Electrical characterization of strontium tartrate single crystals

Article abstract of DOI:10.1016/j.jpcs.2003.10.058

The a.c. and d.c. conductivity of SrC₄H₄O ₆·3H₂O are measured and are found to lie between usual conductivities of semiconductor and insulator. Temperature dependence of d.c. conductivity shows intrinsic conduction, which is confirmed by the slope of lnσ versus lnf data. Due to application of thermal energy, noticeable conductivity peaks imply liberation of water molecules during dehydration and the formation of strontium oxalate. The conductivity plot has a nature similar to the intrinsic-to-extrinsic transition found in normal semiconductors. There occurs Efros hopping conduction in our samples.

Full text of DOI:10.1016/j.jpcs.2003.10.058

Journal of Physics and Chemistry of Solids 65 (2004) 965–973
www.elsevier.com/locate/jpcs
Electrical characterization of strontium tartrate single crystals
*
S.K. Arora , Vipul Patel, R.G. Patel, Brijesh Amin, Anjana Kothari
Department of Physics, Sardar Patel University, Vallabh Vidyanagar 388-120, Gujarat, India
Received 8 May 2003; revised 21 August 2003; accepted 10 October 2003
Abstract
The a.c. and d.c. conductivity of SrC4H4O6·3H2O are measured and are found to lie between usual conductivities of semiconductor and
insulator. Temperature dependence of d.c. conductivity shows intrinsic conduction, which is confirmed by the slope of ln s versus ln f data.
Due to application of thermal energy, noticeable conductivity peaks imply liberation of water molecules during dehydration and the
formation of strontium oxalate. The conductivity plot has a nature similar to the intrinsic-to-extrinsic transition found in normal
semiconductors. There occurs Efros hopping conduction in our samples.
q 2003 Elsevier Ltd. All rights reserved.
Keywords: A. Electronic materials; B. Crystal growth; C. Themogravimetric analysis; D. Electrical conductivity; D. Transport properties
1. Introduction
Ata-Allah [10] have found nearest-neighbor-hopping and
variable-range hopping conduction mechanisms in Zn
doped PrBa2Cu3O72y where emphasis is laid on generalized
hoping model for frequency dependent charge transport in a
dynamically disordered medium [11].
Thermophysical properties of materials are primarily of
interest due to their potential applications in electrochemi-
cal devices such as sensors [1,2]. In particular, the profound
changes that occur in physical and chemical nature,
renouncing phase transitions of a material, may be expected
to reflect information on its electrical conductivity [3,4]
contributed by different charge carriers [5]. Hopping
conduction, which may be phonon-assisted, of particles
between spatially distinct locations is one of the basic
transport mechanisms in solids [6] and it is viewed as an
important proof of the existence of localized states in
disordered solids, which is at present one of the major
problems in solid state theory. This mechanism is
particularly effective and dominates in various low-mobility
materials such as metal oxides, doped semiconductors and
organic systems and hence a large number of substances,
especially those of dielectric nature, both in bulk as well as
thin film form, has been subjected to electrical character-
ization. Most investigations on phosphates [7], fluorides [8]
and oxalates [9] describe electrical conductivity in terms of
electrons, polarons, impurities and thereby the mechanism
of conductivity in these materials has been established.
Interestingly, concerted attention has been devoted to
divalent metal tartrates due to some of their useful
properties [12]. They are ferroelectric and/or piezoelectric
compounds, they exhibit nonlinear optical and spectral
characteristics and hence are used in transducers and many
linear and nonlinear mechanical devices [13]. Strontium
tartrate is one such interesting material which fetched
attraction of researchers to bring the gel growth technique
on a firm footing [14]. We have successfully grown large
(20 £ 12 £ 5 mm3), impressively transparent single crystals
of SrC4H4O6·3H2O employing ionic diffusion of aqueous
SrCl2 through silica hydrogel impregnated with tartrate
ions. Literature survey reveals no work done on electrical
characterization of these crystals. Therefore, inspired by the
work of Bottger and Bryskin [6], it was thought worthwhile
to investigate electrical conductivity and the related
parameters of our laboratory grown crystals.
2. Experimental
*
Corresponding author. Tel.: þ91-2692-226846; fax: þ91-2692-
The electrical conductivity measurements were carried
out (along the crystallographic a-axis) on the grown crystals
236475/237258.
E-mail address: sarorak@yahoo.com (S.K. Arora).
0022-3697/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/j.jpcs.2003.10.058

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S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
in the temperature range 300–673 K using different input
frequencies in the range 500 Hz to 1 MHz. The crystal with
the prominent habit faces {100} was mounted between two
stainless steel electrodes in a sample holder and the whole
assembly was put into a resistance-heated furnace whose
temperature was gradually increased by regulating the input
power through a dimmerstat (AE; 0–270 V, 9 amp) so as to
maintain uniform heating rate of about 10 8C/h. Evidently,
the field was applied along [100] direction of the sample.
The d.c. resistance of the sample was measured by
‘MEGGER’ megohmmeter (MM 29: UK), while the
frequency dependent resistance was determined using
‘Hewlett Packard’ 4284 A LCR meter. The thermoelectric
power measurement on the crystals was carried out
employing the setup TPSS-200, developed by ‘Scientific
Solutions’, India. During the measurement, temperature
gradient ðDTÞ between two ends of sample was kept
constant at 278 K. The experimental setup has the limitation
of temperature range up to 403 K only. The resistivity r and
Hall coefficient RH were determined using van der Pauw
technique employing cross shaped sample geometry [15].
with space group P21, having the unit cell parameters:
ꢀ
a ¼ 7:55;
a ¼ 90;
b ¼ 10:06;
b ¼ 102;
c ¼ 6:47 A
g ¼ 908
Their EDAX spectra showed prominent Sr peak. The as-
grown surfaces evinced dislocation density (estimated by
selective chemical etching of the crystals in acetic acid) of
the order of 102–103 cm22, implying a high degree of
crystalline perfection. The thermograms helped us to
identify the crystals to be trihydrated, hence the chemical
formula SrC4H4O6·3H2O. We have developed for these
crystals an empirical relationship between the experimen-
tally measured quantities of diamagnetic susceptibility xd
and dielectric polarizability a as:
pffiffiffiffi
xd ¼ 26:5882 £ 106 Za
ð1Þ
3.1. Electrical conduction
The graphical plot of ln sdc vs 1=T as obtained for the
crystal is shown in Fig. 1. Although the sample above 363 K
exhibits nearly semiconducting nature, ln sdc ! 1=T curve
is, however, not perfect linear throughout. Apparently, a
hopping conduction in part with a small polaron model [16]
may be operative. Work on Ferroelectricity prevalent around
300 K in the isostructural compound, viz. Rochelle salt, has
been reported in the literature [17]. Therefore, we feel
inclined to suspect in our crystals a ferroelectric transition,
corresponding to the noticeable conductivity anomaly,
manifested by a peak in the curve, indicating relatively
3. Results and discussions
The grown crystals are found to exhibit predominantly a
pinacoid morphology with (010) and (100) grown surfaces
and a sharp (100) cleavage. The X-ray diffraction work
revealed the crystals to be perovskite monoclinic structure,
Fig. 1. Graphical plot of lnðsdcÞ versus 1=T:

S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
967
large polarization related with bound molecular currents
occurring at around 315 K. We regret to give an experimental
evidence to such a transition. A fluctuation of conductivity
above this transition temperature is alsonoteworthy. A sort of
double hump, though feeble, showing fluctuations on a
steady variation in the curve in the lower temperature range
suggests the presence of static imperfections, e.g. a trace of
impurities which might possibly be gel particles entrapped in
the growth matrix. At around this region (marked I in Fig. 1)
where the conductivity exponent n in the equation sðvÞ / vn
lies such that 0:5 , n , 1:0; as described later in this section,
electron hopping influenced by scattering mechanism
appears to be operative, thus supporting the observed
decrease of the conductivity with increasing temperature.
A sudden conductivity inflexion seen to be occurring at
363 K in the curve (Fig. 1) manifests change over of the
conduction mechanism from electron hopping to proton-
hopping type. Such a transition is indicative of some
structural changes to follow with continued heating of the
crystal. In fact, the bonded water molecules become
unstable at around 393 K (at which the index n reaches
maximum, equal to 1.2), giving rise to protonic hopping
conduction, until there occurs an abrupt liberation of two
water molecules at 423 K, as is evident by a sharp, dominant
peak. This is followed immediately by the loss of the third
water molecule at 503 K. These structural changes are in
excellent agreement with the thermogravimetric (TGA) and
differential thermal (DTA) data presented in Fig. 2.
appears to be have been caused about by the anhydrous
strontium tartrate decomposing into the carbonate. This
phase change of the first kind also finds support from the
thermograms presented in Fig. 2. Evidently, the net effect of
applied temperature can be seen to result the following
decomposition reactions:
SrC4H4O6·3H2O 393–513 K SrC4H4O6 þ 3H2O
ðIÞ
ðIIÞ
!
SrC4H4O6 513–538 K SrC2O4·CO þ CO2 þ 2H2O
!
SrC2O4·CO 598–618 K SrC2O4 þ CO
ðIIIÞ
ðIVÞ
!
SrC2O4 643–678 K SrCO3 þ CO
!
It is conjectured that the grown crystals, with three
molecules of water of crystallization, are expected to
conduct by the vehicle mechanism [18] in which H2O acts
as carrier for the proton, thereby justifying proton transport
or diffusion mechanism to be operative, as also proposed by
Clearfield [19].The whole curve (Fig. 1), is thought to be
divided into regions as follows. The Arrhenius relation [20,
21] sdc ¼ s0 exp (Ea=kT) has been used for calculation of
the activation energy, wherever required.
(a) Region I, 315–363 K, where electron hopping mech-
anism operates has the activation energy of 0.5 eV as
obtained from the linear fit of the curve in this region.
(b) Region II, 363–393 K, where proton hopping mech-
anism operates has an activation energy of proton
conduction as 0.5 eV.
There occurs another conductivity anomaly clearly seen
to be occurring at 623 K which indicates yet another
chemical/structural phase change in the sample. This leap
Fig. 2. Simultaneous thermograms obtained through TGA and DTA.

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S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
(c) Region III, 393–423 K, for which one obtains the
activation energy of water translation as 0.89 eV.
(d) Region IV, 423–503 K, for which one obtains the
activation energy of water translation as 0.91 eV.
In order to analyze further the conduction mechanism,
a.c. conductivity of the grown crystals was determined from
the data of capacitance and dissipation factor, employing
the relation,
sac ¼ ve0e0 tand
ð2Þ
Since, the activation energy obtained in steps (c) and (d)
above are closely the same, ,0.9 eV, Grotthus mechanism
appears inapplicable, but certainly the vehicle mechanism
involving proton translation or proton hopping seems
operative [18]. In fact, the presence of protons able to be
exchanged between, and hence able to diffuse through,
interspaces render the material as protonic conductor [22,
23]. There is ion–dipole interaction between dipole
moments of water molecules and the effective ionic charges.
As the temperature rises, the ion–dipole interaction
increases and the effect of band type conduction is
suppressed (region I). When the thermal energy is of the
order of ion-dipole interaction, the contacts between water
molecules and the effective ionic charges will break. This
allows thermally generated charge carriers to develop space
charge in some regions, resulting in a sudden increase in
electrical conductivity, as observed (regions II, III). That the
specific conductivity further increases with temperature is
attributed to dehydration as well as the condensation of the
structural –OH group. This also suggests a mechanism
different from charge transport where the conductivity
depends on the ability of water located on the surface to
rotate and participate. This agrees with the suggestion from
Alberti et al [24] that protons are not able to diffuse along an
anhydrous surface where spacing of the –OH groups is high.
where e0 ¼ 8:852 £ 10212 Fm22 is the constant of permit-
tivity of free space, e0 is the measured dielectric constant of
the medium ¼ C/C0, C0 ¼ ðe0AÞ=d; and tand is the loss
tangent. The data of lnsac vs 1=T as obtained on the gel-
grown single crystals are shown in Fig. 3. The observed
deviation in values of the conductivity for crystalline and
pelletised samples may be explained [25] as follows. When
an electric field is applied on the opposite surfaces of the
crystal the charge carriers move freely in the medium and
reach the other electrode, while in the case of polycrystal-
line pellet some of the charge carriers will be trapped at
grain boundaries and give rise to interfacial polarization,
entailing smaller conductivity. Air pores and grain bound-
aries too in the pellet have a significant effect. The values of
s can be corrected for air pores using the relation,
2=3
s ¼ sp½1 þ f=ð1 þ fÞ
ꢀ
ð3Þ
where sp is the measured conductivity of the pellet, f ¼
ð1 2 rp=rxÞ is the pore fraction, rp is the density of the pellet
and rx is the crystal X-ray density. When rp is close to
rx; s ¼ sp: But in fact rp , rx; so this explains that sp , s;
as observed.
A careful glance at the sac ! T curves in Fig. 3 reveals
the following prominent points:
Fig. 3. Graphical plots of ln sac versus 1=T at different applied frequencies.

S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
969
1. The overall nature of variation of ac conductivity is
temperature as well as frequency dependent.
2. The a.c. conductivity varies from 1.56 £ 10211 to
9.08 £ 1027 V21 over the studied temperature (303–
673 K) and frequency (500 Hz–1 MHz) ranges.
range 323–533 K may be ascribed to increasing phonon–
electron interaction with frequency, thereby restricting
the motion of electrons. The frequency-independent relation
between sac and (1=T) in the high temperature regime
(.533 K) where marked dielectric relaxation takes place
suggests the validity of the equation:
3. The two prominant peaks at 423 and 503 K correspond to
(reaction I) the onset of loosening of water molecules
from SrC4H4O6·3H2O structure and to their liberation out
from the lattice, respectively.
sac ¼ s1exp½2E1=kTꢀ þ s0
ð4Þ
The two types of conductivities have to be different. The d.c.
conductivity arises from the most difficult hops of charged
carrier in percolation paths between the two electrodes,
while the a.c. conductivity owes to the more limited
displacements between the few localized sites. By contrast,
ions move typically over much small, nearest-neighbor
distances and it is particularly interesting to note, therefore,
that neither the magnitude of the a.c. conductivity, its
activation energy nor, in particular, its frequency depen-
dence can be taken as reliable guide to the nature of
dominant carrier responsible for conduction. Further, the
d.c. charge transport is associated with band conduction by
non-localised carriers, with an energy higher than the
mobility edge [26,27], while the ac transport occurs by
hopping between localized states at energy levels inside the
band gap.
4. As the frequency increases, the temperature dependence
of conductivity becomes less and less pronounced. In the
relatively lower range of frequencies, i.e. 500 Hz and
1 kHz, the sample exhibits marked temperature depen-
dence, but in the higher range of frequencies, i.e.
100 kHz to 1 MHz, there is visibly feeble or little
temperature dependence.
5. The sac 2 1=T curve at 500 Hz shows much semblance
with sdc 2 1=T curve (Fig. 1), implying that sac versus T
behavior tends to approach sdc versus T behavior as the
input frequency is lowered.
6. The a.c. conductivity measurements are not able (for
reasons unknown) to detect clearly the oxalate-to-
carbonate conversion of crystals. Also, the anomaly at
315 K observed in sdc vs T curve appears to be smeared
out here, because probably the charge cloud gets
delocalized as it gains momentum from the applied field.
The value of exponent n in the relation sac ¼ Avn is found
by calculating the slopes of the ln sac ! ln f curves (Fig. 4).
A representative sample curve corresponding to 393 K
temperature is shown as inset of Fig. 4. Obviously, n depends
strongly on temperature, corroborating to the observation
The observation that the direct dependence of lnsac on T
is strongly noticed at lower frequencies in the temperature
Fig. 4. Graphical plots of lnsac versus lnf at different environmental temperatures.

970
S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
that the increase in temperature reduced gradually the
frequency dependence of sac; so that the conductivity was
mainly controlled by the applied temperature. The obser-
vation that the magnitude of conductivity is found to be high
for higher frequency at a given temperature supports small
polaron hopping model [28]. There occurs proton–phonon
interaction such that when a proton tries to move, it has a
strain field (a cloud of virtual thermal phonons) forming a
quasi-particle like polaron. When an audio frequency is
applied, this quasiparticle disperses, may be showing a
Gaussian dispersion [29]; such dispersion only leads to
different behaviour at different audio frequencies. When a
cloud of phonons disperses, protons move and contribute to
ionic conduction. One can conceive two types of binding of
protons in such protonic conductors. The protons, which are
weekly bound, are those coupled with thermal acoustic
phonons, and second, the protons which are tightly bound are
those coupled with thermal optical phonons.
expressed as:
S
ln sðTÞ ¼ lns0 2 ðT0=TÞ
Now writting
ð6Þ
ð7Þ
d½lnsðTÞꢀ
WðTÞ ¼
;
d½ln Tꢀ
we have determined from the slope of the plot of ln½WðTÞꢀ vs
ln T; shown in the inset of Fig. 5, the value s ¼ 0:72:
Evidently, the Efros hopping mechanism [33], and not the
Mott’s hopping model [34], is applicable in the present case.
In this variable range hopping (VRH) process, the carrier
jump from one localized state to the other occurs in which
there is an overlap of the wave function.
A plot of lnð1=sdc) vs 1=T0:72 is also drawn (see Fig. 5) for
the dehydrated strontium tartrate by using least square fitting
method and the value of To is determined from the slope of
the above plot. Using this value of To ¼ 3695:6 K, we
calculated the other relevant parameters, namely the most
probable hopping energy, hopping range, etc. as follows.
The constant g2 for the parabolic density of states,
Above the temperature of 423 K, the crystal no longer
remains in crystalline form. It becomes disordered and
hence the conductivity ðsÞ can be expressed by the Zeller
equation [30–32],
2
gðEÞ ¼ g2ðE 2 EFÞ ; is
38p2e3r e30
S
s ¼ s0exp½2ðT0=TÞ ꢀ;
ð5Þ
g2 ¼
ð8Þ
25e6
where the pre-exponential factor so is either independent or
a
where er is dielectric constant ( ¼ 11.258) of the material at
room temperature and eo is the free space permittivity.
The value of tunneling exponent am is calculated as:
2
slowly varying function of temperature, To ¼ e =er ; a21 and
er being the electron localization range and the dielectric
constant of the material, respectively. The index s depends on
the grain size and the temperature range of measurements.
The temperature dependence of the conductivity s is
1=3
kT0ðpg2Þ
am
¼
;
a2m1 being the decay length:
ð9Þ
10:5
Fig. 5. Graphical plot of lnð1=sÞ versus 1=T 0:72
:

S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
971
Table 1
coefficient with temperature. The negative values of the
coefficient over the range of temperatures studied reveals
n-type nature of the grown crystals.
Computed electrical parameters relating to charge hopping conduction
s ¼ 0:72
a2m1¼2:94 nm
In order to analyse the temperature dependence of
thermoelectric power of nondegenerate n-type crystal, let us
consider the expression [37].
T0 ¼ 3695:6 K
Ropt ¼ 1:93 2 2:25 nm
Wopt ¼ 0.052 2 0.061 eV
D ¼ 0.052 eV
g2 ¼ 10.84 £ 1085 J23m23
am ¼ 3.39 £ 108 m21
ꢀ
ꢁꢂ
ꢃ
k
e
EF
kT
Using Eqs. (8) and (9), the temperature dependent optimum
hopping distance Ropt is obtained as,
S ¼ 2
A þ
;
ð13Þ
1=2
Ropt ¼ 0:25a2m1ðT0=TÞ
The average hopping energy Wopt is estimated from the
relation,
ð10Þ
where k is the Boltzmann constant, EF is separation of the
Fermi level from the bottom of the conduction band and
A ¼ ð5=2-sÞ is the constant that varies from 0 to 4, depending
on the scattering process. For example A ¼ 4 and 3 show
charged impurity scattering and lattice scattering, respect-
ively. Differentiating Eq. (13) above results
1=2
Wopt ¼ 0:5kðT0TÞ
;
ð11Þ
and then if Tp is the temperature at which the Eq. (5) begins
to be satisfied, the width of the coulomb gap ðDÞ is written as
[35,36]
ꢀ
ꢁꢂ
ꢀ
ꢁꢀ
ꢁ
ꢀ
ꢁꢃ
dS
dT
k
e
dA
dT
1
dEF
dT
EF
kT2
¼
þ
2
ð14Þ
k
Over the studied temperature range (315–395 K), EF is
almost constant, EF=kT2 term is very slowly decreasing with
temperature that may be considered constant and is
generally negligible [38]. Therefore, Eq. (14) implies that
dS=dT remains nearly constant around an average or mean
value, and this is quite evident from the observation shown
plotted in the inset of Fig. 6.
D ¼ k=2ðT0TpÞ1=2
;
ð12Þ
In the present case, we have taken Tp ¼ 388 K. The above-
obtained values are mentioned in Table 1.
3.2. Thermoelectric power
The variation of thermoelectric power SðTÞ measured as
a function of reciprocal temperature is shown in Fig. 6. We
can recognize a linear-fit steady rise of the Seebeck
Further, for the studied small temperature range, EF is
fairly constant and hence from Eq. (13), if the thermoelec-
tric power S is plotted against the reciprocal of temperature,
Fig. 6. Graphical presentation of Seebeck coefficient versus reciprocal temperature.

972
S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973
Table 2
also been calculated using the formula,
Some other electrical parameters obtained from the experimental data
1
ne ¼
ð19Þ
Parameters
Values
RHe
EF
and all these values are recorded in Table 2.
(100) plane
(010) plane
0.685 eV
0.695 eV
A
4. Conclusions
(100) plane
3.09
(010) plane
3.08
† The d.c. conductivity of strontium tartrate occurs
between the normal conductivities of semiconductor
and insulator.
me*
Nd
r
1.339 £ 10237 kg
1.529 £ 1015 m23
4.225 £ 105 V cm
28.6338 £ 1026 cm2/(volt·s)
2364.62 m3/coulomb
1.714 £ 1010 cm23
mH
RH
ne
† The obtained value of the exponent ðs ¼ 0:72Þ charac-
terises Efros hopping conduction mechanism in our
crystals.
† The activation energy required to move permanent
intrinsic defects in the crystal lattice is equal to 0.50 eV.
† The charged carriers responsible for electrical conduc-
tion in the lower temperature region (,363 K) are
electrons, while in the higher temperature region
(.363 K) are protons.
† The thermal anomaly found in the gel-grown crystals of
strontium tartrate is in excellent agreement with the
observed conductivity anomaly.
a straight line is expected. This is what has been observed
(Fig. 6). Using the slope and the intercept of the line, the
values of EF and A have both been determined. These values
obtained for (100) and (010) habit planes of crystal are given
in Table 2. Using the value A < 3; the scattering parameter
is obtained exactly as s ¼ 21=2; it is to be associated with
lattice scattering. The fact that EF is fairly constant also
implies that the carrier concentration ðneÞ is not changing
with the temperature. Therefore, Eq. (13) can be expressed
as [39],
References
ꢀ
ꢁꢂ
ꢀ
ꢁꢃ
k
e
Nd
ne
S ¼ 2
A þ ln
;
ð15Þ
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where Nd is the effective density of states, given by
ꢂ
ꢃ
3=2
2pmpekT
[4] H. Sharma, K. Kumari, L.S. Singh, R.N.P. Choudhary, Bull. Mater.
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Nd ¼ 2
;
ð16Þ
h2
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¨
[6] H. Bottger, V.V. Bryskin, Hopping Conduction in Solids, Akademie-
and ne ¼ 1:714 £ 1016 m23 is the carrier concentration as
obtained from the Hall Effect measurements (described in
Section 3.3). Using S ¼ 25:036 £ 1025V=K at T ¼ 316 K,
h ¼ 6:626 £ 10234 Js and k ¼ 1:381 £ 10223 J/K, the
computed values of mep and Nd are also given in Table 2.
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3.3. Hall coefficient
´ ´
[12] M.E. Torres, T. Lopez, J. Peraza, J. Stockel, A.C. Yanes, C. Gonzalez-
´
Silgo, C. Ruiz-Perez, P.A. Lorenzo-Luis, J. Appl. Phys. 84 (1998)
The value of r obtained from the van der Pauw technique
is recorded in Table 2. In the range of applied magnetic field
0.27–13.65 Kgauss, we found out DR=DB ¼ 271.4948 V/
gauss from the slope of R versus B plot. So, the Hall
mobility of carriers and Hall coefficient are calculated as:
5729.
´ ´
[13] M. Torres, T. Lopez, J. Stockel, X. Solans, M. Garcia-Valles, E.
´ ´
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(2002) 491.
[14] H.K. Henisch, Crystal Growth in Gels, Pennsylvania State University
Press, USA, 1973.
mH ¼ ðt=rÞðDR=DBÞ:
RH ¼ mHr
ð17Þ
ð18Þ
[15] G. de Mey, Electr. Commun. 28 (1973) 309.
¨
[16] H. Bottger, V.V. Bryksin, Phys. Stat. Sol. (b) 78 (1973) 9.
[17] W. Taylor, D.J. Lockwood, H.J. Labbe, J. Phys.-C, Solid State Phys.
17 (3) (1984) 685.
The negative sign of RH; in consonance with Seebeck
coefficient data (Section 3.2), confirms that strontium
tartrate is an n-type material. It is implied, therefore, that
the conduction may be predominantly contributed by the
tartrate ions. The effective charge carrier concentration has
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