ELEMERT MIGRA'E‘EON 5.03033
GRANE'E‘EC BEKES

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MiCHEGAN STATE UNIVERSEY
Arthur Lifshén
W653

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LIBRARY (“3

Michigan State E
University

  
 
  

THESIS-‘-

 

This is to certify that the

thesis entitled

Element Migration Across Granitic bikes

presented by

Arthur Ltfshin

has been accepted towards fulfillment
of the requirements for

PhoD. degree in 6601082

“U , 8 gluteka

Major professor

 

Date November 17, 1969

 

0-169

 

’r— 1

ABSTRACT

by Arthur Lifshin

This study was designed to examine the nature of diffusion patterns
across an igneous contact zone, both in the intrusive and the country rock.
Previous research indicates that diffusion plays an important role in such
situations.

Continuous samples were taken from small granite dikes and the
adjacent host rock. These samples were analyzed for both major and minor
elements by emission spectrographic techniques. Concentration distrubu-
tions were obtained and a generalized function was determined.

Three types of curves were observed: hyperbolic tangent, hyperbolic
secant, and complex. Evidence from the complex curves indicates that the
system is discontinuous at the contact. These curves cannot be used to
describe the concentration distributions but, however, they can be used to
describe the relative rates of diffusion on either side of the contact and
through the contact itself. Further evidence from the curve types leads to
the hypothesis that the contact acts as if it were a semipermeable barrier
to diffusion of material across it.

A high-frequency and a low—frequency periodicity that is not related
to sampling was found in the distribution. This is thought to be due to
enhancement of normal variation in the rock by a non-equilibrium situation
and by diffusion producing a high frequency periodicity. The low-frequency

periodicity is thought to be caused by the barrier nature of the contact.

Solid-solid diffusion is rejected as the mechanism involved in igneous
contact zone diffusion, leaving a form of fluid diffusion as the postulated
mechanism. The amount of fluid is the main factor controlling the mechanism.
With large amounts of fluid, the fluid is the active diffusing agent (hydrothermal
ore deposits). With small amounts of fluid, diffusion occurs through a static
fluid film surrounding the mineral grains which is a few molecules thick
(granite contact zones). A matrix effect which was found appears to be due
primarily to the texture of the host rock and secondarily to its composition.
Increasing the width of the intrusive increases the thickness of the diffusion

zone, but by a much smaller amount than the increased dike thickness.

 

' WV.———_1

ELEMENT MIGRATION ACROSS GRANITIC DIKES
by
Arthur Lifshin

A Thesis

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

Doctor of Philosophy

Department of Geology

1969

 

 

55. //73
J “/X'70

ACKNOWLEDGEMENTS

The author wishes to express his appreciation to the following people

for their help and aid without which this study could not have been completed.

To Dr. Harold B. Stonehouse for his invaluable help and guidance
throughout the course of the research program.

To the other members of the author's committee, Dr. James Fisher,
Dr. Samuel Romberger, and Dr. James W. Trow, for their help and careful

reading of the manuscript.

To Dr. John C. Colwell, Dr. Robert Ehrlich, Dr. T. Vogel, Alan
Bailey and Michael Katzman for their help, ideas and suggestions which were
invaluable throughout the course of the research.

To my wife, J 0 Anne Lifshin, for her help in reading and typing this
manuscript and for patiently suffering through the entire process.

-4-

TABLE OF CONTENTS

CHAPTER Page

I.Introduction.................... 8

Statement and Object of Thesis. . . . . . . . . . 8
PreviousWork................. 9
Location and Geologic Setting . . . . . . . . . . 15

II. MethodsandTechniques . . . . . . . . . . . . . . 17

Sampling...................17
Sample Description . . . . . . . . . . . . . . 17
Sample Preparation . . . . . . . . . . . . . . 19
Elements Selected for Analysis . . . . . . . . . 19
Spectrographic Analysis. . . . . . . . . . . . . 21
ExternalStandards............... 21
InterruptedArc................24
Precision...................25

III.Results...................... 27

GeneralStatement...............27
CurveDescription........ 27
Distribution of the Elements in the Type Curves . . 35
Specific Form of the Distribution. . . . . . . . 36
Periodicity..................37
Concentration Gradient . . . . . . . . . . . . . 42
Thickness of the Diffusion Zone . . . . . . . . . 47

IV.Discussion.................... 49

GeneralStatement............... 49
NatureoftheContact.............. 49
Periodicity..................52
Factors Controlling Diffusion Rate . . . . . . . . 54

V. Summary and Conclusions . . . . . . . . . . . . . 56
Summary and Conclusion . . . . . . . . . . . . S6
FurtherResearch............... 58

Bibliography..................... 59

Appendices...................... 61

AppendixA-DataTables. . . . . . . . . . . . 61
AppendixB-Data Curves . . . . . . . . . . . 100
Appendix C " lefllSlOll Theow o o o o o o o o o 122

Table

10.
11.
12.
13.

14.

15.

16.

17.

LIST OF TABLES

Summary of the Petrologic Data for the Granit Dikes . .
Summary of the Petrologic Data for the Host Rocks .
Analytical Conditions Used for Emission Spectrographs

Anal-ySis O O ....... O O O O O O l .......

Spectroscopic Analysis Lines . . . . . . . . . .
Maximum Error Determined for the Analysis of the

Standards................ ......

Breakdown of the Various Elements into the Three Curve

Classes 0 O O O O O O O O O O O O I O O O O O O O O O

Breakdown of the Various Elements into the Subgroups of
Type I O O O O O O O O O O O O O 0 O O O I O O O O

Breakdown of the Various elements into Subgroups of
Type E O O O O O O O O O O O O O O O I O O O 0

Parameters of Equation (3.4) for Section 37 . . . .
Parameters of Equation (3.4) for Section 38 . . . . . . .
Parameters of Equation (3.4) for Section 251 .....
Parameters of Equation (3.4) for Section 253 . .
Results of the t Test Between Schist and Granite for

Section 37 O O O I O O O C O O O O O O O O O O O O O 0

Results of the t Test Between Schist and Granite for
&Ction 38 O O O O O O O O O O O O O O O 0 O O O O 0

Results of the t Test Between Schist and Granite for

&ction 251 O O O ..... O O O O O O O O O O O O 0
Results of the t Test Between Schist and Granite for
section 253 O C O ..... O O O O C O O O O O O O 0

Thickness of the Diffusion Zone for Each Element in Each
SectionintheHostRock............. .

-6-

Page

18
20

22
23

26
29
33

34
38
39
40
41

43

44

45

46

48

Figure

LIST OF FIGURE S

Compositional Variations in Homogeneous Rocks
(Dennen,1951)............. .........

Compositional Variations in Contact Zone Rocks
(Dennen,1951)... ..... ......

Compositional Variations in Contact Zone Rocks in Hydro-
therman Veins, Tintic District Mices (Morris & Lovering,
1952) I O O O O O O O O O O O O O O O O O O .......

Sketch Map of the Thomaston Waterbury Area, Connecticut,
Showing Location of Samples . . . . . . .........

Three Classes of the Element Distribution Curves . . . . . .

Generalized Curves for the Subclasses of Type I . . . . . . .

Generalized Curves for the Subclasses of Type II . . . . . .

Page

12

CHAPTER I

INTRODUCTION

Statement and Object:

 

Interactions between an intrusive body and its host rock constitute a
major area within the field of igneous and metamorphic rocks which is replete
with unsolved problems. One aspect, the interchange of material between the
two rock bodies, is of major importance in understanding the chemical pro-
cesses that occur during intrusion. Exchange processes may involve move—
ments of fluids or fluidized materials or molecular diffusion. Contact
phenomena probably involve combinations of these processes on several dif-
ferent scales. On the largest scale this interaction can be seen in veins
proceeding from the main body of the intrusion and in similar phenomena.
Smaller scale interactions are usually manifested by changes in gross mineralogy
near contacts or, more subtly, slight intra-mineralic changes in composition.

This latter type of change may be due to molecular solid-solid diffusion,
or to a fluidized molecular diffusion either by movement of the fluid itself
or by the movement of molecules or ions through a fluid film surrounding the
grains.

The determination of the nature of small scale transfer processes is
the object of this research. Patterns of elemental variations across contacts
of small dikes and the adjacent country rock will serve to limit the possible

mechanisms for small scale transfer.

-9-

The primary objectives of this study are as follows:

1. To determine the extent of interchange of material between
an intrusion and host rock.

2. To determine how the element distribution pattern resulting
from the interchange differs for different elements.

3. From 1 and 2, to postulate mechanisms for element transfer

that could result in the distributions observed.

Previous Work

 

Most of the studies in the area of diffusion in geological systems have
focussed on wall rock alteration in mineral deposits. A few studies have been
done on diffusion in contact metamorphic zones, diffusion in single crystals,
or the theoretical basis of these phenomena.

Most of the experimental studies are of the diffusion of a single element
into individual minerals. These studies are summarized by Fyfe, Turner, and
Verhoogan (1958) and the values of the diffusion coefficients reported by them
are exceedingly small (on the order of 10-6).

Jensen (1964) investigated the mechanisms of solid-solid diffusion from
a theoretical standpoint. Calculated activation energies for solid-solid diffu-
sion by means of lattice defects agree with the activation energies from
experimentally determined diffusion coefficients, suggesting that solid-solid
diffusion probably occurs by movement of the ion through lattice defects in
crystals. The values determined by Jensen and those reported by Fyfe, Turner
and Verhoogan show the improbability of solid-solid diffusion as a mechanism
in the transport of materials over distances greater than a few millimeters to
one or two centimeters indicating that this type of diffusion is important only
in the interchange of material between contiguous mineral grains and cannot be

used to explain larger transport phenomena.

-10..

The interchange of material between an intrusive and its host rock has
been reported for distances many times greater than appears to be possible
through solid—solid diffusion. One possible process for these phenomena is
the introduction of a fluid into the diffusion system either as a passive or
active agent. In the case of the fluid acting as a passive agent, diffusion would
occur within an intergranular fluid film and would yield diffusion coefficients
somewhere between those of solid-solid diffusion and active fluid movement.

Mueller (1966) examined diffusion mechanisms from theory and pub—
lished data in relation to the attainment of equilibrium in metamorphic rocks.
He concluded that solid-solid diffusion is of major importance in the establish-
ment of local equilibrium, but that it cannot be utilized in extensive material
interchange. He asserts that extensive material interchange requires a fluid
or vapor phase. He points out that any substance has a vapor pressure, and
that this is enhanced by increased temperatures and fluids. This essentially
agrees with Jensen's work and adds the idea of a vapor phase playing a role in
the diffusion process to his conclusions.

Dennen (1951) investigated chemical variation in homogeneous rocks
and in contact zones. His findings show that there are minor compositional
variations even in the homogeneous rocks (Figure 1). The composition varia—
tions he found in contact rocks are seen to be completely different from those
determined for the homogeneous rocks (Figure 2). The contact zone distribu-
tion curves show major depletion and enhancement of elements near the contacts
which are of a different order of magnitude from the variations seen in the homo—
geneous rock. It should be noted that the zone of concentration variation in the
contact zone rocks is too large to support solid-solid diffusion as a transport

mechanism and that fluids must be involved. It should also be noted that the

 

 

Figure |- Chemical Variation in a Homogeneous Rock
(from Dennen)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

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-11-

 

 

 

Figure 2 -Chemical Variation Across a Contact of the Medford
Diabase Dike with Rhyolite (from Dennen,l95l)

 

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-12-

 

-13-

diabase-arkose contact curves and the granite-shale contact curves show a
distinct periodicity in zone of concentration variation. This periodicity may
be due to a variation in the rate of diffusion.

Woodard (1968) studied the compositional variation in the Cape Neddick
Gabbro—Kittery Formation contact zone in Maine. He obtained composition
distribution curves similar to those of Dennen's over similar distances.

Morris and Lovering (1952) investigated the distribution of metals in
the wall rock of the Tintic District mines. Their distribution curves show a
major increase in concentration near the ore vein with the element transfer
zone (Figure 3) being from one to two orders of magnitude greater than those
of Dennen's or Woodard's. The availability of fluids in these cases appear
to be the critical difference. The "intrusion" is a hydrothermal vein which
may be considered to be primarily an aqueous fluid in comparison to a granitic
or a gabbroic magma. This leads to the assumption that material transfer has
occurred primarily through liquid diffusion, where the major source of the
fluid is in the "intrusive" itself. In magmatic intrusives, the width of the
material transfer zone is much too large for solid-solid diffusion and seems
to be too small for fluid diffusion, suggesting the possibility of diffusion of
the ions through an effectively static fluid film.

Similar studies by Stonehouse (1954) at Sudbury; Ishikawa, Kuroda and
Sudo (1962) in the Kuroko deposits of J apan; Fullagar, Brown and Hagner
(1967) at the Ore Knob Deposits in North Carolina; and Wehrenberg and Silverman
(1965) at Gilman, Colorado; have yielded results similar to those of Morris and
Lovering. The distribution curves for both major and trace elements which
were determined in these studies show major enhancement or depletion effects
near the contact. The zone of concentration enhancement or depletion varies

from about 5 feet in some of the Kuroko deposits to about 75 feet in some of the

 

 

Figure 3- Heavy Metal Dispersion Pattern, Eureka Hill Mine,
Tintic District, Utah (from Morris 8: Lovering ,l952)

 

 

 

 

    

 

 

     

 

 

 

 

 

 

 

 

 

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Distance from

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Ore Body In feet

 

 

-14-

 

_15-

Ore Knob deposits. The findings of these studies agree with the results of
Morris and Lovering in respect to the material transfer and the thickness of
the transfer zone, but like them do not agree with Dennen's and Woodard's
studies on "normal" igneous contact zones.

Wehrenberg and Silverman (1965) ran a series of experiments in
which zinc, in solution, was diffused through the Yule marble. Their resultant
curves were comparable with the curves from the hydrothermal deposit studies,
but they did not agree with the curves of either Dennen or \l’oodard. This is
another indication that there are major differences between the two types of
contact zones.

In the present study the writer is attempting partially to bridge the
gap between diffusion theory and diffusion in a non-hydrothermal igneous con-
tact zone in which the intrusion contains but little water. Empirical formulations
that describe the real system will be obtained and these formulations will be

related to current diffusion theory if possible.

Location and Geologic Setting

 

The samples for this study were taken from the igneous and matamorphic
rocks in the Thomaston and Waterbury Quadrangles in Western Connecticut
(Figure 4).

Gates (1951, 1954, 1968) mapped the Litchfield, Woodbury and Waterbury
quadrangles and Cassie (1966) mapped the Thomaston Quadrangle in Connecticut.
From their work in this area they have reported that there are two cycles of
deformation in the country rock. The country rock sampled for this study is
the regionally metamorphosed Hartland Formation.

The granites sampled are thought to be related to the Nonewaug Granite
which is intrusive in the area. These Granites are reported by both Gates and
Cassie to be post metamorphic and therefore not affected by the regional folding

and metamorphism in the area.

 

63 Section 25!

05
East Morris Secjign 37 53
_§ Thomaston

 
   

 

Rte. (’09

 

Watertown
2)
6 2°

Figure4. Sketch map of the
Thomaston — Waterbury area
Connecticut, showing location
of samples. ,.

Scale 0.75 inch =I mile

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Vlgterbury
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-]_6-

CHAPTER II

METHODS AND TECHNIQUES

Sampling

Continuous samples were taken in all cases. In the case of narrow width
dikes (maximum width of about two feet), the samples were taken across the
dike and into the host rock. For wider dikes, only that part of the dike near
the contact and the adjacent horizon were sampled. The contact was defined as
that plane which divides the two rock types and was seen as a line of abrupt
mineralogical change. In either case care was taken so that only one horizon
was sampled in the host rock. The term horizon was defined as a mineralogically
homogeneous zone bounded by different mineralogies and probably represents

one original homogeneous sedimentary unit.

Sample Description

 

Three separate dikes were sampled for this study. Their locations are
shown in Figure 4 and the data concerning them is given in Table 1. The dikes
are roughly an order of magnitude apart in thickness which yields the following
thickness ratio: 1:6:120. The mineralogies of the dikes while similar, are
sufficiently different to distinguish one from the other. None of the dikes showed
chilled margins. Two separate sections were taken from the 12-inch wide dike
in order to obtain a replicate sample. The host rock in these sections was
chosen for its similarity.

The locations of the dikes are as follows:

Section 37 and 38 - On state route 109, 3. 1 miles west of

the intersection of state route 109 and US route 6. The outcrop

.-17_

Section
37, 38
251

253

TABLE 1

SUMMARY OF THE DATA FOR THE GRANITE DIKES

 

 

 

Width Quartz K-Feldspar Plagioclase An Muscovite
in inches % % % i %
12 41.6 21.1 21.9 18 15.0
2 36.1 42.1 19.0 17 2.0
240 45.4 31.1 15.7 16 7.4

-18..

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3.4

 

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-19..

is on the east side of the road at the intersection of route 109 and

a northeast trending side road.

Section 251 - By the Thomaston Dam Site on the Naugatuck

River, approximately 100 yards east of the causeway bridge.

Section 253 - On interstate route 84 approximately 200

yards before the first Waterbury exit.

The host rock that was sampled was different for each dike. The only
exception was section 37 and section 38 where similar rock types were sampled
to provide a duplication. The data for the host rocks sampled are given in
Table 2. Sections 37 and 38 are quartz-biotite schists. Section 251 is a
quartz—biotite-hornblende schist and section 253 is a granite gneiss. The three
sections provide enough differences in mineralogy and can be treated as dif-

ferent samples and not as a set of replications.

Sample Preparation

The field samples were sliced parallel to the contact by a diamond saw
to yield sections of approximately 0. 25 inches wide. These sections were
then coarse ground in a Spex Mixer Mill with a high alumina ceramic canister
and ball. An optimum grinding time of 45 minutes per sample was determined
from a plot of grinding time versus emission line intensity. Four hundred
milligrams of the sample were weighed out and mixed with 600 milligrams of
graphite mix. Mixing was done on the Spex Mixer Mill using glass vials and
plastic balls. Comparison with hand mim‘ng and hand grinding using a mortar

and pestle indicated that the mill was at least as good as the hand method.

Elements Selected for Analysis

 

The elements selected for analysis were chosen because of their posi-

tion in the periodic table, and in the case of trace elements, their substitution

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for the major element concerned. In all cases the elements chosen had to fit
the limitations of the analytical technique.

Elements were chosen to obtain a minimum of a full row on the periodic
table and, where possible, to yield multiples in the columns. This decision
was based on the assumption that the mobility of the diffusing ions would be
dependent on a parameter that could be related to atomic number and/or
atomic weight. Such parameters include ionic charge, ionic size, charge
density, etc.

The second item, ionic substitution, follows a similar pattern except
in this case ionic size and ionic charge are of primary importance.

The omission of aluminum and silicon as well as oxygen, sulfur and

similar elements is due to the limitations of the analytic technique.

SpectrographicfiAnalysis

All analyses for both major and minor elements were done by the writer
using emission spectrographic techniques while at the Department of Geology,
Michigan State University. The technique used was that of interrupted arc
with internal standards. Palladium and indium were used as internal standards
(Ahrens, 1950); graphite was added to the mixture for smoother burning.
Table 3 gives the analytical conditions used and Table 4 the Spectral lines

measured.

External Standards

 

In order to obtain useful quantitative data external standards must be
used. The intensity ratios of the unknowns are related to those of the external
standards which are of known composition to obtain the concentration of the
unknown. The following external standards were used in this study:

1. Standard sample rock G-1

TABLE 3

ANALYTICAL CONDITIONS FOR EMISSION SPECTROGRAPHIC ANALYSIS

Equipment: Source unit — Applied Research Laboratories
Multi-source-unit 4

Spectrograph - Bausch and Lomb 2 meter dual grating
Jarrel Ash Mic rophotometer
Seidel calculating board, calibration curve from iron

spectrum by two step filter method (Harvey, 1957)

Excitation: Interrupted arc, 30 ohms
40 mfd
360 mh
15 seconds burn time
sample positive

Electrodes: 0.242 inch graphite electrodes

Transmittance: 80% and 40% plus additional filtering to 27% and 14%
on some lines by means of a split filter

Photography: Plates - Eastman Kodak Spectrum Analysis No. 3

Processing - Developer D 19 3-1/2 minutes
Stop - 3% acetic acid 30 seconds
Fixer - Kodak fixer 10 minutes

Wash - running water 30 minutes

TABLE 4

SPEC TR OSC OPIC ANALYSIS LINE S

 

Element Line* Element Line
Barium 4554. 03 A Lead 2833. 06
Boron 2496. 78 Magnesium 2781.42

Magnesium 2802 . 69
Calcium 3007. 00 Magnesium 2783.00
Calcium 3009. 20
Calcium 3158. 60 Manganese 2801 . 06
Chromium 4274. 80 Nickel 3012. 00
Chromium 4344. 51
Chromium 4351. 77 Palladium 3242. 90
Palladium 3404. 00
Copper 3273 . 94 Palladium 3690. 34
Gallium 2943. 61 Potassium 4047. 20
Indium 3258. 56 Sodium 3302. 99
Indium 3256. 00
Titanium 3326.70
Iron 3011. 48 Titanium 3361. 00
Iron 3075. 72
Iron 31 00. 67 Vanadium 3183 . 41
Iron 3196. 93 Vanadium 3183. 98
Iron 3198. 00
Iron 3199. 52 Zinc 3345. 07
Zirconium 3391.98

*Values of the spectroscopic lines are from the National Bureau of Standards
Monograph 32

-23-

The working curves obtained from the synthetic standards were adjusted to the

values of the standard rock samples G-1 and W—l with a partial correction for

.24~

Standard sample rock W-1

Synthetic standards - Spectrographically pure compounds
of various elements were mixed together to provide a
base of average composition similar to the samples to be
analyzed. Major elements of interest were varied within
this base. Minor and trace elements were added as dilu-
tions in graphite to cover the range of compositions of

interest.

the matrix effect.

Interrgpted Arc

 

Interrupted arc is a technique whereby the are, instead of being continuous,
is mechanically interrupted by a rotary motor rotating at 60 cycles per second.

The main effect of the interrupted arc is to lower the temperature of the sample

in the arc .

The interrupted arc was used in this study instead of the more

commonly used continuous are for the following reasons:

1.

The disadvantages of this method appear to be an enhancement of the matrix

effect of particle size on emission line intensity.

Reduction of CN emission and background over that of the
continuous arc, probably due to the lower temperature of
the interrupted arc.

Shorter arcing time per sample. In the present case, 15
seconds yielded consistant results with as good or better
sensitivity than the 2 minutes or longer required of the

continuous arc .

Correction for the matrix

-25..

effect was done as stated previously. The values of G-1 and W-1 were the
recommended values of Fleischer and Stevens (1962). A correction for
particle size was made by determining an optimum grinding time from a

plot of grinding time versus emission line intensity.

Precision
All the samples were analyzed in triplicate, the standards were ana-
lyzed six separate times and two other samples were analyzed ten times. The

maximum error for the standards are listed in Table 5.

TABLE 5

MAXIMUM ERROR DETERMINED FOR
THE ANALYSIS OF THE STANDARDS

Error in Percent

 

 

Element Concentration
Barium 10%
Boron 1 0%
Calcium 9%
Chromium 1 0%
Copper 10%
Gallium 1 0%
Iron 7%
Lead 10%
Magnesium 8%
Manganese 7%
Nickel 1 0%
Potassium 8%
Sodium 9%
Titanium 10%
Vanadium 10%
Zinc 10%
Zirconium 9%

-26..

CHAPTER III

RESULTS

General Statement

 

An examination of the data curves (Appendix B) indicates the presence
of gradients for most of the elements studied. In most of the curves, the
observed gradients indicate the movement of material within the system
studied. This is best seen in those curves which appear to be convergent
or continuous at the contact (Figures 8, 10, 11, etc.). Other curves do not
show material transfer although a gradient exists. This is seen in Figures
16, 21, 25, etc. In this last case, the concentration distribution on either
side of the contact can best be described as a horizontal straight line.

Most of the curves have a periodicity which is superimposed upon the
general trend of the distribution. Both a high frequency and a low frequency
periodicity can be seen on the same curve. There is an order of magnitude
difference in the two frequencies which indicates distinct differences between

the two types.

Curve Descriptions

 

Examination of the patterns of the curve gradients indicates that they
can be roughly grouped into three classes (Figure 5). The first class can
be described as a generalized hyperbolic tangent (Figure 5a). The second
class can be described as a generalized hyperbolic secant (Figure 5b). The
third class is more complex as the curves are divergent at the contact
(Figure 5c). Table 6 shows the breakdown of the elements into the major

classes.

-27-

 

 

Figure 5- Three Classes of the Element Distribution Curves

Figure 50- Class I Generalized Hyperbolic Tangent

 

 

 

 

Ci

Figure 5b- Class III Generalized Hyperbolic Secant

 

 

Ci
Figure 5c - Class III Complex,Div ergent at the contact

\

 

 

 

 

-23-

 

Section

37

38

251(1)

251(2)

253

BREAKDOWN OF THE VARIOUS ELEMENTS
INTO THE THREE CURVE CLASSES

Type I
Hyperbolic
Tangent

 

K, Mg, Ca, Fe,
Mn,Cu,B

K, Mg, Ca, Fe,
Mn, Cu, Pb,
Ga,B

Na, Mg,Ca, Fe,
Cr, V, Ti, Ga, Mn

Na, Mg,Ca, Fe,
Cr, V, Ti, Ga

K, Na,Ca,Cu,
Ga, Pb

TABLE 6

Type II
Hyperbolic
Secant

Type 11]
Comp] ex

 

 

Na, Ti, Ga, Pb

Na

K

Mn

-29-

none

Ti

none

Mn

Mg, FeV, Ti

-30-

The greatest number of curves are of the type I (generalized hyperbolic
tangent). This class of curves contains the straight line distributions
which may be considered as an extreme form of the hyperbolic tangent.

A few curves fit the type II classification (generalized hyperbolic secant).
Six curves are in the type III class (complex).

The first two main curve classes can be further broken down into
subgroups. The class III curves are all of the same form and hence there
are no subgroups for this class. Figures 6 and 7 show the subgroups for
the corresponding classes. Tables 7 and 8 show the element breakdown
into the subclasses. It may be noted that while the subclasses are dis-
tinct from each other, they are all basically modifications of the same
curves.

The general form of the curve for type I is the hyperbolic tangent

which can be expressed as follows:

Ci = tanh (¢) = (e¢ - e‘¢)(e¢ + e‘¢) (3.1)

where i = concentration of element 1

q) = some function of the distance from the contact

The three subgroups of the type I curve can be generated from the generalized
hyperbolic tangent of type I by changing the function ¢.

The type 11b curve is the inverse of the type Ila curve and can be
generated by a rotation around the x axis. The hyperbolic secant can be

expressed as follows:

ci = sech (¢) = (e¢ + e‘¢)/2

where i = concentration of element i

¢ 2 some function of the distance from the contact

131.11.». H..u.....l...u..... it. . . E
. V a.

 

 

 

 

 

 

 

 

 

 

Figure 6 - Generalized Curves for the Subclasses of the
Class I Curves
Figure 60* - Class Ia Hyperbolic Tangent
x
6i
Figure 6b- Class Ib Straight line with gradient
x
Ci
Figure 6c - Class Ic Straight line , no gradient

 

 

 

 

-31-

 

 

 

Figure 7-Generalized Curve for the Subclasses of the
00553 Curves

Figure 7a - Class Ilia Hyperbolic Secant

/\

 

 

 

 

 

ci
Figure 7b- ClassJIb Inverted Hyperbolic Secant
x

C

 

 

-32-

 

TABLE 7

BREAKDOWN OF THE VARIOUS ELEMENTS
INTO THE SUBGROUPS OF TYPE I

 

 

Section Ia lb 10
37 K, Mg, Ca, Cu, B Fe, Mn none
38 K, Mg, Fe, Mn, Ga, none Ca
Pb, B, Cu
251(1) Na, Mg, Fe, Ga, V, Cr, Ti none
Ca, Mn
251(2) Na, Fe, Ga Ca, Mg, V, ’11, Cr none
253 Ca, K Pb Na, Cu, Ga

M33-

TABLE 8

BREAKDOWN OF THE VARIOUS ELEMENTS
IN"O THE SUBGROUPS OF TYPE II

W Ill.) 1121
37 Ti, Ga
38 Na none

251(1) K none

251(2) 1( none

253 none Mn

-34-

The type III curve is the only curve that is divergent at the contact. A formu-
lation for this type of curve would involve two separate functions, a decay

curve on one side of the contact and a straight line on the other.

Distribution of the Elements in the Curve 'llypes

The majority of the elements fall into the type I or hyperbolic tangent
curves. These curves can be described as a growth or decay curve which
would be expected in a diffusion system. A definite relationship appears
between the Na and K curves for each section. Where the Na is in the type I
groups the K is in the type II group and visa versa. This does not hold for
section 253, probably due to the non-diffusion of the Na. The other elements
in the type II curves do not show any distinct relationships with the type I
curves. No obvious relationships appear for the type III curves, although _
this type of curve could be generated if diffusion occurred only on one
side of the contact without material crossing the contact.

The type Ib and lo curves are those that show no diffusion either with
a gradient (lb) or without one (Ic). Some relationships appear to exist
between these and the type Ia curves, but these relationships are not con-
sistent. The type Ia curves could be further subdivided but the resultant
groupings would be superfluous since they would be due to modifications in
the ¢function.

The previous discussion is based on the assumption that the curves can
be treated as continuous across the contact. The type III curves directly
indicate this. If the reverse assumption is made, that the curves are dis-
continuous at the contact, the curve types then assume other meanings. The
type I curves could be treated either way, but the Ib and lo curves indicate a

discontinuous function.

-36..

In the case of the type II curves, the contact is a point of high con—
centration (IIa) or low concentration (111)) common to both sides. Under the
assumption of continuity this is not easily explained. If one assumes a dis-
continuity, however, the situation can be explained by means of differing
rates of diffusion on either side of the contact. It should also be noted that
the physical system is itself discontinuous at the contact.

Under the assumption of discontinuity the system can still be treated
as a growth or decay curve if each side of the contact is considered independently.
In this case all of the curves can be treated either as a straight line or as a
hyperbolic tangent. The breakdown into types I, II, and III curves can now be

used to indicate relative mobilities within the system.

Specific Form of the Distribution
An approximate solution for the function (bin equation 3. 1 was obtained
by the following method.

1. The data was transformed such that;

0
ll

ln(Ci/CO)/ln(Co/Cm) (3.3)

resultant concentration of element i

where: C
e

Ci = actual concentration of element i

CO = concentration of element i at its midpoint

Cm = minimum value of the concentration of element i
This was done in order tofit the data to the +1 to -1 range of the
(hyperbolic tangent.

2. The values of ¢corrBSponding to arctanh (Ce) were

obtained from a table.

-37-

3. These values were then plotted against X, where
X = x - x0 and x0 is the distance from the contact
corresponding to Ci = Co'

4. A linear regression was performed on these variables
and a generalized expression for ¢ was obtained.

The resultant expression for (D is:

__ _ kX
Ce —— ln(Ci/CO)/ln(CO/Cm) - tanh(b(e - 1)) (3.4)
Tables 9 to 12 show the values of the parameters for each section. There
appear to be no definite relationships between b and k and atomic weight or
atomic number. This may be due to the approximate nature of the data or

to the small amount of data available.

Periodicity
As stated earlier, most of the curves show both a high and low fre-
quency periodicity. A wavelength analysis of this periodicity was done by
means of an autocorrelation program developed by D. Hill (Department of
Geology, Michigan State University) on the CDC 3600 at Michigan State
University. Comparison of the determined wavelengths with the sampling
interval indicated the following.
1. The low frequency periodicity was not related to the
sampling interval.
2. Of the high frequencies for a given curve, some are
distinctly not related to the sampling interval while
others may be related.
All of the high frequencies may be the result of the experimental procedure
and may be viewed as noise within the data. This is not probable as the

low frequency appears to be inherent in the system, and the high frequency

TABLE 9

PARAMETERS OF EQUATION (3.4) FOR SECTION 37

 

 

3.1.9.9991. x0 3.9.- 39/3111 b 1......
Na (G)* 0.30 1.14 2 0.24 0.90
Na (S)** 0.60 0.99 2 1.22 0.49
K (G) -0.30 2.98 2 —0.36 0.43
Mg (S) 0. 90 1. 20 2 0.35 0.99
Ti (G) 0.60 1628 2 -0.08 2.71
Ti (S) 0.55 4568 2 —0.11 5.70
Cu (G) 0.70 112 2 0.17 1.84
Cu (S) 1.25 40 4 -0.12 1.37
Ga (G) —o.40 24 2 -0.11 2.21
Pb (S) 0.30 30 2 0.07 5.00

*(G) indicates that the values are for the granite part of the section.
**(S) indicates that the values are for the schist part of. the section.

-38-

Element

Na
Na

K

Fe

PARAME’ ‘ERS OF EQUATION (3. =1) FOR SECTION 38

(G)*
(S)**

(S)
(5)

Mg (G)
Ms (S)

B
. B

Cu

Ga

Pb
Pb

Ti
V

Zn

*(G) indicates that the values are for the granite part of the section.
**(S) indicates that the values are for the schist part of the section.

(G)_
(S)

(S)
(G)

(G)
(S)

(S)
(S)
(S)

 

0'] U]

.30
.50

.10
.15

.50

.10
.10

.95

.70

TABLE 10

C

0.93
0.50

22

31
15

204

980

86

-39..

C/C

O

a.—.-

 

111

CO

I)

 

.09
.35

.14

.16

.01
.23

.27

.55

.30

.47

.83
.06

.31
.67

.08

.52

.10
.48

.81

.16

PARAMETERS OF EQUATION (3.4) FOR SECTION 251

 

TA 13 LE 1 l

 

 

Element Xo _(__:_g__ Co/C b k

Na (Si)* 0.00 3.70 2 -0.16 3.14
Na (82)“ -0.90 3.16 2 —0.54 0.20
K (Si) -O.20 1.01 2 0.22 0.89
K (S2) 0.00 0.90 2 0.33 0.70
Mg (Si) 0.10 0.23 2 0.34 1.79
Mn (Si) --0.40 1096 2 0.48 0.79
Mn (S2) 0.00 2796 2 -0.29 1.10
Ni (Si) 0. 00 40 2 0. 45 1. 33
Ga (Si) —0. 80 44 2 -0. 01 5. 99
Ga (S2) 0. 15 24 2 —0. 07 29. 90

*(Si) indicates that the values are for the schist (1) part of the section.
“(82) indicates that the values are for the schist (2) part of the section.

-40-

 

TABLE 12

PARAMETERS OF EQUATION (3.4) FOR SECTION 253

 

 

 

 

Element Xo Co Eo/Cm b _l_<___.
K (S)* 0.40 2.44 2 —0.54 0.20
Ca (S) 0.60 1.16 2 0.36 0.40
Fe (S) 0.50 3.14 2 -0.10 0.91
Ba (S) 1.40 60 2 -0.07 1.29
Cr (8) 1.20 84 2 —0.15 0.54
Ti (S) 0.90 1268 2 -0.18 1.80
V (S) 0.80 80 2 —0.21 1.73
Mn (G)** 3.70 346 2 -0.17 0.46
Mn (8) 2.60 790 2 -0. 08 1.07

*(S) indicates that the values are for the schist part of the section.
**(G) indicates that the values are for the granite part of the section.

~41

-42-

may be expected secondary and tertiary frequencies. Some of the higher
frequencies may be due to inhomogeneity to be found in any rock.
Accurate analysis of the wavelengths of the periodicity was found
to be impossible due to the variance in the x position of the points which
is due to the thickness of the samples analyzed. There is some indica-
tion, however, from the analysis, that the wavelengths will correlate
with atomic number or atomic weight. Further experimental work is

needed to determine this with any degree of certainty.

Concentration Gradient

It would be expected that the driving force for the diffusion of an
element would be the existence of an activity gradient within the system.
Since it is not possible to determine the activities, the concentrations were
used as a first approximation.

Unless the diffusion has resulted in the same concentration on both
sides of the contact, differences in base level concentrations on either
side of the contact should still appear. That the concentrations have not
been equalized is shown by the mineralogical differences in the rocks on
either side of the contact. With this in mind, t tests between the rock types
for each element in each section were computed as a determination of
differences in concentration (Walker and Lev, 1953). These values are
presented in Tables 13 to 16.

The results of these t tests do not, in most cases, appear to be
meaningful. Significant differences exist where there is no incfication of
diffusion from the curves and also the reverse. This may be due to the
nature of the t test for this type of data, which seems doubtful. It is more

probable that the concentrations, as a first approximation, are not linearly

TABLE 13

RESULTS OI“ t TEST l’sE‘T'WEE-N SCHIST
AND GRANITE FOR SECTION 37

 

 

Element t
Na 0. 92
K 10. 75*
Mg 19. 70*
Ti 3. 82*
B 3.47*
Ga 6.68*
Ca. 8. 91*
Fe 19. 00*
Mn 20.60""
Cu 11.40*
Pb 0. 82
Zn,Ni. V, Zr not determined

*indicates that the value is significant at 0. 005.

-43..

TABLE 14

RESULTS OF t TEST BETWEEN SCHIST
AND GRANITE FOR SECTION 38

Element

 

Na

K

F e
Mn
C u
Pb

Zn, Ni, V, Zr

 

8.16*
11.40*
29.10*
10.70*

7.90*
17.30*

2.11
26.10*
32.50*
87.40*

7.00*

not determined

*indicaies that the value is significant at 0. 005.

-44-

TABLE 15

RESULTS OF t TEST BETWEEN SCHIST

 

AND GRANITE FOR SECTION 251

 

Element fl“ t2***
Na 6. 50* 7. 30*
K 0. 84 1. 36
Mg 66.80* 24. 70
V 15.60* 12. 90*
Ga 6.20* 9.45*
Zr, Ni not determined not determined
Ca 13. 70* 9.40*
Fe 29.20" 23. 80*
Mn 17.60* 94. 70*
Ti 56. 50* 22. 80*
Cr '28. 80"" 17.20*

*indicates that the value is significant at 0. 005.
**t refers to the schist (1)—gra‘mite part of the section.
***t2 refers to the schist (2)—granite part of the section.

-45-

TA 15 L E 16

RESULTS OF t TEST BETWEEN GRANITE
AND GRANITE GNElSS FOR SECTION 253

 

Element t

Na 1. 30
K 24. 30*
Mg 3. 55*
Ti 4.30*
Pb 15.70*
Cu 3. 70*
Ca 12.20*
Fe 12.50*
Mn 6.20*
V 11. 00*
Ga 1. 07
Ba, Cr not determined

*indicates that the value is significant at 0. 005.

—46-

-47-

related to the activities of the diffusing elements at the conditions under

which the diffusion occurred.

Thickness of the Diffusion Zone

 

The thickness of the diffusion zone is, for the purposes of this section,
operationally defined as that point where the hyperbolic tangent is effectively
equal to one (C8 = 0.999). Table 17 shows the diffusion zone thicknesses for
each element and each section.

The sections are arranged in order of increasing dike thickness. It
should be noted that there is a tendency for the wider dikes to have wider
diffusion zones for a given element. This may be due to the greater amount
of fluid associated with the wider dikes. There is not enough data to
determine what is the relationship between dike width and diffusion zone
thickness. The matrix of the dike and host rock will also effect the diffu—
sion zone width thereby making it difficult to determine such a relationship.

Comparisons within a single section are more fruitful. With partial
and incomplete data, it can be seen that Ni and Mg are comparable in 251(1).
In 251(2) Na and K are comparable and inverse. In section 38, Mg and Fe are
comparable, Na and Ti are inverse. Ti and V in 253 are comparable. These
comparable and inverse relationships of the thickness in a given section are
to be expected from the known atomic parameters of these elements. It is

to be expected that with more data other similar relationships will appear.

TABLE 17

THICKNESS OF THE DIFFUSION ZONE,IN INCHES,

FOR EACH ELEMENT IN EACH SECTION IN THE HOST ROCK

Element

Na
K
Ca

Mg

m

Ga

Ti

Cu

Pb

Ni

Zn

Cr

Section
3 7

1.82

none

none

2.27

none

none

none

none

1.25

2.71

0.82

none

none

none

none

none

Section

1.46

2.20

none

3.10

3.13

none

1.23

none

none

2.51

2.11

none

-48-

Section

251(1) .

0.58

1.71

none

0. 88

none

1.02

none

0.30

none

none

none

none

0. 89

none

none

none

Section

251 2

2.10

2.00

none

none

none

1.37

none

0.24

none

none

none

none

none

none

none

none

Section
_253

none

2.60

3.90

none

3.14

5.03

none

none

1.82

none

none

none

none

1.81

none

5.83

CHAPTER IV

DISC U SSION

Nature of the Contact

 

The contact between the intrusive dike and the adjacent country rock
is a mineralogical and textural discontinuity, which may act as a barrier to
the free migration of elements from. one rock type to the other.

When the various curves are examined, definite indications of
material transfer across the contact appear in some of the curves (Figures
8, 10, 11, etc.) while other curves, show movement of material on one
side of the contact only (Figures 16, 21, 25, etc.). The shape of the curves
suggests that the distribution is discontinuous at the contact. The curve
types described in the previous chapter probably indicate the relative
mobility of an element on either side of the contact. Thus, the contact
serves as a barrier to the free movement of material across it.

For a given element, the barrier can be considered to be permeable
if it allows the free movement of material across it, and impermeable if it
prevents such movement. If some elements can move freely across the barrier
while others cannot, or if some element can cross it only with difficulty, then
the barrier may be considered to be semipermeable. The mechanism of this
barrier is not understood.

Two different hypotheses apply to the treatment of the contact as a
barrier. The first hypothesis is that the contact is a physical barrier to
diffusion. The second hypothesis asserts that the barrier nature of the con—

tact is only apparent and the effect is due to the differing rates of diffusion

-49...

-50..

on either side of the contact, which is to be expected since the material
through which the diffusion is occurring is mineralogically and texturally
different on either side of the contact. This would explain the need for
different functions for a given element on either side of the contact in the
same section. Either or both of the hypotheses will explain the type I
curves (hyperbolic tangent).

The type Ia curves can be explained by the barrier nature of the
contact and/or the differing diffusion rates on either side of it. At present
it is not possible to determine how much of an effect the barrier nature of
the contact has in this curve type. The difference in the curve on either
side of the contact can be handled by changing the diffusion rates which will
result in differing functions.

The term gradient as used below refers to both the concentration
and temperature difference existing during the diffusion process. The
use of concentration alone is due to lack of data on the temperature values.

The type Ib curves have a gradient and no movement of material
across the contact. This can be explained by assuming a very low diffu-
sion rate on either side of the contact and a very low permeability of the
contact.

The type Ic curves require no further explanation beyond the state—
ment that there is no gradient and no movement of material across the
contact.

The type II curves (hyperbolic secant) can be explained by the
assumption of a semipermeable contact which is effectively impermeable
to the diffusion across it. The rate of diffusion on either side of the con-
tact is now no longer of major importance to the argument. Since there is

still a gradient across the contact, there will still be diffusion away from

-51..

the high concentration side of the contact which will not be able to cross the
contact and will, therefore, build up to a high concentration level near the
contact. With a gradient established across the contact and the contact
acting as a semipermeable barrier, a common high or low concentration
point would form at the contact. If the higher side of the gradient is the
side with the higher diffusion rate, there should be an increase in the con-
centration near the contact. This increase should develop at a faster rate
than it can cross the contact. Since the diffusion on the opposing side of
the contact is slow, movement of the transferred material away from the
contact should also be slow resulting in a zone of increased concentration
near the contact. Since both sides have concentrations increasing toward
the contact, the contact should appear as a common high point as is seen
in the type Ila curves.

An explanation for the type III) curves is similar except that the
side having the high diffusion rate is now the low concentration side of the
gradient. In other words, material is removed from the area around the
contact faster than it can be supplied which produces common low at the
contact.

The type III curves (complex), however, can best be explained by
the action of the contact as a physical barrier to diffusion. An explanation
of the type III curves (complex) under the second hypothesis requires the
assumption of a zero rate of diffusion for the element on the one side of the
barrier. Section 253 has four curves in the type III group (complex), and
since the rock types on either side of the contact are very similar (granite—
granite gneiss), this assumption does not appear feasible. Similar argu—
ments also apply to the exclusive use of the second hypothesis for the

type II curves (hyperbolic secant).

-52-

In the light of the above discussion it is proposed that a rational
explanation for the three curve groups lies in the combination of the two
hypotheses into one. This results in the following statement: In consi—
dering interchange of material between an intrusive and its host rock by
diffusion, the contact acts as a barrier to the free movement of material
across it and the rock type on either side of the contact acts as a controlling
factor in the diffusion process. This appears to be quite reasonable since
the assumption of differing diffusion rates with differing matrices cannot
easily be discarded, but as has already been shown, it is not a complete
explanation. Introduction of a semipermeable barrier to diffusion in the
contact adds the necessary conditions for the explanation of the three curve

groups.

Periodicgy

 

As stated previously, the low freqneucy and most of the high fre-
quency periodicities are probably inherent in the diffusion system. No
relationships were found between these periodicities and the sampling
interval. Two factors may account for this periodicity. The first factor
is the normal variation in composition to be found in any "homogeneous"
rock, as reported by Dennen (Figure 1). The second factor is the semi—
permeable nature of the contact as discussed in the previous section.

Figure 1 (Dennen, 1951) shows element distributions for a homo-
geneous rock. It is evident that there are minor variations in composi-
tion, and that the variations are somewhat random in nature. If this rock
system is isolated and the mobility of constituents is increased by
increasing the temperature of the system so that material can move, the

system would be expected to reach an equilibrium distrubution. If the

-53-

increase in temperature is constant over the entire system, the resultant
composition distribution expected is a straight line. If, however, the
temperature increase varies over the system, the resultant composition
distribution would reflect the temperature distrubution. Under this second
set of conditions, the variations in composition already existing within the
rock would be enhanced or depleted depending upon the distribution of the
temperature field. In either case, in the absence of equilibrium, enhanced
or depleted forms of the original compositional variations would still remain.
If the system is under further stress, such as an anisotropic mass inter-
change (diffusion) parallel to the trend of the variations, these variations
should be further enhanced. The system would be analogous to adding
energy to one end of a standing wave.

The semipermeable nature of the contact would act to develop its
own periodicity in the following manner. If material is diffusing out of the
system and the contact is acting as a partial barrier to this diffusion, then
an increase in the concentration of the diffusing element would be expected
at or near the contact. This increase would tend to deplete the adjacent
zone. The increase and depletion is basically a waveform although it is
localized at the contact. If the conditions generating this waveform corres-
pond with the conditions resulting in variations already present in the
rock the variations will be enhanced thereby extending the waveform fur-
ther into the rock away from the contact zone.

The combination of the two factors discussed above should result
in a periodicity similar to that seen in the experimental curves. The low
frequency periodicity being due to the semipermeable nature of the con-
tact and the high frequency periodicity due to the stressing of the original

compositional variation in the rock.

-54-

Factors Controllingpiffusion Rate

 

Of the numerous factors controlling the diffusion rate only two are
evident from the results of this study. These are the "matrix" or bulk
composition and the fluid content of the system. The matrix effect can be
inferred from the values in Tables 9 to 12 (curve parameters) whereas the
fluid effect is estimated from the published values of the diffusion coefficients
(Fyfe, Turner & Verhoogan), the thickness of the diffusion zone as reported
in this research (Table 17) and the diffusion zone thicknesses reported for
wall rock alteration in hydrothermal vein deposits.

The effect of the matrix or bulk composition on the diffusion can be
seen both in the thickness values of the diffusion zone and in the values of
the distribution equation parameters. The values of b and k for any given
element in any one section are different on either side of the contact. These
values are also different from section to section, indicating that the matrix
is a controlling factor in the diffusion rate. It is probable that the matrix
effect, in the case of a fluid or of fluidized diffusion, is composed primarily
of the grain size, orientation, etc. , and secondarily the actual composition
of the grains. If the relative importance of the various factors were known,
it might be possible to assign numerical values to the matrix and thus apply
it to the diffusion system to yield meaningful results. Further research is
needed, however, before this can be done.

The fluids have a major effect on the diffusion system. If the system
were completely dry, which would not be expected in these rocks, diffusion
would have to be entirely solid-solid. The reported diffusion coefficients
(Fyfe, Turner 8: Verhoogan 1958) indicate that solid-solid diffusion is not

feasible for most geological systems. The rocks under consideration are

-55-

not dry and do have a considerable amount of water in them as shown by the
presence of muscovite in them.

If, instead of a dry system, a water bearing system is considered,
two possibilities still remain. The first possibility is that the water or any
other fluid, is in motion itself carrying the diffusing ions. The second case
is where the water, or fluid, is static and simply serves as the medium
through which the material diffuses. The first case is simple fluid diffusion
and the second is a "fluidized" diffusion. It is probable that there is no sharp
line dividing the two types of diffusion because the critical factor would appear
to be the amount of water, or fluid, available and pore space and permeability.
The values reported for the diffusion zone thicknesses in the studies on wall
rock alteration in hydrothermal ore deposits are orders of magnitude greater
than those reported for "normal" igneous intrusives. The hydrothermal
deposits were formed from highly aqueous fluids and it is probable that the
diffusion into the wall rock proceeded by fluid diffusion. In the systems
studied in this research the amount of water available from the intrusive
should be much less than in the hydrothermal deposits and the diffusion
resulting from them should also be much smaller. The order of magni-
tude difference between the two cases, however, leads one to the conclu-
sion that a mechanism of diffusion different from that operating in the
hydrothermal deposits is responsible in this case. What is postulated is
that the fluid acts as a static medium allowing the various ions to diffuse
through it. By necessity this fluid would have to be a film, no more than a
few molecules thick, surrounding the various mineral grains in the rock.
This mechanism is somewhere between solid-solid diffusion on one end
and liquid diffusion on the other. The resultant from this mechanism should

lie somewhere between the other two and as the data indicates, it does.

CHAPTER V

SUMMARY AND CONCLUSIONS

This study was undertaken to determine the nature of diffusion in an
igneous contact zone. The research that has been done in this area shows
that diffusion plays an important role in contact zones. Contact alteration
zones of the granite dikes in this study range up to only one or two feet,
while wall rock alteration in hydrothermal ore deposits cited here show
diffusion zones of up to two hundred feet wide, indicating that there are two
different mechanisms involved. Data on solid-solid diffusion strongly sug—
gests that it is not a feasible mechanism for most geological diffusion
systems.

Continuous samples were taken from small granite dikes and the
adjacent host rock. These samples were analyzed for both major and minor
elements by emission spectrographix techniques. Concentration distribu-
tions were obtained and a generalized function was determined for them of

the form: Ce = tanh (beam)

— b), where Ce is the element concentration
(transformed), x is the distance from the contact less the distance to the
zero point, and b and k are parameters of the equation.

The following three types of curves were observed; hyperbolic,
tangent, hyperbolic secant, and complex. Evidence from the complex curves
indicates that the system is discontinuous at the contact and that these curve
types cannot be used to describe the concentration distributions. These

curve types, however, can be used to describe the relative rates of diffu—

sion on either side of the contact and through the contact itself. Further

' .

-56...

-57..

evidence from the curve types leads to the hypothesis that the contact acts as
a semipermeable barrier to diffusion of material across it. This hypothesized
process and the differing diffusion rates in the rocks on either side of the con-
tact appears to result in the concentration distributions found.

A high and low frequency periodicity was found in most of the curves.
Tests showed that this periodicity was not related to the sampling frequency
except for a few of the high frequencies. Two hypotheses, either separately
or together, yield an explanation of the periodicity. The first hypothesis is
that the normal variations found in any homogeneous rock will be enhanced
under a non-equilibrium system that is undergoing anisotropic stress (diffu-
sion in one direction only) to yield a high-frequency periodicity. The second
hypothesis is that the contact, by acting as a partial barrier to diffusion,
causes the buildup of concentration at the contact with a subsequent depletion
further away. This would generate a low-frequency periodicity. These
processes, together, should produce a periodicity similar to that seen in the
data curves.

The matrix or bulk composition of the rock through which the material
is diffusing exerts a controlling effect on the rate of diffusion. Since the
diffusion process postulated is a fluid or fluidized one, the matrix effect should
be due to the texture of the host rock primarily and secondarily to its mineral
composition.

By rejecting solid-solid diffusion as the mechanism involved in igneous
contact zone diffusion, the mechanism must then be one of a fluid diffusion.
Diffusion in wall rock alteration in hydrothermal ore deposits probably occurs
with fluid movement as the active mechanism; the highly aqueous nature of
the ore fluid and thickness of the resulting diffusion zones supports this

hypothesis. The diffusion zone thicknesses in the granite contact zones

-53-

studied are orders of magnitude smaller than those of the ore deposits indi-
cating either very small amounts of water or a different mechanism. It is
hypothesized that a different mechanism pertains to the diffusion zones in
granite contact zones. That is, that a thin fluid film, perhaps only a few
molecules thick, acts as a static medium through which the material diffuses.
The controlling factor for these two mechanisms is the amount of water

available to the system.

Further Research

 

Two separate research projects lend themselves as a continuation of
this study. The first is an examination of the element concentration distribu-
tion in individual mineral grains as a function of distance from the contact.
This would have the advantage of determining the effect, if any, of solid-
solid and solid vapor diffusion in the system as well as determining the role
of the various minerals in diffusion.

The second project is a laboratory experiment to determine the diffu-
sion coefficients under controlled conditions and to determine the effect of
the matrix and the width of the dike on the thickness of the diffusion zone. This
would be done by putting an artificial melt into a rock and varying the times of
the molten state, the amount of water in the melt, the temperature of the melt,
the thickness of the melt and the rock type used.

Both of these projects should yield data to produce a more definitive

statement of the processes of diffusion in an igneous contact zone.

BIBLIOGR AP HY

Ahrens, L. H. (1950) wectrographic Analysis, Cambridge, Massachusetts.

Cassie, R. M. (1966) The Evolutional of a Domal Granitic Gneiss and its
relation to the Geology of the Thomaston Quadrangle,
Connecticut: Ph.D. Thesis, University of Wisconsin.

Dennen, W. H. (1951) Variations in Chemical Composition Across Igneous
Contacts: Geol. Soc. America Bull., vol. 62, pp. 547-557.

Fleischer, M. and Stevens, R. E. (1962) Summary of New Data on Rock
Samples G-1 and W-l: Geochem. at Cosmochem. Acta, vol. 26

pp. 525-544.

Fullangar, P. D., Brown, H. S., and Hagner, A. F. (1967) Geochemistry of
Wall Rock Alteration and the Role of Sulfurization in the
Formation of the Ore Knob Sulfide Deposit: Econ. Geol. ,
vol. 62, pp. 798-825.

Gates, R. M. (1951) The Bedrock Geology of the Litchfield Quadrangle:
Conn. Geol. Survey, Misc. Ser. No. 3, p. 13.

Gates, R. M. (1954) The Bedrock Geology of the Woodbury Quadrangle:
Conn. Geol. Survey, Quadrangle Report No. 3, p. 23.

Gates, R. M. (1964) The Bedrock Geology of the Waterbury Quadrangle:
Conn. Geol. Survey, Quadrangle Report No. 22.

Ishikawa, H., Kuroda, R. and Sudo, T. (1962) Minor Elements in Some .
Altered Zones of ”Kuroko" (Black Ore) Deposits of Japan:
Econ. Geol., vol. 57, pp. 785-789.

Fyfe, W. S., Turner, F. J. and Verhoogan, J. 1958) Metamorphic Reactions
and Metamorphic Facies, Geol. oc. America Mem. 73,

p. 259.

Harvey, C. E. (1957) Spectrochemical Procedures, Applied Research
Laboratories, Glendale, California.

Jensen, M. L. (1964) The Rational and Geological ASpects of Solid Diffusion:
Canad. Min., vol. 73, pp. 271-290.

Jost, W. (1960) Diffusion in Solids, Liquids, Gases: Academic Press,
New York.

-59-

-60—

Morris, H. T. and Lovering, T. S. (1952) SUpergene and Hydrothermal
Dispersion of Heavy Metals in Wall Rocks near Orebodies,
Tintic District, Utah: Econ. Geol., vol. 47, pp. 685-716.

Mueller, R. F. (1966) Mobility of the Elements in Metamorphism: Jour.
of Geol., vol. 74, pp. 565-582.

National Bureau of Standards (1961) Monograph #32, Tables of Spectral
Line Intensities.

Stonehouse, H. B. (1954) An Association of Trace Elements and Minerali-
zation at Sudbury: Amer. Min., vol. 39, pp. 452-474.

Turner, F. J. and Verhoogan, J. (1960) Igneous and Metamorphic
Petrology: Second Edition, New York, McGraw-Hill.

Walker, H. M. and Lev. J. (1953) Statistical Inference, New York, Holt,
Rinehart and Winston, p. 510.

Wehrenberg, J. P. and Silverman, A. (1965) Studies of Base Metal Diffu-
sion in Experimental and Natural Systems: Econ. Geol. ,
vol. 60, pp. 317-350.

Woodard, H. H. (1968) Contact Alteration in the North Wall of the Cape
Neddick Gabbro, Main: Jour. Geol., vol. 76, pp. 191-204.

APPENDIX A

DATA TABLES

~61-

SPECTROGRAPHKIANALYSES
SECTION 37

X Na Ca K Fe Mg
in. % ”/0 % % Ppm
6.31 1.53 0.45 1.78 0.91 510
6.04 2.17 0.47 1.82 0.85 755
5.78 2.40 0.36 1.58 0.95 500
5.52 2.87 0.51 1.28 0.82 527
5.25 1.98 0.58 1.38 0.84 432
4.99 2.33 0.44 1.52 1.01 387
4.72 2.52 0.40 1.41 1.13 560
4.46 2.13 0.40 1.40 1.11 433
4.20 2.13 0.52 1.50 1.12 347
3.93 2.33 0.40 1.70 0.88 637
3.57 2.55 0.44 1.33 1.23 310
3.30 2.47 0.42 1.19 1.16 308
3.04 2.17 0.35 1.92 0.85 465
2.78 1.93 0.43 2.23 0.98 510
2.51 1.65 0.17 1.78 0.73 370
2.25 1.77 0.28 1.67 0.78 633
1.98 1.97 0.42 1.65 0.96 793
1.72 2.00 0.29 1.77 1.07 490
1.46 1.95 0.37 2.08 0.94 367
1.19 1.90 0.30 1.92 1.12 590
0.93 1.56 0.33 2.05 0.83 650
0.66 1.59 0.49 2.03 0.89 510
0.40 1.07 0.22 2.27 0.84 700
0.13 1.21 0.34 1.95 0.72 2750
Gr

C Mg
Sch ‘%
0.13 0.85 0.79 2.93 10.17 0.17
0.47 0.84 1.01 2.75 9.57 1.61
0.82 2.30 1.33 3.35 12.20 0.81
1.16 1.53 1.22 3.22 9.40 2.15
1.50 2.39 2.19 3.13 11.30 2.32
2.15 2.11 0.86 3.05 8.90 0.64
2.49 2.48 1.83 3.36 10.90 1.20
2.84 1.80 1.01 2.68 7.70 2.72
3.18 2.07 1.52 2.53 11.50 2.14
3.52 2.13 1.16 3.23 9.80 1.17
3.87 1.79 1.72 3.38 14.30 3.28
4.21 1.87 1.41 4.32 13.90 3.05
4.56 1.97 1.28 3.18 11.30 2.82
4.90 1.82 1.14 3.62 9.90 1.82
5.20 2.12 1.98 4.25 14.80 2.14

-62-

H-
53%

OQWOCDNQDUINW

cocoHHHHwamwmwpnupP-rbmmcnmm

0.. O
womwcoczmoocnI—too

C000
0
5' 7

0.13
0.47
0.82
1.16
1.50
2.15
2.49
2.84
3.18
3.52
3.87
4.21
4.56
4.90
5.20

Mn
ppni

73
83
72
96
80
52
47
55
56
75
71
93
106
247
141
65
71
74
69
69
67
96
78
670

2883
3683
4033
3117
2987
2530
3050
2757
3767
3017
3583
2300
2867
3967
4317

Ti
ppn1

763
707
833
637
713
840
993
1050
1000
850
977
670
640
643
490
850
813
847
967
987
1910
837
687
5333

7700
5313
2267
1967
2167
1650
2308
1733
2133
1750
2933
3333
2650
1933
2433

-63-

<

ppni

“QPFPPPPPPPFQQQQPPPPQPQP

SSPSDUDFDUPFZSDDPDDDFDDPS

730
560
430
313
503
300
358
258
590
327
917
1017
677
457
1010

ppnl

p—A

H
HoooooooqqoococomQ-q-qoooomqoooooooow

H

14
13
18
109
37
33
29
23
85
58
367
247
133
142
217

Cu
Ppnl

145
112
308
193
202
260
297
193
235
285
190
273
190
132

98
160
185
220
148
175
134
117

43
163

66
49
33
49
10
23

rF-CDCOGK‘IU‘IQDC‘J

-64—

x Ga Pb Zn Zr
in. ppni ppnn ppni ppni
6.31 12 51 n.d. n.d.
6.04 15 52 n.d. n.d.
5.78 12 54 n.d. n.d.
5.52 16 35 n.d. n.d.
5.25 12 72 n.d. n.d.
4.99 11 64 n.d. n.d.
4.72 11 61 n.d. n.d.
4.46 12 59 n.d. n.d.
4.20 13 78 n.d. n.d.
3.93 12 58 n.d. n.d.
3.57 13 115 n.d. n.d.
3.30 11 84 n.d. n.d.
3.04 9 59 n.d. n.d.
2.78 13 91 n.d. n.d.
2 51 9 43 n.d. n.d.
2.25 11 59 n.d. n.d.
1.98 14 84 n.d. n.d.
1.72 12 66 n.d. n.d.
1.46 13 50 n.d. n.d.
1.19 10 44 n.d. n.d.
0.93 13 46 n.d. n.d.
0.66 14 54 n.d. n.d.
0.40 18 35 n.d. n.d.
0.13 17 35 n.d. n.d.
(3r

C

Sch

0.13 20 28 141 263
0.47 22 32 160 333
0.82 20 55 203 220
1.16 17 58 189 160
1.50 15 70 161 215
2.15 16 49 154 169
2.49 18 67 144 215
2.84 12 52 120 227
3.18 24 67 166 228
3.52 19 50 130 215
3.87 23 92 155 268
4.21 20 47 188 218
4.56 22 60 144 237
4.90 16 45 122 . 298

5.20 27 64 191 202

’U
":32?
B

neeaeesseeaeeeeeeseaesse

? F 5 F P P P P P P F P F P F P F P P F F P P F

in.

15.45
14.95
14.64
14.34
13.84
13.45
12.89
12.35
11.74
11.20
10.67
10.20
9.84
9.30
9.22
8.88
8.55
7.99
7.55
7.05
6.30
5.77
5.05
4.80
4.77
3.94
3.54
2.98
2.54
1.98
1.76
1.65
1.43
1.04
0.79
0.54
0.35

Sch

(3r

SPECTROGRAPHKIANALYSES
SECTION 38

'Na
%,

OOOOOHOHHHHHHOOOOOOOHHHOOOHHOOHHHi—‘Ol—‘O

.99
.13
.91
.12
.35
.10
.23
.79
.61
.35
.13
.57
.68
.75
.04
.13
.06
.78
.80
.93
.93
.98
.92
.92
.01
.08
.06
.06

55

.19
.95
.00
.79
.61
.55
.38
.28

Ca

OOOOOOOOOOOOOOOOOOOOOOOOCOOOOCOOOOOOO

‘%

.63
.47
.41
.48
.52
.49
.50
.33
.24
.39
.34
.17
.23
.32
.48
.42
.46
.55
.39
.44
.43
.43
.61
.42
.41
.37
.41
.47
.52
.47
.45
.47
.50
.45
.30
.41
.22

-65-

71

4.25
3.67
4.17
3.98
4.75
3.87
3.60
4.07
3.78
3.98
5.30
3.55
3.13
3.70
3.98
4.25
3.43
4.15
3.93
3.25
3.72
3.65
3.73
4.37
3.83
3.63
3.70
4.02
3.50
2.27
3.45
2.63
3.57
2.85
3.08
2.92
2.22

«1634:0001fimmmqmqmooootoqooqwooqwcommqmowcbaqooooooooo

.60

.20

Mg
7)

3.43
3.37
3.15
3.05
2.97
2.72
2.18
2.10
2.15
2.58
2.75
2.68
2.23
1.77
3.52
2.90
2.37
2.57
2.65
3.52
2.57
2.72
3.40
2.20
1.78
2.03
2.40
1.88
2.05
2.20
1.75
1.43
1.57
1.28
1.27
1.34
1.30

Sch

CDC)
H

a>a><l<l<3<l6305650101h»¢-$~DDODODDDDDBD§353F‘F‘C>C’
¢>oiu>cam-h1¢>h-c>c>haoionha~aoahA-Joaoahicpnaha~aoa

(D
05
01

10.57
10.90
11.29
11.65
11.90

oHomomooo-qcnn-Ac:upHoomHu-xcopt-ao-‘oowpm

Na

#4:)bah‘hih‘h‘h‘h‘DDthDBDthJP‘bDPJDDhDbDP‘P‘h‘P‘P‘P‘h‘h‘h‘h‘c>

%

.82
.32
.14
.40
.33
.45
.31
.57
.52
.76
.77
.15
.67
.47
.88
.00
.10
.65
.22
.05
.19
.28
.53
.55
.85
.73
.30
.70
.83
.12
.95
.09

Ca

OOOOOOOOOOOOOOO:OOOOOOOOOOOOOOOO

%

.30
.43
.51
.31
.33
.28
.23
.24
.29
.31
.37
.41
.46
.45
.28
.49

.38
.43
.50
.52
.55
.53
.32
.29
.27
.41
.34
.28
.42
.28
.31

‘66-

%

2.37
2.33
2.12
2.57
2.58
2.80
2.05
2.13
2.77
1.98
1.80
2.15
1.35
1.30
1.38
1.35
2.75
2.05
1.87
1.77
1.05
n.d.

1.24
1.33
2.85
2.52
3.08
2.50
1.93
1.85
2.18
1.12

Fe

OOOOOOOOOOOOOOO?OOOOOOOOOOOOOOOO

%

.49
.34
.32
.34
.38
.52
.48
.40
.37
.32
.53
.47
.61
.63
.76
.58

.71
.60
.75
.23
.24
.37
.27
.27
.37
.43
.64

35
45

.33

Mg
ppm

1683
1383
1507
1767
1250
1467
830
967
837
610
660
610
342
450
393
395
377
427
377
413
343
507
370
265
1025
723
733
870
510
500
227
260

-67-

x B Cu Ga Pb T1
in. ppni ppni ppni ppni ppni
15.54 99 483 15 31 1923
14.95 97 687 24 36 2067
14.64 132 447 24 30 2883
14.34 61 530 23 37 2367
13.84 58 335 28 33 2133
13.45 102 530 23 33 2250
12.89 61 362 20 31 1742
12.35 68 430 28 28 1758
11.74 31 417 21 25 1967
11.20 33 340 19 29 1908
10.67 33 333 19 26 1975
10.20 34 500 29 29 2225
9.84 28 427 18 22 2242
9.30 136 497 19 22 2267
9.22 139 423 26 31 2533
8.88 67 453 22 32 2017
8.55 136 480 23 29 2092
7.99 153 580 23 32 2750
7.55 107 530 21 32 2217
7.05 63 467 20 29 2067
6.30 78 338 18 27 1750
5.77 95 388 22 27 2042
5.05 84 733 23 36 2400
4.80 100 433 28 31 1633
4.77 130 430 18 29 1483
3.94 70 655 25 27 2075
3.54 109 523 22 37 1917
2.98 113 467 20 35 1475
2.54 108 590 19 35 1875
1.98 110 440 22 28 1788
1.76 108 444 18 30 1780
1.65 42 283 14 26 1375
1.43 86 185 17 26' 1967
1.04 30 277 14 30 1130
0.79 25 177 20 22 1533
0.54 37 113 17 23 5567
0.35 13 373 18 19 1690
Sch
C
Gr
0.35 17 102 13 28 310
0.74 14 77 21 39 128
1.13 29 58 16 25 293
1.28 11 51 19 33 122
2.01 11 49 17 24 112

2.11 15 208 24 35 145

.58

2.34
2.39
2.74
3.11
3.35
3.78
4.11
4.34
4.56
5.11
5.65
6.07
6.18
6.90
7.15
7.40
7.65
7.90
8.51
8.90
9.65
10.57
10.90
11.29
11.65
11.90

ppnl

HHH
QHH

p—i

Hi—l
ooor—wocomoooqoooo

=5
r-w-t HHHHHQQQH
Hw-QQDNNNoN' ° '

Cu
ppm]

39
29
24
87
293
148
243
148
240
188
n.d.
102
383
223
23
27
85
700
107
109
59
303
178
160
13
38

-68-

(3a

ppni

16
18
18
14
15
15
13
11
10
10

10

10
11
14
11
15
17
14
11
14
14
12

Pb
ppni

27
36
36
48
58
66
72
65
52
74
56
50
69
73
75
75

89
57
48
46
42
80
60
39
49

Ti
ppni

111
137
113
85
142
99
138
101
109
119
67
93
82
105
75
67
89
84
124
88
99
150
92 j
95
64
63

ppnl

527
403
593
430
450
437
413
500
677
607
650
463
860
743
617
333
443
773
407
480
420
427
667
277
257
395
315
370
285
415
438
377
753
200
420
1667
1220

999999
999999

hhi
1313111

3633
2750
2983
2617
2813
2380
2117
2787
2833
2193
2850
2983
2317
2667
3117
2883
3217
2567
2533
2967
2433
2617
3967
3050
3233
3600
2587
2400
3450
3350
2447
2708
2433
1900
2067
2600
1967

81
68
417
257
182
65

-69-

Zr
PPHI

101
85
97
54

107
86
78
80

113
77
89
66
86
71

107
78
73

102
69

101
78
85
44
61
84
75
71

115
55
93
76
86
68
82
93

146
70

999999
999999

Zn
ppni

196
205
197
144
223
201
179
147
188
174
157
159
185
121
233
178
162
179
187
193
167
169
183
115
135
205
170
137
137
190
140
118
140
129
100
140

99

FPF???
9799?”??-

PPPPFP

Ni

45
51
44
48
49
51
56
43
44
47
43
37
32
31
5O
46
46
47
45
56
45
31
33
22
26
39
32
31
29
32
32
35
34
33
31
35
35

-70..

Ni
ppm

Zn
ppm

Z r
ppm

Mn

ppm

pp m

dddddddddddddddddddddddddd
nnnnnnnnnnnnnnnnnnnnnnnnnn

dddddddddddddddddddddddddd
nnnnnnnnnnnnnnnnnnnnnnnnnn

dddddddddddddddddddddddddd
nnnnnnnnnnnnnnnnnnnnnnnnnn

97F027006630007270563935510
2654...)36r0r059295667108987656
121121 35 1... 21 11..

dddddddddddddddddddddddddd
nnnnnnnnnnnnnnnnnnnnnnnnnn

494158146.15780505010570950
33713713516019146959659269
92.22.333.44455666777788900111

11111

in.

1.33
0. 95
0.57
O. 19

Gr
Sch

. 18
.55
92
.19
.56
.93
.30
.67
. 04
.41
.88
.25
.62
.99
.46
.83
.20
.57
.94
.31
.68
.05
.42
.79
.11
.38
.65
.92
10.15
10.46
10.73
11.00
11.27
11.54
11.81
12.08
12.35

customooooooqqmczczmmfihphwwwNMHv-lwooo

SPECTROC HEMICA L ANALYSES
SECTION 250

Na
(70

FONND—O

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.29
.58
.99
.93

.73
.80
.42
.75
.65
.95
.65
.87
.77
.48
.47
.42
.73
.06
.48
.15
.80
.57
. 02
.43
.87
.10
.35
.83
.28
.22
.15
.43
.88
.37
.12
.62
.65
.12
.45
.33
.77

99:7:

49941-499

l"OOOOOOOOOOl—‘HOOOOOOOOOQOOOOl—‘OOOOOOOOO

.89
.63
.82
.87

.80
.87
.87
.88
.85
.85
.90
.98
.93
.07
.95
.93
.76
.72
.98
.97
.84
.76
.67
.90
.83
.82
.82
.71
.22
.01.
.77
.90
.68
.64
.76
.78
.83
.86
.86
.82
.64

-71-

Ca

%

0.
0.
0.
0.

mwmmaqmoomooqqm-qooootsaczmmc:moooomximmocncocooor-aoccz

41
34
39
22

.90
.50
.50
.00
.40
.87
.93
.53
.27
.60
.13
.87
.77
.43
.53
.97
.63
.60
.00
.67
.10
.05
.90
.00
.53
.27
.77
.17
.83
.40
.73
.43
.43
.97
.07
.40
.10

or
/O

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mqmqmmqqmqqqmqr—tqmmqmqqqqqmqqmquoqmmq

.60
.27
.10
.53
.47
.57
.50
.67
.40
.60
.37
.30
.73
.33
.30
.50
.63
.70
.73
.90
.33
.95
.10
.50
.83
.37
.27
.37
.10
.13
.40
.63
.03
.97
.57
.47
.70

0000

999999999999999999999

Mg

999999999

%

. 066
. 056
. 066
. 039

in.

12.
12.
13.
13.
13.
13.
14.
14
14
15.
15.
15.
15.
16.
16.
16.
16.
17.
17.
17.
18.
18.
18.
18.
19.
19.
19.
19.
20.
20.
20.
20.
21.
21.
21.
22.
22.
22.
22.
23.
23.
23.
23.
24.
24.
24.
25
25.

62
89
16
43
70
97
24

.51
.78

05
31
59
86
13
40
67
94
21
48
75
02
29
56
81
O6
33
60
87
14
41
68
95
22
49
80
03
4O
57
84
11
42
65
93
20
51
74

.01

28

Z
n:

HHHHHHHOHHNHHHHHOHHHOHNHHHNNHHHHHNHHNHNHHHHi—‘HHHN‘

58

.45
.73
.63
.40
.90
.83
.63
.62
.77
.18
.80
.22
.83
.88
.50
.68
.15
.73
.77
.73
.28
.00
.58
.27
.41
.48
.06
.81

O3

.16
.33
.95
.00
.23
.19
.06
.37
.02
.18
.48
.95
.33
.00
.00
.43
.04

.19

7)

.60
.49
.12
.03

O
H
N

CD
CD

CD
00

99°9999999999999999999999999H9999H9~99999HHHHH
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O N

-72-

Ca.

.40
77
40
.70
.67
.27
27
.90
.40
10.37
10.30
8.93
9.93
10.67
9.83
10.93
11.10
9.00
12.97
14.13
12.93
9.70
9.97
9.47
8.97
9.23
9.60
7.07
7.40
5.47
6.97
7.23
8.20
7.87
8.40
7.07
6.30
6.17
7.53
11.07
6.53
5.40
8.00
6.43
6.00
7.10
7.60
9.40

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H

H

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m

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%;

.43
.60
.47
.00
.20
.30
.67
.97
.63
.40
.67
.97
.03
.03
.13
.27
.55
.10
.77
.13
.93
.73
.16
.65
.90
.17
.03
.87
.67
.17
.20
.80
.73
.53
.77
.90
.80
.97
.00
.25
.50 -
.po
.00
.57
.30
.90
.97
.07

F’F’F’F’C’F’F’F’F’F’F’F’F’F’F’F’F’C’F’F’F’F’F’F’F’F’F’F’F’F’F’F’F’C’F’F’C’F’F’F’F’F’F’9’
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25.55

25.82.

26.09
26.36
26.63
26.91
27.40
27.89
28.38
28.87
29.36
29.85

30.34 '

30.83
31.32
31.81
32.30
32.79
33.28
33.77
34.26
34.75
35.24
35.73
36.22
36.70
37.17
37.64
38.11
38.58
39.05
39.52
39.99
40.46
40.93
41.40
42.01
42.76
43.51
44.26
44.88
45.37
45.86
46.35
46.84
47.33
47.82
48.31

1Na
7)

1.47
1.57
1.53
1.18
1.27
1.66
1.59
1.45
1.44
1.48
1.28
1.63
1.56
1.48
1.68
1.48
1.80
1.26
1.39
1.53
2.13
1.78
1.78
2.09
1.52
1.47
1.28
1.41
1.70
1.13
1.90
2.40
1.85
1.70
1.75
1.73
1.68
1.37
1.82
1.68
1.83
1.97
0.62
1.51
1.50
1.37
1.32
1.34

OOOOOCOOOHHHCOOOOOOOOHHOOOOHOHHHHOOOOOHHOHHOOOOO

%;

.86
.87
.69
.98
.78
.00
.17
.53
.00
.06
.90
.90
.84
.85
.86
.01
.10
.05
.01
.86
.10
.80
.81
.96
.83
.07
.04
.91
.79
.88
.73

.84
.79
.79
.79
.09
.53
.19
.93
.75
.86
.75
.76
.72
.84
.80
.80

-73-

Ca
%>

9.23
9.00
8.20
8.13
7.80
12.93
7.37
9.40
8.23
9.10
8.07
8.13
7.27
7.13
7.40
8.23
7.33
9.40
7.83
8.17
8.93
9.47
7.03
7.40
6.60
10.97
11.83
11.13
10.43
7.83
12.97
8.97
10.90
10.67
8.87
9.13
7.70
10.43
11.90
7.43
7.50
7.63
7.17
7.43
6.57
9.67
8.47
8.67

7;

.47
.80
.97
.87
.23
.40
.13
.93
.13
.53
.13
.20
.60
.50
.17
.33
.97
.70
.33
.87
.53
.27
.40
.90
.03
.38
.33
.17
.17

a>a>u>c>~a-a~ac:~1u>c>o>c>c=~a-a-q<p-qco<o<:cocn-qcm-qu-qcncncncn-q-Q-Q-qzncncncocnco-qcncncnco

80

.33
.57
.40

30

.37
.83
.53
.70
.03
.47
.93
.50
.70
.57
.97
.20
.47
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C’F’F’F’C’F’C’F’C’F’F’C’F’C’F’F’F’F’F’c’F’F’F’F’F’C’F’C’F’F’C’F’F’F’F’F’F’C’F’F’C’F’F’
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0

.13

CO
CD

in.

48.79
49.28
49.77
50.26
50.77
51.30
51.83
52.32
52.76
53.20
53.64
54.08
54.52
54.96
55.40
55.84
56.28
56.72
57.16
57.60
58.09
58.63
59.17
59.71
60.15
60.79
61.33
61.79
62.17
62.52
62.88
63.60
63.96
64.32
64.68
65.04
65.40
65.76
66.12
66.48
66.84
67.20
67.56
67.92

.Na

HHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

%;

.40
.48
.48
.41
.66
.68
.41
.59
.37
.53
.30
.80
.53
.52
.68
.38
.68
.56
.35
.52
.53
.49
.67
.88
.75
.43

.43
.17
.27
.11
.23
.42
.85
.53
.53
.58
.65
.66
.81
.64
.77
.71
.81

OOOOOOOOCOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOOODO

%;

.70
.83
.89
.93
.84
.75
.85
.78
.72
.84
.75
.80
.67
.77
.73
.69
.80
.78
.73
.63
.76
.69
.69
.75
.69
.77
.76
.64
.73
.82
.83
.63
.69
.71
.68
.64
.72
.79
.74
.80
.78
.77
.82
.78

-74-

Ca
‘%

9.47
8.90
9.40
7.87
8.30
6.93
8.10
11.53
11.87
11.77
9.30
11.47
9.53
11.90
10.67
7.27
7.57
8.93
9.00
7.00
7.93
7.83
7.30
8.50
8.33
7.80
7.53
8.37
8.80
8.17
9.17
9.13
6.57
7.57
7.17
7.27
7.87
10.03
6.87
7.63
8.47
7.80
7.17
6.07

‘%

m4ooooqqqqco-amqocococoqoooooocooooooo-qoooo-qcocoocooooomcacooocooooooqoo

.80
.43
.33
.67
.60
.15
.43
.17

30

.57
.90
.80
.10
.03
.15
.95
.80
.20
.13
.70
.23
.37
.45
.50
.17
.10
.10
.70
.50
.00
.40
.00
.80
.87
.80
.65
.85
.80
.60
.07
.45
.15
.60
.40

0.47
0.42
0.57
0.60
1.67
1.03
1:58
1.92
0.77
0.72
0.80
1.39
0.84
1.71
0.85
0.81
0.92
1.17
1.70
0.89
1.06
1.62
0.85
1.52
1.05
1.05
0.92
0.94
1.01
0.64
0.73
1.05
1.01
0.99
0.90
1.19
1.02
0.87
0.94
0.51
1.11
0.95
1.00
1.04

cocococncncn-a~aczozaaoiunmqh.pcococotoiohahahic>csc>
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CD
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N

10.15
10.46
10.73
11.00
11.27
11.54
11.81
12.08
12.35
12.62
12.89

97
126
83
99
133
137

92
81
78
80
73
120
110
76
126
96
88
135
64
75
132
178
103
74
89
94
82
77
90
77
77
75
115
76
86
64
64
69

Cu
ppm

(0000110

143
178
133
102
187
205
97
11
37
n.d.
82
153
137
104

83
29
21
53
15
230
105
n d

-75-

190

163
77
72
82
62
77
45
70
81

109
97

108
45
48
50

Ga

PPHI

12
12
10
15

34
42
30
23
44
34
28
23
23
32
19
19
39
27
16
33
26
15
25
14
23
31
'28
30
25
25
20
20
19
24
16
15
12
44
21
26
19
28
23

Ti
ppm}

188
162
183
152

‘8200

7267
9133
7100
7833
8600
6500
6600
5200
7267
6433
5367
5400
6267
4800
6800
6100
4750
5733
4467
6167
7250
6400
6533
5533
6100
5467
5500
5167
5300
5900
5467
4767
6067
5650
5300
6800
9100
6100

ppnl

01901149

1013
1050
1013
977
840
1373
847
900
743
787
813
533
827
907
720
820
983
550
710
497
697
715
750
743

' 827

783
703
767
547
820
797
700
647
937
610
1143
870
1000
730

13.
13.
13.
13.
14
14.
14.
15.
15
15.
15.
16.
16.
16
16.
17.
17.
17.
18.
18.
18.
18.
19.
19.
19.
19.
20.
20.
20.
20.
21.
21.
21.
22.
22.
22.
22.
23.
23.
23.
23.
24.
24
24.
25.
25.
25.
25

16
43
70
97

.24

51
78
05

.31

59
86
13
40

.67

94
21
48
75
02
29
56
81
06
33
60
87
14
41
68
95
22
49
80
03
40
57
84
11
42
65
93
20

.51

74
01
28
55

.82

ppni

80
80
112
96
65
67
79
126
99
140
124
145
75
85
137
79
207
106
98
168
208
119
97
130
123
144
132
98
114
153
125
94
140
102
126

133
122

88
108
103
110
112

94

99
149
118
113

Cu
PPm

42

35
48
14
5.1
44
n.d.
175
103
101

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Ga
ppnl

21
16
32
30
17
18
29
70
38
38
44
37
39
39
30
27
41‘
36
36
29
28
12
11
38
24
20
21
20
22
17
12
13
21
18
14
27
19
11
19
25
21
21
17
21
17
25
16

10

Ti
ppn1

6067
4567
6667
6633
4800
5067
4967
.7400
7500
9250
n.d.
6000
6300
7800
9167
6967
9350
9300
8050
9900
7500
5700
4367
7000
4600
5700
5333
4533
5717
5850
4050
3983
3450
5000
4717
4967
5017
6167
4317
4950
5583
5800
4733
4383
5567
5500
5067
6633

ppni

593
707
1037
967
583
680
800
1473
1633
977
1230
1053
817
1263
857
1183
1187
1600
1250
1043
700
713
683
867
543
463
433
387
607
593
567
570
477
623
567
663
540
790
500
413
617
553
523
600
653
653
813
743

in.

26. 09
26.36
26.63
26.91
27.40
27. 89
28.38
28. 87
29.36
29.85
30.34
30. 83
31.32
31. 81
32.30
32. 79
33.28
33. 77
34.26
34. 75
35.24
35.73
36.22
36.70
37.17
37.64
38.11
38. 58
39. 05
39.52
39. 99
40.46
40. 93
41.40
42. 01
42.76
43. 51
44.26
44.88
45.37
45. 86
46.35
46. 84
47.33
47.82
48.31
48.79
49.28
49.77

ppm]

123
91
78

133
99

163

104

101
80
98
71
88
90

100

105

122

106
99
78

121
87
97

101

108

162

148

149
79

124

101

117
87
76

103
84
84

124

105
99

106

106
98
98

108

109

125

110

101

101

Cu

ppnl

H

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Ga
ppm

23
19
17
16
15
29
17
14
15
12
14
16
12
16
15
35
15
11
15
16
14
14
14
16
26
25
26
13
27
21
25
17
17
28
14
21
13
11
10
18
22
15
13

11
13
16
10
12

Ti
ppni

5167
5767
6833
9850
7850
9800
9150
9250
6833
8400
7900
8600
5700
5800
6250
4633
5800
6133
7550
8350
6267
6550
6500
7567
7900
7067
6333
5450
7267
7733
6767
7200
6233
6517
8100
5233
5052
6833
5767
6100
6300

.4700

4783
5500
5950
7350
7767
6533
6400

ppm

620
560
627
667
570
543
563
523
510
717
517
427
580
500
673
513
603
583
1063
603
490
553
693
637
773
623
723
477
933
620
867
637
443
480
547
470
577
510
530
610
610
507
443
660
477
500
567
563
607

50.26
50.77
51.30
51.83
52.32
52.76
53.20
53.64
54.08
54.52
54.96
55.40
55.84
56.28
56.72
57.16
57.60
58.09
58.63
59.17
59.71
60.15
60.79
61.33
61.79
62.17
62.52
62.88
63.60
63.96
64.32
64.68
65.04
65.40
65.76
66.12
66.48
66.84
67.20
67.56
67.92

ppni

91
111
91
109
113
132
110
128
118
114
114
128
114
101
106
116
111
111
98
111
98
107
100
111
113
119
87
97
123
88
89
91
99
94
112
77
89
83
80
90
79

Cu
ppnn

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“#MN’

F’
a.

AWO3NNHNMNO1AN‘

-73-

Ga
ppnn

14
13
10
14
17
14
12
15
13
12
17
11
13
14
11
12

10
12
10
15
14
14

12
13
19
14
14
11
10
11
12
12
16
16
20
17
15
13
17

Ti
ppni

5775
8850
7667
8550
7100
6967
7767
7633
7500
6133
7067
6800
6133
6300
6700
5967
5167
6550
6767
6717
6050
6033
5067
5500
6253
7367
8800
7200
6567
5367
6033
5617
6267
6967
6133
4600
4633
5300
4217
4267
4033

PPnl

483
557
500
513
640
857
680
743
767
690
840
817
607
523
547
643
487
690
563
620
600
660
487
547
523
687
580
647
697
507
620
597
977
653
647
520
563
657
637
630
433

.18
.55
.92
.19
.56
.93
.30
.67
.04
.41
.88
.35
.62
.99
.46
.83
.20
.57
.94
.31
.68
.05
.42
.79
.11
.38
.65
.92
.15
.46
.73
.00
.27
.54
.81
.08
.35
.62
.89

PP“1

9999
9999

108
178
103
83
153
108
106
97
106
94
76
89
143
102
80
117
111
76
n.d.
75
87
91
143
85
97
95
73
79
87
75
63
59
51
143
86
97
74
100
73

PP“1

15
13
11
15

770
1240
1453
1073

947

967

690

897

478
1106

843

733

573

492

523

673

680

525

677

527

618

797

917

563
1160
1300

890
1033

840

960

807

843

747

800
1000

697
1367
1390
1300

“79'

5:3

a z
9‘9‘9‘9‘

272
171
285
237
197
263
195
228
207
290
227
228
160
195
160
240
178
260
n.d.
167
250
205
178
163
235
375
188
345
268
205
207
212
185
202
282
217
273
410
258

215
188
152
134
164
203
171
127
140
157
143
119
181
132
113
142
110
108
n.d.
101
131
155
179
147
130
129
133
118
126
142
135
114
108
153
124
133
140
192
120

180
172
150
132
155
190
128
128
86
120
109
83
120
98
83
99
88
108
59
80
73
98
148
105
97
77
71
82
59
66
60
55
59
85
83
76
81
141
100

13.
13.
13.
13.
14.
14.
14
15.
15
15.
15.
16.
16.
16.
16.
17.
17.
17.
18.
18.
18.
18.
19.
19.
19.
19.
20.
20.
20.
20.
21.
21.
21.
22.
22.
22
22.
23.
23.
23.
23.
24
24.
24.
25
25.
25
25

16
43
70
97
24
51

.78

05

.31

59
86
13
40
67
94
21
48
75
02
29
56
81
06
33
60
87
14
41
68
95
22
49
80
03
40

.57

84
11
42
65
93

.20

51
74

.01

28

.55
.82

Zn
ppni

92
60
130
101
71
66
68
126

137

163
122
117
133
147
120
124

92
177
132
101
117
102

60
129
178
125
125
118
129
146

175'

107
54

Cr
PP“1

1003
618
467
933
983
830
797
957

1110

1703

1170
797

1075

1233

1417

1700

1683

1847

1927

1197

1163
853

1040
977
813
683
853
458
567
710
830
980
780

1057
773
397

1289

1563
900
463

1210
510
463
913
950

1003

1073

1100

-30-

.Ba
ppnl

248
185
173
293
263
197
177
172
202
n.d.
268
n.d.
135
173
280
232
n.d.
265
405
n.d.
n.d.
423
467
n.d.
195
158
177
127
143
160
157
217
142
158
128
150
183
507
157
123
200
138
128
143
190
220
205
530

Zr
ppni

139
108
141
163
89
115
103
145
135
n.d.
194
n.d.
107
116
153
145
n.d.
170
150
n.d.
n.d.
122
134
152
157
148
104
121
147
146
113
127
125
122
130
137
160
109
123
134
164
123
108
150
181
150
157

Ni
ppnl

100
78
126
134
101
115
118
111
140
107
203
147
167
147
178
138
102
139
155
86
72
95
96
85
106
105
103
80
93
95
102
110
105
98
93
81
105
132
95
80
95
107
98
91
115
125
112
125

26.
26.
26.
26
27.
27.
28
28.
29.
29.
30.
30.
31.
31.
32.
32.
33.
33.
34.
34.
35.
35.
36.
36.
37.
37.
38.
38.
39.
39.
39
40.
40.
41.
42.
42.
43.

44
45.
45.
46.
46.
47.
47.
48.
48.
49.

09
36
63

.91

40
89

.38

87
36
85
34
83
32
81
30
79
28
77
26
75
24
73
22
70
17
64
11
58
05
52

.99

46
93
40
01
76
51

.26
.88

37
86
35
84
33
82
31
79
28

Zn
ppm

155
120
98
82
85

87
75
88
79
90
90
82
83
71
149
88
71
78
80
101
72
90
90
153
158
153
88
117
100
135
72
82
110
86
68
95
78
75
84
104
98
102
67
77
86
142
88

ppm

597
987
917

1657

2150

1173

1917

2467

1370

1817

1337

1510

1007

1800

2383
780

1767

1460

2450

1750

1507

1983

1560

1583

1500

1750

1950

1117

1267
665

1793

1753

1087

1183

1433
957
807

1850

1217

1047
593

1167

1017

1423

1800

1463

1350

1433

-31-

18a
ppn1

128
205
192
365
570
n. d.
540
635
307
500
n.d.
410
430
440
435
177
360
420
370
n.d.
370
500
325
292
280
217
198
218
207
183
238
317
215
182
710
207
192
625
435
195
167
275

‘ 285

325
380
283
265
570

ppnl

122
140
148
260
177
n. d.
193
187
153
218
168
147
172
123
155
135
158
178
192
262
155
139
170
150
198
218
203
101
207
160
198
143
105
117
127
69
105
170
127
137
125
98
91
168
142
300
133
167

Ni
ppm

105
99
95

143

111
68

107

108
96

104

116

105
77

102

111
87

101
90

150

119
73

105

108

105

133

133

132
93

118
85
98 ’
87
77
87
84
72

130
97
93

113

122

123

117

140

127

142

105
95

49.77
50.26
50.77
51.30
51.83
52.32
52.76
53.20
53.64
54.08
54.52

54.96 -

55.40
55.84
56.28
56.72
57.16
57.60
58.09
58.63
59.17
59.71
60.15
60.79
61.33
61.79
62.17
62.52
62.88
63.60
63.96
64.32
64.68
65.04
65.40
65.76
66.12
66.48
66.84
67.20
67.56
67.92

Zn
ppnn

9O
78
85
84
114
104
95
87
108
79
87
100
66
97
91
72
70
71
75
80
70
89
80
78
65
96
96
78
78
102
70
69
61
55
58
77
60
95
60
56
51
65

ppnl

1673
1700
1707
1683
2057
2217
1917
1687
1750
1833
1117
1700
2033
1340
1450
1417

960
1413
1107
1020
1650
1300
1157
1240
1783
1667
1717
1133
1700
1417
1650
1317
1783
1440
1750
1417
1153

820
1167
1023
1667
1110

-82..

IBa
PPHI

305
370
395
530
515
n.d.
547
302
563
395
450
237
547
357
395
310
385
367
410
345
547
345
320
277
487
533
603
248
313
550
600
490
633
480
723
473
412
175
460
373
430
380

Zr
ppnl

187
133
192
178
203
153
182
170
192
163
133
113
172
158
120
117
160
145
157
132
205
140
117
122
155
170
182
148
167
162
128
142
118
143
145
130
103
118

97

95
110

98

N1
ppnl

148
123
142

99
137
155
157
145
178
145
132
168
132
125
117
133
128
122
117
118
113
138
110
108
110
118
111

91

92
122

93

88

90
121
101

88

84

80

97

96
113

81

hhl
ppnl

760
563
572
215

3400
2725
2683
3493
2433
3700
2525
2425
2683
2458
2367
2225
2400
3200
2900
2750
2383
5667
2500
2100
2650
3400
3700
2167
2533
2967
2350
3200
2067
2217
2800
2433
2217
2900
2717
2783
2283
2750
2600

-83..

in.

13.
13.
13.
13.
14.
14.
14.
15.
15.
15.
15.
16.
16.
16.
16.
17.
17.
17.
18.
18.
18.
18.
19.
19.
19.
19.
20.
20.
20.
20.
21.
21.
21.
22.
22.
22.
22.
23.
23.
23.
23.
24.
24.
24.
25.
25.
25.
25.

16
42
7O
97
24
51
78
05
31
59
86
13
40
67
94
21
48
75
02
29
56
81
06
33
60
87
14
41
68
95
22
49
80
O3
40
57
84
11
42
65
93
20
51
74
01
28
55
82

Rh}
ppnl

1800
2333
2000
2117
2200
2067
2467
2733
3333
2650
2850
1700
3383
3167
3100
2467
2167
3300
3567
2100
3217
3550
4167
2450
3350
3950
2200
2350
2867
3400
1867
2600
3183
3067
2883
2467
2900
5367
2517
2467
3183
3100
3367
3317
3217
3750
2433
4333

in.

26

29

40

44

46

47
47

.09
26.
26.
26.
27.
27.
28.
28.

36
63
91
40
89
38
87

.36
29.
30.
30.
31.
31.
32.
32.
33.
33.
34.
34.
35.
35.
36.
36.
37.
37.
38.
38.
39.
39.
39.
40.
.93
41.
42.
42.
43.

85
34
83
32
81
30
79
28
77
26
75
24
73
22
70
17
64
11
58
05
52
99
46

40
01
76
51

.26
44.
45.
45.

88
37
86

.35
46.
.33
.82

84

Dbl
ppn1

2633
2617
2250
3383
2817
2483
3050
2950
2700
3050
3633
2933
2783
3500
2783
3050
2800
2517
3033
3283
2883
2100
2800
3150
3917
3850
3050
2017
3050
2883
3217
2433
3050
2733
3217
2583
3800
2583
3750
2700
3700
3233
2933
3000

3433‘

-34-

in.

48

51

54

.31
48.
49.
49.
50.
50.
.30
51.
52.
52.
53.
53.
54.
54.
.96
55.
55.
56.
56.
57.
57.
58.
58.
59.
59.
60.
60.
61.
61.
62.
62.
62.
63.
63.
64.
64.
. 65.

65.
65.
66.
66.
66.
67.
67.
67.

79
28
77
26
77

83
32
76
20
64
08
52

4O
84
28
72
16
60
O9
63
17
71
15
79
33
79
17
52
88
60
96
32
68
O4
40
76
12
48
84
20
56
92

9%)
PP“1

3233
3483
3083
3783
3450
3617
3167
3333
3567
4267
2533
4687
3167
4433
2933
3400
4433
3200
3517
3033
4150
2883
4383
4300
3367
2983
3333
3967
4783
3067
3333
2817
3467
4517
2850
4800
5000
4417
4533
5533
2850
5850
4450
5000
5233

SPE CTR OCHE MICA L ANA L 18 ES
SECTION 251

x Na K Ca Fe IMg
in . (Z) 90 QC 0/0 %
4.84 1.93 2.43 1.47 7.40 0.40
4.77 1.73 2.38 1.52 9.17 0.50
4.50 1.93 2.10 1.88 9.03 0.55
4.23 1.65 2.18 1.43 8.77 0.39
3.98 1.57 1.95 1.31 7.03 0.43
3.69 2.03 1.69 2.42 11.00 0.57
3.44 1.83 1.94 1.71 8.37 0.39
3.24 1.62 1.78 1.33 7.67 0.44
3.07 2.17 1.67 2.47 9.90 0.48
2.83 1.93 1.97 1.18 8.60 0.39
2.38 1.88 2.10 1.26 8.30 0.41
1.80 1.90 1.72 1.28 7.77 0.36
1.29 1.95 1.40 1.70 8367 0.38
1.02 2.42 1.08 1.77 7.83 0.40
0.77 2.05 1.47 1.26 7.43 0.45
0.57 2.05 1.35 2.17 10.53 0.34
0.32 2.13 1.35 1.50 7.63 0.40
0.17 3.13 1.25 1.16 9.57 0.26
Sch

C

Gr

0.15 3.22 1.33 0.24 0.86 0.027
0.50 3.78 1.94 0.33 0.88 0.021
0.77 2.82 3.75 0.27 0.58 0.016
0.96 3.52 2.85 0.23 0.75 0.024
1.15 3.45 1.80 0.29 0.86 0.025
1.34 2.90 1.70 0.34 0.87 0.033
1.56 2.58 1.11 0.29 0.90 0.034
Gr

C

Sch

0.11 2.18 1.18 1.68 9.17 0.38
0.35 2.05 1.13 4.50 5.90 0.39
0.79 1.82 1.09 4.70 6.40 0.36
1.06 2.27 1.31 6.23 7.07 0.29
1.33 1.87 1.41 8.00 7.63 0.35
1.53 2.13 1.55 6.00 7.87 0.46
1.70 1.55 1.92 4.00 7.80 0.34
1.89 2.18 1.40 4.70 7.03 0.45
2.16 1.55 1.59 3.2 6.63 0.39
2.43 2.12 1.94 7.27 7.80 0.42

~85-

01999143000519

.93
.45
.75
.00
.25
.52
.77
.10

HHHHHHHH

%

.64
.78
.86
.91
.97
.65
.58
.68

49

.

QUIQMHNU‘N
(”NO‘DQHQO:
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Fe
%

.50
.00
.73
.77
.33
.63
.00
.47

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%

.33
.39
.29
.30
.39
.38
.35
.43

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0.11
0.50
0.79
1.06
1.33
1.53
1.70
1.89
2.16
2.43
2.93
3.45
3.75

ppnl

1883
2017
2900
1967
1817
2717
2033
2033
2750
1817
1700
1433
2067
2033
2300
1800
1817
1600

360
430
365
397
265
375
301

2517
1917
1783
1783
1583
2067
1383
1383
1317
1650
1333
1592
1083

Ppnl

923
1133
1057

950

737
1050

917

703
1510

540

650

733

910

917

683
1283

763

843

21
14

10
15
34
31

613
257
300
460
483
517
487
433
373
700
277
480
320

”87w

Ti
Ppm

6800
5967

10000

5900
8800
8200
n.d.

6400
6200
7633
7800
6433
n.d.

7467
6467

10000

5867
7933

1493
800
687

1110

1030

1037

1120

8800
7400
5700
6400
7033
6300
6600
7500
6533
8500
5800
7000
5900

ppm

P P ? ? P P F

F F P P P P P P ? F P P P

187
238
133
227
238
243
197
202
208
128
160
192
175
137
165
147
137
207

9999999

9999999999999

N1
ppnl

P F P P P P F

82
81
90
67
63
100
73
75
91
65
58
64
84
70
64
74
68
52

9999999

78
51
51
57
69
58
53
50
52
77
44
55
61

.99

99999
H-JU‘INO
@41ch

~88-

001 V Ti Zr N1
ppnl ppn1 ppn1 ppn1 ppn1
1117 283 4767 n.d. 47
1233 557 7767 n.d. 71
1483 290 6567 n.d. 74
1300 387 6767 n.d. 80
1867 643 7233 n.d. 85

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alCDC)
o
:3- 7

0.11
0.50
0.79
1.06
1.33
1.53
1.70
1.89
2.16
2.43
2.93
3.45

3.75 '

-89-

Ga
ppnl

24
31
25
30
17
24
18
19
22
16
24
18
21
19
20
35

4 20

25

32
52
44
46
38
43
33

30
10
11
14
13
13
14
11
15
12

12
14

Cr
9931

1427
1383
1573
1230
1480
1633
1667
1340
1470
1167
1270
1310
1353
1063

993
1087
1150
1427

13
10
21
11
10
13
13

1233
1000
1520
1954
2240
2434
1826
1740
1134
1694
1280
1654
1526

in.

4.00
4.25
4.52
4.77
5.10

~90—

Ga
Ppnl

12
10
14
18

Cr
ppn1

1480
1500
1706
1880
2460

SPECTROC HEMICA L ANA LYSES
SECTION 253

x Na K Ca F 8 Mg
in. % O/G % ' 90 (70
23.90 2.15 3.65 0.80 0.34 0.20
23.70 2.83 5.27 0.53 0.29 0.24
23.30 3.10 4.32 0.84 0.37 0.22
22.90 2.38 3.57 0.76 0.32 0.23
22.50 2.83 3.47 0.76 0.26 0.19
22.10 2.85 3.80 0.75 0.34 0.22
21.70 2.87 3.92 0.66 0.34 0.23
21.55 2.20 3.97 0.66 0.35 0.30
21.35 2.74 3.68 0.79 0.44 0.32
21.05 2.37 4.17 0.71 0.37 0.34
20.75 2.36 4.38 0.79 0.32 0.31
20.50 3.05 4.02 0.75 0.35 0.24
20.30 2.65 3.77 0.78 0.47 0.26
19.95 2.73 3.85 0.71 0.45 0.30
19.70 2.10 3.77 0.54 0.32 0.26
19.50 2.41 3.63 0.52 0.35 0.23
19.25 2.53 4.08 0.65 0.35 0.24
19.00 2.63 3.58 0.71 0.33 0.25
18.75 2.28 3.58 0.63 0.32 0.31
18.32 2.75 3.48 n.d. n.d. n.d.
17.89 2.40 3.78 0.69 0.45 0.27
17.47 2.43 4.03 0.51 0.25 0.18
17.05 2.71 5.52 0.63 0.28 0.31
16.63 2.90 3.62 0.83 0.33 0.22
16.21 2.55 4.32 0.54 0.51 0.33
15.79 3.15 4.67 0.49 0.45 0.44
14.84 2.20 3.27 0 72 0.24 0.22
14.54 2.17 3.98 0.58 0.30 0.19
14.29 2.53 3.98 0.62 0.31 0:22
13.79 2.40 4.07 0.61 0.34 0.39
13.39 2.47 3.48 0.65 0.29 0.31
13.04 2.58 3.23 0.62 0.27 0.26
12.79 2.47 2.98 0.96 0.25 0.28
12.44 2.95 3. 2 0.87 0.28 0.23
12.04 2.64 3.57 0.78 0.24 0.18
11.74 2.82 3.33 0.90 0.27 0.19
11.49 2.58 3.68 0.96 0.24 0.17
11.09 2.80 3.48 0.77 0.23 0.21
10.74 2.47 3.80 0.65 0.23 0.24
10.14 2.12 3.27 0.77 0.29 0.21
9 89 2.73 3.38 0.77 0.27 0.20
9.39 2.53 3.30 0.78 0.32 0.25
8.74 2.50 3.15 0.63 0.21 0.15
8.39 2.50 3.03 0.52 0.22 0.20
7.94 2.20 2.97 0.85 0.21 0.14

-91-

H-
33%

O
NU’ICDHQNOOODQDt-‘fimld

C
a>hauo~a

gJCJC) C>C>C1hlhlhibahbbabboaaa¢>OIUIUIG50>OD~J~J
H O O O O O O O l O o O 0 O I 0
tr

0 d
haunhna>h4oa-amura-aoac>~:¢>94a>c>uac><1$:s;

CU‘O‘IWOIOUIUIOCOHNOOQ‘DOHNOO

Na
7;

2.70
3.10
2.80
2.40
2.78
2.73
2.92
2.80
2.83
2.90
2.80
3.33
2.55
3.00
2.90
2.78
3.15
2.83
2.75
2.45
2.67

2.65
2.38
2.63
2.82

2.23
.10
65
.50
.47
.75
.33
.83
.78
.60
.60
.28
.23
.98
.50
.93
.70

NNNNNNNNNNNNNNNW

%;

3.23
3.28
2.98
3.83
4.00
4.70
3.28
3.38
2.65
3.08
2.68
2.92
3.15

2.53

ofil§lfll¢t§h¢
rd-qracncp-a
ca-qtocajacn

1.57
1.78
1.80
1.97
1.80
1.60
1.43
1.32
1,67
1.32
1.48
1.28
1.53
1.53
.30
.37
.38
.23
.1o
.10
.49
.62

P‘h‘h‘h‘h‘h‘h‘h‘

-92-

«was

03010563016301
mono-hasn‘tom

9999999999

0 O ‘C O C I 0 O

omomwqummgpqmqw

NMNNNfi NNNHHHHHHNNHHHOO
o on O 0
mfimNQQMwHCD‘DCDAOIGF-‘QCDNODCDO:

90°C“.

3.17
3.33
.53
.60
.77
.77
.32
75
.15
.73
.95
.77
.77
.62
88
80

.45
.21
.08
.95
1.90

h‘h‘h‘h‘D h‘h‘h‘hihihih‘TOF‘h‘ththbD

0.24
0.17
0.13
0.22
0.26
0.17
0.23
0.26
0.12
0.14
0.22
0.17
0.21
0.14
0.13
0.17
0.21
0.15
0.08
0.10
0.11

in.

8.65

9.40
10.13
10.86
11.59
12.32
13.05
13.78

Na
%

2.83
1.83
2.26
2.22
2.60
2.67
2.43
2.92

1.43
1.12
1.28
1.04
0.94
0.96
1.05
1.08

-93..

<99

010°C”

we

N5NDEOHHN

a".

NGGQ—Ommm

c>= c>a 99999999

Fe
%

.73
.17
.28
.40
.96

96

0.16
0.13
0.14
0.13
n. d.
0.09
n. d.
0.13

23.
23.
23.
22.
22.

22

19

19.
19.
19.
19.
18.
18.
17.
17.
.05
16.
16.
15.
14.
.54
.29
13.
13.
13.
12.
12.
12.
11.
11.
11.
10.
. 14
. 89
.39
. 74
.39
. 94

17

14
14

H
OQQQQCDWCDCDO

90
70
30
90
50

. 10
21.
21.
21.
21.
20.
20.
20.

70
55
35
05
75
50
30

.95

70
50
25
00
75
32
89
47

63
21

84

79
39
04
79

04
74
49
09
74

.19
.84

w
:1:

ppm

P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P P
PPQPPPPPPPQPPPPQPQ“99999999999“PPQPPPQPQPPPPPPFP

O

O
v-s

“o
7::
8

999999999999999999999999999999999999999999999999

O

C

999999999999999999999999999999999999999999999999

-94-

Ti.
ppm

517
427
517
487
480
507
600
437
827
553
633
528
643
760
497
597
473
563
600

nd,

575
457
503
477
740
750
527
600
613
553
630
500
570
410
457
720
410
393
477
473
527
560
243
367
223
307
302
252

3<
a

H

mwooalcowqoowmowmrhoounozoqm

H

5
Q.

19010019.-1quArk-bm-qqcomuhm-qmphooubm-qqmcn-

ppm

227
214
245
153
150
167
190
152
162
150
142
153
168
185
133
145
227
190
170
n.d.
183
162
157
198
215
180
138
138
155
138
170
129
170
162
156
156
150
127
139
184
136
162
338
227
248
202
190
160

.49
.19
.94
.64
.39
.24
.84
.14
.84
.54
.24
.04

.39
.19
.89
.44
.15

COOHHHNNNNDDODQMMU‘QO)

50636)
g. H

.15
.44
.73
.02
.31
.60
.89
.18
.43
.72
.01
.30
.70
.10
.45
.75
.30
.15
.85
.15
.55
.10
.65
.40
.13

OCDGDQQQGamfifihwwWNNNHHHF-‘OOO

H

.74'

U!
m

ppnn

999999999999999999
999999999999999999

46
61
58

62
55
24
30
29
31
42
27
39
29
28
17
50
47
23
25
30
34
38
17
21

C)
H

ppm

999999999999999999

999999999999999999

80
96
77
93
76
77
42

72
56
66
52
56
55
61
53
43
37
29
34
56
64
46
31
38

-95-

Ti
ppn1

380
417
302
497
353
183
242
240
193
222
203
213
172
277
212
n.d.
215
257

1080
1610
1497
1027
1580
1933
417
513
817
733
703
730
800
625
570
425
n.d.
920
593
555
870
750
825
435
450

PP“1

raid
timeTU'IQO'Qfith-PCIQO‘ICDCDQQ

51
69
73
51
66
81
23
38
53
30
37
34
48
4O
51
45

30
19
25
49
56
44
27
33

ppnl

153
153
166
166
158
270
325
400
473
393
360
547
390
467
487
447
510
178

1800
1533
1117
1267
1080
820
593
663
963
747
770
610
520
543
763
660
387
420
243
323
540
630
497
313
387

10. 86
11. 59
12.32
13. 05
13.78

IBa
ppm

24
21
19
25
17

C r
99m

32
31
26
38
31

-96-

T i
ppm

562
n. d.
420
n. d.
380

ppm

29
n.d.
19
n.d.
21

ppm

413
263
309
233
327

23.90
23.70
23.30

Cu

ppm

:3
Q;

N .
mummokmwmozmh-

n.d.

GuhU‘I-J'OOUIOCD

-97-

(3a
ppnn

20
20
22
21
18
26
17
22
16
17
25
19
22
21
19
20
18
19
18

20
22
27
19
21
21
16
16
18
21
17
19
18
21
16
17
18
19
16
17
17
19
22
21
19
26
19
23

Pb
91”“

48
63
62
52
48
64
55
56
41
59
64
53
51
52
51
47
50
48
55

60
68
66
54
56
59
55
40
47
48
48 6
45
4O
55
39
49
38
46
43
47
38
42
49
42
61
59
54
57

5.44

mHWQONCflmI-‘CDNOOGQDHDA

9999~H~N~999999999
Efiwmwkkhfihfififiwfirfiww

CC)
11

Sch

H

.44
.73

02

.31
.60
.89
.18
.43
.72
.01
.30
.70
.10
.45
.75
.30
.15
.85
.15

55

.10
.65
.40
.13

qammcouscpahcoJ-xmmub-

.P
$660119»:me

.44-queen;-

n.d

own.

n.d.

11
11
13
10

-93-

(3a
PPm

19
20
22
18
19
21
21
19
23
21
21
22
18
23
24
17
22
17

20
20
21
20
19
21
18
17
19
19
17
16
16
17
33
24

13
17
22
21
24
21
16
14

Pb
ppm

52
48
6O
47
46
6O
52
54
59
51
48
56
47
55
55
55
47
46

36
34
34
29
30
29
34
28
28
31
28
29
31
28
, 33
29

27
30
36
45
41
42
32
27

in.

10.86
11.59
12.32
13.05
13.78

-99-

(3a
Ppnl

14
n.d.

15
n.d.

20

Pb
PD”[1

27
n.d.
29
n.d.
31

in.

10.86
11.59
12.32
13.05
13.78

Cu

-99-

ppm

10
n.d.

n.d.

Ga
PPm

14
n.d.

15
n.d.

20

Pb
ppm

27
n.d.
29
n.d.
31

APPENDIX B

DATA CURVES

~100—

 

Figure 8. Element concentration distribution
for Section 37

5 '" Granite Schist
4 ..
3 .. Contact ,,

 

24$-

 

|.5T’ Ca

in%

 

N
5 Element concentration %
5 x

at

 

in%

 

 

db
—

 

 

1‘ t
3

i I
4 2 I 0' I 2

0-1-

3
6

Distance from the contact in inches

 

~101-

 

 

 

 

 

 

 

 

 

 

 

 

Figure 9. Element concentration distribution
for Section 37
Granite Schist

.5 'Contact

‘9

E

0

O

C

O

0

E

m

E

2

“J .

I41-

12--

'0“

Bib

l.2-- N

1.1.4 ' Fe

in 76

Lou-

0.9‘r ”

o.e--

o.e+ I

65' I: 2'. 2 i J .' é :5. 4 86
Distance from the contact in inches

 

-102-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure l0. Element concentration distribution
for Section 37
Granite Schist
(oozs) Contact
0.6+-
0.4.? W
0.2.. __ _ _
,(0.069)
0.0l-- I Mn
in 76
o.oo-~ c
.2
4“ E
‘5
3‘9 :3
C
C)
2._ 0
“is;
E
0-1- 5 —JT
o.oe-+ ,’
I “fig
0.07“ in Z
0.06"
0.0515
0.04-1-
: : :1 : : I l : : : : 4
s 5 4 3 21412 3 4 s 6
Distance from the contact in inches

 

-103-

 

 

Figure ll. Element concentration distribution
for Section 37

Granite Schist

 

 

 

 

 

 

 

 

lOOO-p V
300.. in PPM
soc"
400+
zoo4r
eooo~§
‘é
7000+};
O
0
sooo--g Ti
° in PPM
5000"
c.-
2
J-
4ooo 2
m
3000"
20004. ‘
IOOOd- M
+ '9 4 : . 1 L . ,
6 5 4 3 2 I A t E 3

Distance from the contact in inches

 

 

-104-

 

 

 

 

 

 

 

 

 

Figure l2. Elementc concentration distribution
for Section 37
Granite Schist
6°" Contact
.30--
.1. Ni
4° in PPM
' 304-
30'!-
20-- W Go
'0“ W in PPM
0..
3001-
200+
Cu
'00., in PPM
I: M
O
Odin:
E
E
m
0
at. g
40Cl ‘3
3004-
* B
200"? in PPM
32
IOO--m
0.7, W
i i i 1‘ i i i i t i i i
6 5» 44 3 2 l l 2 ES 4 £5 6

 

0

Distance from the contact in inches

 

-lOS-

 

 

 

 

 

 

 

 

 

 

Figure l3. Element concentration distribution
fOV Section 37
Granite Schist
Contact
soc--
Zr
200“ In PPM
1007..
I:
.2
zoo-~95
:5; Zn
5 in PPM
l00'1'o
E
120-...»
E
0
IOOq-[fi
607-
SO-F
409-
Pb
20-- in PPM
l I I 1 1 l I l l L l
l l I I I I I l l T I T
6 5 4 5 2 l l 2 5 4 5

Distance from the contact in inches

 

-106-

 

 

 

 

 

 

 

 

Figure l4. Element concentration distribution
for Section 38
Schist Granite
Contact
5" K
in%
4,--
3.11—
- 8
2 - ._
7 *5
I... 2
I:
0
O
C
O
0
o.e-r-
Ca
0.5-1- "1%
0.4-1- '
0.2-.
o.o-.
E
Q)
S
3 " E] No
2“ 1n%
1.. M
o...
I J 1 1 1 I 1 I 1 1 L 1 1 l
T T l 1 l I T I l l l l T I
161412 864202468l0l2
Distance from the contact in inches

 

 

-107-

 

 

Schist

l .

Figure l5. Element

concentration distribution
Section 38

for

Contact

 

 

 

1
Element concentration

1000‘

800-

6 oo~
M9

400- in PPM

T

2004

V

 

 

Granite

in%

Fe
in %

 

 

l
1
I6 l4 I2 K) 8

Distance from the contact in

 

inches

 

~108-

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure l6. Element concentration distribution
for Section 38
Schist Granite
Contact
6ooo--
noood- Ti
in PPM
20004-
0 ‘7 c:
°______.._._____.._____. __ _
400-9 E
75
200+. o W
C
O
o ‘_ O
E
0
E
2
4ooo4- LU
..- WM Mn
2000“ In PPM
6 0041-
4oo--
20°” W
o ..
J l l 1 J1 1 1 1 .L1 1 l
l l V l J T 1 1 1 I 1
16141210 2 24 6810M
Distance from the contact in inches

 

-109-

 

 

 

 

 

 

 

 

 

Figure l7. Element concentration distribution
for Section 38
Schist Granite
'°°' Contact
so.-
Pb
so
1* in PPM
40¢
Outl- .5
‘9
g ' Ga
0 in PPM
504 8
0
2o-- W
ICLb
0..
E
C)
E
eoo-- 2
11.1 Cu
6004 in PPM
4oo-.
zoo...
o _‘_ 1
l 1 l 1 1 1 I 1 1 1 1 1 1
I f l I F F I l I I l l
l6l4lzI08 42L2468l0l2

Distance from the contact in

inches

 

-110-

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Figure l8. Element concentration distribution
for Section 38
Schist Granite
Contact
I:
.9
‘2
E
2000+ 3
8 'l
l000-- °._ 1
_ T
800-. '1 V
l in PPM
600" 1
4004- I
2009
E
O
E
.9.
111
zoo--
Zr
too--
- in PPM
o .-
3001
200.» n
. MW 51 PPM
1004
1 1 1 1 1 1 1 L I 1 1 1 I 1 l
1 | 1 1 1 r’ | I I I l I l l I
161412106642 468|Ol2

0
Distance from the contact in inches

 

 

-111-

 

 

 

 

 

 

 

 

 

 

 

 

Figure 19. Element concentration Distribution
for Section 38
Schist Granite
M—‘T
60i-
4o.»
.5 Ni
20“ ‘6 in PPM
E
8
C
O
0
1601 E
5
'40-11- m r
120-.
100... i
B
BOT ' in PPM
604. « '
40.- J.
zo-h ' {QM
0.1.
l l 1 l 1 1 I 1 l J l
I j I I l I I l l I I I I I I

Distance from the contact in inches

 

-112-

 

 

concentration

Element

Figure 20. Element concentration distribution
for Section 25I

Schist (I) Granite Schist (2)

Contact l Contact
4 4-

Na
3 .. in X M
2‘. M

Ca
in 76

 

 

 

100-

8.. *V’

 

Fe
in 76

5 $57

 

N
r

 

 

 

 

i
U
I

164
"'7
mm-

01-”-
h-I-

. ‘ K
W” “1%
1.. l
6 3 8 F i J, i

0

Distance from the contact in inches

 

-113-

 

 

Figure 2|. Element concentration distribution
for Section 25I
Schist (I) Granite Schist (2)

[P91101931

#0000"

8000"

:1

6000 4

 

 

40009
Ti ‘
in PPM

I

20004

I

60001

5000--

 

 

4000-1-

Element concentration

3000‘

2000--

 

 

'°°°" in PPM

3000..

 

2000--

Mn

l000- in PPMI

 

$

 

 

Oldi-

2-.
N9-

O_..1_.

0-1

Distance from contact in inches

 

 

 

-114-

 

for Section 25l
Schist (I) Granite
Contact :4 It Contact

 

 

 

Figure 22. Element concentration distribution

Schist (2)

300B
Zr
200+ W in PPM
loo--
0..

C

.2

4—

O

‘-

«.—

C

0

O

C

O

0

E

“e’
2000-. g

m
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-115-

 

 

 

Figure 23.

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Section 25l

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-116-

 

 

 

 

 

 

 

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-121-

APPENDIX C

DIFFU SION THEORY

~122—

APPENDIX C

Diffusion Theory

 

Fick's second law of diffusion can be stated as follows (Jost, 1960):

 

 

2
99:13 at (A.1)
9 l; 2
8x
l.»-.1
where a 2 concentration
t= ime
x 2 distance --
D = diffusion coefficient

Equation (A. 1) assumes that D is a constant. If we look at the system after
diffusion has taken place and there is no further movement of material, then

equation (A. 1) reduces to

2
0:13 a; (A.2)
3x

The solution of equation (A.2) is of the form:
L = (CO + Clx) D (A.3)

Therefore a plot of C versus x should be linear. Since equation (3.4) which
describes C as a function of x in nonlinear, equation (A.3) does not apply
and the assumption of constant D is not valid for this case.

If we assume that D is some function of C (D = f(C)) and since equation
(3.4) defines C as a function of x, C = G(x), then D can be defined as a func-

tion of x, D = D(x), and equation (A. 1) becomes:

—123-

-124--

2 _
Q0 = a c Qngxz) 30
a t 1309 6x2 + 9x ax (AA)
In the system under consideration, a dike intrusive into country rock,

the boundary conditions for equation (A.4) are as follows:

Dike Contact Host Rock

atx=0 atx=0 atx=0
t=O t=0 t=0
C=O1 C=C1 C=02

The system under consideration is further complicated by anisotropy, multi-
ple components, multiple phases and a multiplicity of grains. The solution
of equation (A. 4) under the above conditions has not been reported.

If we look at equation (A. 4) at t = tfinal’ then g9;- = 0, and

2 -
0=D(x) [—36-] + WJ [—3.3%] (A.5)
X

Equation (3.4) describes C = f(x) at t = tfinal' Substituting equation (3.4)
into equation (A. 5) yields:
0 = 31959)- + D(x) [1 - (2be(kx)) Tanh (beam) — bf‘ (A.6)

A solution that fits equation (A. 6) is of the form:
D(x) .—.- ew (A. 7)

where w = G(x)

Substituting equation (A. 7) into equation (A. 6) and solving for (w) yields:

‘125-

x = [(2/k)ln(Cosh(be(kx) - b))] - x (A. 8)
Substituting equation (A. 8) into equation (A. 7) results in:

D(x) = e [-131 ln(Cosh(be(kx) - b):| — x (A. 9)
The solution of D is valid only under the following conditions:

t = t and C = tanh(be(kx) - b)

final

This is because there is no reason to assume that equation (3.4) is a general
solution of equation (A. 5) and also because equation (3. 4) is not valid at

t 7‘ tfinal' A general solution of equation (A. 5) would involve C as a function
of both distance and time, C = F(x, t), and would result in a solution for D
involving distance and time or concentration and time, D = G(x, t) or

D = H(C, t). This solution would also have to take into account the barrier
nature of the contact. A solution for the type of system under consideration

at the present is not possible.

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