Presentacin de PowerPoint

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Time scales of magmatic processes from modelling
the zoning patterns of crystals

Fidel CostaInst. Earth Sciences Jaume Almera
CSIC (Barcelona, Spain)Ralf Dohmen and Sumit
ChakrabortyInst. Geol. Mineral. and Geophys.,
Bochum University (Bochum, Germany)
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Table of contents
1. Introduction to zoning in crystals
2. Diffusion equation
3. Diffusion coefficient
4. Modeling natural crystals isothermal case
Initial conditions Boundary conditions

• 5. Problems, pitfalls and uncertainities
• Multiple dimensions, sectioning, anisotropy
• 6. Conclusions and prospects

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1. Zoning in crystals
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X-ray distribution map of olivine from lava lake
in Hawaii Moore Evans (1967)
Development of electron microprobe 1960, first
traverses and X-ray Maps
Among the first applications to obtain time
scales those related to cooling histories of
meteorites (e.g. Goldstein and Short, 1967)
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1. Zoning in crystals
- Major elements, trace elements, and isotopes
- Increasingly easier to measure gradients with
good precision and spatial resolution (LA-ICP-MS,
SIMS, NanoSIMS, FIB-ATEM, e-probe, micro-FTIR)
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Major and trace element zoning in Plag
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Stable isotope zoning ?18O in zircon from
Yellowstone magmas
Bindeman et al. (2008)
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Sr isotope zoning in plagioclase
Tepley et al. (2000)
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1. Zoning in crystals
Diffusion driven by a change in P, T, or
composition
t0, T0, P0, X0
concentration
concentration
distance
distance
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1. Zoning in crystals
- The compositional zoning will reequilibrate at
a rate governed by the chemical diffusion (Ficks
laws)
- Because D is Exp dependent on T and Ds in
geological materials are slow, minerals record
high T events (as opposed to room T)
distance
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1. Zoning in crystals
Crystals record the changes in variables and
environments gradients are a combined record of
crystal growth and diffusion
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2. The diffusion equation
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2. Diffusion, flux, and Ficks law
Diffusion (1) motion of one or more particles
of a system relative to other particles (Onsager,
1945) (2) It occurs in all materials at all
times at temperatures above the absolute
zero (3) The existence of a driving force or
concentration gradient is not necessary for
diffusion
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2. Diffusion, flux, and Ficks law
SOLID
LIQUID
GAS
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2. Diffusion, flux, and Ficks law
Random motion leads to a net mass flux when the
concentration is not uniform equalizing
concentration is a consequence, NOT the cause of
diffusion
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2. Diffusion, flux, and Ficks law
More general formulation by Onsager (1945) using
the chemical potential
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2. Diffusion, flux, and Ficks law
Ficks second law mass balance of fluxes
Analogy gain or loss in your bank account per
month Your salary ( per month) - what you
spend ( per month)
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2. Diffusion, flux, and Ficks law
Ficks second law mass balance of fluxes
1. We need to solve the partial differential
diffusion equation. (a) analytical solution
(e.g., Crank, 1975) or (b) numerical methods
(e.g., Appendix I of chapter)
2. We need to know initial and boundary
conditions. This is straightforward for exercise
cases, less so in nature.
3. We need to know the diffusion coefficient
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3. Diffusion coefficient
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3. Diffusion coefficient Tracer
e.g., diffusion of 56Fe in homogenous olivine
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3. Diffusion coefficient multicomponent
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3. Diffusion coefficient
Perform experiments at controlled conditions to
determine D or DFeMg
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3. Diffusion coefficient
New experimental and analytical techniques allow
to determine D at the conditions (P, T, fO2, ai)
relevant for the magmatic processes without need
to extrapolation
e.g., Fe-Mg in olivine along 001
Dohmen and Chakraborty (2007)
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3. Diffusion coefficient
New theoretical developments allow a deeper
understanding of the diffusion mechanism and thus
to establish the extend to which experimentally
determined D apply to nature (e.g., impurities,
dislocations, etc).
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4. Solving the diffusion equation
Initial and boundary distribution (conditions)
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4. Initial distribution (conditions)
4 strategies for initial distribution
Shape of profile may retain info about initial
distribution
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Initial conditions
1. Use slower diffusing elements to constrain
shape of faster elements

• Examples
• An for Mg in plagioclase (Costa et al., 2003)
• P for Fe-Mg in olivine (Kahl et al., 2008)
• Ba for Sr in sanidine (Morgan and Blake, 2006)

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X-Ray Map of P
Initial conditions
1. Use slower diffusing elements to constrain
shape of faster elements
OLIVINE Examples

• Examples
• An for Mg in plagioclase (Costa et al., 2003)
• P for Fe-Mg in olivine (Kahl et al., 2008)
• Ba for Sr in sanidine (Morgan and Blake, 2006)

X-Ray Map of Fe
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Initial conditions
2. Using arbitrary maximum initial concentration
range in natural samples (this provides maximum
time estimates)
Examples Sr in plagioclase (Zellmer et al.,
1999) Fe-Mg in Cpx (Costa and Streck, 2003
Morgan et al., 2006) Ti in Qtz (Wark et al.,
2007)
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Initial conditions
3. Using a homogeneous concentration profile
Examples Fe-Mg, Ca, Ni, Mn in olivine (Costa
and Chakraborty, 2004 Costa and Dungan, 2005)
O in zircon (Bindeman and Valley, 2001)
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Initial conditions
4. Use a thermodynamic (e.g., MELTS) and kinetic
model to generate a growth zoning profile
Examples Plagioclase (Loomis, 1982)
olivine- Chapter and AGU Poster, Tuesday
afternoon
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Initial conditions
Conc.
100
Equil
Conc.
0
time
distance
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Initial conditions effects on time scales
1. Despite the difference in shapes of the
initial profiles the maximum difference on
calculated time scales is a factor of 1.5
2. Although the initial profile that we assume
controls the time that we obtain, the error can
be evaluated and is typically not very large
3. When in doubt perform models with different
initial conditions to asses the range of time
scales
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4. Boundary conditions
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Boundary conditions
Characterizes the nature of exchange of the
elements at the boundaries of the crystals (e.g.,
other crystals or melt). Two end-member
possibilities
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Boundary conditions
2. Closed no exchange.
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Boundary conditions
2. Closed no exchange. (b) the mineral is
surrounded by a phase where the element does not
partition (e.g. Fe-Mg olivine/plag)
X-Ray Map of Mg
Olivine
Kahl et al. (2008)
Plag
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Boundary conditions
Open boundary
Conc.
100
Equil
Conc.
0
Closed boundary
time
distance
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Boundary conditions effects on time scales
Equilibration in the closed system occurred much
faster
Incorrectly applying a no flux condition to an
open system can lead to underestimation of time
by factors as large as an order of magnitude. But
in general not difficult to recognise which type
of boundary applies to the natural situation
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Boundary conditions effects of crystal growth or
dissolution
(a) Neglecting crystal growth tends to
overestimate time scales
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Non-isothermal process
If there is no overall cooling of heating
trend, results from a single intermediate T are
correct, likely for some volcanic rocks (e.g.,
Lasaga and Jiang, 1995)
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Non-isothermal process
If there are protracted cooling and reheating
(e.g., plutonic rocks) we need to have a T-t path
This affects (a) the diffusion coefficient, (b)
the diffusion equation, and (c) the boundary
conditions.
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5. Potential pitfalls and errors
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Errors and uncertainties associated with time
determinations

• Two types
• (1) those associated with how well we understand
  and reproduce the natural physical conditions
  (e.g., multiple dimension etc), and
• (2) those associated with the parameters used in
  the model (e.g., T, D)

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Effects of geometry and multiple dimensions
These are important depending on the type, shape,
and size of the crystal that we are studying and
on the diffusion time
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Effects of geometry and multiple dimensions
Data acquisition
Neglecting multidimensional effects tends to
overestimate time scales
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Effects of geometry and multiple dimensions
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Effects of geometry and multiple dimensions
1D, t 225 y ------gt 2D, t 60 y almost a
factor of 4!
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Fe-Mg zoning in olivine diffusion anisotropy and
2 dimensional effects
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Anisotropy of diffusion
T6 ?, ?, ???
0, ??, ??
Dt6 ??
Dt6 Da
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Anisotropy of diffusion
Fe-Mg diffusion in olivine Dc 6 Da 6 Db
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Errors and uncertainties on the parameters
2. Experimental D determination at a given T
within a factor of 2
3. Uncertainties in other variables that D
depends on, e.g., oxygen fugacity, pressure.
Typically much smaller
4. One can expect overall uncertainties on
calculated times s of a factor of 2 to 4, e.g. 10
years might mean between 5 - 20 years
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6. Summary of times and contrast with other
types of data
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Turner and Costa (2007), Elements
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The Bishop Tuff comparing crystal diffusion
studies with radioactive data and residence times
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Bishop Tuff geochronological dataResidence
time using zircon ages ca. 50 to 100 ky Time
from diffusive equilibration of Ti in quartz ca.
100 yIs there something wrong?
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Radioactive decay vs. chemical diffusion time
scales
t1 100000 y
Radioactive time t1 t2
Diffusion time t2
Cooling and crystallization Small intrusions
or eruptions Time recorded by isotopes is 100
000 y
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7. Conclusions and Perspectives
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Conclusions and perspectives
(1) Modeling zoning patterns of crystals can be
used to obtain time scales of magmatic and
volcanic processes. The uncertainties can be
limited by careful petrological analysis,
multiple time determinations in a single thin
section, and improved D data.
(2) The ranges of time scales and types of
processes which can be determined is almost
unlimited thanks to the large variety of
elements, minerals, and crystals that can be
exploited. In the future smaller gradients will
be exploited, NanoSIMS, FIB-ATEM
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New developments FIB ATEM
Vielzeuf et al., 2007
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Conclusions and perspectives
(3) Time scales determinations from modeling the
zoning patterns are numerous but still not very
much exploited method. Results so far indicate
that many volcanic processes are short, e.g., lt
100 years. This is typically shorter and within
the error of radiogenic isotope determinations
and more studies using both methods should be
performed.