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Indian Journal of Pure & Applied Physics
Vol. 43, October 2005, pp. 777-782
Dielectric dispersion and microwave dielectric study of marbles
in support of radar investigations
R J Sengwa* & A Soni
Microwave Research Laboratory, Department of Physics, J N V University, Jodhpur 342 005, Rajasthan
Recevied 13 February 2004; revised 11 August 2005; accepted 16 August 2005
The dielectric permittivity ε′ and loss ε′′ of nine marble samples collected from open marble mines of Makarana,
Rajsamand, Ambhaji and Kesariyaji of Rajasthan were studied in the frequency range 100 Hz-100 kHz and also at 10.1 GHz
at room temperature. It is found that the ε′ values of dry marbles decrease with increase in frequency in the range 100 Hz100 kHz. All the studied marbles are governed by the Cole-Cole dielectric dispersion. The values of static dielectric constant
εo, high frequency limiting dielectric constant ε∞, dielectric relaxation strength Δε, distribution parameter α, and relaxation
time for dipole rotation τ were determined from the complex Cole-Cole plots. All these samples have α values greater than
0.5 and their Δε values vary significantly. Further, wide variation in ac conductivity σ is also observed for different samples.
The effect of sample bulk density and variation in the chemical composition on low frequency and microwave permittivity
of the studied marbles have been recognized. The measured values of dielectric permittivity of these marbles were also
compared and discussed with the earlier reported ε′ values of marbles and limestones of other regions. The precise
microwave dielectric measurements of marbles and recognization of their dependence on petrological and chemical
composition are interesting and can be used in support of radar investigations of the Earth’s geology.
Keywords: Geological materials, Marbles, Dielectric constant, Cole-Cole plots, Relaxation time
IPC code: G01R27/26
1 Introduction
Due to variation in bulk density, mineralogical
composition and crystalline structure of rocks and
minerals, their dielectric measurements over wide
frequency range had been the subject of several
researchers1-11. Geological materials exhibit the
dielectric dispersion in low frequency region, which
can be represented by Cole-Cole arcs12. After several
attempts, it is established that the dielectric properties
of rocks and sediments are primarily a function of
mineralogy, frequency, water saturation, porosity,
rock
texture,
component
geometry
and
electrochemical interactions2,7,11. Dielectric dispersion
studies in low frequency region are helpful to
understand the behaviour of induced polarization2,7 in
the materials, while high frequency dielectric
measurements are useful in planning ground
penetrating radar surveys13-15, in microwave remote
sensing9,16 of the Earth’s geology of these materials
deposited areas and calibration of time domain
reflectometry measurements17,18.
In the present paper, the dielectric dispersion
behaviour of popular variety marbles of different
areas of Rajasthan state has been studied. Marbles are
___________
*Email: [email protected]
limestones, which have been crystallized by heat or
pressure during metamorphic processes. Different
names of marbles are derived from the locality where
they are found, the formation in which they occur,
from some peculiarity of structure, colour etc.
2 Experimental Details
2.1 Materials
Marble samples of different varieties were obtained
from the marble mines of Makarana (MK1, MK2 and
MK3), Rajsamand (RS1, RS2 and RS3), Ambaji
(AM) and Kesariyaji (KS1 and KS2). Selected
samples alongwith their chemical compositions are
presented in Table 1.
2.2 Samples preparation for dielectric measurements
Marble rocks were cut by a diamond wheel cutter
and polished to obtain thin plates of thickness ;1.5
mm. Surfaces of the prepared samples were polished
to get very smooth in order to ensure good electric
contacts. Silver plated brass plates were used for the
fabrication of parallel plate capacitors with sample as
dielectrics for the dielectric study in the frequency
range
100 Hz–100 kHz.
X–band
rectangular
waveguide dimension size samples were prepared
INDIAN J PURE & APPL PHYS, VOL 43, OCTOBER 2005
778
Table 1—Chemical composition of marbles (percentage by weight)
Specimen
number
Colour
Makarana marbles
MK1
white
MK2
dirty white
MK3
light pinkish
Rajsamand marbles
RS1
pure white
RS2
pinkish gray
RS3
brownish
Ambaji marble
AM
pure white
Kesariyaji marbles
KS1
greenish
KS2
greenish
CaO
SiO2+MgO
Fe2O3+Al2O3
AI
LOI
44.80
44.24
52.08
1.34+6.85
4.54+3.22
0.60+1.61
0.27+0.63
0.15+0.77
0.13+1.07
1.22
6.52
1.82
43.61
39.23
42.87
30.80
47.88
38.92
1.42+19.74
4.90+0.20
11.38+3.82
0.47+0.55
0.53+0.77
1.58+0.62
2.06
5.82
6.82
44.74
38.88
36.21
54.32
0.32+0.40
0.06+0.26
1.06
42.08
24.08
18.20
18.88+5.23
22.16+5.03
2.51+1.79
1.66+1.02
22.70
31.02
24.70
21.38
from the same marble rock for the measurements of
dielectric constant at 10.1 GHz.
2.3 Dielectric measurements
The values of ε′ and ε′′ of marble specimens in the
frequency range 100 Hz–100 kHz were determined by
measuring the capacitance and dissipation factor of
the parallel plates capacitors with sample as dielectric.
A standard three-terminal dielectric cell is used for
this purpose. These measurements were made with
automatic Keithley LCZ meter model 3330. The
values of ε′ and ε′′ at 10.1 GHz were determined
employing the short-circuited waveguide method19,20
for rectangular waveguide operating in TE10 mode at
room temperature.
3 Results and Discussion
3.1 Low frequency dielectric dispersion
The evaluated permittivity (ε′) values of dry marble
specimens were presented against frequency in Fig. 1.
These plots show dispersion, which is pronounced at
lower frequencies and in some specimen is
comparatively very large. Table 1 shows that marbles
are considered to behave as very heterogeneous
dielectrics with components having differing ε′. In
geologic materials, low frequency dispersion is
believed to be due to polarization associated with
charge build-up at grain boundaries or at grain
imperfections of the sample particles of various
dielectric properties2,7,21. Further, the contribution of
grain sizes is also an important factor in controlling
the low frequency values of ε′. Figure 1 shows that
the low frequency values of Kesariyaji samples (KS1
Fig. 1—ε′ versus log f plots of marbles
and KS2) are comparatively very high. Further
Rajsamand (RS3) and Makarana (MK3) also show
significantly high ε′ values in comparison to the other
studied specimen i.e. MK1, MK2, RS1, RS2 and AM.
Table 1 shows that the specimens KS1 and KS2 have
significantly higher percentage of Fe2O3+Al2O3 in
SENGWA & SONI: MICROWAVE DIELECTRIC STUDY OF MARBLES
779
their heterogeneous composition. Similarly, in case of
Rajsamand Marbles and Makarana marbles,
specimens RS3 and MK3 have higher percentage of
Fe2O3+Al2O3. From the comparative ε′ values (Fig. 1)
with percentage of Fe2O3+Al2O3 in the specimen
composition (Table 1), it can be concluded that the
higher percentage of Fe2O3+Al2O3 increases the ε′
values of these marble specimen of same locality.
Earlier, Emerson and Welsh22 also studied dielectric
dispersion of one specimen of marble and two
different specimen, of limestone of Mt. Moss mine,
Australia. The mineralogical composition of marble
sample and one limestone sample is identical to the
Ambaji (AM) specimen used in the present study.
They observed very low dielectric dispersion. Further,
Emerson and Welsh22 reported ε′ values of the marble
and limestone specimen in the frequency range
1 Hz–160 kHz which are in good agreement with the
ε′ values of AM sample in the same frequency range.
But in case of another limestone specimen, which is
admixture of a variety of ultrafine submicron grains
of silicate and oxide mineral, they observed higher
permittivity. In case of KS1 and KS2, the contribution
in observed high ε′ values may be due to the variation
in their chemical composition.
Loss tangent (tanδ = ε′′/ε′) values of these samples
are plotted against logf in Fig. 2. In case of RS3 only,
loss tan δ peak frequency is found. The observations
of these plots might lead us to speculate that loss tan δ
peak frequency would be lower than 100 Hz in MK1,
MK2, MK3, S1, RS2 and AM while it may be above
100 kHz in case of KS1 and KS2.
Figure 3 shows the variation of ac conductivity of
these samples. For all these samples almost a linear
behaviour is observed between log σ and log f. In
geological materials conduction is expected to be by
motion of weakly bound ions in the lattice or defects
in the ionic bonded structure. Comparatively high
value of conductivity is observed in case of KS1 and
KS2, which is due to the presence of higher
percentage of Fe2O3+Al2O3 in their chemical
composition. Further, significant variation in
ac conductivity is observed for entire marble
specimen.
The complex plane plots (ε′′ versus ε′) of these
marble samples are plotted in Fig. 4. It is found that
the dielectric dispersion of all these samples is
governed by Cole-Cole relaxation behaviour to a
dipole reorientation process. Earlier, several
researchers2,3,8,14,23-25 also reported the Cole-Cole
Fig. 2—Tan δ versus log f plots of marbles
(○ – MK1, Δ – MK2, □ – MK3, ∇ – AM, ● – RS1, ▲ – RS2,
■ – RS3, – KS1 and ▼ – KS2)
dielectric dispersion in different geologic materials.
The Cole-Cole equation12 for dielectric dispersion is
ε∗ ( ω) = ε′ − j ε′′ = ε ∞ +
εo − ε∞
1 + ( j ωτ )
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 and ε∞ were obtained by
extrapolation of the Cole-Cole plots corresponding to
low frequency region and high frequency region on
the real axis respectively. The values of τ and α were
evaluated26 from the relation v/u = (ωτ)1−α. Where u
and v are the distances from the experimental points
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INDIAN J PURE & APPL PHYS, VOL 43, OCTOBER 2005
Fig. 3—Log σ versus log f plots of marbles
(○ – MK1, Δ – MK2, □ – MK3, ∇ – AM, ● – RS1, ▲ – RS2,
■ – RS3, – KS1 and ▼ – KS2)
of Cole-Cole diagram to ε∞ and εo respectively on the
permittivity axis. The evaluated values of εo, ε∞,
dielectric strength Δε = εo – ε∞, α and τ are recorded
in Table 2.
Table 2 shows that the εo values of these marbles of
different regions vary in the range 13.5 – 101. The
significant variation is also observed in the εo values
of same locality marbles. The determined ε∞ values of
these samples were found in the range 8.5 – 11.5. The
dielectric strength Δε values of MK1, AM and RS2
are very small while in case of MK3, RS3, KS1 and
KS2, high values of Δε were observed. Table 2 shows
that the observed α values of all these marble samples
are higher than 0.5. This indicates a distribution of
relaxations, which is consistent with the
inhomogeneous structure of these samples23. The
significant variation in the τ values suggests that
different radius particles contributed in the dipole
rotation, which is also influenced by the diffusion
coefficient of counter ions in the vacancies or defects
in the samples2.
3.2 Microwave dielectric behaviour
The ε′ values of dry geologic materials in
microwave region6,9,27 are almost independent of the
Fig. 4—Cole-Cole plots of marbles
frequency. Further, it is also confirmed9 that 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. Similar
to bulk density, constituents of chemical composition
of the rock equally affected the values of microwave
dielectric permittivity. Sharif11 measured the values of
ε′ and ε′′ of various oxides at 10 GHz (Table 3). Due
to different values of ε′ and ε′′ of these oxides at
microwave frequency, the variation in dielectric
constants of these oxide bearing geologic materials is
expected with the percentage change in their chemical
SENGWA & SONI: MICROWAVE DIELECTRIC STUDY OF MARBLES
781
Table 2—Values of εo, ε∞, Δε, α, τ, density (d) and microwave dielectric constants (ε′ and ε′′) of marble specimens
Specimen
number
Makarana marbles
MK1
MK2
MK3
Rajsamand marbles
RS1
RS2
RS3
Ambaji marble
AM
Kesariyaji marbles
KS1
KS2
εo
ε∞
Δε
α
τ
(ms)
d
(g/cc)
13.45
23.55
52.50
10.10
9.90
11.50
3.35
13.65
41.00
0.52
0.69
0.52
2.630
4.960
5.100
2.70
2.75
2.72
8.06
7.22
7.39
0.57
0.35
0.33
20.15
14.80
68.00
9.60
9.80
9.00
10.55
5.00
59.00
0.68
0.69
0.62
4.720
3.740
0.590
2.82
2.64
2.70
6.86
7.10
7.21
0.41
0.28
0.40
15.70
10.60
5.10
0.68
0.540
2.69
8.03
0.27
101.00
89.00
8.50
10.50
92.50
78.50
0.65
0.65
0.042
0.015
2.72
2.65
6.40
5.80
1.02
0.45
10.1 GHz
ε′
ε′′
Table 3—Values of ε′ and ε′′ of different oxides at 10 GHz (ref. 11)
Oxides
CaO
SiO2
MgO
Al2O3
Fe2O3
ε′-jε′′
8.22-j0.12
4.43-j0.04
5.03-j0.17
12.66-j1.31
16.58-j0.93
composition constituents. Table 1 shows that the
percentage chemical compositions of these marble
specimens are different, while the bulk density is
nearly the same (Table 2). In case of Rajsamand
marbles, the bulk density varies by approximately +
4% of their average value of bulk density. Therefore,
the ε′ values of these marbles can be considered
independent of their bulk density except in case of
Rajsamand marbles. Table 2 shows that the
significant variation in ε′ values of different marbles
at 10.1 GHz is mostly either due to the percentage
variation in their chemical composition or structure
variation of component geometries. Marbles are
CaCO3 (ε′;8) rich, crystalline rocks. Table 3 shows
that the increase in quantity of SiO2+MgO (ε′ < 5) in
the chemical composition will decrease the ε′ values
of marbles. On the other hand, if there is increase in
the percentage of Fe2O3+Al2O3, (ε′ > 12) in their
chemical composition, the value of microwave
permittivity should enhance.
The higher observed ε′ value of KS1 in comparison
to KS2 is due to higher percentage of Fe2O3+Al2O3 in
the composition of KS1. Further, the lower ε′ values
of KS1 and KS2 in comparison to other marble
samples (Table 2) may be due to increase in quantity
of SiO2+MgO in their composition. The observed ε′
values of MK1 and AM were found nearly equal to
the ε′ value of pure CaO (Table 3). It is expected
because of their chemical composition close to pure
CaO. Further, MK3 also has very low percentage of
other oxides in its composition in comparison to the
percentage of CaO. But, low ε′ value of MK3 in
comparison to ε′ value of MK1 may be due to either
its high hardness or variation in components
geometry. The low ε′ value of MK2 in comparison to
ε′ value of MK1 is expected because of the percentage
of increase of SiO2 in its composition. In case of
Rajsamand marbles, the observed ε′ value of RS1 is
low which is due to higher percentage of SiO2+MgO
in its composition in comparison to the percentage of
SiO2+MgO in the composition of RS2 and RS3,
although RS1 bulk density is high. Further, it seems
that the higher ε′ value of RS3 in comparison to the ε′
value of RS2 may be because of the slight increase in
bulk density of RS3 and also the increase in the
percentage of Fe2O3+Al2O3 in its chemical
composition.
The observed values of ε′ of Makarana, Rajsamand
and Ambaji marbles are also in good agreement with
the microwave permittivity values of dry limestone
samples16,27-29. Cervelle and Jin–Kai16 reported the
microwave dielectric constants of dry marbles in the
range 5.22-8.15. The observed ε′ values of the studied
Rajasthan marbles of various localities at 10.1 GHz
were also found in the same range16. For these marble
specimens, the value of microwave permittivity ε′ is
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INDIAN J PURE & APPL PHYS, VOL 43, OCTOBER 2005
found lower than the ε∞ values obtained from ColeCole plots. The difference in ε′ and ε∞ value ranges
from 1.8 to 4.7. This significant difference suggests
that there may be another dispersion above 100 kHz
frequencies in the studied marble samples. The
microwave dielectric loss ε′′ values of these marble
samples have anomalous behaviour, which confirms
that iron cations introduced during marble formation
play a dominant role in the dielectric loss properties22.
In case of KS1, the high value of ε′′ may be due to
high percentage of Fe2O3+Al2O3 in its composition.
4 Conclusions
The results of the present study suggest that the
heterogeneity influences significantly the low
frequency permittivities. The increase in percentage
of Fe2O3 and Al2O3 in the chemical composition of
marbles also enhances permittivity values in low
frequency region. Similar to other geologic rocks and
minerals, these marbles obey the Cole-Cole dielectric
dispersion
behaviour.
Microwave
dielectric
permittivity of these marble specimens of nearly equal
bulk density is governed by the variance in percentage
of chemical composition of different oxides in the
sample. The detailed study of different marbles will
contribute
significantly
in
high
frequency
electromagnetic waves dielectric sensing technique
because the radar investigation of the Earth’s geology
depends on the average dielectric constant of the area
under investigation. Further, the dielectric constant of
marble samples along with their chemical
composition can be used to estimate the individual
contribution and interaction contribution of the
sample constituents to the dielectric constant using the
volumetric dielectric mixing equations.
Acknowledgement
The authors are grateful to the Department of
Science and Technology, Government of Rajasthan,
for financial assistance.
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