Nicolaus Steno

niels bohr

1669- Steno's Law of the constancy of interfacial angles

made fundational contributions to understanding atomic structure and quantum theory

Rene Just Hauy

auguste bravais

1743-1882: the father of modern crystallography

coined the word molecule

unit cell

2D vs 3D

His crystal lattice concept is used to formally define a crystalline arrangment

william hallowes miller

symmetry

came up with crystal faces notation in crystallography

the consistency, the repetiton of something in space and/or in time

a mirror plane:

when looking in a mirror, the resultant image is identical except every part has been translated an equal and opposite direction across and perpendicular to the plane of the mirror

1-fold= 360

2 fold=180

3 fold= 120

4 fold= 90

6 fold= 60

1 2 3 4 6 m 2mm 3m 4mm 6mm

any 2-D pattern of objects surrounding a point must conform to one of these groups

1 2 3 4 6 i m -3 -4 -6

a complete analysis of symmetry about a point in space requires that we try all possible combinations of these symmetry elements

repetition of the unit cell creates a motif

smallest unit of a structure that can be indefinitely repeated to generate the whole structure.

arranged in a pattern described by points in a lattice

we often envision translational symmetry by thinking about a lattice

a=b=c 

alpha=beta=gamma=90 degrees

a=b does not = c

alpha=beta=gamma=90 degrees

a does not = b does not = c

alpha=beta=gamma=90 degrees

a=b does not =c

alpha=beta=90 degrees

gamma= 120 degrees

a does not = b does not = c

alpha=gamma=90 degrees

beta does not = 120 degrees

a does not = b does not = c

alpha does not = beta does not = gamma does not = 90

all crystals except hexagonal referred to by 3 axes: a,b, and c

alpha is angle between b and c

beta is angle between a and c

gamma is angle between a and b

represent intercepts of crystal faces upon crystal axes

1a,1b,1c

1/1,1/1,1/1

invert it, 1/1,1/1,1/1

(1,1,1)

general form (h,k,l)

48 forms (32 general, 16 special: 10 closed isometric; 6 open prisms)

-normals drawn to crystal faces to project them on to a sphere

-the points in the sphere are projected onto an equatorial plane

-where they hit the equatorial sphere is a stereo diagram

1) neutrons are electrically neutral particles in the nucleus

2) protons are positively-charged particles in the nucleus

3) electrons are negatively-charged particles that surround the nucleus

cations are usually smaller than anions

ions increase in size down the PT

ions decrease in size across the PT

oppositely charged ions attract cations, anions

loss or gain of an electron, no sharing

Na+ + Cl- = NaCl in halite

sharing electrons

very strong bonds

form when adjacent atoms have similar or equal electronegativites

diamond, H2

electrostatic forces among electron clouds

less common in rock forming minerals, but very important for minerals like copper, gold

strong metallic bonding indicated by high melting points of metals

sharing of many detached electrongs between positive ions (electron cloud)

the ability of an atom in a crystal structure or molecule to attract electrongs to its outer shell

low=electron  donors

high= electron acceptors

weak bonds: relatively weak electrostatic forces from uneven charge distribution in crystal structure.

weakest attractions found in minerals

ties unchargee or neutral molecules together into a cohesive unit using small residual charges on their surface

-ID minerals with confidence (rock type, rock composition, P-T-X conditions of formation)

-observe rock microstructures (crystallization sequence, paragenesis and reactions, deformation)

-fun, powerful, and cheap

frequency

f=velocity/wavelength

number of wave crests per second passing a particular point

-usually expressed as cycles per second (hertz Hz)

a line drawn perpendicular to the wave front

=direction wave front is moving

light that vibrates in one direction

-unpolarized light vibrates in all directions

-plane polarized light vibrates in 1 direction

velocity changes

light is refracted (rays bent)

light is split into 2 new vibration directions

usually see new colors

it is split into two different waves known as double refraction. There are two basic classes of how these two light waves are affected by mineral structure:

isotropic

anisotropic

transmit light in all directions at equal velocity

i.e. do not reorient light

light slows when it enters a medium (waves bunch up)

=change in velocity and wavelength of light when it moves

denser medium=more electrons=more interactions with light=more energy transferred from the light to the electrons in the medium

(light is slowed down more)

Non-perpendicularly-incident light is refracted when it passes from one substance to another; refraction is accompanied by a change in velocity

n=velocity of light in vacuum/velocity of light in mineral

light striking the surface of the material at right angles should go straight through without deviating

observed in Plane polarized light

relief is a measure of the relative difference in n between a mineral grain and its surroundings

observe the direction that becke line (the white line) moves as the distance between the stage and the ocular increases (as the stage drops)

positive relief-becke lines move in

negative relief- becke lines move out

observed in PPL

results from selective absorption of certain wavelengths of light

observed in PPL

results when different wavelengths are absorbed diffently by different crystallographic directions (as the stage rotates)

light splits into two rays: observed in XPL

produced because most solids have more than one index of refraction=rays have different velocity

slow and fast rays emerge from the grain, combine to produce interference colors

crystal habit (sections through crystals)

cleavage

relief

color in plane polarized light

inclusions; color banding; intergrowths; alteration; oxidation

anisotropic minerals turn dark once every 90 degrees

why? one vibration direction is parallel to the lower polarizer. no light passes through vs max interference colors

parallel

inclined

symmetrical

no extinction angle

mica plate- retardation of 147 nm

quartz wedge

used to determine slow vs fast rays vibration directions in elongate minerals

1) extinction position

2) turn 45 degrees

3) insert 1 wavelength plate

4) observe changes in interference colors

5) determine if slow on slow or slow on fast

shape (crystal form)

cleavage

relief

point count

inclusions

alteration

isometric

-all crystallographic axes are equal

-chemical bondin the same in all directions

hexagonal/trigonal, tetragonal

-all axes except c are equal but c is unique (a high degree of symmetry about the c axis)

orthorhombic, monoclinic, triclinic

-all axes are unequal, therefore vary in every direction in crystal structure and chemical bonding

light travels the same distance/velocity in all directions

so n is same everywhere thus no interference figure is produced.

one circular axis of revolution= optic axis

optic axis always along the c-axis in these systems

all other directions: light rays find the fastest and slowest vibration direction and break into two rays of different velocities.

-one rich in Fe alloys

-another rich in sulfide compounds

-one containing silicates

chemical elemens distribute themselves between those three groups

(one rich in Fe alloys, another rich in sulfide compounds, one containing silicates)

elements that form a gas

escaped the interior of the earth and made our atmosphere

affects the type of crystals that grow

-the faster a magma cools, the less distinct and smaller the crystal shapes become.

temperature. at high temperatures, atoms are very mobile and crystals can grow more quickly

flux: availability of the major elements needed to grow a particular mineral

space to grow

defects in the crystal lattice

-line and point dislocations

-planar defects (twinning in the crystal lattice)

-compositional zoning

geodes have euhedral crystals because they grow out into open (solution-filled) space.

the growth of individual grains is not impeded by the surrounding grains

vacancies

frenkel defect

impurity atom (interstitial)

edge dislocation

screw dislocation

can help maintain charge balance

foreign ion replaces normal one

-solid solution

-not considered a defect

foreign ion is added

called an iterstitial ion

planes displaced relative to each other through shear (spiral sliced ham)

aids mineral growth

mismatch of the crystal structure across a surface

offically grain boundaries count as planar defect

twining

rational symmetrcally-related intergrowth

lattices of each orientation have ddefinite cystallographic relation to each other

simple twins

twins appear to be crystals in contact

simple twins

a volume of atoms (not just a plane) is shared between the two domains

multiple twins-several twin segments repeated by same twin law

cyclic twins- multiple twins not parallel

polysynthetic twins- multiple twins parallel

most abundant elements in crust and mantle

-therefore most imporant bond in mineralogy

-change in T with depth in earth

-steeper with depth

-does not intersect the melting curve for peridotite

-melting is not common in earth's subsurface

molten rock crystallizes over a range of T

partial melt=less dense than surrounding rock

rises and cools and begins to crystallize

1st crystals form at the liquidus

the last drop of melt crystallizes at the solidus

very fast cooling: glassy rock=obsidian

fast cooling: aphanitic (small crystals-fine grained)

slow cooling: phaneritic (big crystals coarse grained)

initially homogeneous solid solution separates into at least 2 different crystalline minerals

-no addition or removal of any materials

-in most cases, it occurs upon cooling below the temperature of mutual solubility or stability of the solution.