Substitutional Effect on Dielectric Losses in Polycrystalline CaxSr1-xTiO3 and PbxSr1-xTiO3 Ferro-Electric Mixed Crystals

Abstract

The Dielectric losses are theoretical investigated for CaxSr1-xTiO3 and PbxSr1-xTiO3 single crystal perovskites in para-electric phase as a function of composition and temperature. In our calculation, the Silverman Joseph`s Hamiltonian augmented with fourth order phonon co-ordinates using double time temperature dependent Green`s Function technique is used. Dielectric loss is estimated for various value of x. The substitutional impurity depend dielectric losses increases with increases in composition x at room temperature and Dielectric loss tangent (tan ?) increases with increasing temperature at constant values of x.

Introduction

I. INTRODUCTION

Strontium titanate (SrTiO3)ST is one of the most interesting and more studied member of ABO3 perovskites family due to its strong ferro-electricity, semi-conductivity, low dielectric losses ,used in super conductivity and potential applications in many devices. It is well known that the ferro-electricity in ABO3 results from the delicate balance between the short-range repulsions favouring cubic structure, and the long-range coulomb interactions favouring tetragonal structure in the case of ST. It is of interest to find out how foreign ions will influence the losses in ST. As an example, divalent (Pb or Ca) may be substituted for divalent strontium in ST. Lattice parameter and curie temperature vary almost linearly with composition.   

The investigation of the dielectric properties provides an important approach in understanding inter and intra molecular interactions models of the motion and conformational change in the macromolecules. The temperature defect and frequency dependence of dielectric loss in ferroelectric perovskites has been the subject of considerable interest due to their extensive use in various applications.

It is very interested to study physical properties of mixed crystals, as it helps in understanding basic mechanism of mixed crystal formation which finds interesting applications. The dependence of physical properties of mixed crystals varies from system to system. The variations in the properties may be linear or non- linear. Also it is very well known that several interesting temperature dependent properties of ferroelectrics results from the temperature dependence of low lying transverse optic mode of vibration[1-3]. The applications of the perovskites lies in the field of ceramic industry, memory display, optical communication, holographic storage media, etc.

Microwave losses in displacive ferroelectrics (BT,ST etc.) have been reported experimentally (Rupprecht and Bell 1961, 1962; Rupprecht et al 1961)[4].The microwave losses in both pure and doped SrTiO3 have been investigated as a function of frequency and temperature. It is found that the loss tangent is proportional to frequency in the range 3-36 kMc/sec. (Rupprecht and Bell 1961, 1962; Rupprecht et al 1962) [5]. In the low-frequency range at room temperature Linz[6] has reported a loss tangent of SrTiO3 which is independent of frequency in the range between 102 and 107 cps.  The microwave losses in mixed and pure SrTiO3 crystals have been experimentally measured  as a function of frequency and temperature by Hung SC et al [7],Zhang L et al [8 ], Kukreti et al [9].

A Linz and K. Herrington [10 ] measured microwave losses in pure CaTiO3 with temperature. Dielectric losses of CaxSr1-xTiO3 has been measured as a function of temperature and frequency for compositions by G.-F. Zhang et al [11]

Kyoung-T. Kim and Chang-I Kim has been measured Dielectric losses for PbxSr1-xTiO3 (PST) as a function of Pb/Sr compositions at constant frequency [12].  Dielectric losses of PbxSr1-xTiO3 (PST) has been measured experimentally and theoretically as a function of temperature and frequency by Y. P. Jiang et al[13], Kyoung-Tae Kim et al [14], Yoshita Somiya et al[15].

Electric field, Frequency and Temperature dependent Microwave losses of pure PbTiO3, KNbO3 ferroelectric perovskites have been theoretically calculated in para-electric phase from the Silverman –Joseph Hamiltonian augmented with fourth order phonon coordinates using Double time temperature Green`s function by Talvinder Singh et al[16]

Microwave loss obeys the Curie-Weiss law (Deorani S .C. et al [2]). This may be taken as a direct evidence for the temperature dependence of the soft mode frequency. At transition temperature, soft mode frequency tends to zero and lattice displacement associated with this mode becomes unstable. This explains the anomalous behavior of the dielectric loss near the phase transition. So theoretically it is now clear that absorption of microwave is not due to the absorption or creation of single phonon.

Energy and momentum cannot be simultaneously conserved in the process, since the microwave photon is negligible (ω/Ω=10-3) compared to that of an excited phonon. It is possible, however, to excite a virtual phonon which subsequently decay into a real phonon due to interactions with lattice imperfections. Imperfection simply play the role of absorbing the excess momentum of the phonons and decay into other vibrational mode of the crystal is also possible.

In our previous paper [17-19] we have discussed variation of dielectric constant and soft mode of CaxSr1-xTiO3 and PbxSr1-xTiO3 mixed crystals with impurity concentration and temperature.CaxSr1-xTiO3 (CST) and PbxSr1-xTiO3 (PST)   solid solutions are basic materials for microwave devices.

The aim of the present work is to discuss the variation of microwave loss tangent (tanδ) with concentration of impurity and temperature  in  CaxSr1-xTiO3 and  PbxSr1-xTiO3  mixed crystals. Using Green`s function method, dielectric losses are theoretically calculated in para-electric phase and the results are compared with the results available elsewhere.

II. THEORY

A. Hamiltonian and Green’s function

The Hamiltonian which includes the anharmonicity upto fourth -order in the potential energy due to interaction of soft mode coordinates, resonant interaction and scattering terms are considered. The impurities introduced are characterized by different mass than the host atoms and with modified nearest neighbour harmonic force constants around their sites. The influence on the anharmonic coupling coefficients in the Hamiltonian, being small is neglected. The modified Hamiltonian of a mixed displasive perovskite, in para-electric phase which includes defects (substitutional impurity),third and fourth order anharmonicity and higher order electric moment term are used in present study and is exactly similar as used earlier20 is given.

IV. DISCUSSION

The calculated values show the comparative variation of loss tangent with defect, frequency

and temperature in CaxSr1-xTiO3 and PbxSr1-xTiO3 mixed crystals.The dielectric loss tangent depends upon anharmonic, resonsnt interaction and scattering terms due to defects.In the present study, the Hamiltonian proposed by Pytte (1970) has been designed in terms of creation and annihilation operators. To evaluate the higher order correlation functions, the renormalized Hamiltonian has been evaluated using the Green's function technique and Dyson's equation. At microwave frequencies the results are in good agreement with the experimental results.

Curie -   Weiss law behaviour of microwave losses may be taken as a direct evidence for the temperature dependence of the polarisation mode frequency. At transition temperature, soft mode frequency tends to zero and lattice displacement associated with this mode becomes unstable. This explains the anomalous behaviour of the dielectric loss near the phase transition. At very high temperatures, loss tangent deviates from Curie-Weiss law due to non linear parameter ξ. The change in Tc caused by impurity, depends upon the change in harmonic force constant between the impurity host lattice atoms mass change due to impurity and canbe negative or positive. In mixed crystals, the major contribution to the loss orginates from the impurity part α in comparision to second and third term i.e. β and ϒ dependent terms (or third & fourth order anharmonic terms).

Figure 1 and Figure 2 shows the variations of Impurity dependent dielectric loss as a function of impurity composition for CaxSr1-xTiO3 and PbxSr1-xTiO3 mixed crystals at Room Temperature. It is very clear from these figures that dielectric loss increases with the  increases in the defects (impurity composition Ca or Pb) but in CaxSr1-xTiO3 loss tangent decreses after x=0.4.

Figure 3 and Figure 4 shows the variations of the dielectric loss as a function of temperature  in  CaxSr1-xTiO3 and PbxSr1-xTiO3  for different concentration  x (x=0.0-0.8) in para electric phase at (1-100) KHz. The dielectric losses increases when temperature increase. The variation in dielectric loss for all values of x are similar trend above the curie temperature. The results of temperature and composition dependence of the dielectric losses are good qualitative and close agreements with experimental and theoretical results of others.[ 2,6,10-16]

References

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Copyright

Copyright © 2022 Sunil Kumar, M S Yadav, Neetu Sharma, S C Deorani. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.