‘rm.
a

V

 

 

 

 
 
 

 

 
 
 

 

J ‘ _ _ ..
u . v n . .. .. ...
u a ,
< ‘Z ‘
‘ . . .: . . A
r . . . z x 4 .
i . _ . _
., , ,
u. x .
. _
. . e. x . ,..
. u L
.. ‘ ., ._. .. _,
a .0 ._ . ‘
. . v I
.7 . a . . A z z ¢ ._
. . "A ,J a ..
., , . a .3
n r u
a .
, ~ V
.1. . . _ «v .
m. ‘_ . a. k .. . . “
I , . . V . . .
h _ ‘ .. .. i. h. 1‘
~ . . r
g A . .
‘ .H ~ .. .
' ‘ K . .
a. . .,\ ... a,“ a .i
u. . . .r . .
f. . . 2 t; ‘ .
\. , ,.\\...\

_: ____:_:__:::_:_:_:=:___ _§:_:_‘:__:_.__

 

fa. r‘ r: ,.;_

. Date

lllllllllllllllig m

  

.i ' _ _ a"
Dianna 1», ., :
'zsaiwcrsfh' ,'

I

.ngA.“ .. 1. nub]... . .

 

This is to certify that the
thesis entitled

A MODEL FOR SURFACE AREA, MINERALOGYI,
AND METAMORPHIC GRADE IN CARBONATES

presented by

GARY R . BYERLY

has been accepted towards fulfillment
of the requirements for

Mega in W

Major professor i K '

.I

.8’

 
 

Bill/71*

 

LIBRARY é‘”

’9
9

-AAfi—‘fl‘flE—gma .—‘A__—;_—__—4v—~—__-Kc

—— —_,. #7 a ___.___ _‘ A

ABSTRACT

A MODEL FOR SURFACE AREA, MINERALOGY,
AND METAMORPHIC GRADE IN CARBONATES

By

Gary R. Byerly

In meta-carbonates ranging from greenschist to
middle amphibolite grade, total and partitioned components
of surface area demonstrate highly significant variation as
a function of both metamorphic grade and percentage of
coexisting phases (calcite, dolomite, quartz, and phlogopite).
Total surface area is a positive linear function of modal
percent second phases (dolomite + quartz + phlogopite),
whereas, calcite-calcite surface area is a negative linear
function at greenschist grade and a very flat second order
function at amphibolite grades. All surface area components
decrease with increasing metamorphic grade. Second phases
control surface area by inhibiting grain boundary migration
and thus grain growth. At low grades, strain induced
recrystallization and grain boundary migration result in a
high surface area aggregate. At higher grades, grain
boundary migration, driven by surface energy differences,
becomes dominant and results in a very low surface area

aggregate.

A MODEL FOR SURFACE AREA, MINERALOGY,
AND METAMORPHIC GRADE IN CARBONATES

By

0/
Gary R.'Byerly

A DISSERTATION

Submitted to
Michigan State University
in partial fulfillment of the reQUirements
for the degree of

DOCTOR OF PHILOSOPHY
Department of Geology

T974

ACKNOWLEDGMENTS

Tom Vogel, for his encouragement and support these
last four years. A good friend and competent teacher.

Bob Ehrlich, for getting me involved with research
as an undergraduate, and making me aware of the philosophy
of science.

Sam Upchurch, Bob Anstey, Bill Cambray, and Charles
Spooner, for their work on my committee.

Kevin, Bruce, Lee, Graham, Steve, and many others,
for their friendship, and their valuable discussions on
this research.

The Coffee-room Gang, including Jean, Jeanne,
Larry, Wendy, Vivian, Stoney, Sue, Jeff, and Duncan, for
just being around.

My Parents, for accepting me as the strange person

I am growing into.

ii

TABLE OF CONTENTS

LIST OF TABLES
LIST OF FIGURES

INTRODUCTION
DISCUSSION OF MODELS
PHASE DISTRIBUTIONS IN META-CARBONATES

Surface Area Variation . . .
Grain Transition Probabilities

DISCUSSION OF RESULTS

REFERENCES .

Page

iv

_a
N-b‘ONw

21

LIST OF TABLES

Table Page
1. Regression Statistics for First Order Models . ll
2. Regression Statistics for Second Order Models . 12

iv

LIST OF FIGURES

Figure

1. Relationship of total and calcite-calcite
surface area to modal percent second phases
(dolomite + quartz + phlogopite) for the
three metamorphic sampling suites .

2. Photomicrographs of representative samples
3. Relationship of grain transition probabilities

to modal percent second phases for the three
metamorphic sampling suites

Page

TO
13

TS

INTRODUCTION

Textures have received much attention for their
relationship to deformation, recrystallization, grain
growth, and phase transformations in metamorphic petrology
(Pitcher and Flynn, l965; Spry, l969). Ehrlich and others
(1972) have shown that in the progressive regional meta-
morphism of a granodiorite textural variables are more
responsive to pressure and temperature changes than
mineralogical or chemical variables. Total rock surface
area and plagioclase surface area as a function of meta-
morphic grade seem to be the most responsive variables.

Quantitative work on phase distributions in meta-
morphic rocks has been noticeably lacking although
theoretical (for example American Society of Metals, 1966;
Fulrath and Pask, l968) and empirical (Underwood, l968; and
DeHoff and Rhines, l970) basis for such work does exist.
The importance of phase distributions or textures has long
been discussed in the geological sciences but in general
in a very qualitative fashion.

This paper is concerned with the textural response
of impure carbonates to progressive regional metamorphism.
By studying a range of modal compositions within each suite

of metamorphic samples, the effects of second phase

I

particles are also evaluated. Two techniques are used for
studying the phase distributions. Surface area is parti—
tioned between the possible grain boundary types and from
these grain transition probabilities are derived. The
following section first gives the reader a review of current
models relating textures to the processes which affect

crystalline aggregates.

DISCUSSION OF MODELS

The importance of surfaces in controlling many
properties of crystalline aggregates is well documented in
the literature of ceramics and metallurgy. Smith's (1948)
discussion of the role of surface energy in controlling
textures is a classic work. Surface energy forces move the
various boundaries in an aggregate to a state of balancing
forces, that is, an equilibrium configuration. White
(1966) has quantitatively demonstrated the surface energy
controls on textures, specifically on preferred phase
distributions in two and three phase aggregates, and with
small impurity additions. He uses parameters similar to
the grain transition probabilities of this paper in addition
to grain size distributions. White observes that total
surface area is maximized at specific modal compositions.
His work supports the concept that second phases exert
strong controls on surface area. With increasing modal
percent of a second phase the grain size of both phases
decreases significantly. He further finds that unlike
boundaries occur significantly more frequently than bound-
aries between like phases. DeVore (1955, 1959) and Voll
(1960) conclude that surface energy effects should be of
major importance in controlling phase distributions in

petrological systems. DeVore (1955) speculates that even

3

modal percentages could be a function of surface energy
controls where slight differences in chemical potentials
were driving reactions, such as in metasomatism.
Recrystallization and grain growth are the solid
state processes responsible for major changes in the
texture of a crystalline aggregate. These processes are a
function of temperature, strain, and dispersed second
phase particles. Recrystallization, Grain Growth, and
Textures (American Society for Metals, 1966) and more
recently Aust (1972) review the relationship of these
variables to recrystallization and grain growth. The
following discussion is derived largely from these sources.
The major effect of increasing temperature is to
overcome thermal barriers to diffusion, which enhances
migration of defects, dislocations, and grain boundaries.
Strain increases the free energy of the crystal, thus
enhancing recrystallization. Variation in strain rates and
temperature can result in two fundamentally different forms
of grain boundary migration. At low temperatures and high
strains grain boundary migration is driven by the increased
free energy of the strained crystal and small recrystallized
grains will grow at the expense of larger, more highly
strained grains. At high temperatures and low strain rates
grain boundary migration is driven by differences in surface
energy, resulting in large grains growing at the expense of
small grains. A coarse grained, low surface area aggregate

is formed.

The distribution of a second phase in an aggregate
effects the properties and resultant texture in several
ways. Grain growth is limited by the inhibition of grain
boundary migration. As sites for recrystallization mucleii,
rapid recrystallization is promoted as a response to
increasing temperature and strain.

Previous textural work in geology has focused pri-
marily on the effects of temperature and strain, with little
on phase distributions. Indeed, most of the studies have
been done on single phase aggregates such as carbonates,
quartzites and dunites. DeVore has attempted to develop
models for preferred phase distributions as a function of
stress orientation and elastic compliance anisotropies in
crystals (1969), and surface chemistry and surface energy
(1955, 1959). Vistelius (1972) has developed a stochastic
model for phase distributions in granitic rocks as a
function of crystallization pathways.

Much of the experimental work in geology has been
with carbonates due to their relative ease of recrystalliza-
tion at times, pressures and temperatures possible in the
laboratory. Heard and Raleigh (1972), Wenk and others
(1973), and Rutter (1974) are recent investigators. Their
experiments and those reviewed by them indicate that above
350°C recrystallization and grain growth in strained calcite
aggregates becomes dominant over mechanisms such as twinning,

translation, and kinking. This first becomes noticeable

with development of calcite porphroblasts in a fine matrix.
With complete recrystallization at higher temperatures a
coarse equidimensional aggregate is formed. Steady-state
flow is possible at temperatures in excess of 250°C for

-14

geological strain rates (mlO sec-1).

PHASE DISTRIBUTIONS IN META—CARBONATES

Marbles from the Grenville Province of southeastern
Ontario were collected for variation in mineralogy and meta-
morphic grade. Metamorphic grade, as determined by
mineralogy of adjacent pelitic units, ranges from green-
schist near Madoc to middle amphibolite near Fernleigh
(Moore and Thompson, 1972).

The sample units for modal and surface area analyses
were defined on the basis of homogeneity of mineralogy and
grain size to minimize sample variance (Ehrlich, 1964). At
lowest grades these homogeneous units range in thickness
from 0.5 to 2 cm and probably represent primary sedimentary
lamella. At higher grades the homogeneous units thicken
to sizes from 1 to 10 cm and may represent some metamorphic
effect on the primary sedimentary lamella.

Sample suites were collected at greenschist, lower
amphibolite, and middle amphibolite grades. Dolomite,
quartz, phlogopite, and calcite are stable in the sample
suites from greenschist and lower amphibolite grades, with
dolomite absent in the middle amphibolite grade suite. At
lower metamorphic grades the samples range from nearly pure
quartzites to nearly pure marbles. The highest grade sample

suite had no samples with less than 60% calcite.

7

Sixteen sample units were chosen from each of the
three metamorphic sample suites. A uniform distribution
of sample units between 50 and 100 percent calcite was
attempted. Surface area analyses were performed using the
method of Kendall and Moran (1963). An unbiased estimate
of surface area is simply twice the number of intersected
boundaries per unit length of transect line. Grain bound-
aries were counted on transects perpendicular and parallel
to the planar direction of the sampling units. Three
transects counting 100 boundaries each were run in both
directions. Parallel surface components were always 5 to
15 percent lower than equivalent perpendicular components,
but conform to similar trends. For this reason all six
traverses were averaged in each sample. The unbiased
estimate of surface area should be made by random transects
through the sample volume. The above technique gives an
average of the minimum (parallel) and maximum (perpendicular)
surface area.

This same data can then be used for estimates of
grain transition probabilities. These variables are the
probability of encountering a specified phase at the next
boundary along a traverse, given only the current phase of
the traverse. This simply amounts to division of the
partitioned surface area by the total surface area for each
sample unit. These parameters are only a different way of

analyzing the surface area data and actually contain less

information than the absolute values of partitioned and
total surface area. Vistelius (1972), Flinn (1970), and
Kretz (1969) have used grain transition probabilities to
characterize phase distributions in igneous and metamorphic
rocks. The use of the entire transition probability matrix
is operationally difficult and the statistical tests
ambiguous, therefore, only selected probabilities will be

examined.

Surface Area Variation

 

In order to demonstrate the strong controls which
both metamorphic grade and mineralogy have on surface area,
total and calcite-calcite surface area are plotted as a
function of modal percent second phases for each of the
three sample suites (Figure 1). In all cases the functional
relationship is statistically significant. Statistics for
both first order and second order regression models are
shown in Tables 1 and 2.

At all three grades the total surface area versus
modal percent second phases has highly significant, positive,
first order correlations. That is, with increasing impuri-
ties in the meta—carbonate the surface area increases
linearly. Variation in calcite-calcite surface area is
also highly correlated with modal percent second phases.

The greenschist trend is negative first order, whereas the
amphibolite trends are negative second order. Photomicro-
graphs of representative samples from each suite are shown

Figure 2.

TO

.N van F mopnmp cw umNPLmEE=m mew mowumwumum cowmmmgmmm

.mmpwam m:m_a5mm

owzagoEmqu mossy mzu Low Amuwaomopgq + Nugmaa + m9PEo~ouv mommgq ucoumm
ucmugwa paves on swam momecam wwwupmuumuwupmo new Pmuou mo awgmcowumpmm--.P mezmwd

8.3.9.326 a
a2< 33:5 .28. 4

COO-SQ 208m «50.: a;

 

 

 

 

:8 o 8 93 a... a 8 o o. .o 9.8 a... o 9 9.8 9.8 . 92 Ho :8 98 9.3 a 8 98 92 L a
4 _ _ q q _ o q . _ _ _ q _ o _ _ _ . ~ 4 4 o
l o I. - [Yb
0 000 000 a $0 m a cam. n0 0
«a a .. o

4 l o Q I u 0 fl
4 r a 4 a w u i w
1 u a a a IT
4 44 W C Q 1..” D Du W
I.” a 04 q i“ Q D I“
a. q 4 8 a 0 q a.
1 .0 I. .0 D I. .0
0 q 0 0
1 u m m
r 1 w q q a. 1 m.
i m 1 w. 4 a 4 a a 1 .u
0 0 q q q 0
1 a a 4 m
w in a. l w
1m im a a 4m
.i in on.»

ogzzfie< 0.3.2 33329.3 .033 5203020

Emus/gum: 901v ooeyns

0. 3 05223292 m z
08. s 23:25
s. s 28:25 :
0. s 23:29; .

 

ll

85.5393
o o . COMO .I o o o osg . o o 9 mg . 62:35.; 0:0
. 28. 3. umwcé . SE. 8.8 Satan 0-0
. . . mums. . 39$ . . . omom . 8.6 Satan 52
3:83.05 28:2
32:382..
o e o NNfiOf o o o g. o 9 0 gm. COEmcmb 0:0
m z 28.- . . . amt... m 2 £3 . men 88.. 3. 0-0
. . . =3. . . $25 . . . 32 . «Em aunts...“ .58
3:22asm $25..
32:338..
ca. 9.8.: 9.9 ~mew. o 0. m3. £053:me 0:0
. .. 82.- .3 884a .. . 23. 8; 833... 0-0
. . 08v. .. . . RS .R . . 20m . new cont 3. .58

E52320

 

8-8: 8.8: 2538 2533 c2328.. wm. 038
.2 .3. 088 .2 .2 0.8... .32 co 858.8
:3... c2328”. 33-“. cosmeamm 53.“. 22:32

 

.mdoos. guano .53“. mo..— m0_._.m_.::m 20350105. 40.55

12

2.
.8. s 2822...;

5 28:25:82 m2

8. a 58:29.. ..
_. s 28:22?

 

 

«20:328..
W Z NR6. o. 88.: no. 83. .0. ma. coin—um: 0:0
0. m§.I ooo OgN. ooo 38$ .99 Nvmo. mmhm mat—4m UIU
m z 88. m 2 En. . ”~32 . . . S8 . 8... 82.3 52
2:22.55 22.2
82:88...
m z 55.- m z 3.8.- . . . $8 . . . . 82. SEES. 0-0
. «~86 . 83. m z 82.~ . 8R. 8; 82.3 0-0
m z :8.- o mam.” m 2 89.0 o o . owwfi 00.0 005:3. Eyck
2:258. :33
82:88...
. 55.- . . . 28.- . . . $8 . . . . $8 . SEES. 0-0
m z 9.8.- m z «:3.- . . . :2 .3 . . . 88. men 82.3 0-0
. 28.- . . RS 4 . . . BB .9 . . . ammo . men 82.3 38
828880
N 8-8: 8-8: 8-8: 6.8: 2.828 2228 8.338. wm .238
.2 . 238 .2 .2 .88 .2 .2 238 .52 co 832.8
:2-.. 538.5. 88-. 538.8: .8.- .. c2388.. 82... 22:32

 

.mdooi «memo 9200mm «0.. m0:m_._.<_.m zo_mmmmowm

.N 0.85

13

.mmgm mommgsm
Pope» mee\ 55 «.mp .mmmmzn ucoumm aw.omu-m mmmgm wommgzm Pmpop mEE\ EE m.op .mmmmga
ucoomm mm. ..o .mpwpoawcaso wpvvwz .mwgm mommgzm page» MEE\NEE m._m .mommza ucoowm

mm.n~--v mwmgm mumwgzm Papa» EE\ EE m.NF .mommna ucoumm RN.m--o "wuwponwcnsm LuzoA

.mmgm mumwgam Pouou mse\~EE N.on .mmegm ucoumm mm._m--n mmwsa mummgsm quop mse\mes m.m¢

.mommcq acoumm nu.p--m .mumgm pawnumcwmgw .mwpqum m>wuuucmmosawg $0 mcamsmoguwsopoca--.m mgzmwu

 

 

14

Surface area progressively decreases with increasing
metamorphic grade, with the major adjustment occurring
between the greenschist and lower amphibolite grades.
Probably the most interesting trend found in the partitioned
surface area is that of the calcite-calcite surface area
with increasing metamorphic grade. In the greenschist grade
suite the calcite-calcite surface area increases linearly
with increasing modal percent calcite. Geometrically this
would indicate the addition of relatively constant sized
calcite grains to the aggregate. At amphibolite grades the
calcite-calcite surface area flattens out to a broad nega-
tive parabola with a maximum value of calcite-calcite
surface area at approximately 20% second phases. This trend
has no simple geometrical explanation, however, it is
apparent that increasingly larger sized calcite grains must

be added to the aggregate to explain the near zero slope.

Grain Transition Probabilities

 

Figure 3 demonstrates the functional relationship of
calcite-calcite transition probabilities to modal percent
second phases. All three grades show similar trends. The
greenschist grade trend has an extremely high correlation
with modal percent second phases, again indicating a simpler
relationship than at amphibolite grades. It should be
evident. however, that grain transition probabilities

contain less information than absolute surface area

15

.N use F mmpnmh cw umNWLmeazm
men mumumwumpm commmmcmmm .mmuwsm m=PFQEmm

owsagosmpms amen» ms» com mmmmga ucoumm “smegma Paves
op mmwpmpwnmnogn cowpwmcmgp :pmcm Do avgmcowumpmm-u.m mcsmwm

«325 950mm 333m .232

 

low. 93 9o. 98 98 92 _.o
q o
. .m . o
my 0 1w 1
D O .J
G D e
u ....
. 0. .. w
4 4 1w N...
o O
u be» u r u
G D D 1%
D D . d
0 n D 0 nm N
D Cm" U m-
0 1%
3__oe._as< .s. p q p . m.
. D 1.0. fl...
o.__oa_€s< ._ a 2. M m.
33359.0 4 sq 1m s
w

 

16

parameters. Variation of grain transition probabilities

with metamorphic grade is not easily recognized.

DISCUSSION OF RESULTS

Several important observations on the phase distri-
butions of progressively metamorphosed carbonates can be
related to the processes of recrystallization and grain
growth. These observations are:

1. Total surface area is highly correlated to
modal percent second phases at all conditions studies in
this paper (greenschist through middle amphibolite grades).
With increasing second phases surface area increases
linearly.

2. Calcite-calcite surface area is negatively
correlated with modal percent second phases at greenschist
grade, but is a very flat second order function at higher
grades.

3. Total and calcite-calcite surface area decrease
with increasing metamorphic grade.

4. Increase in surface area with metamorphic grade
may be discontinuous. With only three metamorphlc sample
suites this is difficult to evaluate. However, all three
suites have distinct surface area to modal composition
trends.

Variation of surface area with mineralogy is in
response to one or both of the following mechanisms.

l7

18

Nucleation may be highly favored at boundaries of second
phase particles. Alternatively, if recrystallization

occurs from random nucleii, second phase particles will
inhibit grain boundary migration and thus limit grain
growth. Either mechanism would explain the direct relation-
ship between modal percent second phases and total surface
area. However, experiments in ceramic systems indicate the
dominant role of second phase particles is to limit grain
growth (American Society for Metals, 1966).

With increasing metamorphism several mechanisms may
be responsible for the decrease in total surface area.
Reactions which remove or coalesce second phase particles
would allow increased grain growth. In these rocks, this
process may contribute to the surface area pattern, but
cannot be a major factor since reactions of this type (e.g.
disappearance of dolomite) occur primarily between the
lower and middle amphibolite grades where the surface area
changes are least dramatic. With increasing temperature
of metamorphism, diffusional processes become dominant.
Progressively less strain build up can occur in the crystals
and consequently less recrystallization takes place. The
driving force of grain boundary migration changes from the
free energy differences between strained and unstrained
crystals (at lower temperatures) to the much smaller surface
energy associated with curvature and orientation differences

(at higher temperatures).

19

This last model explains the change in slope of
calcite-calcite partitioned surface area versus modal
composition. At greenschist grade recrystallization and
strain-induced grain boundary migration favor smaller
calcite crystals, and with increasing modal percent calcite ‘4
an increase in calcite-calcite surface area can be expected.
At amphibolite grades recrystallization becomes less
important and grain boundary migration is driven by surface
energy differences. Second phase particles thus control
the limiting grain size and calcite-calcite surface area
shows no increase with increasing calcite modal percent.

The possibility that decreases in surface area with
metamorphic grade are discontinuous has some justification.
Secondary recrystallization in metals and ceramics often
occurs when an aggregate is stabilized from further growth
by second phase particles or development of a highly
oriented fabric from primary recrystallization. This
results in quantum decreases in surface area from the
recrystallized texture to the secondary recrystallized
texture.

In summary, both metamorphic grade and mineralogy
control significantly the total surface area and partitioned
components of surface area within carbonates ranging from
greenschist to middle amphibolite grade metamorphism.

Second phase particles control the surface area by inhibit-

ing grain boundary migration and thus grain growth at all

20

metamorphic grades studied. The response of surface area

to metamorphism is controlled by the relative contributions
of recrystallization and grain growth. At low grades

strain induced recrystallization and grain boUndary migra-
tion result in a fine-grained aggregate of high surface
area. At higher grades increased lattice diffusion results
in much less strain build up in the crystal lattices. Grain
boundary migration, driven by surface energy differences,
becomes dominant and results in a coarse aggregate of very

low surface area.

REFERENCES

21

REFERENCES

American Society for Metals (Eds.), Recrystallization,
Grain Growth, and Textures, 617 p., American
Society for Metals, Metals Park, Ohio, 1966.

 

 

Aust, K. T., Principles of crystal growth from the solid
state in relation to the preparation of large
single crystals, J. Crystal Growth, 13/14, 57-61,
1972.

DeHoff, R. T., and F. N. Rhines, Quantitative Microscopy,
422 p., McGraw-Hill, New York, 1968.

 

DeVore, G. W., Surface chemistry as a chemical control on
mineral association, J. Geology, 54, 31-55, 1955.

DeVore, G. W., Role of minimum interfacial free energy in
determining the macroscopic features of mineral
assemblages: I. The model, J. Geology, 57,
211-226, 1959.

DeVore, G. W., Preferred mineral distributions of poly-
mineralic rocks related to non-hydrostatic
stresses as expressions of mechanical equilibria,
J. Geology, 77, 26-38, 1969.

Ehrlich, R., The role of the homogeneous unit in sampling
plans for sediments, J. Sed. Pet., 34, 437-439,
1964.

Ehrlich, R., T. A. Vogel, B. Weinberg, D. C. Kamilli,
G. Byerly, and H. Richter, Textural variation in
petrogenetic analyses, Geol. Soc. Amer. Bull., 83,
665-676, 1972.

Flinn, 0., Grain contacts in crystalline rocks, Lithos, 3,
361-370, 1969.

Fulrath, R. M., and J. A. Pask (Eds.), Ceramic Micro-
structures, 1008 p., John Wiley and Sons, New
York, 1968.

 

 

Heard, H. C., and C. 8. Raleigh, Steady-state flow in
marble at 500° to 800°C, Geol. Soc. Amer. Bull.,
83, 935-956, 1972.

22

23

Kendall, M. G., and P. A. P. Moran, Geometrical Probability,
125 p., Charles Griffin and Company, London, 1963.

 

Kretz, R., 0n the spatial distribution of crystals in
rocks, Lithos, 2, 39-66, 1969.

Moore, J. M. Jr., and P. H. Thompson, The Flinton Group,
Grenville Province, eastern Ontario, Canada,
Twenty-fourth International Geological Congress,
Section 1, 221-229, 1972.

Pitcher, W. S., and G. W. Flinn (Eds.), Controls of Meta-
morphism, 368 p., John Wiley and Sons, New York,
1965.

 

Rutter, E. H., The influence of temperature, strain rate,
and interstitial water in the experimental
deformation of calcite rocks, Tectonophysics, 22,
311-334, 1974.

Smith, C. S., Grains, phases, and interfaces: an interpre-
tation of microstructure, Trans. Amer. Inst. Min.
metall. Engrs., 173, 15-51, 1948.

Spry, A., Metamorphic Textures, 350 p., Pergamon Press,
Oxford, 1969.

 

Underwood, E., Quantitative Sterology, 274 p., Addison-
Wesley, Reading, Mass., 1970.

 

Vistelius, A. B., Ideal granite and its properties. I.
The stochastic model, Math. Geol., 4, 89-102, 1972.

Voll, G., New work on petrofabrics, Liverpool and Man-
chester Geol. J., 2, 503-567, 1960.

Wenk, H. R., C. S. Venkitasubramanyan, and D. W. Baker,
Preferred orientation in experimentally deformed
limestone, Contrib. Mineral. Petrol., 38, 88-114,
1973.

White, J., Phase distributions in ceramics, in Ceramic
Microstructures, edited by R. M. Fulrath and
J. A. Pask, pp. 728-762, John Wiley and Sons,
New York, 1968.

 

HICHIGQN STQTE UNIV. LIBRQRIES
1
1

1111111: 111111
31 93 231

2

m HM)
006194