Electrical characterization of strontium tartrate single crystals

Electrical characterization of strontium tartrate single crystals

Journal of Physics and Chemistry of Solids 65 (2004) 965–973 www.elsevier.com/locate/jpcs Electrical characterization of strontium tartrate single cr...

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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 Thermophysical properties of materials are primarily of interest due to their potential applications in electrochemical 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 characterization. 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. * Corresponding author. Tel.: þ 91-2692-226846; fax: þ 91-2692236475/237258. E-mail address: [email protected] (S.K. Arora). 0022-3697/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2003.10.058

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]. 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 The electrical conductivity measurements were carried out (along the crystallographic a-axis) on the grown crystals

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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].

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,

with space group P21, having the unit cell parameters: a ¼ 7:55; a ¼ 90;

b ¼ 10:06; c ¼ 6:47 A b ¼ 102; g ¼ 908

Their EDAX spectra showed prominent Sr peak. The asgrown 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 experimentally measured quantities of diamagnetic susceptibility xd and dielectric polarizability a as: pffiffiffiffi xd ¼ 26:5882 £ 106 Z a

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

Fig. 1. Graphical plot of lnðsdc Þ versus 1=T:

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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 also noteworthy. 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 protonhopping 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. 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

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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: Sr C4 H4 O6 ·3H2 O

!

393 – 513 K

Sr C4 H4 O6 þ 3H2 O

! S C O ·CO þ CO þ 2H O S C O ·CO ! S C O þ CO S C O ! S CO þ CO Sr C4 H4 O6

513 – 538 K

r

2

4

2

598 – 618 K

r

2

4

r

2

4

r

2

643 – 678 K

r

3

4

2

ðIÞ ðIIÞ ðIIIÞ ðIVÞ

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 mechanism 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 mechanism operates has an activation energy of proton conduction as 0.5 eV.

Fig. 2. Simultaneous thermograms obtained through TGA and DTA.

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(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. 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.

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 ve 0 e 0 tand

ð2Þ

where e 0 ¼ 8:852 £ 10212 Fm22 is the constant of permittivity of free space, e 0 is the measured dielectric constant of the medium ¼ C/C0, C0 ¼ ðe 0 AÞ=d; and tand is the loss tangent. The data of lnsac vs 1=T as obtained on the gelgrown 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 polycrystalline 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 boundaries too in the pellet have a significant effect. The values of s can be corrected for air pores using the relation,

s ¼ sp ½1 þ f =ð1 þ f Þ2=3

ð3Þ

where sp is the measured conductivity of the pellet, f ¼ ð1 2 rp =rx Þ 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.

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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. 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. 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 dependence, 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-tocarbonate 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 observation that the direct dependence of lnsac on T is strongly noticed at lower frequencies in the temperature

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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:

sac ¼ s1 exp½2E1 =kT 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 dependence 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. 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

Fig. 4. Graphical plots of lnsac versus lnf at different environmental temperatures.

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that the increase in temperature reduced gradually the frequency dependence of sac ; so that the conductivity was mainly controlled by the applied temperature. The observation 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. 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],

we have determined from the slope of the plot of ln½WðTÞ 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=T 0:72 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, gðEÞ ¼ g2 ðE 2 EF Þ2 ; is

s ¼ s0 exp½2ðT0 =TÞS ;

g2 ¼

ð5Þ

where the pre-exponential factor so is either independent or slowly varying function of temperature, To ¼ e2 =e ra ; a21 and e r 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

expressed as: ln sðTÞ ¼ lns0 2 ðT0 =TÞS

ð6Þ

Now writting WðTÞ ¼

d½lnsðTÞ ; d½ln T

ð7Þ

38 p2 e 3r e 30 25 e 6

ð8Þ

where e r is dielectric constant ( ¼ 11.258) of the material at room temperature and e o is the free space permittivity. The value of tunneling exponent am is calculated as:

am ¼

kT0 ðpg2 Þ1=3 ; 10:5

Fig. 5. Graphical plot of lnð1=sÞ versus 1=T 0:72 :

a21 m being the decay length:

ð9Þ

S.K. Arora et al. / Journal of Physics and Chemistry of Solids 65 (2004) 965–973 Table 1 Computed electrical parameters relating to charge hopping conduction s ¼ 0:72 T0 ¼ 3695:6 K g2 ¼ 10.84 £ 1085 J23m23 am ¼ 3.39 £ 108 m21

a21¼ m 2:94 nm Ropt ¼ 1:93 2 2:25 nm Wopt ¼ 0.052 2 0.061 eV D ¼ 0.052 eV

Using Eqs. (8) and (9), the temperature dependent optimum hopping distance Ropt is obtained as, 1=2 Ropt ¼ 0:25a21 m ðT0 =TÞ

ð10Þ

The average hopping energy Wopt is estimated from the relation, Wopt ¼ 0:5kðT0 TÞ1=2 ;

ð11Þ

and then if T p is the temperature at which the Eq. (5) begins to be satisfied, the width of the coulomb gap ðDÞ is written as [35,36] D ¼ k=2ðT0 T p Þ1=2 ;

ð12Þ

In the present case, we have taken T p ¼ 388 K. The aboveobtained 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

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coefficient with temperature. The negative values of the coefficient over the range of temperatures studied reveals n-type nature of the grown crystals. In order to analyse the temperature dependence of thermoelectric power of nondegenerate n-type crystal, let us consider the expression [37].    k E S¼2 Aþ F ; ð13Þ e kT 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, respectively. Differentiating Eq. (13) above results        dS k dA 1 dEF EF ¼ þ ð14Þ 2 dT e dT k dT kT 2 Over the studied temperature range (315 –395 K), EF is almost constant, EF =kT 2 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. Further, for the studied small temperature range, EF is fairly constant and hence from Eq. (13), if the thermoelectric power S is plotted against the reciprocal of temperature,

Fig. 6. Graphical presentation of Seebeck coefficient versus reciprocal temperature.

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Table 2 Some other electrical parameters obtained from the experimental data

ne ¼

Parameters

Values

EF (100) plane (010) plane

0.685 eV 0.695 eV

A (100) plane (010) plane me * Nd r mH RH ne

3.09 3.08 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

1 RH e

ð19Þ

and all these values are recorded in Table 2.

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 ðne Þ is not changing with the temperature. Therefore, Eq. (13) can be expressed as [39],     k N S¼ 2 A þ ln d ; ð15Þ e ne where Nd is the effective density of states, given by   2pmpe kT 3=2 ; Nd ¼ 2 h2

also been calculated using the formula,

ð16Þ

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 £ 1025 V=K at T ¼ 316 K, h ¼ 6:626 £ 10234 Js and k ¼ 1:381 £ 10223 J/K, the computed values of me p and Nd are also given in Table 2. 3.3. Hall coefficient 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 2 71.4948 V/ gauss from the slope of R versus B plot. So, the Hall mobility of carriers and Hall coefficient are calculated as:

mH ¼ ðt=rÞðDR=DBÞ:

ð17Þ

RH ¼ mH r

ð18Þ

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

4. Conclusions † The d.c. conductivity of strontium tartrate occurs between the normal conductivities of semiconductor and insulator. † The obtained value of the exponent ðs ¼ 0:72Þ characterises 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 conduction 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.

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