PII: S0022-3697(98)00049-3 Pergamon J. Phys. Chem Solids Vol 59, No. 8, pp. 1255–1258, 1998 0022–3697/98/$ – see front matter q 1998 Elsevier Science Ltd. All rights reserved TEMPERATURE DEPENDENCE OF ELECTRIC PERMITTIVITY OF LINEAR DIELECTRICS WITH IONIC AND POLAR COVALENT BONDS M. LJ. NAPIJALO*, Z. NIKOLIĆ, J. DOJČILOVIĆ, M. M. NAPIJALO and L. NOVAKOVIĆ Faculty of Physics, University of Belgrade, Studentski Trg 12, P.O. Box 550, 11000 Beograd, Minor Yugoslavia (Received 20 February 1997; accepted 11 March 1998) Abstract—Results are presented of experimental verification of the relation describing temperature dependence of permittivity of linear dielectrics with ionic and polar covalent bonds. The relation has been derived by means of the thermodynamic method . The verification has been realized on sodium chloride, sulfates, phosphates and arsenates of magnesium and cobalt, as well on barium titanate in paraelectric phase. The experimental results confirm the theoretical relation and, at the same time, indicate the possibility of determining the linearity region of properties of these dielectrics. q 1998 Elsevier Science Ltd. All rights reserved Keywords: A. inorganic compounds, D. dielectric properties er (T ¼ 0) ¼ 1 þ 1. INTRODUCTION In  it was shown that applications of classical thermodynamics of equilibrium processes enable equation of state of dielectrics (paraelectrics) to be deduced. From that equation it is possible to deduce relations that describe temperature dependence of the electric susceptibility (x e) of linear solid dielectrics. One of those relations is: xe ¼ Ce ve ¹ T (1) where C e and v e are constants characteristic of the dielectrics and T is the temperature of the sample. This relation determines x e as an increasing function of temperature, which, by comparison with experimental data, means that it should correspond to dielectrics with ionic and polar covalent bonds (induction or displacement polarizing mechanism). This thermodynamic approach, in this case as in the case of other systems, does not enable the constants C e and v e to be determined as functions of microscopic parameters characterizing the dielectric. This can be accomplished by means of corresponding microscopic theories (which do not exist for dielectrics of this type). From relation (1) it follows for the relative electrical permittivity (e r): er ¼ 1 þ xe ¼ 1 þ Ce ve ¹ t and for the absolute zero of temperature: *Corresponding author (2) Ce ve (3) The type of temperature dependence of e r may be determined experimentally and compared with the theoretical relations (2). This is done in the present paper for a number of dielectrics; the values of the constants C e and v e were also determined. It should be noted that there are numerous examples for the increase of e r with temperature. We shall only mention some newer results. These are data for thallous halides , alkali halides and alkaline earth oxides , alkaline earth fluorides and lead fluoride , potassium chloride , barium molibdate , sodium chlorate and sodium bromate , ammonium sulphate  etc. It should also be mentioned that these dielectrics were examined and described in earlier papers as well. In addition to this, there are several papers dealing with numerical treatment of experimental data (in narrower temperature intervals). We shall only mention a series of papers by Shanker et al. (e.g. , where the other papers of the same author are cited). 2. THE EXPERIMENT Here we present results of determination of e r(T) for a number of dielectrics; the results are employed to prove relation (2). All experiments were carried out on polycrystalline samples—pellets which were made out of originally powered substances by compression at 70 b. The pellets were 13 mm in diameter and 2 mm thickness. The measurements were performed at a frequency of 1 MHz by means of Hewlett-Packard Model 1721B OPT101 1 MHz Digital LCR Meter. A specially designed thermostat was used which allowed measurements in the 1255 1256 M. LJ. NAPIJALO et al. Fig. 1. Temperature dependence of relative permittivity for NaCl: 1, experimental data; 2, curve which corresponds to relation (2). temperature range 290–1300 K, while the temperature of the sample was defined within an error of 0.3%. 2.1. Electrical permittivity of NaCl The temperature dependence of e r(T) for NaCl is shown in Fig. 1 (curve 1). The measurement was performed with a sample of high purity (99.99%) in the temperature region up to 970 K, to achieve premelting (melting point at T M ¼ 1074 K ). A complex form of dependence was found for a small number of dielectrics. As an example we mention double arsenate of sodium and cobalt, MgCoAsO 4, which we have examined . The complex, non-monotonic shape of dependence of e r(T) in the higher temperature region may be explained by competition of a series of electron and ion processes at these temperatures. These processes have been described in a detailed but fragmentary manner in the literature (e.g. [12–15] and also in [16–25]). We limit our attention to the lower temperature region. Dependence e r(T) in this region is well represented by relation (2). Numerical tests resulted in curve 2 in Fig. 1. The following numerical values of the parameters correspond to this curve: Ce ¼ 3720 K, ve ¼ 964 K while the errors are less than 1%. Using these values, we get from relation (3): er (T ¼ 0) ¼ 4:86 It should be noted that the theoretical curve agrees well with the experimental data within the region T # 560 K, which therefore determines the linearity region for NaCl as paraelectrics. 2.2. Electrical permittivity of MgSO 4 and CoSO 4 Fig. 2(a) and Fig. 2(b) show the results of determinations of the temperature dependence of permittivity of magnesium sulfate MgSO 4 and cobalt sulfate CoSo 4. Sulfates are obtained by dehydration of commercial sulfate heptahydrates (purity 99.5%). The temperature Fig. 2. Temperature dependence of relative permittivity for (a) MgSO 4 and (b) CaSO 4: 1, experimental data; 2, curve which corresponds to relation (2). of dehydration of MgSO 4 is T d ¼ 473 K and of CoSO 4 is T d ¼ 693 K . In the temperature region below T ¼ 800 K both substances are isostructural ; at the higher temperatures structural phase transitions occur . It is seen from the figures that a monotonous increase of e r(T) exists in the temperature region examined. Table 1 presents characteristic parameters of these dielectrics, which were obtained by numerical analysis. From the figures it is seen that MgSO 4 may be considered linear in the region T # 620 K while for CoSO 4 the linearity region is T # 650 K. 2.3. Electrical permittivity of Mg 3(PO 4) 2 and Co 3(PO 4) 2 Fig. 3(a) and Fig. 3(b) present temperature dependence of permittivity of magnesium orthophosphate Mg 3(PO 4) 2 and cobalt orthophosphate Co 3(PO 4) 2. The synthesis of these compounds was realized by the procedure described in [28–31], starting with chemicals of 99.5% purity. These phosphates are isostructural within the examined temperature interval [28–31]. On the grounds of experimental data presented in the figures, characteristic parameters of these phosphates were determined by Table 1. Characteristic parameters of Mg and Co sulfates ve e r(T ¼ 0) MgSO 4 CoSO 4 2491 K 1098 K 3.27 3308 K 1191 K 3.78 Temperature dependence of permitticity of linear dielctrics 1257 Fig. 3. Temperature dependence of relative permittivity for (a) Mg 3(PO 4) 2 and (b) CO 3(PO 4) 2: 1, experimental data; 2, curve which corresponds to relation (2). means of numerical analysis. The corresponding data are given in Table 2. The figures show that both the dielectrics are linear in the region T # 560 K. 2.4. Electrical permittivity of Mg 3(AsO 4) 2 and Co 3(AsO 4) 2 Fig. 4(a) and Fig. 4(b) present temperature dependence of permittivity of magnesium arsenate Mg 3(AsO 4) 2 and cobalt arsenate Co 3(AsO 4) 2. These arsenates are synthesized by a procedure analogous to those described in . Their examination is in progress in our laboratory since they are not sufficiently known. The figures indicate an analogous form of the dependence of e r(T) for the arsenates and the phosphates, which could have been expected on the grounds of general characteristics of these compounds (e.g. [32–34]). Numerical analysis of the data enabled determination of characteristic parameters of these dielectrics, which are given in Table 3. From the figures it is seen that the linearity region for both dielectrics is T # 850 K. Fig. 4. Temperature dependence of relative permittivity for (a) Mg 3(AsO 4) 2 and (b) CO 3(AsO 4) 2: 1, experimental data; 2, curve which corresponds to relation (2). Table 3. Characteristic parameters of Mg and Co arsenates Mg 3(AsO 4) 2 Co 3(AsO 4) 2 Ce ve e r(T ¼ 0) 1136 K 797 K 2.42 1394 K 974 K 2.43 2.5. Electrical permittivity of BaTiO 3 Fig. 5 shows the temperature dependence of electrical permittivity of barium titanate BaTiO 3 in the paraelectric phase. As far as we know, this well known ferroelectric Table 2. Characteristic parameters of Mg and Co phosphates Ce ve e r(T ¼ 0) Mg 3(PO 4) 2 Co 3(PO 4) 2 1046 K 867 K 2.21 1811 K 1067 K 2.70 Fig. 5. Temperature dependence of relative permittivity for BaTiO 3: 1, experimental data; 2, curve which corresponds to relation (2). 1258 M. LJ. NAPIJALO et al. has not been studied in the paraelectric phase. Our measurements were performed with the substance synthesized at the Institute ‘M.Pupin’ in Belgrade. For this ferroelectric the temperature of transition into paraelectric phase is T c ¼ 393 K . Our measurements covered the temperature interval from 400 to 1000 K. The upper limit of the interval is considerably lower than the melting point of BaTiO 3 (T M ¼ 1893 K, ). The characteristic parameters for the linearity region, obtained from numerical analysis, are Ce ¼ 5217K, ve ¼ 1346 K It may be seen from the figure that the linearity region for BaTiO 3 lies above T ¼ 600 K. 3. 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