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I E

A.)

LIBRARY

THESIS

Michigan State
University

 

 

 

 

 

ROOM USE ONLY

MINOR ELEMENTS IN QUARTZ

by

John J. Kudlac

A Thesis
Submitted to the College of Natural Science
Michigan State University
in partial fulfillment of the requirements
for the degree of

Master of Science

Department of Geology

1965

MINOR ELEMENTS IN QUARTZ
John Kudlac, MJS.

Michigan State University, 1965

Abstract - Twenty-four clear, crystalline quartz samples were analyzed
for their impurity content. It was found that Aluminum is the major
impurity, with Fe, Ti, Mg, Cr, Ca, Cu and Ag present in smaller amounts.

The unit cell dimensions of the samples were also obtained and
were found to vary by a significant amount (aO varied from 4.9058A to
4.90932. and co from 5.393213 to 5.40253).

A plot of the aluminum content versus unit cell dimensions
showed that the dimensions vary with aluminum content; however, no
particular relationship exists.

In plotting the axial ratio versus "increment ratio", it was
found that as the axial ratio increased the "increment ratio" increased.
This suggests that as a0 increases, cO increases. The increase in cell
dimensions is due to the increase in both substitutional and interstitial
impurities. An examination of specific samples showed that an increase
in a0 and Co with increasing impurity content is caused by a proportional

increase in both substitutional and interstitial impurities.

ACKNOWLEDGMENTS

The writer is grateful to Dr. H. R. Stonehouse for sug-
gesting this problem and for guiding the work through its various
phases.

Appreciation is also extended to Dr. J. Zinn and Dr. W. J.
Hinze who critically read this thesis.

The writer would especially like to thank his wife, Patricia

whose patience and fortitude made possible the completion of this

thesis.

II.

III.

IV.

VI.

INTRODUCTION .

A. Background .

CRYSTAL CHEMISTRY OF ALPHA-QUARTZ

TABLE OF CONTENTS

EXPERIMENTAL PROCEDURES

A. Chemical Analysis

B. X-ray Analysis

RESULTS AND DISCUSSION .

CONCLUSION

SUGGESTIONS FOR FURTHER RESEARCH

BIBLIOGRAPHY

PAGE

11

ll

22

34

47

48

49

LIST OF TABLES

TABLE NO. _ PAGE

1. Sample Locality and Description . . . . 12

11. Conditions for Spectrograph . . . . . . 14

III. Dilution Scheme for Standard Mixes . . 16
IV. Spectrochemical Data: Element Sought,

Wavelength of Spectral Line Used and
Minimum Sensitivity Attained . . . . 31
V. Impurity Content in Quartz . . . . . . 35
VI. Unit Cell Dimensions, Axial Ratios and
”Increment Ratios" of Quartz . . . . 37
VII. Ionic Radii of Elements (After Pauling,

1960) . . . . . . . . . . . . . . . 39

FIGURE

10.

11.

12.

13.

14.

15.

LIST OF ILLUSTRATIONS

Clear Z T v/s Absorbed Z T for the Region 2550-
3530 A . . . . . . . . . . . . . . . . . . .

Clear Z T v/s Absorbed Z T for the Region 3850-
4850 A . . . . . . . . . . . . . . . . . . .

Calibration Curve for the Region 2550-3530 A
Calibration Curve for the Region 3850-4850 A
Working Curve for Aluminum . . . . . . . . . .
Working Curve for Iron . . . . . . .

Working Curve for Titanium . . . . . . . . . .
Working Curve for Magnesium . . . . . . . . . .
Working Curve for Calcium . . . . . . . .
Working Curve for Chromium . . . . . . . . . .
Working Curve for Copper . . . . . . . . . . .
Working Curve for Silver . . . . . .
Aluminum Content versus aO . . . . . . .

Aluminum Content versus co . . .

Axial Ratio versus "Increment Ratio"

PAGE

18

19

2O

21

23

24

25

26

27

28

29

3O

43

44

45

I. INTRODUCTION

In this study, twenty-four quartz crystals were analysed for
their minor element content in order to test the validity of Miller's
(1960) conclusion that the electronic configuration of an ion is the
major factor in determining the ability of an impurity to substitute
isopositionally in a given structure. The unit cell dimensions of
the quartz crystals have been obtained in order to determine the
variation, if any, of cell size with impurity content.

A. Background

 

In recent years the behavior of trace elements during the
fractional crystallization of a melt has been the subject of intense
investigation. Goldschmidt (1937) initiated these studies, when he
proposed the following rules governing the distribution of trace
elements among magmatic minerals. He assumed largely that ionic
bonding prevails and that the ion making the larger contribution
to the energy of the crystal structure is prefered.

(1) For two ions to substitute diadochally one for

another in a crystal structure, the ionic radii must not
differ by more than 15Z.

(2) When two ions possessing the same charge, but
different radii, compete for a position in a crystal
structure, the ion with the smaller radius is prefered.

(3) Ions having similar radii but different charges
(of the same sign) may substitute diadochally in a
crystal; in which case the ion having the larger charge
has preference over the ion with the smaller charge.

However, the assumption that ionic bonding prevails in a
crystal structure has been proven to be erroneous. Studies on
bond lengths, bond energies etc. have indicated that, in general,

a bond between two unlike atoms cannot be described as being

purely ionic or convalent, but will be some combination of the
extreme types, or will be a hybrid bond, resonating between the
two extreme forms. One of the classical differences between ionic
and covalent bonding is that where ionic bonding predominates there
are no special restrictions on the bonds and the radius ratio rule
will apply; that is, the particle (ion) position will depend on
relative sizes of the cations and anions. However, the particle
positions, where covalent bonding predominates, are largely deter-
mined by the directional properties of the bond. For example, the
silicon atom forms four bonds directed toward the corners of a
regular tetrahedron. Therefore, it is of importance in analyzing
a structure to know approximately what type of bond exists in
particular minerals.

The extent to which atoms form ionic or covalent bonds
depends largely on two factors: ionization potential and electron
affinity. These two factors are combined into what is known as the
electronegativity of an atom. Pauling (1960) related the difference
in the electronegativity of atoms to the type of bond that will form
between them. Fyfe (1951), using electronegativity as an indication
of bond type, showed that in ionic compounds two atoms will be mutu-
ally replaceable if their sizes are similar, and that in more covalent
compounds, the atoms will be replaceable only if the number and
directional properties of their bonds are similar.

Ramberg (1952) showed that the distribution of metals among

silicates is only partly governed by the size and the charge of the

ions. He states that the substitution of the metals for one another
in silicates is also dependent on the variable electronegativity of
the oxygen in the structure and the position of the metals in the
electronegativity scale. The value of the electronegativity of

the oxygen in the different silicate structures increases stepwise
from the orthosilicates to the tectosilicates.

Shaw (1953) shows, by a theoretical treatment of and an
experimental approach to binary systems, that it is impossible to
predict whether a trace element will be concentrated in early or late
mineral fractions on the basis of ionic radii. DeVore (l953).suggests
that the differences of the polarizing power of the different cations
as related to the polarizabilities of the anions explains the distribution
and fractionation of elements during crystal growth. The ionization
potential of the cations provides the best measurement of the polarizing
power of the cation.

Ahrens (1952, 1953) again stresses the significance of ionization
potentials as a factor in predicting the behavior of elements during the
crystallization of a magma. Ringwood (l955a,b) discusses the influence
of electronegativity and the role of complex formation as factors
governing the distribution of trace elements.

Because silicates make up a great portion of the rock forming
minerals, it is important to mineralogists, petrologists and geo-
chemists to have a better understanding of the crystal structure of the
silicates and the elements occupying specific positions in their frame-

work. W. L. Bragg (1930) outlined the general nature of many crystalline

silicates by means of X-ray diffraction studies. The isopositional
replacement of Ga(III) and Ge(IV) for Al(III) and Si(IV) in sodium
and potassium feldspars was investigated by Goldsmith (1950).

Colemane (1962) synthesized diopsides and investigated the
effect of ionic substitution on their unit cell dimensions. Miller
(1960) studied the effects of Ga, Fe, Cr, Co, and V substituting into
the crystal lattice of ALPO4, which has a close structural similarity
to SiSi04 (°¢-quartz). He concludes, from this investigation, that
the electronic configuration of the ion, and not the ionic radius, is
the principle factor in determining the ability of an impurity to

substitute isopositionally in a given structure.

II. CRYSTAL CHEMISTRY OF ALPHA-QUARTZ

The structural crystallography of quartz was among the first
to be investigated by X-ray methods (Bragg 1914) and received attention
from.many other workers before it was determined by Gibbs (1926). More
detailed studies were subsequently carried out by Wei (1935) and
Machatschki (1936). Quartz has a crystal structure based on an hexa-
gonal lattice. The unit cell, containing three SiOz molecules, has the
nominal dimensions, ao= 4.91311 and co= 5.40511 (Swanson et a1. 1954).

In the structure of quartz, the silicon atoms are in four-fold
coordination with oxygen and make up the Si04 tetrahedra. This unit is
basic to the structure of all the known polymorphs of silica and the
silicates in general. The exception is stishovite where the silicon
atom is octahedrally coordinated. The tetrahedral configuration of the
Si-O bonds is the result of hybridization of the 3s and 3p3 orbitals of
silicon.

Each oxygen, in the quartz structure, is shared with two silicon
atoms. Thus, the Si04 tetrahedra are linked by the sharing of each of
the corner oxygen atoms. The resulting arrangement is a three dimensional
framework. The SiO4 tetrahedra, in quartz, are almost symmetrical, with
a Si-O bond distance of 1.61A. The Si-O bond is of the intermediate type,
roughly 50% ionic and SOZ covalent.

Many workers have found that the cell dimensions of quartz vary
significantly. However, neither the range of variation nor the dimensions
for the pure end-composition have been clearly established. These variations
in lattice parameters have been attributed to the presence of foreign ions,

the presence of lattice defects (vacancies) and the influence of temperature

and pressure at the time of crystallization. Sabatier and Wyart
(1954) found that the physical conditions of crystallization hardly
affected the lattice parameters of synthetic quartz. However, they
were affected by traces of sodium impurities. Keith (1955), on the
other hand, had found that the cell parameters of synthetic crystals,
which had been grown at higher temperatures, were smaller. Keith and
Tuttle (1952) found that the differences of cell parameters were
accompanied by small differences of the arms inversion temperature.
Both variations are probably associated with solid solution of impurity
ions. Kamentsev (1963) employs theoretical arguments to show that the
temperature of crystallization governs the amount of solid solution in
the quartz structure, and hence that the temperature of formation con-
trols the variation of the unit cell parameters. He concludes that
the amount of structural impurities and the unit cell parameters
decrease the higher the temperature of crystallization and thus, it
seems that the unit cell dimensions of quartz would be affected by
the variation in the minor element content.

Quartz, in its chemical composition, is almost 100% Si02.
There is, however, a small range of variation which may be due to a
limited amount of substitution, to small inclusions of other minerals,
or to the liquid infillings in cavities within the quartz. Lithium,
sodium, aluminum and titantium are the principle elements that enter
into solid solution with natural quartz. Magnesium, iron, calcium
and potassium may also be present in significant amounts and a number
of other elements have been reported in smaller quantities. Germanium,

due to the similarity of its ionic radius to silicon% and due to its

position in the periodic table, is one probable element for substi-
tution in natural quartz, but it is generally not found.

Aluminum is the major element to substitute for silicon in
quartz. To compensate for the valence defficiency, small alkali
ions, Li or Na, or both, enter the structure into interstitial
positions. Other possible combinations are: three substitutional
aluminums plus one interstitial aluminum.and two substitutional
aluminums plus one interstitial magnesium. The maximum extent of
the substitution by aluminum in quartz is not clearly established.
The content of aluminum in quartz ranges from 10-500 ppm.

In general, the unit cell volume increases with increasing
amounts of aluminum. According to Cohen and Sumner (1958), the
substitution of aluminum for silicon increases both a0 and co,
although not equally, while the interstitial type of solid solution

mainly expands a Keith and Tuttle (1952) showed that the amount

0'
of aluminum present in solid solution increases with increasing
temperature of formation of quartz as indicated by the variation

in the high-low inversion temperature of samples taken from different
environments. This same increase of aluminum content with increasing
temperature was also indicated by the variation in the unit cell
dimensions of certain samples of synthetic quartz (Frondel and
Hurlbut, 1955; Keith and Tuttle, 1952). These observations seem to
contradict the conclusions drawn by Kamentsev (1963) mentioned previ-
ously. However, neither the numerical relation between the amount

of aluminum in solid solution and the unit cell dimensions nor the

maximum variation in the amount of aluminum or in the unit cell

dimensions have been determined.

Keith (1955) studied the unit cell dimensions of four quartz
samples and their "increment ratios" (Aa/a/Ac/c). In this study,:a
andAc are the differences of a and c between any two samples of
quartz. By comparing these ratios to the ratio of the strain com-
ponents of quartz, he concluded that impurities should cause a stress
in the quartz lattice and thus the parameters and that the effect
should be greatest in the plane normal to the optic axis.

Cohen (1958) using Keith's "increment ratio" made a com-
parison of the cell dimensions reported in his work. Keith's
Brazilian quartz was chosen for comparison purposes as being of low
impurity content. Its cell dimensions are a0= 4.9129A and c6-5.4045A
(25°C). By comparing the "increment ratio", axial ratio, lattice
constants, impurity analysis and color center formation, he concludes
that, as a generallization, cationic impurities in quartz may be

4

substitutional replacing Si+ , or interstitial. He also proposes

rules (generallizations) which may be used to gain information con-
cerning impurities present where "increment ratios" and axial ratios
correlate. The assumptions made are that interstitial impurities mainly
cause expansion of the a axis and substitutional impurities cause
expansion of both axes. The following are the rules:

(1) a low "increment ratio" (V1.5 or less) indicates
the -quartz contains mainly substitutional impurities and
these impurities have radii larger than Si4.

(2) an intermediate "increment ratio" (“1.4 - 1.7)
indicates both substitutional and interstitial impurities
are present.

(3) a high "increment ratio" (>l.7) or lack of
correlation between this and the axial ratio indicates
a high percentage of the impurity is interstitial.

In a later paper, Cohen (1960) studied samples of synthetic
quartz, by x-irradiating them and by beating them beyond the A -tran-
sition temperature and letting them cool to room temperature. From
the results of these experiments he concludes that aluminum may be
incorporated into “-quartz either interstitially or substitutionally
and that the interstitial aluminum may be precipitated. The pre-
cipitate is most likely a lithium aluminum silicate isomorphous with
ls-quartz. Also, he concludes that visible color center phenomenon
in quartz is related to substitutional aluminum impurity but not to
interstitial aluminum.

The alkali elements, compensating for the valence defficiency
of the substituting aluminum, are present in the concentration range
of 3 to approximately 100 ppm. Up to 200 ppm lithium has been reported
for quartz from a pegmatite containing lithium minerals (Stavrov 1961).
However, due to the erratic precision of determinations, the stochio-
metric relations of lithium and sodium with aluminum or other cations
can not be established.

Infrared absorption studies have established the presence of
(OH) in quartz. Since the OH' radical has about the same radius as
0"2 ions, it is assumed that it would substitute for oxygen. In doing
so, the (OH)' radical provides a valence compensation for aluminum and
other trivalent cations. The content of (OH)", which seems to vary in
successive growth zones of the crystal, is not known.

Another significant minor element in quartz of some igneous
rocks is magnesium. However, it generally is present only in amounts
of 1 ppm or less. ‘Magnesium generally goes into six-coordination with

oxygen, and this element may enter substitutional solid solution in

10

quartz in interstitial positions rather than in substitution for
Si in four-coordination. There has been observed in low-quartz,
which was formed by inversion from high-quartz solid solutions,

the coupled solid solution of Mg and Al amounting up to 8ZIMgA1204.
The Mn and Fe content in colorless quartz is relatively small, 1
ppm or less, although variable. The manner in which they are
contained is not known. Rb, Cs, Ca, Ba, Pb, Ag, Sn, Cu, Zn, U,

Cr, Zr, and V have been found in relatively small amounts or in
traces in quartz. Whether these elements are present in solid
solution or as impurities representing solutions entrapped in

cavities or solid inclusions is not known.

III. EXPERIMENTAL PROCEDURE

A. Chemical Analysis

In this study, twenty-four samples of crystalline quartz
were analyzed for their minor element content. Table I gives the
location and description of each of the samples used. The quartz
samples were prepared for analysis first, by washing with aqua
regia, to remove surface contamination. Then they were heated to
800°C for ten minutes and quenched in distilled water at 25°C. By
doing this the samples were broken down and their grinding was
greatly facilitated. After drying in an oven, pieces were picked
from the center of the samples to further guard against surface
contamination. These pieces were then ground to minus 200 mesh in
an agate mortar.

The spectrochemical analysis of the quartz specimens were
made using the Bausch and Lomb Dual Grating Spectrograph with
Applied Research Laboratories, Multi-source Unit, Model A 11,700.
Table II lists the conditions found to be suitable for analysis
of the samples. The photographic plates used for the analyses
were Kodak SA#3 plates. The exposed plates were developed with
Kodak D-19 developer under the following conditions: developer -
3% minutes, stop - 30 seconds, fixer - 8 minutes, wash - 30 minutes.
The above procedure was carried out at 25°C.

Strontium carbonate and tim oxide were used as internal
standards. It was found that a mixture of powders in the ratio of

28 grams graphite: 1.2 grams SrCO3: 0.3 grams SnOz provided the

11

12

Table 1. Sample Description and Locality

 

 

Sample No. Locality Description
J-l Streigag, Silesia Crystal
J-2 White Plains, Alexander Co.,N.C. Crystal
J-3 Hot Springs, Arkansas Cubes cut from crystal
J-4 Herkimer Co., New York Crystal
J-5 Moneta, Virginia Crystalline Mass
J-6 Lincoln Co., North Carolina Crystal Intergrowth
J-7 Albany, Maine Crystalline Mass
J-8 Mt. Omel, Tzechnen, China Crystal
J-9 Placerville, California Crystal
J-lO Pincusion Peak, California Crystalline Mass
J-ll Chimney Rock, California Crystalline Mass
J-12 Crystal Peak, California Crystalline'Mass
J-l3 White Rock Creek, California Crystal
J-l4 Madagascar Crystalline Mass
J-lS Unknown Crystal
J-l7 Green River, Wyoming Crystalline Mass
J-l8 Brejauba, Minas Geraes, Brazil Crystal
J-l9 Corintho, Minas Geraes, Brazil Crystal
J-2O Hot Springs, Arkansas Crystal

13

Table I. (Continued)

 

 

Sample No. Locality Description
J-22 Cactus Mine, Utah Intergrown Crystals
J-25 Rodrico Silva, Brazil Crystal
J-26 Albany, Maine Crystal
J—27 Murfrisboro, Arkansas Crystal

J-28 Arkansas Crystal

14

Table 11. Conditions for Spectrograph

 

Quartz Samples Iron Rods
Conductance Low Voltage-Interrupted Low Voltage-Interrupted
Voltage 250 volts 250 volts
Current - -
Resistance 40 Ohms -
Inductance 360 360
Capacitance 50 20
Filter No. 3 1
Transmission 100% 100%
Wavelength 2550-3530 A 2550-3530 R

3850-4850 A 3850-4850 K

Time 10 Seconds 5 Seconds

15

best constancy of intensity of the lines corresponding to Sr and
Sn. To obtain a complete and even burning of the quartz powders,
a mix of 2.5 grams of graphite and internal standard mix and 2.0
grams of quartz powder was used. A homogeneous mix was obtained
by grinding graphite mix and quartz powder under alcohol in an
agate mortar. The alcohol was then allowed to evaporate. The
resulting mixture was then packed into the craters, 3/16" deep
and 1/4” diameter, of Spectrographically pure graphite electrodes.
The chemicals used for standards were Johnson Matthey and
Co. Spectrographically Standardized Substances except for LiC03,
Ti02, Cr203 and Ag20, which were Baker Analyzed Reagents (99.7%
pure). A base mixture of standards plus silica was made up which
contained one-tenth of a percent of the following elements: Al,
Li, Na, K, Fe, Ti, Mg, Ca, Cr, Cu, Ge and Ag. The dilution scheme
used is illustrated in Table III.
To construct the calibration curves for the two wavelength
regions used in this analysis, the method described by Harvey (1950)
was employed. First, a preliminary curve is constructed by plotting
data as clear filter transmission versus absorbed step transmission.
In this case, the data was obtained from iron lines of differing
densities. The clear transmission of a particular line is measured,
then the corresponding absorbed step transmission of the same line

is measured. Thus data is obtained which may be plotted as mentioned

above. The percentage of light absorbed (30Z) need not be known for

l6

mm3 Noam .aonH

.mswuw m.N ou xflE men wawun ou powpm

.pasoaaoo umHDoHuumm osu aw ucoEmao onu mo HouUMM owuuoefi>muw map on wcflpuooom

uso 0o£wHoS ouo3 .pocfiauouop on on mucoamao ecu casuaoo now£3 .mpasomeoo onu .¢ xflz cflmuno oak

 

 

0m.H 0mH000.0 05000.0 0m.0 m¢.0 H mo m0.0 0
m0.mH mom~00.0 mNHm00.0 0N.0 0H.0 3 «0 H.0 H
mN.Hm mNHm00.0 m~000.0 0N.0 0H.0 0 mo H.0 m
m.m0 mm000.0 mNH0.0 0N.0 0H.0 m 00 H.0 0
mNH mNH0.0 mN0.0 0N.0 0H.0 a mo H.0 m
NwH NOH0.0 H.0 mm.0 m¢.0 < mo H.0 m
0mm 0m~0.0 mN.0 0.H m.0 m mo m.0 Q
mmm mmm0.0 N.0 0.0 0.0 < m0 «.0 0
00m no.0 m.0 0.H m.0 < mo m.0 0
000a H.0 m.~ u . «m.~ <
AmeHU nuoH xv Amfimuwv N AmEmHUv Amemuwv
unoeoao mo and uaoewao mo N uawwoz Hmuou cw unwfioz.amuoa 0wm mo unwwoz xflz mo uswwmz xflz

unmewao mo unwwoz

means 38:83 40.4. season .8338 .HHH Bees

17

this step of the procedure, but is needed for the next step. Figures
1 & 2 are the preliminary curves for the regions 2550-3530A and 3850-
4850A respectively.

The data from the preliminary curves is now transferred to an
intensity (1) versus transmission (density) plot which is constructed
on 2 cycle log/log graph paper. This is accomplished by arbitrarily
selecting some clear step transmission value, from the preliminary
curve, and giving it a value of I= 1.0. The corresponding absorbed
step transmission value is then assigned a value of I =0.3 (the step
filter used had an absorption value of 30%). For example, to con-
struct the curve in Figure 3, a clear transmission value of SOZ from
Figure l was selected as I= 1.0. Consequently, the absorbed trans-
mission value of 23% is plotted as I= 0.3. Then, 23Z of clear trans-
mission is selected as I =l.0, etc. To go in the opposite direction,
SOZ absorbed transmission is selected as I= 0.3 and, therefore, 76%
clear transmission has I: 1.0. Figure 4 is the calibration curve for
the region 3850-4820 A.

Few points are thus obtained when a preliminary curve is used,
but the validity of the points has been well established since any
random scatter has already been compensated for in drawing the pre-
liminary curve. An advantage in using this method is that the inten-
sities of the iron lines used need not be known.

To construct the working curve for a particular element, the
density of the line corresponding to the particular element and the

density of the line corresponding to the internal standard is obtained.

 

 

100 r
80 -
60,. "
Clear Z
Trans-
mission '
40 r
20 .
0
1 l 1 l l
0 20 40 60 80 100

Absorbed Z Transmission

Fig. 1 Clear Z T v/s Absorbed Z T for the Region
2550-3530A.

l8

 

>uwmcouaH

9N o; no no
a . _ _

.mOmmMnommN cowwom can now o>udo aowuounwamu m .mwm

N.0

 

0H

xuwmcon

0m

0m

Om

00H

hufimcoucH
0.H “.0 m.0 m.0

H

0

 

 

4 _ a _

.mOmwe-omwm nonwom you o>eoo coaooeeafioo e .wam

 

0H

om

0m

0m

00H

huwmcom

1
2

22

These densities are then converted to intensities by means of the
calibration curve. Then, the ratio of the intensity of the parti-
cular element line to the intensity of the internal standard line
is plotted against the concentration of the particular element.
The plotting is done on 2 cycle log/log graph paper. The three
points for each concentration value corresponds to the three samples
of each standard mix which were run in order to provide a repro-
ducibility check. Figures 5, 6, 7, 8, 9, 10, 11 and 12 are the
working curves for Al, Fe, Ti, Mg, Ca, Cr, Cu and Ag respectively.
Table IV lists the particular line used for the analysis of each
element. A working curve was not constructed for Ge, since it
was not detected in any of the samples. The density readings
were made on the Jarrell-Ash "Recording Microphotometer", Model
No. JA-203.

The accuracy of the analyses ranged from 1.5 - 5.2Z. The
precision ranged from 3.1 - 6.6%. The error due to microphoto-

metric readings is approximately 1 - 2Z.

B. X-Ray Analysis
The measurements of the unit cell dimensions of the quartz
samples were made on powders using a General Electric XRD-S dif-
fraction unit. The following conditions were used: Cqu radiation,
scanning speed of 20 per minute, time constant of 4 seconds, slit
width of 1°, collimating slit of 0.20, 50 Kv voltage, 16 ma amperage

and a double nickel foil filter.

1000 r-

700

500 '-

300 *-

ppm A1

100 "

30 -

 

10
0.3

1 1 .J
0.5 0.7 1.0

I A1 3082
I Sn 3141

Fig. 5 Working Curve for Aluminum

23

5

 

.0

7.

0

1000

700

500

300

ppm Fe

100

70

50

30

10

 

 

 

I Fe 3020
I Sn 3141

Fig. 6 Working Curve for Iron

24

r.
_' /
p.
/
/
/
J I l L L
0.3 0.5 0.7 1.0 3.0 5.0 7.0

1000

700

500

300

ppm Ti

100

70

50

3O

10

 

 

 

1.
+-
/
l
/
/
/
/
I I IAL I .L
0.3 0.5 0.7 1.0 3.0 5.0 7.0
I Ti 3372
I Sn 3141

Fig. 7 Working Curve for Titanium

25

1000 *-

700"

500'—

300

ppm M8

100 F”

70 -'

 

30 -'

 

10 I I 1
0.3 0.5 0.7 1.0
I Mg 2852
I Sr 2931

Fig. 8 Working Curve for Magnesium

26

1000 r

700 "

500 "

300 r'

ppm Ca

100 —'

30 h

 

10
0.3

 

1 Ca 4300
I Sn 4524

Fig. 9 Working Curve for Calcium

27

1000 F

700 ’

500 '

300 ”

ppm Cr

100 _'

70

50 F‘

30 '

 

10
0.3

 

I Cr 4255
I Sn 4524

Fig. 10 Working Curve for Chromium

28

1000 '

700 -

500 5'

300 "

ppm Cu

100 "

50 F

30 _'

10

 

0.3

 

I Cu 3273
I Sn 3141

Fig. 11 Working Curve for Copper

29

1000

700

500

300

ppm A8

100

70

50

30

10

 

 

 

I
J I I I L
0.3 0 5 0.7 1 0 3.0 7.0
I Ag 3280
I Sn 3141

Fig. 12 Working Curve for Silver

30

Table IV.

Spectrochemical Data: Element Sought,

Wavelength of Spectral Line Used and

Minimum Sensitivity Attained

31

 

 

Element Line Used Detection Limit
Aluminum 3082A 30 ppm
Iron 302021 30 ppm
Titanium 3372.3. 30 ppm
Magnesium 2852A 30 ppm
Calcium 4300A 15 ppm
Chromium 42553. 15 ppm
Copper 32733. 30 ppm
Silver 3280A 30 ppm

32

Angular values of 29 read to the nearest 0.010 were obtained,
by mannual scanning, for the peaks which represent the following
crystallographic planes: 331, 420, 315, 421, 324 and 216. These
peaks which occur in the 29 region, 1430 to 159°, are sharp, well
defined and of high intensity. In this high angle region, the
doublets are well resolved, thereby minimizing any error due to
misidentification. Corresponding "d" values for the measured
reflections were obtained from the Tables of Interplanar Spacings
For Angle 29 contained in the instruction manual for the above
mentioned diffraction unit.

The unit cell dimensions of each sample of quartz were
calculated from the measured interplanar spacings using the least
-squares scheme outlined below.

From the equation

1- = 4 (h2+ k2+hk) + 12
dz 3 a4 :2

where d interplanar spacing; h,k,l,= Miller indices and a and c
are the cell edges, the equation

2: XcL-r ya (1)
was obtained in which 2 = l/d2,o(= l/a2,,s =l/c2, x= 4/3(h2k§hk)
and y = 12-

Multiplying eq. 1 first by x and then by y and then
rearranging, equations 2 and 3 result.

axza-pxy - xz = 0 (2)

ny-o-fiyz - yz =0 (3)

33

Therefore, for a series of measurements,

M2142; *F" E )Eyt —- EXC zé : O (4)
C L c
and
“me +8322} 222. =0 <5)
( c‘ 6.

Values for equations 4 and 5 were obtained for each set
of data, that is, the interplanar spacings corresponding to 331,
420, 315, 421, 324 and 216 for each sample. Then the equations
were solved simultaneously for o( and@., from which a() and c0 could
be determined quite easily.

Two factors contribute to the error involved in the x-ray
analysis: sample preparation and the measurement of 20. In
calibrating the diffraction unit with a novaculite plate, it was
found that within the region 1430 to 1590, the peak positions could
be reproduced, on an average, to within 120.030. The error due to
sample preparation may be attributed to the differences in the
thickness of the powdered sample from slide to slide. The error
was checked by making five slides of one sample, taking their x-ray
diffraction patterns and measuring the peaks used above. The
change in peak position in relation to the original sample were then
computed and an average value obtained. This value was 310.030.
Combining this value with that above, a maximum error is obtained
due to both factors, that is, 1 0.060. In terms of unit cell
dimensions, this error in the 29 value produces an error of 2:0.0007A

in a0 and an error of i 0.0008A in co.

IV. RESULTS AND DISCUSSION

The twenty-four samples of quartz studied showed a wide
range of impurity content and unit cell dimensions (Tables 5 and
6). Aluminum, with a concentration range of 120-550 ppm, is the
major impurity in quartz. ‘Magnesium has a range of less than 10 to
63 ppm; titanium ranges from less than 10 to 42 ppm; calcium.ranges
from less than 10 to 55 ppm; iron ranges from less than 10 to 50 ppm
and chromium ranges from less than 10 to 20 ppm. The least abundant
impurity ions are copper and silver. Copper is presnet in the amount
of less than 10 to 21 ppm and silver content is less than 10 ppm for
all samples. Both copper and silver may be present in inclusions.

That aluminum is the major impurity ion in quartz may be
explained to its similarity to silicon. The small size of the
silicon ion rules out extensive substitution by quadrivalent ions
such as titanium, zirconium, tin, thorium and uranium. (Table 7
lists the ionic radii of some of the elements of interest.) All of
these ions are considerably larger in size than silicon and generally
go into higher coordination with oxygen. Titanium, the smallest of
these ions, is present in limited amounts in colorless quartz, as
reported above. The presence of titanium may be due to the inclusion
of minute crystals of rutile, Ti02. The higher polymorphs of ‘K-quartz
may contain titanium in larger amounts. In stishovite, where silicon
is in six-fold coordination with oxygen, we might expect the largest
amount of titanium substitution. However, since stishovite is formed
from preexisting quartz by means of shock, the titanium content would

be that of the original quartz.

34

35

Table 5. Impurity Content in Quartz

 

 

Sample No. Concentration (ppm)

Al Fe Ti Mg Cr Ca Cu Ag
J-l 123 44 <10 33 20 21 <10 <10
J-2 127 28 <10 60 nd 10 <10 (10
J-3 120 44 (10 34 nd <10 <10 <10
J-4 510 32 (10 63 <10 <10 <10 <10
J-5 300 29 <10 10 <10 55 <10 <10
J-6 295 44 17 48 17 <10 <10 <10
J-7 420 29 17 12 <10 16 <10 <10
J-8 295 45 20 34 <10 21 <10 <10
J-9 415 35 (10 10 16 15 21 (10
J-lO 420 36 42 32 (10 10 16 <10
J-ll 310 32 25 20 <10 26 16 <10
J-12 400 48 21 24 <10 13 11 <10
J-13 170 31 21 27 <10 <10 11 <10
J-14 345 33 18 22 <10 12 ll <10
J-15 380 35 37 30 <10 10 14 (10
J-l7 370 44 33 49 <10 12 10 <10
J-l8 200 <10 <10 <10 <10 12 <10 (10
J-l9 500 <10 <10 <10 <10 <10 <10 <10

J-20 550 31 10 17 <10 10 <10 <10

36

 

 

Table 5. (Continued)
Sample No. Concentration (ppm)
A1 Fe Ti Mg Cr Ca Cu Ag
J-22 385 15 <10 <10 410 23 <10 <10
J-25 250 <10 <10 23 410 <10 <10 <10
J-26 420 30 <10 31 <10 <10 <10 <10
J-27 280 50 12 33 (10 <10 <10 <10
J-28 370 40 13 29 <10 <10 <10 <10

37

Table 6. Unit Cell Dimensions, Axial Ratios and
"Increment Ratios" of Quartz

 

 

Sample No. ao cO c/a aa/a/Ac/c
J-l 4.9064 5.3994 1.1005 1.4444
J-2 4.9081 5.3994 1.1001 1.1111
J-3 4.9093 5.3947 1.0989 0.3889
J-4 4.9075 5.3932 1.0990 0.5238
J-5 4.9058 5.3986 1.1005 1.2727
J-6 4.9087 5.4017 1.1004 1.8000
J-7 4.9087 5.3963 1.0993 0.6000
J-8 4.9087 5.3978 1.0996 0.7500
J-9 4.9064 5.4010 1.1008 2.1667
J-lO 4.9081 5.3986 1.0999 0.9091
J-ll 4.9070 5.3994 1.1003 1.3333
J-12 4.9075 5.3994 1.1002 1.2222
J-13 4.9087 5.3986 1.0998 0.8182
J-l4 4.9075 5.3978 1.0999 0.9167
J-lS 4.9093 5.4017 1.1003 1.4000
J-17 4.9075 5.3994 1.1002 1.2222
J-18 4.9093 5.4002 1.1000 0.8750
J-19 4.9070 5.4025 1.1010 3.0000
J-20 4.9093 5.4010 1.0002 1.1667

38

Table 6. (Continued)

 

 

Sample No. aO co c/a aa/a/ac/c
J-22 4.9075 5.4017 .1007 2.2000
J-25 4.9070 5.3978 .1000 1.0000
J-26 4.9081 5.4017 .1006 2.0000
J-27 4.9087 5.4010 .1003 1.5000
J-28 4.9081 5.4002 .1003 1.2500

Table 7.

Ionic Radii of Elements
(After Pauling, 1960)

Crystal

0.

0

39

Radii (2.)

41

.50

.53

.68

.80

.71

.02

.97
.65

.99

.52

.64

40

Another quadrivalent ion close in ionic size to silicon
(0.41A) is germanium.(0.53A). Since germanium has a similar ionic
radius to that of silicon and has the same charge as silicon, an
extensive substitution of germanium for silicon might be expected.
Germanium has been introduced into solid solution is synthetic
quartz up to amounts in the range of 0.3Z (Stanley and Theokritoff,
1956; Frondel and Hurlbut, 1955). However, it has been found to be
lacking in the natural quartzes analyzed in this study. The factors
contributing to the scarcity of germanium in quartz are (l) the
great difference in crustal abundance between silicon (277,200 ppm)
and germanium (2 ppm) and (2) the relatively high solubility of
germanium compounds.

As was mentioned above, aluminum is the major impurity ion
in quartz. This is due to the similarities between the silicon ion
and the aluminum ion: (1) the ionic radii are similar, Si+4='0.4lA
and Al+3= 0.50A and (2) the two ions are isoelectronic. Two ions
are isoelectronic when they have the same electronic configuration;
either that of an inert gas in which the outer shell contains eight
electrons, or that of a psuedo-inert gas structure in which the outer
shell contains eighteen electrons. Another similarity is that the
radius ratio of each of these elements to oxygen, Si/O =0.292 and
Al/O =0.357, is within the range of values for tetrahedral coordi-
nation (0.225-0.4l4). Although the aluminum to oxygen ratio is
close to the critical value for octahedral coordination, Al is found

six-coordinated in silicate minerals, but may also substitute for

41

silicon in four-coordination. While the substitution of aluminum
for silicon may be extensive in other silicates, it is rather
limited in quartz. This is due to the limitations put on the
opportunities for valence compensation of the trivalent ion by
the simple composition and the relatively tight crystal structure
of quartz.

The deficiency of valence brought about by the substitution
of aluminum for silicon may be satisfied by either the coupled
entrance of a small monovalent ion, sodium potassium and/or lithium,
into interstitial positions or by the coupled substitution of (OH)
for oxygen. As has been mentioned previously, OH‘ has been found
in quartz, however, the amounts present are not known. The con-
centrations of Li, K and Na were not determined in this study since
the sensitivity of the infrared film used was not adequate to detect
the maximum amount of these elements in the standards (1000 ppm).
However, they should be present, theoretically, in the amounts equal
to that of the aluminum and other trivalent ions present. The dis-
crepancies that arise here may be due to defect structures, the
presence of three interstitial aluminums for one substituted alumi-
num and the substitution of (OH) for oxygen.

The manner in.which iron, calcium and chromium are contained
in quartz is not known. Their presence in the samples analyzed may
be due to solid inclusions or contaminations. The substitution of
magnesium in interstitial positions in quartz has been discussed

previously.

42

Table 6 shows that the unit cell dimensions of quarts are
variable; a0 varies from 4.9058A to 4.9093A and co varies from
5.39321 to 5.40251. This is a variation of one part in 103 for
both parameters, which is consistent with the work of Keith and
Tuttle (1952). The variation of lattice parameters and impurity
content substantiate the conclusions of Keith and Tuttle (1952)
and Keith (1955) concerning the dependence of the variation of
lattice parameters on the presence of impurity ions. However,
the manner in which the impurity ions affect the variation in
lattice parameters has not been confirmed. In an attempt to
clarify the manner of variation, the aluminum content of the
quartz samples was plotted versus the unit cell dimensions, a0
and co (Figures 13 and 14). An examination of these plots shows
that there is no relationship except that the unit cell dimensions
do vary with impurity content.

Also, the cell parameters of the twenty-four quartz sam-
ples were compared to Keith's Brazilian quartz mentioned previously
and the "increment ratios" and axial ratios were calculated (Table
6). A plot of the axial ratio versus the ”increment ratio" (Figure
15) shows a correlation between them, that is, as the axial ratio
increases so does the "increment ratio". This would seem to suggest
that both cell parameters increase with impurity content, although
unevenly. Using Cohen's rules, it was found that most of the sam-

ples contain substitutional impurities, the main impurity being

(A)

4.910

4.909

4.908

4.907

4.906

4.905

T

 

 

 

 

 

I
5 Error = 2: 0.00075.
V
1 1 l I L
100 200 300 400 500
ppm Al

Fig. 13 Aluminum Content versus a0.

43

(A)

.403

.401

.399

.397

.395

.393

 

' Error: 2 0.00083. ‘

I

 

1 I I I I
100 200 300 400 500
ppm Al

Fig. 14 Aluminum Content versus c0.

44

0.N

.:owumm ucoeouoaH: mamuo> oHumm Hmwx< ma .wwm

N.N m; a; o;

0

0

 

N.0

 

me.H

000.H

00H.H

HOH.H

N\U

45

46

aluminum. Three samples, 1, 15 and 27, have an intermediate
”increment ratio" and therefore contain both substitutional and
interstitial impurities. A high percentage of interstitial
impurities are present in samples 6, 9, 19, 22 and 26 since
their "increment ratios" are greater than 1.7.

An examination of the axial ratios of the latter five
samples show that they increase with increasing "increment ratios”
and also with increasing aluminum content. This would seem to
suggest that, although a0 is increasing more than co is increasing,

indicating an increase in interstitial impurities, the increase in

Co indicated an increase in the amount of substitutional impurities.
Therefore, it might be concluded that as the aluminum content
increases, both the amount of substitutional and the amount of
interstitial impurity increases proportionately.

If the axial ratios and increment ratios of samples 12,
17 and 20 are examined, it is found that the former ratios are
equal and the latter ratios are essentially equal. However, their
lattice parameters increase as the aluminum content increases. This
also would suggest that the substitutional and interstitial impurities

increase proportionately with increasing impurity content.

V. CONCLUSION

 

(1) Aluminum is the major impurity in natural, color-
less quartz. Also present as impurities are Fe. Ti, Mg, Cr, Ca,
Cu and Ag. These impurities may be either substitutional or
interstitial. The substitution of aluminum for silicon seems
reasonable in View of the fact that they have similar ionic
radii and are isoelectronic.

(2) The unit cell dimensions of quartz show a wide
range of variation and this variation is due to impurity con-
tent. A plot of the axial ratios and the "increment ratios"
showed that one increased with the other, suggesting that as
aO increases co increases. This is attributed to the fact that
both interstitial and substitutional impurities are present in
quartz. However, substitutional impurities predominate in the
greater majority of quartz.

(3) An examination of specific samples showed that an
increase in a0 and co with increasing impurity content is caused
by a proportional increase of substitutional and interstitial

impurities.

47

VI. SUGGESTIONS FOR FURTHER RESEARCH

1. All the samples used in this study were of hydro-
thermal origin. Thus, it might be said that the curve in Figure
15 is indicative of quartz which grew at a certain temperature
or within a certain temperature range. Therefore, a study of
quartz which grew within different temperature ranges might
produce curves of a different nature.

Also, the quartz samples used were colorless. There-
fore, a study of other types of quartz, i.e. smoky, rose or
amethyst, might also produce curves of a different nature than
that in Figure 15.

2. Analysis of the precipitate obtained from colorless
quartz on heat treatment and the clear portion to determine the
amount of substitutional and interstitial impurities; aluminum
and lithium and/or sodium.

3. The study of other minerals to determine the effects
of impurities on unit cell dimensions and other properties.

4. A study of many more quartz samples to determine

statistically the limits of substitution of impurities.

48

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MIC E

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