Crystal Growth and Glass-Like Thermal Conductivity of Ca 3 RE 2 ( BO 3 ) 4 ( RE = Y , Gd , Nd ) Single Crystals

Crystal growth and thermal properties of binary borates, Ca3RE2(BO3)4 (RE = Y, Gd, Nd), are considered promising crystals for laser applications. These single crystals were grown by the Czochralski method. The crystal and defect structure were characterized. Volumetric chemical methods without prior separation of the components were developed and applied for the determination of the dependence of chemical compositions of the crystals on the growth conditions. The thermal conductivity was investigated in the 50–300 K range. The character of the temperature dependence of thermal conductivity was found to be similar to that of glass. The possible reasons of the observed features of the thermal conductivity were analyzed.


Introduction
Crystal media with disordered structures (where two or more cations can share one type of site) are promising for laser application and have a number of advantages.The structure disordering leads to inhomogeneous broadening of spectral bands of the activator ions.In spite of thermal drift of light-emitting diode (LED) pumping for diodes emitting from 800 to 2000 nm, efficient pumping of the disordered medium could be achieved in the wide range of LED temperatures because of relatively wide absorption bands.Due to relatively wide luminescence bands, the wavelength of laser emission can be tuned in a wide range.For example, in a previous study [1], for disordered Nd-doped binary vanadates the duration of transform-limited pulses has been estimated to be ∆τ = 130-160 fs at 1.07 µm.Therefore, the disordered media could also be a good solution for mode-locked lasers.Ca 3 RE 2 (BO 3 ) 4 (RE = rare earth element) single crystals have been considered promising materials for such an application.The transform-limited pulses of 251 fs have been generated [2].
The structure of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) compounds is orthorhombic (space group Pnma) and consists of isolated BO 3 triangles, and of rare-earth (RE)-oxygen and calcium-oxygen polyhedrons.The RE cations partially occupy three non-equivalent crystallographic Ca sites.A number of papers have been published where spectral-kinetic properties of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) crystals doped with Nd, Yb, and Er/Yb were studied [3][4][5][6].The lasing operation under flash lamp and laser (LED and Ti/sapphire laser) pumping was also demonstrated for different regimes [2,4,[7][8][9].It was shown that the lasers based on these crystals are promising for many scientific tasks and practical uses.However, investigations of these materials are at an early stage; as the thermal properties of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) crystals have not yet been determined.
The Czochralski method is one of the most widely used ones in the industrial production of large single crystals of optical quality suitable for laser applications; for examples, see [10].In particular, this technique was used for the growth of pure, Nd, Yb, Er/Yb-doped Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) single crystals [11].Recently, our team has reported [12] the Czochralski growth of Ca 3 Nd 2 (BO 3 ) 4 crystals.
The defect structure of the given crystal may include a chemical composition inhomogeneities, mosaicity and block structure with low-angle (a fraction of degree) and large angle misorientation.The presence of such defects depends on the crystal growth technique, and on the growth conditions.The efficiency of the lasing operation depends on the crystal quality.Nowadays, the nature of the defects of the borates is not well recognized.Thus, one of the questions is related to the characterization of typical defects in Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) crystals grown by the Czochralski method.
The design of the laser apparatus (optical scheme and type of pumping), the output radiation parameters, and the operation mode depend on thermo-physical properties of the laser gain medium.Another question to be answered for the laser application of the medium is related to its thermal properties.One of the main parameters characterizing the laser gain medium is the thermal conductivity, k.The thermal conductivity of laser gain medium defines the temperature distribution of the active laser element and, consequently, affects the shape of the induced heat lens.Another problem is connected to achieving an effective heat removal from the active element of a high power laser.
The theories of thermal conductivity [13] could be helpful in prediction and analysis of thermal conductivity of materials suitable for lasers.However, the thermal conductivity of multicomponent material cannot be precisely calculated.The thermal conductivity of solids for the low temperature range is sensitive to defects of crystal lattice so it can serve a tool for the characterization of media.Therefore, experimental investigation of the temperature dependence taking into account the peculiarities of the crystal structure and the growth technique is of considerable scientific and practical interest.
This work is devoted to the description of the crystal growth conditions, the characterization of the chemical compositions, and the study of the thermal conductivity of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, Nd) single crystals.

Experimental
CaCO 3 (99.99%),RE 2 O 3 (99.99%)(RE = Y, Gd, Nd) and B 2 O 3 (99.95%)compounds were used as reagents for the solid state synthesis of the charge.The stoichiometric mixture of the initial reagents was placed into a platinum crucible.The mixture of a total mass of 300 g was heated at the rate of 50 • C/h to 110 • C, 230 • C, 450 • C, and 750 • C and kept for 10 h at each temperature.The compound formation was carried out according to the reaction: The obtained material was finely ground.For crystal growth, the charge was transferred to another crucible.Pure Ca 3 RE 2 (BO 3 ) 4 crystals were grown by the Czochralski method using an automated and equipped with a weight control system "Kristall 3M" puller.The growth processes was carried out in inert (argon) and oxygen containing (air) atmospheres.Ir and Pt crucibles with the dimensions of a 45 mm diameter and a 50 mm length were used for argon and air atmospheres, respectively.The pulling and rotation rates were 1.5 mm/h and 20 rpm, respectively.The axial temperature gradient at the crystal-melt interface was 50 • C/cm.The crystals were grown along the [001] crystallographic axis.The crystals investigated in the present study were grown at the same conditions: at fixed temperature gradient, rotation speed, and pulling rate.The crystals had a diameter of up to 20 mm and a length of up to 90 mm (Figure 1).The grown crystals were examined by X-ray diffraction (XRD).No impurity phases and gas bubble inclusions were detected.The next sets of the crystals were grown: the set of Ca3Y2(BO3)4 crystals grown in air; the set of Ca3Y2(BO3)4 crystals grown in argon; the set of Ca3Nd2(BO3)4 crystals grown in argon; the set of Ca3Gd2(BO3)4 crystals grown in air; the set of Ca3Gd2(BO3)4 crystals grown in argon.
To determine the basic host elements of Ca3RE2(BO3)4 borates, volumetric chemical methods were developed.The single crystals were dissolved in a mixture of nitric and hydrochloric acids.For determination of the rare earth elements (Y or Nd, and Gd) and the calcium concentrations, the complexometric method [14] was used.For the Ca3Y2(BO3)4 crystal, the yttrium concentration was determined by means of ethylenediamine acetic acid sodium salt (EDTA) titration in urotropin medium containing xylenol orange indicator at 5.6-5.7 pH.In the aliquot part of the solution, the aggregated concentration of yttrium and calcium was determined using back titration of EDTA excess by zinc sulfate in ammonium chloride-buffered medium at 10 pH.The calcium content was calculated as a difference between the aggregated concentration and the Y concentration.For Ca3Nd2(BO3)4 and Ca3Gd2(BO3)4 crystals, the calcium concentration was determined by means of 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone extraction.Boron was determined by means of the alkalimetric method.Yttrium, neodymium, and gadolinium were masked by the addition of EDTA.EDTA concentration was equimolar to the stoichiometric concentration of yttrium or gadolinium.The titration of boric glycerol acid was performed with a phenolphthalein indicator Powder XRD data were collected using X'PERT MPD Alpha1 Pro diffractometer employing CuKα1 radiation.The structures of the crystals was refined by the Rietveld method (software "Fullprof 2k v.5.30" [15]).High resolution diffraction was performed using an X'Pert MRD diffractomete equipped with primary beam optics based on an multilayer parabolic X-ray mirror and a four-bounce asymmetric Ge(022) monochromator.CuKα1 radiation was used.The optics of the diffracted beam included a three-bounce Ge(022) analyzer.
The dependence of the thermal conductivity k(T) was investigated in the range of 50-300 К by means of the method of stationary longitudinal flow.The facilities and procedure of the measurements are described in detail in [16].To provide flatness of the isothermal surfaces, a resistive heater was fixed on the end face of the sample.The measurement error of the thermal conductivity did not exceed ±6%.The specimens for chemical analysis, XRD, and thermal conductivity study were cut from the cylindrical part of the crystal.

Crystal Structure
Investigation of the crystal structure of Ca3RE2(BO3)4 (RE = Y, Gd, Nd) borate crystals by means of powder diffraction method confirms that these crystals are of orthorhombic (space group Pnma).The unit cell parameters are presented in Table 1.For Ca3Gd2(BO3)4, and Ca3Nd2(BO3)4, the reciprocal space map indicate a compositional homogeneity, as no lattice parameter variation is observed.For Ca3Y2(BO3)4, the reciprocal space map shows a weak reflection of intensity of the order of 2% with the lattice parameter a of a higher value, 7.170 Å (Figure 2); through additional scanning the sample, it was found that this effect is due to a small misoriented grain located at the very side of the sample.
As can be seen from Table 1, the unit cell size has been observed to increase with an increasing size of RE cation (the ionic radius, RY (1.019 Å) → RNd (1.053 Å) → RGd (1.109 Å)).The parameters of To determine the basic host elements of Ca 3 RE 2 (BO 3 ) 4 borates, volumetric chemical methods were developed.The single crystals were dissolved in a mixture of nitric and hydrochloric acids.For determination of the rare earth elements (Y or Nd, and Gd) and the calcium concentrations, the complexometric method [14] was used.For the Ca 3 Y 2 (BO 3 ) 4 crystal, the yttrium concentration was determined by means of ethylenediamine acetic acid sodium salt (EDTA) titration in urotropin medium containing xylenol orange indicator at 5.6-5.7 pH.In the aliquot part of the solution, the aggregated concentration of yttrium and calcium was determined using back titration of EDTA excess by zinc sulfate in ammonium chloride-buffered medium at 10 pH.The calcium content was calculated as a difference between the aggregated concentration and the Y concentration.For Ca 3 Nd 2 (BO 3 ) 4 and Ca 3 Gd 2 (BO 3 ) 4 crystals, the calcium concentration was determined by means of 1-phenyl-3-methyl-4-benzoyl-5-pyrazolone extraction.Boron was determined by means of the alkalimetric method.Yttrium, neodymium, and gadolinium were masked by the addition of EDTA.EDTA concentration was equimolar to the stoichiometric concentration of yttrium or gadolinium.The titration of boric glycerol acid was performed with a phenolphthalein indicator Powder XRD data were collected using X'PERT MPD Alpha1 Pro diffractometer employing CuK α1 radiation.The structures of the crystals was refined by the Rietveld method (software "Fullprof 2k v.5.30" [15]).High resolution diffraction was performed using an X'Pert MRD diffractomete equipped with primary beam optics based on an multilayer parabolic X-ray mirror and a four-bounce asymmetric Ge(022) monochromator.CuK α1 radiation was used.The optics of the diffracted beam included a three-bounce Ge(022) analyzer.
The dependence of the thermal conductivity k(T) was investigated in the range of 50-300 K by means of the method of stationary longitudinal flow.The facilities and procedure of the measurements are described in detail in [16].To provide flatness of the isothermal surfaces, a resistive heater was fixed on the end face of the sample.The measurement error of the thermal conductivity did not exceed ±6%.The specimens for chemical analysis, XRD, and thermal conductivity study were cut from the cylindrical part of the crystal.

Crystal Structure
Investigation of the crystal structure of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, Nd) borate crystals by means of powder diffraction method confirms that these crystals are of orthorhombic (space group Pnma).The unit cell parameters are presented in Table 1.For Ca 3 Gd 2 (BO 3 ) 4 , and Ca 3 Nd 2 (BO 3 ) 4 , the reciprocal space map indicate a compositional homogeneity, as no lattice parameter variation is observed.For Ca 3 Y 2 (BO 3 ) 4 , the reciprocal space map shows a weak reflection of intensity of the order of 2% with the lattice parameter a of a higher value, 7.170 Å (Figure 2); through additional scanning the sample, it was found that this effect is due to a small misoriented grain located at the very side of the sample.a : the X-ray diffraction data for the compound produced by solid state synthesis; b : the X-ray diffraction data for the ground single crystal.(X): calculated from positions of 600, 462, and 606 reflections (Figure 2).(Y): calculated from positions of 512, 048, and 006 reflections at the reciprocal space map (Figure 2).(Z): calculated from positions of 6 5 2, 0 18 0, and 0 15 5 reflections at the reciprocal space map (Figure 2).($) Data for a small grain located at a sample side.
parameter variation among the (sparse) experimental results of different laboratories show that the range of their relative values is about 0.5% (the changes are larger for doped crystals).These variations express the influence of factors such as material purity, composition, and preparation.In particular, the Czochralski growth technique could lead to some excess from the stoichiometry of the grown crystal, visible in the lattice parameter values.In the present study, the discrepancies are marginal and do not indicate significant composition changes.a : the X-ray diffraction data for the compound produced by solid state synthesis; b : the X-ray diffraction data for the ground single crystal.(X): calculated from positions of 600, 462, and 606 reflections (Figure 2).(Y): calculated from positions of 512, 048, and 006 reflections at the reciprocal space map (Figure 2).(Z): calculated from positions of , , and reflections at the reciprocal space map (Figure 2).($) Data for a small grain located at a sample side.The high-resolution diffraction shows small differences in the macroscopic defect structure of the three crystals.The samples were circular plates cut vertically to the growth axis (RE = Y and Gd) and parallel to the axis (RE = Nd).The rocking curves measured for areas of about 20 mm 2 for Ca3RE2(BO3)4 have FWHM values of 71.5″, 51.8′, and 146.3″ for RE = Y, Gd, and Nd, respectively (Figure 3), showing that as for the block structure, mosaicity and homogeneity, the best crystal among the studied ones is Ca3Gd2(BO3)4.The Ca3Gd2(BO3)4 and Ca3Nd2(BO3)4 crystal demonstrate a fully uniform composition; for both, in the irradiated area of the sample, a presence of more than one crystal block is observed.For Ca3Gd2(BO3)4, a difference in orientation discrepancy of the two blocks is 0.04°; the second block is of a minor size (<5% of the irradiated surface).For the Ca3Nd2(BO3)4 crystal, four monocrystalline blocks were observed with misorientations ranging up to 1.5° (here, the block structure can be observed by eye).For Ca3Y2(BO3)4, two blocks are found with misorientation of about 0.1°.However, the second block is a very small grain (the area of about 2%) located at the As can be seen from Table 1, the unit cell size has been observed to increase with an increasing size of RE cation (the ionic radius, R Y (1.019 Å) → R Nd (1.053 Å) → R Gd (1.109 Å)).The parameters of unit cell of Ca 3 RE 2 (BO 3 ) 4 crystals differ marginally from those available in the literature for RE = Y [17] and RE = Gd [18,19]; data for RE = Nd have not been reported yet.A comparison of lattice parameter variation among the (sparse) experimental results of different laboratories show that the range of their relative values is about 0.5% (the changes are larger for doped crystals).These variations express the influence of factors such as material purity, composition, and preparation.In particular, the Czochralski growth technique could lead to some excess from the stoichiometry of the grown crystal, visible in the lattice parameter values.In the present study, the discrepancies are marginal and do not indicate significant composition changes.
The high-resolution diffraction shows small differences in the macroscopic defect structure of the three crystals.The samples were circular plates cut vertically to the growth axis (RE = Y and Gd) and parallel to the axis (RE = Nd).The rocking curves measured for areas of about 20 mm 2 for Ca 3 RE 2 (BO 3 ) 4 have FWHM values of 71.5", 51.8 , and 146.3" for RE = Y, Gd, and Nd, respectively (Figure 3), showing that as for the block structure, mosaicity and homogeneity, the best crystal among the studied ones is Ca 3 Gd 2 (BO 3 ) 4 .The Ca 3 Gd 2 (BO 3 ) 4 and Ca 3 Nd 2 (BO 3 ) 4 crystal demonstrate a fully uniform composition; for both, in the irradiated area of the sample, a presence of more than one crystal block is observed.For Ca 3 Gd 2 (BO 3 ) 4 , a difference in orientation discrepancy of the two blocks is 0.04 • ; the second block is of a minor size (<5% of the irradiated surface).For the Ca 3 Nd 2 (BO 3 ) 4 crystal, four monocrystalline blocks were observed with misorientations ranging up to 1.5 • (here, the block structure can be observed by eye).For Ca 3 Y 2 (BO 3 ) 4 , two blocks are found with misorientation of about 0.1 • .However, the second block is a very small grain (the area of about 2%) located at the very side of the crystal sample.The difference in 2θ is 0.25 • ; the small grain has a larger value of lattice parameter a.

Chemical Composition
Since the thermal conductivity of solids for the low temperature range is sensitive to defects of crystal lattice, the chemical analysis of the grown crystals could be performed.According to the chemical analysis date for all crystals grown both in argon and air atmospheres, the deviation from the stoichiometric composition was determined.The goal of this analysis was to check the excess or deficit of cationic components (a deviation from stoichiometry would be an indicator of point defect presence).In the deviation of the Ca/RE ratio from the stoichiometric one and the boron deficit were studied.
For all Ca3Y2(BO3)4 crystals grown both in argon and air atmospheres, the Ca/Y ratio fluctuated in the frames of 10 wt %, the boron deficit did not exceed 0.5 wt % at the accuracy of measurements ±0.1 wt %.For Ca3Nd2(BO3)4 crystals grown in argon, the deviation of the Ca/Nd ratio did not exceed 6 wt % and the boron concentration was close the stoichiometric one.For all Ca3Gd2(BO3)4 crystals grown both in argon and air atmospheres, the deviation of the Ca/Gd ratio reached 7 wt %.The boron deficit was in the 0-0.3 wt % range.These observations coincide with those from high-resolution diffraction, described in the above paragraph.
Moreover, for the Ca3Y2(BO3)4 crystal with the length of 90 mm grown in argon, the distribution of the host element was investigated.The measurements of the host element content were made with a 1 cm step and the inhomogeneous composition of the crystal grown under these conditions was established.The maximum deviation from the stoichiometric Ca/Y ratio was observed for the upper (no more 5%) and bottom (up to 9%) cones of the crystal.For the cylindrical part of the crystal, the

Chemical Composition
Since the thermal conductivity of solids for the low temperature range is sensitive to defects of crystal lattice, the chemical analysis of the grown crystals could be performed.According to the chemical analysis date for all crystals grown both in argon and air atmospheres, the deviation from the stoichiometric composition was determined.The goal of this analysis was to check the excess or deficit of cationic components (a deviation from stoichiometry would be an indicator of point defect presence).In particular, the deviation of the Ca/RE ratio from the stoichiometric one and the boron deficit were studied.
For all Ca 3 Y 2 (BO 3 ) 4 crystals grown both in argon and air atmospheres, the Ca/Y ratio fluctuated in the frames of 10 wt %, the boron deficit did not exceed 0.5 wt % at the accuracy of measurements ±0.1 wt %.For Ca 3 Nd 2 (BO 3 ) 4 crystals grown in argon, the deviation of the Ca/Nd ratio did not exceed 6 wt % and the boron concentration was close the stoichiometric one.For all Ca 3 Gd 2 (BO 3 ) 4 crystals grown both in argon and air atmospheres, the deviation of the Ca/Gd ratio reached 7 wt %.The boron deficit was in the 0-0.3 wt % range.These observations coincide with those from high-resolution diffraction, described in the above paragraph.Moreover, for the Ca 3 Y 2 (BO 3 ) 4 crystal with the length of 90 mm grown in argon, the distribution of the host element was investigated.The measurements of the host element content were made with a 1 cm step and the inhomogeneous composition of the crystal grown under these conditions was established.The maximum deviation from the stoichiometric Ca/Y ratio was observed for the upper (no more 5%) and bottom (up to 9%) cones of the crystal.For the cylindrical part of the crystal, the deviation was in frames of 3%.The minor boron deficit was observed, but the boron content did not vary along the crystal.
For all crystals grown, both in argon and air, the observed deviation of the Ca/RE ratio from the stoichiometric composition leads to the deficit of positive charge.Obviously, for compensation of the positive charge deficit, the defects in the anion sublattice should be formed: where V B and V O are the boron and oxygen vacancies, respectively.According to the chemical analysis data, the boron deficit was determined for Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) crystal grown both in argon and air.The boron deficit grew for the crystals grown in air.Obviously, the oxygen vacancies dominate in the crystals grown in argon.The concentration of boron vacancies is higher in the crystals grown in air due to more intense boron evaporation from the surface of the melt in the medium containing acid vapors (air) [23].
Thus, the typical defect of the crystal grown by direct crystallization from the melt by means of the Czochralski method is the deviation from the stoichiometric composition.The Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, and Nd) crystals grown in argon with the composition the closest to the stoichiometric one chosen for the thermal conductivity study.Their element composition is presented in Table 2.For comparison, the concentrations of host elements for the best Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd) crystals grown in air atmosphere sets are also shown.

Thermal Conductivity
Unexpectedly, the temperature dependences k(T) of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, Nd) crystals, k(T), is found to be typical for fully disordered media, e.g., glass, but not for ordered ones (crystals).The absolute values of the obtained thermal conductivity are also typical for glass.At room temperature, they are within a narrow range between 0.9 ± 0.05 W/(m•K) and 1.04 ± 0.06 W/(m•K).(Figure 4).
Unexpectedly, the temperature dependences k(T) of Ca3RE2(BO3)4 (RE = Y, Gd, Nd) crystals, k(T), is found to be typical for fully disordered media, e.g., glass, but not for ordered ones (crystals).The absolute values of the obtained thermal conductivity are also typical for glass.At room temperature, they are within a narrow range between 0.9 ± 0.05 W/(m•К) and 1.04 ± 0.06 W/(m•К).(Figure 4).(1) The A, B, C, and D coefficients for the investigated crystals are quoted in Table 3.The change over from one cation to the cations with another mass and ionic radius does not essentially affect neither the absolute value nor the temperature behavior of the thermal conductivity.The monotonic increasing dependences k(T) may be interpreted as follows.According to generally accepted ideas of phonon heat transfer, the thermal conductivity may be presented by the Debye expression: where C is the heat capacity of a unit of volume, ν is the average velocity of sound phonon propagation, and l is the average length of phonon free path [24].At the intense phonon scattering on the structure defects, l approaches its least value and depends slightly on the temperature.Because the sound velocity weakly depends on the temperature, the rise of heat capacity at rather low temperatures defines the increase in the thermal conductivity.The Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, Nd) crystals have practically the same value of thermal conductivity, therefore we may conclude that the substitution of RE cations does not essentially affect phonon scattering in comparison with the intense phonon scattering on other structure inhomogeneities.The same temperature behavior of thermal conductivity and the low values of thermal conductivity of ~1 W (m•K) at room temperature were observed for binary Ca 9 RE(VO 4 ) 7 (RE = La, Nd, Gd) vanadate crystals, which are also characterized by the inhomogeneous composition [25].The thermal conductivity of the crystal is directly connected with its thermal capacity and elastic characteristics.Thus, we can conclude that these parameters are almost identical for the investigated crystals.
the crystal sample.The difference in 2θ is 0.25°; the small grain has a larger value of lattice parameter a.

Figure 4 .
Figure 4. Temperature dependence of the thermal conductivity k(T) for Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, Nd) crystals along the c axis.

Table 1 .
Unit cell parameters of Ca 3 RE 2 (BO 3 ) 4 (RE = Y, Gd, Nd) crystals derived from powder and high-resolution (HR) XRD.The values obtained from high-resolution diffraction are given in italics; these values generally agree with those obtained from the powder diffraction; several discrepancies are attributed to the peak shifts occurring for strongly asymmetric reflections.

Table 1 .
Unit cell parameters of Ca3RE2(BO3)4 (RE = Y, Gd, Nd) crystals derived from powder and high-resolution (HR) XRD.The values obtained from high-resolution diffraction are given in italics; these values generally agree with those obtained from the powder diffraction; several discrepancies are attributed to the peak shifts occurring for strongly asymmetric reflections.