- Email: [email protected]
Growth of negative solubility lithium sulfate monohydrate crystal by slow evaporation and Sankaranarayanan–Ramasamy method
Journal of Crystal Growth 345 (2012) 1–6
Contents lists available at SciVerse ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Growth of negative solubility lithium sulfate monohydrate crystal by slow evaporation and Sankaranarayanan–Ramasamy method K. Boopathi, P. Rajesh, P. Ramasamy n Centre for Crystal Growth, SSN College of Engineering, Kalavakkam 603110, Tamil Nadu, India
a r t i c l e i n f o
abstract
Article history: Received 1 June 2011 Received in revised form 24 December 2011 Accepted 18 January 2012 Communicated by S.R. Qiu Available online 28 January 2012
Single crystals of negatively soluble lithium sulfate monohydrate (LSMH) have been grown by conventional and Sankaranarayanan–Ramasamy (SR) methods. A negatively soluble material has been grown for the first time by the SR method. The size of the grown crystal is 40 mm length and 15 mm diameter. The solubility of the material has been found at different temperatures. The grown crystals were subjected to high resolution X-ray diffraction studies, UV–vis analysis, dielectric measurements, Vickers micro-hardness, piezoelectric measurements, laser damage threshold and second harmonic generation studies. Crystalline perfection of the grown crystals was analyzed using HRXRD. The grown crystals were found to be transparent in the entire visible region. The SR method grown crystal has higher hardness, lower dielectric loss, higher piezoelectric charge coefficient and higher laser stability compared to the conventional method grown crystal. The powder Kurtz method confirms that LSMH has SHG efficiency. & 2012 Elsevier B.V. All rights reserved.
Keywords: A1. Solubility A2. Growth from solutions B1. Lithium compounds B2. Piezoelectric materials
1. Introduction In the recent years considerable attention is being given to the materials that possess unique NLO, piezoelectric and pyroelectric properties. Lithium sulfate crystallizes in the polar point group 2 (C2) (monoclinic sphenoidal). The crystal structure of LSMH was first determined by Ziegler [1] in 1934 without localization of hydrogen positions and was later confirmed by Larson and Helmhotz [2]. Ozerov et al. [3] completed the structural knowledge of Li2SO4 H2O by adding the hydrogen positions as determined from a neutron diffraction study. Lithium sulfate monohydrate, although it has been known for more than 100 years, is among the group of nonferroelectric polar crystals, yet a crystal with outstanding properties, such as high pyroelectricity [4] and piezoelectricity [5]. Its electromechanical properties were investigated in detail in the early days of application of piezoelectric crystals [6,7]. The crystals are used for the special ultrasonic probes in combination with water and biological tissue. About its nonlinear optical behavior, however, there are surprisingly few data given in the literature: in 1967, Hobden [8] analyzed the phase-matching conditions for SHG. Studies on nonlinear optical properties, determination of pyroelectric coefficient, neutron diffraction
n
Corresponding author. Tel.: þ91 9283105760; fax: þ 91 44 27475166. E-mail addresses: [email protected], [email protected] (P. Ramasamy). 0022-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2012.01.036
studies at different temperature and Raman studies on polar phonons of the Li2SO4 H2O crystal [9–13] have also been reported. Priya et al. [14] have reported the growth and various properties of the crystal grown by the slow evaporation method; the size of the grown crystal was 14 8 5 mm3. Czapla et al. [15] have investigated the steady state nonlinear optical polarization in lithium sulfate crystal. In the phase matched direction Bohaty et al. [16] have observed high efficiency conversion from pump power to Stokes and anti-Stokes lines by the cascaded selfstimulated Raman scattering effect. The temperature dependences of the pyroelectric coefficient and of the spontaneous polarization have been investigated by Gavrilova et al. [17]. The growth and various applications of inorganic materials like KDP, ZnSO4, lithium iodate, niobate crystal such as potassium lithium niobate and borate crystal like lithium borate have already been reported [18–20]. It is seen from the literature that lithium on its combination with materials like glycine and selenate [21,22] proves to be highly NLO active. Though the crystal has been used for several years there is no report on solubility studies. All the above reports have given only the various properties of the crystal. The lithium sulfate monohydrate has negative solubility behavior. The solubility of this material is reverse, i.e. with increasing temperature the solubility decreases. The crystal has good piezoelectric properties. Special requirements for piezoelectric materials depend on the intended usage. Among the required special properties are high electrical and mechanical strengths. The slow evaporation method yields small size single crystals with different crystallographic faces; for
2
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
the application point of view, specific orientation with good quality is needed. The crystal with specific orientation can be grown by the Sankaranaryanan–Ramasamy method [23]. The negatively soluble lithium sulfate monohydrate crystal has been successfully grown for the first time by the Sankaranaryanan– Ramasamy method. In this article, we have presented the solubility, HRXRD, optical, mechanical, dielectric and piezoelectric properties, laser damage threshold and SHG efficiency. Using the same material ingredients the crystal has been grown by the conventional method and the properties are compared with the SR method grown crystal.
2. Experimental procedure 2.1. Solubility studies and preparation of solution The title compound lithium sulfate monohydrate is hereafter called as LSMH. It was used for the solubility and for all the experiments, after several recrystallizations. The solubility of LSMH in water was determined as a function of temperature in the range 45–25 1C. To determine the equilibrium concentration, the LSMH solution was prepared using deionized water as the solvent. The solution was maintained at a constant temperature and continuously stirred using a magnetic stirrer to ensure homogeneous temperature and concentration throughout the volume of the solution. On reaching saturation, the content of the solution was analyzed gravimetrically. The solubility curve of LSMH is shown in Fig. 1. It is seen from the figure that lithium sulfate monohydrate has negative solubility behavior. The measurement shows the solubility of LSMH in 100 ml as 36.8 g at 45 1C and 40.6 g at 25 1C. 800 ml of saturated solution of LSMH was prepared at room temperature. The prepared solution was filtered using a whatman filter paper. The filtered solution was divided into two parts: 300 ml for the slow evaporation method and 500 ml for the SR method. The LSMH used in the present study was bought from M/s. SRL (AR grade), India, and the deionized water was obtained from a Millipore water purification unit. The resistivity of used deionized water is 18.2 MO cm.
2.2. Crystal growth The growth of LSMH single crystal was carried out by conventional and SR methods. The prepared 300 ml saturated solution was taken in a 500 ml beaker for the conventional method growth. The beaker was closed with porously sealed cover and
Fig. 1. Solubility curve of lithium sulfate monohydrate.
U-Shaped portion
Seed Crystal Fig. 2. Photograph of LSMH crystal grown by the (a) conventional method (b) modified ampoule and (c) and (d) SR method grown crystals.
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
Diffracted X-ray intensity [c/s]
1200 LSMH (SEST) (100) planes MoK α1 (+,−,−,+) 800
18" 400
0 -100
Diffracted X-ray intensity [c/sec]
the solution in the beaker was allowed to evaporate. After a few days, small crystals were seen in the beaker. After 3 weeks of growth the colorless transparent crystals were harvested and the sizes of the grown crystals were up to 12 10 4 mm3, shown in Fig. 2(a). An SR method setup was arranged [23] to grow unidirectional LSMH crystal. A suitable seed crystal was selected from the slow evaporation technique for the single crystal growth. The seed crystal was mounted at the bottom of the ampoule. 500 ml of the saturated solution was used for the growth. The saturated solution was carefully transferred into the growth vessel. The growth vessel was placed in a dust free chamber. To optimize the crystal growth, three SR method setups were arranged simultaneously. In the first system the temperature applied at the top of the ampoule [23] was 38 1C and at the bottom, 33 1C. In this condition spurious nucleus formed at the U-shaped top portion of the ampoule; after 2 weeks this nucleus started to grow and it fell on to the growing crystal. In this stage the growth of the crystal was discontinued. In the second SR method setup with modified ampoule as shown in Fig. 2(b), applied temperature at the top of the ampoule was 35 1C and at the bottom the temperature was room temperature. In this case also spurious nucleation was formed and started to grow but here we could prevent its fall on the crystal. After 40 days of growth, size of grown crystal was 15 mm in diameter and 30 mm in length; the grown crystal is shown in Fig. 2(c). In the third system, the applied temperature at top and bottom of the ampoule was 35 1C. In this case spurious nucleation was not formed in the U-shaped portion of ampoule. After 55 days good quality crystal of size 15 mm in diameter and 40 mm in length was harvested. The SR method grown crystal is shown in Fig. 2(d).
3
1200
-50
0 Glancing angle [arc s]
50
100
50
100
LSMH (SR) (100) plane MoK α1 (+,−,−,+) Vacancy
800 8" 400
0
3. Characterization studies 3.1. High-resolution X-ray diffraction (HRXRD) analysis Fig. 3(a) shows the diffraction or rocking curve (RC) recorded for a typical conventional grown lithium sulfate monohydrate single crystal specimen using (100) diffracting planes in symmetrical Bragg geometry. As seen in the figure, the RC contains a single sharp peak and indicates that the specimen is free from structural grain boundaries. The FWHM (full width at half maximum) of the curve is 1800 which is somewhat more than that expected from the plane wave theory of dynamical X-ray diffraction [24] for an ideally perfect crystal. The broadening of rocking curve without the presence of any splitting can be attributed to a variety of defects like randomly oriented mosaic blocks, dislocations, Frankel defects, implantation induced defects (due to simultaneous existence of vacancies as well as interstitial defects) etc. But depending upon the nature of asymmetry, as investigated in the earlier as well as recent articles, one can expect predominant occupation of vacancy or interstitial defects [25–30], which can be realized in the following way. For a particular angular deviation (Dy) of glancing angle with respect to the peak position, the scattered intensity is much more in the negative direction in comparison to that of the positive direction. This feature clearly indicates that the crystal contains predominantly vacancy type of defects than that of interstitial defects. This can be well understood by the fact that due to vacancy defects, as shown schematically in the inset, the lattice around these defects undergoes tensile stress and the lattice parameter d (interplanar spacing) increases and leads to give more scattered (also known as diffuse X-ray scattering) intensity at slightly lower Bragg angles (yB) as d and sinyB are inversely proportional to each other in the Bragg equation (2dsinyB ¼nl, n and l being the order of reflection and wavelength, respectively, which are fixed). However, these point
-100
-50
0 Glancing angle [arc s]
Fig. 3. High resolution diffraction curve recorded for (100) plane for (a) conventional method grown crystal and (b) SR grown single crystals of LSMH.
defects with much lesser density as in the present case hardly give any effect on the performance of the devices based on such crystals. If the concentration is high, the FWHM would be much higher and often lead to structural grain boundaries [27]. Point defects up to some extent are unavoidable due to thermodynamical considerations and growth conditions [28]. Fig. 3(b) shows the RC for the SR-grown LSMH specimen recorded under identical experimental conditions as those of Fig. 3(a). The curve is quite sharp with a single peak and having FWHM of 800 , which is much lesser than 1800 , FWHM of conventional method grown crystal. The chemical bonding theory of single crystal growth shows that the growth shape is strongly related to crystallographic characteristics [31–36]. The lesser FWHM value of SR-grown specimen clearly indicates that the structural perfection of SR-grown crystal is much better than that of SEST-grown crystal. As far as the shape of the RC is concerned, the asymmetry resembles that of Fig. 3(a). This type of asymmetry in both conventional and SR-grown specimens indicates the possibility of loss of water of crystallization from the grown crystals. 3.2. Optical transmission studies The optical transmission spectrum of grown crystals was recorded in the wavelength range from 200 to 1100 nm using a Perkin Elmer lambda 35 UV–vis spectrometer. The transmittance of the conventional and SR method crystals was 42% and 54%, respectively. Fig. 4 shows the UV–vis spectrum of grown crystals. The transmittance studies were repeated several times for the
4
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
Fig. 4. UV–vis spectra of grown crystals.
different parts of the grown crystals and the same results were obtained. The above result indicates that the SR method grown crystal has higher transparency than the conventional method grown crystal. There are steps in the transmission curves between 300 and 400 nm. This is due to change of optics in the photometer. 3.3. Dielectric measurements The study of dielectric response gives more information about lattice dynamics and the electric field distribution and charge transport mechanism in the crystal [37]. Dielectric constant and dielectric loss measurements were performed on a LSMH single crystal using an LCR meter (Agilent). The opposite parallel faces of the crystals were coated with high-grade silver paste placed between two copper electrodes and thus a parallel plate capacitor was formed. The capacitance of the crystal was measured at the frequencies 1 kHz, 10 kHz, 100 kHz and 1 MHz and various temperatures (not shown in the figure). The dielectric constant of the crystal was calculated using the relation er ¼ Ccrys/Cair where Ccrys is the capacitance of the crystal and Cair is the capacitance of the same dimension of air. Fig. 5(a) shows the dielectric constant of conventional method and SR grown crystals as a function of temperature at 1 kHz frequency. It is observed from the figure that the dielectric constant of conventional method grown crystal slightly increases initially with increase in temperature; after that it decreases with increase in temperature. The dielectric constant of the materials is due to the contribution of electronic, ionic, dipolar and space charge polarizations, which depend on the frequencies [38,39]. At low frequencies, all these polarizations are generally active [40,41]. The large value of dielectric constant at low frequency is due to the presence of space charge polarization. Space charge contribution will depend on purity and perfection of the crystal and it has noticeable influence in the low frequency region. It is seen from the figure that the dielectric constant is higher in the SR method grown crystal than in the conventional method grown crystal. Fig. 5(b) shows the dielectric loss of the grown crystals at various temperatures and 1 kHz frequency. It is observed from the figure that the dielectric loss increases with increase in temperature for the grown crystals and dielectric loss is very low for the SR method grown crystal compared to the crystal grown by the conventional method. The characteristic of low dielectric loss with high frequencies for grown crystals suggests that the grown
Fig. 5. Frequency dependence of (a) dielectric constant and (b) dielectric loss at 1 kHz.
crystals possess enhanced optical quality with lesser defects and this parameter is of vital importance for nonlinear optical materials in their application [42]. 3.4. Measurement of micro-hardness Hardness is one of the important mechanical properties of the materials [43–45]. It can be used as a suitable measure of the plastic properties and strength of a material [46]. Stillwel [47] defined hardness as resistance against lattice destruction, whereas Ashby [48] defined it as an ability of a crystal to resist a structural breakdown under an applied stress. This resistance is an intrinsic property of the crystal. Hardness is generally taken as a ratio of applied load to the area of indentation. Both in the conventional method and SR method grown crystals (100) plane was selected for the micro-hardness studies. Vickers hardness measurements were made on the crystals using a Leitz–Wetzler hardness tester fitted with a diamond pyramidal indenter. The static indentations were carried out using a Vickers indenter for varying loads. For each load (p), several indentations were made and the average value of the diagonal length (d) was used to calculate the
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
Fig. 6. Vickers micro-hardness of grown crystals.
micro-hardness of the crystals. The Vickers micro-hardness number was determined using Hv¼1.8544p/d2 kg/mm2. A plot drawn between the hardness number and corresponding loads is shown in Fig. 6. It is observed from the figure that hardness of SR method grown crystal is more than the hardness of conventional method grown crystal. In the case of melt grown crystals, dislocations present in the crystal result in higher hardness [49]. However, in the case of solution grown crystal it is seen that defects present in the crystal result in lower hardness. This is due to the fact that in solution grown crystals micro-particles of solution that get into the crystal are responsible for crystal defects and the inclusion of solution microparticles into the crystal results in decrease of hardness. Hence SR method grown crystals are reported to have higher hardness than the conventional method grown crystal [50,51].
5
Hence a way to increase the efficiency is to focus the beam into the crystal. However this often leads to the breakdown of the materials, catastrophically damaging the maximum permissible power for a particular crystal defined as damage threshold. The laser damage threshold (LDT) of an optical crystal is an important factor affecting its applications. The laser damage threshold depends on specific heat, thermal conductivity, optical absorption, etc. If the material has high specific heat, the laser damage threshold will be high. If the material has a low laser damage threshold it severely limits its applications, even though it has many excellent properties like high optical transmittance and high SHG efficiency [53–55]. A Q-switched Nd: YAG laser operating at 1064 nm radiation was used. The laser was operated at the repetition rate of 10 Hz with the pulse width 0.05 s. For the LDT measurements a 1 mm diameter beam was focused on the sample with a 30 cm focal length lens. The multiple shots LDT measurements were made on conventional method grown and SR method grown samples. Initially 30 mJ was applied on the surface of conventional method grown crystal up to 30 s; no damage was observed. The energy was increased up to 85 mJ and no damage was observed. On applying 90 mJ a small dot was seen on the surface. Finally a crack was seen on applying 95 mJ for 30 s. Similarly for the SR method grown crystal the same procedure has been followed; initially 30 mJ was applied up to 30 s and no damage was observed. On applying 95 mJ a small dot was seen on
3.5. Piezoelectric studies The piezoelectric substance is one that produces an electric charge when a mechanical stress is applied. The piezoelectric property is related to the polarity of the material [52]. The crystals were subjected to piezoelectric characterizations. Finely polished basal surface of the crystal was coated with high grade silver paste and dried at 60 1C for various measurements. Piezoelectric charge coefficient (d33 pC/N) is an important parameter associated with piezoelectric material which is defined as the amount of charge developed at the opposite surfaces of the material when one unit force is applied across it. The piezoelectric charge coefficient d33 (pC/N) was measured using a piezometer (PM300, Piezo Test, UK). A constant tapping force of 0.25 N at a frequency of 110 Hz was applied on the electrode surfaces of as grown and poled LSMH crystals. Without poling the crystal the piezoelectric measurement was carried out for the grown crystal. Piezoelectric charge coefficient for the conventional method is 0.22 pC/N and for the SR method crystal, 0.29 pC/N. After poling under a field of 2 kV/cm for 20 min at room temperature, d33 value of the LSMH crystal grown by conventional method crystal is increased to 0.34 pC/N and the LSMH crystal grown by SR method has higher piezoelectric coefficient of 1.36 pC/N, i.e. four times higher than that of the conventional method. 3.6. Laser damage threshold In nonlinear optical crystals the harmonic conversion efficiency is proportional to the power of the fundamental beam.
Fig. 7. Laser damage profile of (a) conventional method grown crystal and (b) SR method grown crystal.
6
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
the surface and finally a crack was observed on applying 105 mJ up to 30 s. From the above observation the SR method grown crystal is known to possess higher laser stability. Fig. 7(a) and (b) shows laser damage profile of conventional and SR method grown crystals. The measured higher laser damage threshold indicates suitability of the crystal for device fabrication. 3.7. SHG measurements Qualitative measurement of the conversion efficiency of the crystals was determined using the powder technique developed by Kurtz and Perry [56]. The crystals were ground into powder and densely filled into a quartz cell. A fundamental wave with a pulse width of 9 ns, repetition frequency of 10 Hz, a beam diameter of 1 mm and a wavelength of 1064 nm radiated from the Nd: YAG laser source was focused on the sample by a lens with focal length of 120 nm. The powdered LSMH crystal sample was used for the SHG analysis. KDP crystal powdered to the identical size was used as a reference material in the SHG measurements. An emission of green light was seen in the sample. The transmitted fundamental wave was absorbed by a CuSO4 solution and the second harmonic signal was detected by a photomultiplier tube and displayed on a storage oscilloscope. The SHG efficiency of the LSMH is less than that of KDP.
4. Conclusions A single crystal of negatively soluble LSMH crystal was successfully grown by the unidirectional solution crystallization method. From the high resolution X-ray diffraction (HRXRD) studies, the crystalline perfection of the grown crystal was identified. The FWHM value of SR method grown LSMH is low compared to that of conventional method grown LSMH. The HRXRD result shows that the SR method grown crystal has good crystalline perfection. Higher transparency and higher hardness values have been achieved in the SR method grown crystal. Dielectric measurements reveal that dielectric constant is high and dielectric loss is low in the SR method grown crystal compared to the crystal grown by conventional method. The piezoelectric coefficient of SR method grown crystal is four times higher than that of the conventional method grown crystal. The laser damage threshold studies reveal that SR method grown crystal has higher laser stability. The SHG efficiency of LSMH has been confirmed by the powder Kurtz method.
Acknowledgment
[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
The authors are thankful to Dr. G. Bhagavannarayana, Material Characterization Division, NPL, New Delhi, India, for providing HRXRD studies, Dr. C.K. Mahadevan, Department of Physics, S.T. Hindu college, India, for providing the dielectric measurement, Prof. K. Kishan Rao, Kakataya University, Warangal, for the microhardness measurements, Dr. Binay Kumar, Department of Physics and Astrophysics, University of Delhi, India, for the piezoelectric measurements and Dr. S. Kalainathan, VIT University, Vellore, for the laser damage threshold measurements facilities.
[42] [43]
References
[52]
[1] G.E. Zeiler, Zeitschrift fur Kristallograhie 89 (1934) 456. [2] A.C. Larson, L. Helmhotz, Journal of Chemical Physics 22 (1954) 2049. [3] R.P. Ozerov, L.E. Fykin, N.V. Rannev, G.S. Zhdanov, Doklady Akademii Nauk SSSR 148 (4) (1963) 1069;
[44] [45] [46] [47] [48] [49] [50] [51]
[53] [54] [55] [56]
R.P. Ozerov, L.E. Fykin, N.V. Rannev, G.S. Zhdanov, Soviet Physics Doklady 8 (1963) 131. W. Ackermann, Annals of Physics 46 (1972) 197. F. Spitzer, Doctoral Dissertation, University of Gottingen, 1938. W.P. Mason, Piezoelectric Crystals and Their Applications to Ultrasonics, Van Nostrand, New York, 1950; Moscow, IL, 1952. R. Bechmann, Proceedings of the Physical Society, London, Section B 64 (1952) 375. M.V. Hobden, Journal of Applied Physics 38 (1967) 4365. S.B. Lang, Physical Review B4 (1971) 3603. L. Bayarjargal, L. Bohaty, Acta Crystallographica A61 (2005) C393. J.O. Lundgren, et al., Journal of Chemical Physics 80 (1984) 423. L. Bayarjargal, Crystal Research and Technology 43 (2008) 1138. R.P. Canterford, et al., Journal of Physics C8 (1975) 1750. R. Priya, S. Krishnan, C. Justin Raj, S. Jerome Das, Crystal Research and Technology 44 (2009) 1272. Z. Czapla, M. Debska, E. Lebedeva, A. Pirozerski, Acta Physica Polonica A 99 (2001). L. Bohaty, P. Becker, H.J. Eichler, J. Hanuza, M. Maczka, K. Takaichi, K. Ueda, A.A. Kaminskii, Laser Physics 15 (2005) 1509. N.D. Gavrilova, E.G. Maksimov, V.K. Noviko, S.N. Drozhdin, Fizika Tverdogo Tela 27 (1985) 2597. G. Pasupathi, P. Philominathan, Materials Letters 62 (2008) 386. S. Podlojenov, J. Stade, M. Burianek, M. Muhulberg, Crystal Research and Technology 41 (2006) 344. C. Galez, Y. Mugnier, J. Bouillot, C. Rosso, Journal of Optical Materials 19 (2002) 33. P. Becker, S. Ahrweiler, P. Held, H. Scheneeberger, L. Bohaty, Crystal Research and Technology 38 (2003) 881. M.R. Suresh Kumar, H.J. Ravindhra, S.M. Dharmaprakash, Journal of Crystal Growth 306 (2007) 36. K. Sankaranaryanan, P. Ramasamy, Journal of Crystal Growth 280 (2005) 467. B.W. Batterman, H. Cole, Reviews of Modern Physics 36 (1964) 681. K. Lal, G. Bhagavannarayana, Journal of Applied Crystallography 22 (1989) 209. G. Bhagavannarayana, A. Choubey, Yu.V. Shubin, Krishan Lal, Journal of Applied Crystallography 38 (2005) 448. G. Bhagavannarayana, G. Parthiban, S. Meenakshisundaram, Crystal Growth and Design 8 (2008) 446. G. Bhagavannarayana, P. Rajesh, P. Ramasamy, Journal of Applied Crystallography 43 (2010) 1372. G. Bhagavannarayana, S.K. Kushwaha, Shakir Mohd, K.K. Maurya, Journal of Applied Crystallography 44 (2011) 122. K. Senthilkumar, S. MoorthyBabu, G. Bhagavannarayana, Journal of Applied Crystallography 44 (2011) 313. Ren Xiue, Xu Dongli, Xue Dongfeng, Journal of Crystal Growth 310 (2008) 2005–2009. Xue Dongfeng, Xu Dongli, Journal of Crystal Growth 310 (2008) 1385–1390. Xiaoxing Yan, Dongli Xu, Dongfeng Xue, Acta Materialia 55 (2007) 5747–5757. D.L. Xu, D.F. Xue, Journal of Crystal Growth 286 (2006) 108–113. Xue Dongfeng, Zou Longjiang, Wang Lei, Yan Xiaoxing, Modern Physics Letters B 23 (2009) 3761–3768. Dongfeng Xue, Xiaoxing Yan, Lei Wang, Powder Technology 19 (2009) 98–106. S. Dinakaran, S. Jerome Das, Journal of Crystal Growth 310 (2008) 410. D. Xue, N. Iyi, N.K. Kitamura, Journal of Applied Physics. 92 (2002) 4638–4643. D. Xue, K. Kitamura, Solid State Communications 122 (2002) 537–541. M. Meena, C.K. Mahadevan, Crystal Research and Technology 43 (2008) 166. S.M. DharmaPrakash, P.Mohan Rao, Journal of Materials Science Letters 8 (1989) 1167. C. Balarew, R. Duhlew, Journal of Solid State Chemistry 55 (1984) 1. Xingtao Keyan Li, Fangfang Wang, Zhang, Dongfeng Xue, Physical Review Letters 100 (2008) 235504. Ke Yan Li, Dong Feng Xue, Chinese Science Bulletin 54 (2009) 131–136. Keyan Li, Dongfeng Xue, Physica Scripta T139 (2010) 014073. C.C. Desai, J.L. Rai, Bulletin of Materials Science 5 (1983) 453. C.W. Stillwel, Crystal Chemistry, McGraw Hill, New York, 1938. N.A. Ashby, Journal of Nuclear Engineering 6 (1951) 33. U.V. Subba Rao, V. Hari Babu, Pramana 11 (1978) 149. Urit Charoen-In, P. Ramasamy, P. Manyum, Journal of Crystal Growth 312 (2010) 2369. D. Nagaraju, P.V. Raja Shekar, T. Bhaskar Rao, K.Kishan Rao, Materials Letters 64 (2010) 267. H. Nakatani, W.R. Bosenberg, L.K. Cheng, C.L. Tang, Applied Physics Letters 53 (1988) 2587. J.N. Sherwood, Pure and Applied Optics 7 (1998) 229. I.V. Kityk, B. Marciniak, A. Mefleh, Journal of Physics D: Applied Physics 34 (2001) 1. Ge Wenwei, et al., Journal of Alloys and Compounds 456 (2008) 503. S.K. Kurtz, T.T. Perry, Journal of Applied Physics 44 (1968) 455.
Contents lists available at SciVerse ScienceDirect
Journal of Crystal Growth journal homepage: www.elsevier.com/locate/jcrysgro
Growth of negative solubility lithium sulfate monohydrate crystal by slow evaporation and Sankaranarayanan–Ramasamy method K. Boopathi, P. Rajesh, P. Ramasamy n Centre for Crystal Growth, SSN College of Engineering, Kalavakkam 603110, Tamil Nadu, India
a r t i c l e i n f o
abstract
Article history: Received 1 June 2011 Received in revised form 24 December 2011 Accepted 18 January 2012 Communicated by S.R. Qiu Available online 28 January 2012
Single crystals of negatively soluble lithium sulfate monohydrate (LSMH) have been grown by conventional and Sankaranarayanan–Ramasamy (SR) methods. A negatively soluble material has been grown for the first time by the SR method. The size of the grown crystal is 40 mm length and 15 mm diameter. The solubility of the material has been found at different temperatures. The grown crystals were subjected to high resolution X-ray diffraction studies, UV–vis analysis, dielectric measurements, Vickers micro-hardness, piezoelectric measurements, laser damage threshold and second harmonic generation studies. Crystalline perfection of the grown crystals was analyzed using HRXRD. The grown crystals were found to be transparent in the entire visible region. The SR method grown crystal has higher hardness, lower dielectric loss, higher piezoelectric charge coefficient and higher laser stability compared to the conventional method grown crystal. The powder Kurtz method confirms that LSMH has SHG efficiency. & 2012 Elsevier B.V. All rights reserved.
Keywords: A1. Solubility A2. Growth from solutions B1. Lithium compounds B2. Piezoelectric materials
1. Introduction In the recent years considerable attention is being given to the materials that possess unique NLO, piezoelectric and pyroelectric properties. Lithium sulfate crystallizes in the polar point group 2 (C2) (monoclinic sphenoidal). The crystal structure of LSMH was first determined by Ziegler [1] in 1934 without localization of hydrogen positions and was later confirmed by Larson and Helmhotz [2]. Ozerov et al. [3] completed the structural knowledge of Li2SO4 H2O by adding the hydrogen positions as determined from a neutron diffraction study. Lithium sulfate monohydrate, although it has been known for more than 100 years, is among the group of nonferroelectric polar crystals, yet a crystal with outstanding properties, such as high pyroelectricity [4] and piezoelectricity [5]. Its electromechanical properties were investigated in detail in the early days of application of piezoelectric crystals [6,7]. The crystals are used for the special ultrasonic probes in combination with water and biological tissue. About its nonlinear optical behavior, however, there are surprisingly few data given in the literature: in 1967, Hobden [8] analyzed the phase-matching conditions for SHG. Studies on nonlinear optical properties, determination of pyroelectric coefficient, neutron diffraction
n
Corresponding author. Tel.: þ91 9283105760; fax: þ 91 44 27475166. E-mail addresses: [email protected], [email protected] (P. Ramasamy). 0022-0248/$ - see front matter & 2012 Elsevier B.V. All rights reserved. doi:10.1016/j.jcrysgro.2012.01.036
studies at different temperature and Raman studies on polar phonons of the Li2SO4 H2O crystal [9–13] have also been reported. Priya et al. [14] have reported the growth and various properties of the crystal grown by the slow evaporation method; the size of the grown crystal was 14 8 5 mm3. Czapla et al. [15] have investigated the steady state nonlinear optical polarization in lithium sulfate crystal. In the phase matched direction Bohaty et al. [16] have observed high efficiency conversion from pump power to Stokes and anti-Stokes lines by the cascaded selfstimulated Raman scattering effect. The temperature dependences of the pyroelectric coefficient and of the spontaneous polarization have been investigated by Gavrilova et al. [17]. The growth and various applications of inorganic materials like KDP, ZnSO4, lithium iodate, niobate crystal such as potassium lithium niobate and borate crystal like lithium borate have already been reported [18–20]. It is seen from the literature that lithium on its combination with materials like glycine and selenate [21,22] proves to be highly NLO active. Though the crystal has been used for several years there is no report on solubility studies. All the above reports have given only the various properties of the crystal. The lithium sulfate monohydrate has negative solubility behavior. The solubility of this material is reverse, i.e. with increasing temperature the solubility decreases. The crystal has good piezoelectric properties. Special requirements for piezoelectric materials depend on the intended usage. Among the required special properties are high electrical and mechanical strengths. The slow evaporation method yields small size single crystals with different crystallographic faces; for
2
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
the application point of view, specific orientation with good quality is needed. The crystal with specific orientation can be grown by the Sankaranaryanan–Ramasamy method [23]. The negatively soluble lithium sulfate monohydrate crystal has been successfully grown for the first time by the Sankaranaryanan– Ramasamy method. In this article, we have presented the solubility, HRXRD, optical, mechanical, dielectric and piezoelectric properties, laser damage threshold and SHG efficiency. Using the same material ingredients the crystal has been grown by the conventional method and the properties are compared with the SR method grown crystal.
2. Experimental procedure 2.1. Solubility studies and preparation of solution The title compound lithium sulfate monohydrate is hereafter called as LSMH. It was used for the solubility and for all the experiments, after several recrystallizations. The solubility of LSMH in water was determined as a function of temperature in the range 45–25 1C. To determine the equilibrium concentration, the LSMH solution was prepared using deionized water as the solvent. The solution was maintained at a constant temperature and continuously stirred using a magnetic stirrer to ensure homogeneous temperature and concentration throughout the volume of the solution. On reaching saturation, the content of the solution was analyzed gravimetrically. The solubility curve of LSMH is shown in Fig. 1. It is seen from the figure that lithium sulfate monohydrate has negative solubility behavior. The measurement shows the solubility of LSMH in 100 ml as 36.8 g at 45 1C and 40.6 g at 25 1C. 800 ml of saturated solution of LSMH was prepared at room temperature. The prepared solution was filtered using a whatman filter paper. The filtered solution was divided into two parts: 300 ml for the slow evaporation method and 500 ml for the SR method. The LSMH used in the present study was bought from M/s. SRL (AR grade), India, and the deionized water was obtained from a Millipore water purification unit. The resistivity of used deionized water is 18.2 MO cm.
2.2. Crystal growth The growth of LSMH single crystal was carried out by conventional and SR methods. The prepared 300 ml saturated solution was taken in a 500 ml beaker for the conventional method growth. The beaker was closed with porously sealed cover and
Fig. 1. Solubility curve of lithium sulfate monohydrate.
U-Shaped portion
Seed Crystal Fig. 2. Photograph of LSMH crystal grown by the (a) conventional method (b) modified ampoule and (c) and (d) SR method grown crystals.
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
Diffracted X-ray intensity [c/s]
1200 LSMH (SEST) (100) planes MoK α1 (+,−,−,+) 800
18" 400
0 -100
Diffracted X-ray intensity [c/sec]
the solution in the beaker was allowed to evaporate. After a few days, small crystals were seen in the beaker. After 3 weeks of growth the colorless transparent crystals were harvested and the sizes of the grown crystals were up to 12 10 4 mm3, shown in Fig. 2(a). An SR method setup was arranged [23] to grow unidirectional LSMH crystal. A suitable seed crystal was selected from the slow evaporation technique for the single crystal growth. The seed crystal was mounted at the bottom of the ampoule. 500 ml of the saturated solution was used for the growth. The saturated solution was carefully transferred into the growth vessel. The growth vessel was placed in a dust free chamber. To optimize the crystal growth, three SR method setups were arranged simultaneously. In the first system the temperature applied at the top of the ampoule [23] was 38 1C and at the bottom, 33 1C. In this condition spurious nucleus formed at the U-shaped top portion of the ampoule; after 2 weeks this nucleus started to grow and it fell on to the growing crystal. In this stage the growth of the crystal was discontinued. In the second SR method setup with modified ampoule as shown in Fig. 2(b), applied temperature at the top of the ampoule was 35 1C and at the bottom the temperature was room temperature. In this case also spurious nucleation was formed and started to grow but here we could prevent its fall on the crystal. After 40 days of growth, size of grown crystal was 15 mm in diameter and 30 mm in length; the grown crystal is shown in Fig. 2(c). In the third system, the applied temperature at top and bottom of the ampoule was 35 1C. In this case spurious nucleation was not formed in the U-shaped portion of ampoule. After 55 days good quality crystal of size 15 mm in diameter and 40 mm in length was harvested. The SR method grown crystal is shown in Fig. 2(d).
3
1200
-50
0 Glancing angle [arc s]
50
100
50
100
LSMH (SR) (100) plane MoK α1 (+,−,−,+) Vacancy
800 8" 400
0
3. Characterization studies 3.1. High-resolution X-ray diffraction (HRXRD) analysis Fig. 3(a) shows the diffraction or rocking curve (RC) recorded for a typical conventional grown lithium sulfate monohydrate single crystal specimen using (100) diffracting planes in symmetrical Bragg geometry. As seen in the figure, the RC contains a single sharp peak and indicates that the specimen is free from structural grain boundaries. The FWHM (full width at half maximum) of the curve is 1800 which is somewhat more than that expected from the plane wave theory of dynamical X-ray diffraction [24] for an ideally perfect crystal. The broadening of rocking curve without the presence of any splitting can be attributed to a variety of defects like randomly oriented mosaic blocks, dislocations, Frankel defects, implantation induced defects (due to simultaneous existence of vacancies as well as interstitial defects) etc. But depending upon the nature of asymmetry, as investigated in the earlier as well as recent articles, one can expect predominant occupation of vacancy or interstitial defects [25–30], which can be realized in the following way. For a particular angular deviation (Dy) of glancing angle with respect to the peak position, the scattered intensity is much more in the negative direction in comparison to that of the positive direction. This feature clearly indicates that the crystal contains predominantly vacancy type of defects than that of interstitial defects. This can be well understood by the fact that due to vacancy defects, as shown schematically in the inset, the lattice around these defects undergoes tensile stress and the lattice parameter d (interplanar spacing) increases and leads to give more scattered (also known as diffuse X-ray scattering) intensity at slightly lower Bragg angles (yB) as d and sinyB are inversely proportional to each other in the Bragg equation (2dsinyB ¼nl, n and l being the order of reflection and wavelength, respectively, which are fixed). However, these point
-100
-50
0 Glancing angle [arc s]
Fig. 3. High resolution diffraction curve recorded for (100) plane for (a) conventional method grown crystal and (b) SR grown single crystals of LSMH.
defects with much lesser density as in the present case hardly give any effect on the performance of the devices based on such crystals. If the concentration is high, the FWHM would be much higher and often lead to structural grain boundaries [27]. Point defects up to some extent are unavoidable due to thermodynamical considerations and growth conditions [28]. Fig. 3(b) shows the RC for the SR-grown LSMH specimen recorded under identical experimental conditions as those of Fig. 3(a). The curve is quite sharp with a single peak and having FWHM of 800 , which is much lesser than 1800 , FWHM of conventional method grown crystal. The chemical bonding theory of single crystal growth shows that the growth shape is strongly related to crystallographic characteristics [31–36]. The lesser FWHM value of SR-grown specimen clearly indicates that the structural perfection of SR-grown crystal is much better than that of SEST-grown crystal. As far as the shape of the RC is concerned, the asymmetry resembles that of Fig. 3(a). This type of asymmetry in both conventional and SR-grown specimens indicates the possibility of loss of water of crystallization from the grown crystals. 3.2. Optical transmission studies The optical transmission spectrum of grown crystals was recorded in the wavelength range from 200 to 1100 nm using a Perkin Elmer lambda 35 UV–vis spectrometer. The transmittance of the conventional and SR method crystals was 42% and 54%, respectively. Fig. 4 shows the UV–vis spectrum of grown crystals. The transmittance studies were repeated several times for the
4
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
Fig. 4. UV–vis spectra of grown crystals.
different parts of the grown crystals and the same results were obtained. The above result indicates that the SR method grown crystal has higher transparency than the conventional method grown crystal. There are steps in the transmission curves between 300 and 400 nm. This is due to change of optics in the photometer. 3.3. Dielectric measurements The study of dielectric response gives more information about lattice dynamics and the electric field distribution and charge transport mechanism in the crystal [37]. Dielectric constant and dielectric loss measurements were performed on a LSMH single crystal using an LCR meter (Agilent). The opposite parallel faces of the crystals were coated with high-grade silver paste placed between two copper electrodes and thus a parallel plate capacitor was formed. The capacitance of the crystal was measured at the frequencies 1 kHz, 10 kHz, 100 kHz and 1 MHz and various temperatures (not shown in the figure). The dielectric constant of the crystal was calculated using the relation er ¼ Ccrys/Cair where Ccrys is the capacitance of the crystal and Cair is the capacitance of the same dimension of air. Fig. 5(a) shows the dielectric constant of conventional method and SR grown crystals as a function of temperature at 1 kHz frequency. It is observed from the figure that the dielectric constant of conventional method grown crystal slightly increases initially with increase in temperature; after that it decreases with increase in temperature. The dielectric constant of the materials is due to the contribution of electronic, ionic, dipolar and space charge polarizations, which depend on the frequencies [38,39]. At low frequencies, all these polarizations are generally active [40,41]. The large value of dielectric constant at low frequency is due to the presence of space charge polarization. Space charge contribution will depend on purity and perfection of the crystal and it has noticeable influence in the low frequency region. It is seen from the figure that the dielectric constant is higher in the SR method grown crystal than in the conventional method grown crystal. Fig. 5(b) shows the dielectric loss of the grown crystals at various temperatures and 1 kHz frequency. It is observed from the figure that the dielectric loss increases with increase in temperature for the grown crystals and dielectric loss is very low for the SR method grown crystal compared to the crystal grown by the conventional method. The characteristic of low dielectric loss with high frequencies for grown crystals suggests that the grown
Fig. 5. Frequency dependence of (a) dielectric constant and (b) dielectric loss at 1 kHz.
crystals possess enhanced optical quality with lesser defects and this parameter is of vital importance for nonlinear optical materials in their application [42]. 3.4. Measurement of micro-hardness Hardness is one of the important mechanical properties of the materials [43–45]. It can be used as a suitable measure of the plastic properties and strength of a material [46]. Stillwel [47] defined hardness as resistance against lattice destruction, whereas Ashby [48] defined it as an ability of a crystal to resist a structural breakdown under an applied stress. This resistance is an intrinsic property of the crystal. Hardness is generally taken as a ratio of applied load to the area of indentation. Both in the conventional method and SR method grown crystals (100) plane was selected for the micro-hardness studies. Vickers hardness measurements were made on the crystals using a Leitz–Wetzler hardness tester fitted with a diamond pyramidal indenter. The static indentations were carried out using a Vickers indenter for varying loads. For each load (p), several indentations were made and the average value of the diagonal length (d) was used to calculate the
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
Fig. 6. Vickers micro-hardness of grown crystals.
micro-hardness of the crystals. The Vickers micro-hardness number was determined using Hv¼1.8544p/d2 kg/mm2. A plot drawn between the hardness number and corresponding loads is shown in Fig. 6. It is observed from the figure that hardness of SR method grown crystal is more than the hardness of conventional method grown crystal. In the case of melt grown crystals, dislocations present in the crystal result in higher hardness [49]. However, in the case of solution grown crystal it is seen that defects present in the crystal result in lower hardness. This is due to the fact that in solution grown crystals micro-particles of solution that get into the crystal are responsible for crystal defects and the inclusion of solution microparticles into the crystal results in decrease of hardness. Hence SR method grown crystals are reported to have higher hardness than the conventional method grown crystal [50,51].
5
Hence a way to increase the efficiency is to focus the beam into the crystal. However this often leads to the breakdown of the materials, catastrophically damaging the maximum permissible power for a particular crystal defined as damage threshold. The laser damage threshold (LDT) of an optical crystal is an important factor affecting its applications. The laser damage threshold depends on specific heat, thermal conductivity, optical absorption, etc. If the material has high specific heat, the laser damage threshold will be high. If the material has a low laser damage threshold it severely limits its applications, even though it has many excellent properties like high optical transmittance and high SHG efficiency [53–55]. A Q-switched Nd: YAG laser operating at 1064 nm radiation was used. The laser was operated at the repetition rate of 10 Hz with the pulse width 0.05 s. For the LDT measurements a 1 mm diameter beam was focused on the sample with a 30 cm focal length lens. The multiple shots LDT measurements were made on conventional method grown and SR method grown samples. Initially 30 mJ was applied on the surface of conventional method grown crystal up to 30 s; no damage was observed. The energy was increased up to 85 mJ and no damage was observed. On applying 90 mJ a small dot was seen on the surface. Finally a crack was seen on applying 95 mJ for 30 s. Similarly for the SR method grown crystal the same procedure has been followed; initially 30 mJ was applied up to 30 s and no damage was observed. On applying 95 mJ a small dot was seen on
3.5. Piezoelectric studies The piezoelectric substance is one that produces an electric charge when a mechanical stress is applied. The piezoelectric property is related to the polarity of the material [52]. The crystals were subjected to piezoelectric characterizations. Finely polished basal surface of the crystal was coated with high grade silver paste and dried at 60 1C for various measurements. Piezoelectric charge coefficient (d33 pC/N) is an important parameter associated with piezoelectric material which is defined as the amount of charge developed at the opposite surfaces of the material when one unit force is applied across it. The piezoelectric charge coefficient d33 (pC/N) was measured using a piezometer (PM300, Piezo Test, UK). A constant tapping force of 0.25 N at a frequency of 110 Hz was applied on the electrode surfaces of as grown and poled LSMH crystals. Without poling the crystal the piezoelectric measurement was carried out for the grown crystal. Piezoelectric charge coefficient for the conventional method is 0.22 pC/N and for the SR method crystal, 0.29 pC/N. After poling under a field of 2 kV/cm for 20 min at room temperature, d33 value of the LSMH crystal grown by conventional method crystal is increased to 0.34 pC/N and the LSMH crystal grown by SR method has higher piezoelectric coefficient of 1.36 pC/N, i.e. four times higher than that of the conventional method. 3.6. Laser damage threshold In nonlinear optical crystals the harmonic conversion efficiency is proportional to the power of the fundamental beam.
Fig. 7. Laser damage profile of (a) conventional method grown crystal and (b) SR method grown crystal.
6
K. Boopathi et al. / Journal of Crystal Growth 345 (2012) 1–6
the surface and finally a crack was observed on applying 105 mJ up to 30 s. From the above observation the SR method grown crystal is known to possess higher laser stability. Fig. 7(a) and (b) shows laser damage profile of conventional and SR method grown crystals. The measured higher laser damage threshold indicates suitability of the crystal for device fabrication. 3.7. SHG measurements Qualitative measurement of the conversion efficiency of the crystals was determined using the powder technique developed by Kurtz and Perry [56]. The crystals were ground into powder and densely filled into a quartz cell. A fundamental wave with a pulse width of 9 ns, repetition frequency of 10 Hz, a beam diameter of 1 mm and a wavelength of 1064 nm radiated from the Nd: YAG laser source was focused on the sample by a lens with focal length of 120 nm. The powdered LSMH crystal sample was used for the SHG analysis. KDP crystal powdered to the identical size was used as a reference material in the SHG measurements. An emission of green light was seen in the sample. The transmitted fundamental wave was absorbed by a CuSO4 solution and the second harmonic signal was detected by a photomultiplier tube and displayed on a storage oscilloscope. The SHG efficiency of the LSMH is less than that of KDP.
4. Conclusions A single crystal of negatively soluble LSMH crystal was successfully grown by the unidirectional solution crystallization method. From the high resolution X-ray diffraction (HRXRD) studies, the crystalline perfection of the grown crystal was identified. The FWHM value of SR method grown LSMH is low compared to that of conventional method grown LSMH. The HRXRD result shows that the SR method grown crystal has good crystalline perfection. Higher transparency and higher hardness values have been achieved in the SR method grown crystal. Dielectric measurements reveal that dielectric constant is high and dielectric loss is low in the SR method grown crystal compared to the crystal grown by conventional method. The piezoelectric coefficient of SR method grown crystal is four times higher than that of the conventional method grown crystal. The laser damage threshold studies reveal that SR method grown crystal has higher laser stability. The SHG efficiency of LSMH has been confirmed by the powder Kurtz method.
Acknowledgment
[4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41]
The authors are thankful to Dr. G. Bhagavannarayana, Material Characterization Division, NPL, New Delhi, India, for providing HRXRD studies, Dr. C.K. Mahadevan, Department of Physics, S.T. Hindu college, India, for providing the dielectric measurement, Prof. K. Kishan Rao, Kakataya University, Warangal, for the microhardness measurements, Dr. Binay Kumar, Department of Physics and Astrophysics, University of Delhi, India, for the piezoelectric measurements and Dr. S. Kalainathan, VIT University, Vellore, for the laser damage threshold measurements facilities.
[42] [43]
References
[52]
[1] G.E. Zeiler, Zeitschrift fur Kristallograhie 89 (1934) 456. [2] A.C. Larson, L. Helmhotz, Journal of Chemical Physics 22 (1954) 2049. [3] R.P. Ozerov, L.E. Fykin, N.V. Rannev, G.S. Zhdanov, Doklady Akademii Nauk SSSR 148 (4) (1963) 1069;
[44] [45] [46] [47] [48] [49] [50] [51]
[53] [54] [55] [56]
R.P. Ozerov, L.E. Fykin, N.V. Rannev, G.S. Zhdanov, Soviet Physics Doklady 8 (1963) 131. W. Ackermann, Annals of Physics 46 (1972) 197. F. Spitzer, Doctoral Dissertation, University of Gottingen, 1938. W.P. Mason, Piezoelectric Crystals and Their Applications to Ultrasonics, Van Nostrand, New York, 1950; Moscow, IL, 1952. R. Bechmann, Proceedings of the Physical Society, London, Section B 64 (1952) 375. M.V. Hobden, Journal of Applied Physics 38 (1967) 4365. S.B. Lang, Physical Review B4 (1971) 3603. L. Bayarjargal, L. Bohaty, Acta Crystallographica A61 (2005) C393. J.O. Lundgren, et al., Journal of Chemical Physics 80 (1984) 423. L. Bayarjargal, Crystal Research and Technology 43 (2008) 1138. R.P. Canterford, et al., Journal of Physics C8 (1975) 1750. R. Priya, S. Krishnan, C. Justin Raj, S. Jerome Das, Crystal Research and Technology 44 (2009) 1272. Z. Czapla, M. Debska, E. Lebedeva, A. Pirozerski, Acta Physica Polonica A 99 (2001). L. Bohaty, P. Becker, H.J. Eichler, J. Hanuza, M. Maczka, K. Takaichi, K. Ueda, A.A. Kaminskii, Laser Physics 15 (2005) 1509. N.D. Gavrilova, E.G. Maksimov, V.K. Noviko, S.N. Drozhdin, Fizika Tverdogo Tela 27 (1985) 2597. G. Pasupathi, P. Philominathan, Materials Letters 62 (2008) 386. S. Podlojenov, J. Stade, M. Burianek, M. Muhulberg, Crystal Research and Technology 41 (2006) 344. C. Galez, Y. Mugnier, J. Bouillot, C. Rosso, Journal of Optical Materials 19 (2002) 33. P. Becker, S. Ahrweiler, P. Held, H. Scheneeberger, L. Bohaty, Crystal Research and Technology 38 (2003) 881. M.R. Suresh Kumar, H.J. Ravindhra, S.M. Dharmaprakash, Journal of Crystal Growth 306 (2007) 36. K. Sankaranaryanan, P. Ramasamy, Journal of Crystal Growth 280 (2005) 467. B.W. Batterman, H. Cole, Reviews of Modern Physics 36 (1964) 681. K. Lal, G. Bhagavannarayana, Journal of Applied Crystallography 22 (1989) 209. G. Bhagavannarayana, A. Choubey, Yu.V. Shubin, Krishan Lal, Journal of Applied Crystallography 38 (2005) 448. G. Bhagavannarayana, G. Parthiban, S. Meenakshisundaram, Crystal Growth and Design 8 (2008) 446. G. Bhagavannarayana, P. Rajesh, P. Ramasamy, Journal of Applied Crystallography 43 (2010) 1372. G. Bhagavannarayana, S.K. Kushwaha, Shakir Mohd, K.K. Maurya, Journal of Applied Crystallography 44 (2011) 122. K. Senthilkumar, S. MoorthyBabu, G. Bhagavannarayana, Journal of Applied Crystallography 44 (2011) 313. Ren Xiue, Xu Dongli, Xue Dongfeng, Journal of Crystal Growth 310 (2008) 2005–2009. Xue Dongfeng, Xu Dongli, Journal of Crystal Growth 310 (2008) 1385–1390. Xiaoxing Yan, Dongli Xu, Dongfeng Xue, Acta Materialia 55 (2007) 5747–5757. D.L. Xu, D.F. Xue, Journal of Crystal Growth 286 (2006) 108–113. Xue Dongfeng, Zou Longjiang, Wang Lei, Yan Xiaoxing, Modern Physics Letters B 23 (2009) 3761–3768. Dongfeng Xue, Xiaoxing Yan, Lei Wang, Powder Technology 19 (2009) 98–106. S. Dinakaran, S. Jerome Das, Journal of Crystal Growth 310 (2008) 410. D. Xue, N. Iyi, N.K. Kitamura, Journal of Applied Physics. 92 (2002) 4638–4643. D. Xue, K. Kitamura, Solid State Communications 122 (2002) 537–541. M. Meena, C.K. Mahadevan, Crystal Research and Technology 43 (2008) 166. S.M. DharmaPrakash, P.Mohan Rao, Journal of Materials Science Letters 8 (1989) 1167. C. Balarew, R. Duhlew, Journal of Solid State Chemistry 55 (1984) 1. Xingtao Keyan Li, Fangfang Wang, Zhang, Dongfeng Xue, Physical Review Letters 100 (2008) 235504. Ke Yan Li, Dong Feng Xue, Chinese Science Bulletin 54 (2009) 131–136. Keyan Li, Dongfeng Xue, Physica Scripta T139 (2010) 014073. C.C. Desai, J.L. Rai, Bulletin of Materials Science 5 (1983) 453. C.W. Stillwel, Crystal Chemistry, McGraw Hill, New York, 1938. N.A. Ashby, Journal of Nuclear Engineering 6 (1951) 33. U.V. Subba Rao, V. Hari Babu, Pramana 11 (1978) 149. Urit Charoen-In, P. Ramasamy, P. Manyum, Journal of Crystal Growth 312 (2010) 2369. D. Nagaraju, P.V. Raja Shekar, T. Bhaskar Rao, K.Kishan Rao, Materials Letters 64 (2010) 267. H. Nakatani, W.R. Bosenberg, L.K. Cheng, C.L. Tang, Applied Physics Letters 53 (1988) 2587. J.N. Sherwood, Pure and Applied Optics 7 (1998) 229. I.V. Kityk, B. Marciniak, A. Mefleh, Journal of Physics D: Applied Physics 34 (2001) 1. Ge Wenwei, et al., Journal of Alloys and Compounds 456 (2008) 503. S.K. Kurtz, T.T. Perry, Journal of Applied Physics 44 (1968) 455.