Myron G. Best. Igneous and metamorphic 2003 Blackwell Science
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errors in, for example, an assumed activity model,
which applied to all samples cancel out.
SUMMARY
Mineral reactions and equilibration in subsolidus meta-
morphic systems are hindered by sluggish kinetic rates,
especially where the catalytic effect of a fluid phase is
absent and where large activation energies of breaking
Si–Al–O bonds require substantial overstepping of
equilibrium conditions. Metastable persistence and
nucleation of new phases outside their stability field
plague interpretations of mineral assemblages. The
generally sluggish kinetics of subsolidus mineral reac-
tions are both friend and foe to the metamorphic
petrologist. Friend in that reactions going down grade
from peak P–T conditions are so extremely slow that
the equilibrated assemblage is frozen into the rock;
only at the highest temperatures, especially where there
is fluid infiltration or deformation, is the assemblage re-
equilibrated. Disequilibrium features including zoning
in minerals and inclusion assemblages in poikiloblasts,
and more rare reaction textures are preserved to aid in
reconstructing metamorphic histories. Foe in that the
petrologist can never be totally certain that the miner-
als constituting a rock represented a state of stable
thermodynamic equilibrium, despite satisfaction of the
criteria discussed in Section 16.1.
Simple applications of Le Chatelier’s principle can
provide qualitative insights into the behavior of per-
turbed and equilibrating metamorphic systems and
the direction of mineral reactions. In response to in-
creasing P on a rock, phases of smaller molar volume
(greater density) are stabilized, whereas increasing T
has the opposite effect of expanding the rock so that
phases of greater molar volume as well as greater en-
tropy are stabilized. The specific response to increasing
P and T as a rock is buried more deeply in the Earth
depends on which geothermal gradient it follows.
Thermodynamic calculations and experimentally de-
termined mineral stabilities guide investigations of
mineralogical reactions in metamorphic systems, allow-
ing quantitative elucidation of P–T–X conditions of
metamorphism via mineral thermobarometers and pet-
rogenetic grids.
Discontinuous reactions take place under univariant
conditions that go to completion at a single T (or P)
at whatever P (or T) they are encountered. They are
manifest in metamorphic terranes by a sharp isograd,
kinetics permitting. Such reactions include polymor-
phic transitions as well as net transfer reactions that are
depicted in triangular composition diagrams by switch-
ing of tie-line mineral compatibilities and by a terminal
disappearance of a critical phase. The P–T stability
field of a particular crystalline phase is unaffected by
the presence of a component or phase with which it
does not react but is reduced where it can react with
another phase. Hence, olivine alone is stable well into
the mantle but as olivine-bearing basaltic rocks are
subjected to increasing P during burial complex het-
erogeneous reactions with plagioclase consume olivine
at modest pressures in the crust. Further reactions
between plagioclase and pyroxenes create aluminous
pyroxenes and garnet in granulite-facies rocks and
eventually, under deep crustal and upper mantle con-
ditions, plagioclase-free eclogites are created.
Most rock-forming minerals are solid solutions and
break down incongruently via a combination of divari-
ant exchange reactions that are continuous over a
range of P and T and univariant discontinuous reac-
tions. In metamorphic terranes, the first appearance of
a newly stabilized solid solution can be delineated as
an isograd. Continuing exchange reactions and chang-
ing chemical compositions of phases through the cor-
responding metamorphic zone can be monitored in
triangular composition diagrams by continuous shift-
ing of tie-lines.
Volatile fluids and reactions involving them are
widespread in metamorphic systems except possibly at
highest grades where rocks have been “dried out” by
successive devolatilization reactions and perhaps par-
tial melting. Most volatiles are C–O–H species, chiefly
H
2
O and CO
2
but locally including CH
4
as well as
more exotic S-bearing volatiles, N
2
, H
2
, Cl, and F.
Fluids can contain significant concentrations of dis-
solved mineral components, especially Na, Si, and many
others. Fluids originate from the hydrosphere of the
Earth, from crystallizing intrusive magmas, and from
generally endothermic devolatilization reactions.
The conditions under which volatile-liberating
mineral reactions take place depend on P, T, and the
composition of the fluid in the system. For a given P,
the maximum thermal stability of a volatile-bearing
phase is greatest where the fluid in the system is the
same volatile species and P
fluid
P. Hence, hydrous
phases are stable to highest T in the presence of a
pure aqueous fluid but this stability T diminishes as
the mole fraction of water, X , decreases in the fluid,
or as P decreases less than P
fluid
, such as occurs by
addition of CO
2
or any other volatile species to the
system.
Investigations of mixed-volatile (H
2
O–CO
2
) reac-
tions in calc–silicate rocks have provided rich insights
into fluid compositions and flow during metamor-
phism. Depending on the permeability of the rock and
access to fluid, a mixed-volatile reaction can follow a
closed-system, internally buffered course that is ther-
mally driven; or it can follow an open-system behavior
in which infiltrating fluid from an external source,
and perhaps introduced heat, drive the reaction. These
contrasting conditions lead to contrasting product
H
2
O
H
2
O
Metamorphic Mineral Reactions and Equilibria
517
mineral assemblages. Infiltration of aqueous fluids is
responsible for the production of water-bearing talc
and tremolite during low-grade metamorphism of
initially anhydrous siliceous dolostones, as well as
significantly lower temperatures of metamorphism of
calc–silicate rocks in general, compared to temperat-
ures in closed systems. Infiltration of large amounts
of fluid through metamorphic terranes is indicated by
veins and grossly perturbed O-isotopic ratios around
granitic intrusions. In these cases the time-integrated
fluid/rock ratio can be relatively large.
Permeability is enhanced in metamorphosing rocks
by mineral reactions and deformation. Solid phases
produced by devolatilization reactions occupy a smaller
volume than solid reactant phases; consequently, inter-
connected grain-scale openings may be created during
the progress of the reaction. If the devolatilization re-
action produces more fluid than can be accommodated
in existing pores spaces—the usual case—and at a
greater rate than can be dissipated for a given state of
permeability, P
fluid
can exceed the tensile strength of
the rock, causing hydraulic fracturing. These fractures
can range from pervasive microcracks to more widely
spaced fractures of larger aperture through which large
volumes of flowing fluid can be channeled. Because
devolatilization reactions are episodic during the course
of metamorphism, permeability production is also
likely episodic, perhaps accounting for crack-seal veins
in metamorphic terranes.
Flowing fluids create low-variance metasomatic
rocks such as skarns in contact aureoles, hydrothermal
ore deposits, and hydrothermally altered seafloor rocks
that are essential in the generation of arc magmas in
subduction zones. On a smaller grain scale, movement
of ions through fluid pathways in different domains of
an open system appears to explain how mineral reac-
tions actually progress.
CRITICAL THINKING QUESTIONS
16.1 Justify the characterization of the Al
2
SiO
5
and CaCO
3
systems as consisting of only one
component, even though there are three
chemical elements in each.
16.2 Justify the univariant nature of the discontinu-
ous reactions in Figure 16.4.
16.3 Discuss how differing Fe/Mg ratios and Si, Al,
and Na contents would influence the P of
reactions involved in the transition from
basalt to eclogite.
16.4 Categorize the different types of metamorphic
mineral reactions and indicate fundamental
principles that govern them.
16.5 Discuss how different proportions of CO
2
and H
2
O in the fluid phase influence mineral
equilibria in the zeolite facies. Specifically,
under what conditions is the assemblage
analcite quartz more stable than albite
H
2
O? Zeolite minerals CO
2
more stable
than calcite clay minerals quartz H
2
O?
16.6 Using Le Chatelier’s principle and other
relevant concepts, justify the curvature of
the two univariant reaction curves in Figure
16.18b that have H
2
O and CO
2
on opposite
sides of the reaction.
16.7 How would the univariant breakdown curves
for micas in Figure 14.31 be shifted under
conditions of P P
fluid
? Of X 1?
What geologic situation(s) might cause these
conditions?
16.8 Discuss the different types of reactions
responsible for isograds.
16.9 A sequence of alternating thin beds of shale
and limestone that contains quartz sand grains
appears to have been metamorphosed to a
higher T than adjacent much thicker beds
presumed to have experienced the same
metamorphic T. How might this happen? Is
T the only controlling factor in metamorphic
grade?
16.10 Imagine a “world” in which carbonate minerals
are never in contact or have any chemical com-
munication with silicate minerals. How might
metamorphic systems be different in this world
from those on Earth?
16.11 The transition from amphibolite-facies to
anhydrous granulite-facies assemblages can
take place by a prograde increase in T. How
else might this transition occur isothermally by
changing the CO
2
content of the fluid in the
rock system? Draw a diagram depicting how
T and X stabilize the two assemblages.
16.12 The infiltration of large volumes of aqueous
fluids has been well documented during
metamorphism of carbonate-bearing rocks.
Does infiltration of fluid not play a role in
metamorphism of more widespread mafic and
pelitic rocks? Discuss fully.
16.13 Propose two geologically realistic histories for
the rocks shown in Figure 16.6. In other words,
what changes in geologic setting might have
created the coronas?
16.14 Discuss possible geologic histories of the rocks
illustrated in Figure 16.8.
16.15 Discuss the utility of CaCO
3
and Al
2
SiO
5
polymorphs as indicators of P–T conditions.
Consider both equilibrium and kinetic
implications.
CO
2
H
2
OH
2
O
518 Igneous and Metamorphic Petrology
16.16 Compare and contrast Darcy’s Law for advect-
ive flow of a liquid through a permeable rock
and Newtonian flow of a viscous material
(Sections 6.1 and 8.1.3).
16.17 Using Figure 16.4 as a guide, what can you say
about the stability of grossular alone without
any other phase that can react with it?
16.18 Account for the contrast between the straight
univariant lines for solid–solid reactions and
the curved lines for devolatilization reactions in
P–T space.
16.19 Using Figure 16.10: (a) Describe what happens
to the composition of clinopyroxene that con-
tains 50 mol % of the jadeite end-member and
coexists with quartz and sodic plagioclase as P
increases above 15 kbar at 670°C. (b) Suppose
a rock contains an apparent equilibrium assem-
blage of quartz sodic plagioclase clinopy-
roxene that contains 80 mol % of the jadeite
end-member. An independent mineral ther-
mometer indicates an equilibration T of 400°C.
What was the equilibration P?
16.20 Was it just the whim of the experimentalists
that equilibria for the garnet–biotite thermome-
ter were investigated in the laboratory at
550–800°C but for the GASP barometer at
650–1250°C, mostly beyond common meta-
morphic temperatures? Provide a reasonable
explanation.
PROBLEMS
16.1 Determine the positions and slopes of the
kyanite–sillimanite and andalusite–sillimanite
boundary lines in the Al
2
SiO
5
stability diagram
using the calculations in Section 16.3.1 as a
guide. Note that the low-P metastable extension
of the kyanite–sillimanite boundary line can be
extrapolated through the stability field of
andalusite, intersecting the T-axis where
P 1 atm. Discuss your results. How well do
your calculated boundary lines agree with
Figure 16.3? Account for any differences.
16.2 Write a balanced equation for the reaction
anorthite enstatite → pyrope quartz. How
does this compare with reaction 16.9. Using
data in Robie and Hemingway (1995) show
that this reaction has a positive slope in P–T
space.
16.3 Plot the composition of a basalt listed in any
table in Chapter 13 on an ACF diagram. Com-
pare your plotted composition with Figure 16.9
and discuss the nature of changes in mineral
assemblages through the granulite and eclogite
facies.
16.4 Some Ca–Mg–Fe–Al garnets in granulite-facies
rocks show replacement by a fine-grained inter-
growth of aluminous orthopyroxene Mg–Fe
spinel cordierite. Using S and V values in
Robie and Hemingway (1995), postulate how
this symplectite might have originated.
16.5 In the internally buffered example in Advanced
Topic Box 16.5, calculate the volumetric
changes in tremolite, dolomite, and quartz.
Their molar volumes are 272.90, 64.34, and
22.69 cm
3
/mole, respectively (at 1 bar and
298K). Comment on these changes. Would
they be visible petrographically? Partial answer:
V
Dol
4.83 cm
3
per 100 cm
3
of rock. This
loss in reactant dolomite is only about 5% of
the rock, which would be barely visible.
16.6 Using thermodynamic data in Table 16.2 for
quartz and coesite determine the position and
slope of the inivariant boundary curve between
the stability fields of these two polymorphs in
P–T space. Compare your results with Figures
5.11 and 18.35.
16.7 Draw a P–T diagram for the continuous reac-
tion 16.18, fully labeling all fields and univariant
lines.
Metamorphic Mineral Reactions and Equilibria
519
F
UNDAMENTAL
Q
UESTIONS
C
ONSIDERED IN
T
HIS
C
HAPTER
1. What factors and solid-state processes are
involved in the development and evolution of
metamorphic fabric?
2. How does solid-state crystallization interact with
grain-scale ductile deformation under
nonhydrostatic states of stress to produce the
characteristic anisotropic fabric of tectonites?
3. How can the tectonic history of complex
polymetamorphic rocks be unraveled from
metamorphic fabrics?
INTRODUCTION
The kinetically controlled equilibrating path from an
initial to a more stable final state in changing metamor-
phic systems is a complex interplay between subsolidus
crystallization, grain boundary stabilization, and, in
tectonites of orogens, more or less concurrent grain-
scale ductile deformation. It is incumbent on the
petrologist to understand these processes, which are
commonly episodic and repeated during polymetamor-
phism, by careful study of the metamorphic fabric.
Understanding what constitutes a stable equilibrium
mineral assemblage depends on an accurate interpreta-
tion of textures. Determination of P–T–t paths must
recognize mineral zonation, inclusions in poikiloblasts,
and relict minerals and textures. Rocks metamor-
phosed to high grade and then totally retrograded can
be distinguished by critical fabric features from rocks
of the same mineral assemblage that never reached the
high grade (McGregor and Friend, 1997). Accurate
interpretation of ductile shear fabric can reveal the
sense (direction) of shear and tell whether the fault was
contractional or extensional; this can be of paramount
importance in reconstructing the tectonic history of
complex metamorphic terranes.
There are, of course, parallels between the kinetic
paths followed by crystallizing magmas and recrystal-
lizing metamorphic rocks as intensive variables change
and a state of more stable equilibrium is approached in
the system. In both, new more stable crystalline phases
of lesser free energy first nucleate and then grow by
diffusion of ions, replacing initial metastable phases.
However, the kinetically controlled process paths in
evolving metamorphic fabrics differ in significant ways,
principally because of the subsolidus nature of meta-
morphism (excluding partially melting rock systems)
and the intimate role played by ductile deformation in
the evolution of tectonites. In more detail:
1. Mineral growth takes place in the solid state so that
growing crystals must compete with others for
space while reacting grains being consumed create
space. This environmental milieu is quite different
from crystallizing magmas where crystals expand
more or less freely in a melt during growth. In
Evolution of
Imposed
Metamorphic
Fabrics: Processes
and Kinetics
17
CHAPTER
metamorphic rocks, the most efficient avenue for
diffusion of ions to growing grains lies along inter-
grain boundaries. Although some metamorphic
systems may be completely devoid of any fluid,
most contain a solution of H–O–C-bearing volatile
components and locally S-, Cl-, F-, and N-bearing
components also. Because of the low porosity of
metamorphic rocks under elevated P, this fluid is
likely to be only thin threads along three-grain
boundaries or isolated pools at multiple grain cor-
ners (Section 16.7.2). In rocks where decompos-
ing reacting minerals are liberating volatiles the
fluid pressure may be sufficiently high to induce
hydraulic fractures (Section 8.2.1 and Figure 8.2).
2. Grain boundary adjustments minimizing the sur-
face energy of the grain aggregate (Section 6.4)
are of greater consequence during the long time
periods of metamorphic episodes, particularly in
deep crustal regional terranes of orogens.
3. Metamorphic rocks in orogens are commonly de-
formed by pervasive grain-scale ductile processes
under nonhydrostatic stress, resulting in a pre-
served anisotropic tectonite fabric. Existing grains
are destroyed to varying degrees and new grains
grow concurrently with deformation; in many
cases, deformation is progressing while mineral
reactions are creating new mineral assemblages.
In metamorphic tectonite systems, deformation and
recrystallization are intimately intertwined. The two
processes can have a synergetic or feedback rela-
tion; as one acts it influences the other, which in
turn has an effect on the first. The presence of a
volatile fluid can have a profound effect on this
synergism because it is an important factor both in
deformation and in mineral equilibration and re-
crystallization, as found in the Chapter 16. In con-
trast, anisotropic fabric resulting from deformation
of a body of magma is uncommon because the body
responds by flow of the melt phase, perhaps pro-
ducing flow layering or igneous lamination. Even in
magmas of high crystallinity, individual mineral
grains may reveal only limited deformation because
its effects are erased at high magmatic temperatures.
4. In subsolidus metamorphic systems, kinetic rates
are slower, in some instances by many orders of
magnitude, and there is more metastable persist-
ence of mineral phases, compared to higher T mag-
matic systems. Although metamorphic systems
tend toward states of equilibrium, nonequilibrium
effects can occur and the petrologist needs to be
aware of their possible presence.
This chapter deals with fabrics imposed during
metamorphism—in contrast to relict fabrics preserved
from the protolith that were described in Chapter 14.
Nucleation and crystallization in static, nondeforming
metamorphic rocks are considered first, while sub-
sequent sections deal with the compounding effects of
deformation and fluid involvement during recrystal-
lization in tectonites.
Summaries of fabric development include Spry
(1969), Barker (1990), and Shelly (1993); Kretz (1994)
is an advanced treatment. Passchier and Trouw (1996),
Snoke et al. (1998), and Vernon (2002) provide well
illustrated interpretations of tectonite fabrics.
17.1 SOLID-STATE CRYSTALLIZATION
UNDER STATIC CONDITIONS
In the simplest of metamorphic systems, recrystalliza-
tion takes place without concurrent deformation.
Typical of such systems is thermal metamorphism or
metasomatism in contact aureoles around passively
intruded magmas where recrystallization is activated by
changes in T or by introduced advecting fluids.
As defined in Section 14.1.2, recrystallization in-
cludes both adjustment of grain boundaries of existing
stable phases, such as of quartz grains during heating of
a quartzite, and formation of new stable product grains
from unstable reactants, as in the growth of garnet
porphyroblasts from decomposing grains of chlorite,
muscovite, and quartz.
Formation of an entirely new phase grain in a crys-
talline solid aggregate depends on four processes:
1. Destruction of pre-existing reactant phases by re-
moval of ions from grain surfaces; in the presence
of a fluid phase this is a dissolution process.
2. Diffusive transport of ions through the intergran-
ular medium from reactant to product phases.
3. Nucleation of newly stable crystalline product grains.
4. Grain growth—the incorporation of transported
nutrient ions onto the grain surface.
These steps may even be involved in polymorphic
transitions, as suggested in Section 16.10.1.
Each of these four kinetic processes proceeds at a
different rate. Some petrologists believe that the first
two steps are the slowest and, therefore, control the
overall rate of formation of the new product grains.
The consistent recurrence of essentially the same
sequence of mineral zones in regional terranes implies
that nucleation and growth keep pace with changing
metamorphic conditions (Ridley and Thompson, 1986).
On the other hand, the persistence of lower grade relict
phases into higher grade rocks suggests the sluggish-
ness of their destruction. Because of the exceedingly
slow interdiffusion of NaSi and CaAl in plagioclase
(Figure 6.4), breakdown reactions could be similarly
slow and require large overstepping to accomplish.
Rubie (1998) claims that plagioclase might survive for
millions of years at 20 kbar and 600°C in the stability
field of jadeite grossular kyanite quartz without
Evolution of Imposed Metamorphic Fabrics: Processes and Kinetics
521
any of these phases nucleating. Even in the presence of
water, zoisite may be the only phase to readily nucleate
at intracrystalline sites in plagioclase.
Once a grain is created, there may be diffusion of
ions internally through its atomic structure, especially
in solid solutions, to equilibrate the chemical com-
position with changing metamorphic conditions. This
intragranular diffusion depends upon the existence of
point defects in the crystal lattice (Figure 6.5) and is
generally much slower than intergranular diffusion
along grain boundaries (Figure 17.1) by a few orders of
magnitude. The more widely spaced and disorganized
atoms in the intergrain layer (see highly schematic
depiction in Figure 6.9) allow for greater freedom of
movement of ions. But the fastest diffusion path, by as
much as 16 orders of magnitude (Rubie, 1986), is in an
intergranular fluid along grain edges (Section 16.7.2).
Volumes of such fluid are too small to possess the
thermodynamic properties of larger bulk volumes of
a separate H–O–C fluid solution and instead may be
viewed as “dissolved” in the disordered intergrain
boundary layer. Diffusion is enhanced in intergranular
aqueous fluids because hydrogen bonds are more eas-
ily broken than much stronger Si–O bonds, effectively
reducing the activation energy of diffusion. At high in-
stantaneous fluid/rock ratios, a distinct separate fluid
phase can exist in pore spaces in the rock. In a static
separate aqueous phase, rates of diffusion of ions are
estimated to be about 10
8
m
2
/s (Rubie, 1986), which
is generally orders of magnitude faster than in silicate
melts and possibly an order of magnitude greater than
in an intergranular fluid. If the fluid is advecting, mater-
ial transport rates can be faster than in a static fluid
volume. Clearly, prograde devolatilizing reactions in
rocks that liberate fluids furnish opportunities for
greatly enhanced rates of diffusion, material transport,
and formation of new product phase grains.
17.1.1 Nucleation and Growth
Homogeneous nucleation probably never occurs in
solid rocks because of grain boundaries, internal
cracks, foreign mineral inclusions, crystal defects, and
other phase discontinuities that provide favorable,
relatively higher energy sites for heterogeneous nucle-
ation, overcoming activation energy barriers (Sections
6.5.2 and 3.6). A smaller overstep of the equilibrium
condition is required. Grain boundaries serve as nucle-
ation sites for new phases (Figure 17.2). The presence
of volatile fluids can play a catalyzing role so that
nucleation of new product mineral grains in devolatil-
ization reactions may require less overstepping than
in solid–solid reactions. Nucleation is probably easy
where a new product phase nucleates and grows in an
epitaxial manner on a substrate of a reactant phase of
similar atomic structure, such as micas and chlorites on
similar sheet silicate clay minerals and double-chain
amphibole overgrowths on single-chain pyroxene (Fig-
ure 14.7). This may also account for the fact that pro-
grade biotites formed in fine-grained chlorite-bearing
pelitic rocks are typically not large porphyroblasts, as
are garnets and staurolites, whose nucleation is not so
favored.
Nucleation likely continues over some range of
changing metamorphic conditions, possibly increasing
in rate with increasing overstepping beyond the condi-
tion where a mineral reaction begins.
Many observations of rock fabrics as well as con-
trolled experiments indicate that nucleation and
grain growth are parallel processes in metamorphic
systems. As in crystallizing magmas (Section 6.5.4),
if the ratio of growth rate to integrated nucleation
rate is large following the onset of a mineral reaction,
then large grains result, such as porphyroblasts and
inclusion-riddled poikiloblasts in metapelites (Figures
522 Igneous and Metamorphic Petrology
Lattice
diffusion
Grain-boundary
diffusion
Diffusion through
surrounding fluid
17.1 Three paths of diffusive transfer allowing ions to move from an unstable compressed grain margin to a less stressed surface where growth
occurs. Of the three paths, diffusion through the grain (lattice diffusion) has the greatest activation energy and is the slowest, whereas
diffusion through an intergranular fluid is the fastest.
Evolution of Imposed Metamorphic Fabrics: Processes and Kinetics
523
14.10, 14.25 and 16.2). Numerous small grains, such as
Mn-rich garnets in some metacherts, probably reflect
high nucleation rates compared to growth rates.
Two competing, rate-limiting processes operate in
solid-state mineral growth: transport of nutrient ions
to the growing crystal face, or diffusion-controlled
growth, versus incorporation of nutrient ions onto the
crystal face, or interface controlled growth. (Compare
growth of crystals in melts, Section 6.5.3.) Both pro-
cesses occur at an increasing rate at increasing over-
stepping beyond the condition at which the formative
reaction begins. In Figure 17.3, the function along the
x-axis is designated as the reaction affinity that was
defined in Section 16.10 as the overstep, (T T
eq
)
multiplied by the entropy change for the particular
reaction. This affinity is the thermal driving force for
crystallization as the system departs from the equilib-
rium condition. In other situations, the affinity is a
measure of the degree of supersaturation of a product
phase in a solution. As the affinity increases, growth
rates increase (as does nucleation rate) but because
interface-controlled growth increases exponentially it
is rate limiting at small (T T
eq
) whereas the slower
diffusion-controlled growth is limiting at large (T
T
eq
). The absence of a fluid phase in a rock would
significantly reduce intergranular diffusion rates and,
consequently, growth would require large overstep-
ping. The presence of a fluid increases diffusion rates
so that the rate-limiting interface-controlled growth
process becomes paramount. Which rate-limiting
growth process prevails can depend on the meta-
morphic environment and the nature of the reaction,
and it may well change during the progress of the
reaction.
Contact Metamorphic Aureoles. In contact aureoles
and in relatively anhydrous, coarse-grained granitoids
(a) (b)
Quartz
Quartz
Garnet
(c)
17.2 Schematic crystallization of garnet poikiloblast. (a) Multiple nucleation sites occur at hypothetical quartz triple junctions. (b) During sub-
sequent growth and further nucleation at additional sites, separate grains merge. (c) Further growth consumes more quartz, perhaps by
reaction with nearby chlorite (not shown), leaving unreacted quartz as inclusions. Denser stippling suggests greater concentration of Mn
in earlier garnet. Redrawn from Daniel and Spear (1998).
Rate of growth/nucleation
(a)
T
eq
Nucleation
Diffusion-controlled
growth
Interface-
controlled growth
Reaction affinity = ∆S(T T
eq
)
Proximity to intrusion
Forsterite grains
Intrusion
1–3 mm long
0.3 mm
(b)
17.3 Interplay of nucleation and crystal growth in a simple envir-
onment of thermal metamorphism. (a) Rates of nucleation
and two contrasting processes of crystal growth versus the
reaction affinity that drives them, which is effectively the
overstepping beyond the equilibrium T
eq
at which a mineral
reaction begins. The controlling growth mechanism for any
reaction affinity is the one with the slowest rate (heavy line).
(b) Forsterite nucleation and growth in a contact aureole in
siliceous dolomite, Death Valley, California. Redrawn from
Roselle et al. (1997). Close to the granitic intrusion where heat-
ing was rapid, there was a large reaction affinity or overstep-
ping of the T driving equilibrating crystallization of forsterite.
Nucleation was rapid relative to diffusion-controlled growth so
that numerous small forsterites crystallized. Farther from the
intrusion, heating was slower, overstepping less, and fewer
larger forsterites crystallized because nucleation and growth
rates were reversed.
and high-grade metamorphic protoliths, considerable
overstepping may be required for nucleation and
growth, compared to prograde devolatilizing reactions
in pelites. The role of overstepping is illustrated in a
study of forsterite size and shape in a contact meta-
morphic aureole in Death Valley, California (Roselle
et al., 1997). Close to the intrusion where there was
rapid heating resulting from advecting hydrothermal
solutions, appreciably overstepped reactions in the
siliceous dolomite country rock yielded numerous,
small forsterite grains because slow diffusion-controlled
growth rates were less than nucleation rates (Figure
17.3). Farther from the contact, slower heating resulted
in lesser overstepping so that interface-dominated
growth on few nuclei produced large robust forsterites.
Experiments on olivine growth (Donaldson, 1976)
indicate formation of elongate and tabular crystals
where growth rates exceed nucleation rates and the
converse for equant olivines.
Cashman and Ferry (1988) discovered a significant
difference in the crystal size distribution in metabasite
hornfelses in a contact aureole and garnet–mica schists
in a regional metamorphic terrane. The hornfelses
have a linear size distribution such that the smallest
grains are the most numerous and the largest the
least numerous. This implies a continuous process of
nucleation and growth through the aureole, but over
a relatively brief interval of time. The schists, on the
other hand, have a bell-shaped size distribution in
which most grains are of intermediate size, whereas
smallest and largest grains are less numerous. This size
distribution is interpreted to have developed initially as
a linear one but over the much longer time, perhaps
10
4
–10
5
y, of metamorphism in the regional terrane
many grains became coarser at the expense of smaller
ones by slow Ostwald ripening (see below).
Formation of Garnet Porphyroblasts in Regional Schists.
Porphyroblastic and anisotropic fabrics are the major
noncompositional aspects of metamorphic rocks that
demand explanation. Porphyroblasts are to metamor-
phic rocks what phenocrysts are to volcanic rocks, but
their origins must be different. Among the common
porphyroblasts that include staurolite, kyanite, and
garnet (Figures 14.8–14.10), garnets have attracted the
most attention because they are the most widespread,
especially in moderate grade amphibolites and pelitic
schists, are typically compositionally zoned so that
something of their history of element uptake can be de-
ciphered, and commonly contain inclusions and curved
inclusion trains that provide insights about mineral re-
actions and deformation during growth, respectively.
The nucleation and growth of garnet porphyroblasts
serves as a model for the formation of any new mineral
grain in a metamorphic rock and is informative for this
specific index mineral in Barrovian zones.
Porphyroblasts and poikiloblasts result from a low
cumulative nucleation rate but high growth rate. These
conditions are favored in prograde devolatilization
reactions that have large entropy changes (Section
16.10), allowing small oversteps in the reaction affinity
function, combined with greatly enhanced rates of
ion mobility in the liberated fluid. But another factor
enters into the development of porphyroblastic alumi-
nosilicates, namely, their large surface energy that
places them high in the crystalloblastic series (Section
14.1.1). Examination of the thermodynamic expression
in Advanced Topic Box 6.2 (substituting a reactant
solid phase in lieu of a melt) shows that for product
grains possessing a large surface energy the nucleation
rate curve is displaced toward higher values of (T
T
eq
). The overall effect, then, is to retard nucleation of
aluminosilicates while allowing rapid diffusion in the
fluid-rich environment.
Textural evidence for diffusion-controlled growth
along matrix-grain boundaries is seen in porphyro-
blasts that have grown by fingerlike extensions between
engulfed matrix grains (Figure 17.2). For such growth,
a concentration gradient develops around a growing
garnet, which, in three dimensions, is a more or less
spherical zone depleted in nutrient ions. As the zone
expands outward from the growing garnet at a rate
dependent on the rate of diffusion of the slowest ion
moving toward it, additional garnet nucleation is sup-
pressed in the depleted zone. Overall, garnets will not
be randomly distributed and there will be a tendency
for later nucleating garnets growing in the depleted en-
vironment to be smaller. From an analysis of the spatial
distribution and size of thousands of garnets in many
rock samples by computed X-ray tomography (Figure
17.4), Carlson and associates (e.g. Carlson et al., 1995)
have concluded that a model of thermally accelerated
diffusion-controlled growth best explains the forma-
tion of garnet porphyroblasts.
Other investigators (e.g. Daniel and Spear, 1999)
find garnet distributions and sizes that are more
random, which is consistent with interface-controlled
growth in a homogeneous matrix.
Whereas most porphyroblasts in all kinds of rocks
appear to have nucleated at a single site, based on a
regular concentric pattern of compositional zoning (see
below), Daniel and Spear (1999) document patterns of
zoning in garnets that indicate multiple nuclei and co-
alesced growth within a single porphyroblast (Figure
17.2). Pre-existing matrix grains not consumed in the
garnet-forming reaction were enclosed as inclusions,
creating poikiloblastic texture.
17.1.2 Equilibration of Grain Size and Shape
The tendency of grain aggregates at elevated tempera-
tures over time to minimize their overall surface energy
by adjustment of grain boundaries (Sections 6.4 and
524 Igneous and Metamorphic Petrology
6.6.2) governs many aspects of metamorphic fabric.
This is a secondary phenomenon after initial nucleation
and growth. Few values of surface energies of silicate
mineral exist, but for a given mineral grain depend on
atomic structure, the type of neighboring grains and
their orientation, and grain size.
Grain Size. Because aggregates of increasingly smaller
grains have increasingly greater surface areas relative to
their volume, their surface energy increases. For any
one grain, surface energy increases with decrease in
radius of curvature of the surface. Hence, energy is
reduced if curvature is straightened or small grains are
consumed by expanding large ones (Figure 14.5). The
most stable grain size would theoretically be one in
which there is a single crystal of each phase in the
aggregate. However, this ideal stable state is never real-
ized in nature because the driving force for grain coars-
ening, sometimes called Ostwald ripening, becomes
vanishingly small long before a minimum energy state
is reached. This can be seen for quartz, whose average
interfacial energy is 5 10
5
J/cm
2
. An increase in
grain size from 8 to 40 micrometers (microns) is driven
by an energy reduction of 6.7 J/mole, whereas further
increase from 40 to 1200 micrometers reduces the
energy by only 0.0033 J/mole (Tullis and Yund, 1982).
Hence, for all but the smallest grain sizes in rocks,
surface-energy driving forces are orders of magnitude
smaller than the internal Gibbs free energies of solid
phases that drive mineral reactions. Accordingly, coars-
ening requires the most favorable kinetic conditions of
elevated T and long time periods.
Monomineralic aggregates are most likely to show
coarsening, whereas in polyphase rocks, such as horn-
felses in contact aureoles (Figures 14.25 and 16.23),
prograde reactions may override coarsening effects. On
the basis of experimental measurements at 1000°C and
15 kbar over many days, Tullis and Yund (1982) ex-
trapolated conditions for coarsening of wet microcrys-
talline quartz to more normal metamorphic conditions
of 600°C and 3 kbar; from an initial grain size of 100
micrometers, it would require 10
5
y to achieve coars-
ening to 0.6 mm and 10
6
y to 2.3 mm. Coarsening rates
for limestone are much faster, accounting for the
occurrence of much coarser marbles (Figure 14.4b)
than quartzites.
The presence of small grains of a “second phase”
can retard coarsening of major larger grains by “pin-
ning” their boundaries, effectively suppressing grain
boundary migration. Mas and Crowley (1996) found an
order of magnitude variation in the size of calcite grains
in a Massachusetts marble that had apparently experi-
enced uniform P, T, and strain histories. Only a few
modal percent of a second phase (quartz, mica, alkali
feldspar, apatite, Fe–Ti oxide) was effective in suppress-
ing grain growth during greenschist facies condition.
Evolution of Imposed Metamorphic Fabrics: Processes and Kinetics
525
(a)
0cm4
(b)
17.4 Fabric of a garnet–kyanite–biotite–quartz–feldspar tectonite, Mica Dam, British Columbia. (a) Conventional photograph of hand
sample. Note white quartz vein on left. (b) Image generated from high-resolution computed X-ray tomography (Denison et al., 1997).
A wedge of rock has been artificially extracted from the upper right of the image to reveal the underlying three-dimensional aspect of
the fabric. Brighter grayscales correspond to more dense materials so that garnet porphyroblasts are prominent light gray spots, kyanite
porphyroblasts are darker gray but slightly lighter than the adjacent polygranular lenses of biotite, and darkest gray to black is quartz.
A color image of this same sample from a different perspective is on the cover of the August 28, 1992 issue of Science (Carlson and
Denison, 1992). Computed X-ray tomography (CT) data from the University of Texas High-Resolution CT Facility. Photograph, CT
image, and caption courtesy of William D. Carlson and Richard Ketchum.
Figure 17.5 shows second-phase suppression on the scale
of a single photomicrograph. Small flakes of graphite are
particularly effective in pinning boundaries of somewhat
larger quartz and mica grains in phyllites and schists.
Grain Shape. The stable equilibrium shapes of meta-
morphic mineral grains have been discussed by, among
others, Kretz (1966, pp. 392–8) and Vernon (1970). In
monomineralic aggregate of ideal grains possessing
isotropic surface energy, the interfacial or dihedral
angle ( in Figure 11.7; see also Section 6.6.2 and
Figure 6.22) between adjacent grain boundaries is
120°. In three dimensions, stable grains with minimum
surface areas (and energies) have shapes like those
in Figure 6.23. This ideal dihedral angle relates to
planar or smoothly curving grain boundaries with no
relationship to the orientation of the crystal lattices in
neighboring grains. In real monomineralic rocks this
geometry is closely approached in granoblastic texture
(Figures 6.24 and 14.5c).
More anisotropic, less symmetric crystals—such as
monoclinic amphiboles and micas—have quite different
atomic arrays on different crystallographic planes. This
affects the manner in which different rational crystal
faces in an isolated crystal or different surfaces in a
grain in an aggregate react, dissolve, or grow; chemical
processes on grain surfaces are crystallographically
specific. An obvious example is the contrast between
the (001) and {010} or {110} faces in sheet silicates,
such as mica. The (001) plane is typically a large crystal
face and is also a perfect cleavage because of the weak
atomic bonding across it. The surface energy is lower
on this surface than on faces parallel to the crystallo-
graphic c-axis where edges of Si–Al–O tetrahedral
layers are exposed with unsatisfied bonds. Consequently,
in monomineralic aggregates of mineral grains possess-
ing strong surface energy anisotropy, equilibrium dihe-
dral angles can deviate from the ideal 120° intergrain
angle in thin sections. Lower energy grain boundaries
dominate the texture. Grain boundaries tend to lie
more or less parallel to crystallographic planes in one
(or rarely both) of two adjacent grains (Figure 17.6a).
Some grain boundaries are not planar but sawtooth-
like; this larger surface area is actually a more stable
one because it is made of the most stable, least energy
crystal faces of adjacent oblique crystals (Figure 17.6b).
In polyphase aggregates, grains of higher surface
energy adjust their boundaries to form more or less
rational crystal faces against adjacent anhedral grains
that possess lower surface energy. This is the rationale
behind the crystalloblastic series. For example, some-
what rectangular quartz grains are sandwiched or
“truncated” between euhedral flakes of muscovite in
a quartz–muscovite schist (Figure 17.7). Any other
boundary relationship—such as euhedral grains rank-
ing low in the series juxtaposed against anhedral high-
series grains—would have greater overall aggregate
energy. Additional examples of stable grain boundaries
include inclusions of quartz and feldspar that have
“negative” dodecahedral crystal faces in host garnet
poikiloblasts (Kretz, 1966).
17.1.3 Intragrain Textural Features
Features within metamorphic mineral grains can be
important in providing records of processes involved in
their growth.
526 Igneous and Metamorphic Petrology
(a)
0 0.1mm
(b)
0 0.1mm
17.5 Aggregate of quartz and black (opaque) magnetite in fine-grained ironstone protolith. More abundant grains of minor “second phase”
magnetite in lower left suppressed grain coarsening evident in upper right. (a) Plane-polarized light. (b) Cross-polarized light.