CC BY
38
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а также представить ряд величин (5.1, 5.2, 5.5, 5.7) в виде, более соответствующем их физическому содержанию.
СПИСОК ЛИТЕРАТУРЫ
1. Попов И.П. Об электромагнитной системе единиц //Вестник Челябинского государственного университета. Физика.- Вып. 7.- 2010.- №12(193).- С. 78-79.
2. Патент 49245 (RU). Система представления структуры постоянной Планка/ Попов И.П.//Б.И.П.М. 2005. № 31.
3. Мешков И. Н., Чириков Б. В. Электромагнитное поле. -Новосибирск: Наука, 1987.-Ч. 1.- 272 с.
4. Carter J. The Other Theory of Physics.- Washington, 1994.
5. Киттель Ч., Найт М., Рудерман М. Механика. Беркелеев-ский курс физики. - М.: Наука, 1975.
6. Фейнман Р., Лейтон Р., Сэндс М. Фейнмановские лекции по физике. Т. 6. Электродинамика.- М.: Мир, 1965. -339 с.
T.N. Novgorodova, V.A. Kulikov Kurgan state university, Kurgan, Russia
THE INFLUENCE OF INGOMOGENITY ON THERMOELECTRIC PROPERTIES OF (BI,SB)2TE3 ALLOYS
Аннотация: В статье обсуждаются свойства твердых растворов BixSb2-xTe3+y, полученных методом вертикальной зонной перекристаллизации. Анализ состава образцов показал, что введение избыточного теллура приводит не только к появлению прослоек теллура, но и к изменению распределения висмута и сурьмы по сечению образцов. Использование модели гетерогенной слоистой структуры позволило объяснить увеличение теплопроводности при температурах выше 200 К и анизотропию коэффициента термоэдс. Обнаружено, что неоднородные твердые растворы при температуре ниже 200 К имеют термоэлектрическую эффективность выше, чем более однородные сплавы.
Ключевые слова: термоэлектричество, теллуриды висмута, термоэлектрическая эффективность.
T.N. Novgorodova, V.A. Kulikov Kurgan state university, Kurgan, Russia
THE INFLUENCE OF INGOMOGENITY ON THERMOELECTRIC PROPERTIES OF (BI,SB)2TE3 ALLOYS
The summary:The properties of solid solutions BixSb2-xTe3+y grown by method of vertical zone crystallization are discussed. Analysis of component distribution shows, that the addition of excess of tellurium leads not only to appearance of tellurium streaks, but also changes the distribution of bismuth and antimony across the samples. The application of heterogeneous layer structure model has given an opportunity to explain the appearance of additional heat transport at temperature above 200 K and anisotropy of thermoelectric power. Heterogeneous solid solutions have higher figure of merit in comparison with Z of more homogeneous alloys at T< 200 K.
Key words: thermoelectricity, tellurides of bismuth, thermoelectric figure of merit.
Introduction
The interest to the investigation of thermoelectric materials based on the tellurides of bismuth and antimony depends on their sufficiently high figure of merit (Z) at low
temperatures. Now the considerable volume information about properties of these alloys grown by different methods is accumulated [1,2]. However, big variety of growing methods leads to considerable difficulties in the interpretation of their properties and, consequently, does not allow to predict the ways of increasing the figure of merit of both materials and devices. In this connection, it is actual to investigate the properties of Bi2Te3 - Sb2Te3 solid solutions having different ratio of bismuth and antimony tellurides, obtained by a single method. Together with the investigation of temperature dependences of thermoelectric power (), electrical () and thermal () conductivities it is necessary to analyze the homogeneity of the obtained materials. Only such a complex approach allows to interpret correctly some peculiarities of temperature and concentration dependences of thermoelectric properties of materials containing bismuth and antimony tellurides.
The preparation of the specimens
In this work Bi Sb Te, solid solutions with x = 0; 0.2;
x 2-x 3+y ' '
0.5; 1.0; 1.5; 1.8; 2.0 and y = 0 ' 0.15 are being investigated. The initial components were melted in quartz ampoules pumped out up to 10-3 mm Hg. Then the ingots were grown by the method of vertical zone crystallization. The melting zone was created by the inductive heater. The application of the inductive heating allows to achieve big temperature gradient near the phase boundary (~ 200 K/cm) and ensures good mixing of the melt, which prevents the beginning of concentration overcooling of the melt at the corresponding selection of the speed of zone motion.
The samples obtained by this method are directional polycrystals and consist of crystal grains, cleavage planes which are on the whole parallel to the grown direction. The crystallites which are the closest to the ingot surface have the largest deviation of cleavage planes from ingot axis, but this deviation does not exceed 150. In the cross section the orientation of grains, that is the direction of C3 - axis, was chaotic. The measurements of b, t and d were carried out on the samples cut from the middle part of ingots.
The analysis of the component distribution at the cross section of the samples
The inductive heating was hardly used for growing of (Bi,Sb)2Te3 alloys earlier. Big gradient of temperature and rapid mixing of melt creates the growing conditions which differ considerably from the ones of other growing methods. Of course, it must influence the structure of samples obtained by the use of conductive heating. In this connection, the phase analysis of component distribution across the samples was carried out. This analysis was executed by electronic microscope JSM-840 with X-ray electronic zond LINC 860-500.
The results of quantitative analysis showed that the composition of solid phase corresponds on an overage to charging. However, the noticeable inhomogeneity of components component distribution across the samples was discovered. This heterogeneity depends on Bi:Sb ratio and the amount of tellurium excess. Bi05Sb15Te3+y solid solutions are the most homogeneous alloys.
The solid solutions with big contents of bismuth (Bi18Sb02Te3+y , Bi15Sb05Te3+y) have two phases: Bi-Sb-Te and Bi-Te. The area of sectors containing no antimony depends on quantity of tellurium excess. So the specimen of BiSbTe304 has two phases, but in BiSbTe305 the antimony is distributed through almost all the cross section of the sample. Further increase of tellurium excess leads to the appearance of tellurium streaks.
The solid solutions with large contents of antimony (Bi02Sb18Te3+y) also have two phases: Bi-Sb-Te and Sb-Te.
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The increase of tellurium excess leads to the increase of the area of sectors containing Sb-Te phase.
In most cases the distribution of components (Bi, Sb, Te) across the specimens become more inhomogeneous with the increase of tellurium excess. The change of component contents in different points of sample can reach 5-10 weight %, which does not exclude the formation of new compounds with crystal structure and properties different from the structure and properties of (Bi,Sb)2Te3 alloys.
Thermoelectric properties of BixSb2-xTe3+y solid solutions
The thermoelectric power b, electrical resistivity s and thermal conductivity d were measured along cleavage planes in temperature range 100 - 300 K. The application of inductive heating to obtain BixSb2-xTe3+y alloys leads to change of their properties in comparison with the properties of alloys grown by other methods.
The addition of tellurium excess allows to obtain both p- and n-type conduction. Bismuth telluride change its conduction type when only 0.6 at.% of tellurium excess is added. The addition of tellurium excess in the investigated alloys change not only absolute values and , but also the slope of their temperature dependences. It is not possible to explain these changes with the help of the standard model and acoustic mechanism of scattering.
The properties of Bi15Sb05Te3+y and BiSbTe3+y alloys are of great interest in this relation. The thermoelectric power of Bi15Sb05Te304 alloy begins to decrease at the temperature of more than 160 K (fig. 1). At the same time electrical resistivity also decreases at T>160 K (fig.2). These temperature dependences of and usually respond to the appearance of intrinsic conduction. However, the calculation of energy gap fg in the assumption that the changes of b(T) and s(T) dependences are connected with the appearance of opposite sign carriers leads to value fg ~0.04eV, which disagrees with the data of other authors [3,4]. The electrical resistivity of Bi15Sb05Te36 solid solution also has maximum near 200 K (fig. 2), but the temperature dependence of the thermoelectric power of this alloy has no peculiarities (fig. 1).
The thermoelectric power b of BiSbTe305 alloy is equal
300
250
g 200
100
50
0
80 120 160 200 240 280 320 T, K
Fig. 1. Variation of the thermoelectric power b with absolute temperature for Bi15Sb05Te3 samples 1 - y=0; 2 - y=0.03; 3 - y=0.04; 4 - y=0.05; 5 - y=0.085
to ~20 nV/K and has weak temperature dependence (fig. 3). At the same time the electrical resistivity of this solid solution increases monotonously in all temperature ranges (fig. 4). It is impossible to explain such temperature dependences using the standard zone model.
The temperature dependences of thermal conductivity of all the investigated solid solutions are approximately identical. The thermal conductivity decreases at the range of 100 ' 180 K, and then remains practically constant (fig. 5). All the investigated samples have the lattice thermal conductivity dL which is proportional to 1/T at the temperature below 160180 K. The deviation of temperature dependence from the low 1/T above 180200 K is hard to
10
S
£ 6 С
CD
2
0
80 120 160 200 240 280 320 T, K
Fig. 2. Variation of the electrical resistivity S with absolute temperature for Bi15Sb05Te3+r samples. The signs of curves have the same meaning as in fig. 1
250
200
W 150
>
ЧО
О
"5 100
50
0
80 120 160 200 240 280 320 T,K
Fig.3. Variation of the thermoelectric power b with absolute temperature for BiSbTe3 samples 1 - y=0; 2 - y=0.025; 3 - y=0.04; 4 - y=0.05; 5 - y=0.12
explain by means of the appearance of bipolar diffusion. Temperature dependences and are the evidence that in this alloys intrinsic conduction up to 280300 K is absent.
The mentioned peculiarities of temperature dependences , and are evidently caused by heterogeneity of the composition of the investigated solid solutions. Bismuth and antimony tellurides and their solid solutions have at least two types of heterogeneities. One of them is connected with the inhomogeneity of bismuth and antimony distribution, which causes the changes , and in different points of the sample. Moreover, the addition of tellurium excess leads to the appearance of tellurium streaks along cleavage planes.
The influence of composition inhomogeneities upon thermoelectric properties of alloys was calculated with help of the model of heterogeneous layer structure (HLS). In this model the sample is considered to be a combination of
3.5
3.0
2.5 Q 20
W
I
s 1.5
Ck
1.0
0.5
0.0
80 120 160 200 240 2S0 320 T, K
Fig. 4. Variation of the electrical resistivity S with absolute temperature for BiSbTe3+y samples. The signs of curves have the same meaning as in fig. 3
80 120 160 200 240 280 320 T, K
Fig. 5. Plot of the thermal conductivity d against absolute temperature for BiSbTe3+y alloys. The signs of curves have the same meaning as in fig. 3
parallel layers with different composition having different properties. The calculation showed that the change of layer thickness leads to the change the slope of temperature dependences b(T) and s(T) , and also to the change of their absolute values. Such changes in particular were observed in alloys with tellurium excess. Phase analysis also showed that the addition of tellurium excess changes the phase ratio in the samples. Calculated temperature dependence for heterogeneous sample, consisted of layers with opposite conduction types agrees very well with experimental dependence for BiSbTe305.
The existence of tellurium streaks influences the change of and very little, as they have small volume. However, the existence of tellurium streaks leads to the appearance of vortical currents causing additional heat transport, that is to the increase of thermal conductivity. In this case the additional thermal conductivity is determined on the whole by the difference of layer power coefficients. It is known that tellurium thermoelectric power changes the sign at about 200 K. It is the change of in tellurium that causes the appreciable additional heat transport in heterogeneous samples above 180 K.
The calculations made with the help of HLS model allowed to explain some peculiarities of temperature dependences of thermoelectric properties of BixSb2-xTe3+y solid solutions by the existence of heterogeneity of component distribution. Thus, it can be affirmed, that the distinction of properties of materials based on Bi2Sb3 grown different methods is caused to a great extent by various degrees of the sample heterogeneity.
Anisotropy of thermoelectric power and electrical resistivity
The existence of layer heterogeneity must lead to the appearance of anisotropy of thermoelectric power and resistivity of materials even if the properties of layers are isotropic. In
this case the value of Eb >bn .b and coefficient of
resistivity anisotropy k > sn/s depend on the correlation of layer parameters (b , s ) and ratio of their thickness. Predicted dependences of Eb and were observed for Bi15Sb05Te3+y alloys. For the first time appreciable anisotropy of thermoelectric power Eb ■ 150 nV / K was discovered.
Bi15Sb05Te304 alloy has maximum Eb (fig. 6). This alloy is the most heterogeneous as the phase analysis has revealed. In accordance with the calculation the samples consisting of layers with p- and n-type conduction can have the value
Eb > 100 '150 nV / K. The analysis of the temperature dependences of thermoelectric power and resistivity of Bi15Sb05Te304 alloy also confirmed that it consist of the layers with different conduction type.
The figure of merit of BixSb2-xTe3+y solid solutions
The change of b(T) , s(T) and d(T) dependences
caused by heterogeneity of alloy composition leads to the increase of the figure of merit Z of inhomogeneous materials in comparison with more homogeneous alloys at low temperatures. The temperature dependences Z(T) for BixSb2-xTe3+y solid solutions are shown in fig. 7. At temperature below 240 K inhomogeneous solid solution Bi15Sb05Te3 03 has Z higher than the well - known homogeneous Bi05Sb15Te306. Moreover the weak temperature dependence of the figure of merit allows to use this heterogeneous solid solution in higher cascade of thermoelectric cooling devices.
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BECTHHK Kry, 2010. №2
SCI 120 160 200 240 230 320 T, K
Fig. 6. Temperature dependences of anisotropy of thermoelectric power Eb for Bi15Sb05Te3y samples. 1 - y=0; 2 - y=0.03; 3 -y=0.04; 4 - y=0.05; 5 - y=0.085
M 2.0
Kl
80 120 1(50 200 240 280 320 T,K
Fig. 7. Plot of the measured figure of merit against absolute temperature for samples of composition BixSb2xTe3+y.
1 - Bii.sSbo.2Tes ;
4 -
2 -Bi1.5Sb0.5Te3.03 : Bl0.5Sb,.5Te3.06 : 5 *
3 -BiSbTe303, ' Bi0.2Sb1.8Te3.03
CONCLUSION
The vertical zone crystallization leads to appearance of layer heterogeneity of BixSb2_xTe3+y solid solutions. The inhomogeneity of component distribution across the ingots depends on Bi:Sb ratio and the value of tellurium excess. The existence of longitudinal layer inhomogeneity changes not only absolute values of b, s and d, but also their temperature dependences. The application of heterogeneous layer structure model has given an opportunity to explain the appearance of additional heat transport at temperature above 200 K and anisotropy of
thermoelectric power. Heterogeneous solid solutions have higher figure of merit in comparison with Z of more homogeneous alloys at T< 200 K.
REFERENCES
1. Jim W.M., Rosi F.D. Compound Tellurides and Their Alloys for Peltier Cooling - a Review// Sol.St.Electron. - 1972. - V.15.
- P. 1121 - 1140.
2. Гольцман Б.М., Кудинов В.А., Смирнов И.А. Полупроводниковые термоэлектрические материалы на основе Bi2Te3.
- М.:Наука, 1972. - 319с.
3. Кутасов В.А., Лукьянова Л.Н. Концентрационная зависимость параметра анизотропии в n-Bi2Te3 и твердых растворах на его основе//ФТТ. - 1986. - Т.28. - Вып.3. - С.899-902.
4. Middendorff A., Landwehr G. Evidence for a Second Band in p-Bi2Te3. from Magneto-Seebeck and Shubnikov-de Haas Data // Sol.St.Com. - 1972. - V.11. - No.1. - P.203-206.
А.П. Тыщенко
Курганский государственный университет, г. Курган, Россия
III НАЧАЛО ТЕРМОДИНАМИКИ -ПОСТУЛАТ ИЛИ ТЕОРЕМА?
Аннотация: В статье рассматриваются методические аспекты изучения 3 начала термодинамики.
Ключевые слова: 3 начало термодинамики, теорема Нернста.
A.P. Tyshchenko
Kurgan state university, Kurgan, Russia
ТНЕ THIRD LAW OF THERMODYNAMICS, A POSULATE OR THEOREM?
Abstract: The article deals with methodical aspects of the Third Law of Thermodynamics.
Keywords: the Third Law of Thermodynamics, Nernst principle.
В [1-4] было указано, что в молекулярно-кинетичес-кой теории вещества можно дать конкретную и однозначную интерпретацию понятия температуры.
Температура тела (системы) в общем случае определяется как усредненная энергия, которую частица тела (системы) передает за один элементарный акт взаимодействия другому пробному или иному телу.
С другой стороны, известно, что понятие энтропии в физике дается третьим началом термодинамики (теоремой Нернста). Это начало трактуется как постулат, вытекающий из экспериментов по исследованию теплоемкости тел в широком температурном диапазоне. Между тем в [1-4] показано, что интегральная форма третьего начала термодинамики может быть получена в результате простых логических построений, вытекающих из определения температуры. Суть этих построений заключаются в следующем.
Выполним мысленно следующий эксперимент. Поместим идеальный газ, имеющий температуру Rj, в замкнутый сосуд бесконечно большой теплоемкости с температурой, равной абсолютному нулю (нуль-термостат). Пусть идеальный газ охлаждается в ходе квазистатического процесса. Первая малая теплота Q1 будет передана при начальной температуре Rj, в результате потери
