IACS Institutional Repository

Dave, Roshni

Pandey, R

Muni / Pliy- *1 (4) 437-443 (2007) 
The temporal periodic variations of the total ozone content 
at Udaipur, a near tropical station 
Roshni Dave and R Pandfcy* 
Department of Physics, M L S University, Udaipur-3l3 001, Rdjasthan, India 
E-mail pandey_r(" yahoo com 
Received 27 December 2006, accepted 23 March 2007 
Abstract : This paper attempts to discuss periodicities related to variations in the total ozone content (TOC) 
at a near tropical station, Udaipur (24 6°N, 73.7°E) These periodicities are related with periodicities of solar radio 
emission at 10 7 cm and sun spot number The Fast Fourier Transform (FFT) technique was used to obtain the 
power spectra, from which the periodicities were deciphered The harmonics obtained can be separated into 
quasi-biennial oscillation (QBO) with period of about 2 5 years, annual and semi-annual modulation with period 
of about 350-400 days and about 180 days, respectively, and with a period of about 27-30 days corresponding 
to the solar rotation period 
Keywords : Total ozone content, solar radio emission, sun spot number 
PACS Nos. : 92.70.Cp, 96.60.tg, 94.05 sp 
1. Introduction 
Ozone is one of the most important atmospheric trace gases that absorbs both, 
incoming ultra violet radiations from the sun and outgoing infra red rays from the earth's 
surface. Ozone forms a layer in the stratosphere which is thinnest in the tropics and 
denser towards the pole [1-3]. The amount of ozone, which is measured in Dobson 
unit, is about 260 DU near tropics and higher elsewhere. About 90% of total 
atmospheric ozone is found in the stratosphere near between 20 km to 60 km, the rest 
10% ozone is found in the troposphere, near the surface of earth [4-7]. 
The most important role played by ozone is in the absorption of UV-B radiations 
(280 - 320 nm) which is the most dangerous form of UV radiations that can reach the 
ground level. Atmospheric ozone shields life at the earth's surface from most of the 
harmful components of solar radiations. Thus, its impact on biological life on earth is 
temendous. If the ozone depletes, the ultraviolet radiations at Earth's surface will 
^spond ing Author © 2 0 0 7 I A C S 
438 Roshni Dave and R Panciey 
increase [8,9], endangering all forms of biological life on earth For this reason alone 
measurement of atmospheric ozone is necessary 
After the discovery of ozone hole [10], assessment of long term and short term 
trends of ozone in different regions of globe has become a frontline topic of research 
[11-13] Several workers have also pointed out the role of nitrous oxide, chlorine and 
chlorofluorocarbons, produced mainly by anthropogenic activities, in the depletion of the 
ozone layer [14-16] 
Since the incoming solar ultra violet radiation has a direct bearing on the 
production of ozone, variation of ozone with solar flux has been attracting researchers 
attention for years [17,18] The solar flux is influenced by magnetically active regions 
(sun spots) on the sun The solar flux increases as solar activity increases This 
shows that the production of ozone should be more sensitive to variations in solar flux 
The influence of solar activity on changes in total ozone content (TOC) has been 
considered by Paetzold [19,20] His analysis of vertical sounding data, for the period 
1958-1968, obtained using optical ozone probes has shown that the TOC changes are 
related to the phase of solar activity Ruderman and Chamberlain [21] have suggested 
that during solar minimum condition, there is an increase in the low energy cosmic 
rays in the earth's atmosphere, which will increase NOx, resulting in a decrease of 
ozone Variations in TOC on different time scales, ranging from 11 year solar cycle 
down to annual, semi-annual and 27 day solar rotation period have been reported by 
different workers [22-27] In some of these studies variations in ozone related to quasi 
biennial oscillation and planetary wave periodicities have also been reported [28] But 
most of these studies pertain either to the mid latitudes or the equator 
The present work concerns with finding the short term and longer term periodicities 
in the TOC for a tropical station, Udaipur (Geog Lat 24 6° N, Geog Long 73 7° B) 
The data set used in this study comprises observation of the TOC, measured by the 
total ozone mapping spectrometer (TOMS) onboard the Nimbus-7 satellite during the 
period 1979-1990, encompassing the solar cycle number 20 The data are daily 
averages on a spatial grid with a 1° x 1 25° latitude-longitude cell, over the geographic 
location of Udaipur The TOC (in Dobson Units), provided by the TOMS, has been 
derived from the absorption of diffused solar ultra-violet emission at different wavelengths 
(312 nm and 331 nm) Although the satellite data suffers from the long term drift of 
the instrument, comparison of the TOMS data with the ground based sun photometer 
at Udaipur [29] and elsewhere [30] has established that the trends of TOC variations 
obtained by the two systems are the same. 
The effect of the solar activity on changes in the TOC has been customarily 
investigated using the solar flux at 10 7 cm. For this purpose, we have used solar radio 
emission data at 10.7 cm, received by solar radio monitoring from the Dominion 
Astrophysics Observatory (Canada) The accessible database includes two components, 
the measurement of sun radio flux and its average value Each radio flux can be 
Ihe temporal periodic variations of the total ozone content at Udaipur a near tropical station 439 
presented in three aspects 'observable', 'corrected', and 'URSI series D' In our case, 
we have used the observable radio fluxes, which are direct response by the antenna 
system on the received radiation The flux of radio emission at 10 7 cm is given in 
terms of solar flux unit, (SFU) (1 SFU = 10~22 WM * |Hz~1) It may well be argued that 
the solar flux at 10 7 cm may not be a true representative of the level of solar activity 
Since the sunspot numbers are a true representative of the solar activity, we have used 
the data on the daily values of the sunspots during tfie period 1979 to 1990 obtained 
from SIDC, Royal Observatory, Belgium All the thre# time series, namely, the TOC, 
solar flux and the sunspot numbers were subjected to the Fast Fourier Transform (FFT) 
analysis separately, to determine various periodicities^ associated with each 
2 Methodology 
The fast Fourier Transform (FFT) technique has been used to extract the periodicities 
associated with the quasi periodical fluctuations in the time series It is known that any 
signal of a natural origin represents a set of spectral harmonics, which can be 
tepresented as the sum of regular harmonics only under specific approximations Thus, 
the physical interpretation of such a signal is problematic Using standard Fourier 
decomposition, this problem can be solved 
FFT, which is generally applicable on continuous time series, can be applied to 
discrete one, provided that the sampling period is small [31] In our case, the sampling 
period is one day and total no of days is 4096 Hence the highest frequency that could 
be detected corresponds to a time period of two days 
When a non periodic time series is subjected to the FFT analysis, the resulting 
spectrum suffers from the leakage As a result of this leakage, the signal energy 
smears out over a wider range of frequencies in the FFT whereas it should have been 
m a narrow range of frequency [32] The problem of leakage can be reduced, but not 
eliminated through the use of a suitable windowing function A number of window 
functions are being employed, depending on the type of data, admissible spectral 
leakage, required frequency resolution and amplitude accuracy Hanning window function 
is one which is commonly used in geophysical applications and qualifies to be good 
ws-a-ws the three points mentioned above [3?] Therefore, the data was filtered through 
a Hanning window prior to the FFT computation 
The FFT analysis provides amplitude (real and imaginary parts) at each frequency, 
from which power can be calculated Thus the absolute random error associated with 
each power estimate would be 100%, as the error is equal to V(2//V), where N is the 
number of degrees of freedom (2 in the present case) In power spectral analysis, to 
reduce this error, smoothing over frequency or over segments is normally employed 
But that under estimates the amplitudes of the peaks, resulting in suppression of 
Periodicities Hence, we have not performed the smoothing Only those peaks in the 
sPectrum would be considered which would stand out clearly 
440 Roshni Dave and R Pandey 
3. Results and discussion 
Figure 1 gives a plot of total ozone content at Udaipur for the period 01/01/1979 to 
12/05/1990. The chosen period corresponds to a total of 4096 (= 212) days, or the data 
points. This number is so chosen because the analysis by the FFT requires the 
number of data points to be an exact power of 2. 
In this figure, the annual variation is clearly seen. There are broad maxima that 
occur around April-June and minima around November-December. The pattern is in 
conformity with the earlier studies for the tropical region [1,33]. The annual average of 
the TOC is about 260 DU. Along with this, many larger and small periodicities might 
be hidden and could be extracted through the FFT analysis. 
Figure 2 gives the power spectrum of the TOC data given in Figure 1. In power 
spectrum analysis, it is customary to plot the spectral power density versus the 
frequency. But in the present case the abscissa is Time (number of days), which is 
the inverse of the frequency. This has been done to relate the quasi periodicities in 
terms of the number of days, such as annual and semi-annual. 
Figure 1. Total columnar ozone measured by TOMS over 
Udaipur from January 1979 to December 1992. Annual 
variation in TOC is observable clearly. The maxima and 
minima occur during April-June and November-December, 
respectively. 
Figure 2. Result of power spectrum analysis of 
the TOC for the period 1/1/1979 to 12/5/1990 The 
annual, semi-annual periodicities and the ones 
associated with the QBO and the solar rotation 
period (27 days) are observed clearly. 
The spectrum shows a number of prominent peaks which could be identified as 
steady quasi periodical processes observed on select periodicities. The strongly marked 
annual component and the components with a period of about 2.7 years and 1.7 years 
are easily distinguished. Similar periodicities have also been reported in previous [23,33] 
and recent work [34]. The component at 2.7 year is the quasi biennial component. Its 
power changes with time, reaching maximum at end of each solar cycle [34]. Thus, 
as opposed to the annual component with a constant period, the quasi biennial 
The temporal periodic variations of the total ozone content at Udaipur, a near tropical station 441 
component represents the sum of two close range harmonics with periods of 1.7 and 
2.7 years. These components are probably connected with the well known quasi-
biennial fluctuations of the stratospheric winds above the equator (QBO variations). 
Besides, a number of components with period* ranging from 180 days (semi-
annual) to 27 days (connected with the solar rotation period) are also observed. 
To study the solar activity influence on the TO^, we have used coincident time 
series of the TOC and the radio emission data, represented by the solar flux at 10.7 
cm. A plot of the solar flux for the period 1/1/1979 to 31/12/1992 is given in Figure 
3. Beside the 11-year solar cycle variation of the flux^ a number of periodicities could 
be associated. These could be brought out through pie FFT analysis. 
The power spectrum analysis of the solar flux | at 10.7 cm is shown in Figure 
4 The low frequency component seen around 4.k years may represent a sub-
harmonic of the 11 year solar cycle. The work by Sych et al [36] also reveals a similar 
sub-harmonic at about 5 years. The other two components observed at 180 and 400 
days could be associated with the semi-annual and annual periodicities respectively. 
The 27 day periodicity is also visible which is probably connected to the rotation period 
of the sun. 
2000 3000 
No. of Day* 
Figure 3. Solar flux data measured by Dominion 
Astrophysics Laboratory, Canada from January, 
1979 to December, 1992. The 11-year solar cycle 
variation and the annual periodicities are obvious. 
Figure 4. Result of power spectrum analysis of the 
solar flux data for the period 1/1/1979 to 12/5/1990. 
The annual, semi-annual periodicities and the ones 
at 4.2 year, 250 days and the solar rotation period 
(27 days) are observed clearly. 
As discussed earlier, the sun spot number could be a better representative of the 
solar activity, periodicities in the TOC have been compared with the ones in the sun 
spot numbers. Figure 5 shows the plot of the sun spot numbers for the period January 
1979 to December 1992. The plot grossly resembles that of the solar flux data. The 
11-year solar cycle variation is seen conspicuously. 
In this figure, the 11 year cycle variation is seen clearly. There are two broad 
442 Roshni Dave and R Pandey 
maxima and a minimum. Along with this, many large and small periodicities of annual 
semi annual and solar rotation might be hidden and could be extracted through the 
FFT analysis. 
Figure 6 shows the power spectrum of sun spot number of data plotted m 
Figure 5. 
I t l U P 
2000 3000 
No o1 Days 
Figure 5. A plot of the sun spot numbers measured 
by SI DC, Royal Observatory, Belgium from January 
1979 to December 1992. 
No of Days 
Figure 6. Result of power spectrum analysis of the 
sun spot number for the period 1/1/1979 to 12£ 
1990 The annual, semi-annual periodicities and the 
ones at 2 2 year and the solar rotation period (27 
days) are observed clearly. 
The spectrum shows two prominent peaks at 400 and 800 day. Peak at 400 day 
could be identified as annual component. Beside these, a number of components with 
periods ranging from 180 days (semi-annual) to 27 days (connected with the solar 
rotation period) are also observed. 
4. Conclusions 
In this study, we have applied the fast Fourier transform to obtain the periodicities in 
the TOC spanning about a solar cycle. The dominant periodicities in the TOC are the 
QBO, annual, semi-annual and those related to the solar rotation period. In order to 
look for the causes of these periodicities, the solar radio emission data at 10.7 cm 
and the sun spot number data for the same solar cycle were also subjected to the 
FFT analysis. For these data also, the obtained spectrum could be divided into 
harmonics with solar periodicities, namely, the quasi-biennial oscillation (2.5 years), 
annual and semi-annual periodicities (365 and 180 days) and modulation with periods 
of 27 days related to the solar rotation. It appears that the periodicities in the TOC 
follow that in the solar flux as well as the sunspot numbers. 
Acknowledgments 
The TOC data was taken from TOMS onboard NIMBUS-7 satellite, National Space 
jhe temporal periodic variations of the total ozone content at Udaipur, a near tropical station 443 
Science Data Center at NASA, USA The solar flux data and the sun spot number 
were taken from Dominion Astrophysical Laboratory, Canada and SIDC, Royal Observatory, 
Belgium, respectively 
References 
[1] D K Chakrabarty and P Chakrabarty NATO Advanced Institute on Atmospheric Ozone p123 (1979) 
{2] C Prabhakar, E B Rodgers and V V Salomonson Pure Appl Gfophys 106 1226 (1973) 
[3] Julius London and SamuelJ Oltmans J Appl Geophys 117 345(1978) 
[4] B H Subbaraya, Shyam Lai and M Naja Mausam 52 97 (2001) 
[5] J Fishman, A E Woznaik and J K Creilson Atmos Chem Phys. 3 893 (2003) 
[6] B H Subbaraya, S Lai, S Venkataramani. A G Ishov, S P Perov Knd T M McElroy J Atoms Terr Phys 56 
1557 (1994) 
[7] R D Hudson and A M Thompson J Geophys Res 103 22129(1998) 
[8] J R Herman, P K Bhartia, J Ziemke, Z Ahmmad and D Larko Geophys Res Lett 23 2117 (1996) 
(9] IMAP Final Report-IV, ISRO-IMAP-SR-46-95 (1995) 
[10] J C Ferman, B G Gardener and J D Shanklin Nature315 207 (1985) 
[11] B H Subarraya and S Lai Space Research in India Accomplishments and Prospects 1 (1999) 
[12] N Saraf and G Beig Geophys Res Lett 31 5 (2004) 
[13] R D Bojkov and V E Fioletov J Geophys Res 100 16537 (1995) 
[14] P J Crutzen Q J Royal Meteorol Soc 96 320 (1970) 
[15] S Stolarski and R J Cicerone Can J Chem 52 1610 (1974) 
[16] M J Molina and F S Rowland Nature 249 810 (1974) 
[17] W J Blackshear and R K Tolson Geophys Res Lett 5 921 (1978) 
[18] B James Pollack, J William Borucki and B Owen Toon Nature 282 5739 (1976) 
[19] H K Paetzold Annates de Geophys 25 347 (1969) 
[20] H K Paetzold, F Pisclatr and H Zschozner Nature 240 106 (1972) 
[21] M A Ruderman and J W Chamberlain Planet Space Sci 23 247 (1975) 
[22] Y Sahai, R P Kane and N R Teixeira Pure Appl Geophys 120 615 (1982) 
[23] R P Kane, Y Sahai and N R Teixeira Pure Appl Geophys 122 747 (1984) 
[24] R p Kane Pure Appl Geophys 125 131 (1987) 
[25] M Cervino and G Giovanelli Nuovo Qm 14C 575 (1991) 
[26] E Echer, F L Guarnien, N R Rigozo and L E A Vieira Tellus 56A 527 (2004) 
[27] K N Visheratin, N E Kamenogradskn, F V Kashm, V K Semenov, V P Sinyakov and L I Sorokma Atmos 
Oceanic Phys. 42 184 (2006) 
[28] J R Ziemke and J L Stanford J. Geophys Res 99 23041(1993) 
[29] R Pandey and B M Vyas Curr. Sci 86 305 (2004) 
[30] P Raj Ernest, P C S Devara, G Pandithurai, R S Maheshkumar, K K Dam, S K Saha and S M Sonbawne 
J Geophys. Res. 109 D08309 doi 10 1029/2003JD004195 (2004) 
[31] E O Brigham Fast Founer Transform and Applications (Englewoods Cliffs, NJ Prentice-Hall) (1988) 
[32] R w Ramirez The FFT, Fundamentals and Concepts (New Jersey Prentice-Hall) (1985) 
I33] D Nandrta Ganguly and K N Iyer J Indian Geophys Union 9 189 (2005) 
(34] MShiotani J Geophys Res 97 7625(1992) 
(35] R A Sych, G K Matafonov, A Ju Belinskaya and N J Ferreira J. Atmos Solar Terr Phys. !67 1779 (2005) 


English

The Temporal Periodic Variations of the Total Ozone Content at Udaipur, a Near Tropical Station

Misra, Prasanta K

Indian J. Phys. 81 (1) 25-31 (2007) 
Heavy-fermion systems 
Prasanta K Misra 
Department of Physics, University of Houston, Houston, TX 77204, USA 
E-mail : Prasanta.Misra@mail.uh.edu 
Abstract : Starting from reminiscences of my stay at Berhampur University during 1974 to 1984, where i did considerable 
amount of research in a variety of subjects in Condensed Matter Physics, I present a brief review of heavy fermion systems 
which also includes my work done both at Berhampur and in USA. 
Keywords : Heavy fermion systems, Anderson Hamiitonian, Fermi-liquid model, metamagnetism 
PACSNos. : 71 10.-W, 71.10.Ay, 75.30.Mb 
1. Introduction 
l have been asked to give a brief summary of my research on magnetism at 
Berhampur University. I started working on magnetism as a PhD student at Tufts 
University under the supervision of Professor Laura M Roth. The title of my PhD. thesis 
was 'Theory of Diamagnetic Susceptibility of Metals", part of which was published in 
Physical Review. The main feature was to use the pseudopotential theory of Phillips 
and Kleinman to derive a theory of diamagnetic susceptibility of metals. This was a 
significant advancement over Landau's free electron theory. After a brief stint as post-
doctoral fellow with Leonard Kleinman at University of Texas at Austin, I joined Utkal 
University in July 1968 and continued to work on magnetism with my graduate 
students. In January 1972, I went to University of Texas at Austin for two years as 
Research Scientist to work again with Professor Kleinman on magnetism. In March 
1974, I joined Berhampur University as Professor and Head of Department of Physics. 
I spent'10.5 years there during which N C Das (Theory of Magnetic Pseudopotentials), 
S K Misra (Many-Body Theory of Magnetic Susceptibilty of Solids), G S Tripathi (Spin-
Orbit and Many-Body effects on Knight Shift), T Sahu (Magnetic Susceptibilty of 
Tetrahedral Semiconductors), J C Mohanty (Crystal Field Effects and Magnetic 
Susceptibility of Mixed-Valence Systems), L K Das (Theory of Knight Shift in Metals), 
N Panigrahi (Magnetic and Dielectric Susceptibilities of Model Amorphous 
Semiconductors), B Misra (Theory of Knight Shift due to Indirect Nuclear Hyperfine 
© 2007 IACS 
26 
PrasantaKMisra 
Interactions) and S Misra (Theory of Knight Shift in Narrow-Gap Semiconductors) 
completed their PhD thesis under my supervision. In this brief review of my Berhampur 
University days, I have listed their publications in the references chronologically (Ref. 
1-26) but omitted any of my publications which is neither related to magnetism nor to 
their work. I have been amazed by the dedication, hard work and zeal with which all 
of them worked and their confidence in me. In 1995, I went to Berhampur University 
on a sabbatical and renewed working with G S Tripathi and T Sahu. I am very proud 
no note that both of them have grown in stature as physicists. Indeed, if I could travel 
back in time, I would return to Berhampur University, a place my family and I will 
always cherish and which is now firmly entrenched in the Indian Physics map. 
2. Overview of heavy-fermion systems 
The heavy-fermion system is a loosely defined collection of intermetallic compounds 
containing lanthanide (mostly Ce, Yb) or actinide (mostly U, Np) elements. Recently, 
other compounds such as quasi two-dimensional Ce Co ln5 and 'Skutterdite' PrOs4Sb12 
have been shown to exhibit such behavior. I will present an overview of the 'exotic' 
properties of these systems, the only common feature of which is that they have large 
effective mass; (50-1000) times greater than the mass of a free electron below a 
coherence temperature. The effective mass is estimated through the electronic specific 
heat. The specific heat Cv of a solid can be expressed as 
CWT - y 4<5T2 , (1) 
where y = VmkFkgm*/?>h2t m* is the effective mass of the electron and T is the 
absolute temperature. For heavy-fermion systems, y abruptly increases below the 
coherence temperature T*. There is an additional spin-fluctuation term for UPt3. Some 
of the other properties of heavy-fermions include (i) an enhanced Pauli spin susceptibility 
indicating a large effective mass; (ii) the Wilson ratio is approximately one; (iii) a huge 
T2 term in the electrical resistivity and (iv) highly temperature-dependent de Haas-van 
Alphen oscillation-amplitudes at very low temperatures. 
The intense interest in heavy-fermion systems started with the discovery of 
superconductivity in CeCu2Si2 by Steglich et al [27]. The big surprise was that, up to 
that time, magnetism and superconductivity were considered to be contradictory 
phenomena. However, in CeCu2Si2, the ^-electrons which are responsible for local 
magnetic moments at higher temperatures are also responsible for superconductivity 
below the critical temperature Tc. After the discovery of high- Tc superconductivity in 1986 
and the realization that both high-Tc superconductors and heavy-fermions are not only 
highly correlated electron systems but also exhibit 'nearness* to magnetism at the 
superconducting phase, the interest in these systems grew rapidly. 
At first it was assumed that while most rare-earth compounds which have either 
localized 4f-electrons (cerium) or B-f electrons (uranium) are mixed-valence systems, a 
few become Heavy-Fermions below the coherence temperature. However, it has been 
djscovered that other compounds also exhibit the same properties. At present, 
Heavy-fermion systems 27 
approximately fifty heavy-fermion systems have been discovered and there is no 
uniformity in their properties. Below a certain temperature, some exhibit superconductivity; 
some others exhibit either ferromagnetism or antiferrom^gnetism; and several heavy-
fermions become semiconductors. Some heavy-fermions |tre Fermi liquids while some 
others are non-Fermi liquids. Both magnetic and sup#rconducting quantum critical 
points have been observed in some of these systems. Th£ only common feature is the 
large effective mass and the fact that they are highly-corfelated electron systems. The 
wide interest is due to the many unsolved theoretical problems and the wide variety 
of possible technological applications. The theory of thqjse systems lags behind thd 
experiment although several powerful techniques have been applied. These include 
Bethe ansatz method, 1//V expansion method, renormalizatifcn group technique, Dynamical 
Mean Field theory and Quantum Critical Point. There am -several theories for heavy-
fermion superconductivity in which there is widespread Interest since there is lot of 
similarities with high-7c superconductivity. There are a large number of review articles 
and proceedings of international conferences on heavy-fermions. A few of these (by no 
means complete) are mentioned in Ret. [28]. 
3. Exact diagonalization of periodic Anderson model in finite clusters 
In the 1980's, it became obvious that the three phenomena of mixed-valence, Kondo, 
and heavy-fermion behavior, at least in Ce systems, correspond to different regimes of 
one fundamental phenomenon. In order to correlate these regimes and to study their 
dependence on the various relevant parameters, we considered the application of the 
periodic Anderson model to small clusters [29]. The periodic Anderson model relevant 
to a four-atom cluster (our results for larger clusters are qualitatively similar) with 
periodic boundary conditions is given by the Hamiltonian 
W - ' Z ^ ^ M + ^ L ^ ^ X + ^ ^ U ^ + ^ ^ ^ + ^ C,.). (2) 
Here, t is the hopping integral of the extended orthogonal orbitals between sites / and 
j (restricted to nearest neighbors). C]a and Clo are the creation and annihilation 
operators for these extended orbitals with spin <x. There is one extended orbital per 
spin with a mean energy which is the origin of the energy scale. f*ta and fla are the 
creation and annihilation operators for the localized f orbitals with energy Et U is the 
Coulomb repulsion between two electrons of opposite spin in the f orbital and describes 
a short-range interaction between them. V is a positive hybridization parameter between 
the localized and the band orbitals in neighboring sites. U is positive while t and f can 
have either sign. The total number of electrons is one per site. We considered the 
application to small clusters of four sites of equal length (square, rhombus, and 
tetrahedron) thereby including the importance of band structure effects. For example, 
our model Hamiltonian for a tetrahedron is identical to that of an fee lattice if the 
Brillouin zone sampling is restricted to four reciprocal-lattice points, the zone center r, 
and the three square-face-center points X. 
28 PrasantaKMisra 
The Hamiltonian (2) is conveniently considered on a basis of states diagonal in 
occupation numbers. We note that spin is a good quantum number and the states can 
be classified as spin singlets, triplets and quintets. We constructed a computer 
program to diagonalize the Hamiltonian within subspaces of fixed values of Sr We have 
calculated the f-state occupation (n,)> temperature dependence of specific heat (Cv) and 
the magnetic susceptibility (zf) of /^electrons for a large number of parameters. We 
found that the mixed-valent, Kondo and magnetic regimes depend sensitively on l//|f|, 
and Et/\t\ and the geometry of the clusters but not on U. When Efl\t\ is large and 
negative, for small values of V/\t\ (n, * 1), the many-body ground state is nonmagnetic, 
but the next two excited states are magnetically ordered and nearly degenerate with 
the ground state. The specific heat rises sharply at low temperatures and the system 
exhibits heavy-fermion behavior. In some cases, the ground state is magnetically 
ordered but nearly degenerate with a nonmagnetic excited state and well separated 
from other states. This corresponds to heavy-fermions with magnetically ordered ground 
state. In some cases, there is a transition from the Kondo lattice to a magnetic regime 
and subsequent reentry into either a Kondo-lattice or a mixed-valence regime as E, is 
gradually increased from large negative values. We also find that mixed valence and 
magnetic order can coexist for a very narrow range of Ef for some choice of 
parameters. 
4. Fermi-liquid model for Kondo lattice systems 
I present an outline of a Fermi liquid theory for some Kondo lattice systems (CeCu2Si2, 
CeAI3 etc.) in which spin-orbit effects are specifically included [30]. The ground state 
of a Kondo ion is a singlet, and a renormalized resonant level (RL) is a good 
description of the low-energy behavior of such a system. The RL, which is characterized 
by an effective width A* and an effective f level position E*t describes a renormalized 
f state with 2J + 1 = N scattering channels, each with a azimuthal quantum number 
mr For a Kondo lattice, the scattering at each Kondo site can be described by a 
phase shift 
*v(f) = «(M) + ( f - M ) / ^ + 5 ; v > f V v v ^^(0 , (3) 
where v and v' denote the spin-orbital states of the localized / level, TK is the Kondo 
temperature and S(M) is fixed by the valence of the Kondo ion and by using the Friedel 
sum rule. Requiring that the scattering of the lattice at T » 0 (6nv, = 0) is coherent 
leads to the KKR2 equations whose solutions near v, EK% correspond to energies of 
single quasi-particle excitations. Two quasi-particles interact when one 'senses' the 
virtual polarization of a Kondo ion induced by another. This interaction is characterized 
by the parameters <p„,. In cerium systems, only the / = 3 phase shift is important 
The spin-orbit splitting between J = 5/2 and 7/2 is much larger than A\ and therefore 
S$(e) is large in the J = 5/2 state. It is easy to show, by using a procedure similar 
to the KKR2 method and including spin-orbit effects, that the band structure is obtained 
from 
Heavy-fer/n/or; systems 29 
det||(/c* - E)6knSt „ , + rknSi ^ v | | = 0, (4) 
where r is a complicated function [30] of Bessel functions, Clebsch-Gordon coefficients 
and spherical harmonics. After considerable algebra, we Obtain the secular equations 
of a hybridization Hamiltonian * 
^ X M . S ^ W C ^ C ^ ^ (5) 
Here, en(K) is the energy of the n-th Brillouin zone obtained by diagonalizing the 
Hamiltonian containing the kinetic energy term and t&e corresponding spin-orbit 
pseudopotential term (including I = 3), yJkStkniS> are the hybridization potentials derived by 
us [30] and Ckns (C\ns)\ fksJ (flj) are the usual fermion Operators. The energy EfJ is 
dispersionless but the hybridization term mixes the localized states with the extended 
states of all Brillouin zones. The Hamiltonian (5) can be transformed into one with one 
extended band only by a projection method suggested by Heine. If this procedure is 
adopted, one obtains the hybridization of one conduction band with localized states 
which have dispersion in their energy and one obtains a periodic Anderson Hamiltonian 
in which spin-orbit effects are explicitly included. 
We have used degenerate perturbation theory to construct Bloch functions which 
are eigenfunctions of the Hamiltonian in eq. (4). We have used these functions to 
evaluate the momentum and spin matrix elements which occur in the general 
expressions for spin magnetic susceptibility {%s) of Misra et al. and for Knight shift {Ks) 
of Tripathi et al. and shown that K$ is not directly proportional to %$ a result which is 
well known for Kondo-lattice systems. 
5. Metamagnetism and paramagnetism in heavy-fermions 
A high magnetic field can either suppress antiferromagnetism or induce 'metamagnetism'. 
Metamagnetism, which manifests macroscopically in an abrupt increase of the bulk 
magnetization at a critical field (Hc), has been widely studied in both itinerant systems 
as well as in some heavy fermions (i.e., CeRu2Si2, UPt3 and Sr3Ru207). The metamagnetic 
transition, which is associated with a hysteresis in the magnetization curve, disappears 
at high temperature. We consider a variant of the periodic Anderson Hamiltonian in the 
momentum-space representation in an applied magnetic field H [31] 
W
 ~ ZjkaEckCkaCkcr + UcZjkkqCkiq1CktCl' -qlCk'l + ZjkaEfkfkJka 
+»Blk{H,(cUckt - clcki + fk\fk, - f*jki) 
) M C J A T H V * T K ] } . (6) 
All these terms are explained in Ref. [31]. The Hamiltonian has been written in this 
form since we wish to explain metamagnetism based on spin fluctuations (caused by 
30 PrasantaK Misra 
the transverse components of the magnetic field H, and HJ and their damping in the 
high field state. We have used a mean field approximation (MFA) for the electron 
correlation energies. For the high field magnetic state, we have derived equations of 
motion for the magnetization and spin-fluctuation amplitudes using Heisenberg's equation. 
Spin fluctuation and magnetization dampings are considered phenomenologically. 
Metamagnetism is shown to be driven by the transverse part of the applied field and 
strong electron-electron correlations are found to be important in the high field state. 
We now analyze the low field paramagnetic susceptibility in the limit of H2 - * 0, 
in the presence of many body and conduction electron moment and local moment 
interactions, the one-electron Green's function satisfies the equation [31] 
(C, - H)G(r, r', Hz, n„ £) = S[r - r'), (7) 
where K = ?i0 + 'H3^H^^r^H,,^). (8) 
The details of our numerical calculations for CeRu2Si2 are explained in Ref. [31]. The 
m vs. h curve Ref. [31] shows hysterisis behavior, i.e. there are two critical fields of 
metamagnetic transition (hm) at 5.8 and 6.6 T. The average 6.2 T is not very different 
from the experimental value of 7.8 T. The average jump in the magnetization is 0.68 //0 
as compared to the predicted experimental value of 0.5 /uB. The slope of m vs. h curve 
is steeper for h<hm compared to h>hm. Which is also in agreement with experimental 
observation. Thus, most of the systematics observed in case of metamagnetic transition 
are explained by our model qualitatively. 
References 
[1J S P Mohanty and P K Misra Phys. Lett. A48 128 (1974) 
{2] N C Das and P K Misra Solid State Commun. 22 667 (1977) 
[3] G S Tripathi, L K Das, P K Misra and S D Mahanti Hyperfine Int. 9 495 (1981) 
[4] T Sahu and P K Misra Phys. Lett. A85 165 (1981) 
(5] G S Tripathi, L K Das, P K Misra and S D Mahanti Solid State Commun. 38 1207 (1981) 
[6] S K Misra, P K Misra and S D Mahanti Solid State Commun. 39 51 (1981) 
[7J J C Mohanty, P K Misra and S D Mahanti J. Phys. C14 L1125 (1981) 
[8] G S Tripathi, L K Das, P K Misra and S D Mahanti Phys. Rev. B25 3091 (1982) 
[9] T Sahu and P K Misra Phys. Lett. A87 475 (1982) 
[10] S K Misra, P K Misra and S D Mahanti Phys. Rev. B26 1903 (1982) 
[11] T Sahu and P K Misra Phys. Rev. B26 6795 (1982) 
[12J 8 K Misra and P K Misra Phys. Lett. A92 300 (1982) 
[13] J C Mohanty and P K Misra J. Phys. C16 2779 (1983) 
[14] S Misra, G S Tripathi and P K Misra J. Phys. C17 869 (1984) 
[15] B Misra, L K Das, T Sahu, G S Tripathi and P K Misra Phys. Lett. A106 81 (1984) 
[16J J C Mohanty and P K Misra J. Phys. C17 L117 (1984) 
[17] N Panigrahi, T Sahu and P K Misra J. Phys. C17 LB69 (1984) 
[18], N Panigrahi, T Sahu and P K Misra J. Phys. C18 L169 (1985) 
{19} S Misra, G S Tripathi and P K Misra J. Phys. C19 2007 (1986) 
Heavy-fermion systems 31 
[20] B Misra, T Sahu, G S Tripathi and P K Misra Phys. Lett. A114 272 (1986) 
[21] S Misra, G S Tripathi and P K Misra J. Phys. C20 277 (1987) 
[22] T Sahu, N Panigrahi and P K Misra Phys. Lett. A121 317 (1987) 
[23] G S Tripathi, B Misra and P K Misra J. Magn. Magn. Mater. 67 271 {1987) 
[24] T Sahu, N Panigrahi and P K Misra Key Eng. Matter 13-15 693 (1987) 
[25] T Sahu, N Panigrahi and P K Misra Physica B162 57 (1990) 
[26] B Misra, L K Das, N C Sahu, G S Tripathi, P K Misra J. Phys. Condensed Matter. 2 9891 (1990) 
[27] F Steglich, J Aarts, C D Bredl, W Lieke, D Meschede, W Franz and J Schafer Phys. Rev. Lett. 43 1893 
(1979) 
[28] G R Stewart Rev. Mod. Phys. 56 755 (1984); Rev. Mod. Phys. 73 79? (2001); C M Verma Comments Solid 
State Phys. 11 221 (1985); J. Magn. Magn. Mater. 47 606 (1985); Ptysica B 359-3611478 (2005); P A Lee 
et al, Comm. Condensed Matter. Phys. 12 98 (1986); A Georges eial. Rev. Mod. Phys. 68 13 (1996); P 
Coleman Physica B 259-261 353 (1999); J D Thompson et al, J. Magn. Magn. Mater. 226-230 5 (2001); 
Q Si J. Magn. Magn. Mater. 226 30 (2001); Q Si et at, Nature An 604 (2001); F Steglich J. Magn. Magn. 
Mater. 226-230 1 (2001); Physica B 359-361 326 (2005); F Steglich etal, Physica B 329-333 441 (2003); 
R Joynt and L Taillefer Rev. Mod. Phys. 74 235 (2002); A S Edel$tein J. Magn. Magn. Mater. 256 430 
(2003) 
[29] P K Misra, D G Kanhere and J Callaway Phys. Rev. B35 5013 (1987); J Callaway, D P Chen, D G Kanhere 
and P K Misra Phys. Rev. B38 2583 (1988); J Callaway, D P Chen, Q Li, D G Kanhere and P K Misra 
Quantum Simulations of Condensed Matter Phenomena (ed) J D Doll and J E Gubernatis 19 (Singapore : 
World Scientific) (1990) 
[30] P K Misra and J Callaway J. Phys. Condensed Matter. 1 4485 (1989) 
[31] G S Tripathi, B G Mahanty and P K Misra Physica B 339 164 (2003)

Heavy-Fermion Systems

Suman, C K

Prasad, K

Choudhary, R N P

Dielectric Relaxation in Tungsten-Bronze Pb2Bi3NdTi5O18 Ferroelectric

Gajjar, P N

Mishra, S R

Jani, A R

Indian J. Phys. 81 (1) 125-129(2007) 
Electrical resistivity of liquid K-Rfe-Cs alloys 
P N Gajjar*, S R Mishra and A R Janl 
•Department of Physics, University School of Sciences, Gujarat University, Ahmedabad-380 009, Gujarat, India 
Department of Physics, Sardar Patel University, Vallabh Vidyanagar-388 120, Gujarat, India 
E-mail pngajjar(cr)rediffmail com 
Abstracts : A model potential consisting of varying cancellation of attractive and repulsive potentials within 
the core is applied for the first time to study the electrical resistivity of liquid K-Rb-Cs alloys The influence of 
exchange and correlation effects are also studied by including local-field correlation functions due to Hartree, 
Taylor, Ichimaru-Utsumi, Fand etal and Sarkar et al The results for electrical resistivity of pure metallic components 
(K, Rb and Cs), liquid binaries (K-Rb, Rb-Cs and K-Cs) and liquid ternary (K-Rb-Cs) favours the formulation of our 
new model potential The comparison of present results with those obtained due to self-consistent energy 
independent model potential and experimental findings also confirm the validity of our model in the study of 
ternary alloys 
Keywords : Pseudopotential, electrical resistivity, alloys 
PACSNos. : 71 15H, 72 15CZ 
1. Introduction 
Alloys, the investigation of which is a general topic now days, are materials of common 
interest for scientist and researchers. Recently, ternary and quaternary alloy combinations 
have been of prime importance. The electrical resistivity and absolute thermoelectric 
power of liquid Indium-Nickel-Manganese ternary alloy was calculated by Auchet et al. 
[1], following the Fiber-Ziman formalism [2]. For simple liquid metals, structural and 
electrical properties were also studied significantly over the past few decades [3-6]. 
Khajil [7] has calculated the electrical resistivity of alkali-based binary alloys using the 
Faber-Ziman method modified for mean free-path. However the investigation related to 
multi component liquid metallic alloys of simple metals is still to be explored fully 
under the Fiber-Ziman formulation and pseudopotential theory. It was also pointed out 
by Jin et al. [8] that the Ziman type theory can be applied successfully in the 
prediction of the electronic transport properties for simple binary alloy systems but a 
close examination of its applicability to multicomponent systems is still needed. These 
all motivated us to consider further application of the pseudopotential theory to study 
Corresponding Author : © 2 0 0 7 , A C S 
126 P N Gajjar, S R Mishra andARjant 
electrical resistivity of alloys containing three different simple metallic constituents K-
Rb-Cs, using our model potential [9,10]. The model pseudopotential has been successfully 
applied previously to the calculation of electronic properties of alkali metals and their 
binary alloys [10]. The influence of exchange and correlation effects are also investigated 
by including local field correlation functions due to Hartree (H) [11], Taylor (T) [12], 
Ichimaru-Utsumi (IU) [13], Farid et al. (F) [14] and Sarkar et al. (S) [15]. 
2. Interatomic pair potentials 
The effective interatomic interaction for the ternary alloy system A-B-C can be written 
as [9,10], 
nr) = [^f]^\F(l) 
J n 
Sin(gr) 
qr 
<fdqt (1) 
where F(q) is the energy wave number characteristics. Also Z and S20 are the effective 
valence and atomic volume of the ternary alloy system, respectively. It is noted by Jin 
et al [8] and Alblas et al [16] that such calculated 420 do not contain serious error 
as indicated by the fact that the maximum volume contractions are 1.0% for K-Cs and 
5.7% for Na-Cs. 
3. Electrical resistivity 
The expressions for the electrical resistivity for liquid metals, binary and ternary alloys 
are given by [8] 
SC /a / /(Q)|VV /(q)|2+2(CA)1/2a1,(Q)lV l(q)lV2(q) 
ta i f i f t r ^WuM, ! . , ] *2(C!Ci)"'a2a(q)W1{qWM\- <2> 
"'[*<,. 
Here, afS(q) is the partial-structure factors and W,(q) the screened form factors, 
calculated with exchange-correlation effects included for the /-type ion in the alloy with 
different concentration. 
Figure 1 shows the electrical resistivity of binary combinations K-Rb, K-Cs and 
Rb-Cs investigated for full range of concentration. 
The computed electrical resistivity for the ternary K-Rb-Cs liquid alloys at 100°C 
are summarized in Table 1, along with the theoretical results obtained by Jin et al [8] 
using self-consistent energy independent model potential (SC-EIMP). 
For liquid K and Cs, the computed resistivity due to F [14] local field correlation 
functions generates good agreement with the experimental findings [17-19]. While for 
Rb« the results due to S [15] screening function gives excellent agreement with 
experimental data [17-19]. 
The comparison with the results of SC-EIMP calculation of Jin et al [8] also 
Electrical resistivity of liquid K-Rb-Cs alloys 127 
Table 1. The electrical resistivities calculated for K-Rb-Cs alloys at various concentrations Q at 100°C. The 
bracketed values show the percentage deviation with respect to the Experimental value. 
Alloys 
K-Rb-Cs 0.6 
0.4 
0.4 
0.2 
0.2 
0.2 
•'Rb 
0.2 
0.2 
0.4 
0.2 
0.4 
0.6 
•'Cs 
0.2 
0.4 
0.2 
0.6 
0.4 
0.2 
rc 
(a.u.) 
Qo 
(a.u.) 
Present calculations with 
different local 
field correlation ftinction 
Expt. 
[17-19] 
SC-
EIMP 
Jin 
2.8580 
3.0488 
2.8883 
3.3296 
3.0791 
2.9185 
40 
30 
20 
10 
Pw PI A U Pr Ps 
(liQ cm) {yQ cm) (u i i cm) | u Q cm) (uX2 cm) 
551.52 16.73 39.42 44.45 ,. 55.75 
604.34 21.40 47.99 53.05 • 57.89 
568.82 18.68 41.09 45.95 54.62 
657.16 24.68 58.21 63.20 73.01 
621.64 19.92 45.79 50.71 55.78 
586.12 19.63 42.59 47.61 51.91 
L • * - **~ 
r • * * * • 
L__ ._ _i i. 
• 
• 
K-Rb 1 
-J 
• * 1 
1 - , . 1 
et al [8] 
37.89 
36.66 
36.75 
46.06 
34.73 
33.92 
31.80 
40.48 
33.23 
45.84 
40.55 
34.14 
20 40 60 80 
Concentration (atomic %) 
Figure 1. The computed electrical resistivity of K-Rb, K-Cs and Rb-Cs binary alloys along with Experimental 
data. 
favours our results. For liquid K, Rb and Cs, the deviation of present findings from 
experimental data [17-19] is 0.5% to 16%, while for SC-EIMP [8] findings, such 
deviation is 9% to 84%. 
For liquid binaries K-Rb, K-Cs and Rb-Cs, the highest resistivity is obtained for 
Ko.7CSo.3, which is also supported by experimental data [17-19]. In the SC-EIMP 
128 P N Gajjar, S ft Mishra and A ft Jam 
calculation of Jin et al [8] resistivity of binaries increases with increase in atomic 
volume of the alloy and highest resistivity was obtained for Ko.2CSo.8 which is in contrast 
to experimental observation [17-19]. 
There is a pronounced maximum in the binary K-Cs alloys located at the highest 
atomic concentrations of the heavier elements i.e. at about 60-70 atomic % of Cs, 
Such a maximum also appears for liquid K-Rb-Cs system, when the concentration of 
Rb is set to 20 atomic %. The resistivity of K-Rb-Cs ternary increases substantially 
from K-rich alloy to Rb-rich alloys and to Cs-rich alloys. It is also predictable that, the 
presently computed electrical resistivity of ternary K-Rb-Cs systems changes smoothly 
with the concentration of each component and form a well defined "electrical resistivity 
surface" at 100°C as shown in Figure 2. 
Atomic % of Cs 
Figure 2. The electrical resistivity surface of ternary K-Rb-Cs alloys at 100°C. 
It is found that comparing to static screening of Hartree [11], the local field 
correlation function due to F [14] affects the results of electrical resistivity very largely. 
The influence of various local field correlation functions on the resistivity with respect 
to static H [11] dielectric function for K-Rb alloys are 96-102% for T [12], 119-126% 
for IU [13], 133-142% for F [14] and 63-1% for S [15] screening functions. Such 
screening influence for K-Cs alloys are 139-102% for T [12], 143-126% for IU [13], 
173-142% for F [14] and 47-1% for S [15] screening. Similarly, for Rb-Cs alloys, the 
screening influences are 139-95% for T [12], 143-119% for IU [13], 173-133% for F [14] 
and 1-63% for S [15], respectively. 
We have also computed the effect of screening on the ternary K-Rb-Cs alloys. 
The deviation with respect to H [11] are 116-135% for T [12], 142-165% for IU [13], 
164-233% for F [14] and 71-126% for S [15] screening functions. 
We observed that, among the presently calculated resistivities, the p calculated 
by H [11] function is giving lower value while that of F [14] gives higher value. Hence 
Electncal resistivity of liquid K-Rb-Cs alloys 129 
m the resistivity surface, the results due to these two screening functions are plotted. 
4. Conclusions 
The present model potential is proved capable of explaining the electrical resistivities 
of pure metals, binary alloys and ternary alloys The computed resistivities for the 
ternary alloys form an "electrical resistivity surface" in the full range of concentration. 
It is also concluded that, the Ziman type formulation alopg with the pseudopotential 
theory are found applicable in the study of electrical resistivities of the multi-component 
alloys 
Acknowledgment 
The work is supported under DRS/SAP of UGC, New Delhi SRM also acknowledges 
the support of UGC for providing DRS/SAP Fellowship 
References 
[1] J Auchet, A Rhazi and J G Gasser J Phys Condons Matter 11 3043 (1999) 
[2] Z M Ziman Proc Phys Soc 91 701 (1967) 
[3] P B Thakore P N Gajjar and A R Jam Indian J Pure Appl Phys 38 811 (2000), Conden Matt Phys 4 473 
(2001), 5 493 (2002) 
[4] W Greertsma, D Gonzalez and L H Gonzalez Braz J Phys 33 406 (2003) 
[5] J Hafner Phys Rev A16 351 (1977) 
[6] W H Young Rep Prog Phys 55 1769 (1992) 
[7] T Khajil Phys Chem Ltquid 37 773 (1999) 
[8] Z H Jin, K Lu, Z Q Hu and H B Liu J Phys Condons Matterd 1393 (1997) 
[9] Minal H Patel, A M Vora, P N Gajjar and A R Jani Physica B304152 (2001), Commun Theor Phys 38 365 
(2002) 
[10] P N Gajjar, A M Vora and A R Jani Mod Phys Lett B18 573 (2004), Indian J Phys 87 775 (2004) 
[11] W A Harrison Elementary Electronic Structure (World Scientific Singapore) (1999) 
[12] R Taylor J Phys F Met Phys 8 1699 (1978) 
[13] S Ichimaru and K Utsumi Phys Rev B24 7385 (1981) 
[14] B Fand, V Heme, G Engel and IS Robertson Phys Rev 4811602 (1993) 
[15] A Sarkar, D Sen, S Haldar and D Roy Mod Phys Lett B12 639(1998) 
[16] B P Alblas, W Van der Lugt, O Mensies and C Van Dijk Physica B106 22 (1981) 
[17] J Hennephof, W Van der Lugt, G W Wright and T Manen Physica 61 146 (1972) 
[18] J Hennephof, C Van der Marel and W Van der Lugt Physica B94 101(1978) 
[19] J F Devlin, M R Leenstra and W Van der Lugt Physica 66 593 (1974)

Electrical Resistivity of Liquid K-Rb-Cs Alloys

Indian J. Phys. 81 (1), 169-172 (2007) 
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Notes for Contributors

Pathak, A K

Mukherjee, T

Maity, D K

Structure, Energy and IR Spectra of K-nNH3 Cluster : A Theoretical Study

Indian Association for the Cultivation of Science

Not a member yet

The Temporal Periodic Variations of the Total Ozone Content at Udaipur, a Near Tropical Station

Heavy-Fermion Systems

Dielectric Relaxation in Tungsten-Bronze Pb<SUB>2</SUB>Bi<SUB>3</SUB>NdTi<SUB>5</SUB>O<SUB>18</SUB> Ferroelectric

Electrical Resistivity of Liquid K-Rb-Cs Alloys

Notes for Contributors

Structure, Energy and IR Spectra of K-nNH<SUB>3</SUB> Cluster : A Theoretical Study

The Curl Equations for an Induced Renner-Teller Type Model

Advisory Board and Editors

Foreword

Aspects of Electron Dynamics in a Helium Atom Under an Intense Laser Field

6,371

8,071