IACS Institutional Repository

Yurtseven, H

Tilki, O

English

Critical Behaviour of the Thermodynamic Quantities Near the Melting Point in Thesolid Phase of Hexadecane

Mishra, D K

Mishra, P K

Sahu, D R

Behera, D

Roul, B K

Effect of Ho and Nd Substitution in La0.67Ca0.33MnO3 CMR Manganites

Biswas, S

Hussain, S A

Bhattacharjee, D

Indian J. Phys. 82 (2), 173-177 (2008) 
Orientation of carbazole molecule in the mixed 
Langmuir-Blodgett films 
S Biswas3 b, S A Hussain3 and D Bhattacharjeea* 
"Department of Physics, department of Chemistry, Tnpura University, 
Suryamanmagar-799 130, Tnpura, India 
E-mail tuphysic(o sanchamet in 
Abstract This paper reports the molecular orientation of carbazole (CA) molecules in the mixed Langmuir-
Blodgett (LB) films of carbozole in stearic acid (SA) matrix Changes in the intensities of the absorption bands are 
observed by rotating the LB films, keeping the direction of the incident radiation unchanged Maximum intensities 
of the absorption bands are observed when the LB films are kept at an angle of 45° with the incident radiation 
For other angles of orientations , intensities of the absorption bands are minimum. This certainly confirms the fact 
that CA molecules have preferred orientation on the substrate of the LB films 
Keywords Nonamphiphilic, Langmuir-Blodgett films, UV-Vis absorption spectroscopy 
PACS Nos. 68 47 Pe, 68 18-g, 74 25 Gz, 74 62 Fj 
1. Introduction 
Thin films with carefully designed structures and properties have attracted a great deal of 
interest in recent years due to their potential applications in fabricating various optoelectronic 
and molecular electronic devices [1-5]. These applications require, in general, well ordered 
films consisting of molecules with specific properties, carefully aligned with respect to 
each other and the substrate possessing high degree of stability to thermal and chemical 
changes. The Langmuir-Blodgett (LB) technique has been used to fabricate the thin films 
with ideal two dimensional systems, well-controlled composition, structure, thickness and 
molecular orientations [1]. The bulk properties of the materials incorporated into LB films 
can be controlled with ease by the organization of molecules in the films and also by 
changing various LB parameters [1]. 
Amphiphilic molecules consists of a hydrophilic (water soluble) and a hydro-phobic 
(water insoluble) parts are the ideal for LB film deposition [1]. However, recent investigations 
suggest that certain non-amphiphilic molecules when mixed with a- long chain fatty acid 
Corresponding Author 
©2008IACS 
174 S Biswas, S A Hussain and D Bhattacharjee 
(e.g. stearic acid or arachhidic acid) or with an inert polymer matrix (e.g. polymethyl 
methacrylate or polystyrene) form excellent LB films [1,6-7]. These non-amphiphilic 
molecules are easily available with a wide range of varieties having different interesting 
physical properties. Also it has been observed that in some cases the optical and electrical 
characteristics of these non-amphiphilic materials are changed markedly when they are 
incorporated into some inert matrices or restricted geometry [1,6-7]. Detailed investigations 
of these non-amphiphilic molecules into restricted geometry of LB films are extremely 
important from the point of view of their various technical applications. In this paper we 
report a unique observation of orientation of a well known non-amphiphilic carbazole (CA) 
molecules in the mixed LB films of CA doped in stearic acid (SA) matrix, using UV-Vis 
absorption spectroscopy. 
Non-amphiphilic CA and its derivative have found extensive technological applications 
in organic photoconductors [2] and electroluminescent devices [3-5]. They have their unique 
photophysical characteristics such as intense and well characterized absorption and 
fluorescence spectra [8-9] Owing to their excellent optical and electronic properties, various 
derivatives of carbazole were synthesized and studied in the Langmuir-Blodgett films [6, 
8-13]. However the orientation of CA molecule in LB films was not studied before. 
2. Experimental 
CA was purchased from Aldrich Chemical Company, USA and vacuum sublimed followed 
by repeated recrystalization before use. SA (purity 99%) from sigma, USA, was used as 
received. The solvent chloroform (SRL, India) was of spectral grade and its fluorescence 
spectra were checked before use. Langmuir-Blodgett film deposition instrument (Apex, 
2000C, India) was used for the study of monolayer characteristics and also for multilayer 
film deposition. The subphase used was triple distilled deionised water having pH 6.5 in 
equilibrium with atmospheric carbon dioxide. The solution of CA, SA as well as CA-SA 
mixtures are prepared in chloroform solvent and were spread on the subphase with the 
help of micro syringe. Surface pressure was recorded by Wilhelmy plate arrangement 
described elsewhere [7]. All the films are 10 bilayered. Fluorescence grade quartz slides 
were used for film deposition and deposition was carried out at a surface pressure of 15 
mN/m. 
UV-Vis absorption spectra of these films were measured by a Perkin-Elmer Lambda 
25 spectrophotometer. All the measurements were performed at room temperature (25°C). 
3. Results and discussion 
Figure 1 shows the UV-Vis absorption spectra of mixed LB films of CA (0.5 M) in SA 
matrix placed at angles 0°, 15°, 30°, 45°, 60° and 75° with the incident radiation alongwith 
the CA solution and microcrystal spectrum for comparison. 
Absorption spectrum of CA in chloroform solution shows distinct bands within 225-350 
nm region with intense and sharp high energy bands having peaks at 247 and 292 nm 
alongwith a weak hump at around 258 nm, owing due to S2-S1 transition which is directed 
Orientation of carbazole molecule in the mixed Langmuir-Blodgett films 175 
parallel to the long axis of the molecule There are two other low intense but prominent 
vibrational bands in the 300-350 nm regions, with maxima at around 319 nm and 331 nm 
corresponding to S ^ S Q transition which is directed parallel to the short axis of the molecule. 
200 250 300 350 400 450 
Wavelength (nm) 
Figure 1 UV-Vis absorption spectra of mixed LB films of CA (0 5 M) in SA matrix placed at angles 0°, 
lr> 30° 45°, 60° and 75° with the incident radiation alongwith the CA solution and microcrystal spectrum 
The CA microcrystal spectrum also shows almost identical vibrational band system 
except an increase in intensity However, the high energy bands in the microcrystal 
spectrum become broadened and blue shifted In addition, the band with peak at 292 nm 
in CA solution spectrum is totally absent in the corresponding microcrystal spectrum 
This may be due to the aggregation of CA molecules [6] 
The absorption spectra of the mixed LB films of CA in SA matrix, kept at various 
angles with the incident radiation are also shown in Figure 1 Interestingly it was observed 
that when the mixed LB films were kept at an angle of 45° with the incident radiation 
prominent vibrational bands are observed both at the high energy and low energy region. 
These bands are remarkably similar with the microcrystal bands. However, for other angles, 
namely, 0°, 15°, 30°, 60° and 75° which the films make with the incident radiation, no 
absorption bands are observed. 
The appearance of absorption bands at a particular angle of orientation of the films 
with the incident radiation definitely concludes the fact that carbazole molecules have a 
specific orientation in the LB films. 
A schematic representation of the alignment of the carbazole (CA) molecules on the 
substrate of the LB films is shown in Figure 2. 
176 S Biswas, S A Hussain and D Bhattacharjee 
A plausible explanation is that at 45° angle of orientation of the LB films with the 
incident radiation, the electric field of the incident radiation is along the direction of the 
dipole moment of the CA molecules. Hence maximum absorption of incident radiation 
occurred. For other angle of orientation direction of the electric field of the incident radiation 
does not coincide with the direction of the dipole moment of the CA molecules resulting 
almost no absorption. 
Figure 2. Schematic representation of the alignment of the carbozole (CA) molecule on the substrate of 
the LB films. Inset shows the molecular structure of CA (a). 
4. Conclusion 
In conclusion, our results show that carbazole molecules have specific orientation in the 
mixed LB films. The angle dependence absorption studies of the mixed LB films indicate 
that when the mixed LB films are kept at an angle of 45° with the incident radiation, 
prominent absorption bands are observed. 
Acknowledgment 
The authors are grateful to DST and UGC Govt, of India for providing financial assistance 
through FIST-DST Project No. SR/FST/PSI-038/2002 and UGC minor research project No. 
Ref No. F1-1/2000(FD-lll)/399 and Sanction Ref. No. F. 31-30/2005 (SR). 
References 
[1] A Ulman, An introduction to Ultrathin Organic Films : From Langmuir-Blodgett Films to Self 
Assemblies, (New York : Academic Press) (1991) 
[2] N Kim and E W Stephen Macromoiecules B18 741 (1985) 
[3] A Aokl, Y Tamagawa and T Miyashita Macromoiecules 35 3686 (2002) 
[4] K K Justin Thomas, J T Lin, Y T Tao and C H Chuen Chem. Mater. 16 5437 (2004) 
[5] F Sanda, T Nakai, N Kobayashi and T Masuda Macromoiecules 37 (2004) 
Orientation of carbazole molecule in the mixed Langmuir-Blodgett films 177 
[6] S A Hussain, P K Paul and D Bhattacharjee J. Colloid Interface Science 299 785 (2006) 
[7] S Deb, S Biswas, S A Hussain and D Bhattacharjee Chem. Phys Lett 405 323 (2005) 
[8] Krishanu Ray and T N Misra Langmuir 13 6731 (1997) 
[9] A K Dutta Langmuir 12 5909 (1996) 
[10] Y Liu and M Liu Thin Solid Films 415 28 (2002) 
[11] Jiu-Yan Li, Ming-Li Peng, Li-Ping Zhang, Li-Zhu Wu, Bo-Jie Wang and Chen-Ho-Tung J. 
Photochemistry Photobiology A 150 101 (2002) 
[12] T Nagamura, K Toyozawa, S Kamata and T Ogawa Thin Solid Films 210 332 (1992) 
[13] N Ohta, S Okazaki and S Y I Yamazaki Thin Solid Films 258 305 (1995) 


Orientation of Carbazole Molecule in the Mixed Langmuir-Blodgett Films

Khan, Ayan

Atre, Rajneesh

Panigrahi, Prasanta K

Indian J P/m.82(2), 185-188(2008) 
Complex envelope soliton in Bose-Einstein condensate with 
time dependent scattering length 
Ayan Khan*, Rajneesh Atre and Prasanta K Panigrahi 
Physical Research Laboratory, Navrangpura 
Ahmedabad-380 009, Gujarat, India 
E-mail akhan(« prl res in 
Abstract We elaborate on a general method to find complex envelope solitons in a cigar shaped Bose-
Einstein condensate in a trap The procedure incorporates time dependent scattering length, oscillator fre-
quency and loss/gain A variety of time dependencies of the above parameters, akin to the ones occurring in the 
experiments can be tackled 
Keywords Bose-Einstein condensate, solitons 
PACS Nos. 67 85 Hj, 03 75 Lm 
1. Introduction 
Coherent atom optics is a subject of much current interest for its relevance to both basic 
physics and technology. For this purpose, lower dimensional condensates eg., cigar 
shaped Bose-Einstein condensates (BECs) have been the subject of active study in recent 
years [1]. Intense investigations above the behavior of the condensate in the presence of 
time varying control parameters like, scattering length, oscillator frequency etc., are being 
carried out for the purpose of optimal control. In BEC, solitary waves have been 
experimentally observed, both in repulsive and attractive domains [2,3]. These have been 
understood from the non-linear Gross-Pitaevskn (GP) equation describing weakly coupled 
BEC, 
ih
^dt^
 2mV2 + U\¥{rj)\2 + v\v{r,t), (1) 
Corresponding Author 
© 2 0 0 8 IACS 
186 Ayan Khan, Rajneesh Aire and Prasanta K Panigrahi 
where U = 4nfi2as(t)/m, as = the s-wave scattering length, and Vis the external potential 
The scattering length, which is the coefficient of nonlineanty in GP equation, can be 
adjusted both in sign and magnitude through Feshbach resonance Recently a family of 
exact solutions of quasi-one dimensional GP equation with time varying scattering length 
loss/gain, in the presence of oscillator has been obtained [4] These are chirped solitons 
with real envelope In recent years, solitons with complex envelope is generating interest 
in different areas of physics These are known as Bloch solitons in condensed matter 
physics In optical fibers one also finds these solitons In BEC, complex solitons have 
been investigated [5-9] Ve«-y recently complex envelope solitons in optical lattices has 
been reported [10] 
2. Result and discussion 
In the present study, we explicate a method to obtain general complex envelope solitons 
in cigar shaped BEC, in a trap incorporating time dependent scattering legnth, oscillator 
frequency, and loss/gain We have constructed the two hydrodynamic equations in this 
scenario and have found their solutions Our analysis starts with uasi-one dimensional 
non-linear Schodinger equation (NLSE) derived from three dimensional GP equation with 
an additional loss/gain term g(f) and time dependent chemical potential v(f) In dimensionless 
units this is given by [4], 
' ^ — C ^ + I M W ^ ^ (2) 
We assume following ansatz solution 
, , G(f) l 
(3) y,(zJ) = ^)F[A(t){z-l(t)}]exp / { * ( * 0 + * ( * 0 } + ^ 
where yJA(t)F\A(t) z- /(f)| exp [/^(z,f)]carries the signature of complex envelope Further 
G(t) and /(f) have been defined as, 
G(t) = ^g(t')dt\ l(t) = j\(t')dt' (4) 
The phase is chirped as, 
0(zj) = a(t) + b(t)z-^c(t)^i where, a(f) = ^ - 1 |% 2 ( f ' )d f ' 
Substitution of the above ansatz in eq (2) allows one to separate this equation in 
imaginary and real parts The knowledge of the earlier conditions, leads one to write the 
imaginary euation as, 
- u F ^ - F ^ - l F ^ a n d 
Complex envelope sohton in Bose-Emstem condensate etc 187 
X = u -
2Cn 
(5) 
Here prime denotes derivative with respect to 7, where 7 = A{t)[z- l(t)] We have set 
(/, + cl - A)/A = u, At= Ac and C0 is an integration constant Redefining C0 - (i/F02 ) , 2 , 
P _ >/a and F0 - ^/o^ Eq (5) leads to, 
x' = uh (6) 
We have imposed the boundary condition, # ' -> 0 for a -> a0 The local phase velocity 
of the solitary pulse is described by % and local density is described by o\ a0 represents 
equilibrium density 
From the real equation one can extract a Riccati type equation, ct cl{t)- M(t) which 
yields the solution of c(t) The real equation also yields, 
F" = JUF-2KF3=X'2F-2UX'F, 
where K =y0/A0 Applying the following consistency conditions, one obtains 
Y(t) = y0e~GA(t)/A0,b(t) = A(t), 
A(t) = A0exp f c(f)dt' 
Jo 
Dark Sol icon at a 0 
v(t) = A 2J" 
2 ' 
Accelaration 
(7) 
Chirp 
Figure 1. (a) Density profile of the condensate and (b) chirp controlled soliton motion 
188 Ayan Khan, Rajneesh Atre and Prasanta K Panigrahi 
and, 
F ' ^ F - 2 K - F 3 - 4 - 0 ,
 (8) 
where e = // - L/2 and X = u2F04. Integration of eq.(8) leads to the convenient form, 
This solution for eq.(9) ib, 
a(z f f )^a0 1-cos20sech2 A(z-l)cos6 (10) 
These are the dark and grey solutions in the distributed scenario. 
3. Conclusion 
In conclusion, for quasi-one dimensional GP equation in an oscillator potential with time 
dependent coupling and loss/gain, a general complex dark soliton profile is obtained. In 
the presence of expulsive oscillator the motion of the condensate is controlled by the 
sign of the chirp, /.&, whether the soliton is accelerating or decelerating. 
References 
[1] F Dalafovo, S Giorgmi, L P Pitaevskii and S Stringari Rev. Mod Phys 71 463 (1999) 
[2] L Khaykovich et a/, Science 296 1290 (2002) 
[3] K E Strecker, G B Patridge, A G Truscott and R G Hulet Nature 417 150 (2002) 
[4] R Atre, P K Panigrahi and G S Agarwal Phys. Rev. E73 056611 (2006) 
[5] A D Jackson, G M Kavoulakis and C J Pethick Phys. Rev. A58 2417 (1998) 
[6] A D Jackson and G M Kavoulakis Phys. Rev Lett. 89 070403 (2002) 
[7] S Komineas and N Papanicoalou Phys. Rev Lett 89 070402 (2002) 
[8] S Komineas and N Papanicolaou Phys Rev A67 023615 (2003) 
[9] S Komineas and N Papanicolaou Phys. Rev. A68 043617 (2003) 
[10] MA Porter, M Chugunova and D E Pelinovshy Phys. Rev. E74 036610 (2006) 


Complex Envelope Soliton in Bose-Einstein Condensate with Time Dependent Scattering Length

Maiti, Santanu K

,,,/,„„./Wivt. 82 (3), 281-287 (2008) 
Persistent current and low-field magnetic susceptibility in 
n -fold twisted Moebius strips 
Santanu K Maiti 
Theoretical Condensed Matter Physics Division, 
Saha Institute of Nuclear Physics, 1/AK Bidhannagar, Kolkata-700 064, Indu 
E-mail santanu maiti(« saha ac in 
Abstract . We study persistent currents and sign of these currents in the limit </> - >0 for n-fold twisted 
Moebius strips threaded by a slowly varying magnetic flux </> concerning the dependence of the total number of 
pioctrons A/,, chemical potential JU , number of twist n and randomness In odd-fold twisted Moebius strips 
urrent gets </>0/2 flux-quantum periodicity only when vi = 0 (transverse hopping stregth), while, it shows </>0 
flux-quantum periodicity as long as the electrons are allowed to hop along the transverse direction (v * 0) On 
trie other hand, current always exhibits <f>0 flux-quantum periodicity for even-fold twisted Moebius strips, 
irrespective of the transverse hopping strength (v±) The sign of the low-field currents also strongly depends 
on the number of twist n. For v =- 0 the sign of the low-field currents can be mentioned exactly in old-fold 
twisted Moebius strips those are characterized by fixed Ng only In absence of any impurity current shows 
nlways the diamagnetic nature irrespective of No i e , whether Nt is odd or even, while, in presence of impurity 
it exhibits respectively the diamagnetic and the paramagnetic behavior for the systems with odd and even Nr 
The sign of these low-field currents cannot be predicted exactly when the electrons are allowed to hop along the 
transverse direction Since then it strongly depends on the Nc, JU and specific realization of randomness 
Keywords Persistent current, Magnetic Susceptibility and Moebius Strip 
PACS Nos. 73 23 -b, 73.23 Ra, 75.20.-g 
1. Introduction 
With the advance in nanoscience and technology, the fabrication of sub-micrometer devices 
has become possible and an emerging tendency in modern science is to propose and to 
investigate systems containing smaller and smaller structures. The resulting systems 
approach the so-called mesoscopic regime where the quantum phase coherence leads to 
important corrections to the electronic properties of the devices. The most exciting in the 
view of applications are the electronic properties of such systems. In what follows, we 
shall concentrate to one of the most striking evidences of quantum phase coherence, the 
so-called persistent current in nomal conducting loops. The pioneering work of Buttiker, 
© 2 0 0 8 IACS 
0.TPI 
282 Santanu K Maiti 
Imry and Landauer [1] has predicted that a small conducting isolated ring threaded by
 a 
slowly varying magnetic flux 0 carries an equilibrium current which persists in the system 
and vanes periodically with the applied flux. Since then the phenomenon of persistent 
current in mesoscopic systems has been studied quite extensively in the literature both 
theoretically [2-8] and expenmetally [9-13] At sufficiently low temperatures, the electron 
transport is completely phase coherent and in these small systems the energy levels are 
discrete The phase coherence of the electrons and the discreteness of the energy levels 
play important role in the existence of the persistent current in these systems We assume 
that the magnetic field doesn't penetrate the ring circumference anywhere and thus the 
electrons always move in field-free space This system can be mapped onto the band 
structure problem of a one-dimensional infinite crystal The idea is that once the electron 
circles the ring, it gets exactly the same potential as before, but now has acquired an 
additional phase 2n<p/Q0 Thus a close connection is obtained between the states of an 
electron in a loop and the 1D Bloch problem by identifying 27r0/0o with kL [2], where L 
is the circumference of the loop In a recent experiment, Tanda et al [14] have fabricated 
a microscopic NbSe3 Moebius strip and it raises some interesting questions regarding 
the topological effect on the persistent currents and the low-field magnetic susceptibiltiy 
in twisted Moebius geometries Here we investigate in detail all the above mentioned 
properties for n-fold twisted Moebius strips 
This paper is specifically organized as follows. In section 2, we describe in detail the 
characteristic properties of the persistent currents in n-fold twisted Moebius strips specified 
by the fixed chemical potential v , instead of the fixed number of electrons Ne The 
topological effect on the sign of the low-field currents are investigated in section 3 Finally 
we conclude our results in section 4. 
2. Persistent current in n-fold twisted Moebius strips with fixed V 
In this section we focus our study on the behavior of persistent currents in n-fold twisted 
Moebius strips concerning the value of n and try to emphasize some intuitive points 
relevant to the flux periodicities of these currents. Figure 1 shows the schematic view of 
a simplest one-fold (n = 1) twisted Moebius strip which encloses a magnetic flux 0 We 
assume that the magnetic field does not penetrate the circumference of the strip anywhere 
and hence the additional Zeeman term should not be taken into account during the 
Figure 1. Schematic view of a one-fold (n = 1) twisted Moebius strip threaded by a magnetic flux 
persistent current and low-field magnetic susceptibility in Moebius strips 283 
calculations. To describe such a Moebius strip with N rungs we use the tight-binding 
mode' Hamiltonian which can be written within the non-interacting picture in this form 
2N 2N 2/V 
where f, 's are the on-site energies, cj(cf) is the creation (annihilation) operator of the 
electron at site /, the phase factor 6 = 2n0/N, v is the nearest-neighbor hopping strength 
along the longitudinal direction and v± is the perpendicular hopping strength To introduce 
the impurities in such a strip we set the site energies (e, 's) in the form of incommensurate 
potentials through the relation f, = £, Wcos(iXn), where A is an irrational number, and 
as a typical example we take it as the golden mean (1 +V5J/2 and IV is the strength of 
the disorder Setting A = 0 , we get back the pure system with identical site potential W 
In the obvious reason we do not take any disorder averaging since the impurities are 
given from this incommensurate distribution function Here we use the convention ch2N = 
c and for the sake of simplicity we take the units c = e - h = 1 All the calculations in 
this article are performed only at absolute zero temperature ( 7 = 0 ) . 
Now we concentrate our study on the characteristics of the persistent currents in n-
fold twisted Moebius strips those are described with the fixed chemical potential v , 
instead of specifying the total number of electrons Ne The current carried by an energy 
eigenstate is obtained by taking the first order derivative of the energy with respect to the 
Figure 2. /(<*>) versus 0 curves both for the perfect (W = 0) and the disordered (W = 1) three-fold 
(n = 3) twisted Moebius strips characterized by fixed chemical potential n = 0 with (a) v, - 0 and (b) 
vi = -1 The solid and the dotted curves correspond to the results for the perfect and the disordered 
strips, respectively 
284 Santanu K Maiti 
flux 0 [15] The total current of the system is then determined by adding the individua' 
contributions of all the energy levels having energies less than or equal to A< As the 
chemical potential is fixed, the total number of electrons Ne varies as a function of 0, tn 
contrary to the systems those are described with fixed Ne where the chemical potential 
changes with the flux 0 We will describe all the essential features of our study for the 
two limiting cases of the transverse hopping strength (v i ) One is the case where v = 
0 and for the other case we take v± * 0 . 
Let us first describe the behaviour of the persistent currents in odd-fold twisted Moebius 
strips for the two limiting cases As illustrative examples, in Figure 2 we display the 
persistent currents for some 3-fold (n = 3) twisted Moebius strips considering the system 
size N = 40 and the chemical potential n = 0 Figure 2(a) corresponds to the currents for 
the zero transverse hopping strengtn, while, Figure 2(b) corresponds to the currents (or 
the non-zero transverse hopping with strength vL = - 1 The solid and the dotted curves 
are respectively for the perfect (W = 0) and the dirty (W = 1) strips In the impurity-free 
strips, sharp transitions appear in the persistent currents (solid curves of Figure 2(a)) for 
some particular field points associated with the degeneracy of the energy eigenstates at 
these respective field points On the other hand, in the presence of impurity all the 
degeneracies move out and the currents vary continuously (dotted curves of Figure 2(a)) 
with the flux <(> and get much reduced values The removal of such degeneracy can be 
very well understood from the standard interpretation of the perturbation theory and the 
reduction of the current amplitude is due to the localization effect of the energy eigenstates 
in presence of the impurity More kinks appear (see the solid curve of Figure 2(b)) when 
Figure 3. /(</>) versus <p curves both for the perfect (W = 0) and the disordered (W = 1) two-fold 
(n = 2) twisted Moebius strips characterized by fixed chemical potential ;/ = 0 with (a) vx = 0 and (b) 
vx = -1 The solid and the dotted curves correspond to the results for the perfect and the disordered 
strips, respectively 
Persistent current and low-field magnetic susceptibility in Moebius strips 285 
the electrons are allowed to hop along the transverse direction in the perfect strip The 
appearance of these additional kinks at different field points depends on the choices of 
the chemical potential v . All these kinks disappear as long as the impurities are 
introduced in the system. The most significant observation is that the current exhibits 
0 ;2 flux-quantum periodicity only when v± = 0, but, for non-zero value of it the current 
shows the similar 0O periodic nature as in a regular multi-channel cylinder [15] This can 
be understood as follows. In odd-fold twisted Moebius strips if v = 0 then an electron 
which moves along the longitudinal direction traverses twice the path length to reach its 
initial position and encloses 20 flux Accordingly, the current gets 0O 2 flux-quantum 
periodicity On the other hand, for v± * 0 the electron can hop along the transverse 
direction and hence we get the usual <j>0 periodic currents 
When the number of twist n becomes an even then a Moebius strip becomes a regular 
two-channel mesoscopic cylinder. For such a case we get the quite similar behavior of 
persistent currents as obtained in small regular cylinders those have been studied previously 
m the literature [15] As representative examples, in Figure 3 we plot the characteristic 
leatures of persistent currents for some 2-fold twisted Moebius strips for both the two 
limiting cases considering the same system size and the chemical potential as described 
earlier The solid and the dotted curves correspond to the same meaning as in Figure 2 
As expected both for the two limiting cases we get only QQ periodic currents Thus we 
can predict that the number of twist and the transverse hopping have significant role in 
the determination of the periodicity of the persistent currents Quite similar features are 
also visible for the strips described with fixed number of electrons A/e [15] which we do 
not describe here 
3. Characterization of the sign of the low-field currents 
The determination of the sign of the low-field currents is an another important issue for 
this particular study. This can be done by calculating the magnetic susceptibility x(0) m 
the limit 0 - ^ 0 The general expression of the magnetic susceptibility is expressed in 
the form 
167T d(t> 
Here we describe quite briefly about the sign of the low-field currents both for the strips 
those are characterized with fixed Ne and V , concerning the values of n and vx . 
Let us first consider the case where the strips are characterized by the fixed number 
of electrons Ne. For the odd-fold twisted Moebius strips and the zero transverse hopping 
strength the sign of the low-field currents is exactly predictable It is always diamagnetic 
in nature for impurity-free Moebium strips irrespective of Ne i e., whether Ne is even or 
odd On the other hand, in the presence of impurity the sign of the low-field currents 
286 Santanu K Maiti 
becomes diamagnetic and paramagnetic for the strips containing odd and even N 
respectively. This is the general feature of any regular one-channel, since here vL = o 
mesoscopic loop described by the fixed Ne and is independent of the specific realization 
of the disordered configurations [15]. When vx * 0 , the systems are not treated as one-
channel loops and the sign of the currents cannot be specified exactly even in the absence 
of any impurity. Then it depends on Ne and for disordered systems it also depends 
significantly on the specific realization of the disordered configurations. For the case of 
even-fold twisted Moebius strip as the system maps into the regular multi-channel cylinder 
the sign of the low-field currents is no longer predictable exactly, even if the system is a 
perfect one. 
Similar arguments are also valid for the Moebius strips described with fixed chemical 
potential v , instead of Ne, but in this case the sign of the low-field currents cannot be 
predicted even for the Moebius strips with odd n and v± = 0 i.e., when the systems 
become one-channel systems. Both for the Moebius strips with odd and even n, tho sign 
of the low-field currents strongly depends on the choices of /v and in dirty systems it 
depends on the specific realization of the disordered configurations. 
4. Conclusion 
In conclusion, we have studied the characteristic features of the persistent currents and 
the sign of these currents in the low-field limit for some n-fold twisted Moebius strips 
concerning the dependence of the total number of electrons A/e, chemical potential /< 
number of twist n and randomness. We have used the tight-binding formulation to compute 
the results and all the calculations have been performed at absolute zero temperature (T 
= 0). Several kink-like structures appear in the persistent currents at different field points 
for the impurity-free Moebius strips depending on the choices of v . These kinks arise 
due to the existence of the degenerate energy eigenstates at these respective field points 
and they disappear as long as the impurities are switched on and accordingly, the current 
varies continuously with the flux 0 . The most significant observation is the existence of 
the 0o/2 flux-quantum penodicty in odd-fold twisted Moebius strips for the limiting case 
when vL = 0. In such a situation an electron which moves along the longitudinal direction 
encircles the loop twice to reach its original position and therefore it encloses 20 flux 
which reveals 0o/2 periodic currents. On the other hand, in all other cases we get the 
usual 0O periodic currents. 
At the end, we have concentrated on the sign of the low-field currents. For the Moebius 
strips with odd n and vx = 0, the systems can be treated as one-channel systems and 
only for such cases the sign of the low-field currents can be predicted exactly provided 
the systems are described by fixed number of electrons Ne. In impurity-free systems 
current shows only the diamagnetic sign whether the systems contain odd or even Ne 
But in the dirty systems the low-field current shows the diamagnetic and the paramagnetic 
nature for the systems with odd and even A/e, respectively. For all other cases the systems 
are equivalent to multi-channel systems and the sign of the currents cannot be predicted 
Persistent current and low-field magnetic susceptibility in Moebius strips 287 
exactly Then it strongly depends on Ne, n and the specific realization of the disordered 
configurations. 
References 
f i i M Buttiker, Y Imry and R Landauer Phys Lett 96A 365 (1983) 
n] H F Cheung, Y Gefern, E K Riedel and W H Shih Phys Rev B37 6050 (1988) 
-3] H F Cheung a n d E K Riedel Phys Rev Lett 62 587 (1989) 
41 V Ambegaokar and Y Eckern Phys Rev Lett 65 381 (1990) 
<5] B L Altshuler, Y Gefen and Y Imry Phys Rev Lett 66 88 (1991) 
jb) F von Oppen and E K Riedel Phys Rev Lett 66 84 (1991) 
71 A Schmid Phys Rev Lett 66 80 (1991) 
18] M Abraham and R Berkovi ts Phys Rev Lett 70 109 (1993) 
[9] L P Levy, G Dolan, J Dunsmui r and H Bouchiat Phys Rev Lett 64 2074 (1990) 
10] V Chandrasekhar, R A Webb , M J Brady, M B Ketchen W J Gal lagher and A Kleinsasser Phys 
Rev Lett 67 3578 (1991) 
111] D Mailly, C Chapel ier and A Benoit Phys Rev Lett 70 2020 (1993) 
t l 2 ] E M Q Janwala , P Mohanty, M B Ketchen and R A Webb Phys Rev Lett 86 1594 (2001) 
r13] R Deblock, R Bel , B Reulet, H Bouchiat and D Mailly Phys Rev Lett 89 206803 (2002) 
14] S Tanda, T Tsuneta, Y Okaj ima, K Inagaki, K Yamaya and N Hatakenaka Nature 417 397 (2002) 
US] S K Maiti Physica E31 117 (2006)

Persistent Current and Low-Field Magnetic Susceptibility in n-Fold Twisted Moebius Strips

Chaliha, S

Borah, M N

Sarmah, P C

Rahman, A

ImlumJ Phvs 82 (3), 303-3!0(2008) 
Optical and electrical properties of thermally evaporated 
ZnSe thin films 
S Chaliha1*, M N Borah1, P C Sarmah2 and A Rahman1 
department of Physics, Gauhati University, Guwahati 781 014, Assam, India 
-' Department of Electronics, Regional Research Laboratory Jorhat 785 006 Assam, India 
E-mail sumbitcC" gmail com 
Abstract Zinc Selenide (ZnSe) thin films were deposited onto glass substrates by thermal evaporation 
technique From optical studies, different optical constants were calculated and the transition of the deposited 
films were found to be direct allowed transition The optical band gap of the films were found to be in the range 
from 2 6eV to 2 7eV The films deposited at elevated substrate temperature followed by heat treatment in 
vacuum have showed stable electrical nature The electrical conductivity of the ZnSe films were found to be 
about 10 T ohm-' cm-' and found to increase to about 10^ ohnrr'cm 1 when films were doped with Al or Cu From 
the conductivity measured at different temperatures, the activation energy of the films were calculated and 
found to be between 0 1 eV to 0 2 eV for low temperature regions and between 0 5 eV to 0 6 eV for high 
temperature region 
Keywords Thermal evaporation, optical constants, optical band gap, electrical conductivity, activation energy 
PACS Nos. 81 15 Ef, 78 20 Ci, 72 20 -i 
1. Introduction 
Zinc selenide (ZnSe) is one of the ll-VI semiconductors that have been studied intensively 
in recent years. This fact is due to its direct and wide band gap It is suitable candidate 
for the solar cells, blue laser diode, light emitting diode, thin film transistors and other 
optoelectronic devices. A variety of methods for preparation of ZnSe films have been reported 
by different authors like chemical vapour deposition, electrodeposition, photochemical 
deposition, pulsed laser deposition and vacuum evaporation [1-5]. Electrical and optical 
properties of semiconducting films are essential requirement for proper application in 
optoelectronic devices, and these properties are very sensitive to deposition conditions 
and technique used. In this paper some optical and electrical properties (transmission 
' Corresponding Author Department of Physics, Bahona College, PO Bahona, Jorhat-785 101, Assam, 
India 
© 2008 IACS 
UP 
304 S Chaliha, M N Borah, P C Sarmah and A Rahman 
spectra, absorption coefficient, refractive index, extinction coefficient and electrical 
conductivity) of ZnSe thin films deposited by thermal evaporation method have been 
reported. 
2. Experimental 
ZnSe thin films were prepared by thermally evaporating ZnSe polycrystalline powder (99.99% 
purity) under vacuum, at a pressure of less than 10~5 Torr onto chemically cleaned glass 
substrates placed at a distance of approximately 8 cm from the vapour source. During 
deposition of the films the substrates were kept at different elevated temperatures. The 
prepared films were annealed in vacuum at higher temperature for one hour. For preparation 
of Al-doped and Cu-doped films, the pure metal Al or Cu was co-evaporated along with 
ZnSe and then the films were annealed at a temperature of 350°C in vacuum. X-ray 
diffraction patterns of the samples were taken by using Cu Ka radiation. The thickness of 
the films were measured by the multiple-interference method developed by Tolansky [6] 
and were in the range between 180 and 380 nm. Transmission spectra were obtained 
using a UV-VIS spectrophotometer (Carry 300, Varian), at room temperature. All electrical 
measurements were done in vacuum under pressure of 10""2 Torr using a rotary pump 
The currents were measured with the help of a system electrometer (6514, Keithley). The 
details of experimental arrangement was given else where [7]. 
3. Results and discussion 
3.7 Structural property: 
The x-ray diffraction study of ZnSe films prepared at higher temperature indicates (Figure 
1) that the samples are polycrystalline and have a cubic zincblende structure. The 
crystallites are preferentially oriented with the (111) planes parallel to the substrate. However, 
as deposited ZnSe films deposited at room temperature show amorphorus in nature. The 
900 
800 
700 
600 
soo 
§400 
U300 
200 
100 
0 
10 20 30 40 60 60 7 
2-Theta (degree) 
Figure 1. X-ray diffraction pattern for a ZnSe thin film with a thickness of 300 nm, substrate temperature 
180°C. 
Optical and electrical properties of thermally evaporated ZnSe thin films 305 
average sizes of the crystallites of the films were determined from FWHM (&>„) of the 
XRD spectrogram using the Scherrer's formula [8] 
D = O.99A/fe>„cos0 (1) 
Where t^o js full width at the half maximum of [111] peak of XRD pattern and A is the 
wave length of the incident X-ray. The average crystallite sizes was found in the range 
between 200 and 300 A. The crystallite size increases with increasing film thickness and 
substrate temperature during deposition. Moreover, heat treatment after film deposition 
also shows an increase of the crystallite size. 
3 2 Optical properties: 
The thermally deposited ZnSe films showed high transmittivity to visible light. Figure 2 
illustrate the transmission spectra for a ZnSe film before and after heat treatment. The 
experiments showed that transmission coefficient strongly depends on the film structure, 
which is determined by the film thickness and its deposition conditions. It was observed 
that for the heat treated sample the transmission coefficient is greater than the value 
obtained before the heat treatment. This fact is probably due to the increase in crystallite 
size The crystalline boundaries contain structural defects, impurities etc. These factors 
might influence the absorption process. 
100-
300 400 500 600 700 800 
Wave length (nm) 
Figure 2. The transmission spectra for a ZnSe film with f = 380 nm, Tb = 180°C, (a) before and (b) after 
the heat treatment. 
The number of the interference fringes in the transmission curves is determined by the 
thickness of the film. For the comparatively thick films, the refractive index, in the spectral 
domain of the medium and strong transmission, is calculated using the Swanpoel method 
[9] of creating envelopes of the interference maxima and minima. Firstly an approximate 
value of refractive index (say nj is calculated using the expression [9] 
306 S Chaliha, M N Borah, P C Sarmah and A Rahman 
1/2 | 1 / 2 
N+(N2~n2s) (2) 
where N^2ns(Tmax -Tmin)/TmaxTmin + (2n62 + l ) / 2 and ns is the refractive index of the 
substrate used. In this last expression Tmax and Tmin are the transmission maximum ana 
minimum at the same wavelength (A). 
With this value of the refractive index of the film, the 'order' m of the different extremes 
of the transmission curve is determined with the equation for interference fringes 
2nt - mA (3» 
In our case the thickness of the film, f, was known. 
The values of m are then approximated to the close integer (for maxima) or half integer 
(for minima) m0 [10]. These values of mQ are used to determine the new value of the 
refractive index n from the same relation (3). In the interferene free zone the refractive 
index were obtained by extrapolation of the refractive index obtained in the interference 
zone using Cauchy dispersion rule 
A 7 - 4 + B / / 1 2 . (4) 
Nearly at the absorption edge the absorption coefficient can be calculated from 
transmittance (T) using the expression [6] 
« = / / f l n ( / / T ) . (5) 
The extinction coefficient (k) is estimated from the value of a and A using the formula 
k - cd/4n . (6) 
0.25 
02
 & 
1 
0.15 — 
0.1 
0.05 
24 
300 400 500 600 700 M O 900 
Wave length (run) 
Figure 3. Variation of refractive index (n) and extinction coefficient (k) with wave length of a vacuum 
deposited ZnSe film, t = 380 nm, Ts = 180°C 
Optical and electrical properties of thermally evaporated ZnSe thin films 307 
Figure 3 illustrates the dependence of n and k of a typical ZnSe film on wave length 
Table 1 summarized the calculated values of n, a and k of a typical ZnSe film at selected 
wave lengths in the interference region 
Table 1 Value of refractive index absorption coefficient and extinction coefficient of a typical film 
- _ 180°C) of thickness 380 nm at selected wavelengths 
/ (nm) 
756 (mm) 
641 (max) 
564 (mm) 
505 (max) 
ni 
2 407 
2 409 
2 4185 
2 447 
m 
2 42 
2 82 
3 26 
3 68 
"TD 
25 
3 
35 
4 
n 
2 487 
2 538 
2 597 
2 658 
(X (101 cm 1) 
49 034 
62 567 
76 620 
108 49 
k 
0 0295 
0 0320 
0 0344 
0 0436 
The fundamental absorption occurred due to allowed direct transitions may be described 
by the well known relation [11], 
ahv - A(hv~Eg) 1/2 (7) 
where hv is the incident photon energy, E represents the energy bandgap and A is 
characteristic parameter The analysis of our experimental data shows that for all samples 
the dependences of (ahv)2 as a function of the photon energy hv, indicates the direct 
nature of fundamental band-to-band transitions The plot of (ahv)2 against hv for a few 
typical are shown in Figure 4 The values of bandgap width, Eg, have been determined by 
extrapolating the linear portions of the respective curves to (ahv)2 = 0 For the investigated 
250 
200 
> 
Figure 4. The (ahv)2 vs photon energy hv plots tor a few heat treated ZnSe films (a) Ts = 80°C f = 220 
nm (b) Ts = 130°C, t = 205 nm, (c) Ts = 180°C, t = 235 nm and (d) Tb = 180°C t = 380 nm 
308 S Chahha, M N Borah, P C Sarmah and A Rahman 
samples these values ranged between 2.6 and 2 7 eV, which is in good agreement with 
the earlier reported values [5, 12, 13]. The transmittance and optical band gap of a few 
ZnSe films prepared at different substrate temperatures (Ts) are represented in Table 2 
Table 2. Some optical parameters of a few ZnSe films 
Rm 
ZnSe (annealed) 
ZnSe (annealed) 
ZnSe (annealed) 
ZnSe (annealed) 
Substrate 
Temperature 
80°C 
130°C 
180°C 
180°C 
Thickness 
(nm) 
220 
205 
235 
380 
Transmittance 
% 
63% 
74% 
70% 
70% 
Band gap 
(eV) 
2 63 
2 66 
2 63 
2 61 
3.3. Electrical properties: 
The as grown films were found to be highly resistive and their conductivity at room 
temperature was in the order of 10~7 ohm*"1 cm"1 similar to the values reported by earlier 
workers [13] The electrical behaviour of as deposited ZnSe films were found to be unstable 
The resistivity of the films decreased with increase of substrate temperature upto 180C,C 
After deposition, the films were subjected to a heat treatment in vacuum, consisting of 
several heating and cooling cycles up to a temperature of 250°C and there after found 
stable. The resistivity of the films were found to slowly decrease with time showing again 
effect and became nearly stable after about 7 days when kept in dry air or in vacuum 
Doping of the films enhanced conductivity considerably. The plots of in cr vs 1000/T 
(Figure 5) for all the films show a nearly linear dependence with two slopes within the 
temperature range of 25°C to 120°C 
-7 
-10 
-12 
-13 
-14 
24 25 26 27 28 29 30 31 32 33 34 
1000/T(K-1) 
Figure 5. Inrr vs T r plots of ZnSe films (a) undoped, T& = 80°C, f = 220 nm, (b) undoped, Ts = 130°C 
f = 205 nm, (c) undoped, T$ = 180°C, f = 235 nm, (d) Al doped, Ts = 180°C, f = 225 nm and (e) Cu doped, 
Tc = 180°C, f = 215 nm 
Optical and electrical properties of thermally evaporated ZnSe thin films 309 
The temperature dependence of electrical conductivity can be described by 
<T = <T0exp(-Ea / /cr ) (8) 
here Ea is the thermal activation energy 
Table 3 Values of electrical conductivity and activation energy of a few ZnSe films 
Film 
ZnSe 
ZnSe 
ZnSe 
ZnSe Al 
ZnSe Cu 
Sub temp 
(Ts) °C 
80 
130 
180 
180 
180 
Conductivity 
Ohm~1 cm"1 
6x10"7 
2x10"6 
5x10"6 
1 4x1 O^ 
1 8x10- 5 
Sheet resistivity 
(109) ohm 
71 
23 
17 
317 
2 86 
cm""1 
Activation 
Range 1 
0 207 
0 176 
0 137 
0098 
0 099 
eV 
energy 
Range 2 
0 602 
0 59 
0 5876 
0 536 
0 506 
In the low temperature range the lower value of activation energy is attributed to electron 
hopping among the localized donor states The values of activation energies (Ea) up to 
the temperature 120°C corresponds to different impurity levels due to excess zinc in case 
of undoped films and different dopants for doped films The Table 3 shows the conductivity 
and activation energy of a few undoped and doped ZnSe films 
4 Conclusions 
ZnSe thin films obtained by vacuum evaporation onto glass substrates at higher 
temperatures show the polycrystalline nature of the films The crystallites are preferentially 
oriented with (111) plane parallel to the substrate surface The shape of the transmission 
spectra is strongly influenced by the preparation conditions of films and heat treatment 
The spectral dependence of the refractive index indicates a normal dispersion The values 
of energy gap, calculated from the absorption spectra, range between 2 6 and 2 7 ev The 
as grown ZnSe films were found to be highly resistive and the resistivity was found to 
decrease with increase of substrate temperature and heat treatment Doping of the films 
enhanced the electrical conductivity considerably From variation of conductivity with 
temperature, two activation processes were observed for all the films corresponding to two 
temperature regions. 
Acknowledgment 
Two of us (S Chaliha and M N Borah) wish to thank the UGC, India, for awarding fellowship 
to carry out this research work. 
References 
[1] T L Chu, S S Chu, G Chen, J Britt, C Ferekides and C Q Wu J Appl Phys 71 3865 (1992) 
[2] G Riveros, H Gomez, R Hennquez, R Schrebler, R E Marotti and E A Dachiele Sol Energy Mater 
Sol Cells 70 255 (2001) 
310 S Chaliha, M N Borah, P C Sarmah and A Rahman 
[3] R Kuaresan, M Ichimura and E Arai Thin Solid Films 414 25 (2002) 
[4] G Perna, V Capozzi, M C Plantamura, A Minafra, P F Biagi, S Orlando, V Marotta and A Gardir, 
Appl Surf. Sci 186 521 (2002) 
[5) S Venkatachalam, D Mangalraj, Sa K Narayandass, K Kim and J Yi Physica B358 27 (2005) 
[6] K L Chopra Thin Film Phenomena (New York : McGraw-Hill) (1969) 
[7] S Chaliha, M N Borah, P C Sarmah and A Rahman Proc. of the DAE Solid State Physics Symposium* 
(India) 50 395 (2005) 
[8] B D Cullity Elements of X-ray Diffraction (Philippines : Addison-Wesley Pub Co. Inc) 102 (1978) 
[9] R Swanepoel J Phys E16 1214 (1983) 
[10] E Marquez, J Ramirez-Malo, P Villares, R Jimbnez-Garay, P J S Ewen and A E Owen J. Phys D25 
535 (1992) 
[11] J I Pankove Optical Processes in Semiconductors (New York Dover Pub Inc) 34 (1971) 
[12] M Bedir, M Oztas, O F Bakkaloglu and R Ormanci Eur. Phys. J. B45 465 (2005) 
[13] G I Rusu, M E Popa, G G Rusu and luha Salaoru Appl Surf Sci. 218 222 (2003)

Optical and Electrical Properties of Thermally Evaporated ZnSe Thin Films

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Radiation and Dissipation Effect on Unsteady MHD Micropolar Flow Past an Infinite Vertical Plate in Porous Medium with Time Dependent Suction

Front Title

Srinivasan, A

Pattanaik, A K

Indian J. Phys. 82 (5), 505-511 (2008) 
Fragility of Pb modified germanium chalcogenide glasses 
A Srinivasan* and A K Pattanaikf 
Department of Physics, Indian Institute of Technology Guwahati, Guwahati 781 039, Assam India 
Presently at Department of Physics, UCE Burla, Sambalpur-768 018, Onssa, India 
E-mail asrinu" ntg ernet in 
Abstract Bulk chalcogenide glasses with compositions PbAGe42^Se^ (3 * x c 15) (series I), Pb^Ge^Se^x 
. 171 x<24) (series II), Pb„Ge4? ,Se48Te10(3 < x< 15) (series III) and Pb^Ge^Se^ Je l 0(17 < x<24) (series IV) were 
prepared by the melt quenching technique The heat capacity jump at glass transition ( ACp ) and the activation 
energy for viscous flow ( Et}) of the four series of glasses were obtained from differential scanning calonmetry 
(DSC) studies The composition dependence of ACp and E}] of series I and III showed minima near the 
composition with x = 9 at wt % Pb Similarly the ACp and En data of series II and IV exhibited minimum near the 
composition with x = 21 at wt % Ge Since ACp and Eq could be associated with the fragility of the glass 
network the data obtained have been used to understand the changes occurring in the glass network as a 
function of composition The results have also been discussed in the light of the majority charge carrier reversal 
occurring at the specific compositions in the respective series of glasses 
Keywords Chalcogenide glasses, fragility, heat capacity jump, activation energy 
PACS Nos. 61 43Fs, 64 70Pf, 65 60+a 
1. Introduction 
Chalcogenide glasses are generally p-type semiconductors with the Fermi level pinned 
near the middle of the band gap by charged defects present in these glasses [1 ] After 
the pioneering work by Toghe et al [2], it is now generally accepted that incorporation of 
appropriate amounts of either Bismuth (Bi) [2] or Lead (Pb) [3] in bulk Ge-Se glasses 
leads to the reversal of the majority charge carrier from /> to n-type. Attempts have been 
made to attribute the majority charge carrier reversal (MCCR) phenomenon in Bi modified 
Ge-Se glasses to percolation of Bi clusters [4], high degree of polarisation of Bi [5], 
existence of defect states [6], efc. The MCCR in Pb modified Ge-Se glasses has been 
attributed [7] to changes induced in electronic structure of the glass by the energetically 
disposed sp3d2 band of Pb. Electrical properties of PbxGe42.xSe48Te10 glasses indicate 
4
 Corresponding Author 
© 2 0 0 8 I A C S 
506 A Srinivasan and A K Pattanaik 
[11] that MCCR occurs in this glass system at x = 9 at. wt. of Pb. It is worthy to point 
out that calorimetric parameters of Bi and Pb modified chalcogenide glasses [8-12], such 
as glass transition temperature (T) and crystallisation temperature (7"c), heat capacity 
jump at glass transition, activation energies and thermal diffusivity [13, 14] consistently 
show anomalous features at the compositions at which the conduction type change occurs 
Glass forming liquids are classified as 'fragile' or 'strong' on the basis of the magnitude of 
the heat capacity jump at Tg as well as from the extent of deviation of viscosity versus 
temperature Arrehenius plots [15]. However, the effect of compositional variation on glassy 
network has not been investigated in detail in Pb-Ge-Se(-Te) glasses. Differential scanning 
calorimetic (DSC) study of two series of Pb-Ge-Se and Pb-Ge-Se-Te glasses has been 
taken up to understand the changes occurring in the glassy network as a function of 
composition by evaluating the different factors contributing to the fragility of glass. 
2. Experimental 
The melt quenching technique was used to prepare bulk glasses with composition 
PbxGe42.xSe58 (0 < x < 15) (series I), Pb20GexSe80.x (17 < x < 24) (series lli, 
PbxGe42_xSe48Te10 (0 < x < 15) (series III) and Pb20GexSe70.Je10 (17 < x < 24) (series IV) 
Appropriate amounts of high purity (99.999%) elements sealed in fused silica ampoules 
under a vacuum of 10~5 mbar were slowly heated to 1300 K in a rotary furnace. After 
providing sufficient time for homogenisation at this temperature, the ampoules were suddenly 
dropped into cold water to form glass. The amorphous nature of as-quenched glass samples 
was verified by X-ray diffraction technique. The majority charge carrier type in each 
composition was determined from the sign of the Seebeck coefficient. Thermoelectric 
power measurements performed on thin slices of as quenched glasses established that 
the MCCR occurred at Pb concentration of ~9 at. wt. % in the series I and III, and at Ge 
concentration of -21 at. wt. % in the series II and IV. Non-isothermal studies were performed 
with a Perkin-Elmer DSC 7 differential scanning calorimeter. Constant heating rates ranging 
from 5 °C.min"1 to 25 °C.min"1 were used. All the DSC runs were performed using alumina 
sample pans under dry nitrogen atmosphere. The instrument was calibrated with indium 
and zinc melting point standards prior to data collection. Standard software supplied along 
with the DSC instrument was used for obtaining the characteristic temperatures and heat 
capacity data from the DSC curves. 
3. Results and discussion 
The kinetic parameters of glass transition and crystallisation can be estimated from the 
DSC data by several methods [16,17], which are based on the assumption that the 
temperature of a kinetically controlled reaction shifts with heating rate. According to one 
such method due to Bartenev [18], 
d[W0)]/d[UTg] = -Etl/R (1) 
where 0 is the heating rate, En is the activation energy of the kinetic reaction, Tg is the 
glass transition temperature and R is the universal gas constant. The activation energy 
fragility of Pb modified germanium chalcogemde glasses 507 
En is also referred to [19] as the activation energy for viscous flow The degree of fragility 
<rrr> [20] of the glass at the glass transition is given by, 
(m) = Ej(2.3RTg) (2) 
The activation energy of viscous flow (En) estimated from the slope of the \n(0) versus 
1000/7^ plots for two series of Pb-Ge-Se and Pb-Ge-Se-Te glasses are shown in Figure 1 
and Figure 2, respectively Tg values obtained at heating rates of 5, 10, 15, 20 and 
25°C mm1 from DSC measurements plotted and fitted using least squares fitting procedure 
for determining En Since the kinetically controlled reaction is the glass transition and 
the estimated activation energy is a measure of the hindrance or resistance posed by the 
glassy network to the glass transition phenomenon, it can be concluded from the figures 
that the glass transition is least hindered for the glasses at x = 9 at wt % Pb in series 
I and III, and at x = 21 at wt % Ge in series II and IV A minimum in the activation 
energy also implies that the glasses at these compositions undergo minimal configurational 
changes at the glass transition The activation energy values obtained for the two series 
of glasses are tabulated in Table 1 
Table 1 Activation energy of viscous flow (En) glass transition temperature <& 20 °C mm ' degree of 
fragility <m> and heat capacity jump at 7" ( \Cp) of various compositions of Pb-Ge-Se(-Te) glasses 
Glass £„ T <rrr> ACp Glass Etl Tq <m> ACp 
Composition 
Series 1 
P^Ge^Se^ 
PbnFGexSBm 
Pb(>jGe33Se58 
P b 1 G e ; 9 S e 5 8 
P b i G*zfi*m 
Series III 
P ^ G ^ S e ^ 
P^Ge^Se^Te^ 
Pb0QGe33Se48Te10 
^ ^ S e ^ 
Pbi5Ge27Se48Te10 
(kJmole1) 
392 
335 
272 
294 
380 
407 
268 
249 
245 
313 
(K) 
544 
527 
524 
527 
530 
536 
522 
517 
514 
515 
37 7 
33 3 
27 2 
29 2 
37 5 
39 7 
26 9 
25 2 
24 9 
31 8 
(Jg1K1) 
0 44 
019 
016 
0 20 
0 28 
0 34 
0 26 
0 21 
0 25 
0 28 
Composition 
Series II 
Pb^Ge^So^ 
Pb20Ge19Se61 
PD20Ge21Se59 
P b 2 0 G e 2 2 5 S e 57 5 
Pb^Ge^Se^ 
Series IV 
Pb20Gel7Se53Te10 
Pb,0Ge19Se51Te10 
Pb20Ge21Se49Te10 
Pb^Ge^
 5Se47 5Te10 
Pb20Ge,4Se46Te10 
(kJmole1) 
298 
251 
205 
334 
360 
298 
213 
208 
303 
329 
(K) 
495 
533 
544 
535 
524 
496 
510 
518 
516 
508 
31 5 
24 6 
197 
32 7 
35 9 
31 4 
21 9 
21 0 
30 7 
33 9 
(Jg'K 
0 45 
0 17 
0 15 
0 19 
0 45 
0 20 
0 18 
0 13 
018 
0 20 
The degree of fragility values estimated for various glass compositions in the four 
series of glasses are listed in Table 1 The En and Tg values used for estimating <m> 
are also listed in Table 1 <m> varied between 19 7 ± 0 4 and 39 7 ± 0 4 These low <m> 
values are signatures of the 'strong' nature of covalently bonded chalcogemde glasses 
508 A Srinivasan and A KPattanatk 
However, a consistent variation in <m> value could be seen within each series with a 
minimum near at x = 9 at. wt. % Pb in series I and III, and at x = 21 at. wt. % Ge m 
series II and IV. Hence, one can conclude that <m> values also indicate a minimum m 
fragility at the compositions at which the p- to n-type carrier change occurs in Pb-Ge-Se 
[3,21] and Pb-Ge-Se-Te [11,21] glasses. When <m> is minimum, the glass and its high 
temperature crystalline phase have minimum configurational difference. This factor m 
combination with the directional nature of the covalent bond existing between the elements 
seems to provide a favourable situation for the electronic interaction leading to the unpinning 
of the Fermi energy level towards the conduction band [21]. 
m
o
le
") 
c 
ill 
400 
380 
360 
340 
320 
300 
280 
260 
1 ' 
\ 
\ 
] 
•\ r— 
Series 1 
* 
* 
— ' — i — * — — i — ' • - i •••"•• 
\ 
,—,—.—. 
• — • — 
i; 
-
i 
i * 
360-
340^ 
C 320 
o 300-
2 280-
~ - 2 6 0 
LU 
240-
220-
200-
• 
» ! t 
—, . 1 . 1 1 1 ^-
Series 11 
4 
* 
- T — . — r — , — r — i — i — r -
i 
6 8 10 12 
Pb at. wt. % 
14 16 16 17 18 19 20 21 22 23 24 25 
Ge at. wt. % 
Figure 1. Variation of activation energy of viscous flow ( Et)) as a function of composition of 
PbxGe42.xSe58 (3 < x < 15) (series I) and Po^Ge^Se^., (17 < x < 24) (series II) glasses Dotted line 
merely connects adjacent data points 
The heat capacity (specific heat at constant pressure) jump at the glass transition 
temperature is an inherent property of a glass [22]. The heat capacity jump (also referred 
to as the excess heat capacity at 7 ) , is expressed as ACp = (Cp/ -Cpg} , where C„ 
420 
400 
— 380 
i 360 
^ 340 
££320 
^ 3 0 0 
280 
260 
240 
i 
-j 
\ 
— . , — — • 1 1
 r • 
Series III 
\ 
\ 
- i — • -
-,—.— 
i — • — 
* 
i 
•J 
340 
320 
^ 300 \ 
o 280 
3 260-1 
^240-1 
220 
200-1 
Series IV 
* 
* 
--I 
6 8 10 12 
Pb at. wt. % 
14 16 16 17 18 19 20 21 22 23 24 25 
Ge at. wt. % 
Figure 2. Variation of activation energy of viscous flow ( £,,) as a function of composition of 
PbxGe42.xSe48Te10 (3 < x < 15) (series III) and Pb20GexSe70_Je10 (17 < x < 24) (series IV) glasses. Dotted 
line merely connects adjacent data points. 
Fragility ofPb modified germanium chalcogenide glasses 509 
and C are the heat capacity of the liquid and the glassy states across the glass transition. 
The value of the excess heat capacity reflects the amount of configuration change occurring 
m the network at the glass to liquid transition. According to Angell [23], ACp could be 
correlated [24] with the fragility of a glass. Fragile glasses exhibiting a large &Cp undergo 
more configurational change at the glass transition. Strong glasses exhibit a small &Cp 
and minimal configuration changes at 7^ . The variation of the heat capacity jump at T 
(ACP) of the four series of glasses is shown in Figure 3 and Figure 4, respectively. The 
0 45 
0 40 
^0.35 
o) 0 30 
T" 0.25 
0.20 
0 15 
n 
* 
* 
* 
' ' • • r • i 
Series 1 i 
* * 
03 06 09 13 
Pb at. wt. % 
15 
0.4 
0) 
V 0.3 
3 
Sfo.2 
n 1 
• * 
-
» 
p — - — r — — — T 
Series II 
t 
— 1 . L 
* 
\ 
-
__._! 1 
16 18 20 22 
Ge at wt. % 
24 
Figure 3. Variation of heat capacity jump at Tq (ACp) as a function of composition of PbxGe42 xSe58 (3 -
x • 15) (series I) and Pb20GexSe80x (17 r x < 24) (series II) glasses Dotted line merely connects adjacent 
data points 
excess heat capacity at the T shows a minimum near the composition with x = 9 at. wt. 
% Pb for series I and III, and x = 21 at. wt. % Ge for series II and IV, which are the 
compositions at which the p- to n-type transition occurs [3,11,21]. Thus the minimum in 
fragility is associated with the composition at which MCCR occurs in these glasses. A 
small ACp is also a proof of a strong thermodynamic behaviour which indicates that the 
0.32 
!? 0.28 
\ 0.24 O 
0.20 
[ I 
h 
I 
-
»— 1 
1 
1 
, 
* T~ " — i • ' •> 
Series III 
1 
i 
_j ^ 
— i — 
-
11 
, i 
03 06 09 13 
Pb at. wt. % 
15 16 18 20 22 
Ge at. wt. % 
0.21 
^^.^ 
-gO.18 
3 
a 
S^0 15 
n 19 
' « ' i 
I 
• « 
i • — • 
i 
. 
_, *- —r ,— x 
Series IV , -
i 
i . « — 
i i 
i J 
* i j 
i 1 
24 
Figure 4. Variation of heat capacity jump at Tg(ACp) as a function of composition of PbxGe42.xSe4BTe10 (3 
* * < 15) (series III) and Pb20GexSe70.Je10 (17 < x < 24) (series IV) glasses. Dotted line merely connects 
adjacent data points. 
510 A Srinivasan and A K Pattanaik 
glass is not far away from its thermodynamic equilibrium. A minimum in ACp has been 
observed when glasses undergo a floppy to rigid transition [25,26] in Ge-As-Se [27] Ge-
Sb-Se [28,29], Ge-As-Te and Si-As-Te [29] glasses. In the case of Pb-Ge-Se-Te glasses 
the composition dependence of Tg suggests the presence of a relatively large number o< 
hetero-nuclear bonds near the compositions at which the p- to n-type transition occurs 
This could give rise to an optimally coordinated 3-d structure, leading a rigid glassy network 
as reflected by the minimum in the excess heat capacity data. 
4. Conclusions 
The composition dependence of E^, <m> and ACp of two series of Pb-Ge-Se and PL 
Ge-Se-Te glasses has been obtained from DSC data. These parameters show subtle 
variation in their values among the different series of glasses. These variations are to be 
expected since the percentages of group IV and VI elements vary in each of these series 
of glasses, leading to variation in the nature of the bonding between the atoms. But within 
each series, the composition dependence of E7?, <m> and ACp consistently show a 
minimum at x = 9 at. wt. % Pb and x = 21 at wt. % Ge, for both the Pb-Ge-Se and Pb 
Ge-Se-Te glasses, which are the compositions at which the conduction type change occurs 
This clearly shows evidence of a fragility change associated with the conduction mechanise 
change. Although the change in conduction mechanism is an electronic property, thf 
current results clearly indicate that there is a structural basis to the electronic transition 
occurring at specific compositions in the lead modified chalcogenide glasses. 
Acknowledgment 
Financial assistance from the Department of Atomic Energy, Government of India is gratefully 
acknowledged. 
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