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Shear viscosity of square - well fluid 
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Front Contents

Anurag

Tewari, Ashutosh

Khanna, K N

Indian J. Phys.%\(\2\ 1295-1302(2007) 
Shear viscosity of square - well fluid 
Anurag, Ashutosh Tewan and K N Khanna* 
Department of Physics, VSSD College, Kanpur-208 026, India 
E-mail knkannaC" rediffmail com 
Received 02 March 2007, accepted 7 September 2007 
Abstract A formula for the shear viscosity of the square well fluids is proposed through the modified pair 
correlation function in hard sphere system The results are compared with the expressions of the viscosity and 
diffusion coefficients derived by Nigra and Evans for square-well fluid, the diffusion coefficient is changed into 
viscosity coefficient by employing Stokes- Einstein relation The numerical results of the viscosity obtained by 
employing Stokes - Einstein relation The numerical results of the viscosity obtained by employing Stokes -
Einstein relation are found poor at low temperatures 
Keywords Diffusion coefficient, viscosity coefficient, Stokes - Einstein relation 
PACS Nos. 31 15 Md, 31 15 Bs, 05 10 Ln 
1. Introduction 
The study of viscosity of fluid is of great interest in various research areas both applied 
and fundamental. The parameters such as composition, mass, density and temperature 
are required for the understanding of fundamentals and microscopic behaviors of fluid and 
fluid mixtures. Thus in the recent past considerable interest has been shown in obtaining 
accurate and reliable values of transport properties for a variety of fluids and fluid mixtures. 
During the last few years, there has been a growing appreciation of the role of the 
nearly harmonic molecular motions in dense fluids [1-5] Tang and Evans [6] derived a 
damped harmonic oscillator equation of motion for the velocity time correlation function. In 
that work, the VTC function term arose from Enskog theory [7] describing uncorrected 
binary collisions and the memory term describing oscillatory frequency arose from correlated 
back scattering. In an other paper, Tang and Evans [8] investigated the wave vector and 
frequency dependence of the time correlation function (tcfs) at /C= 0. This theory describes 
the Enskog theory for the HS system, which can be used for normal fluids. In the present 
Corresponding Author 
©2007IACS 
1296 Anurag, Ashutosh Tewari and K N Khanna 
work, we have employed the Evans's expression of the shear viscosity of hard sphere for 
wave number K -> 0 to describe the shear viscosity of the square-well fluid. The second 
motivation for this study is to investigate the validity of the Stokes-Einstein relation at low 
temperatures. 
2. Theory 
Thermodynamic transport properties, such as shear viscosity, can provide evidence fo 
coherent phenomenon. The coherence takes the form of free translation interrupted by 
collisions and this effect is reflected in the wave vector dependence of the Shear Viscosity 
Thus, Tang and Evans [8] treated the shear viscosity as consisting of an Enskog part 
plus a harmonic mode contribution. They described a wavenumber and frequency dependent 
Enskog theory for a very dense fluid. This theory ri(K, Z) reduced to the improved Enskog 
results i.e. ri(K ->Q, Z) which will be applicable to normal fluids. The Shear Viscosity is 
defined by them as (see equation (38) of reference [8]) 
r/(K -> 0, Z) = mpcr2 
10
 2 
mpcr 
(
 6 ^ 
1 +—cr3pg(cr) 
15 Hyy ' (1) 
where fE is the Enskog friction arising from uncorrelated binary collisions and is given by 
VST fE = —p*g(o)w (2) 
and P = V'(KBT), Zis the collision frequency per particle (Z= 3/2 fE), w = ^KBT mcr2 ; 
p* =TT/6 per3 is the packing fraction. On Solving, we get the shear viscosity of dense 
fluid with two body correlation function in the hard sphere system [8,4] 
r)HS = mpa'to < 
5yfn 
96 p*g(cr) 
1 + 8p*flf(cT)f + 8p*flf(cT)| 
5 I 5yfn I (3) 
Where g(a) is the pair correlation at contact for hard sphere system 
(g(°) = (1 - P'/2)/(1 - p *)3) and p* = (ff/6) per3 = (/r/6) p x . For a square well fluid the 
pair correlation function can be defined by using the Chapman-Enskog method of solution 
or by LonguesMHiggins and Valleau solution of velocity auto correlation function [details 
see in reference 9] as 
gS0(cr) = lgsw(o)
 + X*Egsw(Xc)\. (4) 
Shear viscosity of square - well fluid 
1297 
Where gsw{X<r) is the radial distribution function of square-well fluid evaluated at 
ACT • The expression of E and gsw(to) are defined by Yu et al [9]. 
Thus the shear viscosity in square well system becomes 
Vsw - mPv' 
KT 
ma2 
5
^ .(u?£l£?^f
 + §£^(£) 
5 5VTT 96 p*gbU(a) (5) 
In the present work, the value gsw(a) is determined in high temperature approximation 
(HTA) [10]. Hence 
,sw 
<r»» 4 7 * d?] T* ' (6) 
where g(a) is the radial distribution function of hard sphere at contact and a, is the 
mean attractive energy as given below [10]. 
,sw 
- 4 p * f ( A 3 - l ) 
( W w / 2 ) 
(1-Peff) (7) 
c,, c2, Cj are the matrices and are given in reference [10]. Throughout the paper, we 
have defined the reduced viscosity as 
^,7/{(mKT) 1 / V' 3 }. 
Thus the expression for the reduce shear viscosity rf can be written as 
risw = P! '3 
b4n 
96p*gso(cr) 
SO/ 
1 + Bp'STW 
N2 SQ/ 
.8p*flT» 
$4n (8) 
Another (second) way to compute Shear Viscosity is the time evaluation of the 
dynamical variable described by a Smoluchowski equation. Nigra and Evans [11] considered 
a classical fluid subject to an effective two-body intermolecular force, derived from a square-
well fluid, undergoing dynamics as described by a Smoluchowski equation for pair diffusion. 
Specifically, they represented the time correlation functions (tcfs) of intermolecular forces 
1298 Anurag, Ashutosh Tewari and K N Khanna 
appropriate for D and v as the sum of two independent parts : that arising from repulsion 
and that from attraction. Inclusion of attractive part is the main theme of Nigra and Evans 
work [11]. The Shear viscosity is the time integral of the stress tcf [11]. 
7j = J L [drv..drN idt e PuJxy e'u Jxy (9) 
With ZN the AZ-particle configurational integral iL the system /V-particle Liouville operator 
and JP the xy component of the potential part of the stress tensor. The equation (9) is 
solved (see equation (64) of reference [11] as 
Vsw - WHS + 
4f2n(?iof KT p2g1(Atr)n 
isqb (10) 
Where rjHS, DHS, D0, f, (ft(ACT) and n are defined as 
1HS = 
KT 
2no Dt 'HS (11) 
and 
D - * 
°
HS
 ' »«V) (12) 
3>« 8pcH 
(KT 
nm (13) 
(r = KT/e), (14) 
(15) 
n = 
1U5+4 
11(10-f) A 5 - 2 4 ^ ' 
We can solve the equation (10) as 
*lsw =
 8 < J ^ \a!*W+^^pl*VtT\n\ 
2n 15 
(16) 
(17) 
Shear viscosity of square - well fluid 1299 
Further (third method), shear viscosity of the square-well fluid can be determined from 
self-diffusion coefficient of square-well fluid by employing Stokes-Einstein relation. In the 
Stokes-Einstein (SE) relation, the self diffusion coefficient D of a particle in a classical 
fluid and the shear viscosity v of the fluid are connected by 
D-KT 
2nr)o 
with KTthe thermal energy and o the diameter of the reference spherical particle which 
interact with the surrounding fluid in accord with hydrodynamic slip boundary conditions. 
Thus, we need as expression of diffusion coefficient under the same condition in which 
shear viscosity is determined. 
The self-diffusion coefficient for square-well potential is defined by Nigra and Evans as 
[11]. 
DHS 
DstV =
 1
 + 8p*A3gi(AcT)^F (18) 
where 
7A3+2 
~ (42A 3 -7 fA 3 -8 f ) ' 
The Stokes-Einstein relation is written as 
2ncrT]swDsw = 1 (19j 
KT 
Hence Isw = J £ " (l + 8p* A 8 ^ ) / ^ ) (20) 
• _ Vsw 
*« *
sw
 ' (mKTfz p"2/3 
= ±pl,3gHS(o)(u4np^9M°)f2F\ (2D 
3V:T V J J 
3. Results and discussion 
In the present work, as expression of the shear viscosity for the square-well fluid is 
derived from the hard sphere system. It has been shown that the equilibrium rad.al 
1300 Anurag, Ashutosh Tewan and K N Khanna 
distribution function gsw(cr) and gsw{Jio) of square-well fluid can predict the shear 
viscosity for a square-well fluid The present results are compared with the results of the 
expression of the shear viscosity proposed by Nigra and Evans [11] for a square-well 
Ol*s 
4 60 
4 20 
3 60 1 
3 20 
2 80 H 
2 40 
2 00 4 
1 60 4 
120 
0 80 4 
0 40 
T = 30 
PRESENT WORK 
NIGRA AND EVANS 
• - • - • - • - • - BY SE RELATION 
0 1 02 0 3 04 0 5 
(P*) 
06 07 08 1 0 
Figure 1. Plot of the reduced Shear viscosity r/* vs reduced density p * at V - 3 0 Present results 
( ), Nigra and Evans ( ) and results of the reduced viscosity employing Stokes-Einestem 
relation ( - • - • - • - ) 
fluid. They have calculated the shear viscosity by employing time correlation function with 
the contribution of delta function, hard sphere forces and from soft forces of square well 
fluid. The equation derived by Nigra and Evans are presented here by equation (10) It has 
been further modified to reduced units and presented by equation (17) We find a good 
agreement in-between present results and with those obtained by equation (17) proposed 
by Nigra and Evans [11] at all temperatures. Further, we have also calculated the shear 
viscosity obtained from diffusion coefficient by employing Stokes-Bnstein relation i.e. equation 
(21). Figures 1 to 3 show the reduced shear viscosity coefficient as a function of the 
reduced density at various reduced temperature. T = 3.0, 2.0 and 1.5. It can be seen 
that at V = 3.0 both the equations (8) and (21) predict good agreement with equation 
Shear viscosity of square - well fluid 
1301 
r = 2o 
0l*s 
- PRESENT WORK 
NIGRA AND EVANS 
— BY S E REUNION 
Figure 2. Plot of the reduced 
( )t N,gra a n c i Evans (— 
relation ( - • - • - • - ) 
Shear viscosity r\* vs reduced density />* at T = 2 0 Present results 
) and results of the reduced viscosity employing Stokes-Einestem 
r = i 5 
0 i \ w ) 
4 60 
4 20 
3 60 
3 20 
2 80 
2 40 
2 00 
160 
1 20 
0 80 i 
0 40 
f — NIGRA AND EVANS 
— . _ . - . — . — . — - . -
 BY S-E RELATION 
/ 
; 
> / ' f / ' 
' ! 
• ' i / ' 
i /; / / / 
/ / / 
/ A / / ' /X' / / ' //?' 
^ 
_ — . — 1 — ' — I — ' — ' — - 1 — ' — — * - * 
Figure 3. Plot of the reduced 
( )f N i g r a and Evans ( -
relation ( - • - • - • - ) 
0 1 0 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 1 0 
<P#) 
Shear viscosity i)* vs reduced density p * at T = 1 5 Present results 
) and results of the reduced viscosity employing Stokes-Einestem 
1302 Anurag, Ashutosh TewariandKNKhanns 
(17) i.e. with the equation proposed by Nigra and Evans. As the temperature decreases 
i.e. P = 2.0 and P = 1.5 the equation obtained by employing Stokes-Einstein relation 
shows the deviation from the equation (17) predicted by Nigra and Evans. Nigra and 
Evans also pointed out the severe failure of Stokes-Einstein relation at low temperatures 
close to the glass transition temperature. Molecular dynamics simulation of high-density 
hard sphere fluid (super cooled liquid)clearly show a breakdown of the Stokes-Einstein 
equation [12]. These results [11,12] support the present work that Stokes-Einstein relation 
cannot be used for square-well fluid at low temperatures. 
Acknowledgment 
Ashutosh Tiwari is thankful to CSIR for financial assistance. 
References 
[1] R W Zwanzig J. Chem Phys. 79 4507 (1983) 
[2] T M Wu and R F Lonng J. Chem, Phys. 99 8936 (1993) 
[3] G Seeley, T Keyes and B Madan J. Chem. Phys. 95 3847 (1991) 
[4] G T Evans J. Chem. Phys. 121 3667 (2004) 
[5] Y Wan and R M Stratt J Chem. Phys 100 5123 (1994) 
[6] S Tang and G T Evans Phys. Rev. Lett. 72 1666 (1994) 
[7] J H Ferziger and H G Kaper Mathematical theory of transport in gases (North-Holland, Amsterdam) 
(1972) 
[8] S Tang and G T Evans J. Chem. Phys. 1031544 (1995) 
[9] Y X Yu, M H Han and G H Gao Phys. Chem Chem. Phys. 3 437 (2001) 
[10] A Gil-Villegas, A Galindo, P J Whitehead, S J. Mills and G Jackson J. Chem Phys. 106 4168 
(1997) 
[11] P Nigra and G T Evans J. Chem Phys. 122 244508 (2005) 
[12] S K Kumar, G Szamel and J F Douglas J. Chem. Phys. 124 214501 (2006)

Shear Viscosity of Square - Well Fluid

Indian J. Phys. 81 (12), 1325-1328 (2007) 
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Influence of Finite Range of Nuclear Interaction on the Coulomb Breakup of 11Be

Sarma, Amal Kr

Singh, N Nimai

Indian J. Phys. 81(3) 389-394 (2007) 
€) 
Baryogenesis from inverted hierarchical mass 
models with tribimaximal mixings 
Amal Kr Sarma* and N Nimai Singh 
Department of Physics, Gauhati University, Guwahati-781 014, Assam, India 
E-mail : arnalk_s@yahoo.co.in 
Received 7 September 2006, accepted 1 December 2006 
Abstract: We estimate the baryon asymmetry for two specific structures of Inverted Hierarchical mass models: 
bimaximal mixings(BM) and tribimaximal mixings (TBM), both with opposite CP-parity. Starting from the light 
neutrino mass matrices, the heavy right handed Majorana neutrino mass matrices are constructed via inverse 
seesaw relation. The estimated baryon asymmetry for tribimaximal mixing mass model with down quark mass 
matrix taken as Dirac neutrino mass matrix is found to be consistent with the experimental value. Through the 
estimation of baryon asymmetry, we establish the validity of tribimaximal mixings of inverted hierarchical neutrino 
mass model. The present calculation also discriminates the three possible choices of Dirac neutrino mass matrix. 
Keywords : Seesaw mechanism, inverted hierarchy, lepton and baryon asymmetry. 
PACS Nos : 14.06.Pq. 11.30.Er, 11.30.Fs, 13.35. Hb 
1. Introduction 
The inverted hierarchical pattern of light left-handed neutrinos (m, * rr^ > m3) are best 
understood in terms of two mass models[1]: Inverted hierarchical type-2A (lnvT2A) and 
Inverted Hierarchical type-2B(lnvT2B) based on the relative CP-parity between m l and m2. 
For lnvT2Bt the mass pattern is (m .-m0> m). The inverted hierarchical model of neutrinos 
1 2 3 
with odd CP parity (m1f -m2, m3) generally predicts nearly bimaximal mixings in the 
diagonal basis of the charged lepton mass matrix. A familiar mass matrix of lnvT2B is 
generally given by 
(8% 1 n 
K o) % 1 S9 6 2 <>3 
1 $3 S2j 
* Corresponding Author 
On leave from D.R.College, Golaghat-785 621, Assam, India O 2007 IACS 
390 Amal Kr Sarma and N Nimai Singh 
where SXZ3 < 1. The diagonalisation of mass matrix (1) gives following mass eigenvalues: 
m w = ^M(*' + <52 +S3)±x]m3 = m0(«52 -<S3); 
x2 = 8 + (6* + *1 + <S§) - 2<S,<!>2 - 2 ^ 3 + 2<52<53 
and the three mixing angles are calculated as 
tan2 023 = \ sin(9t3 = 0, tan2012 = — - - — — . 
( d 1 - d 2 - d 3 J 
Such a simplest form (1) is found to be realised within seesaw framework [2] 
mLL = -mLRMRRm[R using diagonal form of Dirac neutrino mass matrix mm = fHaQ(Xn9Xl,ijy 
and a suitable non-diagonal texture of heavy Majorana mass matrix MRR. For each pair of 
(m,n), the corresponding texture of MRRare different, and the light neutrino mass matrices, 
m a are left unaffected. For example, we use the following form of mafrom Ref.[1]: 
mLL = 
r0 1 1 
! -(A3-A4)/2 -(A3 + A4)/2 
[l -(A3 + A4)/2 -(A3-A4)/2j 
kn,
 (2) 
Using the input values ^=0.3, m0=0.035eV, the corresponding oscillation parameters are 
calculated as Am^ = 9.30x 10~5eV2,Am%3 = 2.50 x 10~3e\/2,tan2 012 = 0.98,sin2 2023 = !O,sin013 
= o. The predicted solar angle is nearly maximal. Several attempts have been made to tone 
down solar mixing angle but the effect is not so satisfactory to the experimentally accept-
able level. It has been pointed out [3] that there is also a possibility to realise the 
tribimaximal mixings [4] within the inverted hierarchical mass matrix in eq.(1), provided the 
numerical values of <Sif2,3 are comparatively larger but smaller than 1. As a specific 
example, we follow the ref [3] and use the following values : ^ = 0.56855627, 
S2 =0.71572329, <53 = 0.12477548, m0 = 0.035eVin eq.(1). The predictions on neutrino oscil-
lation parameters are : Am^ = 8.34 xWseV21Amf3 =195xlO~3eV2,tan2012 =0.45, tan2023 
= io, sin013 = 0. The solar angle is slightly smaller than tribimaximal mixing and agrees with 
recent data. The above prediction does not require any fine tuning of the solar angle from 
charged lepton sector or from renormalization effects. 
The inverted hierarchical neutrino mass matrix in eq.(1) with bimaximal mixings as well 
as tribimaximal mixings is independent of pair of (m,n) appeared in mLRwithin the frame-
work of seesaw formula, and this can however, be fixed in the estimation of baryon 
asymmetry[5] via lepton asymmetry [6-8], which depends on the texture of MRn. For our 
interest, we take up three different cases [9] of (mtn) dependence on mLR and MRRa$ 
allowed by 50(10) grand unified theory : 
Case 1 : mLR • charge lepton mass matrix with (m,n) * (6,2); 
Case 2 : mLR sup quark mass matrix with (mtn) s (8,4); 
Case 3 : mLR sdown quark mass matrix with (m,n) » (4,2). 
Baryogenesis from inverted hierarchical mass models etc. 391 
For a particular choice of m
 LL, one can have three possible structure of MRR depending 
on the above choice of (m,n). The choice of non-diagonal mLR in the basis of diagonal MRR, 
plays crucial role in the calculation of baryon asymmetry via lepton asymmetry produced 
by the decay of lightest of heavy Majorana neutrino M,[10]. 
In this work, we start with light Majorana neutrino mass matrix mLLand translate this 
matrix to MRRvia the inversion of seesaw formula^ MRR=-mTLRmilmLR. Using the right-
handed Majorana mass MRR% we estimate the baryon asymmetry for bimaximal and 
tribimaxima cases for three different choices of Diraft neutrino mass matrix mLR. In Section 
2, we briefly mention and expression for lepton an^l baryon asymmetry and in Section 3, 
we present one representative example of numerical calculation and results. Finally in 
Section 4, we conclude with summary and discussion. 
2. Expression for lepton and baryon asymmetry 
For hierarchical mass structure of heavy right handed Majorana neutrinos, considering the 
out of equilibrium and CP-violating decay of physical Majorana neutrino M^ the CP asym-
metry is expressed as [11] : 
e i = 
3M, *"[{**mt±h\ 
id/2 /uui\ (3) 16*^ (hh\ 
where h = m'LR I vis the 3x3 Dirac neutrino Yukawa coupling matrix normalised to h& = 1 in 
the basis, where MRR\§ diagonal with real and positive eigenvalues. For quasi-degenerate 
structure /.e.,'for My*M2 <M3, one has to consider the resonance enhancement factor 
R = Mi/2(\M2\-\Mi\) and the expression (3) is modified to [12, 13]: 
Again the electoweak sphaleron interaction [6,14,15] partly converts the lepton asym-
metry to baryon asymmetry. The baryon asymmetry of the universe Yg"which is defined 
as the ratio of baryon number density (r?B) to photon number density (nr) in standard 
model (SM) case, is expressed in terms of washout factor k, and e, as [12]: 
VSS*'=5S. = 0.0216/(:161 (5) 
How much the produced asymmetry is washed out is described by Boltzmann equation 
and its solution can be parametrized by a parameter K known as dilution factor [16] : 
0.3 „ ^ ^ ^ ^ « « 6 
K(ln/C) 
1 
2 > / K 2 + 9 
35- iMOStfSIO0 , 
i fO£K<10, ^ 
392 Amal Kr Sarma and N Nlmai Singh 
where K = mlm\ with m=(ttf)^IM is the effective neutrino mass and 
1 6
*f 1 v2 
m=— r * -9* is the equilibrum neutrino mass [17]. In standard model scenario 
3V5 2 Mpf 
g*= 106.75 is the value of the massless degree of freedom and Mp, = i-2xio19GeV is the 
Planck's constant. Out of equilibrium decay of M} is characterised by K < 1 condition. 
3. Numerical calculation and results 
For numerical calculation of baryon asymmetry we choose a basis UD where 
M%* - URMRRUR = 6\aQ(MvM2lM3) with real and positive eigenvalues [18,19]. We transform 
mLR = diag(Am,An,l)v to the URbasis by mLR -» m'LR = mLRUR. In this prime basis the Dirac 
neutrino Yukawa coupling becomes h = (mLRUR)/v. 
As an example, we consider tribimaximal pattern of mLL discussed in Section 1. The light 
neutrino mass matrix is given by (in eV) 
f-0.0198595 -0.0349297 -0.0349297 
mLL9 i -0.0349297 0.025 -0.004358371 
(-0.0349297 -0.00435837 0.025 
Taking Dirac neutrino mass matrix as down quark mass matrix (case 3) i.e., 
mLR = diag(A4,A2,l)v,with A = 0.3 and v = i74GeV we have the correponding MRR$n GeV) as 
MRR = 
(-144 x1010 -2.70 x1011 -3.01x1012>| 
-270 x 1011 5.03 x 1012 -3.69 x 1013 
-3.01 x1012 -3.69 x1013 6.21 x1014 
The mass eigenvalues are M%* = diag(9.76xio10f 2.89xio12,6.23xio14). For this structure, 
we found (hhf)u = 6.56xl0"5,lm(^mL^t)11 = = 7.09x10"16,m1 =2.03x10"2e^«l08x10"3el/,K 
= 18.73. and ic, = 0.008. The lepton asymmetry is found to be e,= 2.08xio -6. Following eq 
(3), we found Y^ = 3.78xio~10 which is consistent with the experimental bound [20] : 
Yg"8 =(6.1^2)10"10. We follow the same procedure to estimate lepton and baryon asym-
metry for other cases. For quasi-degenerate structure which appears in bimaximal case, 
we use eq.(4) to calculate lepton asymmetry. Such degeneracy is found to be lifted in 
tribimaximal case and the expression in eq.(3) is used. For all the cases under consid-
eration, the heavy mass eigenvalues are collected in Tablel the effective mass parameters 
and dilution factors are presented in Table 2. Finally, the estimated lepton and baryon 
asymmetry are collected in Table 3. 
Baryogenesis from inverted hierarchical mass models etc. 393 
Table 1. The three right-handed Majorana neutrino masses in GeV for bimaximal case(BM) and 
tribimaximal case(TBM). 
(m.n) BMJM/I 
(4,2) 6.2783 x 101 \ 6.2838 x 101, 5.38 x 1016 
(6,2) 5.6527x1010, 5.6532x1010, 5.38x1016 
(8,4) 4.5971x10s. 4,5974x108, 5.34x1016 
i 
jWxIO1 0 
l8.10x108f 
6.56x106, 
TBM|/lfy| 
2.89x1012, 6.23x1014 
2.83x1012,6.23x1014 
2.30x10t0, 6.21 x1014 
Table 2. Contains the values of effective mass parameter m1 in eV, decay parameter K and 
dilution factor K, for bimaximal (BM) and tribimaximal (TBM) case. 
(m,n) 
(4.2) 
(6,2) 
(8,4) 
BM 
m, 
3.16 x10'3 
2.85 X10"4 
2.83 x 10"4 
K K 
1 
2.19 0.2 
0.26 0.17 
0.26 0.17 
m, 
2.03 x10*2 
198 x10'2 
1.98 x10"2 
TBM 
K 
18.73 8.40x10"3 
18-37 8.66x10'3 
18.37 8.66 x10"3 
Table 3. Calculation of lepton asymmetry e, and baryon asymmetry Vfl for bimaximal case (BM) 
and tribimaximal case (TBM) for three choices of (m,n). 
(m,n) 
(4,2) 
(6,2) 
(8,4) 
BM 
€ 1 
1.64x10* 
147 x10"2 
1.62 x10"4 
YB 
4.25 x10 s 
5.40 x 10 5 
5.94 x10'7 
€1 
2.08x10* 
1.55 x10*9 
1.28x10*" 
TBM 
YB 
a78x10"10 
289 x10*13 
240 x10'16 
4. Summary and discussion 
We start with the bimaximal and tribimaximal mixing pattern of inverted hierarchical light 
neutrino mass matrix mu. Heavy right-handed Majorana neutrino mass matrices Mm are 
constructed via inverse seesaw relation. In case of bimaximal mixing pattern of light 
neutrinos, we observe that the corresponding heavy right handed neutrino masses manifest 
quasi-degenerate structure i.e., M,*M2<M3. This peculiar structure of heavy masses 
enhance the produced asymmetry known as 'Resonance enhancement" by modifying the 
propagator. This scenario completely changes when we come to tribimaximal mixing (TBM) 
pattern, with hierarchical pattern of heavy neutrinos i.e., M1 < M2 <M3. This type of hierar-
chical structure will bypass the resonance enhancement effect and this is clearly seen in 
the produced asymmetry. For bimaximal case, the range of lepton asymmetry is found to 
be 10-4 <et<10"2 whereas in tribimaximal scenario, the range is 10~11 <e1<10"6. Our esti-
mated baryon asymmetry YB * 3.78 x 10"10 for tribimaximal mixing pattern with down quark 
mass matrix taken as Dirac neutrino mass matrix is consistent with the experimental 
394 Amal Kr Sarma and N Nimai Singh 
value [20]. For hierarchical structure of heavy Majorana neutrino masses, the condition 
M, > 4xl08GeV satifies the famous Davidson-Ibarra bound [21], In the present calculation, 
we are able to establish the validity of tribimaximal mixing in inverted hierarchical mass 
model, and also to discriminate the three possible choices of Dirac neutrino mass matrix 
through the estimation of baryon asymmetry. 
Acknowledgment 
One of us (AKS) would like to thank UGC(NER), India for awarding a fellowhip under FIP 
programme, X-th Plan. 
References 
[I] N Nimai Singh and M Patgiri IJMP A17 3629(2002); M Patgiri and N Nimai Singh IJMP A18 
443(2003); N Nimai Singh, M Patgiri and M K Das Pramana J. Physics 66(2) 361(2006) 
[2] M Gell-Mann, P Ramond and R Slansky in Supergravity, Proc. Workshop (New York: Stony Brook) 
(1979), (Eds) P Van Nieumenhuizen and D Freedman ( Amsterdam : North- Holland), (1979); 
T Yanagida KEK Lectures, (1979) (unpublished); R N Mahapatra and G Senjanovic Phys. Rev. 
Lett. 44, 912(1980) 
[3] N Nimai Singh, M Rajkhowa and A Borah hep-ph/0603154, hep-ph/0603189 
[4] GI Low and R R Volkas Phys. Rev. D68 033007(2003); P F Harrision and W G Scott hep-ph/0402006 
[5] A D Sakharov JETP Lett 5 24(1967) 
[6] V A Kuzmin, V A Rubakov and M E Shaposhnikov Phys.LetL B155 36(1985) 
[7] M Fukugita and T Yanagida Phys. Lett. B174 45( 1986) 
[8] M A Luty Phy Rev. D45 455 (1992) 
[9] P M Fishbane and P Kaus J. Phys. G: NucL Part. Phys. 25 1629( 1999) 
[9] P M Fishbane and P Kaus J. Phys. G: NucL Part. Phys. 25 1629( 1999) 
[10] U Sarkar, hep-ph/9810247; M Flanz, E A Paschos and U Sarkar Phys. Lett. B345, 248 (1995); 
W Buchmuller, P Di Bari and M Plumacher NucL Phys. B665, 445(2003), hepph/0302092; 
W Buchmuller, P Di Bari and M Plumacher Nucl.Phys B643 367(2002); G F Giudice, A Notari, 
M Raidal, A Riotto and A Strumia, Nucl.Phys. B685 89(2004), hep-ph/0310123 
[I I] N Sahu and S U Sankar Phys ftev.D71 013006(2005), hep-ph/0406065; T Hambye and G Senjanovic 
Phys Lett. B582 73(2004), hep-ph/0307237; S Antush and S F King Phys.LetL B597 199 (2004) 
hep-ph/0405093 
[12] Carl H Albright and S M Barr Phys. Rev. D70 033013(2004) hep-ph/0404095 
[13] T Hambye ICTP Summer School Lecture Notes(2004) 
[14] E W Kolb and M S Turner The Early Universe, (New York: Addison-Wesely) (1990); J A Harvey and 
M S Turner Phys. Rev. D42 3344(1990) 
[15] NSManton Phys. Rev.D28 2019(1983); FR KlinkhamerandN SManton P/7ys. Rev. 0302212(1984) 
[16] AS Joshipura, E A Paschos and W Rodejohann J HEP 0108 (2001); NucL P/iys.B611227 (2001) 
[17] W Buchmuller hep-pW0306047 
[18] K S Babu, A Bachri and H Aissaoui Nucl.Phys.B7ZB 76 (2006) hep-ph/0509091 
[19] E K Akhmedov, M Frigerio and A Y Smirnov JHEPO309 021 (2003) hep-ph/0305322 
[20] D N Spergel et a/, Astrophys J. SuppL 148 175(2003) astro-ph/Q302209 
[21] S Davidson and A Ibarra Phys. Lett. B535 25(2002)

English

Baryogenesis from Inverted Hierarchical Mass Models with Tribimaximal Mixings

Chakrabarti, S

Sasmal, S

Saha, M

Khan, R

Bhoumik, D

Chakrabarti, S K

Indian /. Phys. 81 (5 & 6), 531 -538 (2007) 
Unusual behavior of D-region ionization time at 18.2kHz 
during seismically active days 
S Chakrabarti1'2*, S Sasmal1, M Saha\ R Khan1, D Bhoumik1 
and S K Chakrabarti13 
1
 Centre for Space Physics, 43 Chalantika, Gana Station Road, Kolkata-700 084, India 
2
 Maharaja Manindra Chandra College, 20, Ramkanta Bose Street, Kolkata-700 003, India 
J S N Bose National Centre for Basic Science, JD Block, Salt Lake, Kolkata-700 098, India 
E-mail sonah(fr>csp res in 
Received 2 April 2007, accepted 7 June, 2007 
Abstract We have been monitoring the VTX3 station at Vijyanarayanam which transmits Very Low 
Frequency (VLF) signal at 18.2 kHz using the Stanford University made receiver stationed at our Centre We 
observe significant anomalies of the formation time of the D-region of the ionosphere at the Sunrise during the 
seismically active days. We have analyzed this data for over five months (1" November 2006 to 28m April 2007) 
and have noticed that during or before the earthquakes which took place in the neighboring region, the formation 
time is very anomalous in comparison to the normal days and therefore this may be used as a precursor to the 
earthquakes. We suspect that this abnormal behavior is due to the Lithosphere-lonosphere coupling. To our 
knowledge this anomalous behaviour has never been reported before 
Keywords ' Physics of the ionosphere, radiowave propagation, D region, ionospheric disturbances, 
earthquakes 
PACSNos. : 96.35.Kx.96.35.Kx.94.20.de, 94.20.Vv, 91.30.Px 
1. Introduction 
The physics of earthquake is very complex. The occurrence of earthquake is connected 
with the earth's crystal dynamics involving the structure of tectonic plates, and with the 
microscopic processes involved in the friction, electric discharges and release of various 
gases from the cracks. 
Corresponding Author 
©2007IACS 
532 S Chakrabarti et al 
Can earthquake be predicted and the associated tragedies be averted ? A variety of 
prediction methods have been tried for centuries, ranging from accounts of 'earthquake 
weather* to arrangements of the planets and uneasiness of animals. All these have been 
unsuccessful. Beginning in the 1960s, a major scientific effort towards reliable earthquake 
prediction grew rapidly in seismically active lands particularly in Japan, the former Soviet 
Union, China and United States. Among different precursory phenomena mentioned in the 
literatures on earthquake prediction, the ionospheric ones are probably the youngest. The 
first publications concerning the ionospheric effects connected with the earthquakes were 
published just after the Alaskan 'Good Friday1 earthquake in 1964 (Bolt, 1964; Davis & 
Baker, 1965). 
The ionosphere is a part of the upper atmosphere where there are enough electrons 
and ions to effectively interact with the electromagnetic fields. As a conducting medium, 
it plays an important role in the global electric circuit, and as a partly ionized gas, it is 
subjected to the laws of plasma physics. Due to its electromagnetic properties, the 
ionospheric plasma interacts with the Earth's magnetic field and to a considerable extent, 
is controlled by it. Ionosphere is sometimes referred to as magneto-active plasma. 
The ionosphere plays a major role in radio propagation, that varies strongly with 
frequency. At extremely low frequency (ELF, 3-1000 Hz) and very low frequency (VLF, 3-
30 kHz) the ionosphere strongly affects propagation over even shorter paths. ELF and 
VLF waves have long been used for subsurface remote sensing and geophysical prospecting, 
and sub-ionospheric VLF propagation irregularities and unusual ELF-VLF generation have 
even been suggested as precursors to major earthquakes (Molchenov and Hayakawa, 
1998; Parrot, 1994). 
There are several papers in the literature, which recognize that some electromagnetic 
phenomena would take place prior to an earthquake. Two possible methods have been 
proposed for the study of sub-ionospheric VLF/LF propagation data to understand seismo-
ionospheric perturbation. The first one is based on the analysis of night time amplitude 
and/or phase anomalies (Horic, 2007). The second method is called the 'terminator time' 
method, which is based on the determination of characteristic times of minima in the 
amplitude/phase diurnal variations during sunrise and sunset (see, Hayakawa, Molchenov, 
Ondoh, Kawai, 1996; Hayakawa, Molchanov, Shima, Shvets and Yamamoto, 2003; Maekawa 
and Hayakawa, 2006). This method has been used to interpret the results prior to the 
Sumatran earthquake of December 26th, 2004 (Chakrabarti et al 2005). 
The Centre for Space Physics VLF receiving station in Kolkata (22°34' N, 88°24,E) 
has been monitoring VLF signals almost continuously at 18.2kH2 transmitted by the 
VTX3 station located at Vijayanarayanam (8°26' N, 77°44' E), which is at a distance of 
1943 km from the receiver. Some preliminary results involving the monitoring of the sudden 
ionospheric disturbances (SID) and meteor showers have been reported (Chakrabarti et al 
2002; 2003). There, we used CSP-made single loop antennas. More recently, we have 
installed a receiver made by the Stanford University which is capable of monitoring multiple 
VLF stations. In the present paper, we report the narrowband results from this receiver. 
Unusual behavior of D-region ionization time at 18.2 kHz etc 533 
We will concentrate on the variation of the CMayer preparation time (DLPT) on each day 
during the sun-rise and demonstrate that just before or during earthquake activities, the 
time taken is anomalously high. In fact, we see anomalous behaviour, especially a large 
scale fluctuation of this time around seismically ac|ve days. To our knowledge, this has 
Figure 1. The Great Circle Path (GCP) between the receiver and the transmitter. The locations of the 
approximate earthquakes are also shown schematically. 
never been pointed out in the literature. The deficiency of our method is that while we can 
predict with pretty much certainty that earthquake will take place, we cannot be certain of 
its exact location. However we believe that an accurate prediction would be possible by 
placing several antennas at strategic locations. We are in the process of installing such 
antennas and the results will be reported in due course. 
In the next Section, we present a brief description of the receiving system at CSP. In 
Section 3, we present the results of seismologically passive and active days, in order 
that the distinction may be made. The DLPT is found to be significantly different just 
before and during earthquakes. Indeed, one could expect DLPT to be higher or lower than 
the average value. These results are also presented in this section. Finally, in Section 4, 
we draw concluding remarks. 
534 S Chakrabarti et al 
2. Brief description of the receiver 
The VLF laboratory consists of a cross-loop receiving antenna with a pre-amplifier and a 
GPS system attached to it for time stamp. The signals are fed into the AWESOME 
(Atmospheric Weather Educational System for Observation and Modeling of Effects) receiver 
made at Stanford University Star Laboratory. The software supplied (SUVLF-DAQ) is capable 
of separately storing broadband (0 to 50kHz) and narrowband data. Narrowband data from 
up to eight stations from the east-west and north-south antennas are stored. Figure 2 
shows the antenna on the CSP laboratory. 
Figure 2. Cross-loop antenna at CSP. 
The data is continuously stored in the ISRO sponsored data bank for future analysis. 
The block diagram of the system is shown in Figure 3. 
lOhmimH 
Antenna Preamp 
Line 
Receiver 
t 
GPS 
Receiver 
CSP 
Computer 
i 
CSP Data 
Bank 
VLF Receiver Block Diagram of CSP 
Figure 3. Block Diagram of the VLF receiving system at Centre for Space Physics. 
3. Results and analysis 
Figures 4a and 4b show the usual whole day pattern of the VLF amplitude data for 00:00 
hrs to 24:00 hrs without any interruption. Along X-axis we plot time in minutes and along 
V-axis, we plot the amplitude of the signal in decibel. In the day time, the effects are 
mainly due to solar irradiation on the ionosphere. At nighttime, the perturbations occur 
due to scintillation effects. During the sunrise, the signal amplitude drops and reaches a 
Unusual behavior of D-region ionization time at 18.2 kHz etc 535 
minimum value. This is called the sunrise terminator. The time taken, i.e., TA 
D-Layer preparation time or DLPT. 
TB is our 
110, 
Kolkata 14-Dec-2006 VTX Amplitude 
QUIET DAY 
Kolkata 09-Dec-2006 VTX Amplitude 
400 600 800 1000 
Time (minutes) after 00 00 001ST 1200 1400 200 400 600 800 1000 Time (mmutes) after 00 00 00 IST 1200 1400 
Figure 4a. VLF data from VTX3 on a seismically 
quiet day. 
Figure 4b. VLF data from VTX3 on a seismically 
active day 
From these figures, it is clear that DLPT is different in the two days. We call a day 
seismologically active if DLPT is very far from the average. We observe that this DLPT 
fluctuates erratically immediately before, during and immediately after the earthquakes. 
Otherwise, it is a quiet day. Figure 5 shows the variation of DLPT with date from 5th 
130 
125 
120 
115 
110 
105 
100 
95 
90 
85 
80 
75 
79 
65 
60 
55 
50 
45 
40 
35 
30 
25 
20 
15 
10 
5 
0 
Dates of Earthquake Average 
Standard Deviation 
0 
11/06 
10 
mmlmimnlimmtiluui 
20 30 40 
12/06 
50 60 70 
DATE 
01/07 
80 90 100 
02/07 
110 120 
, 03/07 
Figure 5a. Ionization time with date for 1st November 2006 to 28th of February 2007. The central curve 
is the mean and the one above and below are 2o away from the mean. Filled squares represent the 
seismically active days. 
536 S Chakrabarti et at 
November 2006 to 28th February, 2007. The mean curve is drawn removing the data of 
the days on which there has been earthquakes with magnitude 3.5 or higher. The curves 
representing ± 2 o (where a is the standard deviation around the mean) are also plotted. 
1
 Dates of Earthquake * Average 
: Standard Deviation 
y-2a 
150 160 170 180 
Figure 5b. Same as Figure 5a 
04/07 DATE 
for the month of April, 2007. 
Days of the major earthquake events are marked with squares. It is clearly seen that 
close to seismologically active days, the fluctuations are either very high or very low. The 
correlation of earthquakes with anomalous DLPTs is thus established. Table 1 shows the 
deviation of DLPT from the mean in o on all the days during this analyzed period. 
We note from the table that generally speaking, anomalous DLPTs (be they very much 
above or below the average) occur 'around' earthquakes. However, we do not find any 
correlation between the magnitudes of the earthquake and the DLPTs. This is mainly 
because we ignore two vital parameters such as the distance of the epicenter from the 
great circle path and the depth under the earth's surface in which the earthquakes occur. 
4. Discussions and Concluding Remarks 
In this paper, we have presented examples of unusual behaviour of the formation time of 
the D-layer around seismologically active days. We find that the so-called D-Layer 
Preparation Time or DLPT shows large scale fluctuations. For instance if the degree of 
ionization due to 'seismo-electric' effects is less and diffused, then the VLF radio wave 
will have to enter deeper inside the D-layer for an effective reflection to take place resulting 
in a longer value of DLPT. On the other hand, if the ionization is strong and concentrated 
In a thin layer below the E-layer then the reflection will occur by this layer much before 
the normal time. Thus DLPT Is could be expected to be lower also. This additional effect 
on and above the average effect due to the solar irradiation causes the DLPT to be 
Unusual behavior ofD-region ionization time at 18.2 kHz etc 
Table 1. The observed deviation of DLPT from the mean around seismically active days 
537 
Date 
7/11/06 
29/11/06 
30/11/06 
05/12/06 
09/12/06 
•15/12/06 
* 18/12/06 
'05/01/07 
17/01/07 
'25/01/07 
11/02/07 
14/02/07 
*16/02/07 
21/02/07 
27/02/07 
1/04/07 
21/04/07 
27/04/07 
Earthquake 
Magnitude 
5 0 
3 9 
6 2 
5 0 
5 2 
3 5 
5 7 
3 4 
5 9 
4 0 
5 0 
4 0 
4 8 
3 6 
3 5 
7 5 
6 1 
6 0 
(16/12/06) 
(17/12/06) 
(07/01/07) 
(24/01/07) 
(15/02/07) 
H„ , „ t » , . . . 
Observed DLPT 
in minutes 
42 \ 
6 7
 \ 
29 * 
95 
85 
76 
112 
76 
69 
70 
79 
74 
33 
75 
58 
67 
71 
70 
Deviation in a 
1 0 
2 8 
1 9 
4 2 
3 5 
2 9 
5 2 
2 6 
2 04 
2 05 
2 6 
2 2 
2 5 
2 3 
1 7 
3 0 
2 5 
2 3 
Country of the 
Earthquake 
Pakistan 
India 
Indonesia 
Myanmar 
North Sumatra 
India 
North Sumatra 
India 
South Sumatra 
India 
North Sumatra 
Indonesia 
Nepal 
India 
India 
Solomon Islands 
Papua New Guinea 
North Sumatra 
* Anomalous DLPT before or after the earthquake which occurs on dates in second column 
** The earthquake data is taken from the website http //www imd ernet in 
sometimes very high or very low. We find that these extreme values are often deviated 
from the mean by more than 2 a, i.e., our conjecture is valid above 95% confidence level. 
The subject of earthquake prediction through VLF effects is in its infancy. We suspect 
that what we observe is due to Lithosphere-lonosphere coupling, but quantitative explanations 
are still lacking. It is possible that some kind of exchange between the ionization and 
neutral bubbles could be responsible for such anomalous behaviour. 
Acknowledgments 
The authors thank Prof. U. Inan and Dr. M. Cohen of Stanford University Star Laboratory 
for providing us with the VLF receiving system and helping us with our set up. S. Sasmal 
thanks ISRO RESPOND project which supports his study. 
References 
(1] B A Bolt Nature 202 1095 (1964) 
[2] S K Chakrabarti, S Pal, K Acharyya, S Mandal, S Oiakrabarti, R Khan and B Bose Indian J. Phys. 
768 693 (2002) 
538 S Chakrabarti et al 
[3] S K Chakrabarti, K Acharyya, B Bose, S Mandai, A Chatterjee, N M Nandi, S Pal and R Khan 
Indian J. Phys. 77B 173 (2003) 
[4] S K Chakrabarti, M Saha, R Khan, S Mandai, K Acharyya and R Saha Indian J. Radio Space 
Physics, 34 332 (2005) 
[5] K Davies and D M Baker J. Geophys. Res. 70 2251 (1965) 
[6] M Hayakawa, O A Molchanov, T Ondoh and E Kawai J. Atmos. Electr. 16 247 (1996) 
[7] M Hayakawa, O A Molchanov, N Shima, A V Shvets and N Yamamoto in Seismo Electromagnetics: 
Lithosphere Atmosphere-Ionosphere Couplings, (ed.) M Hayakawa & O A Molchanov (TERRAPUB, 
Tokyo, Japan), p. 223 (2003) 
[8] T Horic, S Maekawa, T Yamanuchi and M Hayakawa Int. J. Remote Sensing (in press) (2007) 
[9] S Maekawa and M Hayakawa Trans. Inst Electr Engnrs. Japan 126(4) 220 (2006) 
[10] O A Molchanov and M Hayakawa J, Geophys. Res. 103 17489 (1998) 
[11] M Parrot J. Geophys. Res. 99 23339 (1994) 


Unusual Behavior of D-Region Ionization Time at 18.2kHz During Seismically Active Days

Ubale, A U

Mankar, R B

Daryapurkar, A S

Raut, R R

Sangawar, V S

Indian J. Phys. 81 (5 & 6), 555-565 (2007) 
Structural and optical properties of nanostructured PbS 
thin films chemically deposited at room temperature 
A U Ubale*, R B Mankar, A S Daryapurkar, R R Raut and V S Sangawar 
Thin Film Physics Laboratory, Department of Physics, 
Govt Vidarbha Institute of Science and Humanities, 
Amravati-444 604, Maharashtra, India 
E-mail ashokuu (r^yahoocom 
Received 15 March 2007, accepted 16 May, 2007 
Abstract Nanostructured PbS thin films were deposited on to glass, by a chemical deposition method, 
Successive Ionic Layer Adsorption and Reaction (SILAR) at room temperature For deposition of PbS thin films, 
lead acetate was used as cationic and thioacetamide as anionic precursor in aqueous medium The structure 
and surface morphology of the films were characterized by X-ray diffraction and Scanning electron microscopy 
The optical investigation showed that depending on thickness, films have direct allowed transitions in the range 
1 86-2 36 eV The decrease in dc dark resistivity with increase in grain size was also examined 
Keywords Nanostructured thin film, PbS, SILAR method 
PACS Nos. 61.10 Nz, 68 55 Jk and 81 55 Gh 
1. Introduction 
Nanostructured thin films have attracted the attention of an increasing number of researchers 
from several disciplines in the last ten years due to their outstanding electronic and 
optical properties and extensively useful applications in various optoelectronic devices. 
[1,2]. The small size of nanoparticles, which is responsible for the different properties 
(electronic, optical, electrical, magnetic and mechanical) of nanoparticles and nanostructured 
materials with respect to the bulk material, makes them suitable for new applications. 
The lead chalcogenide thin films are widely used in infrared detecting devices, diode 
lasers, humidity and temperature sensors and in solar control coatings j[3-6]. 
Corresponding Author 
©2007IACS 
556 A U Ubale, R B Mankar, A S Daryapurkar, R R Raut and V S Sangawar 
Different workers have reported chemical deposition of PbS on different types of 
substrates with characterization [7-11]. Acharya and Bose [12] used lead acetate and 
thiourea to grow polycrystalline PbS thin films at 303 K. Nair and Nair [13] have deposited 
PbS films at 302 K from a bath containing Pb*2 ions and thiourea in the 1:3 molar ratio. 
Sharma et al [14] have studied effect of Cu doping on crystallite size and carrier density 
of PbS thin films. The SILAR technique is relatively new and less investigated method, 
first reported in 1987 by Ristov et al [15]. Nicolau ascribed the name SILAR to this 
technique in 1985[16,17]. SILAR and Chemical Bath Deposition (CBD) [18] techniques 
are based on successive adsorption and reaction of species on the substrate surface 
from aqueous solutions. In the present paper, an attempt has been made to deposit 
nanocrystalline PbS thin films by Successive Ionic Layer Adsorption and Reaction (SILAR) 
technique by using lead acetate as cationic and thioacetamide as anionic precursor. By 
using thioacetamide as sulphide source, different chalcogenide thin films were prepared 
by many workers [19-22]. In chemical bath deposition, film formation takes place when 
ionic product exceeds the solubility product. This also results into the precipitate formation 
into the solution and hence sometimes the control over the process was lost. The SILAR 
method takes care of all these difficulties by immersing substrate into separately placed 
cationic and anionic precursors and rinsing between every immersion with ion-exchanged 
water. The aim of this paper is to deposit PbS thin films of different thicknesses at room 
temperature (300 K) by SILAR method and to study their structural, optical, and electrical 
properties. Analyzing X-ray diffraction pattern, crystal structure of films and grain size 
were estimated. 
2. Experimental details 
2.1. Substrate cleaning: 
The important thing before the deposition of films is the careful cleaning of the substrates. 
As the adherence of the film has a direct bearing on the cleanliness of the substrate, 
above procedure was adopted, while cleaning the substrates. The slides were washed 
with liquid detergent and then boiled in cone, chromic acid (0.5 M) for 2 hours and then 
kept in it for 48 hours. The substrates are then washed with double distilled water. Finally, 
the substrates are dried using AR grade acetone before use. 
2.2. PbS film formation: 
The SILAR involves an alternate immersion of the substrate in a solution containing a 
soluble salt of the cation of the compound to be grown and then in a solution containing 
a soluble salt of the anion of the compound to be grown. The substrate supporting the 
growing film is rinsed in high purity deionized water after each immersion. The deposition 
of PbS thin films on glass slides at room temperature was achieved using 100 ml of 0.01 
M lead acetate as cationic and 100 ml of 0.01 M thioacetamide as anionic precursor 
solution. The pH of thioacetamide solution was adjusted to 12 by adding ammonia in it. 
The rinsing and immersion time periods were experimentally optimized to get good quality 
film. The cleaned glass substrates were immersed in lead acetate for 20s, where Pb2+ 
Structural and optical properties of nanostructured PbS thin films etc 557 
ions get adsorbed on the substrate. The substrata was then rinsed with deionized water 
for 30s to remove loosely attached Pb2+ ions frofn the substrate. The rinsed substrate 
was then immersed in thioacetamide solution for ^Os, where S2~ ions were adsorbed and 
reacted with Pb2+ ions to grow PbS on the sub^rate. The unreacted ions were again 
removed by rinsing the substrate in deionized wjjlter for 30s. Adsorption, reaction and 
rinsing times in SILAR were optimized by varyirfg number of deposition cycles to get 
good quality PbS thin films. Thus, single deposition cycle consists of 20s adsorption of 
Pb2+ ions, 30s rinsing in water, 20s adsorption antf reaction of S2" ions with preadsorbed 
Pb2+ ions on the substrate and 30s rinsing with water. By repeating such deposition 
cycles the preparative parameters for the room temperature (300 K) deposition of PbS 
thin films are summarized in Table 1. 
Table 1. Optimized preparative parameters for the room temperature deposition of PbS thin 
films. 
Parameters 
Concentration (M) 
PH 
Immersion time (second) 
Rinsing time (second) 
Precursors solutions 
Lead acetate 
0.01 
-5 
20 
30 
Thioacetamide 
0.01 
-12 
20 
30 
2.3. Characterization of PbS films : 
The average thickness of the film was measured by the gravimetric and Fizzau's method. 
The two-point dc probe method of dark electrical resistivity was used to study the variation 
of resistivity with temperature. The copper block was used as a sample holder and chromel-
alumel thermocouple was used to measure the temperature. The area of the film (0.5 
cm2) was defined and silver paste was applied to ensure good ohmic contact to PbS 
films. For the measurement of resistivity, a constant voltage of 16 V was applied across 
the sample through a transistorized power supply unit (TPSU) and the current was noted 
using a digital (Keithley) nanoammeter in the temperature range 303-480 K. The structural 
studies were carried out using Philips PW 1710, diffractometer, with Cu-Ka radiation having 
wavelength 1.5405 A°. The optical characteristics were studied using Hitachi 330 
spectrophotometer to find band gap energy. Using JSM-6360 scanning electron microscope 
carried out the microstructural studies. 
3. Results and discussion 
3.1 Reaction Mechanism : 
The SILAR is based on sequential reaction at the substrate surface. The formation of 
PbS may involve following steps. When the substrate was immersed into cationic precursor 
where Pb2* ions get adsorbed on to the substrate surface. 
PtyCHgCOOk -» Pb2+ +2CH3COCr, 0) 
558 A U Ubale, R B Mankar, A S Daryapurkar, R R Raut and VS Sangawar 
After rinsing in deionised water, substrate was immersed into anionic precursor where 
Pb2* ions react with S2" to give PbS which can be explained by using tautomeric form of 
thioacetamide: 
S SH 
CHo-C-NHo -»CHo- C =NH (2) 
In alkaline medium, 
SH 
I 
C H 3 - C = NH + O T 
SH-+OH- -^S 2 -+H 2 0 , 
Pb2 ++S2~->PbSi • 
OH 
C H 3 - C =NH + SH~f (3) 
(4) 
(5) 
Using optimized conditions and by changing number of SILAR cycles, the films having 
thicknesses 38 to 189 nm were prepared. The films with number of SILAR deposition 
cycles less than 50 were discontinuous and therefore number of cycles was taken more 
than 50. Figure 1 shows variation of film thickness with number of SILAR deposition 
cycles. 
200 
100 600 700 200 300 400 500 
Number of SILAR cycles 
Figure 1. Variation of PbS film thickness with number of deposition cycles. 
3.2. XRD studies: 
Structural identification of PbS films was carried out with X-ray diffraction in the range of 
angle 20 between 10 to 100° . Figure 2 shows the XRD results for PbS thin films, which 
Structural and optical properties of nanostructured PbS thin films etc 559 
were nanocrystalline in nature. The observed brftad hump in XRD pattern is due to 
amorphous glass substrate. The comparison of XRDidata with standard ASTM data (JCPDS 
card 5-592) is given in Table 2, which confirms cfcbic phase (galena) of PbS. The well 
defined (111), (200), (220), (311) and (222) peaks Were observed in XRD pattern. 
:o 50 40 SO 90 50 60 "*0 
2G(deg) 
Figure 2. X-Ray diffraction patterns of PbS thin film of different thicknesses: (A) 55 nm; (B) 72 nm ; 
(C) 96 nm and (D) 189 nm. 
The average crystallite size of PbS in the film was determined from the line (200) by 
using Scherrer formula [23]: 
cf=A/)3cos0, (6) 
where A is the wavelength used (1.54 A°); p is the angular line width at half maximum 
intensity in radians; e is the Bragg's angle. Figure 3 shows variation of grain size with 
film thickness. 
3.3. Resistivity studies: 
The dark electrical resistivity of PbS films was studied in the temperature range 303 to 
480K using dc two-point probe method. Figure 4 shows the variation of log of resistivity 
560 A U Ubale, R B Mankar, A S Daryapurkar, R R Raut and V S Sangawar 
Table 2. Comparison of crystallographic data for PbS thin films with the JCPDS card 5-592. 
Standard data 
d (A°) 
3.429 
2.969 
2.099 
1.790 
1.714 
hkl 
111 
200 
220 
311 
222 
Observed d (A0) 
Thickness 
55 nm 
3.431 
2.963 
-
-
-
Thickness 
72 nm 
3.426 
2.976 
2.091 
-
-
values for PbS film 
Thickness 
96 nm 
3.431 
2.978 
2.103 
1.788 
-
Thickness 
189 nm 
3.428 
2.971 
2.095 
1.789 
1.712 
75 125 175 225 
Film thickness (nm) 
Figure 3. Variation of grain size with film thickness of PbS. 
(log p) with reciprocal of temperature (1/T) x 103. It is seen that resistivity decreases with 
temperature indicating semiconducting nature of films. The electrical resistivity of 
2.7 2.9 3.1 
1/Tx103(K*1) 
3.5 
Figure 4. Variation of Jog (j>) vs. 1/T x 103 (K*1) for PbS films with different thicknesses: 
(A) 38 nm; (B) 55 nm; (C) 72nm ; (D) 96nm ; (E) 142nm and (F) 189nm. 
Structural and optical properties of nanostructured PbS thin films etc 561 
nanocrystalline material is expected to be higher than in the corresponding coarse-grained 
polycrystalline materials [24]. The thermal activation energy was calculated using the 
relation 
p = p0exp(E0/KT), 
0.9 
(7) 
10 30 50 70 90 110 130 150 
Thickness(nm) 
Figure 5. Variation of activation energy of PbS with film thickness. 
where, p is resistivity at temperature 7, p0 is a constant, K is Boltzmann constant 
(8.62 x 10~5 eV/K) and £0 is the activation energy required for conduction. Figure 5 
shows variation in activation energy from 0.64 to 0.11 eV as thickness changes from 38 
to 189nm. These observations may be due to size effects that are arising because of 
quantum confinement of charge carriers within the particles. Several workers reported the 
decrease in activation energy with increase in grain size [25,26]. 
250 300 350 400 
Temperature difference (K) 
450 500 
Figure 6. Variation of thermoemf and temperature difference of PbS film with different thicknesses: (A) 
55 nm; (B) 96 nm; (C) 142 nm and (D) 189 nm. 
562 A U Ubale, R B Mankar, A S Daryapurkar, R R Raut and V S Sangawar 
3.4. Thermoemf measurements: 
Figure 6 shows the variation of thermoemf with temperature difference for PbS films of 
different thicknesses. From the thermoemf measurement, it was observed that the polarity 
of thermally generated voltage at the cold end is positive, indicating that the films are of 
p-type. Increase in thermoemf with increasing film thickness is attributed to the decrease 
in electrical resistivity caused by increase in grain size. 
3.5. SEM studies: 
The SEM of the PbS thin films of thicknesses 55, 96, 142 and189nm deposited on glass 
substrate was examined (Figure 7). The surface of the film is smooth and well covering to 
the glass substrate. The grains are very small with unequal size and shape; also their 
grain boundaries are not well defined. Also they reveal that the grain sizes of the films 
are increased with thickness. Particulate can always be seen on the film surfaces. 
Figure 7. SEM images of PbS film of thicknesses: (A) 55 nm; (B) 96 nm; (C) 142nm and 
(D) 189nm. 
3.6. Optical absorption: 
The optical absorption of PbS thin films was studied in the wavelength range of 300 to 
850 nm and the variation of optical density {at) with wavelength (A) is shown in the 
Structural and optical properties of nanostructured PbS thin films etc 563 
300 400 500 600 700 
Wavelength(A) 
800 900 
Figure 8. Plot of optical absorption ( a t ) vs. wavelength for PbS films with different thicknesses: (A) 38 
nm, (B) 55 nm; (C) 72 nm ; (D) 96 nm ; (E) 142 nm and (F) 189 nm. 
Figure 8. All the films show higher absorption on the shorter wavelength side. The nature 
of the transition (direct or indirect) is determined by using the relation 
a = 
A(hu-Eg)" 
hu 
(8) 
1UUU 
800 
where hv is the photon energy, Eg is 
the band gap energy, A and n are 
constants. For allowed direct transitions, 
n s 1/2 and for allowed indirect 
transitions, n = 2. The plots of (ahvf 
versus ftvwere shown in Figure 9 for 
PbS films having different thicknesses. 
Since the variation of (ahv) with hv 
for PbS films is a straight line indicating 
that the involved transition is direct one. 
Band gap energy, Eg was determined by 
extrapolating the straight-line portion to 
the energy axis for zero adsorption 
coefficient (a) . Figure 10 shows variation 
in optical band gap energy from 1.86 to 
2.36 eV with thickness from 189 to 38 
> 
> 
JC o 
600 
400 
200 
1.2 1.6 
—\ 
3.2 2 2.4 
hv (eV) 
Figure 9. Plot of (ahv)2 vs. to tor PbS films wun 
different thicknesses: (A) 38 nm; (B) 55 nm; (C) 72 nm; 
(D) 96 nm ; (E) 142 nm and (F) 189 nm. 
564 A U Ubale, R B Mankar, A S Daryapurkar, R R Raut and V S Sangawar 
nm. This is attributed to the crystallite size-dependant properties of the energy band gap. 
Similar 'blue/red shift' in band gap energy lE^ values for the films with smaller thickness 
and/or crystallite sizes have been reported for chemically deposited thin films [27,28]. 
2.4 
? 
^ 2 . 2 
S? 
<D 
5 o 
a 2 t 
& 1.8 
1 6 l 
* _ 
- • • . _ 
- • . 
^ ^^. 
^ • ^ 
i •' 
"^ 
50 100 
Thickness (nm) 
150 200 
Figure 10. Variation of optical band gap energy, £ with film thickness. 
4. Conclusions 
Growth of nanostructured PbS thin films at low temperature by a simple chemical method, 
Successive Ionic Layer Adsorption and Reaction (SILAR) is possible. An XRD study 
shows nanocrystalline structure with cubic phase (galena). Optical studies show that the 
absorption spectrum is due to transition from one band to another and is mainly caused 
by allowed direct transitions. The optical band gap energy varies from 1.86 to 2.36 eV 
with thickness. The electrical resistivity and therefore activation energy are observed to be 
thickness dependent. The results of XRD and SEM show that the deposited PbS film 
consists of nano-sized grains (6-18 nm), and the grain size increases with increasing film 
thickness. 
Acknowledgment 
The authors are thankful to the University Grants Commission, WRO, Pune (India), for 
financial support under the project (No: F47-15/2003). Also we would like to thank Prof. 
A. Mahajan of Indian Institute of Technology, Bombay (India), for the XRD measurements. 
References 
[1] B R Chackraborty, B Roy, R Bhattacharya and A K Datta J. Phys. Chem. Solids 41 913 (1980) 
[2J Y Wang and N Herron J. Phys. Chem. 95 525(1991) 
[3] R Resh, G friedbacher, M Grasserbauer, T Kannianinen, S Lindross, M Leskela and L Ninisto Appl 
Surf. Sci. 120 51 (1997) 
[4] J J Valenzuela-Jauregui, R Ramirez-Bon, A Mendoza-Galvan and M Sotelo-Lerma Thin Solid Films 
441 104 (2003) 
[5] I Pop, C Nascu, V lonescu, E Indrea and i Bratu Thin Solid Films 307 240 (1997) 
[6] C Nascu, V Vomir, I Pop, V lonescu and R Grecu Mater.Sci.Engg. B841 235 (1996) 
[7] K K Nanda and S N Shau AppLPhys. Lett79 2743 (2001) 
Structural and optical properties of nanostructured flbS thin films etc 565 
I* 
[10] 
[11 
(12: 
[13] 
[14: 
[15; 
[16! 
[17: 
[181 
[19] 
[20] 
[21 
[22 
[23 
[24; 
[25: 
[2& 
[2r 
[28 
S Watanabe and Y Mita J. Electrochem.SocA 16 989 (1969) 
I Pintitie, E Pentia, D Petre, L Pintilie and T Btila JAppl. Phys.78-3 1713 (1995) 
K M Gadave, S A Jodgauri and C D Lokhande Thin Solid Films 245 7 (1994) 
N Sharma, D K Pandya, H K Seghal and K L Chopr4 Thin Solid Films 59 157 (1979) 
H N Acharya and H N Bose Phys. Stat. Sol. K-43 (1|73) 
P K Nair and M T S Nair J. Phys. D 23 150 (1990) -• 
T P Sharma, R Kumar, G Jain and S C Mishra Indian, J. Pure Appl. Phys. 29 583 (1991) 
M Ristov, G J Sinadinovskt and I Grovdanov Thin Scjid Films 126 63 (1985) 
Y F Nicolau Appl. Surf. Sci. 22 1061 (1985) 
Y F Nicolau and J C Menard J. Crystal Growth 92 128 (1988) 
R Ortega-Borges and D Uncot J. Electrochem. Soc. 140 3464 (1993) 
P Parmanik, P K Basu and S Biswas Thin Solid Film$ 150 269 (1987) 
S Biswas, A Mandal, D Mukherjee and P Parmanik J, Electrochem. Soc. 133(1) 48 (1986) 
P K Basu and P Parmanik 1 Mater.Sci.Letl. 5 1216 (1986) 
P Parmanik, and S Biswas J. Solid State Chem. 65 145 (1986) 
B D Cullity Elements of X-ray Diffraction (MA : Addition-Wesley) p102 (1978) 
P K Nair, V M Garcia, A M Fernadez, H S Ruiz and M T S Nair J.Phys. D 24 441 (1991) 
C A Estarde, E A Myers, R A Zingaro, D C Dufner, P K Nair and M T S Nair Heteroatom Chem. 6 
349 (1995) 
S S Kale and C D Lokhande Mater Chem. Phys. 62 103 (2000) 
G Hodes, A Albu-Yaran, F Decker and P Matsuke Phys. Rev. B 36 4215 (1987) 
G Hodes Israel J. Chem. 33 95 (1993)

Structural and Optical Properties of Nanostructured PbS Thin Films Chemically Deposited at Room Temperature

Sahoo, S

Maharana, L

Behera, B R

The Effect of Both Z and Z'-Mediated Flavor-Changing Neutral Currents on Bs → μ+μ- Decay

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Front Contents

Shear Viscosity of Square - Well Fluid

Notes for Contributors

From Editor's Desk

From Editor's Desk

Influence of Finite Range of Nuclear Interaction on the Coulomb Breakup of <SUP>11</SUP>Be

Baryogenesis from Inverted Hierarchical Mass Models with Tribimaximal Mixings

Unusual Behavior of D-Region Ionization Time at 18.2kHz During Seismically Active Days

Structural and Optical Properties of Nanostructured PbS Thin Films Chemically Deposited at Room Temperature

The Effect of Both Z and Z'-Mediated Flavor-Changing Neutral Currents on B<SUB>s</SUB> → μ<SUP>+</SUP>μ<SUP>-</SUP> Decay

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