IACS Institutional Repository

Gour, M S

Khare, P K

Singh, Ranjeet

Indian J. Phys. 80 (1), 89-93 (2006)
ft-U!
a A o t e
------
/ J P ) |
Charge decay characteristics of polystyrene
M  S Gour*, P K Khare* and Ranjeet Singh
^Department of Physics. Hindustan College of Science & Technology. F«rah. Mathura. Uttar Pradc.sh, India 
'•‘Department of Post Graduate Studies and Research in Physics and Electronics.
Rani Duigavati University, Jabalpur-482 001, Madhya Pradesh, India
Received 21 February 2005. accepted 27 Octt$>er 2005
Abstract : Tlie charge decay behavior of polystyrene (PS) samples, *  40 pm in thickrui^s, was investigated by means of transient currents (in 
charging and discharging mode) and thcnnally stimulated discharge currents (TSDC) incasurciHents as a functitm of polarizing fields, and temperatures. 
The order of currents ha.s been found to increase with increasing these parameters. The current-time characteristics have different values of slopes 
lying between 0.45 to 0.65 and 1.66-1.99. The TSDC thermograms of PS ctmsist of a peak located around 60—85®C. Comparative studies of the 
is<K’hmnaI characteristics (i.e. current-temperature plots at constant times) with the thermally stimulated discharge current, indicated a strong resemblance 
between two techniques. It is suggested that both the dipolar orientation due to molecular mechanism of motions with the side chains and space 
charges due to trapping of injected charge carriers in energetically distributed traps may be responsible for the observed currents.
Keywords : Charge decay, transient currents, thermally .stimulated discharge currents, dipolar orientation, space charge mechanism.
PA<:S Nos. : 77.22.Ej, 77.22.Gm, 77.22.Jp
1 he mechanism and character o f conduction in polymers 
has been the subject o f many investigations. The 
movement o f charge carriers in polymeric dielectrics has 
received a great attention because o f its importance in 
science and technology [1*2J. The thermally stimulated 
discharge current (TSD C ) technique is a simple but 
effective tool for extracting information about the internal 
structure and molecular relaxations, as well as the 
establishment and decay o f space charge due to trapping 
of charge carriers and their subsequent thermal release 
from traps in polymers [3,4], TSDC reveals the molecular 
mobility o f the material’s structure as well as the 
movement o f the charge accumulated at different interfaces 
[51. Transient currents observed upon the application or 
removal o f a step voltage has been studied extensively 
|6~10] to give an insight into the polarization processes. 
By carrying out the measurements o f absorption and 
short circuit isothermal desorption (discharging) currents 
at various temperatures, the information such as space
Corresponding Author
charge structure (including the trap distribution o f  energy 
and also the volume o f the polymer) can be obtained. 
Such dc step response technique, in which the current 
response is measured as a function o f time after a dc 
voltage is applied to, or removed from the sample is 
isothermal analogous o f  TSDC. It determines the 
discharging current at constant temperature instead o f 
varying temperatures.
Polystyrene is known to have a good charge storage 
capability owing to the presence o f the phenyl group, 
which is more electronegative than the methyl group but 
less than fluorine and hydrogen 111]. The present paper 
describes the results o f simultaneous studies o f absorption 
and discharging current and thermally stimulated discharge 
current (TSDC) o f PS thermoelectret under field and 
temperature conditions.
Commercial grade polystyrene (PS ) used in the present 
study was supplied by Chemical Agency Bombay. In the 
present investigation, samples were thermally poled with
<e> 2006 lACS
90 M S Goun F K K/iare and Ranjeet Singh
field iEp) o f 10-200 kV/crn al various tcmi>eratures {!],) 
O 0~\2irC ).
7'hc sample preparation, vacuum deposition ol 
electrcxlcs, effective electrode area and geometry, the 
preconditioning o f the samples and the measurement 
procedure for transient and T'SDC in this work were 
exactly the same as reported in the earlier work (10,121. 
The heating rate was 3‘^ C/min.
Current-lime characteristics o f transient currents in 
charging and discharging modes arc shown in Figures 1-
4. The order o f current in charging cunents is higher
Figure 2. Charging characteristics of PS films with various al 1), 120'('
Fi|;ure 1. Charging characteristics of PS films with vanous h^s at 7), 70''C.
than current observed in discharging mode. Figures 1 
and 2 show typical charging currents v.v. time 
characteristics for different £^ /s {i.e, 10, 50, 75, 100 and 
200 kV/cm) at 70 and 12CK^ C, respectively. It is evident 
from these figures that the nature o f charging transient 
currents is approximately similar for all the E,,’s at both 
the temperatures 70 and 120°C) except for poling 
fields n o , 50 and 75 kV/cm) at 70°C. The charging 
currents decreases with time. However, in other cases, 
the charging currents show an increasing trend and become 
saturated after about 45 min. It is also clear that with 
increase in the applied field, the magnitude o f charging 
current increases. Figures 3 and 4 depict the variation o f
Figure 3, Discharging charactensties of PS films wilh variou.s EpS at Tp 7 (f C.
discharging currents with time. With all the E/s (10, 50, 
75, 100 and 200 kV/cm) at 70 and 120‘^ C, currents 
decreasing with time. In all the cases, nature o f  
discharging currents is found similar. The magnitude o f 
discharging currents increases with increase in Ep. There 
appears to be a process o f iheimal activation over the 
whole range o f temperature. It is found that charging as 
well as discharging currents have been characterized wilh 
logarithmic slopes smaller in magnitude (<1 ) during the 
range o f short limes, and then goes to the longer time
Charge decay characteristics o f polystyrene 91
Figuru 4. Discharging characteristics of 1>S films with various ii^ ’s at 1], J 20°C.
region (with n = 1.9) where current tends to approach 
the saturation or steady state current. The samples were 
charged with different fields (1(>~100 kV/cm) at different 
temperatures. The representative results for samples 
charged with 50 kV/cm at different 7),’s (30» 60, 90 and 
110“C). The TSDC thcmiograms show a single peak 
located at around 60-85°C (Figure 5). The slight shift in
Tunc (min.)
J'igureS. Thermally stimulated discharge current spectrum of PS films poled 
with 50 kV/cm at different (i.e. 30, 60, 90 and 110®C).
peak observed could be due the slight change in the 
electret forming conditions and the heating rate. A  limited 
number o f measurements were made with samples o f 5, 
10 and 25 /4m thicknes.s over a temp>eraturc range with 
silver, copper, lead and tin electrodes for charging and 
discharging transients as well as TSDC studies (results 
not shown) and it is found that there is no evidence o f 
thicknes.s- and electrode-dependence.
A number o f mechanism have been proposed [13-15] 
to explain the current transients observed in homogeneous 
in.sulators. The dc step response measurements, in which 
the current response is measured as a function o f time 
after a dc voltage is applied to, or removed from the 
sample, are c|bite similar to TSDC measurements, except 
for the temp^aturc being constant. However, when the 
measure men tsi are made at various temperatures, it is 
possible to ccHlect the dc step data at a specific time and 
to plot them as a function o f temperature [3,4,6]. When 
an eleclrct is heated to obtain the TSDC, the peak which 
generally appears near is due to the randomization o f 
the oriented dipoles or due to the release o f charge 
carriers from the traps [16]. Since PS is a non-polar 
amorphous polymer, dipoles cannot be the main cause o f 
polarization. The phenyl group in PS acts as a strong 
trapping site for the space charges during electret 
formation, which are released during TSDC measurement 
around T^ ,. For any given electric field, the time- 
dependence o f transient current is found to obey the law 
o f dielectric responses [17,18]. In the present study, the 
large currents obtained after the application o f field, 
subsided to much smaller steady values after a certain 
length o f time. This is because as the total current is the 
sum o f absorption currents which decays with time and 
static currents which remains constant. The absorption 
cunent reduces to zero when sample is polarized. It is 
observed that the rate o f fall o f the absorption current is 
low for lower Ep than for higher £' ’^s Le, at higher fields, 
the current approaches a stable value in relatively shorter 
time after the field is applied. It means that the 
polarization time decreases with the increase o f 
suggesting a dependence o f the resistance o f  the film  on 
the level and duration o f applied field. The time-dependent 
absorption current suggests that the polarization in sample 
may be due to dipolar orientation and trapping o f charge 
carriers in the bulk, whose injection from the traps will 
increase with increasing Ep and Tp, The sudden application 
o f voltage causes cloud o f carriers Le, a space charge, to
92 M S Gour, F K Khare and Ranjeet Singh
be injected from the contact into the sample. This free 
charge gives rise to a burst o f current. However, one 
must take into account the effects o f trap densities in the 
sample. The free charge forced into the sample settles 
into the traps and one observes the decay o f current, the 
rate being determined by the capture cross section o f 
traps for free earners. The magnitude o f charging current 
is greater than the discharging currents at corresponding 
temperatures. It appears that charge involved in the 
charging period is greater than the discharge period. The 
possible reason for this difference may be that the initial 
transients occur with empty traps and currents will be as 
large as allowed by the injecting barriers. As the traps 
become filled, the current reduces to the space charge 
limited currents with traps. In the discharging period, on 
the other hand, the trapped carriers will be discharged 
towards both electrodes showing a smaller current in the 
external circuit. The Curie-Von Schweidicr law was not 
found to be obeyed for a longer period o f time and the 
latter becomes progressively shorter (/.c. more and more 
limited period o f time) with the increase in temperature
[19]. The decrease in free volume lowers the mobility o f 
chain segments and also charge carriers. The decrease in 
mobility may be expected to reduce the conductivity. At 
higher Zip’s, a change in mobility may take place faster 
than at lower £p\s and also recombination o f charge 
carriers may be more. The above processes may be 
responsible to make the observed current in the present 
case to approach a stable value in relatively shorter 
periods under higher fields [20]. In the present case, the 
charging currents for samples poled at (with Ep's
100 and 2tK) kV/cm) and 120‘ C^ (with all £p’s) was 
found to increase monotonically with time and tend to 
saturate. Under higher Ep and 7'p, the electrons and holes 
are likely to drift through the sample bulk and accumulate 
at the metal-polymer interfaces, because the contacts are 
supposed to be blpcking to transport. The hetero space 
charge formed at the metal-polymer interface will result 
in a very intense field over the interface. Such a high 
field may cause the continuous increase in current with 
time. In the present case the current has been observed 
to be activated thermally. Tunneling can be unequivocally 
eliminated as a possible mechanism in the present case, 
since the currents are strongly temperature-dependent. 
Furthermore, the electrode polarization mechanism seems 
not to be operative in the present case. The electrode 
polarization predicts the strong dependence o f the electrode 
material on the decay o f the transient currents. Moreover,
uniform and electrode polarization requires the charging 
and discharging currents at a particular instant to vary 
linearly with charging field. The charging and discharging 
at various times after the application or termination of 
field arc found to follow the power law-dependence on 
field. The ob.servcd divergence from Ohms law at high 
fields and the thermal activation o f discharge current at 
various prescribed times, indicate the space charge 
formation. The various facts including non-polar structure 
o f PS, power law-dependence o f current on field observed 
values o f and thermal activation o f current over
temperature range as observed in present case, indicate 
that the space charge due to accumulation o f charge 
carriers near the electrodes and trapping in the bulk may 
be supposed to account for the observed currents. The 
decay o f current in the long time region for different 
samples, indicates the existence o f energetically distributed 
localized trap levels in the sample. It seems that at 
shorter times, only the shallow traps get emptied 
contributing to stronger current. However, at longer times, 
deeper traps with long detrapping times release their 
charges and the current decays at longer times. 
Discharging current, measured at various pre.scribcd times, 
vs. temperature plots (results not shown), arc characterized 
by a peak located at however, no shift is observed
in the peak temperature with lime o f observation. The 
peak is broad and probably it contains several minor 
processes, one o f which may be associated with the 7’^. of 
the polymer and the other may be due thermal release of 
trapped carriers. The broadness o f  the peak may he 
explained by assuming a distributed or multiple dielectric 
relaxations, which may be due to di.stribution in activation 
energy when the rotation o f the dipoles does not proceed 
in the .same environment. Alternatively, it may be due to 
di.siribution in relaxation time, when the rotational masses 
o f dipoles are not equal. The broadness o f the peak in 
the present case is, however, most likely to be distribution 
in relaxation time, because the peak is occurring near 
o f the polymer.
The TSDC thermogram shows a peak centered at 60'“ 
85”C. The value o f activation energy (E )  has been found 
to be 0.38 eV, This peak may be either due to dipolar 
origin or migration o f charge carriers through microscopic 
distance with trapping. In PS, the possibility o f  permanent 
dipole alignment is ruled out. However, the p>olarization 
process may be assumed to be due to the local movement 
o f molecular chains causing the release o f  trapped charge-
Charge decay characteristics o f polystyrene 93
I'hc origin o f space charge in PS can possibly be due to 
the injection o f charge carriers from electrode, the charge 
trapped in the amorphous crystalline interface o f the 
polymer or the microscopic ion displacement. The phenyl 
group in PS acts as a strong trapping site for the space 
charges during TSD measurement.
The equivalent time (/J at the TSDC peak temperature 
/,„ was evaluated from the relation [21]
E (I)
where, h is the reciprocal heating rale and K is the 
Boltzman's constant. Using the values o f T„, and E  for 
the observed peak, UT„,) was found to be 3.88 min. The 
ISDC peak, thus can rcavsonably be compared with the 
isochronal vs. T  plot at a constant equivalent lime o f 
4.0 min. The E  values obtained from isochronals were 
found to be 0.42 cV and agree well with the activation 
energy o f 0.38 cV  obtained from the TSDC peak. The 
value o f E  is small compared with the 1 eV typically 
required for the measurement o f ions, hence suggesting 
Die simultaneous action o f dipolar orientation ( i f  any) 
along with the migration o f clectrons/holes released from 
the valence band through microscopic distances with 
subsequent trapping.
The present study clearly exhibits that the TSDC 
peak can be investigated by isothermal step response 
measurements. The decay o f charge/discharge currents 
ciin best be described in terms o f a space charge 
mechanism and hence, (he observed TSDC peak can at 
least partly be attributed to the dissipation o f space 
charges during heating in a short circuit.
References
11J P K Kharc and Ranjcct .Singh Polymer International 34 407 (1994)
(21 A K Jonscher J. Phys. D 11 601 (1978)
(31 J Van Turnhoul Ihermally Stimulated Discharj^e of Polymer 
Elecrrects (Amslcrdarn : Elsevier) (197.5)
|4J G M Sesslar (ed.) Elect rets (New York . Springer-Verlag)
|5] E Neagu and R Ncagu Mater, U>tr. 16 213 (1993)
[61 J Vanderschuren and A Linkcns J. Appl Phys. 49 4195 (1976)
[7] D K Dasgupta and K Joyner J. Ph\s. U9 829 (1976)
[81 K M()hana Raju, P M Reddy and N M Murthy Indian./. Pure Appl. 
Phys 32 160(1994)
[91 P K Khafe Indian J. Pure Appl Phys 32 160 (1994)
[10) M S Gour. Recta Singh, P K Khare and R Singh Polymer 
Internaninal 36 33 (1995)
[11] M M  Per^an J. Electrochem. Soe. 119 892 (1972)
1121 P K Khaij ,^ P L Jam and R K Pandey Bull. Muter. Sci. 24 401 (2CK)1)
113) R H Wclilcn J. Appl. Phys. 43 1178 (1972)
( I4| A K JonsfcChcr J. Non-Cryst. Solids 8 293 (1973)
[15] Ranjcei $ingh, N Dasgupta and L P Yadav Indian J. Pure Appl. 
Phys. 22 222(1984)
116} D K Davis and P J Lcxrk m Perlman (ed.) Electreci.s, Charlie Storage 
and Transport in Dielectrics (Princeton, NJ : Electrochemical Sck.)
[171 M Aguliar, F Jaque and F J Balla-Calleja J. Mater. Sci U^ tt. 16 
2079(198!)
[18] P K Khare, R K Pandey, R R Chourasia and P L Jam Polymer 
Inrernational 49 719 (2(X)0)
[I9| L E Struik Physical Ageing in Amorphous and Other Materials 
(Ameslcrdam : ELsevier) (1978)
[20| P K Khare and S K Jain Indian J, Pure Appl. Phys. 35 408 (1997)
[21] P H  Ong and J Van Turnhout in Perlman (ed.) Elect rets. Charge 
Storage and Transport m Dielectrics (lYincelon NJ : Eicctnxrhemical 
ScH.*.)


Charge Decay Characteristics of Polystyrene

Forthcoming Publications - 1

De, S S

De, B K

Adhikari, S K

Indian J. Phys. 8 0  (2 ),  167-172  (2 0 0 6 )
A report on some speciHc features of the atmospheric electric potential
gradient in Kolkata
S S D e '', B K De\ S K Adhikari ',S K Sarkar’ , R B e r a A  Guha' and P K Mandal'
' C’cntie of Advanced Study in Kaifio Physics and Filcctronics, Uiiivcrsiiy oi C'alcutia,
92, A. P. ( ’ Road, Kolkata - 700 009. India
Department of Physics, lYipura IJnivcisily. Agariala. Suriyarnaninagai
 ^ Department of Physics, j^^nivcrsity of ('alcutta, 92, A f  
Kolkitii - 700 009, India
- 799 130, Tripura, India 
C Road.
E-mail de^syatn_sundar@yahoo co in
i!
R ct c iv e d  6  J u n e  2P0f>, n a  epft'ii 1 4  O ei e m b e r 2 0 0 5
Abstract ; The results of measurement of surface potential gradieni of the atmospheie in Kolkata (latitude 22‘*34' N) will be picsciited The 
observed fields at daytime and night time are seen to be higher and show considerable fluctuations from the daily averages of electiic field and also a tew 
hours difference in phase with the observations made at different tropical and temperate latitudes. The mean value of the potential gradient averaged 
foi 35 days over a period from February 2004 to January 2005 is around 200 Vm * and the maximum and minimum values are 1 14 times and 0 S8 limes 
the mean value, respectively. The results are discussed in terms of the variations of the local factors as well as distiibulion of thunderstoim activities.
Keywords Atmospheric electricity, potential gradieni. global electric field, thunderstorm activity
VACS Nos. 92 00.Pw, 92 OO Qx
1. Introduction
Electric fieltd at a point on the earth'.s surface depends on the 
major thunderstorm activity o f the globe and on the local 
environmental factors. There exists a correlation between the 
local electric field and worldwide thunderstorm distribution.
Various models for thundercloud electric field have been 
developed to investigate their behaviour into the region between 
the surface o f the earth and the upper atmosphere 1 1”3].
Also, there are models for the determination o f 
electromagnetic fields and charge distribution during lightning 
14, 5\. The surface-air temperature variations both at tropical 
latitudes (± 25^) and temperate latitudes (±  60^) and its upward 
trend [6, 7 ] are found to be very much interrelated with the 
global lightning activity [8 ). Such analysis could monitor the 
lightning activity over the global atmosphere.
Global weather activity maintains a potential difference of 
about 250 K V  between earth-ionosphere waveguide, which 
generates a potential gradient o f about 12 0  Vm'^ at the earth’s
orresponding Author
surface. A  vertical conduction current is maintained due to the 
finite conductivity o f air resulting in a DC global circuit. Electric 
field intensity undergoes diurnal and seasonal llucluations and 
found to be greater at the northern hemisphere during winter 
than in the summer. During fair weather electricity, there would 
be no process o f charge separation taking place in the 
atmosphere and the electrical phenomena are reasonably steady 
[9|. Within such fair-weather condition (quasi-static state), 
electric field, current density and conductivity over the surface 
o f the earth are subjected to both global and local variations. 
Global variations are associated mainly with tropical 
thunderstorms.
The production o f high potential difference between the 
earth and the ionosphere due to the total number o f  
thunderclouds acting together at any time, drives the air-earth 
current downward from the lower region o f the ionosphere to 
the surface pf the earth in the fair-weather region. This current 
in the nonpolluted areas varies in accordance with the 
ionospheric potential and columnar resistance, while in the 
polluted areas, due to the high aerosol content in the lower 
layer o f the atmosphere, the columnar resistance increases f 10 ].
©2006 lACS
170 5 S De et a l
Quarterly Diurnal Variation of Pot Gradient over Kolkata 
(Hourly Average)
E>
C9
oQ.
E>
“O
CO
O
“oa*
r - -  280
’£>
240 -J
------ -^----- ,------ ,------ ,------ ,------ ,------ ,------ 1------ , ,------ ,
, / February 2004 to May 2004. 90-J
220 _ 
200 -
/ ■ ■ :
/
/ ■ - -  
// \
85-
80-
UJ
180 - ^  75- 
o
2004 and January 2005 {Figure 8 j. The analysis shows that iht 
rms fluctuation in our measurements is around 33%.
(From Feb 2004 to Jan 2005)
190 -
— 1-----------r------1---- 1-------1---- »-------1------ •------ 1------
180 -
/ June 2004 to September 2004
170 J
/ \ : \
160 J 
160 J
140 -
V — - -
' \  ' ' , V -
~ r T"
Q
70 -  
66- 
60 -  
55- 
50
%■ «
• if ■
■ •
cyJE = 0  32952
260
• I  240 4
CO
O  220
o
Q- 200 -
1---- '---- 1---- -----1---- - --- 1---- - --- 1---- ^
\ October 2004 to January 2005
00 00
— I-----1-------1------1
04 00 08 00 12 00 
ur
16 00 20 00 24 00
Figure 6. Quarterly dturnal variation of poiciuiul gradient over Kolkata
M onthly diurnal variation of potential gradient over Kolkata  
(H ourly  A verag e )
February 2004
V
UU 02 IM 06 IJ8 10 12 14 10 16 JO .
\2
March 2004
180 190 200 210 220 230
Pot Gradient 'E' (Vm ’)
Figure 8. Plot of yearly mean values of KMS fluctuation of the poienii.ii 
gradient
Figure 9 shows the variation o f rms fluctuation {<T; //. i 
with respect to universal time. It is clear that the rms nuctuaiu i. 
is maximum around 0400 UT and 1000 UT and it is minimum 
around 0700 UT and 1900 UT.
We calculated the area under each diurnal variation of cvn\ 
month and plotted the percentage variation in Figure 10 lujJi 
bar represents atmospheric activity with respect to vciik
potential gradient in Kolkaia 
is clear that in winter seasons 
the potential gradient beconuN 
higher compared to Monsom 
season.
r -J
f v
April 2004
' U4 Ob Uri 10 12 14
UT
16 Jii 2-' 24 b IJ 14 K.
UT
K \ y '
1 r
V/
June 2004
I) 12 14 16
UT
July 2004
UT
I
October 2004
V
•\
no 02 04 06 0« J 12 14 10 16 20 22 24
UT
320
2^0
January 2005
UT UT
Figure 7. Monthly diurnal variation of potential gradient over Kolkata.
00  02 04 06 08 10 12 14 16 18 20 22 24
UT
Additionally, the obsetved 
average dturnal variation ot ihc 
potential gradient (as shown m 
F'igurc 2 ) is much different 
phase and amplitude from iht? 
universal value. The pt;ak 
observed at 16 UT is about 3 hi 
earlier in phase than predicic' 
under the world-wid 
thunderstorm activity Th 
amplitudes o f the diuin^ ' 
variation are much larger in on 
observations than the result 
obtained by other workers II- 
16J.
The variations ol 
potential gradient presented it 
different records, follow rnostl) 
the general trend o f fluctuation;
A report on some specific features etc 171
exctpung that the results iire interrogated by local elTects other 
than the global reasonings. The high value obtained as a 
consequence of the poor value ol' conductivity o f the air at the 
earth’s surface in Kolkata. It is due to the presence o f excessive 
jx>ljuuuit pjirticles (7 x 10'^  -1.15 x 10 )^ per c.c. [data t')bUiined 
Indian M eteoro log ica l Department by private 
communicationj, containing aerosols, aitken nuclei, CO^ from 
li>ssil luel etc,, wliich reduce the mobility o f the atmosplm^ic 
constituents [141.
(From Feb 2004 to Jan 2005)
Figure 9. Plol of yearly mean cliiinial flucniation of RMS fluctuation of 
ilie potential gradient
4. INdlutants and their effects on local electric potential 
^adient
Kolkata is a densely populated city, surrounded by small and 
large-scale industries. A ir is greatly invaded by pollutant 
pmicles emitted from many types o f industries. Thus, Kolkata 
tails under smjill-scale f;ur weather condition where tluctuation 
ot electric field and air-earth current are perturbed by ionization 
and ditferent aerosols which are produced locally [9J. Fine 
; piirticles having diameter less than 0 .1 fxm (Aitken nuclei), are
(from Feb 2004 to Jan 2005)
April May Juna July Aug
Month
Sapt Oct Nov Dac Jan
I
I iRure 10. Plot of monthly percentage variation of atmospheric activity 
 ^uced from integration of diurnal variation of tlie potential gradient of
month.
distributed in air, whicli lower the conductivity and increases 
the cc l^umnar resistance 117]. The atmospheric turbulence forces 
the positive space chiirges to higher altitudes against the forces 
o f the existing electric field. This generator effect o f the 
turbulence, affects the atmospheric electric field and current 
locally. The aerosol particles in the industri:il area o f Kolkata 
steadily changes their status at different times o f the day by 
coagulation, sedimentation, charge tnuisfer, initiated by the Ux:al 
physics c^ f precipitation. Industrial iictivity injects the particulate 
matter into the atmosphere [15].
It IS found that the diurnal vanalions of pt>tential gradients 
in Kolkata near town areas are caused rruiinly by urbiinization, 
industry and tralTic. The atmospheric suspensions, known as 
Haz^ e, arc mostly j^resent to the lower layers o f the atmosphere 
[18|. The rate o f productum and vertical transport o f ]x^llutant 
p;irticles determine the daily vanation of atmospheric |X)llution.
Ions strongly influence the electrical conductivity o f the 
atmosphere. If aerosols, such as cloud or fog dn^plels, haze or 
pollution panicles are present, small ions attached to them, form 
Marge ions’ , thereby reducing their mobility find the atmt i^sphenc 
conductivity. Thus, one o f llie possible reasons o f high value 
of the |X)tential gradient over Kolkata is due to the poor viUue ol 
the electneal conductivity o f the atmosphere. Pollutant particles 
due to smokes from combustion processes (domestic and 
industruil origin), reaction o f natural iind anthropogenic gaseous 
species, wind blown dusts reduce the conductivity f 19]. Aerosol 
particles (composed of combustion products and soil particles), 
which ixm smaller than 5gm in diameter, tend to form more stable 
suspension in air [20. 21 j. The presence o f nuclei (pollution 
particles artificial or natural) may combine with ions and 
decrease tlie concentration of, or immobilize the small ions, 
hereby the conductivity is reduced. It is very common with 
Aitken nuclei (smi^ke with about 0.1 /xm diaiTieter) due to which 
local electric field increase [22, 23]. The influence o f fossil fuels 
(CO2 emission) within the jxillutants is also resjxinsible for high 
value o f electric field. The variation o f energy consumption o f 
traffic (oil and gasoline) in Kolkata would contribute to a high 
Aitken count and there are changes in atmospheric dispersion 
that reduce the conductivity of the medium.
Moreover, differential heating by solar radiations may lead 
to convection and redistribution o f small ions and hence, 
decrease the effective conductivity o f the air which is supportive 
to liigher potential gradient.
5. Discussion
It is thus clear tliat the worldwide thunderstorm activity is not a 
direct factor affecting the electric field in Kolkata. The peak 
observed at 16 UT is about 3 hours earlier than the predicted 
worldwide thunderstorm activity, although the value is typically 
quite higher as described. Some measurements show tenperature
172 S S De et al
inversion conditions that influenced the diurnal behaviour of 
the electric field.
The atmospheric electric field is expressed as £ = ,
where V is the potential difference from the lower level of the 
ionosphere to the earth’s surface, A is the conductivity of the 
air and R is the columnar resistance. For fair weather, V and R 
change very little. £ is then controlled mainly by /land those 
parameters upon which /I depends. Thus, the local conductivity 
can vary over a considerable range without introducing a 
significant change in the columnar resistance. Because of various 
parameters on the land surface influencing the conductivity 
value, land measurements are not suitable to study global effects. 
Of course, fair weather measurements made over clean places 
like oceanic surfaces, high mountains, represent global effects 
and have been made useful for investigating the behaviour of 
global electric circuit.
Although the results presented here are mostly influenced 
by local effects giving much higher diurnal values of atmospheric 
potential gradients, these are in accordance with the trend of 
variation of potential gradient measured at the tropical ocean, 
the Bay of Bengal followed by certain lead in phase and amplitude
[24]. In their field curve of 40  days measurements, a maximum 
around 10 UT and a small secondary peak at 1900 UT occur, 
while the observation of 35 days average over Kolkata depicts 
the maximum at 0500 UT with a secondary peak at 1600 UT 
followed by the phase lead by 3 hours from the measurement in 
Indian Ocean, Bay of Bengal and Arabian Sea. The observed 
phase lead may be due to the local influence in the atmosphere 
over Kolkata. Moreover, our results also indicate a tendency to 
manifest the thunderstorm activity over Asia-Australia region 
which becomes maximum at 0800 UT. It is worthwhile to mention 
that the measurement at Asiatic tropical zones exhibit the 
resemblance of peak thunderstorm activity at 0800  UT of Asia- 
Australia region. So apart from local influences, in a tropical 
region, continental thunderstorm activity plays an important 
role in modulating the global electric circuit.
To explore regional thunderstorm activities and their effects 
on the global electric circuit, the data of atmospheric 
conductivity. Maxwell current and Schumann resonance 
phenomenon would be helpful along with the vertical potential 
gradient. Simultaneous measurements of the above mentioned 
parameters at different latitudes would definitely help in
understanding global as well as regional thunderstorm acti vitn^s 
It will allow critical re-examining of certain parameters oi 
atmospheric electricity which have served as de facto standards 
of global electric circuit.
Acknowledgments
The work has been funded by Indian Space Research 
Organization (ISRO) through S. K. Mitra Centre for Research m 
Space Environment, University of Calcutta, India.
References
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(21 P T Y Valinov and P T Tonev J  G eop h ys  Res  JOO 1477 
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(1996)
[4] M Dejnakanintra and C G Park J. G eo p h y s  Res. 79 1901 d‘P4
[5J R Kumar, R Jagdish and V Singh J. A tm os. Terr. Phys  57 124^ 
(1995)
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[9] T Ogawa J. G eo p h y s  Res. 90 5951 (1985)
[10] R C Sagalyn and G A Fauchcr J  A tm os Terr Phys  5 251
[11] R V Anderson M o n  W eather R ev . 95 899 (1967)
(121 J A Chalmers A tm o \ p h e r i<  e l e r t n n t y  2'“* edn (New >ork 
Pergamon) (1967)
[13] M Takagi and N Kanada P u re  A p p l  G eo p h y s  100 44 (I072i
[14] D Yeboah-Amankawah J. A tm os  Terr P h y s  51 1035 (I0X‘)) 
(151 B K Sapkota and N C Varshneya ./ Atm os Terr Phys  52 1 
[16] C G Deshpandc and A K Kamra J. G e o p h y s  Res  106 I42(r
(2001)
117] H Israel A tm osp h e rie  E lectric ity , Volume I; Fundamentals.
C o n d u c t i v i t y  (  I s r a e l  P r o g r a m  f o r  S c ie n t i f i c  Translation  
Jeru,Salem  ) (1970)
[18] A IVIani and B B Huddar Pure Appl Geophys 100 154 (1072)
[19] J M Prospero A ero so l Pa rtic les  in G lo b a l  Tropospheric  niemisin 
(Washington D. C.- National Academy IYe.ss) (1984)
[20] P S Guest, W H Mach and J W Winchester J. G eoph ys Res 89 
1459 (1984)
[211 W C Malm, J F Sisler, D Huffman, R A Eldred and T A CahiHi 
G eo p h y s . R es . 99 1347 (1990)
[22] H Flyger, K Hansen. W J Megaw and L C Cox J. A p p l Met 1* 
161 (1973)
[23] K Miura and T Sekikawa A tm os. E n v iron . 24b 1401 (1990)
[24] A K Kamra, C G Deshpande and V Gopalakrishnan J. Geoph^  ^
R es .  99 21043 (1994)


A Report on some Specific Features of the Atmospheric Electric Potential Gradient in Kolkata

Sastry, Sreehari

Lakshmi, Vijaya K

Ramakrishnancharya, M

IndianJ. Phys.m{2), 173-176(2006)
S y n th e s i s ,  c h a r a c t e r i z a t i o n  a n d  d i l a to m e t r i c  s tu d i e s  o n  
N - ( p - n - t r i  a n d  t e t r a  d e c y I o x y b e n z y l id e n e ) - p - to lu id in e
S Sreehari Sastry*, K Vijaya Lakshmi, M Rsiinakrishnancharya, Nanchara Rao, O Sahaya Baskaran
and C Ra^achandra Prabhu'
Department of Physics. Acharya Nagarjuna Uiaiversity. Nagarjunanagar 522 510, Andhra Pradesh. India 
' Faculty of Physics, Department of Applied Sciences, Higher College of Technology,
P.O Box -74, Al^Khuwair-133, Muscat, Oman
E-mail srccflari. ssastry @yahoo com
Received 17May 2005, accepted II November 2006
abstract Synthesis, characterization and phase transition studies are earned out on two Schiff base liquid crystal materials vie.. N-(p-/i-
ridct.vloxybenzyhdenc)-/7-toluidine, 130 1 and N-(/7-/i-tetradecyloxybenzylidene)-p-ioluidine, 140.1. The characterization studies (pha.scs and 
ihasc transition temperatures) are carried out using polarising microscope equipped with hot stage and differential scanning calorimeter. The phase 
lansition studie.s are carried out using dilatometric technique The results infer that these two compounds possess only one monotropic liquid 
rystalline phase viz., smectic-A. The order of phase transition across isotropic to smectic-A is found to be of first order l^ie results are discussed in 
iit light o f  the data available on other nO.m liquid crystal compounds
keywords Liquid crystal, synthesis, phase transition, dilatometry. density measurements 
•ACS Nos. 42.70 Df. 6 l30E b  64.70.Md
Introduction
"he homologous series, viz., N-(p-n-alkoxybenzylidene)-/?-/t- 
IkyUinilines, popularly known as nO.ms, exhibit rich but subtle 
l^ymorphism [1-31. The compounds are model systems to study 
he different types o f melting and attracted the interest of both 
hcoreticians and experimentalists. Dilatometric technique is one 
t the powerful tools to study the order o f phase transitions [4j.
a part o f systematic studies on nO.m compounds, this 
ommunication presents the synthesis, characterization and 
ilatometric studies on two Schiff base compounds, 
ndecyloxybenzylidene)-/7-toluidine (130.1) and N-(p-/i- 
;tradecyloxybcn2yIidene)-p-toIuidine, (140.1), The density 
udies are carried out to infer the nature o f isotropic-smectic- 
phase transition. The pressure dependence o f transition 
emperatures across the transition, is estimated from the 
leasured volume jumps and enthalpy data. The results arc 
iscussed in the light o f the reported data on the nO.ms’ liquid 
•■ystalhne compounds, which exhibit isotropic to smectic-A 
"ansition.
j Corresponding Author
2. Experimental
An Olympus polarising microscope (BX 50) along with Instec 
temperature controller with ±0.1 temperature accuracy was 
used for the textural identification o f liquid crystal phases and 
the determinations o f phase transition temperatures. Perkin- 
Elmer DSC-7 was used to determine the transition temperatures 
and relevant enthalpy o f transitions. A U-shaped bi-capillary 
pyknometer in conjunction with a cathetometer, was used to 
study the temperature variation o f density. The absolute error 
in the determination o f density is ±0.1 kg.m'^. The cooling rate 
followed during the density measurements was l®C/h in general, 
0.5^/h at the vicinity of isotropic to smectic—A transition.
The compounds in the present study are synthesized 
following the standard procedure [5]. The molecular structure 
for the compounds is given below.
..O
ns 13 and 14
©2006IACS
3. Results and discussion
174 S S reekari Sastry et a I
Figure 1. Miscibility diagram of 130.1 in 20.16.
This phase o f 130.1 is co-miscible with the phase o f 20.16. 
This confirms that the identified liquid crystalline phase o f 130.1 
and 140.1 is smectic-A.
The DSC thermo grams o f  130.1 and 140.1 are shown in 
Figures 2 and 3. The transition temperatures along with enthalpy 
values from thermal microscopy and DSC, are presented in 
Table 1.
3.2 Dilatometric studies on 130.1 and 140.1 :
The density measurements are carried out on both these 
compounds using dilatometer technique, which is equipped with 
temperature variation accessory. The variations o f density and
Table 1. Phase tran.sition temperatures (in®C) in heating aiul cooi„, 
cycles due to thermal microscopy. DSC and density measureineuts
3.1 Characterization and phase identification in 130.1 and 
140.1 :
The compounds 130.1 and 140.1, exhibit a single-phase variant 
in between solid crystal and isotropic liquid. The observed phase 
is monotropic.
On c(K)ling from isotropic liquid, a liquid crystalline phase
separates out in the form o f batonnets at 76.3‘XI? and 76.5 ”C 
in 130.1 and 140.1, re.spectively. These batonnets float in the 
isotropic liquid and finally, coalesce U> form focal conic fan 
structure, a characteristic texture o f smectic-A pha.se. This phase 
also exhibits homeotropic texture indicating it as an orthogonal 
phase. These observations indicate that the phase is smectic- 
A.
For further confirmation o f this phase, miscibility studies 
are carried out. The compounds, 130.1 and 140.1 are mixed with 
20.16 (independently), which also exhibit a single-phase 
smectic-A variant. As a representative case, the miscibility 
diagram o f 130.1 in 20.16 is shown in Figure 1.
Compound Crysial- Smeclic-A-
Hcati ng/< 'ooli ng Smectic-A isotropic Meliii
130.1
C TM 65.0 76.3
H DSC 84
C DSC* 64 2 76.5
C Density 76.3
140.1
f: TM 68.6 76 5
H DSC 8? <>(.
C DSC 67 2 76 6
c Density 76 5
20  -  
1 5
130 1
Heating
^  Cooling
1 J' 5®C/Minute 
U  10"C/Minute
60 65 70 75 80 85
Temperature (®C)
90
Figure 2, DSC thermogram of 130 I heating and cooling foi ditfti 
scan rates
Figure 3. DSC thermogram of 140.1 heating and cooling for 
scan rates
Synthesis, characte risa tion  and diiatometric studies etc 175
ermal expansion coefficient (a )  with temperature o f these 
,mpKiunds are shown in Figures 4 and 5.
gure 4. Variation of density and thermal expansion coefficient M^ i^th 
nporaturc in 130 1
jure 5. Variation of density and thermal expansion coefficient with 
jperature in 140.1
The estimated contribution o f molar volume per methylene 
)up increment o f nO,l series in the isotropic liquid at 
Iniind to be 16.4 x 10'  ^m"' mol ‘ in 130.1 and 15.5 x 10^ m  ^
’ in 140.1. These are found to be in good agreement with 
: reported values o f other nO.m compounds 40 .m [6], 50.m 
1, 60.m [8,9], 70.m [10,11], 80.m [9,12, 13,14,11], 90.m 
5,16,17,11], lOO.m 118] and 120.m [19] series o f nO.m 
mpounds. It is further noticed that these results are in 
cment with the reported values o f 16.42 x 10'  ^to 17.2 x 10'  ^
’ mol ‘ for methylene group contribution for isotropic liquids.
The density jumps { A p f 100) and the computed 
ermal expansion coefficient maxima at isotropic-smectic>A 
Insition = 1 / M vid M vjd T ) for these compounds along 
1th other compounds [20] which exhibit isotropic-smectic-A 
ase transition, are given in Table 2.
2. Smectic-A thermal range, density jump, thermal expansion 
P maxima and pressure dependence of transition temperatures 
!~A transition in nO.m compounds.
P'Pound
I I
^^'-Thcrnml A pfp  X 100 dT .^ tdP
range I0-4OC-I K.k.bar '
I 1.3 0.57 98.7 14.86
4.5 0.93 133.7 15.85
The isotropic-smectic-A transition is accompanied by a 
change from a disordered molecular arrangement o f isotropic 
liquid to a long-range orientation o f the molecules with 
simultaneous growth o f periodic layer arrangement in smectic- 
A  phase. Generally, this transition is regarded as t)f first order. 
The density jumps {Ap/p>iUyO) estimated from the vertical 
distance between density values tif extrapolated curve from 
isotropic and smectic-A regions at the observed transition 
temperatures across the transitions are 0,51^ /v for 130.1 and 
0.93% for 14.01 (Table 1). The larger density jump observed 
across / ~ transition than at /-nematic or /-cholesteric 
transition is due to the transformation o f random orientation o f 
molecules in isotropic phase into ordered molecular phase (which 
possess both long range orientational order with one 
dimensional periodic t>rdering) compared to only long range 
orientational order in nematic phase. .
The reported [6-19] minimum and maximum jumps across 
I-smectic-A transition are 0.35% and 2%. This shows that the 
values o f density jumps observed for these two compounds fall 
in the middle range. The large density jump and the calculated
thermal expansion coefficient maximum ( ) 98.7 x 10 ** ’
and 133.7 x 10"^%? * in 130.1 and 140.1, respectively, confirm 
the order o f the transition as first order.
The higher slope value o f density for the smectic-A phase 
(33.4 X I f o r  both the compounds) suggests the denser packing 
o f molecules and higher structural ordering in smectic-A phase 
compared to isotropic phase. It is interesting to note that the 
density slope in the isotropic phase o f 9.34 x 10'** fur 130.1 is 
found to be in agreement with value reported for other 
compounds o f nO.m series while the value o f 18.9 x 10'** for 
140.1 IS found to be higher.
The /- 5  ^ transition can also be visually observed in the 
pyknomeler bulb. 'The translucent smectic-A phase grew 
uniformly in the lower part o f the bulb and the less dense 
isotropic liquid appeared to float above smectic-A phase with a 
clear boundary between them. This type o f co-existence and 
the embryos appearing simultaneously at the bottom o f the 
bulb suggest nucleation growth analogy o f the isotropic to 
smectic-A transition. Further, the embryos, which are devek>ped 
at the bottom o f the bulb appeared with a characteristic 
translucent appearance rather than with a uniform, opaque, milky 
nematic appearance throughout the bulb. This suggests the 
simultaneous development o f orientational and translational 
order.
The pressure dependence o f  transition temperatures 
estimated from the Clausius-CIapeyron equation l(d l\./dP) = 
7'^ , (d M /A H )] (where 7^, dM ,^, AH are transition temperature, 
change in volume and enthalpy, respectively) is 14.86 K.k b a r ’ 
and 5.85 K.k bar ’ in the compounds 130.1 and 140.1,
176 S Sreehari Sastry et al
respectively. The observed poor agreement in the pressure 
dependence o f transition temperature (Table 1) among 
different compounds, which accounts the mesophase thermal 
stability in the domain o f chemical environment, may be due to 
the parameters being obtained in different experimental 
conditions.
3.3 DSC characterization o f  the order o f  pfiase transition:
The differential scanning calorimetry is an extensive technique 
not only for the detection o f phase transitions, quantitative 
determination o f the associated enthalpy changes at the 
transition and for the qualitative analysis o f materials (purity, 
isothermal crystallization efc.), but also for the determination o f 
the order o f transition whether first or second order. Navard and 
Haudin \21 ] proposed an elegant and simple methtxi to determine 
the order o f phase transition from the DSC peak heights or 
material quantities. The order o f phase transition can be 
determined from the magnitude o f the ratio (AO o f different 
enthalpy peak heights performed with two different scan
rates (/'  ^and Tj), which is a function o f the ratio o f the scanning 
rates,  ^(=  /?>, keeping the weight o f compound constant. It 
follows that for a first order transition, N  varies as the square 
root o f y?, while for second order transition, N  should be directly 
proportional to R. Here, wc have used R—2 {i.e., keeping the 
mass o f the sample constant, the DSC thermograms are obtained 
for scan rates 10 ‘X" /min and 5 °C/min).
The DSC thermograms scanned at 10 °C/min and 5 °C/min 
are shown in Figures 2 and 3 for the two compounds, 
respectively. The heights calculated for 10 ®C/min {hf^ and 5 ®C/ 
min (h^) are 4.5 and 3.1 in 130.1 and 4.1 and 3.1 in 140.1, 
respectively. The Navard and Haudin parameters, (h 2 /hj = R) 
are 1.45 and 1.37 for both the compounds, respectively. The 
values suggest that the order o f  transition in these 
compounds is o f the first order.
4. Conclusions
(i) The thermal microscopic textural observations show 
that the compound exhibits a monotropic smectic-A 
phase.
(ii) The data available on a number of nO.m compounds 
which exhibit isotropic to smectic-A transition, reveal 
that the density jumps across this transition varies 
between 0.36% to 1.99%. The density jump in the 
present compound (0.93 %) falls in the middle range 
of the observed values (0.36% to 1.99%).
(iii) It is interesting to note that the Isotropic-smectic-A 
phase transition can be visually observed in the 
pyknometer with the smcctic-A phase settling to the, 
bottom and the isotropic phase floating over it.
(iv) The observed density jump and the calculated them 
expansion coefficient ( a  ) confirm the order cw i 
transition as first order, which is further contiim 
from the value o f Navard and Haudin paranKti 
{h  ^/hj = 1.37) obtained form DSC.
Acknowledgments
We are thankful to Prof.V.G.K.M. Pisipati for providi, 
experimental facilities at the Centre for Liquid Crystal Resear, 
and Education, Acharya Nagarjuna University. Finatiu 
support rendered by University Grants Commission (No.I i( 
18/2003(SR)J, New Delhi is greatly acknowledged.
References
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[3 ] A Wiegeleben, L Richter, J Deresch and D Demus Mol ( 
CrvM. 59 329(1980)
[4 ] D Demus, G Konig, D Marzotko, R Ruramki, A Hauler I Lm 
C Salhmann and W Wcissflog Cryst K(\s Terhnol 2V 44 
(1994)
[5 ] V G K M Pistpati, A K George, C'h Srinivasii and N MiiriN , 
Naturforsrh. 58a 103 (2003)
[6 ] J V Rao, N V S Rao, V G K M Pisipati and C R K Muity /<< / h- 
Phys Chem. 84 1137 (1980)
[71 V G K M Pisipati, N V S Rao, P V Datta Prasad and P R AIjiuh 
Z-NaturforscJi. 40a 472 (1985)
[8 ] V G K M Pisipati, N V S Rao. M K Rao, D M Potukuclii .uullH, 
Aiapati Moi. Crvst. Ltq Cryst. 146 89 (1987)
[91 D Saran, B Bahadur and V G Bhide Mol Cryst IJq. C rvsi 51 i! | 
(1979)
[10] N V S Rao. V G K M Pisipati. Y Gouri Sankar and J S R Mun 
Acustica 60 163 (1986)
[11] Jitendra Nadh. C G Rama Rao, M Srinivasulu, D M Potukii 
and V G K M Pisipati Mol. Cryst. l.iq. Cryst 366 457 (2I)()
[121 V G K M Pisipati and N V S Rao Phase Trans 3
[13] C Rama Chandra Prabhu and V G K M Pisipati Cry^ st /?< s 7c(/w 
37 269 (2002)
[14] P Bhaskara Rao, N V S Rao, V G K M Pisipati and D .Saran fri 
Res. Teehnol. 24 723 (1989)
[15] P R  Aiapati, D M Potukuchi, P Bhaskara Rao. N V S Hao. \  ^
M Pisipati and A S Paranjpe Uq.Cry.st. 5 545 (1989)
[16] V G K M Pisipati, N V S Rao, M W  Nagi Reddy. C G Kama K 
and G Padmavathi Cryst. Res. Teehnol. 26 709 (1991)
[17] N V S  Rao. D M  Potukuchi, P V Sankara Rao and V  Ci 
Pisipati Liq. Cryst. 12 127 (1992)
[18] C Rama Chandra Prabhu Ph.iX Thesis. (Nagarjuna linnets' 
India) (1998)
[19] M Srinivasulu, D M Potukuchi and V G K M 
Naturforsch. 52 7 13 ( 1997)
[20] Ch Srinivasu Ph.D Thesis. (Nagarjuna University, India)
[21] P Navard and J M Haudin J. Thermal Analy^^  ^
(1984)


Synthesis, Characterization and Dilatometric Studies on N-(p-n-Tri and Tetra Decyloxybenzylidene)-p-Toluidine

Shinde, G N

Achole, P D

Indum J. Phy^ - «H2), 187-190 (2006)
( Ilh
M u l t i p l e  f e e d b a c k  t h i r d  o r d e r  a c t iv e - /?  f i l t e r  w i th  v a r y i n g  t a p p i n g  r a t i o  B
G N 3hinde* and P D Achole
Research Laboratory in Electronics, Yeshwant College, 
Nanded 431 002, Maharashtra. India
E-ma|l . shmdegn @ yahoo co in
Received J2 2005, accepted 11 November 2005
Abstract A third order active-/? filter using operational Mliplifiers (op-amp) and resistors, is designed with multiple feedback and feedforward
i n p u t  signal It is studied for different values of tapping ratio B. Center frequency circuit merit factor Q and the positive feedback resistor R which 
t.ips K, arc kept constant at 60 kH?. 10 and 4(K) f2. respectively. The circuit exhibits low pass, band pass and high pass response at corresponding output 
p o i n t s  I’he gain roll-off in low-pass response is unaffected by varying tapping ratio B. Band pass response for B -  0 5 shows better gam roll-off and 
IS more symmetric in nature Bandwidth of the circuit decreases as B is increased In high pass respon.se, overshoot increases with increase in B The gain 
u ill  p c i  octave in the transient part is about -t-14 dB for all values of B except 0,5. but the gain gets stabilised almost at 0 dB for B = 0 5.
T h u s .  I t  gives better performance for B =s 0.5. It is easy to design, suitable for monolithic 1C implementation and useful for high frequency 
) p c i . n i o n  II also gives better pass band gain
Keywords Center frequency, feedforward, filter, merit factor, multiple feedback, lapping ratio and third order 
PACS Nos. 84.30 Vn, 07.50 Ek
1. Introduction
rhe proposed active-/? circuit is designed and realized using 
op-amp |uA741C. It is an internally compensated op-amp. An 
iniernally compensated op-amp is represented by ‘ integrator* 
model 11-3]. Various configurations o f third order active-/? filter 
have been proposed [4-7].
The third order active-/? filter proposed in this paper, uses 
both positive and negative feedback i.e, multiple feedback and 
input signal fed forward [5, 8]. Change in the value o f B varies 
the feedback. This filter has been studied for different values of
The filter gives low pass, band pass and high pass response.
Circuit configuration
higure 1 shows circuit diagram o f the proposed third order 
active-/? filter. It uses three op-amps (p-A 74IC ) with identical 
gam-bandwidth-product (GB) and five resistors. The negative 
feedback is incorporated using resistors /?p /?2 and Ry Outputs 
“Of the three op-amps arc fed back to the inverting terminal o f the
^^ r^responding Author
first op-amp. The resistor /?, which in turn, is connected to non­
inverting terminal o f the second op-amp to constitute positive 
feedback, taps /?2- The tapping point o f /?2 by R is changed i.e. 
B is varied. The input signal is fed forward to inverting input o f 
the second op-amp.
R.
Figure 1. Circuit diagram for a multiple feedback third order active-R 
filter with varying tapping ratio B.
©2006IACS
188 G N SItinde and P D Achole
3. Circuit analysis and design equations
Op-amp P.A741C that is an internally compensated op-amp is 
represented by single pole model, also known as the ‘ integrator’ 
model [2J. Its gain is complex and is given by = 2fr F
(1)
where
Aj, = open loop D. C, gain of the op-amp.,
cOq = open loop-3 dB bandwidth of the op-amp =
27tFq ,
AqWq = GB = gain-bandwidth-product of the op-amp. 
For S »  cOn
A(S) = (\ W o )IS  = GB/S. (2)
Transfer functions of the proposed third order active-/? filter: 
for low pass, T^p^S): for band pass, T^p (5) and for high pass, 
r^^(S)is given below.
( 5 ) = - ( 1/ ) GB, GBj GS,/(x 15 ’ + X ,5 - + A-,5 + X4 ).
(3)
V (S )  = - ( 1//?4)GB, GB, s/(x,.s’ + + X,S + X4),
(4)
Tf,p(S) = (I//?4 ) 53/(X ,5’ + X .S -  + X 3 S + X 4 ), (5)
where
X, =(l/B,) + (l/(fl/f3))+ (l/«3) + (l//f4) - ( ( l -B )  RM)/B,
X 2  =GB2(BM) + GS,((1/B,) + (1 -B ) BjM) ,
X3 = {GB3 GB2 IRi)^GB2 GB,(RM),
X^  = GB,GB^GBJ R^ ,
M = \I{RR2  + B(\-B)RI) .
The circuit has been designed using coefficient-matching 
technique with general third order filter transfer function [31-
r (S ) = [ « 3  + S^+H , S + H 4]/
[s ^  +  <Wo((l / G )+  0-S- +  col ((1 I Q ) + l ) S  +  0} l\ .  (6)
Design equations are obtained by comparing eqs. (3), (4)
and (5) with (6).
X, =(VB,)+(l/(fi^2))+(l/R3) + (l/ «4 )-(a -S ) RM)lB = \
(7)
X 2  = GB, ( )  + Gfl, ((1//?,) + (1 -  B)/?2 W )
= <Wo((l/G+l). (8,
X 3  = (GB 3 GB,/B 3 ) + GB,GB|(/?iW) = <W(?((l/!y-i i),„,
X 4 =  GB 3 GB 2 G B , /R 3 =  (Og . (lOi
Eq. (7) to (10) are used to determine values of/?j, /?„ 
for different values of Q.
Table 1. Resistance values.
B Designed values ( Q  ) 
Used -values ( Q  )
/?, BR 3 il li!l<
0.12 55.70 k 4.17 k 500 67k
55 70 k 4 17 k 500 3 67k
0 3 2.40 k 3 25 k 974 2 ?7k
2.40 k 3 25 k 972 2 2Kk
0 5 1.58 k 3 03 k 1 515k )
1 58 k 3.02 k 1 51k 1 su
0.7 1.27 k 3 25 k 2 27k ()74
1.27 k 3.25 k 2 28k 670
09 1 00 k 4 41k 3 97k 44!
1 06 k 441 k 3 97k 440
Values of/?,, R^ , R^  and R^  for some values of B with 
kHz, Q = 10 and R = 400 are given in the Table I. Ftn pi acticdi
implementation, the values of all the resistances are impedance | 
scaled by 100.
The resistances R^  and R^  remain unaltered for chan^ zesin | 
B. The designed values are 81.30 k and 113 , respeciiveh
The values used are 81.25 k X2 and 113 42, respective ly
4. Experimental
The circuit performance is studied for different values of B with 
= 60 kHz, G = 10 and /? = 400 42. The general operating 
frequency range o f this filter circuit is 10 Hz to 1 MHz, as the 
operating frequency range of pA 741C op-amp is 10 Hz to i- 
MHz [9J. The value of GF (= GB  ^= GB^^ GB^) \s2^ (5.6) iO' 
rad / sec.
This circuit is also studied for different values of f'tr  ^
and R.
5. Results and discussion
From experimental study o f this filter, following observations 
are noticed for low pass, band pass and high pass at th« 
corresponding output terminals. Response of the circuit
Multiple feedback third order active-R filter with varying tapping ratio B 189
tudied for different values o f B (0 .12,0.3,0.5,0.7 and 0.9.) For 
^^ li^ ation of the circuit, the resistances must be positive. Hence, 
le value o f B has limit. In this ca.se, the theoretical limit is 
1154 0.9999.
4} U)w pass response :
igure 2 shows the low pass response for different values o f 
The cu to ff frequency is found to shift. The shift is almost the 
m ie for all values o f iS for which the circuit is studied.
Gain roll-off /octave in the leading part o f the stop band is 
slightly larger for B — 0.5. The gain roll-off is almost the same 
(lOdB/octave) for other values o f Gam roll-off in the trailing
Gain roll-off per octave near cutoff frequency in the stop 
nd IS smaller as compared to that away from the cutoff 
quency. For instance, for B — 0.5 with cutoff frequency at 32 
tz, the gain roll-off per octave for the octave 50 kHz to 100 
is -6.5 dB whereas for the octave 200 kHz to 400 kHz, it is - 
dB. The gain roll-off is not affected by change in B. Thus the 
'^uii exhibits almost identical low pass response for all the 
lues of B for which the circuit is studied.
\) Band pass response :
gure 3 shows band pass response o f  the filter circuit for 
l^ terent values o f B. Shift in the center frequency is observed 
t all values o f B. The shift is almost the same for all values o f 
decreased below and increased above 0.5.
Bandwidth o f the circuit decreases as B is increased. In the 
band, distribution o f frequencies is more symmetric for 
•5 i.e. the curve for B =  0.5 is more symmetric. Maximum 
ss band gain increases as the value o f B  is increased.
part o f the stop band is almost the same for all values o f B. It is 
higher for the input signal frequencies near - 3 dB cutoff 
frequency and decreases for the higher signal frequencies. For 
instance, for B = 0.5, the gain roll-off / octave for the octave 1 (X) 
kHz to 200 kHz is -14 dB whereas for the octave 500 kHz to
1 MHz, it is -lOdB.
Thus, the circuit exhibits better band pass response for 
B = 0.5.
(C )  High pass response :
High pass response o f the filter for different values o f B is shown 
in Figure 4. In transient part o f the response, gain roll-off per 
octave is small (12.5 dB) for B =  0.5 anc} large for other values 
o f B.
Overshoot occurs in the response. The frequency at 
which overshoe^ occurs is the same (80 kHz) for B < 0.5. 
is also same for B > 5 but slightly less (70 kHz). Peak 
magnitude o f the overshoot increases with increase in B. 
The gain gets stabilized almost at 0 dB for all values o f 
B = 0.5 at about 300 kHz signal frequency and for other values o f 
B, the gain gets stabilized almost at -  0.5dB at about 400 kHz 
signal frequency.
Thus, the high pass response o f the circuit is better for B iS
05.
190 G  N  Sh inde and  P  D  A ch o le
6. Conclusion
The circuit gives low pass, band pass and high pass response. 
In low pass response, the gain roll-off almost remains unaffected 
by varying tapping ratio B, It gives slightly better gain roll-off
and more symmetric pass band in band pass response toi /j
0.5. Bandwidth of the circuit decreases as B is increased In hi- 
pass response, overshoot increases with increase m B ij 
gain roll-off per octave in the transient part is about +14 dH | 
all values of B except 0 .5, but the gain gets stabilized almosi n 
dBforB = 0.
Thus, it gives better performance for center tap 
It uses only three op-amps and five resistors.
Acknowledgments
Authors are thankful to the UGC, Western Regional OH ice. Pm 
(India) for providing financial assistance to Dr. G. N. wShmdc (i 
Research project and FIP to R D. Achole.
Rcfereiicc.s
f l ]  Michael A Soderstrand Inti J Electronics 40 417 (1976)
121 S Snniva.san Inti J, Electronics 40 5 (1976)
[.“^ l C5 N Shinde, P D Achole and P R Mirkule hujian J rin^  T 
237 (2003)
[4J O N Shinde, P B Paul and P R Miikutc Sadhana 2S 19] 9 
I5J A B Kadam and A M Mahajan ./ Instrum Sot' India 25 
(1995)
f61 K Radhakrishna Rao and S Srinivasasn IEEE ’Dmw ( uai 
Systems CAS-21 260 (1974)
[7] M A Soderstrand and S K Mitra Inti J Electt onn \ .hi: 
(1971)
1«1 Cl N Shinde et al, Bull. Pure Appl Sci 21 7« (200?)
19] Budak and J) M Pelrela IEEE Trans Circuit Jhctns ( 'I-I9 ' 
(1972)


Multiple Feedback Third Order Active-R Filler with Varying Tapping Ratio B

Singh, C P

Chauhan, R S

iian J. Phys. 80 (3), 311-312 (2006) i^?ep ly  to C o m m en t
Reply to: “Comment on the paper ‘Analysis of thermal expansivity of 
alkali halide crystal’: NaF as an example’
[I n d ia n  J . P li^s . 78 1215 (2004)]
C P Singh alsid R S Chauhan*
Deparimeni of Physics, R B S Coflcgc, Agra-282 002. Ullar Pradesh, India 
E-mail : rvschauhanC*yahoo.com
Received 24 November 2005
In the present Comment, Kumar e t a l  have made a case 
against the recent work on thermal expansivity of alkali 
halides published by Singh and Chauhan [IJ. However, the 
Comment by Kumar e t  a l  is a very weak one and the 
aigumenls given are not valid for the reasons given 
helow :
( 1)
(2)
Tills is true that there are few misprints in the paper 
by Singh and Chauhan 11), for example the fourth 
column D for NaF in Table 3 and caption to Figures
2—4. In fact, the original version of the paper 
contained the plots for all the eight cry.stals, but 
following a suggestion made by the referee, they 
were reduced to three only. However, the correction 
could not be made in the caption to Figures 2—4. 
This is an easily understandable happening but 
Kumar e t a l  have written unwanted statements (one 
can see the last paragraph written by them on 
pages 5 and 6, and the similar statements also 
given in the beginning).
The mistake in printing of one column only for NaF 
encouraged Kumar e t  a l  to write a paper. Why did 
they not include remaining seven crystals in their 
analysis? Certainly, NaF cannot be an example, 
which they have mentioned in the title of the paper.
(3) Singh and Chauhan [1] have rectified an error in the 
formula of thermal expansivity a  adopted by Kumar 
13].
’Corresponding Author
a  = OTo + cc'T , (1)
Eq. (1) was not consistent as it does not yield 
O’ = at r  = T q . So eq. (1) was modified as
cr = CTo + a \ T  -  To). (2)
It was found by Singh and Chauhan [1] that this 
correction modified significantly the final results for 
the temperature dependence of interatomic distances 
in case of alkali halides.
(4) In the present Comment, Kumar e t  a l  emphasised
that their eq. (1) is correct. They redefined the 
boundary condition <ar = oTo al T =  0. However, 
Singh and Chauhan performed their analysis by 
revising the Kumar analysis given in Ref. (3]. In 
that paper, Kumar has taken = <afo at T = Tq and 
not at r  = 0. One can easily verify from Ref. [3] that 
the values of are at 300 K which is also the 
initial temperature taken by Kumar in his calculations. 
Singh and Chauhan have emphasised that eq. (1) is 
not valid when represents the thermal
expansivity at >  0.
(5) Kumar e t a l  have used eq. (7) to justify the validity 
of eq. (4). It should be mentioned that at T = 0, eq. 
(7) yields = 3.912 x 10“^  which is not the value 
for NaCl at room temperature. Thus, in eq. (8) 
is not the value of at T =  Tq. On the other hand, 
in eq. (4) of Kumar e t  a l ,  cCq is certainly the value 
of a  at r  = To = 300 K [3]. Thus, eq, (4) is not
02006 lACS
312 C  P  S in gh  a n d  R  S  C hauhan
(6)
consistent with the boundary condition at T = Tq 
for which cx^  corresponds. This has clearly been 
dem ostrated in the paper by Singh and C hauhan 
(First paragraph o f  ‘R esults and D iscussions’ and 
the results given in Table 2 ) .
As m entioned in our paper [1 ]  we have taken
guidance from Dr. Jai Shanker. It is worth mentionin 
here that Dr. M K um ar also com pleted hi.s Phf) 
under the guidance o f  Dr. Jai Shanker.
Reference
f I ] C P Singh and R S Chauhan Indian J, Phys. 78 1215 (2004)


Reply to: “Comment on the Paper ''Analysis of Thermal Expansivity of Alkali Halide Crystals’: NaF as an Example”

Kar, A

Bose, C

,ulmJ 8 0 (4 ), 357-360 (2006)
Ground state energy in a spherical GaAs-(Al,Ga)As quantum dot
with parabolic confinement
f
'I
A KarlmdC Bose'
D epa rtm en t o f  B le c tron ic s  a ^ l  'Ie le c t>m ir.un ica tu )ii B n i; in e e iin g .
Jaclavpur l) t i iv e rs a | ',  K o lka ta  700 032, Ind ia
\
E m a il ju d e e ^ O l 543 hot m a il com  
RcrcivtuJ 7 Oitoher 200^ >, accepted 21 Frh/iunv 2006
hslract A n  a lle m p t i.s made lo  d e r iv e  Ihe g round  stale energy o f  a sphenea l dot hav in g  I'ln ile  quan tum  w e ll w ith  p a rabo lic  p o te n tia l The
nvrd icsult is com pu ted as a fu n c tio n  o f  the size o f  CJaAs-A l.Ga, .As sphc iica l (juantum  dot, fo i d iffe re n t b a r iie i heigh ts o f  the po ten tia l w e ll The  
oiinvl kvc ! in a parabo lic  do t is found  to  he m uch h ighc i than that in a s im ila r dot w ith  squa te*we ll po ten tia l.
rwAords g u a n tu m  do t, ene rgy leve ls , sem iconducto rs . l l l - V  com po tinds
U S Nos. . 73.21.La,71.55.Eq.
Introduction
iKinium dots (QDs) are designable mesoscopic atoms easily 
leviable in bulk electronics. Such zero-dimensional structures, 
-ing solid state systems with an atomic like density ol states, 
ivc attracted much interests for an efficient replacement of 
her quantum heterostructurcs for emerging semiconductor 
-\iccs. These semiconductor QDs exhibit various interesting 
opcriies, which indicate their large applicability to electronic 
id optoelectronic devices [1-5], For designing and proper 
metioning o f these devices, the quantized energy level 
Juciures in such quasi-zero dimensional (QOD) systems have 
' be known very accurately.
Studies reported on Q O D  structures have m ostly  dealt w ith  
uantum wells (Q W s) ha v in g  square w e ll [xHentia l (SW P) w ith  
niteor in fin ite barrier height. B u t in  p ractica lly  realizable QW s, 
'c potential p ro file s  assume a pa rabo lic  fo rm  rather than the 
juare or rectangu lar shape, w h ic h  has been so prevalent, 
^^ -'cntly, few works on parabolic w e ll w ith  in fin ite  barrier height 
iwc been reported [6»7]. B u t cons ide ring  a w e ll w ith  a f in ite  
^•ner height is a m ore p ractica l approach, since potentia l w e ll 
infinite barrier height is not realizable at a ll. The most popular 
nf lattice-matched m ateria ls  used fo r  the rea liza tion  o f  a
‘Tfesponding Author
heterostruciure is CuiAs and AI^CkIj ^As. At the heteroinlertace 
o f these two materials, the maximum conduction band edge 
discontinuity which acts as the well barrier is limited to only
0.33eV. Thus, the actual scenario is fur from the ideal case for an 
infinite barrier QW, and the finiteness of the well barrier must be 
taken into consideration in order to estimate the electronic energy 
states in a QD.
In this communication, the lowest electronic state will be 
derived for a finite barrier spherical QD with parabolic 
confinement. The ground level energy will be computed for 
CiaAs - A1 Ga, ^As QDs of different barrier heights realized by 
varying Al-concentration (a ) in (Al,Ga)As alloy, the barrier 
material.
2. Theoretical background
The Hamiltonian in a spherical QD can be expressed, in the 
effective mass approximation, as
H o = - (7 iV 2 »> * )V ^ + V (r ).  (1)
where m* is the effect! ve mass o f electron. For a dot o f radius R
with parabolic potentia l w e ll, the c o n fin in g  po tentia l V ( r )  can
be described as
02006lACS
358 A K a r and C Bose
V { r )
_ U \ / 2 )m l (0 - r - ,  r <  R. 
~ \  r > R ,
(2)
where m*, is the e ffec tive  mass o f  e lectron in the dot m ateria), 
0 )  is the parabola frequency, and V^  ^ is the height o f  the potentia l 
barrier. In a f in ite  Q D , is essen tia lly  the conduction  band 
o ffse t due to the band gap d is c o n tin u ity  between G aAs, the dot 
m ateria l and A I^G a ,^A s , the em bedding m ateria l. In the case o f  
a parabolic Q D , the baixier height is related to the dot size through 
the rclatit^n
(3)
Using the above conditit^ns, the Schrodmger equation for the 
well and the barrier regions can be written as:
) V V  + (yl2)m1jo-r-y/ = Ey/■
•or r < R  (4a)
and
-(^iV2w,‘ ) V-v/ + V„v/ = Eyi,
fo r  r >  R,  (4b)
where ////* is the e ffective  mass o f  e lectron in the ba n ie r m aterial.
F or a spherical Q D , the electron w ave function  corresponding 
to the unperturbed H a m ilto n ia n  can be w ritte n  in  the standard 
factorized form  [8 ] as
y/{r, 0, <!>) = -  K„,,((9,<*), (5)
w here x A r )  and y,,,, ( 0 ^ 0 )  are the  rad ia l and the angle 
dependent parts o f  the w a ve fu n c tio n ; /. m  be ing the associated 
quantum  numbers.
The ab<ive fac to riza tio n  y ie ld s  the rad ia l part o f  eq.(4a) as
d ~ Z i ( ' ' ) J d r -  - -  /I-/-" -/(/ + l)/;--J^,(/-) = Q, (6)
w h e re k~ =  2m*^e ( h~  and A  =  / ; / ^ E / h  .
The so lu tion  to  th is  equa tion  is o f  the fo rm  [8 ]
X , { r )  =  C r ‘* ' E x p { - ^ r " / 2 )
f/[</ +  3/2-//)/2.(f + 3/2);ylr^], (7)
where U  stands fo r  c o n flu e n t hyp e rg eom e tric  fu n c tio n , C  is a 
constant and j u ^  k " / 2 A  =  E / h w  .
Thus, fo r  the low est energy leve l { i .e.  / =  //z =  0 ) ,  the cIluk, 
w a ve func tion  in the w e ll reg ion  is ob ta ined fro m  eqs.(5) 
as
yf,y„ =  N^ E x p  { - A r - / 2 )  
u [ o / 2 - M „ ) / 2 3 / 2 - , A r ^ - ] ,
where the constant takes the va lue o f  ih
constant C  in to  accoun t, and / /^  =  E^^jUto  , hem j ti, 
g round state energy o f  the Q D .
F or ca lcu la tions  pe rta in in g  to  the barrie r, the grouiul stdi 
wave fu n c tio n  can be ob ta ined in a s im ila r  mannei. ,is
= A . (1 / y ) Exp{-X{)r ) ■
where X { )  =  -  E^^) !  and is another cimsKn
t(  ^be determ ined fro m  the c o n tin u ity  o f  the wave lunciiun ih 
w e ll boundary. The e lectron w a ve fu n c tio n  fo r  the ban lei ici-m 
thus f in a lly  becomes
y//,o =  N , R  E x p { - A R - / 2 )  
u [ 0 l 2 - p „ ) / 2 . 2 / 2 - . A R - ] i \ / r )  E x p { x u U i / )  (iO
F urthe r a p p lica tio n  o f  the boundary  con d ition  lor a i 
c o n t in u ity  across the  in te r fa c e  be tw e e n  the dot and ih 
em bedding m aterial, y ie lds the fo llo w in g  transccndcnial eijiiatu'
2(/ '[(3/2-/.„)/2.3/2;a/?q ^  
(y[(3/2-//o)/2.3/2;/l/?d
where is the d e riv a tiv e  o f  the con flu e n t hypergeoincin 
fun c tion  U  w ith  respect to  . S o lv in g  the above eci.dl 
nu m erica lly , the low est unpertu rbed energy i>f an clcctu i 
con fined in a spherical Q D  w ith  f in ite  ba rrie r parabolic potentu 
w e ll can be obtained.
3. Discussion
For num erica l com p u ta tio n  o f  the ground state energy in a Imite 
G aAs-A l^.G aj_^As Q D , w e have assumed tha t the band p?  
d is c o n tin u ity  in these tw o  sem iconducto rs  is distributed about 
60%  on the con du c tion  band and 40%  on the valence hand, 
w h ile  the  to ta l band  gap  d if fe re n c e  is a fu n c tio n  ot 
concen tra tion  (x ) g iven  by  ~  1-247 x  .
H ere, a ll the m ate ria l param eters o f  G aA s and Al^Ga, 
have been taken fro m  R e f. 19]. In  the present analysis, the valuta 
o f  A l-c o n c e n tra iio n  has been lim ite d  to  0 .45, since for ' 
the nature o f  energy band s truc tu re  o f  the AI^Ga^.^A.s all^ ’)
Ground s ta te  energy in a  S fd ie n c a l GnAs-(As.Gci)As q u a n tu m  d o t etc 359
I h inges to indirect band gap, and the present barrier height 
ncatmtMit will no longer be valid. Figure 1 exhibits the variation 
he ground state energy with the radius o f a spherical GuAs- 
\\ Ga As QD with parabolic potential well, for three different 
illov compositions. The obvious lowering in the ground level 
eneigy with increase in dot size is evident from the figure; lack 
()1 earner conlinement in large dots being respcmsible for such 
Liieiuy lowering. For the sake o f  comparison, standard 
established results for spherical GaAs-AI^Ga, ^ As QD with SWPf 
h.ivc also been presented in the same figure.
035|- I
thecarrier confinement is so weak that even a small increase in
other hand, in the ca.se o f a QD with parabolic potential well, the 
radius ot a quite large dot is effectively small at the bottom o f 
the QW, making the confinement o f the carriers still feasible, 
and thereby maintaining distinct energy values for different 
barrier heights. However, in large dots, the ground state energy 
becomes almost independent o f dc>t size.
l inurc 1, The y io u n d  s la te  e ne rg y  as a f i i i i c l io n  o f  the rad ius  R c^f a 
^phuiL.il ( i. iA s -A l Ua, A s Q D  w ith  a p a ia bo lie  (s o lid )  and a sc.]uaie (b io k cn )  
wfll po luu ia l fo r three d if fe re n t A1 concen tra tio ns - (a ) .v =  0 .45 , (b ) \ -
\ 0 iO mul (L) \ = 0 15
A ctmiparison between the energy levels in a QD with 
paiabolie and .square well potential leads to the conclusion that 
ihe physical confinement o f the carrier is stronger in the case of 
parabolic potential. In the case o f a square well, throughout its 
height, the width o f the well is uniform and equal to the dot 
diameter 2R. But, in the case o f a parabolic well, the well width 
vaiie.s within the dot; starting from zero at the bottom o f the 
v^ell. Its width increases gradually to the maximum value 2R at 
the lop of the well where the barrier height is I'hercfore, 
carriers in a parabolic well can be thought o f as being confined 
an effectively smaller dot with respect to those in a square 
'^ cll. As a result, the carrier confinement is stronger in a QD with 
parabolic potential profile and the lowest energy level lies higher 
h^an the corresponding energy level in a dot with SWP. It is 
luiiher to be noted that in the case o f  SWP, the ground levels 
QDs with different bairier heights converge for large dots, 
energy level then approaches to that in bulk material, where
height o f the potential barrier w ill not cause any 
appreciable shift in the corrcspK>nding energy levels. On the
Dot Radius (nm)
Figure 2. The  g io u n d  state c u c ig y  o f  a p a rabo lic  w e ll as a fu n c lio n  o f  
the lad ius R  o f  a sphenca l CiaAs-Al^CJa, ^As Q I)  fo r three d if ie ie n t parabola  
fieq iienc ics ; (a) fo =  3.."^2157 x  1<)-^ lad ian /sec, (b ) gj =  2 71205 x  I ( ) - '  
radian/see and (c ) to =  I 01771 x  lO '^  lad ian /sec
Figure 2 shows the variation o f the ground stale energy 
with the dot radius for different curvatures o f the confining 
parubc l^ic potential. Here, the typical values o f curvature for the 
parabolic potential /.c.. those o f parabola frequency (u have 
been estimated from eq.(3) for a dot o f radius 10 nm, with three 
barrier heights corresponding to three Al- concentrations .x' 
— 0.45, 0,30 and 0.15. The figure shows that as the dot radius 
g(^es on increasing, the ground level energy initially increases 
and gradually saturates. For a finite potential well, the barrier 
height IS related to the dot radius through eq.(3). Therefore, f(^ 
a particular value o f co . the barrier height essentially 
increases with dtn size, resulting in stronger carrier confinement 
and thereby, lifting the lowe.st energy level. However, .such effect 
is pn^minent only upto moderately large dots. Beyond those 
values o f dot radii, the carrier confinement becomes so weak 
due to the size o f the quantum dot itself that further increase in
does not influence the ground energy significantly. Thus, 
the energy levels for different (o eventually saturate with 
increasing dot .radius; smaller the value o f aj , larger the value 
o f dot radius at which the energy saturation takes place.
4. Conclusion
In the present work, the ground state energy in a spherical QD 
having finite quantum well with parabolic potential has been
360 A Kar and C  Bose
derived. The derived result has been computed as a function of 
the dot size for different barrier heights of the potential well 
formed in a GaAs -  (AbGa)As QD. In a finite QD, higher values 
of ground level energy have been obtained in a well with 
parabolic potential as compared to that of SWR Therefore, our 
observation implies a stronger confinement in a practically 
realizable QD, where the confining potential can be better 
described by a parabola rather than a square - the most common 
and simple assumption.
Acknowledgment
C. Bose wishes to thank the Centre for Nanoscience and 
Technology of Jadavpur University for financial support.
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[9] S Adachi J Appl. Phys 58 R1 (1998)


Ground State Energy in a Spherical GaAs-(Al,Ga)As Quantum Dot with Parabolic Confinement

Panigrahy, N N

Mahapatra, D

Panda, B N

Debye Frequency and Interplay of Superconductivity and Antiferromagnetism in Tc High Superconductors

Mahalakshmi, S

Manja, Srinivas

I inJmnJ- rhy^ -» » ( 2 0 0 6 ) c p y i ^ io te
IR  and X-ray studies on nickel ferrite with rare earth doping
S M a h a la k s h r n i’ i\0d  K S r in iv a s a  M a n ja
D e pa rtm e n t o f  P h y s ic |, P ond iche i iy  U n iv e rs iiy ,
P onc lie he riy ^605  014 . In d ia
R -m a il • m aha la l|shm ism  C«Pgmai! com
K c c e iv e d  19 Scptcn iln^t 2(ip5. a r n 'p r c d  19 Ja n u a ry  2000
Abslract : The n ic ke l tc n ite  o l e om po s iiio n  Ni^ Fe^^ w ith  .v =  0.3 , 0 5.0 7, 0 9 doped w ith  neodym ium  and g a d o lin iiin i w e ie  stud ied by in lia ie d  
ahsoipiion spectroscopy. The  IK  spec trum  .showed tw o  m a in  abso rp tion  bands and v, in the range o f  4 0 0 cm '-6 0 0 cm  ‘ a iis in g  from  the octahedra l 
.mil u tiahedra l com p lexes The  p o s it io n s  o f  a h so ip tio n  bands are com po s it io na l dependent who.se dependence co u ld  be a tt iib u le d  to  the va r ia tio n  m  
uitiDn -  n \> g e ii bond d is tances . T h e  fo rce  cons tan t o f  te trahed ra l and oc tahed ra l sites supports  ca tion  d is t r ib u t io n  W ith  the a dd it io n  o f  g a d o lin iu m  
.ll)^oll)llon bands and were  fo u n d  to  be b ioadencd  and the peaks arc d iffu sed . The  la ttice  constants w c ie  found  to  decrease w ith  the a dd it io n  
[ iKfulwnuini and g a d o lin ium .
[ K e \uo rds F e rrite s , in f la te d  spec tra , in te i io n ic  d is tances
|r ,U  S Nos. 61 lO .N / ,  75 50 O g . 78  30 - j
I he infrared s p e 'c tro s c o p y  i.s a n  im p o r ta n t  a n d  n o n d e s tr u c tiv e  
diaiactcnsing to o l  w h ic h  p r o v i d e s  q u a l i t a t i v e  in f o r m a t io n  
icijaiding structuriil d e ta i ls  o f  c r y s t a l l in e  m a te r ia l  ( I j .  'F h is 
kvhnicjue is b a s e d  u p o n  th e  f a c t  t h a t  a c h e m ic a l  s u b s ta n c e  
shows m a rk e d  s e le c tiv e  a b s o r p t io n  in  th e  in f r a r e d  re g itm . T h e  
icsiilts fro m  IR  a b s o r p t io n  s tu d y  c a n  b e  u s e d  to  in te r p r e t  th e  
ilcctncal a n d  m a g n e tic  p r o p e r t ie s  o f  th e  f e rr i te s  1 2 ) . T h e  v a r io u s  
absorption b a n d s  p r e s e n t  in  th e  s p e c tr u m  r e p r e s e n t  th e  d e ta i ls  
icgaiding f u n c tio n a l  g r o u p s  a n d  th e ir  l in k a g e s  c a n  b e  e x p lo r e d . 
They are fo u n d  to  b e  d e p e n d e n t  o n  a to m ic  m a s s , c a t io n ic  ra d iu s , 
cation -  a n io n  b o n d  d i s t a n c e s ,  c a t io n  d is t r ib u t i o n  etc. I n f r a r e d  
''Peciral a n a ly s is  h a v e  b e e n  c a r r ie d  o u t  f o r  s e v e ra l  f e rr i te s  a n d  
reported tw o  a b s o r p t io n  b a n d s  w i th in  th e  w a v e n u m b e r s  ( 8 0 0  ~  
200)cnr* [ 3 | ,  w h ic h  a re  a ttr ib u te d  to  th e  te tra h e d ra l a n d  o c ta h e d ra l 
group c o m p le x e s  o f  th e  s p in e l  s t r u c tu r e ,  r e s p e c t iv e ly . T h e  IR  
spectra o f  s o m e  m ix e d  C o - Z n  a n d  M g - Z n  f e rr i te s  h a v e  a ls o  b e e n  
reported [ 4 ] .  F a rT R  s p e c tra l  s tu d ie s  o f  m ix e d  L i- Z n  fe rr ite s  w e re  
m ade b y  R a v in d c r  [ 5 ] .  H e  h a d  c o r r e la te d  v, , vs a n d  
bands to th e  F c"'^ io n  c o n c e n tr a t io n . IR  a b s o r p t io n  s p e c tr o s c o p y  
‘ind the re s u lts  s h o w in g  th e  c o m p o s it i o n a l  d e p e n d e n c e  o f  f o r c e  
y<^nstant, a re  a t t r ib u te d  to  th e  c a t i o n  o x y g e n  b o n d  d is ta n c e s  
TTie s tr u c tu r a l  d i s to r t io n  in  c a s e  o f  c h r o m iu m  s u b s ti tu te d
Voi•t^ J'Ponding Author
n ic k e l f e rr i te  ha.s b e e n  s tu d ie d  (Vf. 'f h e  IR  .sp ectra  o f  C d , C o , 
M g , N i , Z n , C u  etc c o n ta in in g  f e rr i te s  h a v e  b e e n  re p o rte d  18 ,9 1 .  
T h e  X -ra y  s tu d ie s  fo r  z in c  s u b s ti tu te d  N i-P b  fe rr ite s  w a s s tu d ie d  
b y  S a b le  e ta l  1 1 0 ) .  In  th is  w o r k , w e  h a v e  r e p o rte d  a n a ly s is  fo r  
IR s p e c tra  a n d  X -ray  s tu d ie s  o f  Ni^ ^ 4  fe rr ite  sy.stern
in n a n o p h a s e  w ith  x  =  0 . 3 ,  0 . 5 ,  0 . 7  a n d  0 . 9  a n d  d o p e d  w ith  
n e o d y m iu m  &  g a d o lin iu m .
T h e  s a m p le s  h a v in g  g e n e r a l  c h e m ic a l  fo r m u la  N i^
(w h e r e  x  =  0 . 3 ,  0 . 5 ,  0 . 7  a n d  0 . 9 )  w e re  p r e p a r e d  b y  ta k in g  th e  
n e c e s s a r y  a m o u n t  o f  n ic k e l c h lo r id e  a n d  iro n  p o w d e r  a c c o r d in g  
to  th e  s to ic h io m e tr ic  ra tio  N i^ F e , ^  ( ) ^  .
T h e  w e ig h e d  c h e m ic a ls  w e re  d is s o lv e d  in  d ilu te  H ^ S O ^ a n d  
h e a te d  s lo w ly  to  e v a p o r a te  th e  s o lv e n t. T h e  r e m a in in g  m ire  
w a s  t r a n s f e n e d  in to  a p o rc e la in  c ru c ib le  a n d  w a s k e p t in a fu rn a c e  
a n d  h e a te d  in  a ir  fo r  f o u r  h rs  a t 5 0 0 ^ ’C . T h e n  it w a s  a llo w e d  to  
c o o l s lo w ly , till th e  ro o m  te m p e ra tu re  is re a c h e d . T h e  fire d  s a m p le  
w a s  g r in d e d  to  f in e  p o w d e r  a n d  w a s  a g a in  h e a te d  to  95 0^^C  f o r  
tw o  h rs . A fte r  c o o lin g , it w a s  g r in d e d  to  a  f in e  p o w d e r .
T o  c o n f ir m  tihe c o m p le tio n  o f  m o le c u la r  s ta te  r e a c tio n , th e  
s a m p le s  w e re  s u b je c te d  to  c h a r a c te r iz a t io n  b y  X -ra y  d i f f r a c tio n  
a n d  I n f r a - r e d  a b s o r p t io n  s p e c tr o s c o p y . T h e  IR  a b s o r p t io n  
s p e c tra  o f  f in e ly  c r u s h e d  p o w d e r  o f  th e  s a m p le  w e r e  o b ta in e d  in
© 2 0 0 6 1ACS
402 S M ahalakshm i and K  Srin ivasa M an ja
th e  ra n g e  o f  i 0 0 0  c m ’ * to  2 0 0  c m ' ‘ b y  u s in g  F IT O  -  S H I M A D Z U  
S p e c tro p h o to m e te r  m o d el 8 7 0 0  w h e re  K B r is u se d  as th e  m e d iu m . 
T h e  s p e c tru m , t r a n s m itta n c e  ( % )  a g a in s t  w a v e  n u m b e r  (c m  *), is 
u s e d  fo r  in te r p r e ta tio n  o f  th e  r e s u lts . X - r a y  d if f r a c to g r a m s  w e re  
ta k e n  u s in g  R ig a k u - m in i  fle x  s y s te m  w ith  C u -k cx  r a d ia tio n  o f  
w a v e le n g th  1 . 5 4 1 8  A. N i-  f i l te r  w a s  u s e d . 7 'h e  s a m p le  w a s  
s c a n n e d  b e tw e e n  80^^and 2^ \
T h e  p o w d e re d  s a m p le  N i J ^ e  u n d e r  in v e s tig a tio n  re v e a ls  
th e  f o rm a tio n  o f  s in g le  p h a s e  c u b ic  s p in e l  s tr u c tu r e  s h o w in g  
w e ll d e f in e d  r e f le c tio n  fro m  a llo w e d  p la n e s . F r o m  th e  X -ra y  
d if f r a c tio n  p e a k s , a v e r a g e  p a r tic le  s iz e  w a s  e s t im a te d  u s in g  
S c h e r r e r ’s f o rm u la  ( t ~ 0 . 9 A  /B r o s  Q . w h e r e  t = p a r tic le  s iz e  o f  
th e  c r y s ta l , A — w a v e le n g th  o f  th e  C u -k cx  r a d ia tio n , B  = fu ll 
w id th  at h a lf  m a x im u m  o f  th e  d if f r a c tio n  p e a k  ta k e n  in r a d ia n s  ) ,  
It w a s  f iiu n d  to  b e  in  th e  r a n g e  o f  1 9  to  3 2  n a n t> m e te rs  fo r  all th e  
s a m p le s . L a tt ic e  c o n s ta n ts  o f  th e  s a m p le s  w ith  a n d  w ith o u t  
i m p u r i t i e s  a r c  g i v e n  in  T a b l e  1 b e lo w . T h e  v a r i a t i o n  o f  
c o n c e n tr a t io n  a n d  la tt ic e  c o n s ta n t  w a s  f o u n d  to  b e  a s tr a ig h t  
lin e  fo r  n ic k e l f e rr i te s . U s u a lly  in  a  s o l id  s o l u t io n s  o f  s p in e ls  
w ith in  th e  m is c ib i l i ty  r a n g e , a  l in e a r  c h a n g e  in  la t t ic e  c o n s ta n t  
w ith  c o n c e n tr a t io n  o f  th e  c o m p o n e n t  is  c ^b serv e d  1 1 1 ) .  W ith  th e  
a d d it io n  o f  i m p u r i t ie s , th e i r  la t t ic e  c o n s t a n t s  w e r e  f o u n d  to  
d e c r e a s e . D u e  to  N d ^ ^  - s u b s ti tu tio n , th e  la tt ic e  c o n s ta n t  is f o u n d  
to  d e c r e a s e  s lig h tly . S u c h  r e d u c t io n  in  th e  la tt ic e  c o n s ta n t  in 
r a re  - e a r t h  s u b s ti tu te d  fe rr i te s  s y s te m  w a s  a ls o  r e p o rte d  [ 1 2 ,1 3 ] .
l^ kblc 1. Lattice constant (a) for pure nickel and doped nickel ferrite
I t  is  fo u n d  th a t  s p e c tr a  c o n s is t  o f  tw o  s ig n if ic a n t  alxson'i-pii,’
C one N i^*(.v) a (A “ ) C one  N i^ ^ (d o p cd ) atA **)
0 .3 3 6 9 4 4 0 3 (N d ) 3 .7 7 7 7
0 5 3 .8 8 01 0 .5 (N d ) 3 .7 1 4 8
0 .7 3 .9 1 9 5 0 .7 ( ( }d ) 3 8 5 5 4
0 .9 3 .8 0 1 9 0 9 (G d ) 3 .7 6 0 7
F T IR  a b s o rp tio n  s p e c tr a  fo r  a ll s a m p le s  a rc  o b ta in e d  fro m  IR  
s p e c tr o p h o to m e te r  a n d  th e  ty p ic a l  s p e c tr a  f o r  th e  s a m p le  x  =
0 . 5  is g iv e n  in  F ig u r e  1.
b a n d s , o n e  a r o u n d  5 5 0 c m ' * a n d  th e  o t h e r  a ro u n d  
A b s o r p tio n  b a n d s  o b s e r v e d  (T 'a b le s  2 ,  3  ) in  th is  ra
Lll
c h a r a c t e r i s t i c s  o f  s p i n e l  s t r u c t u r e  h a v in g  tw o  suhlaIl|^.^. 
te tr a h e d r a l  ( A )  s i te  a n d  o c ta h e d r a l  ( B )  s i te  [3 J .
Table* 2 Position of IR absorption bands (v*, i%) for nickel fenni;
C one N i- ^ ( x ) c, (cm  *) V, ')
0 .3 5 4 7 .7 4 68  7
0 .5 5 5 1 .6 4 66  7
0  7 5 55  5 4 72  5
0  9 5 6 9  0 4 74  5
Tabic 3. P os ition  o f  IR abso rp tion  bands (»’ , 1%) fo r doped n iek rl kn i
C \m c  N i ‘ " ( 0 i ', ( c m  ' ) iS(cm ' )
0 .3 5 4 9 .7 4 72  5
0  5 5 5 3 .5 4 04  1
0 .7 5 5 1 .6 4 44  6
0 9 5 6 9 .9 3 64  5
T h e  a b s o r p t io n  b a n d  Vj, o b s e r v e d  at a r o u n d  5 5 0 c r n  isdi 
to  m e ta l o x y g e n  s t r e tc h in g  v ib r a t io n a l  m o d e s  a n d  it is aiti ihuk 
to  Fe^'*’— 0 “‘ v i b r a t i o n s  a t  th e  t e t r a h e d r a l  s i t e ,  wheicMs i 
o b s e r v e d  a t 4 6 0 c m “ ‘ is a s s ig n e d  to  o c ta h e d r a l  F c “^ -  ( ) “ i uu 
c o m p le x e s  |4 ] .  It w a s  f o u n d  th a t  th e  posititM is ol bamls ,ii 
c o m p o s it io n  - d e p e n d e n t .  T h e s e  tw o  b a n d s  a re  s h a rp  and siior 
in  in te n s i t ie s .
It w a s  o b s e r v e d  th a t  f o r  n ic k e l  f e r r i te s  w ith o u t  impuiitu* 
th e  a b s o r p tio n  b a n d s  i*j a n d  v% w e r e  in c r e a s in g  w ith  th e  inciea' 
in c o n c e n tr a t io n  o f  N i b u t f o r  d o p e d  f e r r i te s , th e  absorjMu 
b a n d s  w e re  f o u n d  to  d e c r e a s e . T h e  a b s o r p t io n  b a n d s  i)hsci\c 
in 3 1 0 , 2 6 8 c m ’' a re  id e n tif ie d  to  b e  th e  p e a k s  o f  v ^ a n d  lui tl 
s a m p le s  w ith o u t  im p u rity !  1 4 J . F o r  th e  d o p e d  sa m p le s , m >! 
n u m b e r  o f  p e a k s  a r e  o b s e r v e d  d u e  to  th e  s p l i t t in g  o f  i  ^ and i 
b a n d s  b y  th e  d o p i n g  io n s . T h e  p e a k s  o b s e r v e d  aro u n d  
c m ''  a n d  4 6 0 c m * ' a re  n o t  s h a r p  fo r  th e  d o p e d  sam ples Hi 
b r o a d e n in g  o f  t h e  b a n d s  is  d u e  to  a d d it io n  o f  g a d o lin iu m  in th 
s a m p le s  o f  N i f e rr i te s  o f  c o n c e n tr a t io n  0 . 7  a n d  0 . 9 )  .This l;u
is a ls o  s u p p o r te d  b y  S r iv a s ta v  a n d  S r in iv a s a n  1 8 ].
O n  s u b s ti tu tio n  o f  Nd*^''' a n d  Gd-^"^ ,th e  p o s i t io n  o f  v  ^ ham 
s h if t  to w a r d s  lo w e r  s id e , w h ic h  s u g g e s ts  th e  o c c u p a n c y  ofN J 
a n d  Gd'^''* O c t a h e d r a l  ( B )  s i te .  H o w e v e r  o n  s u b s titu tio n  
im p u rit ie s  a s  sa id  b e f o r e  b r o a d e n in g  o f  v ^ h a n d  ta k e  p lac e  whic 
m a y  b e  d u e  to  o c c u p a n c y  o f  c a t io n s  o f  d i f f e r e n t  charactei o 
th e  s a m e  s i te ,
b y  th e  r e la tio n  v =  i/27t  (K / M )* '^  ,
V =  V ib r a tio n a l  f r e q u e n c y  o f  th e  io n ,
K  =  f o r c e  c o n s ta n t  o f  th e  io n ,
M  =  r e d u c e d  m a s s  o f  th e  io n .
!R  and X -ra y  studies on n ickel fe r r ite  w ith ra re  earth doping 403
The decrease in vibrational frequencies indicates th a t  the 
ond length decreases. It is found to decrease the octahedral 
,rce c o n sta n t which supports the occupancy of neodymium 
niJ u a d o lin iu m  on B site. The compositional dependence of 
)icc constants are attributed to the cation oxygen bond 
i>tanccs I6 j.
The results obtained from IR absorption spectra o f th0 
amples under investigation, reveal cubic spinel structure 
[lowing two significant absorption bands. ;
The absorption bands and are found in th^ 
expected range and the difference in band position! 
is due to the difference in the for th^
octahedral and tetrahedral complexes. f
I'hc positions of the absorption bands ard 
composition*depcndent which could be attributed to 
the variation in cation ~ oxygen bond distances.
0)
(II)
(111) Variations in the force constant of tetrahedral and 
octahedral sites support predicted cation distribution, 
where in adding gadolinium, and the absorption 
bands \’j and were found to be broadened and the 
peaks are diffused.
The lattice constants were found to decrease by the addition 
neodymium and gadolinium.
Reft* rcnccs
(11 M Isliil, M Nakuhila and 'P Yamanka S o l id  S to le  C 'n m m u n  11 
209 (1972)
(2) VAM Miabcr /V/vs. S lo t  S o l 33 563 (1969)
(3) R D Waldron /V/vn Kcv. R99 1727 (1955)
(4) OSJosyulu andJ Sobhanadii r i n \ .  S lu t. S o l 65(a) 479(1981)
|5) n Ravinder M a tc f  U t t  40 205(1999)
|6J r  li Kolekai, P N Kamblc and A S Vamgankai Indian ./ /V/vs 
68(a) 529 (1994)
[7 ]  A K Ghalagc, S ( '  r'boudhait, S A I’aiil and S K Paranjape ,/ 
M a t e r  S ( i  ) . e t t , 15 1548 (1996)
(81 C  M Srivaslav and T T Srinivasan ./. A p p l /Viva. 5 3  8 1 4 8  (1 9 8 2 )
(9J P Nalwanj and V S Darsham* Pramana- / Phvs 28 (j75 (1987)
[101  M Sable. H K  Labde and N R Shamkiiwar l in l l .  M a t e r  S e i 28  
35 (2005)
(111  CMi Whinfrey. 1) W Fickail and A T auber./ A m  C h e m . S o r  8 2  
2(>9S (1900)
(12] N Rezlescu and B Re/leseu l e t  r ite s  P r o c .  I C P  1 225 (1997)
(13J tv Rc/le.scu. N Re/lcscii, P D I’opa, L Rezicseu, V  Pasnicu and M 
L ('rails M o t e t  R es . H u ll 33 225 (1998)
(141 Osama Mohameil Hemeda. Mohsen Mohamed Baiakat, Dalai 
Mohamed llcmcda Tto k J Plivs 27 537 (2003)


IR and X-Ray Studies on Nickel Ferrite with Rare Earth Doping

Singh, U P

Singh, Ashok K

Singh, D P

Erratum - Energetic Electrons' Energy Release Efficiency to Amplify Hiss-Type Waves

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