L mm

1
(No Transcript)
2
A Typical CSD
AT-67
14.0
12.0
10.0
8.0
ln(n) (no./cm4)
6.0
4.0
2.0
0.0
2.0
1.5
1.0
0.5
0.0
L (mm)
A CSD of plagioclase in a high-alumina basalt
from Atka Island, Alaska, from Resmini (1993).
CSDs may be characterized by their slope
and intercept. Numerous CSDs from a suite of
samples may be represented as points on a plot of
CSD intercept vs. slope as shown next (pl. 3).
3
The CSD Intercept vs. Slope Relationship
20.0
17.5
Dome Mountain, NV (plagioclase)
15.0
Atka, AK (plagioclase)
Intercept (no./cm4)
12.5
10.0
Crater Flat, NV (olivine)
7.5
5.0
-20.0
-15.0
-10.0
-5.0
0.0
Slope (mm-1)
Intercept and slope values for numerous CSDs
(from Resmini, 1993). Note the linear trends.
The modal abundance of plagioclase in the Dome
Mtn. rocks is 6.5 vol..
4
Method

• Build CSDs for increasing distances from the
  contact of theJaeger (1957) infinite-half sheet
  of magma (a sill proxy) (eq. 1)CSDs generated
  for 1, 5, 50, 100, and 500 meters from contact
• Use the Cashman (1993) nucleation rate, I,
  expression (eq. 2)
• Crystal growth rate, G, is by the Distribution
  of Mass method(see next slide)

Cooling rate expression from Jaeger (1957) for an
infinite half-sheet of magma
eq. 1
Crystal nucleation rate (I) relation of Cashman
(1993)
eq. 2
Symbols and values are given in the Symbol Table,
below.
5
Method
Growth Rate By Distribution of Mass
6
Method
CSDs are thus generated for various positions
within an infinite half-sheet of magma. All CSDs
are calculated assuming complete solidification
(i.e., 100 solids). From each CSD, the slope
and intercept parameters are extracted and
subsequently plotted.
7
ln(n)
Intercept
Wallrock
ln(n)
Contact
Slope
L (mm)
2
Infinite Half-Sheet of Magma
3
1
Magma
8
Results CSDs Generated From The Model
5 Meters
50 Meters
ln(n), no./cm4
ln(n), no./cm4
L (mm)
L (mm)
Typical model CSDs and a table of all CSD
parameters.
9
Typical Model CSD Evolution
The CSD Located 5 Meters From the Contact
20
18
16
19
Values refer to percent solids.
18
14
17
12
16
CSD Intercept, no/cm4
ln(n), no/cm4
10
y 1.1737Ln(x) 13.37
15
8
2
R
0.9954
100
14
6
10
13
4
5
50
12
2
0
20
40
60
80
100
0.0
0.2
0.4
0.6
0.8
1.0
1.2
L (mm)
Percent Solids
The evolution of the CSD located 5 m from the
sill contact. Note that CSD slope is constant
throughout the solidification interval and that
CSD intercept evolves vs. percent solids as
shown. This behavior is important to note
because in subsequent plates, model results for
100 solids will be compared to natural CSDs
calculated for minerals with significantly
lower modal abundances.
10
The CSD Intercept vs. Slope Relationship
20.0
Model CSDs
1 m
5 m
17.5
50 m
100 m
15.0
500 m
Intercept (no./cm4)
12.5
Atka, AK
Dome Mountain, NV
10.0
7.5
Crater Flat, NV
5.0
-20.0
-15.0
-10.0
-5.0
0.0
Slope (mm-1)
The plot of plate 3 now with the model CSDs
included. The modal abundance of plagioclase in
the Dome Mtn. rocks is 6.5 vol. whereas the
model CSDs are for 100 solids. The model
CSDs define a trend similar to that of the
natural CSDs.
11
Offset of Model CSD Trend Due to Higher Modal
Abundance
20.0
Model CSDs
17.5
15.0
Intercept (no./cm4)
Increasing Time
Constant CSD Slope
12.5
Increasing Solids
10.0
7.5
5.0
-20.0
-15.0
-10.0
-5.0
0.0
Slope (mm-1)
As indicated in plate 9, a CSD evolves throughout
the solidification interval with constant slope.
Thus, a point on a plot of CSD intercept vs.
slope evolves in time (i.e., as a function of
increasing solids) by moving vertically along
the intercept axis, as shown. Intercept value
maps modal abundance.
12
Discussion

• The model intercept vs. slope trend shows
  concavity the natural sampletrends are
  apparently linear. The scatter inherent in the
  natural data maybe masking a curved trend.
• Though not shown here, different values of I and
  m in eq. 2 of plate 4 willyield suites of CSDs
  with trends different from that shown in plate
  10.Thus, the definition of intercept vs. slope
  trends for suites of samplesmay constrain
  nucleation rate kinetic parameters.
• The intercept vs. slope trend of the model CSD
  data indicates that loweroverall CSD intercepts
  and low absolute values of the slope are due
  tolonger, slower cooling.
• Thus, in addition to providing information on
  nucleation kinetics, the CSDintercept vs. slope
  relationship for a suite of samples may bound
  coolingtimes. Such bounds may then be related
  to magmatic system size.

13
Summary and Conclusions
14
Symbol Table
15
Acknowledgements
Partial funding for this work provided by The
Boeing Company.
References
Additional Information
Pre-prints of a manuscript currently in review at
the Journal of Volcanology and Geothermal
Research are available below.