Indian Journal of Radio & Space Physics
Vol 37, February 2008, pp 57-63
Dielectric properties of some minerals of western Rajasthan
R J Sengwa*,1 & A Soni2
1
Dielectric Research Laboratory, Department of Physics, J N V University, Jodhpur 342 005, Rajasthan, India
2
Well Logging Services, Oil and Natural Gas Corporation Limited, Rajahmundry 533 106 (AP), India
*Email: rjsengwa@rediffmail.com
Received 10 May 2006; revised 9 July 2007; accepted 10 October 2007
Dielectric constant ε′ and loss ε′′ of dry samples of clay, siliceous earth, fuller’s earth, gypsum, lignite, calcite,
tourmaline and magnesium rock of opencast mines of western Rajasthan, India, were studied in the frequency range 100 Hz
- 100 kHz and also at X-band microwave frequencies. It is observed that the values of ε′ decreases with increase in
frequency in low frequency region. Exceedingly high ε′ values were found for clay, siliceous earth and, fuller’s earth at
lower frequencies in the 100 Hz to 100 kHz frequency range. The complex plane plots (ε′′ versus ε′) of these minerals are
the Cole-Cole arcs. The low frequency limiting dielectric constant εo, high frequency limiting dielectric constant ε∞,
relaxation time of dipole rotation τ and, distribution parameter α of these materials were determined using the Cole-Cole
plots. All these minerals have large value of α, and their τ values varies in the range from ≈ 0.1 to 11 ms. Frequency
dependent ac conductivity of these minerals has been determined and discussed and, the contribution of sample bulk density
and percent weight of the constituents of their chemical composition on the microwave values of ε′ and ε′′ has been explored
for the studied samples.
Keywords: Minerals, Dielectric constant, Dielectric dispersion, Conductivity
PACS No.: 78.20.Ci, 84.40.Xb, 91.60.Pn
1 Introduction
The measurements of dielectric constant ε′ and loss
ε′′ of minerals and rocks over wide frequency range
have remained the subject of several investigations1-8.
Geologic materials exhibit complex dielectric
responses in low frequency region, i.e. 10–3 - 106 Hz.
The complex dielectric responses of these materials can
be represented by empirical models, in which the real
and imaginary dielectric responses have fractional
power law dependencies upon frequency9-11. In case of
rocks and minerals, due to samples bulk density
variation or variations in the chemical composition and
crystalline structure among mineral constituents, there
may be significant variability among measurements
made for a given rock sample of the sample’s spatial
inhomogeneity. The effect of microstructure on the
electrical properties of heterogeneous systems is an
issue of great interest for both fundamental and applied
research. Therefore, it is interesting to characterize the
dielectric properties of the rocks and minerals of
different areas in low frequency region to comprehend
their behaviour of induced polarization.
The dielectric properties of rocks and sediments are
primarily a function of mineralogy, porosity, water
saturation, frequency, and depending on the rock
lithology, component geometries and, electrochemical
interactions3,5,7,8,12. Above 1 MHz frequency, there is
small variation in the frequency dependent ε′ values
of dry rocks and minerals. In microwave frequency
region, i.e. 1-100 GHz, most of dry geologic materials
have almost frequency independent values of ε′.
Therefore, the precise dielectric study of rocks and
minerals in high frequency radio waves or at
microwave frequencies is required for their use in
planning ground-penetrating radar surveys8,13-15. In
microwave remote sensing16,17 and in calibration of
time domain reflectometry measurement18-20.
In the present paper dielectric properties of
different minerals of opencast mines of western
Rajasthan have been reported in the frequency range
of 100 Hz - 100 kHz and also at 10.1 GHz. The
purpose of this study in 100 Hz – 100 kHz frequency
range is to understand the complex dielectric
dispersion and electrochemical polarization behaviour
of these minerals of different chemical composition.
The need of 10.1 GHz precise dielectric measurement
is their use in support of radar investigations. Eight
soil and rock samples, i.e. clay, siliceous earth,
INDIAN J RADIO & SPACE PHYS, FEBRUARY 2008
58
fuller’s earth, gypsum, lignite, calcite, tourmaline and
magnesium rock sample were collected from the
opencast mines of different areas of western
Rajasthan for their dielectric study. These samples
and their locations along with latitude and longitude
and chemical composition are presented in Table 1.
All the samples were chemically analyzed with the
standard gravimetric and titrimetric procedures.
2 Experimental details
2.1 Sample preparation for dielectric measurements
The thin sections of each sample were cut by a
diamond wheel cutter to obtain thin plates of
thickness
~0.14 cm and of dimensions
(1.225 cm × 1.474 cm) and polished to get smooth
surfaces in order to ensure good electrical contact.
Silver plated brass plates were used for the fabrication
of parallel plate capacitors with sample section as
dielectric for their dielectric measurements in the
frequency range 100 Hz - 100 kHz. For microwave
frequency dielectric measurements two different
length (~ 1.4 cm and 0.9 cm) and X-band wave-guide
dimensions (2.286 × 1.016 cm) sections of each
mineral sample were prepared from the same block.
The prepared sections of the samples were dried by
heating above 120°C using hot plate drying system.
2.2 Dielectric measurements
The values of ε′ and ε′′ of these minerals, in the
frequency range 100 Hz - 100 kHz, were determined
by measuring the capacitance and dissipation factor of
parallel plate capacitor with each sample section as
dielectric using indigenous designed dielectric
measurement cell for solid samples with automatic
Keithley LCZ meter (model 3330). The values of ε′
and ε′′ at 10.1 GHz were determined employing the
short-circuited rectangular wave-guide set up
operating in TE10 mode21-23. The sample length
variation method (two point method) was used for the
measurement of the shift in minimum for sample with
reference to the shorted end without sample. The
measured values of shift in minimum and the voltage
standing wave ratio of the two different lengths’
sections of each mineral were used to evaluate the
values of ε′ and ε′′ at 10.1 GHz. The experimental set
Table 1 Weight percent of different oxides in the chemical composition of the minerals of western Rajasthan
Sample Mineral
No.
(location)
(latitude longitude)
1
2
3
4
6
7
8
5
Clay
(Falka Falki-Jetaran
Pali)
(26°24′ 73°56′)
Siliceous earth
(Bariyara-Barmer)
(26°26′ 71°04′)
Fuller earth
(Bharkha-Barmer)
(26°00′ 71°23′)
Gypsum
(Mohangarh)
(27°15′ 71°15′)
Calcite
(Beawer)
(26°06′ 74°24′)
Tourmaline
(Beawer)
(26°06′ 74°24′)
Magnesium rock
(Beawar)
(26°06′ 74°24′)
Lignite
(Giral-Barmer)
(26°04′ 71°16′)
*LOI is the loss on ignition
SiO2
CaO
MgO
Fe2O3
Al2O3
74.24
0.56
0.30
0.11
16.57
8.03
86.70
1.96
0.20
1.05
6.01
3.80
50.44
0.70
4.53
5.90
22.78
1.6
33.10
0.08
0.3
0.5
20.76
0.66
54.88
0.10
0.06
0.48
43.17
34.72
1.00
1.40
15.8
25.95
33.90
16.80
12.0
4.7
2.70
Fixed carbon
38.85
Volatile matter
48.95
Ash
11.19
Na2O
1.88
0.52
K2O
TiO2
1.11
1.19
LOI*
SO3
12.81
0.10
19.54
0.05
28.90
Moisture
1.04
43.65
Total sulphur
3.05
SENGWA & SONI: DIELECTRIC PROPERTIES OF MINERALS OF WESTERN RAJASTHAN, INDIA
59
Frequency dependent ε′ values of the studied
minerals are depicted in Fig. 1. In all the figures,
numbers 1, 2, 3, 4, 5, 6, 7 and 8 are allotted to
represent the clay, siliceous earth, fuller’s earth,
gypsum, lignite, calcite, tourmaline and magnesium
rock sample, respectively. The same sample numbers
have been used in the tables also. Figure 1 shows that
the ε′ values of these mineral samples decrease with
the increase in frequency in the range
100 Hz - 100 kHz. The low frequency dispersion of
dry samples is believed to be due to polarization
associated with charge build up at grain boundaries or
at grain imperfections of the sample heterogeneous
particles of different-value dielectric constants and
conductivities. Further, the contribution of grain sizes
and their distribution are also important factors in
controlling the ε′ values5,25. The ε′ values of clay,
siliceous earth and fuller’s earth are plotted on log
scale in Fig. 1. The comparatively high ε′ values of
these soft minerals in comparison to those of other
minerals show that there is large grain induced
polarization with different geometric microstructure
of heterogeneous system of clay, siliceous earth and
fuller’s earth. Figure 1 also shows that the dielectric
constant of calcite has very small low-frequency
dispersion.
Figure 2 shows the variation of loss tangent (tanδ =
ε′′/ε′) against frequency of these dry minerals. High
Fig. 1Variation of permittivity ε′ with frequency of the dry
minerals (1–clay; 2–siliceous earth; 3–fuller’s earth; 4–gypsum;
5–lignite; 6–calcite; 7–tourmaline; 8–magnesium rock sample)
Fig. 2Tan δ versus frequency plots of the dry minerals (1–clay;
2–siliceous earth; 3–fuller’s earth; 4–gypsum; 5–lignite; 6–calcite;
7–tourmaline; 8–magnesium rock sample)
up and the detailed procedure of the evaluation of ε′
and ε′′ is the same as reported earlier by Nelson
et al.23
The dielectric properties of clay, siliceous earth and
fuller’s earth were also studied at different
frequencies in the range 8-12.5 GHz, using HP8510C
vector network analyzer. The values of ε′ and ε′′ at
8-12.5 GHz were determined from the measured
values of magnitude and phase shift of scattering
parameters, i.e., reflection parameter S11(ω) and
transmission parameter S21(ω) and by using the
procedure
developed
by
Hewlett-Packard
Corporation24. For the measurements of S11(ω) and
S21(ω), X-band rectangular wave guide sample holder
was used. The thickness of each sample section, used
for measurement, is kept at 0.445 cm. For the best
accuracy and repeatability, the full 2-port calibration
with step sweep mode and averaging is used. All
these measurements were made at room temperature.
3 Results and discussion
3.1 Dielectric behaviour in 100 Hz - 100 kHz range
INDIAN J RADIO & SPACE PHYS, FEBRUARY 2008
60
tan δ values were observed in case of clay, siliceous
earth and fuller’s earth in comparison to the tan δ
values of other minerals. In case of clay, fuller’s
earth, gypsum, calcite and tourmaline, the loss tanδ
peak frequency is clearly observed. For the sample of
siliceous earth, lignite and magnesium rock, the tanδ
peak frequency is not appeared even at frequencies as
low as 100 Hz. Observation of these curves might
lead one to speculate that peak value for tan δ would
be in the frequency range 10–5-102 Hz at room
temperature. Figure 2 also shows that the frequency
corresponding to the peak value of tan δ is different
for different minerals. In these minerals it is
maximum for clay, which is around 1.8 kHz.
The ac conductivity of these dry mineral samples in
the frequency range 100 Hz - 100 kHz are depicted in
Fig. 3. For these minerals a linear behaviour is
observed between log σ and log f. From Fig. 3, it is
found that among these samples tourmaline have
comparatively very low conductivity, whereas clay
has high conductivity. In case of lignite and
Fig. 3 Conductivity σ versus frequency plots of the dry
minerals (1–clay; 2–siliceous earth; 3–fuller’s earth; 4–gypsum;
5–lignite; 6–calcite; 7–tourmaline; 8–magnesium rock sample)
magnesium rock sample, the values of ac conductivity
are found equal. Comparatively, the maximum
variation in ac conductivity of these mineral samples
at same frequency is of the order of ≈ 10–4 - 10–5
(Ω cm)–1. Most rock forming minerals are known to
have ionic bonded structure. Hence, the conduction in
the studied mineral samples is expected to be by
motion of weakly bound ions in the lattice or defects
in the samples. Comparatively high ac conduction
values of clay, siliceous earth and fuller’s earth shows
the presence of large number of weakly bound ions in
these soft minerals.
It is found that all these minerals have a Cole-Cole
relaxation effect9, which is due to a dipole orientation
process of some kind, related perhaps to defects or
impurities. The Cole-Cole type behaviour of different
geologic materials is also reported by several
investigators3-5,8,14,26-29. The Cole-Cole equation9 for
dielectric dispersion is
ε*(ω)= ε ′ – jε ′′ = ε ∞ +
ε0 − ε∞
… (1)
1 + ( jωτ) 1− α
where εo is the low frequency limiting value of
permittivity or static dielectric constant, ε∞ the high
frequency limiting value of permittivity, ω the angular
frequency, τ the characteristic relaxation time of the
dipole rotation in the system and, the α parameter
controls the broadness of the distribution (0 <α <1).
The values of εo, ε∞, τ and α of these samples were
obtained by the non-linear least-square fit method to
the Cole-Cole equation. The accuracy of the evaluated
values of εo, ε∞ and τ are ± 3%, ± 2% and, ± 5%,
respectively. The evaluated values of εo, ε∞, τ and α
of these minerals and their bulk density d (g/cc) are
recorded in Table 2.
Table 2 shows that the observed εo value of clay is
around 74500, which is exceedingly high. The high
Table 2Values of dielectric parameters of the dry minerals of western Rajasthan
Sample No.
1
2
3
4
5
6
7
8
Mineral
Clay
Siliceous earth
Fuller’s earth
Gypsum
Lignite
Calcite
Tourmaline
Magnesium rock
d,
g/cm3
εo
1.16
0.82
1.45
1.47
1.03
2.60
2.92
2.19
74500
866
14700
35.6
80.2
10.9
31.8
55.3
ε∞
78
70
80
23.6
14.7
8.3
11.2
8.2
∆ε = εo–ε∞
74422
796
14620
12
65.5
2.6
20.6
47.1
α
0.27
0.39
0.22
0.63
0.53
0.77
0.57
0.47
10.1 GHz
τo, ms
9.19
2.12
11.38
4.32
7.67
0.11
1.39
1.72
ε′
ε′′
2.94
2.15
5.70
3.63
3.14
7.50
6.69
3.98
0.48
0.20
2.11
0.04
0.04
0.01
0.23
0.32
SENGWA & SONI: DIELECTRIC PROPERTIES OF MINERALS OF WESTERN RAJASTHAN, INDIA
value of εo of fuller’s earth is also observed. Siliceous
earth has the value of εo nearly 866. Other studied
samples have εo values less than 100. The very high εo
value in case of clay and siliceous earth is not
surprising. The high value of static dielectric constant
of many dry geologic materials were also reported
and discussed4,20,27. The value of dielectric relaxation
strength ∆ε = εo – ε∞ of these samples are shown in
Table 2. In case of calcite, the value of ∆ε is very
small. Table 2 shows that all these samples have large
value of α. The finding of the non-zero α indicates a
distribution of relaxations, which is consistent with
the heterogeneous structure of these samples27. The
evaluated values of relaxation time of the dipole
rotation in the samples of these minerals were found
in the range 0.1-11 ms. In case of calcite, the observed
τ value is comparatively very small. Significant
variation in the observed τ values suggests that the
particles of different radius contributed in the dipole
rotation in these minerals. Further, the diffusion
coefficient counter-ions in the vacancies or defects
inside the mineral lattice also moderate the τ values of
geological materials5.
3.2 Microwave dielectric behaviour
The evaluated values of ε′ and ε′′ of these minerals
at 10.1 GHz are recorded in Table 2, which shows
that there is wide variation in the ε′ values of the
studied mineral at microwave frequency. Ulaby et al.1
investigated the dielectric properties of 80 rock
samples in the microwave frequency region, e.g.
0.5-18 GHz and confirmed that the variation in the
bulk density of rock accounts for 50% of the observed
variance in the ε′ values, whereas the loss factor ε′′ is
very poorly correlated with the bulk density of
different rock. Further, it is found that chemical
composition and crystal structure are presumed to be
important determinants of dielectric loss. The
investigations by the authors, of dielectric constant of
limestones3, marbles8 and Indian granites29 also
favours the results of Ulaby et al.1 at microwave
frequencies. In case of limestones3 and marbles8, the
effect of each constituent of their chemical
composition on ε′ values at microwave frequency is,
indeed, possible due to the complete chemical
61
analysis of these samples. In Fig. 4, the values of ε′
are plotted against their bulk density d. A reference
straight line with ε′ = 1 at d = 0 is also drawn in
Fig. 4. Although the ε′ values of these samples
increase with the increase in their bulk density, all the
points of experimental ε′ values do not exactly lie on
the reference straight line. This confirms that the
weight percent of the constituents of chemical
composition of these minerals equally affects the
values of microwave dielectric permittivity.
Earlier, Sharif12 measured the values of dielectric
constants of different dry oxides at 10 GHz using
fixed frequency waveguide experimental set up,
which are recorded in Table 3. The different values of
dielectric constant of various oxides suggest that the
variation in percentage of chemical composition of
the mineral constituents can significantly change the
ε′ values. The variation in the observed ε′ values of
soft minerals, i.e. clay, siliceous earth and fuller’s
earth are mainly due to the variation in their bulk
density. Relatively high ε′ value of fuller earth is due
to a high percentage of Al2O3 and Fe2O3 in its
chemical composition. Fuller’s earth and gypsum
have almost equal density but the ε′ value of gypsum
is found to be 3.63 whereas fuller’s earth has
ε′ = 5.70. Gypsum has ≈ 94% CaSO4.2H2O in its
composition and has a relatively low value of
dielectric constant (Table 3). Comparatively, observed
higher ε′ value of tourmaline is mainly due to its
higher value of bulk density.
Fig. 4Variation of permittivity ε′ at 10.1 GHz with density of
the dry minerals (1–clay; 2–siliceous earth; 3–fuller’s earth; 4–
gypsum; 5–lignite; 6–calcite; 7–tourmaline; 8–magnesium rock
sample)
Table 3 Values of ε′ and ε′′ of different oxides at 10 GHz (Sharif, 1995; Ref. 12)
Oxides
SiO2
Al2O3
Fe2O3
CaCO3
MgCO3
CaSO4
MnO2
ε′
ε′′
4.43
0.04
12.66
1.31
16.58
0.93
8.22
0.12
5.03
0.17
5.01
0.08
75.74
26.29
62
INDIAN J RADIO & SPACE PHYS, FEBRUARY 2008
The observed ε′ value of magnesium rock sample
is lower than the ε′ values of fuller’s earth and
tourmaline, which is due to very low percentage of
Fe2O3 and Al2O3 in the chemical composition of the
rock sample. In case of calcite, the observed ε′ value
is slightly lower than that of pure CaCO3 (Table 3),
which may be due to the presence of other oxide
impurities in the chemical composition of calcite
sample. Further, the effect of crystal structure on the
ε′ value of the calcite cannot be ruled out. Similar to
earlier inference1 these results also suggest that SiO2,
Al2O3 and Fe2O3 are the main oxides of significance
in estimation of microwave permittivity ε′ values of
clay, siliceous earth, fuller’s earth, tourmaline and
magnesium rock sample with their bulk density
values. Table 2 shows that the ε′′ values of studied
samples are not consistent with density at 10.1 GHz.
From the observed ε′′ values, it is inferred that these
values are not directly governed by the sample bulk
density. In case of fuller’s earth it seems that the large
value of ε′′ may be due to the presence of Na2O and
K2O in its chemical composition. Further, Table 2
shows that the ε′ values of these samples at 10.1 GHz
are lower than the ε∞ values determined from their
Cole-Cole relation. The significant difference
between the value of ε′ at microwave frequency and
the ε∞ suggests that there may be second dispersion
region in the frequency range 100 kHz - 10 GHz for
clay, siliceous earth, fuller’s earth and gypsum.
The dielectric constant and loss values of
Pittsburgh coal samples were extensively studied by
Nelson et al.2,30 over the frequency range 1 MHz - 20
GHz using HP network analyzer and different
frequency range LCZ bridges, and at 11.7 GHz, using
short circuited wave guide measurements. They found
that the ε′ values of dry coal samples are frequency
dependent in the studied frequency range and vary
significantly with density. At 11.7 GHz, the evaluated
ε′ value of Pittsburgh coal30 (dry) of density 1.48 g/cc
is 4.21. In the present study, the ε′ value of dry lignite
sample from the Giral mine (Barmer, Rajasthan) is
found to be 3.14. The lower value of ε′ of lignite, in
comparison to the Pittsburgh coal, is because of its
comparatively low value of density.
To confirm the effect of frequency on ε′ and ε′′
values in microwave region, the samples of clay,
siliceous earth and fuller’s earth were studied over the
X-band frequencies using HP8510C vector network
analyzer. The measured ε′ and ε′′ values are plotted in
Fig. 5Variation of ε′ and ε′′ values of different minerals with
microwave frequencies in X−band region (1–clay; 2–siliceous
earth; 3–fuller’s earth)
Fig. 5. Clay and siliceous earth show the X-band
microwave frequency independent ε′ values, whereas
in case of fuller’s earth, very small decrease in ε′ and
ε′′ values were observed with increase in frequency in
the range 8 GHz - 12.5 GHz. This suggests that some
dry geologic materials also have the microwave
frequency dependent values of ε′ and ε′′. Further, it is
found that the ε′ values determined by short-circuited
wave-guide measurement are in good agreement with
the ε′ values obtains by network analyzer.
4 Conclusions
The evaluated values of ε′ and ε′′ of various
minerals of opencast mines of western Rajasthan in
the frequency range 100 Hz - 100 kHz and also at
X-band microwave frequencies confirm that the
percentage of the oxides of their chemical
composition and sample bulk density play an
important role to settle the values of dielectric
constant. All these materials obey the Cole-Cole
dielectric dispersion in the frequency range
100 Hz - 100 kHz. The reported values of ε′ and ε′′,
their chemical composition and bulk density based
interpretation can be applied to examine the various
existing frequency dependent empirical models of
dielectric
dispersion
of
similar
geologic
SENGWA & SONI: DIELECTRIC PROPERTIES OF MINERALS OF WESTERN RAJASTHAN, INDIA
materials5,7,31,32. These empirical dielectric models are
widely used to model and interpret inducedpolarization, ground-penetrating radar data, and time
domain reflectometery data. Further, an improved
understanding of the empirical model parameters
facilitates the geophysical prediction of subsurface
geochemical properties. The laboratory evaluated
microwave frequency ε′ values of these minerals are
useful for the interpretation of radar images and in the
mapping of the surface deposited minerals of western
Rajasthan by using microwave remote sensing
technique.
16
17
18
19
20
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