SlideShare a Scribd company logo
1 of 5
Download to read offline
Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583
                                                                                                            www.elsevier.com/locate/jpcs




                Self-organization processes in impurity subsystem
                                of solid solutions
                                                        E.I. Rogacheva*
                           Department of Physics, Kharkov Polytechnic Institute, National Technical University,
                                                 21 Frunze St, Kharkov 61002, Ukraine


Abstract
   New experimental results proving the existence of critical phenomena in the range of small impurity concentrations
(,1.0 at.%) in a number of ternary solid solutions based on IV– VI semiconducting compounds are presented. An anomalous
decrease in X-ray diffraction linewidth and an increase in the lattice thermal conductivity and heat capacity in this concentration
range were observed. The experimental results are analyzed on the basis of percolation theory and fluctuation theory of the
second order phase transitions. From the experimental data, the critical exponents for the lattice thermal conductivity and lattice
heat capacity are determined. It is suggested that self-organization processes (a short-range or long-range ordering of impurity
atoms) accompany the percolation phenomena. The results obtained in this work represent another evidence to the proposition
about the universal character of critical phenomena accompanying the transition from an impurity discontinuum to an impurity
continuum.
q 2003 Elsevier Ltd. All rights reserved.
Keywords: A. Semiconductors; A. Alloys; C. X-ray diffraction; D. Critical phenomena; D. Thermal conductivity




1. Introduction                                                          nature of impurity potential, for any type of the interaction
                                                                         between dopants (deformational, electrostatic, dipole –
    Solid solutions represent a broad class of substances, the           dipole, etc) one can designate the radius of impurity atom
most widespread and having a great potential for practical               ‘action sphere’, within which the crystal properties differ
applications. In the framework of generally accepted notions             considerably from those of the matrix, as R0 : In accordance
of the physico-chemical analysis, the physical properties in             with one of the problems of percolation theory, viz.
the solid solution region change in a monotonic way, and the             ‘problem of spheres’ [9,10], there is a critical concentration
appearance of concentration anomalies of properties                      (percolation threshold xc ) at which the channels penetrating
indicates the intersection of phase region boundaries.                   the whole system appear and an infinite cluster consisting of
However, for a number of semiconductor solid solutions                   overlapping spheres of radius R0 is formed. The effective
we observed [1 – 8] concentration anomalies of different                 value of xc depends on the range of interactions in the
properties (microhardness H; charge carrier mobility m;                  system, i.e. on R0 : The formation of the infinite cluster is
lattice thermal conductivity lp ; etc.) in the range of small            accompanied by critical phenomena, which must manifest
impurity concentrations (, 1.0 at.%), which indicated the                themselves in the case of the solid solutions through
presence of concentration phase transitions (PTs). We                    anomalies in the concentration dependences of different
suggested [1] that these PTs have the universal character,               properties. When the percolation threshold is reached, there
corresponding to the transition from an impurity disconti-               appear channels, along which internal elastic stresses caused
nuum to an impurity continuum, and take place according to               by the impurity atoms are partially compensated due to the
a percolation scenario [9,10]. Assuming that the properties              overlapping of impurity deformational spheres. As a result,
are isotropic and taking into consideration a short-range                the movement of dislocations and propagation of elemen-
                                                                         tary excitations are facilitated. An increase in the dislocation
 * Tel.: þ380-572-400-092; fax: þ380-572-400-601.                        mobility, a decrease in the effective phonon and electron
   E-mail address: rogacheva@kpi.kharkov.ua (E.I. Rogacheva).            cross-section under the formation of percolation channels
0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved.
doi:10.1016/S0022-3697(03)00245-2
1580                       E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583

lead to a drop in H [1,7,8], a growth in lp [6] and m [1,3– 5]
which we observed in the critical region.
    To prove the suggestion about the universal character of
the concentration anomalies of physical properties in solid
solutions, it is necessary to expand the scope of objects and
properties to be studied, to perform a more detailed analysis
of experimental data, and to further develop theoretical
grounds. In this work, the new experimental results on the
concentration dependences of the X-ray diffraction (XRD)
linewidth B; lattice thermal conductivity lp ; and specific
heat C in the range of small impurity concentrations in
ternary solid solutions based on IV– VI (SnTe, PbTe, and
GeTe) semiconductor compounds [11], are presented. The
new results are considered jointly with the previously
obtained data and discussed within the framework of the
above mentioned ideas we have been developing in our
studies.



2. Results and discussion

    The experimental details of the sample preparation,
XRD study, measurements of the thermal conductivity and
the heat capacity were described earlier in Refs. [2 – 8].
    In Fig. 1, the room-temperature dependences of B on the
impurity content in PbTe– CdTe and PbTe –Bi2Te3 solid
solutions based on PbTe are presented. For comparison, we
also show previously obtained data for the PbTe –GeTe [2],
SnTe– Te [12] and CuInSe2 – CdS [13] systems. In deficit
solid solutions (SnTe – Te [12]), the increase in the Te              Fig. 1. The dependence of a relative change in the XRD linewidth
content within the SnTe homogeneity region (50.15 –                   DB=B on the dopant concentration in solid solutions PbTe–CdTe
50.8 at.% Te) corresponds to the increase in the concen-              (a),(b), CuInSe2 –CdS [13] (c), SnTe–Te [12] (d), PbTe–GeTe [2]
tration of cation vacancies (, 0.5– 3.2%) caused by the               (e), and PbTe–Bi2Te3 (f). a: (400) diffraction line; b: (800)
deviation from stoichiometry and playing the role similar to          diffraction line.
the role of impurity atoms. It is seen that in all studied solid
solutions in a relatively narrow range of concentrations of a
second component (, 0.5 – 2.0 mol%), an anomalous                     homogeneity region relative to the stoichiometric compo-
decrease in B is observed.                                            sition [12].
    It is known that among the main factors that cause a                  A subsequent sharp decrease in B shows that internal
broadening of XRD lines, apart from instrumental factors              stresses in the crystal decrease. This is in good agreement
related to the experimental conditions, are (1) the micros-           with a drop in H in the vicinity of the critical composition,
tresses in crystal and (2) a small size of coherent scattering        which was observed in all studied systems [15] and was
regions [14]. In homogeneous disordered solid solutions               attributed to the decrease in internal stresses level with the
with a sufficiently large grain size, the main reason of a             reaching of the percolation threshold and the formation of
broadening of XRD lines is microstresses caused by a                  percolation channels.
difference in sizes of impurity and host atoms. Since all                 Impurity atoms are centers of local distortions in the
studied solid solutions were prepared and investigated under          crystal lattice, sources of internal stresses and strains
the same conditions, the effect of all variables except               decreasing in an inverse proportion to the cube of the
microstresses could be ruled out. That is why the broadening          distance [16]. Since noticeable displacements of atoms are
of XRD lines we observed after the introduction of the first           created within one or two interatomic distances from an
portions of the impurity (Fig. 1) is easy to explain. In the          impurity atom, one can consider elastic fields as short-range.
SnTe– Te system (Fig. 1(d)), we do not observe the initial            At small impurity concentrations, when distances between
increase in B because alloys with concentrations of cation            impurity atoms are much larger than R0 ; elastic fields created
vacancies smaller than , 0.5% do not exist in the                     by separate atoms practically do not overlap. As the impurity
equilibrium state due to a significant shift of the SnTe               concentration increases, elastic fields of neighboring atoms
E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583                      1581

begin to overlap, which leads to a partial compensation of
elastic stresses of opposite signs. After percolation channels
via deformational fields of separate atoms are formed, the
interaction of impurities becomes cooperative. As the
impurity concentration increases, the overlapping of defor-
mational spheres and the compensation of microstresses
gradually spread over the entire crystal (the density of
‘infinite cluster’ grows [9,10]), leading to a decrease in the
overall level of elastic strains in the crystal lattice, which, in
turn, results in a decrease in B: Further introduction of
impurity atoms into this new medium (‘impurity liquid’)
causes new distortions of the crystal lattice and, consequently
a broadening of XRD lines.
                                                                       Fig. 2. The lattice thermal conductivity lp vs. the dopant
    The formation of continuous chains of impurity                     concentration in the SnTe– InTe (a) and PbTe–GeTe (b) solid
deformational spheres upon reaching the percolation                    solutions. a: T ¼ 300 K; b: T ¼ 170 K:
threshold must stimulate redistribution of impurity atoms
in the crystal lattice leading to the realization of their
configuration with a minimum thermodynamic potential.                       As is seen, in the PbTe– Bi2Te3 system (Fig. 2(f)), also at
Elastic interactions between impurity atoms, similarly to              least two anomalous regions are observed—in the vicinity of
Coulomb interactions, can lead to the formation of                     1 mol% Bi2Te3 and near 3 mol% Bi2Te3. Under the doping
configurations of impurity atoms, which correspond to                   of PbTe with Bi2Te3, Bi atoms and vacancies are introduced
minima of the elastic energy. Possible self-organization               into the cation sublattice simultaneously. The Coulomb
processes may include a long-range ordering of impurity                attraction between charged defects of opposite signs (Bi3þ
atoms (‘crystallization of impurity liquid’), a formation of           and V22) stimulates processes of chemical interaction
                                                                               Pb
complexes (short-range ordering), a change in the localiz-             leading to the formation of neutral molecular complexes
ation of impurity atoms in the crystal lattice, etc. Under             such as Bi2Te3. Thus, in addition to separate impurity atoms,
isovalent isomorphic substitution a long-range ordering is             new structural elements appear, and the formation of
more likely. Under heterovalent substitution when the                  percolation channels through these elements becomes
structure of a matrix differs from the structure of a dopant,          possible. On the basis of the above considerations one can
the probability of a short-range ordering in solid solutions           suggest that the first anomaly in the B dependence on the
increases. The introduction of a dopant in the form of a               impurity content is connected with the formation of
stable chemical compound stimulates the formation of                   percolation channels linking Bi atoms, while the second
neutral chemical complexes corresponding to the compo-                 anomaly is related to the formation of percolation channels
sition of this compound. When a certain concentration of               through Bi2Te3 complexes. This suggestion is supported by
chemical complexes is reached, the formation of percolation            the fact that it is after 3 mol% Bi2Te3 that the charge carrier
channels linking complexes and accompanied by a decrease               concentration in the PbTe– Bi2Te3 system does not change
in internal stresses becomes possible.                                 any more [17].
    The very convincing argument in favor of self-                         In Fig. 2, the concentration dependences of the lattice
organization and ordering, which take place upon reaching              thermal conductivity lp in SnTe –InTe and PbTe– GeTe
the critical concentration of an impurity, is a dramatic               solid solutions are presented. As is seen, in these systems an
decrease in B; in some cases down to the value observed in             anomalous increase in lp takes place in the range of small
an impurity-free host-material (the PbTe – Bi2Te3 and                  impurity contents. In the PbTe – GeTe system, two anom-
PbTe– CdTe systems).                                                   alous regions, whose locations correspond to those of
    When the solid solution region is sufficiently wide,                anomalies in the B dependences on the impurity content, are
different variants of ordering can be realized with                    observed. We have registered an anomalous increase in lp
increasing impurity concentration. To all appearances,                 in the range of small impurity concentration earlier in the
two extrema observed in the concentration dependence of                PbTe– MnTe system [6] and attributed it to a decrease in the
B in the isovalent PbTe– GeTe system (Fig. 1(e)), can be               effective phonon cross-section as a result of the formation of
attributed to the realization of different types of ordering           percolation channels near the percolation threshold and a
[2]. A simple calculation shows that a composition of                  decrease in an overall level of elastic stresses in the crystal
1 mol% GeTe is optimal for an ordered distribution of                  lattice. The increase in lp up to the values of a host-
impurity atoms over the sites of a simple cubic lattice                compound, which was observed in the PbTe – MnTe system
with a ¼ 3 a0 ; whereas at , 1.6 mol% GeTe, a super-                   [6] is another argument in favor of the suggestion about the
structure of impurity atoms with a fcc lattice and unit cell           self-organization processes in impurity subsystem of crystal.
parameter of a ¼ 4 a0 (where a0 is the unit cell parameter                 In accordance with the modern views [9,10,18], there is an
of the studied alloy) can be formed.                                   analogy between percolation phenomena and the second-order
1582                         E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583

PTs. In both cases, in the vicinity of a transition, the                a dynamic scaling hypothesis for a second order PT, is
properties of a system are determined by strongly developed,            equal to w ¼ 0:33; which is in perfect agreement with the
interacting fluctuations, peculiarities of thermodynamic                 experimental data [18]. This value is rather close to the
quantities obey a power law, and their exponents are called             critical exponents of lp we obtained for the PbTe– MnTe
critical exponents. Both percolation and second-order PTs               and SnTe– InTe systems, which represents another evidence
manifest themselves through critical phenomena, and are                 for a close analogy between second order PTs and
characterized by the universality of critical exponents and             percolation phenomena.
scaling laws.
    The heat capacity C is a universal property showing
anomalous behavior ðC , lT 2 TC l2a Þ in the vicinity of any            3. Conclusion
temperature second-order PT [18]. It can be suggested that a
percolation transition in solid solutions will also be                      New experimental data, which confirm our earlier
accompanied by an anomaly in C ðC , lx 2 xc l2a Þ: In                   suggestion about the universal character of critical phenom-
Ref. [19], for the first time anomalous growth in C in PbTe–             ena accompanying the transition from ‘an impurity vapor’ to
MnTe solid solutions in the range of small impurity                     ‘an impurity condensate’, were obtained for IV –VI-based
concentration (1 – 1.25 mol% MnTe) was detected.                        solid solutions. The analysis of these data and the data
    From the experimental concentration dependences of C                obtained in our earlier works shows that a narrowing of
in the PbTe– MnTe system [19], plotting the Cðlx 2 xc lÞ                XRD lines in the critical region occurs in all studied solid
dependences in a double-logarithmic scale, we determined                solutions including the case when the crystal is ‘doped’ with
the critical exponent for the specific heat as a ¼ 0:12 ^                vacancies (the SnTe– Te system [12]). The existence of the
0:02: This value is rather close to the value of a known from           range of anomalous growth in the lattice thermal conduc-
the theory of the second-order PTs and confirmed                         tivity and heat capacity in this critical region is confirmed.
experimentally [18].                                                        It is suggested that the formation of percolation channels
    In the PbTe– GeTe system, we detected an anomaly in                 through impurity centers upon reaching the percolation
the specific heat similar to the one observed in the PbTe–               threshold stimulates self-organization processes (long- and
MnTe system [19] (Fig. 3(b), curve 2). The pronounced                   short-range ordering) in the impurity subsystem. The
peak in the isotherms of C proves the existence of critical             narrowing of the XRD line width and the increase in
phenomena. As far as the PbTe– GeTe system is concerned,                the lattice thermal conductivity up to the values observed in
the accurate determination of the critical exponent is                  the impurity-free host compound, which were registered in a
complicated, since at least two anomalies are observed in               number of systems, represent a convincing evidence for
the concentration dependences of B and lp :                             ordering.
    An estimate of the critical exponent for the lattice                    On the basis of our experimental data, the estimates of
thermal conductivity using the experimental data for the                the specific heat and the lattice thermal conductivity critical
PbTe- MnTe system [6] and for the SnTe– InTe system                     exponents are made in the approximation of percolation
(present work), which was made assuming lp , lx 2 xc l2w ;              theory and fluctuation theory of the second order PTs.
yielded w ¼ 0:25 ^ 0:05: It is known [18] that the
theoretical value of the lp critical exponent w ðl ,
lT 2 TC l2w Þ; calculated for superfluid Helium 4 using
                                                                        Acknowledgements

                                                                           The author thanks Pinegin V.I. and Tavrina T.V. for their
                                                                        assistance in carrying out the X-ray studies.



                                                                        References

                                                                         [1] E.I. Rogacheva, Critical phenomena in heavily-doped semi-
                                                                             conducting compounds, Jpn. J. Appl. Phys. 32 (Suppl. 32-3)
                                                                             (1993) 775 –777.
                                                                         [2] E.I. Rogacheva, V.I. Pinegin, T.V. Tavrina, Percolation
                                                                             Effects in Pb12xGexTe, Proc. SPIE 3182 (1998) 364–368.
                                                                         [3] E.I. Rogacheva, N. Sinelnik, O.N. Nashchekina, Concen-
                                                                             tration anomalies of properties in Pb12xGexTe, Acta Phys. Pol.
Fig. 3. The dependence of the lattice thermal conductivity lp (a) and        A 84 (1993) 729–732.
specific heat C (b) of PbTe-based solid solutions on MnTe (a),(b)         [4] E.I. Rogacheva, I.M. Krivulkin, V.P. Popov, A. Lobkovskaya,
and GeTe (b) concentration. a: PbTe–MnTe (data from [6]); b: 1—              Concentration dependences of properties in Pb12xMnxTe solid
PbTe–MnTe (data from Ref. [19]), 2—PbTe–GeTe.                                solutions, Phys. Stat. Solidi A 148 (1995) K65–K67.
E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583                       1583

 [5] E.I. Rogacheva, I.M. Krivulkin, The temperature and               [12] E.I. Rogacheva, G.V. Gorne, S.A. Laptev, A.V. Arinkin, T.B.
     concentration dependences of the charge carrier mobility in            Vesene, Concentration dependences of properties in SnTe
     PbTe – MnTe solid solutions, Semiconductors 36 (2002)                  homogeneity region, Izv. AN SSSR, Neorgan. Mater. 22
     966–970.                                                               (1986) 41– 44.
 [6] E.I. Rogacheva, I.M. Krivulkin, Isotherms of thermal              [13] E.I. Rogacheva, T.V. Tavrina, Effect of CdS doping on
     conductivity in PbTe–MnTe solid solutions, Fiz. Tverd.                 structure and properties of CuInSe2, Funct. Mater. 8 (2001)
     Tela 43 (2001) 1000–1003.                                              635 –641.
 [7] E.I. Rogacheva, T.V. Tavrina, I.M. Krivulkin, Anomalous           [14] Ya.S. Umanskii, X-ray Study of Metals and Semiconductors,
     composition dependence of microhardness in Pb12xGexTe                  Metalurgiya, Moscow, 1969, p. 38.
     semiconductors solid solutions, Inorg. Mater. 35 (1999)           [15] E. Rogacheva, Concentration-dependent microhardness in
     236–239.                                                               semiconductor solid solutions, Izv. AN SSSR, Neorgan.
 [8] E.I. Rogacheva, A.S. Sologubenko, I.M. Krivulkin, Micro-               Mater. 25 (1989) 754–757.
     hardness of Pb12xMnxTe semimagnetic solid solutions, Inorg.       [16] T. Suzuki, H. Yoshinaga, S. Takeuchi, Dislocation Dynamics
     Mater. 34 (1998) 545– 549.                                             and Plasticity, Syokabo, Tokyo, 1986, Mir, Moscow.
 [9] D. Stauffer, A. Aharony, Introduction to Percolation Theory,      [17] E.I. Rogacheva, S.A. Laptev, V.S. Ploskaya, B.A. Efimova,
     Taylor & Francis, London, 1992, pp. 15–88.                             Solid solutions based on PbTe in the Pb –Bi–Te system, Izv.
[10] B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped            AN SSSR, Neorgan. Mater. 20 (1984) 1350–1353.
     Semiconductors, Nauka, Moscow, 1979, Springer-Verlag,             [18] A.Z. Patashinskiy, V.L. Pokrovskiy, The Fluctuation Theory
     New York, 1984.                                                        of Phase Transitions, Nauka, Moscow, 1982.
[11] A.V. Lyubchenko, E.A. Sal’kov, F.F. Sizov, Physical               [19] E.I. Rogacheva, I.M. Krivulkin, Concentration anomaly of
     Foundations of Semiconductor Quantum Photoelectronics,                 heat capacity in the Pb12xMnxTe semimagnetic semiconduc-
     Naukova Dumka, Kiev, 1984.                                             tors, Inst. Phys. Conf. Ser. 152 (1998) 831– 834.

More Related Content

What's hot

Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20
Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20
Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20Al Baha University
 
organo clay studies
organo clay studies organo clay studies
organo clay studies Sankhadip Das
 
Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...
Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...
Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...IOSR Journals
 
Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...
Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...
Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...iosrjce
 
Sandrogreco Tautomeric Equilibria In Relation To Pi Electron Delocalization
Sandrogreco Tautomeric Equilibria In Relation To Pi Electron DelocalizationSandrogreco Tautomeric Equilibria In Relation To Pi Electron Delocalization
Sandrogreco Tautomeric Equilibria In Relation To Pi Electron DelocalizationProfª Cristiana Passinato
 
ACS 238th Meeting, 2009, Rasulev
ACS 238th Meeting, 2009, RasulevACS 238th Meeting, 2009, Rasulev
ACS 238th Meeting, 2009, RasulevB R
 
Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...
Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...
Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...Al Baha University
 
Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...
Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...
Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...IOSR Journals
 
The effect of hygroscopic growth on urban aerosols
The effect of hygroscopic growth on urban aerosolsThe effect of hygroscopic growth on urban aerosols
The effect of hygroscopic growth on urban aerosolsAlexander Decker
 
Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...
Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...
Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...peertechzpublication
 
Bioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis Leaves
Bioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis LeavesBioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis Leaves
Bioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis LeavesIJEAB
 
Thermodynamics and adsorption studies of rhodamine-b dye onto organoclay
Thermodynamics and adsorption studies of rhodamine-b dye onto organoclayThermodynamics and adsorption studies of rhodamine-b dye onto organoclay
Thermodynamics and adsorption studies of rhodamine-b dye onto organoclayInnspub Net
 
Shubham patil personal
Shubham patil personalShubham patil personal
Shubham patil personalShubham Patil
 
Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...
Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...
Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...Alexander Decker
 
A Hierarchical Model for the Analysis of Scattering Data of Complex Materials
A Hierarchical Model for the Analysis of Scattering Data of Complex MaterialsA Hierarchical Model for the Analysis of Scattering Data of Complex Materials
A Hierarchical Model for the Analysis of Scattering Data of Complex MaterialsAkinola Oyedele
 
Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...
Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...
Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...IOSR Journals
 

What's hot (20)

Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20
Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20
Journal of the Taiwan Institute of Chemical Engineers 0 0 0 (2016) 1–20
 
organo clay studies
organo clay studies organo clay studies
organo clay studies
 
Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...
Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...
Spectral studies of 5-({4-amino-2-[(Z)-(2-hydroxybenzylidene) amino] pyrimidi...
 
D0212016025
D0212016025D0212016025
D0212016025
 
Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...
Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...
Structural and Dielectric Properties of Lanthanum Substituted Lead ZirconateT...
 
Sandrogreco Tautomeric Equilibria In Relation To Pi Electron Delocalization
Sandrogreco Tautomeric Equilibria In Relation To Pi Electron DelocalizationSandrogreco Tautomeric Equilibria In Relation To Pi Electron Delocalization
Sandrogreco Tautomeric Equilibria In Relation To Pi Electron Delocalization
 
ACS 238th Meeting, 2009, Rasulev
ACS 238th Meeting, 2009, RasulevACS 238th Meeting, 2009, Rasulev
ACS 238th Meeting, 2009, Rasulev
 
Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...
Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...
Influence of the alkyl chain length of alkyltriazoles on the corrosion inhibi...
 
Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...
Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...
Spectroscopic, Thermal, Magnetic and conductimetric studies on some 7-hydroxy...
 
The effect of hygroscopic growth on urban aerosols
The effect of hygroscopic growth on urban aerosolsThe effect of hygroscopic growth on urban aerosols
The effect of hygroscopic growth on urban aerosols
 
Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...
Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...
Vibrational Characterization and Antioxidant Activity of Newly Synthesized Ga...
 
Taiwan (2016)
Taiwan (2016)Taiwan (2016)
Taiwan (2016)
 
Bioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis Leaves
Bioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis LeavesBioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis Leaves
Bioadsorption of Pb2+ and Cu2+ on Eucalyptus Camaldulensis Leaves
 
Thermodynamics and adsorption studies of rhodamine-b dye onto organoclay
Thermodynamics and adsorption studies of rhodamine-b dye onto organoclayThermodynamics and adsorption studies of rhodamine-b dye onto organoclay
Thermodynamics and adsorption studies of rhodamine-b dye onto organoclay
 
Crystal growth and Design
Crystal growth and DesignCrystal growth and Design
Crystal growth and Design
 
Shubham patil personal
Shubham patil personalShubham patil personal
Shubham patil personal
 
Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...
Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...
Coordination modes of a new ligand derived from pyrazoline with cr(iii), mn(i...
 
A Hierarchical Model for the Analysis of Scattering Data of Complex Materials
A Hierarchical Model for the Analysis of Scattering Data of Complex MaterialsA Hierarchical Model for the Analysis of Scattering Data of Complex Materials
A Hierarchical Model for the Analysis of Scattering Data of Complex Materials
 
17
1717
17
 
Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...
Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...
Studies On The Cobalt(II) And Copper(II) Complexes Of 2,5-Substituted 1,3,4-T...
 

Viewers also liked

La actividad industrial en España
La actividad industrial en EspañaLa actividad industrial en España
La actividad industrial en EspañaMaximiliano Concheso
 
Crystal defects linear defects (dislocations)
Crystal defects   linear defects (dislocations)Crystal defects   linear defects (dislocations)
Crystal defects linear defects (dislocations)hyperm2m
 
Mme 323 materials science week 5 - imperfection in solids
Mme 323 materials science   week 5 - imperfection in solidsMme 323 materials science   week 5 - imperfection in solids
Mme 323 materials science week 5 - imperfection in solidsAdhi Primartomo
 
Crystal imperfections dislocations
Crystal imperfections dislocationsCrystal imperfections dislocations
Crystal imperfections dislocationsGulfam Hussain
 
05 dislocation theory
05 dislocation theory05 dislocation theory
05 dislocation theorypradip_gupta1
 
Preformulation testing of solid dosage forms
Preformulation testing of solid dosage formsPreformulation testing of solid dosage forms
Preformulation testing of solid dosage formsGaurav Kr
 
Solid solution strengthening
Solid solution strengtheningSolid solution strengthening
Solid solution strengtheningJAYESH PAREKH
 
Mme 323 materials science week 1 - intro to materials science & engineering
Mme 323 materials science   week 1 - intro to materials science & engineeringMme 323 materials science   week 1 - intro to materials science & engineering
Mme 323 materials science week 1 - intro to materials science & engineeringAdhi Primartomo
 

Viewers also liked (16)

La actividad industrial en España
La actividad industrial en EspañaLa actividad industrial en España
La actividad industrial en España
 
Industrias españolas
Industrias españolasIndustrias españolas
Industrias españolas
 
Crystal defects linear defects (dislocations)
Crystal defects   linear defects (dislocations)Crystal defects   linear defects (dislocations)
Crystal defects linear defects (dislocations)
 
Mme 323 materials science week 5 - imperfection in solids
Mme 323 materials science   week 5 - imperfection in solidsMme 323 materials science   week 5 - imperfection in solids
Mme 323 materials science week 5 - imperfection in solids
 
L 06
L 06L 06
L 06
 
Dislocations
DislocationsDislocations
Dislocations
 
Solid Solutions
Solid SolutionsSolid Solutions
Solid Solutions
 
Crystal imperfections dislocations
Crystal imperfections dislocationsCrystal imperfections dislocations
Crystal imperfections dislocations
 
Solid solution
Solid solutionSolid solution
Solid solution
 
05 dislocation theory
05 dislocation theory05 dislocation theory
05 dislocation theory
 
Preformulation testing of solid dosage forms
Preformulation testing of solid dosage formsPreformulation testing of solid dosage forms
Preformulation testing of solid dosage forms
 
solid solutions
solid solutionssolid solutions
solid solutions
 
Dislocation
DislocationDislocation
Dislocation
 
Solid solution strengthening
Solid solution strengtheningSolid solution strengthening
Solid solution strengthening
 
L 03
L 03L 03
L 03
 
Mme 323 materials science week 1 - intro to materials science & engineering
Mme 323 materials science   week 1 - intro to materials science & engineeringMme 323 materials science   week 1 - intro to materials science & engineering
Mme 323 materials science week 1 - intro to materials science & engineering
 

Similar to 2003 self-organization processes in impurity subsystem of solid solutions

Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...
Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...
Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...IRJET Journal
 
Taking A Look At Superconductors
Taking A Look At SuperconductorsTaking A Look At Superconductors
Taking A Look At SuperconductorsClaudia Brown
 
reactivity in chemisorption and catalysis of monometallic particles
reactivity in chemisorption and catalysis of monometallic particlesreactivity in chemisorption and catalysis of monometallic particles
reactivity in chemisorption and catalysis of monometallic particlesPRASHANTH GOPI
 
Interaction of Components in Molecular Optoelectronics for the Next Generati...
Interaction of Components in Molecular Optoelectronics for the  Next Generati...Interaction of Components in Molecular Optoelectronics for the  Next Generati...
Interaction of Components in Molecular Optoelectronics for the Next Generati...Scientific Review SR
 
Probing spin dynamics from the Mott insulating to the superfluid regime in a ...
Probing spin dynamics from the Mott insulating to the superfluid regime in a ...Probing spin dynamics from the Mott insulating to the superfluid regime in a ...
Probing spin dynamics from the Mott insulating to the superfluid regime in a ...Arijit Sharma
 
Physical Characterization of a Method for Production of High Stability Suspen...
Physical Characterization of a Method for Production of High Stability Suspen...Physical Characterization of a Method for Production of High Stability Suspen...
Physical Characterization of a Method for Production of High Stability Suspen...Editor IJCATR
 
Lattice Energy LLC - Two Facets of W-L Theorys LENR-active Sites Supported b...
Lattice Energy LLC -  Two Facets of W-L Theorys LENR-active Sites Supported b...Lattice Energy LLC -  Two Facets of W-L Theorys LENR-active Sites Supported b...
Lattice Energy LLC - Two Facets of W-L Theorys LENR-active Sites Supported b...Lewis Larsen
 
A study the effect of zr o3 on the electrical and mechanical properties
A study the effect of zr o3 on the electrical and mechanical propertiesA study the effect of zr o3 on the electrical and mechanical properties
A study the effect of zr o3 on the electrical and mechanical propertiesAlexander Decker
 
E zarkadoula zirconia
E zarkadoula zirconiaE zarkadoula zirconia
E zarkadoula zirconiaMuse Degefe
 
Ieee m-2012
Ieee m-2012Ieee m-2012
Ieee m-2012bpnv38
 
Bicrystalline Titania Photocatalyst for Reduction of CO2 to Solar Fuels
Bicrystalline Titania Photocatalyst for Reduction of CO2 to Solar FuelsBicrystalline Titania Photocatalyst for Reduction of CO2 to Solar Fuels
Bicrystalline Titania Photocatalyst for Reduction of CO2 to Solar FuelsA'Lester Allen
 
Jobs and mole-ratio method.pdf
Jobs and mole-ratio method.pdfJobs and mole-ratio method.pdf
Jobs and mole-ratio method.pdftanveercdr
 

Similar to 2003 self-organization processes in impurity subsystem of solid solutions (20)

Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...
Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...
Calculation of lattice thermal expansion coefficient of RBO4 (R=lanthanides, ...
 
B04710508
B04710508B04710508
B04710508
 
B04710508
B04710508B04710508
B04710508
 
1204.5674v1
1204.5674v11204.5674v1
1204.5674v1
 
Taking A Look At Superconductors
Taking A Look At SuperconductorsTaking A Look At Superconductors
Taking A Look At Superconductors
 
reactivity in chemisorption and catalysis of monometallic particles
reactivity in chemisorption and catalysis of monometallic particlesreactivity in chemisorption and catalysis of monometallic particles
reactivity in chemisorption and catalysis of monometallic particles
 
Interaction of Components in Molecular Optoelectronics for the Next Generati...
Interaction of Components in Molecular Optoelectronics for the  Next Generati...Interaction of Components in Molecular Optoelectronics for the  Next Generati...
Interaction of Components in Molecular Optoelectronics for the Next Generati...
 
Probing spin dynamics from the Mott insulating to the superfluid regime in a ...
Probing spin dynamics from the Mott insulating to the superfluid regime in a ...Probing spin dynamics from the Mott insulating to the superfluid regime in a ...
Probing spin dynamics from the Mott insulating to the superfluid regime in a ...
 
Dr khalid elhasnaoui 2
Dr khalid elhasnaoui 2Dr khalid elhasnaoui 2
Dr khalid elhasnaoui 2
 
Physical Characterization of a Method for Production of High Stability Suspen...
Physical Characterization of a Method for Production of High Stability Suspen...Physical Characterization of a Method for Production of High Stability Suspen...
Physical Characterization of a Method for Production of High Stability Suspen...
 
G04614154
G04614154G04614154
G04614154
 
Lattice Energy LLC - Two Facets of W-L Theorys LENR-active Sites Supported b...
Lattice Energy LLC -  Two Facets of W-L Theorys LENR-active Sites Supported b...Lattice Energy LLC -  Two Facets of W-L Theorys LENR-active Sites Supported b...
Lattice Energy LLC - Two Facets of W-L Theorys LENR-active Sites Supported b...
 
A study the effect of zr o3 on the electrical and mechanical properties
A study the effect of zr o3 on the electrical and mechanical propertiesA study the effect of zr o3 on the electrical and mechanical properties
A study the effect of zr o3 on the electrical and mechanical properties
 
E zarkadoula zirconia
E zarkadoula zirconiaE zarkadoula zirconia
E zarkadoula zirconia
 
Ieee m-2012
Ieee m-2012Ieee m-2012
Ieee m-2012
 
Bicrystalline Titania Photocatalyst for Reduction of CO2 to Solar Fuels
Bicrystalline Titania Photocatalyst for Reduction of CO2 to Solar FuelsBicrystalline Titania Photocatalyst for Reduction of CO2 to Solar Fuels
Bicrystalline Titania Photocatalyst for Reduction of CO2 to Solar Fuels
 
Madkour and elroby
Madkour and elrobyMadkour and elroby
Madkour and elroby
 
Solid solution and non stoichiometry
Solid solution and non stoichiometrySolid solution and non stoichiometry
Solid solution and non stoichiometry
 
Jobs and mole-ratio method.pdf
Jobs and mole-ratio method.pdfJobs and mole-ratio method.pdf
Jobs and mole-ratio method.pdf
 
NMR 7..pptx
NMR 7..pptxNMR 7..pptx
NMR 7..pptx
 

2003 self-organization processes in impurity subsystem of solid solutions

  • 1. Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583 www.elsevier.com/locate/jpcs Self-organization processes in impurity subsystem of solid solutions E.I. Rogacheva* Department of Physics, Kharkov Polytechnic Institute, National Technical University, 21 Frunze St, Kharkov 61002, Ukraine Abstract New experimental results proving the existence of critical phenomena in the range of small impurity concentrations (,1.0 at.%) in a number of ternary solid solutions based on IV– VI semiconducting compounds are presented. An anomalous decrease in X-ray diffraction linewidth and an increase in the lattice thermal conductivity and heat capacity in this concentration range were observed. The experimental results are analyzed on the basis of percolation theory and fluctuation theory of the second order phase transitions. From the experimental data, the critical exponents for the lattice thermal conductivity and lattice heat capacity are determined. It is suggested that self-organization processes (a short-range or long-range ordering of impurity atoms) accompany the percolation phenomena. The results obtained in this work represent another evidence to the proposition about the universal character of critical phenomena accompanying the transition from an impurity discontinuum to an impurity continuum. q 2003 Elsevier Ltd. All rights reserved. Keywords: A. Semiconductors; A. Alloys; C. X-ray diffraction; D. Critical phenomena; D. Thermal conductivity 1. Introduction nature of impurity potential, for any type of the interaction between dopants (deformational, electrostatic, dipole – Solid solutions represent a broad class of substances, the dipole, etc) one can designate the radius of impurity atom most widespread and having a great potential for practical ‘action sphere’, within which the crystal properties differ applications. In the framework of generally accepted notions considerably from those of the matrix, as R0 : In accordance of the physico-chemical analysis, the physical properties in with one of the problems of percolation theory, viz. the solid solution region change in a monotonic way, and the ‘problem of spheres’ [9,10], there is a critical concentration appearance of concentration anomalies of properties (percolation threshold xc ) at which the channels penetrating indicates the intersection of phase region boundaries. the whole system appear and an infinite cluster consisting of However, for a number of semiconductor solid solutions overlapping spheres of radius R0 is formed. The effective we observed [1 – 8] concentration anomalies of different value of xc depends on the range of interactions in the properties (microhardness H; charge carrier mobility m; system, i.e. on R0 : The formation of the infinite cluster is lattice thermal conductivity lp ; etc.) in the range of small accompanied by critical phenomena, which must manifest impurity concentrations (, 1.0 at.%), which indicated the themselves in the case of the solid solutions through presence of concentration phase transitions (PTs). We anomalies in the concentration dependences of different suggested [1] that these PTs have the universal character, properties. When the percolation threshold is reached, there corresponding to the transition from an impurity disconti- appear channels, along which internal elastic stresses caused nuum to an impurity continuum, and take place according to by the impurity atoms are partially compensated due to the a percolation scenario [9,10]. Assuming that the properties overlapping of impurity deformational spheres. As a result, are isotropic and taking into consideration a short-range the movement of dislocations and propagation of elemen- tary excitations are facilitated. An increase in the dislocation * Tel.: þ380-572-400-092; fax: þ380-572-400-601. mobility, a decrease in the effective phonon and electron E-mail address: rogacheva@kpi.kharkov.ua (E.I. Rogacheva). cross-section under the formation of percolation channels 0022-3697/03/$ - see front matter q 2003 Elsevier Ltd. All rights reserved. doi:10.1016/S0022-3697(03)00245-2
  • 2. 1580 E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583 lead to a drop in H [1,7,8], a growth in lp [6] and m [1,3– 5] which we observed in the critical region. To prove the suggestion about the universal character of the concentration anomalies of physical properties in solid solutions, it is necessary to expand the scope of objects and properties to be studied, to perform a more detailed analysis of experimental data, and to further develop theoretical grounds. In this work, the new experimental results on the concentration dependences of the X-ray diffraction (XRD) linewidth B; lattice thermal conductivity lp ; and specific heat C in the range of small impurity concentrations in ternary solid solutions based on IV– VI (SnTe, PbTe, and GeTe) semiconductor compounds [11], are presented. The new results are considered jointly with the previously obtained data and discussed within the framework of the above mentioned ideas we have been developing in our studies. 2. Results and discussion The experimental details of the sample preparation, XRD study, measurements of the thermal conductivity and the heat capacity were described earlier in Refs. [2 – 8]. In Fig. 1, the room-temperature dependences of B on the impurity content in PbTe– CdTe and PbTe –Bi2Te3 solid solutions based on PbTe are presented. For comparison, we also show previously obtained data for the PbTe –GeTe [2], SnTe– Te [12] and CuInSe2 – CdS [13] systems. In deficit solid solutions (SnTe – Te [12]), the increase in the Te Fig. 1. The dependence of a relative change in the XRD linewidth content within the SnTe homogeneity region (50.15 – DB=B on the dopant concentration in solid solutions PbTe–CdTe 50.8 at.% Te) corresponds to the increase in the concen- (a),(b), CuInSe2 –CdS [13] (c), SnTe–Te [12] (d), PbTe–GeTe [2] tration of cation vacancies (, 0.5– 3.2%) caused by the (e), and PbTe–Bi2Te3 (f). a: (400) diffraction line; b: (800) deviation from stoichiometry and playing the role similar to diffraction line. the role of impurity atoms. It is seen that in all studied solid solutions in a relatively narrow range of concentrations of a second component (, 0.5 – 2.0 mol%), an anomalous homogeneity region relative to the stoichiometric compo- decrease in B is observed. sition [12]. It is known that among the main factors that cause a A subsequent sharp decrease in B shows that internal broadening of XRD lines, apart from instrumental factors stresses in the crystal decrease. This is in good agreement related to the experimental conditions, are (1) the micros- with a drop in H in the vicinity of the critical composition, tresses in crystal and (2) a small size of coherent scattering which was observed in all studied systems [15] and was regions [14]. In homogeneous disordered solid solutions attributed to the decrease in internal stresses level with the with a sufficiently large grain size, the main reason of a reaching of the percolation threshold and the formation of broadening of XRD lines is microstresses caused by a percolation channels. difference in sizes of impurity and host atoms. Since all Impurity atoms are centers of local distortions in the studied solid solutions were prepared and investigated under crystal lattice, sources of internal stresses and strains the same conditions, the effect of all variables except decreasing in an inverse proportion to the cube of the microstresses could be ruled out. That is why the broadening distance [16]. Since noticeable displacements of atoms are of XRD lines we observed after the introduction of the first created within one or two interatomic distances from an portions of the impurity (Fig. 1) is easy to explain. In the impurity atom, one can consider elastic fields as short-range. SnTe– Te system (Fig. 1(d)), we do not observe the initial At small impurity concentrations, when distances between increase in B because alloys with concentrations of cation impurity atoms are much larger than R0 ; elastic fields created vacancies smaller than , 0.5% do not exist in the by separate atoms practically do not overlap. As the impurity equilibrium state due to a significant shift of the SnTe concentration increases, elastic fields of neighboring atoms
  • 3. E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583 1581 begin to overlap, which leads to a partial compensation of elastic stresses of opposite signs. After percolation channels via deformational fields of separate atoms are formed, the interaction of impurities becomes cooperative. As the impurity concentration increases, the overlapping of defor- mational spheres and the compensation of microstresses gradually spread over the entire crystal (the density of ‘infinite cluster’ grows [9,10]), leading to a decrease in the overall level of elastic strains in the crystal lattice, which, in turn, results in a decrease in B: Further introduction of impurity atoms into this new medium (‘impurity liquid’) causes new distortions of the crystal lattice and, consequently a broadening of XRD lines. Fig. 2. The lattice thermal conductivity lp vs. the dopant The formation of continuous chains of impurity concentration in the SnTe– InTe (a) and PbTe–GeTe (b) solid deformational spheres upon reaching the percolation solutions. a: T ¼ 300 K; b: T ¼ 170 K: threshold must stimulate redistribution of impurity atoms in the crystal lattice leading to the realization of their configuration with a minimum thermodynamic potential. As is seen, in the PbTe– Bi2Te3 system (Fig. 2(f)), also at Elastic interactions between impurity atoms, similarly to least two anomalous regions are observed—in the vicinity of Coulomb interactions, can lead to the formation of 1 mol% Bi2Te3 and near 3 mol% Bi2Te3. Under the doping configurations of impurity atoms, which correspond to of PbTe with Bi2Te3, Bi atoms and vacancies are introduced minima of the elastic energy. Possible self-organization into the cation sublattice simultaneously. The Coulomb processes may include a long-range ordering of impurity attraction between charged defects of opposite signs (Bi3þ atoms (‘crystallization of impurity liquid’), a formation of and V22) stimulates processes of chemical interaction Pb complexes (short-range ordering), a change in the localiz- leading to the formation of neutral molecular complexes ation of impurity atoms in the crystal lattice, etc. Under such as Bi2Te3. Thus, in addition to separate impurity atoms, isovalent isomorphic substitution a long-range ordering is new structural elements appear, and the formation of more likely. Under heterovalent substitution when the percolation channels through these elements becomes structure of a matrix differs from the structure of a dopant, possible. On the basis of the above considerations one can the probability of a short-range ordering in solid solutions suggest that the first anomaly in the B dependence on the increases. The introduction of a dopant in the form of a impurity content is connected with the formation of stable chemical compound stimulates the formation of percolation channels linking Bi atoms, while the second neutral chemical complexes corresponding to the compo- anomaly is related to the formation of percolation channels sition of this compound. When a certain concentration of through Bi2Te3 complexes. This suggestion is supported by chemical complexes is reached, the formation of percolation the fact that it is after 3 mol% Bi2Te3 that the charge carrier channels linking complexes and accompanied by a decrease concentration in the PbTe– Bi2Te3 system does not change in internal stresses becomes possible. any more [17]. The very convincing argument in favor of self- In Fig. 2, the concentration dependences of the lattice organization and ordering, which take place upon reaching thermal conductivity lp in SnTe –InTe and PbTe– GeTe the critical concentration of an impurity, is a dramatic solid solutions are presented. As is seen, in these systems an decrease in B; in some cases down to the value observed in anomalous increase in lp takes place in the range of small an impurity-free host-material (the PbTe – Bi2Te3 and impurity contents. In the PbTe – GeTe system, two anom- PbTe– CdTe systems). alous regions, whose locations correspond to those of When the solid solution region is sufficiently wide, anomalies in the B dependences on the impurity content, are different variants of ordering can be realized with observed. We have registered an anomalous increase in lp increasing impurity concentration. To all appearances, in the range of small impurity concentration earlier in the two extrema observed in the concentration dependence of PbTe– MnTe system [6] and attributed it to a decrease in the B in the isovalent PbTe– GeTe system (Fig. 1(e)), can be effective phonon cross-section as a result of the formation of attributed to the realization of different types of ordering percolation channels near the percolation threshold and a [2]. A simple calculation shows that a composition of decrease in an overall level of elastic stresses in the crystal 1 mol% GeTe is optimal for an ordered distribution of lattice. The increase in lp up to the values of a host- impurity atoms over the sites of a simple cubic lattice compound, which was observed in the PbTe – MnTe system with a ¼ 3 a0 ; whereas at , 1.6 mol% GeTe, a super- [6] is another argument in favor of the suggestion about the structure of impurity atoms with a fcc lattice and unit cell self-organization processes in impurity subsystem of crystal. parameter of a ¼ 4 a0 (where a0 is the unit cell parameter In accordance with the modern views [9,10,18], there is an of the studied alloy) can be formed. analogy between percolation phenomena and the second-order
  • 4. 1582 E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583 PTs. In both cases, in the vicinity of a transition, the a dynamic scaling hypothesis for a second order PT, is properties of a system are determined by strongly developed, equal to w ¼ 0:33; which is in perfect agreement with the interacting fluctuations, peculiarities of thermodynamic experimental data [18]. This value is rather close to the quantities obey a power law, and their exponents are called critical exponents of lp we obtained for the PbTe– MnTe critical exponents. Both percolation and second-order PTs and SnTe– InTe systems, which represents another evidence manifest themselves through critical phenomena, and are for a close analogy between second order PTs and characterized by the universality of critical exponents and percolation phenomena. scaling laws. The heat capacity C is a universal property showing anomalous behavior ðC , lT 2 TC l2a Þ in the vicinity of any 3. Conclusion temperature second-order PT [18]. It can be suggested that a percolation transition in solid solutions will also be New experimental data, which confirm our earlier accompanied by an anomaly in C ðC , lx 2 xc l2a Þ: In suggestion about the universal character of critical phenom- Ref. [19], for the first time anomalous growth in C in PbTe– ena accompanying the transition from ‘an impurity vapor’ to MnTe solid solutions in the range of small impurity ‘an impurity condensate’, were obtained for IV –VI-based concentration (1 – 1.25 mol% MnTe) was detected. solid solutions. The analysis of these data and the data From the experimental concentration dependences of C obtained in our earlier works shows that a narrowing of in the PbTe– MnTe system [19], plotting the Cðlx 2 xc lÞ XRD lines in the critical region occurs in all studied solid dependences in a double-logarithmic scale, we determined solutions including the case when the crystal is ‘doped’ with the critical exponent for the specific heat as a ¼ 0:12 ^ vacancies (the SnTe– Te system [12]). The existence of the 0:02: This value is rather close to the value of a known from range of anomalous growth in the lattice thermal conduc- the theory of the second-order PTs and confirmed tivity and heat capacity in this critical region is confirmed. experimentally [18]. It is suggested that the formation of percolation channels In the PbTe– GeTe system, we detected an anomaly in through impurity centers upon reaching the percolation the specific heat similar to the one observed in the PbTe– threshold stimulates self-organization processes (long- and MnTe system [19] (Fig. 3(b), curve 2). The pronounced short-range ordering) in the impurity subsystem. The peak in the isotherms of C proves the existence of critical narrowing of the XRD line width and the increase in phenomena. As far as the PbTe– GeTe system is concerned, the lattice thermal conductivity up to the values observed in the accurate determination of the critical exponent is the impurity-free host compound, which were registered in a complicated, since at least two anomalies are observed in number of systems, represent a convincing evidence for the concentration dependences of B and lp : ordering. An estimate of the critical exponent for the lattice On the basis of our experimental data, the estimates of thermal conductivity using the experimental data for the the specific heat and the lattice thermal conductivity critical PbTe- MnTe system [6] and for the SnTe– InTe system exponents are made in the approximation of percolation (present work), which was made assuming lp , lx 2 xc l2w ; theory and fluctuation theory of the second order PTs. yielded w ¼ 0:25 ^ 0:05: It is known [18] that the theoretical value of the lp critical exponent w ðl , lT 2 TC l2w Þ; calculated for superfluid Helium 4 using Acknowledgements The author thanks Pinegin V.I. and Tavrina T.V. for their assistance in carrying out the X-ray studies. References [1] E.I. Rogacheva, Critical phenomena in heavily-doped semi- conducting compounds, Jpn. J. Appl. Phys. 32 (Suppl. 32-3) (1993) 775 –777. [2] E.I. Rogacheva, V.I. Pinegin, T.V. Tavrina, Percolation Effects in Pb12xGexTe, Proc. SPIE 3182 (1998) 364–368. [3] E.I. Rogacheva, N. Sinelnik, O.N. Nashchekina, Concen- tration anomalies of properties in Pb12xGexTe, Acta Phys. Pol. Fig. 3. The dependence of the lattice thermal conductivity lp (a) and A 84 (1993) 729–732. specific heat C (b) of PbTe-based solid solutions on MnTe (a),(b) [4] E.I. Rogacheva, I.M. Krivulkin, V.P. Popov, A. Lobkovskaya, and GeTe (b) concentration. a: PbTe–MnTe (data from [6]); b: 1— Concentration dependences of properties in Pb12xMnxTe solid PbTe–MnTe (data from Ref. [19]), 2—PbTe–GeTe. solutions, Phys. Stat. Solidi A 148 (1995) K65–K67.
  • 5. E.I. Rogacheva / Journal of Physics and Chemistry of Solids 64 (2003) 1579–1583 1583 [5] E.I. Rogacheva, I.M. Krivulkin, The temperature and [12] E.I. Rogacheva, G.V. Gorne, S.A. Laptev, A.V. Arinkin, T.B. concentration dependences of the charge carrier mobility in Vesene, Concentration dependences of properties in SnTe PbTe – MnTe solid solutions, Semiconductors 36 (2002) homogeneity region, Izv. AN SSSR, Neorgan. Mater. 22 966–970. (1986) 41– 44. [6] E.I. Rogacheva, I.M. Krivulkin, Isotherms of thermal [13] E.I. Rogacheva, T.V. Tavrina, Effect of CdS doping on conductivity in PbTe–MnTe solid solutions, Fiz. Tverd. structure and properties of CuInSe2, Funct. Mater. 8 (2001) Tela 43 (2001) 1000–1003. 635 –641. [7] E.I. Rogacheva, T.V. Tavrina, I.M. Krivulkin, Anomalous [14] Ya.S. Umanskii, X-ray Study of Metals and Semiconductors, composition dependence of microhardness in Pb12xGexTe Metalurgiya, Moscow, 1969, p. 38. semiconductors solid solutions, Inorg. Mater. 35 (1999) [15] E. Rogacheva, Concentration-dependent microhardness in 236–239. semiconductor solid solutions, Izv. AN SSSR, Neorgan. [8] E.I. Rogacheva, A.S. Sologubenko, I.M. Krivulkin, Micro- Mater. 25 (1989) 754–757. hardness of Pb12xMnxTe semimagnetic solid solutions, Inorg. [16] T. Suzuki, H. Yoshinaga, S. Takeuchi, Dislocation Dynamics Mater. 34 (1998) 545– 549. and Plasticity, Syokabo, Tokyo, 1986, Mir, Moscow. [9] D. Stauffer, A. Aharony, Introduction to Percolation Theory, [17] E.I. Rogacheva, S.A. Laptev, V.S. Ploskaya, B.A. Efimova, Taylor & Francis, London, 1992, pp. 15–88. Solid solutions based on PbTe in the Pb –Bi–Te system, Izv. [10] B.I. Shklovskii, A.L. Efros, Electronic Properties of Doped AN SSSR, Neorgan. Mater. 20 (1984) 1350–1353. Semiconductors, Nauka, Moscow, 1979, Springer-Verlag, [18] A.Z. Patashinskiy, V.L. Pokrovskiy, The Fluctuation Theory New York, 1984. of Phase Transitions, Nauka, Moscow, 1982. [11] A.V. Lyubchenko, E.A. Sal’kov, F.F. Sizov, Physical [19] E.I. Rogacheva, I.M. Krivulkin, Concentration anomaly of Foundations of Semiconductor Quantum Photoelectronics, heat capacity in the Pb12xMnxTe semimagnetic semiconduc- Naukova Dumka, Kiev, 1984. tors, Inst. Phys. Conf. Ser. 152 (1998) 831– 834.