Growth, transformation and deformation
Twin Crystal Contact
A composition surface is a plane
Twin Crystal Interpenetrant
A composition surface is irregular
Twin Crystal Simple
There are two component parts to the twin
Twin Crystal Multiple
There are more than two component parts to the twin
Polysynthetic Twin Crystal Multiple
The twin plane remains parallel throughout the aggregate
Cyclic Twin Crystal Multiple
The twin plane is repeated in a circular fashion at regular angular intervals
Normal Twin Crystal Multiple
The twin axis is perpendicular to the composition plane (or a possible crystal face)
Parallel Twin Crystal Multiple
The twin axis lies in the composition plane, parallel to a zone axis
Complex Twin Crystal Multiple
The twin axis lies in the composition plane, perpendicular to a zone axis (rare)
A synthetic mineral vs A real mineral
A real mineral is naturally occurring with a specific
chemical composition and characteristic
crystal structure
A man-made mineral is not naturally occurring
Is Agate a mineral?
Agate is partially crystalline but not arranged like quartz would be, it’s a amorphas = mineraloid
Amorphas
Not completely crystalline and atoms are not perfectly arranged, glass is an example of being amorphas; eventually will turn into a mineral (glass will cloud)
Why do most minerals not grow into perfectly formed crystals?
Crystals need ideal growing conditions and room to grow. When many different crystals grow near each other, they mesh together to form an anhedral mass (competition for space)
Cylindrical Mineral Symmetry example
Rotational symmetry and therefore infinite rotation because the vertical faces are smooth and circular. If you add an edge, you’ll turn it into a 1 fold
Centre of Symmetry
The regularity of position of like faces and edges, going from the centre of the crystal
Trigonal System
Triad
Defined by a three-fold rotation axis, and can be generated from the cubic crystal system by stretching the cube along its diagonal. The symmetry requires the primitive vectors to have the form
a = b, α = β = π/2, γ = 120º
What are 2 examples of an isometric crystal form?
Tetrahedron and an Octahedron
Where is the Interfacial Angle in a crystal?
The angle between the normal to two faces as indicated in the diagram
Crystal Habit
The characteristic external shape of an individual crystal or crystal group
Its crystallographic forms, plus how well developed each form is
A crystal that is a rectangle table shape or a book
Tabular
A sea urchin shaped crystal
Radial
A mass of anhedral grouped crystals
Granular
Vertical perfect columns stacked tightly like a licorice
Parallel
( )
Miller indices
{ }
Crystal form
[ ]
Zone axis
(011bar) what does 1bar mean?
This means that the face is cutting along the negative c-axis
(011bar0) and (0011), which one is false?
(0011) is false because if you add the first three together, you must get zero. You get 1 when you add 0+0+1.
How many plane lattices can you make on paper?
5 plane lattices (1, 2, 3, 4, 6)
What is quartz’s crystal shape?
Hexagonal
What is olivine’s crystal shape?
Orthorhombic
What is zircon’s crystal shape?
Tetragonal
What is halite’s crystal shape?
Cubic
What is gypsum’s crystal shape?
Monoclinic
What is kyanite’s crystal shape?
Triclinic
What is calcite’s crystal shape?
Rhombohedral
Is a Dipyramid’s form open or closed?
Closed
Is a Pinacoid’s form open or closed?
Open
Is a Rhombohedron’s form open or closed?
Open
Is a Dihedron’s form open or closed?
Open
Is an Octahedron’s form open or closed?
Closed
Is a Tetragonal Trapezohedron’s form open or closed?
Closed
If the vibration direction
of the light is constrained
to lie in a single plane, the
light is _____.
plane polarised
What is Relief?
Determined in PPL, it’s a measure of the relative difference in refractive index (n) between a mineral grain and its surroundings
What is the Becke line test?
A distinct line of white will separate from
the grain boundary as you defocus the grain downwards, positive when the refractive index of the mineral is higher than the refractive index of the medium, and negative when the opposite occurs
What are Interference Colours?
Light waves, under certain conditions, have the ability to interfere with one another
Measured on a colour scale with 4 orders
Isotropic minerals
As light enters the mineral there is no complication - it
vibrates in all directions parallel to the wavefront
Anisotropic minerals
As light enters it is split into two light waves,
which are polarised at right angles to each other and
which travel at different velocities. The n for these two
rays must be different. This effect is termed double
refraction
What is Birefringence?
Is the difference in refractive indexes (n) for any
section through an anisotropic mineral
Birefringence can be represented graphically in terms
of variation of n in different directions
_______ (seen under XPL) are produced as a consequence of light being split into 2 rays on passing through an anisotropic mineral
Interference colours
Extinction
Stage rotation of an anisotropic mineral in XPL
causes it to go in and out of view (every 90°).
With the intensity of interference colours increasing at 45° away from extinction
Pleochroism
The ability of a mineral to absorb different wavelengths of transmitted light depending upon its crystallographic orientations, biotite exhibits this
Changes in absorption colour (in PPL) as stage rotated
Uniaxial vs Biaxial
The optical indicatrix is a 3-D representation of how the
refractive indices (of light waves) (n) varies within a
particular mineral
Uniaxial - 1 axis
Biaxial - 2 axis
Isotropic indicatrix
Optically isotropic minerals all crystallize in the isometric system
The Refractive index is the same in all directions, thus the indicatrix is a perfect sphere
Birefringence may be considered to be zero
Uniaxial indicatrix
Tetragonal and hexagonal minerals have 2 different unit cell dimensions (a, c) and a high degree of symmetry about the c axis
2 indices of refraction are required to define the dimensions of the indicatrix (nε, nω), which is an ellipsoid
The maximum birefringence of uniaxial minerals is always [nε - nω]
What is the Optic sign?
The dimensions of the indicatrix along the c axis may be either greater or less than the dimensions at right angles
In ____, nε is greater than nω and thus the extraordinary rays are slow rays
optically positive minerals
In ____, nε is less than nω and thus extraordinary rays are fast rays
optically negative minerals
Cleavage
Appears as straight lines in a thin section
Types of Extinction
Parallel
– Mineral extinct parallel to the cleavage
Inclined
– Mineral extinct at some angle to cleavage
Symmetrical
– Go extinct at angles symmetrical with cleavage
What are Interference Figures?
Is obtained to rapidly determine the optical
character, that is, whether a mineral is uniaxial or biaxial, and to determine the optic sign
A ____ is produced when the mineral’s optic axis is perpendicular to the microscope stage
Uniaxial Axis Figure
If a mineral grain is orientated with the optic axis parallel to the microscope stage, an ____ is produced
optic normal interference figure
If blue is in the upper right of the figure then it is
Positive
If yellow is in the upper right of the figure then it is
Negative
What are Biaxial Minerals?
Minerals with the lowest symmetry and three crystal axes of unequal length, and in most cases one inter-axis angle ≠ 90°
Called because they have two directions in which light
travels with zero birefringence
Biaxial minerals have
__ unequal crystal axes
3
Unlike the crystallographic axes, the
three optical directions are always at ____
right angles to each other
Biaxial Indicatrix
- 2 optic axes
- Indices of refraction nα, nβ, nγ
- nα < nβ < nγ so γ is always slow
- What is max. birefringence?
- 3 indices, only 2 light rays in mineral
- Both are extraordinary-rays
- Y is the optic normal
BXa Figure
Acute bisetrix figure
Produced if the (X or Z) is oriented perpendicular to the
stage
Optic axes are vertical
Relatively low order interference colours
Optic Normal (Flash) Figure
• Produced if a mineral grain is oriented with the
ON vertical
• Grains display maximum interference colours (as
X and Z are horizontal)
• Similar to uniaxial flash figure
• Not used for sign determination
2V
Spacing between melatopes
If 2V = ___ , the isogyre is a straight line
90º
Biaxial positive vs negative
If the mineral is positive, Z is the acute bisectrix, and X the obtuse bisectrix
If the mineral is negative, X is the acute bisectrix, and Z the obtuse bisectrix
What is Snell’s Law?
If the frequency (ƒ) of light remains constant, V and λ will depend upon the medium of transmission. Light passing from a medium of one velocity to a medium of another velocity will be refracted according to Snell’s
Law
Solid-solution Geothermometry
If the composition of a mineral phase can be expressed as a proportion of 2 pure end-member phases, chances are that this solid-solution series is T dependent
Presence of certain indicator minerals & mineral
assemblages in rocks can be considered as _______
Mineral phase geothermometers
The partitioning of Fe + Mg in minerals crystallizing in
equilibrium in magmatic or metamorphic systems is a
variation of ________
Solid-solution geothermometry
The T at which a mineral-forming reaction takes place or the range of T within which a mineral is stable can be determined by:
- Experimentation
- Thermodynamic calculation
- Empirical observation of minerals in the environment they formed
Most mineral-forming reactions are ____
T sensitive
