Opaque Minerals

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Opaque Minerals

• Lecture 4

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Important Opaques

• Moon ilmenite (FeTi03),chromite
• Asteroids troilite (FeS), carbon (C )
• Mars magnetite (Fe3O4)
• Dark minerals, with weak spectral features

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Odd behavior of opaques (normal in thermal
infrared)

• Pyrite (FeS2)
• Fine particles darker than larger particles
  (better emitters)
• From Geochemical Analysis, Pieters and Englert

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More oddity

• Troilite (FeS)
• From BE Clark, Spectral mixing of S-type
  asteroids, JGR 100 e7, p14443 1995
• Note smaller sizes are brighter

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• For transparent particles, single scattering
  albedo increases with decreasing grain size.
• For absorbing particles, single scattering albedo
  must decrease with decreasing grain size
• Volume vs. surface scattering
• Nice words, but doesnt address the question

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Back of the envelope

• Paradoxically, highly absorbing materials are
  also highly reflective (e.g metal)
• Why would reducing the grain size decrease the
  single scattering albedo?
• Why would volume scattering decrease the
  albedo?
• R(thick) gt R(thin)T(thin) must be true

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Geometry of Fresnel, normal incidence
In our case, n21 and k20
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n and k and complex numbers

• n and k are the complex indices of refraction
• nnik
• When k is small (lt1/1000), absorption is weak and
  n governs the angle of refraction at boundaries
  between media (Snells Law), and k governs
  absorbance
• When k is comparable to n, then n has little to
  do with refraction, both are highly coupled
• n is complex only for mathematical convenience.
  Complex mathematics make describing the behavior
  of harmonic oscillators (like light)more
  convenient (for somebody).
• n and k are simply parameters describing the
  behavior of harmonic oscillators. Light behaves
  like a harmonic oscillator.

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Fresnel Reflectance at normal incidence for thick
layer (d big)
In vacuum or air, n01 p,s subscript refers to
polarization state If k approx equal to n, R is
about 1.
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Reflectance and transmission of thin absorbing
films
n21
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The necessarys
For thin film in air, n0,21, k0,20
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Problem

• If these equations are correct, for absorbing
  particles, RthinTthin lt Rthick
• In other words, the single scattering albedo goes
  down when d decreases because the sum of
  reflectance and transmission are less than for a
  thick particle

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The homework problem

• Show RT as a function of d, where d is in the
  range from 10nm to 100 microns
• How does RT compare to R for a thick medium?
• Sanity check RT should equal R thick, when d
  is big.
• Note because of the trig terms, the answer will
  oscillate as a function of d. Also d is in same
  units as wavelength (see defs of alpha and gamma)

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