Formation and Growth of Ice Crystals

1
Formation and Growth of Ice Crystals

• Direct observations show that liquid water clouds
  are very common at temperatures well below 0C
  (i.e., -20C)
• In the laboratory, small droplets of pure H2O
  freeze only when cooled to temperatures of -40C
  (the spontaneous freezing level)
• At higher temperatures, pure water droplets
  freeze only if injected with tiny foreign
  particles called ice nuclei.

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Common Ice Crystal Shapes
Hexagonal Plates
Hexagonal Prisms
Stellar Crystal/ Dendrites
Ice needles
3
Molecular Structure of Ice

• X-Ray and neutron diffraction experiments have
  shown the basic crystal structure of ice at
  atmospheric temperatures to consist of six oxygen
  atoms arranged in a hexagon. Each oxygen atom is
  bonded to two hydrogen atoms and each hydrogen is
  bonded to two oxygen atoms.

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Ice Formation

• Generally considered to be of two types
• 1. Deposition - transformation from vapor to
  solid
• (the reverse is sublimation) Note that
  homogeneous deposition does not occur in the
  atmosphere.
• 2. Freezing - transformation from liquid to solid

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Qualitative Description of Freezing(homogeneous)

• Consider a volume of air with T lt 0C in which
  water droplets are suspended
• The H2O molecules in a drop at a given instant
  may come into temporary alignment similar to that
  of an ice crystal.
• Such molecular aggregates may grow but they may
  also be destroyed by random molecular motions.
• If an aggregate happens to grow to such a size
  that it is no longer affected by these thermal
  agitations, the entire droplet quickly freezes.
  The probability of growth of an aggregate to this
  critical size increases as T decreases. (Fleagle
  and Bussinger)

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Qualitative Description of Freezing(heterogeneous
)

• Add a foreign particle to droplet
• The particle makes the initial growth more
  probable by attracting a surface layer of H2O
  molecules on which the ice crystal lattice can
  form more readily than in the interior of the
  liquid.
• Freezing of a droplet requires that only one
  aggregate reach critical size.

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Ice Nucleation Mechanisms

• Heterogeneous Deposition - vapor is transformed
  to ice on a nucleus
• Condensation Followed by Freezing - droplet forms
  on a nuclei which then freezes
• Contact - nuclei makes contact with a droplet
  which then freezes
• Immersion- nuclei becomes immersed in a droplet
  which then freezes about the nuclei.

The relative importance of the different modes
has not been established. It is difficult to
distinguish between deposition and freezing
mechanisms. Usually refer to the process as ice
nucleation and the nuclei as ice nuclei.
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Ice Forming Nuclei
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Important Features of Ice Nuclei

• Temperature
• Lattice structure - many of the most active
  natural nuclei have crystal structures similar to
  ice.
• Molecular binding -
• low interfacial energy
• Theory not yet able to explain which is most
  important but, the most common natural nuclei
  appear to be surface clays such as kaolinite.
  However, it has been discovered that bacteria in
  decaying plant leaf material can be effective
  nuclei, but its importance has not yet been
  established.

10
Ice Nuclei Concentration

• Typical concentration is one nucleus per liter
  of air at a temperature of -20C, increasing by a
  factor of ten for each additional 4C of cooling.
  However, the count on any given day may be
  greater or less than the typical values by an
  order of magnitude!
• Taking 104 cm-3 as the typical concentration of
  atmospheric aerosols, one nucleus per liter is
  only one aerosol particle in 107! That is, ice
  forming nuclei are a very rare component of
  atmospheric aerosols.

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If Nuclei Are So Rare, Why Are There So Many
Crystals?

• Once freezing of supercooled droplets starts, it
  progresses rapidly through a cloud.

The entire shell may explode to produce hundreds
of splinters, each of which can act as a freezing
nucleus
As interior freezes and expands the outer shell
may rupture through which a jet of water emerges
and freezes to form a spike
Also, collisions between crystals
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Diffusional Growth of Ice Crystals

• Basic Assumptions
• The surface of the crystal has uniform
  temperature therefore, it has uniform vapor
  pressure.
• The vapor pressure at an infinite distance is
  assumed uniform as is the temperature.
• The vapor pressure and vapor density in the
  neighborhood of the crystal may be represented by
  surfaces that follow the contour of the crystal.
• Beyond a certain neighborhood of the crystal
  these surfaces approach a spherical shape.

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Vapor Diffusion
Contours of vapor density

• The flux of water vapor to the crystal by
  diffusion occurs in the direction normal to the
  surfaces of constant vapor density. Therefore,
  near a sharp point vapor diffuses toward the
  point from all directions. Ice may accumulate
  more rapidly there than on flat surfaces.

14
Ice Crystal Growth Equations

• where Tc and T are the temperatures of the
  crystal and environment (), respectively, K is
  the thermal conductivity of air, and C is the
  crystal shape factor.

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Shape Factor

• The shape factor is nothing but the capacitance
  of a subject. It depends upon the geometrical
  shape of the crystal. It has units of length.
  Examples

See Houghton, H. G., 1950 J. Meteor., 7, 363-369.
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Crystal Growth Rate Solution

• Let

Following the procedure used for a water droplet,
obtain
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Comparison of Droplet and Crystal Growth

• For a liquid water droplet of radius r

For an ice crystal
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Saturation Vapor Pressure Relativeto Ice and
Liquid Water
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Growth of different shapes is temperature
dependent

• A molecular kinetic approach is required to
  explain different habits/shapes.

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Growth by Accretion

• Definitions (following Rogers and Yau, 1989)
• Accretion is sometimes reserved for the capture
  of supercooled droplets by an ice-phase
  precipitation particle. If the droplets freeze
  immediately on contact, this forms a rimed
  crystal or graupel. Slow freezing creates a
  denser structure e.g. - hail.
• Coalescence is the capture of small cloud
  droplets by larger cloud drops.
• Aggregation is the clumping together of ice
  crystals to form snowflakes

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Growth by Accretion - cont.

• The derivation of an equation for the continuous
  growth of ice crystals by capture of other
  crystals or cloud droplets would follow the same
  procedures as for liquid drops. Complications
  arise due to difficulties in prescribing the
  dependence of crystal fall speeds and their
  collection efficiencies.
• Snowflake sizes indicate that significant
  aggregation occurs only for T gt -10C.

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Crystal Fall Speeds
Fig. 9.7 from Rogers and Yau, 1989
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Snowflake Growth - Qualitative

• Must have an appropriate number of ice nuclei to
  initiate freezing - 0.1 to 1 per liter at -20C.
• Crystals form around nuclei and grow by
  diffusion.
• A few crystals grow faster and larger than their
  neighbors by either enhanced diffusion or by
  chance collisions with other crystals or
  droplets.
• These crystals fall faster than their neighbors
  and grow by diffusion and by collisions with
  other crystals or cloud droplets until they reach
  a size where they can fall against an updraft and
  reach the ground. A snowflake of 1 cm diameter
  requires a cloud depth of about 1500 m.

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Times Required for Growth by Different Processes
Droplet collision - coalescence
crystal - diffusional growth
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Precipitation Growth - Summary

• Condensation-diffusion is more effective for ice
  clouds than for water clouds
• In warm clouds, coalescence is the major scheme
  for precipitation to occur
• In cold clouds, both diffusion and aggregation
  are important

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Homework for Chapter 8 and 9 Due Nov. 6, 2007
a) write the CC equations for saturated water
vapor pressure over bulk ice and water es(T),
esi(T) b) Determine the temperature at which
esi(T)- es (T) reaches maximum c) Determine
the maximum value.