Test 2 Flashcards
Linus Pauling (1901-1994)
American Chemist, won the noble prize for Chemistry and Peace
Pauling’s Rules - Rule 1 - The radius ratio Rule
The sum of the ionic radii determines the cation-anion distance, while the cation-anion radius ratio determines the coordination number (C.N.) of the cation
Pauling’s Rules - Rule 2 - The electrostatic valence rule
In stable Ionic Struct., the valence of each anion is = to the sum of the strengths of the electrostatic bonds to it from the cations
Pauling’s Rules - Rule 3 - Sharing of polyhedron corners, edges, and faces
The existence of edges and faces, the more sharing, the less stable. this effect is large for cations with high valency and small coordination #, and is especially large when the radius ratio approaches the lower limit of stability of the polyhedron
Pauling’s Rules - Rule 4 - Crystals containing different cations
In a crystal containing different cations, those of high valency and small coordination number tend not to share polyhedron elements with each other
Pauling’s Rules - Rule 5 - The rule of parsimony
The # of different kinds of constituents in a crystal tends to be small
Structure Terms
- Corner Sharing - 1 atom shared
- Edge Sharing - 2 atoms shared
- Face Sharing - 3 atoms shared
Isostructural
Having the same, or a corresponding, structure
Crust
Top Component of Lithosphere
Major elements of Earths crust
Earth’s crust is composed predominantly of eight elements. O, Si, Al, Fe, Ca, Na, K, Mg. Measured in weight %
Minor and trace elements
Minor = 0.1 - 1 weight % Trace = <0.1
Given in ppm or ppb
ex// C
Mantle
layer bounded below by a core and above by a crust
Upper Mantle
The upper mantle is dominated by the mineral olivine, Mg2SiO4
Effects of pressure begin to affect atomic structures
Transition Zone
From about 410 to 660 Km below the surface, Olivine transforms into denser structures
Wadsleyite and Ringwoodite
Hydrous, to about 1 weight % water
Lower Mantle
Pressures are so great that Si becomes (CN = VI), and some Mg becomes (CN = VIII) (perovskite structure)
Core
- Core divided into 2 sections, Liquid outer core, Solid inner core
- There is a definite chemical discontinuity between the lower mantle and the outer core
- The main elements in the core are an Fe and Ni alloy
- Increasing temperature first melts the alloy to make the outer core
- Increasing pressure freezes the alloy to produce the inner core
Outer Core
Liquid, 2900 to 5100 Km below the earth Composition is Fe with about 2% Ni Density of 9.9 gm/cm3 is too low to be pure metal Silica makes up 9-12%
Inner Core
Solid, 5100 to 6371 Km below surface
80% Fe, 20% Ni alloy
Pressures reach about 3 megabars
Temperature at the center is about 7600ºC
Ores
Trace elements in the gold group, the platinum group, mercury, lead, and others
Effects of pressure
As pressure increases, minerals transform to
denser structures, with atoms packed more
closely together
Victor Goldschmidt
Swiss-born Norwegian mineralogist and petrologist who laid the foundation of inorganic crystal chemistry and founded modern geochemistry
Goldschmidt’s Rules - Size
Atomic substitution is controlled by size (i.e.,
radii) of the ions (Free substitution can occur if size difference is <15%, Non if >30%)
If there is a small difference of ionic radius the
smaller ion enters the crystal preferentially
Goldschmidt’s Rules - Charge
Atomic substitution is controlled by charge
of the ions –> cannot differ by more than 1
For ions of similar radius but different
charges, the ion with the higher charge
enters the crystal preferentially
Factors affecting solid solution - Temperature
Minerals expand at higher T
Greater tolerance for ionic substitution at higher T
Factors affecting solid solution - Pressure
Increasing pressure causes compression
Less tolerance for ionic substitution at higher P
Availability of ions
Ions must be readily available for substitution to occur
Spin State - High
Mostly unpaired e-
Bigger atomic radii
Spin State - Low
Paired e-
Smaller atomic radii
Types of Crystalline Substitution - Omission and Substitutional
Substitutional - Mg^2+ ~ Fe^2+
Omission - Ca^2+ + Void ~ 2 Na+
Types of Crystalline Substitution - Vacancy
normally vacant sites ([]) can be filled as part
of a coupled substitution
[] + Si4+ = Na+ + Al3+
Types of Crystalline Substitution - Interstitial
Atom or ion occupies space in between the normal sites
Often H+
Ex// Beryl
Schottky Defect
Vacant lattice site
Frenkel defect
Wen an atom or cation leaves its original place in the lattice structure to create a vacancy while occupying another interstitial position
HCP Stacking defect
H H C H H
CCP Stacking defect
C C H C C
Grain Boundary Defect
Two lattices grow together, with some displacement of
ions
Polymorphous minerals
Polymorphism is the ability of a specific chemical composition to crystallize in more than one form.
Result of pressure
ex// Al2SiO5
Ditypous minerals
Same chemical composition, different stacking
Pseudomorphic minerals
mineral formed by chemical or structural change of another substance
Stable vs. metastable
A material being truly unchanging vs. A material where a change cannot be observed because the changing is too slow to be observed.
Mineraloids
A naturally occurring, inorganic solid that does not exhibit crystallinity.
ex// Opal
Ex-solution
Process through which an initially homogeneous solid solution separates into at least two different crystalline minerals without the addition or removal of any materials.
Order-Disorder
If one type of ion substituting for another
prefers a certain type of site over another
the structure is ordered.
Metamict
Alpha radiation emitted from the radioactive
elements is responsible for degrading a mineral’s
crystal structure
If structure destroyed, then it is metamict
Atomic Arrangement
Minerals must have a highly ordered atomic arrangement
Unit Cell
Simplest (smallest) parallel piped outlined
by a lattice
Auguste Bravais
French physicist known for his work in crystallography, the conception of Bravais lattices, and the formulation of Bravais law.
Bravais Lattice
a two or three (space lattice) dimensional array of points
Lattice Requirements
Environment about all lattice points
must be identical
Unit cell must fill all space, with no
“holes”
Types of lattice (P,I,C,F,R)
P = Primitive I = Body - Centered C = Centered F = Face - Centered R = ?
Crystal System - Isometric
P, I, F
a=b=c
α = β = γ = 90 ̊
Crystal System - Tetragonal
P, I
a = b ≠c
c > a
α = β = γ = 90 ̊
Crystal System - Orthorhombic
P, I, C, F
a ≠ b ≠c
c > a > b
α = β = γ = 90 ̊
Crystal System - Hexagonal - Hexagonal
a = b ≠ c α = γ = 90 ̊ β = 120 ̊
Crystal System - Hexagonal - Rhombohedral
a = b = c α = β = γ ≠ 90 ̊
Crystal System - Monoclinic
P, C
a ≠ b ≠c
α = γ = 90 ̊ (β ≠ 90 ̊)
Crystal System -Triclinic
P
a ≠ b ≠c
α ≠ β ≠ γ ≠ 90 ̊
Arrangement of Ions
Ions can be arranged around the lattice point
only in certain ways
These are known as point groups
Point Group
Point indicates that, at a minimum, one point in a pattern remains unmoved
Group refers to a collection of mathematical
operations which, taken together, define all
possible, nonidentical, symmetry combinations
Symmetry Elements
Rotation
Reflection
Inversion
Symmetry Operation
Any action which, when performed on an object, leaves the object in a manner indistinguishable from the original object
Motif
The smallest representative unit of a structure
2/m
2-fold rotation with a mirror plane perpendicular to it
2mm
2-fold rotation with 2 parallel mirror planes
3m
3-fold rotation with 3 parallel mirror planes
3/m
3 fold with a perpendicular mirror plane
2/m 2/m 2/m
Three 2-fold axes, mutually perpendicular, with a mirror plane perpendicular to each
Ditetragonal dipyramid
Has 4/m 2/m 2/m symmetry
Two 4-sided pyramids attached at a square base
Derivative Structures
Stretching or compressing the vertical axis
Lowers symmetry
Complex symmetry operations
Complex operations involve a combination of two simple operations
Roto-inversion and Roto-reflection
Roto-inversion
This operation involves rotation through a specified angle around a specified axis, followed by inversion through the center of symmetry
Donated with Bar
Roto-reflection
Transformation which is the combination of a rotation about an axis and a reflection in a plane perpendicular to that axis.
Hexagonal Scalenohedron
bar3 2/m
William Hallowes Miller
British Mineralogist and Crystallographer
Miller indices
Notation
Lattice Points = 100
Line/axis = [100]
Miller indices/faces = (100)
Form = {100}
Law of Haüy
Crystal faces make simple rational intercepts on crystal
axes
Law of Bravais
Common crystal faces are parallel to lattice planes that have high lattice node density
Form
Classes of planes in a crystal which are symmetrically equivalent
Isometric form
{100}(Cube),{111}(Square Dipyramid) encloses space, so it is a closed form
Open Forms – Tetragonal
{100}(Rectangle) and {001}
Pedion
Open form with single face
Pinacoid
Open form consisting of two parallel planes
Dome
Open form consisting of two intersecting planes, related by mirror symmetry
Sphenoid
Open form consisting of two intersecting planes, related by a two-fold rotation axis
Pyramids
A group of faces intersecting at a symmetry axis
Open form
Prisms
A prism is a set of faces that run parallel to an axes in the crystal
Open form
Dipyramaid
Two pyramids joined base to base along a mirror plane Closed Form
Disphenoid
A solid with four congruent triangle faces, like a distorted tetrahedron
Dodecahedrons
A closed 12-faced form
{110}
Tetrahedron
It is a four faced form that results form three bar4 axes and four 3-fold (3m) axes
Trapezohedron
The trapezohedron results from 3-, 4-, or 6-fold axes combined with a perpendicular 2-fold axis
Tetrahexahedron
A 24-faced closed form with a general form symbol of
{0hl}
Related to cube
Pyritohedron
The pyritohedron is a 12-faced form that occurs in the crystal class 2/m bar3
Forms Related to the Octahedron
Trapezohderon
The Diploid
Hexoctahedron
Trigonal trisoctahedron
Rhombohedron
bar3 2/m , 32, and bar3
Mineral size and weight range
Size = nm to m Weight = ng to Mg
Methods of crystal growth
From solution, usually (aq)
From a melt
By sublimation from a gas phase
Crystallization from an aqueous system
Nucleation and supersaturation
Nucleation
Usually form from the initial crystallization products of solutions or melts
Various ions must combine to form an initial regular structure pattern of a crystal
Supersaturation
Achieved by Increasing concentration, Changing pressure, and changing temperature.
Slow cooling leads to a few nuclei and large crystals Rapid cooling leads to many nuclei, small crystals
Melts
Growth is similar to aqueous dehydration
Low temperatures allow the attractive forces to overcome thermal vibration, holding clusters together
Vapor/Sublimation
Cooling allows dissociated atoms or molecules to join
Like ice on a window
Destruction of nuclei
Nuclei have very large surface area/volume
Unsatisfied bonding on outer surfaces leads
to dissolution
Crystallization only takes place when some
nuclei survive long enough for growth to
occur
Critical Size
Above the critical size, the nuclei are relatively stable, and growth can begin
If nuclei grow rapidly, their surface area/volume declines, and they may reach and exceed a critical size
Law of Bravais
The most likely crystal face to grow are those planes having the highest density of lattice points
Rate of Growth
Faces composed of all anions or all cations are very high energy
They attract ions of the opposite sign, and grow rapidly
Eventually they grow themselves out of
existence, leaving the slower growing faces
Vectoral Properties
Some properties of crystals depend on the
direction in which they are measured
ex// Hardness, speed of light, conductivity
Discontinuous Vectoral Properties Examples
- Color banding in minerals
- Dendritic growth
- Rate of solution etching by a solvent
- Cleavage
- Hardness
Continuous Vectoral Properties Examples
• Index of refraction, related to the velocity of light • Seismic velocities in crystals • Electrical and thermal conductivity • Thermal expansivity
Crystal Intergrowths
During crystal growth, one crystalline substance may grow on a crystalline substance of different composition and structure
Called epitaxial growths
Twin Operations
Reflection (Twin Plane)
Rotation (Twin Axis)
Inversion (Twin Center)
Twin Law
Must Define
- The type of twin operation
- The orientation of the twin element associated with the operation
Contact Twinning
Have a planar composition surface separating two individual crystals
Polysynthetic Twinning
Multiple contact twinning
The compositions surfaces are parallel to one another
{010}
ex// Plagioclase
Cyclic Twinning
If the composition surfaces are not parallel to one another
Like a flower
Penetration twin
Have an irregular composition surface separating 2 individual crystals
Defined by twin center or axis
Origin of Twinning
- Growth twins
- Transformation twins
- Glide or deformation twins
when two separate crystals share some of the same crystal lattice points in a symmetrical manner
Growth Twins
When accidents occur during crystal growth and a new crystal is added to the face of an already existing crystal,
Transformation Twins
Occurs when a preexisting crystal undergoes a transformation due to a change in pressure or temperature
Spinal Law (Isometric)
Twin reflection on (bar1 bar1 1) plane
Color Sources
Selective absorption Crystal Field Transitions Charge Transfer (Molecular Orbital) Transitions Color Center Transitions Dispersion
Visible Light
400-700 nm
Electromagnetic spectrum
Short to long Gamma X ultraviolet Vis. Infrared radar FM TV shortwave AM
Interaction of Light with a Surface
Transmitted Refracted Absorbed Reflected Scattered
Crystal Field Splitting
Partially filled 3d subshells allow transitions between the split d orbitals found in crystals
3s2 3p6 3d10-n 4s1-2
Octahedral Splitting
3 orbitals are lowered in energy, 2 are raised
Tetrahedral Splitting
2 orbitals lowered in energy, while 3 are raised
Square Planar Splitting
total removal of ions along z axis produces a square
planar environment
Early observations of magnetism
Ancient Greeks, especially those near the city of Magnesia, and Chinese, observed natural stones that attracted iron
CALLED LODESTONE
Bohr magnetron
Each orbiting electron possesses a magnetic moment equal to 1 Bohr Magnetron
Spin Contribution to magnetism
Largely responsible for the 3d electrons contribution to the magnetic moment and is proportional to the number of unpaired d electrons
Orbit Contribution to magnetism
Moving electrical currents generate magnetic forces
3d e-
Three d electrons have large spin and relatively
low orbital contributions to magnetic moments
Shielded by 4s
4f e-
the 4f e- are well-shielded by outer e-
Not involved in bonding and both orbital and spin effects contribute to the total magnetic moment
Magnetic susceptibility
Ratio of induced magnetization to the strength of the
external magnetic field causing the induced magnetization
Diamagnetic
Minerals possessing ions with totally paired
electron spins
weakly repelled from the magnet
No transition elements are present, and the net
magnetic moment is zero
Paramagnetic
Unpaired e- present
Net field 0
Attracted to a magnet in a strong magnetic field
Curie temperature
Transition to a paramagnetic state with increased T
Ferromagnetic
Adjacent moments are aligned
Magnetism is due to unbalanced electron spin
in the inner orbits of the elements concerned
Antiferromagnetic
Alternate atoms have oppositely directed
moments
Magnetic susceptibility is low but increases
with increasing T up to the Néel temperature
Above, becomes paramagnetic
Ferrimagnetic
Adjacent atoms have antiparallel alignment
strong magnetism may exist
Magnetic moments of different ions is different
Magnetic separation
Used in processing minerals since many minerals, especially those containing iron
Aerial Remote Sensing of Magnetism
Plane flies magnetron 100-300m above ground
ex// To fond sulfide ore bodies
Paleomagnetism
Ferrimagnetic minerals are permanently magnetized
This reveals polarity reversals, and can aid in the study of plate motions
