Crystal Morphology

1
Crystal Morphology

• Growth of crystal is affected by the conditions
  and matrix from which they grow. That one face
  grows quicker than another is generally
  determined by differences in atomic density along
  a crystal face
• Internal order the same here however!!!

2
Why did we go through all this?

• Lattice types and space groups are important in
  describing the arrangement of atoms in space
• These arrangements result in planes of atoms
  which are spaced at defined intervals, controlled
  by the mineral structure, which is described by
  crystallography
• They describe possible planes in crystalline
  structures where ions are aligned. Light and
  high-energy particles interact with those planes,
  which yield powerful diagnostic tools!

3
How does that translate to what we see??

• Internal order creates changes in planar spacings
  for different atomic arrangements

What can we use to see these planar spacings??
4
X-rays

• Another part of the electromagnetic spectrum
  between 100 and 0.2 Å.
• Plancks law Ehn hc/l
• Where n is frequency, l is wavelength, h is
  Plancks constant, and c is the speed of light

5
X-ray generation

• X-rays are generated by striking a target
  material with an accelerated e- which causes an
  excitation. When his excitation relaxes, or
  goes back down to standard state, an X-ray is
  emitted
• Usually given in terms of the energy levels those
  e- come from and go to ? different levels yield
  X-rays of different energies (all dependent on
  the material)
• K, L, M shells of a material, from that those
  shells have different transitions and
  characteristic relaxations (a, b, g)
• Cu Ka is the most intense peak and most commonly
  used (though others are possible and have a
  different wavelength, which can be useful!)

6
X-Ray interaction

• Scattering oscillation of incoming X-rays
  transfer energy to electrons in material,
  emitting secondary radiation at about the same
  frequency and energy as the incoming beam
• Interaction of X-rays with same material causes
  some electrons to go into an excited state, which
  upon relaxation, emits radiation characteristic
  of the atom it excited ? basis for XRF, used to
  identify chemical makeup of materials
• As with other interactions with minerals, there
  can also be reflection and transmission of X-rays
  (depending on thickness), but we dont typically
  use that information.

7
Interference

• Constructive and destructive interference wave
  properties interact to either cancel out or
  amplify each other.
• When 2 centers are emitting energy at some
  wavelength, they will interfere with each other

Plane view
8
Experiment

• Relationship between light as particles vs. light
  as waves
• Light scattered by mesh - as it travels and
  interacts, some waves compliment each other while
  different waves cancel each other

9
Diffraction

• Combine elements of interference with striking
  the x-ray at an angle to the material
• Relationship between wavelength, atomic spacing,
  and angle of diffraction for 3-D structures
  derived by von Laue
• Braggs determined that you could simplify this
  and treat it as a reflection off of the planes
  within an atom

10
Braggs Law

• nl2dsinT
• Where n is the order of diffraction (always an
  integer), l is the wavelength of incident
  radiation, d is the spacing between planes, and T
  is the angle of incidence (or angle of
  reflection, they are equal)

11
Diffraction

• Relationship between diffraction and wavelength
• The smaller the diffracting object, the greater
  the angular spacing of the diffraction pattern
• i.e. the smaller the separation between planes,
  the wider the spacing between diffraction lines
• What then is diffraction??
• The failure of light to travel in straight lines
  (much to Newtons dismay)
• Youngs 2 slit experiment proved light could bend
  scattered and affected by constructive and
  destructive interference
• Bright red constructive dark destructive

12
Braggs Law

• nl2dsinT
• Where n is the order of diffraction (always an
  integer), l is the wavelength of incident
  radiation, d is the spacing between planes, and T
  is the angle of incidence (or angle of
  reflection, they are equal)
• Diffraction here is between parallel planes of
  atoms ? the space between them (d) determines the
  angle of diffraction.
• Looking at the laser pattern again ? where is
  Braggs Law satisfied and how many orders of
  diffraction do we see?

13
Red Laser analogue

• We see orders of diffraction resulting from light
  coming between grid spacing 2, 3, 4, 5, etc.,
  apart. In a mineral, multiple parallel planes
  yields similar patterns at higher orders of
  diffraction theoretically the angle keeps
  increasing ? what do we notice about the
  intensity though?

14
Braggs Law

• nl2dsinT
• Just needs some satisfaction!!