1. 1

2. 2 2.01.51.00.50.0 2.0 4.0 6.0 8.0 10.0 12.0 14.0 L (mm) ln(n) (no./cm 4 ) AT-67 A Typical CSD 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. 3 5.0 7.5 10.0 12.5 15.0 17.5 20.0 -20.0-15.0-10.0-5.00.0 The CSD Intercept vs. Slope Relationship Dome Mountain, NV (plagioclase) Crater Flat, NV (olivine) Atka, AK (plagioclase) Slope (mm -1 ) Intercept (no./cm 4 ) 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. 4 Crystal nucleation rate (I) relation of Cashman (1993): Method Cooling rate expression from Jaeger (1957) for an infinite half-sheet of magma: Symbols and values are given in the Symbol Table, below. (of the liquid) Build CSDs for increasing distances from the contact of the Jaeger (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) eq. 2 eq. 1

5. 5 Method Growth Rate By “Distribution of Mass”

6. 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. 7 Wallrock Magma Contact Infinite Half-Sheet of Magma L ln(n) L L L (mm) ln(n) ln(n°) Slope  1 Intercept 3

8. 8 Results: CSDs Generated From The Model 5 Meters 50 Meters L (mm) ln(n), no./cm 4 Typical model CSDs and a table of all CSD parameters. ln(n), no./cm 4

9. 9 Typical Model CSD Evolution The CSD Located 5 Meters From the Contact y = 1.1737Ln(x) + 13.37 R 2 = 0.9954 12 13 14 15 16 17 18 19 20 0 406080100 Percent Solids CSD Intercept, no/cm 4 2 4 6 8 10 12 14 16 18 0.00.20.40.60.81.01.2 5% 10% 50% 100% L (mm) ln(n), no/cm 4 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. Values refer to percent solids.

10. 10 5.0 7.5 10.0 12.5 15.0 17.5 20.0 -20.0-15.0-10.0-5.00.0 Dome Mountain, NV Crater Flat, NV Atka, AK Model CSDs The CSD Intercept vs. Slope Relationship Slope (mm -1 ) Intercept (no./cm 4 ) 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. 1 m 5 m 50 m 100 m 500 m

11. 11 5.0 7.5 10.0 12.5 15.0 17.5 20.0 -20.0-15.0-10.0-5.00.0 Model CSDs Increasing Time Constant CSD Slope Increasing % Solids 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. Offset of Model CSD Trend Due to Higher Modal Abundance Slope (mm -1 ) Intercept (no./cm 4 )

12. 12 Discussion The model intercept vs. slope trend shows concavity; the natural sample trends are apparently linear. The scatter inherent in the natural data may be masking a curved trend. Though not shown here, different values of I’ and m in eq. 2 of plate 4 will yield suites of CSDs with trends different from that shown in plate 10. Thus, the definition of intercept vs. slope trends for suites of samples may constrain nucleation rate kinetic parameters. The intercept vs. slope trend of the model CSD data indicates that lower overall CSD intercepts and low absolute values of the slope are due to longer, slower cooling. Thus, in addition to providing information on nucleation kinetics, the CSD intercept vs. slope relationship for a suite of samples may bound cooling times. Such bounds may then be related to magmatic system size.

13. 13 Summary and Conclusions

14. 14 Symbol Table

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