Elastic Moduli in Cadmium Selenide Doped with Chromium
N. S. Averkiev1, I. B. Bersuker2, V. V. Gudkov3, I. V. Zhevstovskikh3,4, M. N. Sarychev3, S. Zherlitsyn5, Sh. Yasin5,6, Yu. V. Korostelin7
1A. F. Ioffe Physical Technical Institute of the Russian Academy of Sciences, St. Petersburg, Russia.
2Institute for Theoretical Chemistry, University of Texas at Austin, Austin, USA.
3Institute of Physics and Technology, Ural Federal University, Ekaterinburg, Russia.
4M. N. Miheev Institute of Metal Physics, Ural Branch of the Russia Academy of Sciences, Ekaterinburg, Russia.
5Dresden High Magnetic Field Laboratory, Helmholtz-Zentrum, Dresden-Rossendorf, Germany.
6College of Engineering and Technology American University of the Middle East, Egaila, Kuwait.
7P. N. Lebedev Physical Institute of the Russian Academy of Sciences, Moscow, Russia.
DOI: 10.4236/jamp.2017.51004   PDF    HTML   XML   1,114 Downloads   1,720 Views   Citations


Temperature dependence of elastic moduli , , and the latter for the piezo-active and non-piezo-active versions, have been measured in the interval of 4 - 180 K at 28 - 262 MHz in a CdSe: Cr2+ crystal. Anomalies below 40 K have been found for all the moduli, except . The interpretation of the results has been carried out involving the Jahn-Teller effect and relaxation between the equivalent distortions of the tetrahedral CrSe4 centers.

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Averkiev, N. , Bersuker, I. , Gudkov, V. , Zhevstovskikh, I. , Sarychev, M. , Zherlitsyn, S. , Yasin, S. and Korostelin, Y. (2017) Elastic Moduli in Cadmium Selenide Doped with Chromium. Journal of Applied Mathematics and Physics, 5, 26-30. doi: 10.4236/jamp.2017.51004.

1. Introduction

The CdSe crystal under consideration in the present paper is a piezo-electric crystal (often used in devices). Hence, relaxation in this crystal can be observed also in the system of electric current carriers (electrons and holes). Low temperature peaks of attenuation observed at 10, 30 and 90 MHz in CdSe [5] were interpreted as due to such relaxations described by the modified Hutson and White model [6]. The authors justified such interpretation of the nature of these relaxations based on the fact that the anomalies were found only for piezo-active modes. Therefore, starting experiments on the CdSe: Cr2+ system, we expected to find two relaxation processes: one in the JT subsystem, subject to the problem, and another in the electric subsystem. These two subsystems are essentially independent, and their contributions to the complex elastic moduli are additive (the real part of them describes dispersion and imaginary one?dissipation). The aim of the present work is also to find out whether or not both of the relaxation mechanisms manifest themselves in an ultrasonic experiment carried out on high-quality CdSe: Cr2+ crystals.

2. Experiment

The sample of the CdSe crystal doped with Cr2+ ions was cut off a single crystal grown in P. N. Lebedev Physical Institute of the Russian Academy of Sciences. The seeded physical vapor transport method reported in [7] was used with CrSe source for doping. The concentration of the chromium impurities nCr was about 1018 cm−3. Measurements were carried out with the help of setups operating as frequency variable bridge at Dresden High Magnetic Field Laboratory and at Ural Federal University. Ultrasonic waves were generated and registered by LiNbO3 piezoelectric transducers at the frequencies of 28 - 262 MHz.We have carried out the experiments using the waves propagating along crystal axes described by the following moduli:, , and (the latter for piezo-active and non-piezo-active versions) (see Table 1). The choice of the moduli was done in view of possible manifestation of both the Jahn-Teller effect (JTE) subject to the expected in this case problem, and the relaxa-

Table 1. Elastic moduli studied and properties of corresponding waves.

tion in the electric subsystem. In other words, we studied (i) the moduli which should reveal anomalies due to the JTE without piezo-electricity (namely,) and non-piezo-active version of), (ii) the modulus which is piezo-active and, besides, should reveal the JT anomalies (piezo-active version of), and (iii) the modulus, which is piezo-active but should not be sensitive to the JTE.

3. Results

Anomalies of relaxation type (e.g., shown in Figure 1) have been observed in the moduli corresponding to distortions of trigonal (T-type, , both versions: piezo-active and non-piezo-active) and tetragonal (E-type,) symmetry, justifying their JT nature. Meanwhile, no anomalies were found in the modulus, which is piezo-active, but does not correspond to any symmetry distortions of the JT problem in the active centers of this crystal. Figure 2 shows the temperature dependence of two piezo-active moduli: and. One can see that the relaxation type anomaly is observed only for the symmetry modulus of the JT problem. This fact proves that the contribution of the electric subsystem to the elastic moduli is negligible (within the accuracy achieved in our experiments).Actually this result is in contradiction with the conclusions of Ref. [5]. The possible reason of this controversy maybe in the quality of our crystal: the method of its growth makes it possible to achieve lower conductivity.

4. Summary

The temperature dependence of the elastic moduli, , and

Figure 1. Temperature dependence of the non-piezo-active and piezo-active elastic moduli (curves 1 and 2, respectively).,. Frequency: 53 MHz.

Figure 2. Temperature dependence of the piezo-active elastic moduli (measured at 50 MHz) and (53 MHz) (curves 1 and 2, respectively)., ii = 33 or 44,. Curve 2 is shifted for clarity.

(the latter for piezo-active and non-piezo-active versions) have been measured in the interval of 4 - 180 K at 28 - 262 MHz in CdSe:Cr2+ crystals grown with the use of the seeded physical vapor transport method. Low temperature anomalies of relaxation origin have been found for all the moduli, congruent to distortions of the CrSe4 centers due to the JT problem, but independent of their piezoelectric properties. No relaxation type anomalies has been found for the modulus, which is not related to symmetry moduli, but it is a piezo-active mode. These facts prove that piezoelectricity does not contribute to the moduli within the accuracy of our experiments, and all the observed anomalies of relaxation origin in this system are due to the JTE.


This research was carried out with support of RFBR (project 15-02-02750 a) and UrFU Center of Excellence Radiation and Nuclear Technologies (Competitiveness Enhancement Program), and FASO of Russia (the theme Electron 01201463326).

Conflicts of Interest

The authors declare no conflicts of interest.


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