Lattice Vibrations and Thermal Properties of Stoichiometric KYb(WO4)2 Crystal Hongyang Zhao,†,⊥ Jiyang Wang,*,† Jing Li,† Guogang Xu,† Huaijin Zhang,† Lili Yu,† Wenlan Gao,‡ Hairui Xia,‡ and Robert I. Boughton#
CRYSTAL GROWTH & DESIGN 2008 VOL. 8, NO. 11 3978–3983
State Key Laboratory of Crystal Materials, Shandong UniVersity, Jinan 250100, China, School of Physics and Microelectronics, Shandong UniVersity, Jinan 250100, China, and Department of Physics and Astronomy, Bowling Green State UniVersity, Bowling Green, Ohio, 43403 ReceiVed January 8, 2008; ReVised Manuscript ReceiVed June 23, 2008
ABSTRACT: Single crystal KYb(WO4)2 (KYbW) has been grown by the top-seeded solution growth (TSSG) method. Polarized Raman and infrared spectra have been recorded at room temperature. The lattice vibration modes were calculated, and the strongest peaks appear at 760 and 908 cm-1 with a line-width ∆ωR of 14.2 and 10 cm-1, corresponding to relaxation times of 0.747 and 1.061 ps, respectively. This makes KYbW attractive for stimulated Raman scattering (SRS) applications and for use in the picosecond regime. Differential thermal analysis and thermal gravimetric analysis curves, high-temperature X-ray diffraction patterns, specific heat, thermal expansion and thermal conductivity have been studied. The thermal expansion anisotropy of KYbW is weaker than that of KGd(WO4)2 (KGW), but stronger than that of KLu(WO4)2 (KLuW). The thermal diffusivity along the c-axis is large (λc > λa > λb). The results are consistent with the anisotropic structure of crystalline KYbW.
I. Introduction The monoclinic double tungstate crystals KRe(WO4)2 (KReW) are widely used laser host materials. They have been attracting ever more attention in optical applications as efficient laser media. They especially exhibit large χ3 nonlinearities that are useful for stimulated Raman scattering (SRS).1 The Yb3+ ion that can be pumped by InGaAs lasers is favorable as a potential dopant in the 1 µm region.2 Recently, highly efficient laser operation has been demonstrated for Yb: KReW with Re ) Y, Gd, and Lu.3-10 Stoichiometric laser materials are excellent for use in laser devices with thin disk or waveguide designs and are quite suitable for diode laser pumping.11 It was therefore decided to attempt the growth of crystalline KYb(WO4)2 (KYbW), and the attempt was successful. Polarized Raman and IR spectra and the thermal properties were analyzed. Raman studies are useful for the analysis of the important lattice phonons. The IR spectrum was used as a supplement to assign the modes more accurately. As a laser material, information about the thermal properties that contribute to heat generation and therefore to laser stability are crucial. Differential thermal analysis (DTA)/thermal gravimetric analysis (TA), high-temperature X-ray diffraction patterns, specific heat, thermal expansion and thermal diffusion were measured. DTA/ TG and high-temperature X-ray diffraction patterns are useful for the analysis of phase transition and structure. For monoclinic KYbW crystal, the thermal expansion and thermal conductivity are very important not only for crystal growth but also for the design of laser devices.
II. Experimental Procedures Crystalline KYb(WO4)2 was grown by the TSSG method using K2W2O7 as the solvent. The reagents used were K2CO3, WO3, and Yb2O3 (99.99% purity). The molar ratio of solute to solvent is 1:4. * Corresponding author. Tel: +86 53188564963. E-mail:
[email protected]. † State Key Laboratory of Crystal Materials, Shandong University. ‡ School of Physics and Microelectronics, Shandong University. # Bowling Green State University. ⊥ Also affiliated with Department of Material Science and Engineering, Shanghai Institute of Technology.
The raw materials were mixed in a platinum crucible and heated at a temperature about 150 °C higher than the saturation temperature. The saturation temperature was determined by the tentative seed method. The raw materials were kept under these conditions for 3 days to homogenize the solution. A seed crystal of KYbW oriented along the c-axis was put into the melt, and then rotated at 30 rpm in the center of the crucible. The rate of cooling was 1-3 °C /day, and after 30 days a KYbW crystal was obtained. KYbW is a member of the monoclinic KReW family with a space group of C2/c. We have listed five different systems of coordinates;12 they are the physical coordinates (X, Y, Z), crystallographic coordinates (a, b, c), refractive-index coordinates (ng, nm, np) corresponding to (nz, ny, nx), thermal-expansion coordinates (RI, RII, RII), and thermalconductivity coordinates (k1, k2, k3). When we study the different properties of the crystals, the selection of the appropriate coordinate system is very important. According to the standards of the U. S. Institute of Radio Engineers (IRE),13 we selected Y | b-axis, Z | c-axis and X ⊥ bc plane as the physical coordinates. Among them, the crystallographic b-axis is the C2 symmetry axis. The crystal was carefully cut and polished along the X, Y and Z axes to a size of 4.4 × 5.4 × 6.5 mm3 for measuring the polarized Raman spectrum. Two wafers cut along the a, b, c* directions and along the a*, b, c directions with sizes of 6.1 × 7.1 × 5.1 mm3 and 4.4 × 5.4 × 6.5 mm3, respectively, were polished and used to measure the thermal expansion along a, a*, b, c, c* with lengths of 6.1, 4.4, 7.1, 5.4, and 5.1 mm. Five pieces of size of 6.0 × 6.0 × 2.0 mm3 were cut to measure the thermal diffusion coefficient. The room temperature Raman spectrum was measured using a JASCONRS-1000DT micro Raman spectrophotometer with a double scan from 50 to 1200 cm-1. The instrument has a slit width of 100 µm and a spectral resolution of 2 cm-1. The powder transmission spectrum was recorded from 50 to 1200 cm-1 on a Nicolet-Nexus 670 FTIR spectrophotometer using KBr as the reference sample. DTA and TA were studied using a Diamond TG/DTA apparatus that was made by the Perkin-Elmer Company. High-temperature X-ray powder diffraction patterns were measured using a D8 X-ray diffraction instrument made by the Bruker Company. The powder sample weighed 33.30 g and was kept in an Al2O3 crucible. It was heated at a constant rate of 20 K/min. The thermal expansion was measured using a thermalmechanical analyzer made by the Perkin-Elmer Company. The first step in the measurement procedure was to initialize the probe. After that, the initial state, such as the initial temperature and the heating rate were set. Then, the sample was placed on the sample plate with the probe touching the sample surface. The initial height was recorded and the measurements were initiated. The samples were heated at a constant rate of 5 °C /min from 28 to 500 °C. The thermal diffusion
10.1021/cg800021h CCC: $40.75 2008 American Chemical Society Published on Web 09/26/2008
Properties of Stoichiometric KYb(WO4)2 Crystal
Figure 1. Raman spectra of symmetry Ag in KYbW at room temperature from 50 to 1200 cm-1 with scattering configurations j , X(YY)X j , Y(XX)Yj , and Y(XZ)Yj . X(ZZ)X
Figure 2. Raman spectra of symmetry Bg recorded in KYbW. coefficient was measured between 30 and 300 °C using a laser flash apparatus (Netzch LFA 447 Nanoflash).
III. Raman and Infrared Spectroscopy A. Raman Spectroscopy. The structure of KYbW has been previously recorded.11 It crystallizes in the monoclinic space group C2/c. The unit cell parameters are a ) 10.590(4) Å, b ) 10.290(6) Å, c ) 7.478(2) Å, V ) 130.70(2)°, and Z ) 4.11 The W atoms in the 8f position of the C1 symmetry are coordinated by six oxygen atoms.14 According to the crystal structure and The International Table for Crystallography,15 the atomic Wyckoff position is 4e for K and Yb and 8f for the 4 O atoms. KYbW crystallizes in the point group C2h that contains two formulas in the primitive cell.16 Thus there are 24 atoms in the primitive cell and 72 degrees of freedom. Following the method reported in previous papers,12,17 the geometrical scattering configurations were confirmed and the Raman spectra of KYbW corresponding to symmetry species Ag and Bg were observed and are shown in Figures 1 and 2. It can be seen that the Raman peaks at high wavenumber are stronger than the peaks at low wavenumber. The appearance of the stronger and
Crystal Growth & Design, Vol. 8, No. 11, 2008 3979
Figure 3. Room temperature IR spectrum of crystalline KYbW.
more numerous Raman peaks reveal the many anionic groups and their distortions in the primitive cell and also have implications for potential nonlinear properties of the crystal.13,18 The study by this means of the anionic groups as important units in the crystal is crucial. In crystalline KYbW, the intermolecular interactions between the tungstate ions lead to the formation of a polymeric structure consisting of
oxygen bridges coupling the WO6 polyhedra.19 The WO6 octahedral polyhedron is important in the lattice vibration spectrum. It possesses a vibration spectrum that is called the characteristic spectrum.20 There are 15 internal vibrational degrees of freedom, or 6 kinds of normal vibrational modes in an octahedral molecule MO6 with the Oh symmetry. The six kinds of normal vibrational modes can be classified as stretching ν1, ν2 and ν3 modes and bending ν4, ν5 and ν6 modes; they are related as follows: ν1 > ν3 > ν2, ν4 > ν5 > ν6, ν2 > ν4 and ν5 j configu≈ 2ν6.13,14 We focused the analysis on the X(ZZ)X ration. Strong peaks appear at 760 and 908 cm-1, which possess line-widths ∆ωR of about 14.2 and 10 cm-1, respectively, corresponding to relaxation times of 0.747 and 1.061 ps,22 respectively. This estimate indicates that crystalline KYbW is a possible candidate for use in picosecond pulsed lasers.1,2,11 Because of the large anisotropy of crystalline KYbW, the ν5 line splits into lines at 346 and 319 cm-1 and the ν6 line splits into lines at 237 and 220 cm-1. It is clear that the Raman peaks at ν5 and ν6 are consistent with ν5 ≈ 2ν6. ν6 is a silent mode, and is only observed because of the distortion of the WO6 octahedron. B. Infrared Spectroscopy. The infrared spectrum of KYbW is shown in Figure 3. The IR spectrum was used as a supplement to the Raman spectra to assign the modes more accurately. Using data on other tungstate crystals11,14,20,23,24 that contain the WO6 octahedron for comparison, the modes are assigned as shown in Table 1. Because of the strongly distorted WO6 units and the large anisotropy of monoclinic crystals, a few peaks split or shift to other positions, such as ν3, which splits into lines at 841 and 779 cm-1.
3980 Crystal Growth & Design, Vol. 8, No. 11, 2008
Figure 4. DTA and TA curves of crystalline KYbW. Table 1. IR Phonon Frequency (cm-1) and Mode Assignment IR result Au/Bu
assignment
IR result Au/Bu
assignment
925 (ν1)1 W-O symmetric stretching modes 891 (ν1)2 841 (ν3)1 779 (ν3)2 633 555 (ν2) 481 (ν4)1 450 (ν4)2 393
356 (ν5)1 in plane O-W-O bending mode 314 (ν5)2 285 essentially K+ translational modes 204 essentially Yb3+ translational modes 183 O-W-O symmetric 151 essentially W6+ translational stretching mode modes out of plane bending 123 vibration mode 108 72 essentially WO6 rotational (librational) modes
IV. Thermal Properties A. Melting Point and Enthalphy of Fusion Measurements. Figure 4 shows the DTA and TG curves of crystalline KYbW. A sharp endothermic peak was observed in the temperature range of 1039.60 to 1084.40 °C, with the peak occurring at 1058.36 °C, which is identified as the melting point of crystalline KYbW. From the TG curve we can see that the mass change is 0.37% from 100 to 1000 °C. It can be seen that the shape of the TG curve changes at about 1049 °C, which is
Zhao et al.
evidence that fusion takes place at this temperature. There is a second-order phase transition from 802.19 to 833.88 °C, which indicates that the crystal cannot be grown by the Czochralski (CZ) method and should be grown by the TSSG or similar method. B. High-Temperature X-ray Powder Diffraction Pattern. Figure 5a shows the X-ray powder diffraction pattern of crystalline KYbW at 800 and 900 °C illustrating the observation that the location and strength of the diffraction peaks change with temperature over this range. It is assumed that there is a second-order phase transition between 800 and 900 °C that is consistent with the DTA results. Figure 5b shows the X-ray powder diffraction pattern of crystalline KYbW over the temperature range of 1000 to 1100 °C and at 1200 °C. Because the shape of the diffraction peaks at 1000 and 1100 °C changes considerably, it is assumed that the sample begins to melt at some point between 1000 and 1100 °C. The DTA curves indicate that the melting point is 1058.36 °C, which lies in this temperature range. An attempt was made to analyze the structure using the pattern fitting method, but the approach was not successful. A possible explanation is that the transition between the monoclinic and tetragonal phases has taken place between 800 and 900 °C, the structure has radically changed, and the appropriate cell parameters cannot be obtained. C. Thermal Expansion and Density Curve. A harmonic lattice vibrations produce thermal expansion when the crystal is heated. The amount of vibration and therefore expansion is related to the structure and composition of the crystal and the force among the ions, so the study of thermal expansion is important in order to predict crystal growth and assess possible applications of the crystal.25 The thermal expansion tensor [Rij]26 is a symmetrical second-rank tensor, and for KYbW the [Rij] is
{
R11 0 R31 R22 0 0 R31 0 R33
}
(1)
In order to determine [Rij], we have to measure thermal expansion coefficients along at least four different directions. On the (010) plane, the thermal expansion coefficients corresponding to the three orientations ξ1 ) 0°, ξ2 ) 90°, ξ3 ) 130.702°, measured with respect to the crystallographic c-axis, are Rc ) 14.71 × 10-6 K-1, Ra* ) 9.29 × 10-6 K-1, and Ra ) 8.51 × 10-6 K-1, respectively. The thermal expansion curve of KYbW is shown in Figure 6.
Figure 5. (a) X-ray powder diffraction patterns of crystalline KYbW at 800 and 900 °C, (b) X-ray powder diffraction patterns of crystalline KYbW at 1000, 1100, and 1200 °C.
Properties of Stoichiometric KYb(WO4)2 Crystal
Crystal Growth & Design, Vol. 8, No. 11, 2008 3981 Table 2. Comparison of Thermal Expansion of Different Crystals in KReW Series
Figure 6. Thermal expansion of crystalline KYbW vs temperature.
The expansion coefficient Rb ) a22 ) 0.80 × 10-6 K-1. The three crystallographic expansion coefficients R11, R31, and R33 can be obtained using the method reported by Krishnan et al.,26 and they are calculated to be 9.29 × 10-6 K-1, 3.12 × 10-6 K-1, and 14.71 × 10-6 K-1, respectively. The thermal expansion tensor in the conventional frame is
(
)(
)
a11 0 a31 9.29 0 3.12 0 a22 0 ) 0 × 10-6 K-1 0.80 0 a31 0 a33 3.12 0 14.71
crystal
R1 (× 10-6 K-1)
R2 (× 10-6 K-1)
R3 (× 10-6 K-1)
R3/R1
KYbW* KYbW32 KLuW28 Yb: KLuW33 KGW29
7.87 8.72 8.98 12.8 10.64
2.12 2.57 3.35 7.8 2.83
16.13 16.68 16.72 22.2 23.44
2.05 1.91 1.86 1.73 2.20
mFwater/(m-m′), where F is the density of the as-grown crystal, Fwater is the density of water at the experimental temperature (32 °C), m is the sample weight in air and m′ is the sample weight immersed in water. From these measurements the density of the crystal at 32 °C is calculated to be 7.555 g/cm3. The density of a rectangular sample along the a, b, c* directions can be calculated using the following equation F ) m/V ) m/abc*, where m is the mass of the sample and a, b and c* are its dimensions. When the sample is heated, the length of the sides will expand to be
(
a ) a0 × 1 +
where φ denotes the angle from the principal Z axis to the c-axis. The radius of the Mohr’s circle is rM2 ) 1/4(a33 - a11)2 + a312 ) 17.08, rm ) 4.13. The principal expansion coefficients are R1 ) 1/2(a11 + a 33) - rm ) 7.87 × 10-6 and R3 ) 1/2(a11 + a33) + rm ) 16.13 × 10-6. Since the principal Y axis coincides with the crystallographic b-axis, the principal expansion coefficient is R2 ) 2.12 × 10-6 K-1. The volume coefficient of thermal expansion is β ) R1 + R2 + R3 ) 24.8 × 10-6 K-1. We can see that the thermal expansion presents a large anisotropy. The results suggest that the crystal is quite sensitive to temperature, so when the crystal is heated or cooled, the temperature change should be kept at a low rate in order to avoid the formation of cracks in the crystal. The rigid joining of the WO6 and YbO6 polyhedra occurs along the b-axis, so it is difficult for the crystal to stretch much along this direction and the thermal expansion coefficient is small there. A comparison of thermal expansion values for the KReW series is shown in Table 2. The ratio of R3/R1 was used to determine the anisotropy of the monoclinic crystals. This ratio for KYbW is 2.05, which is larger than that of KLuW (1.86)28 and smaller than that of KGW (2.20).29 Because the thermal expansion anisotropy decreases through the KReW series,28,30,31 the thermal anisotropy of KYbW in the (010) plane is only larger than that of crystalline KLuW in the KReW series. The density of the as-grown crystal is obtained using the method of Archimedes. It is calculated using the equation F )
)
(
)
where ∆a/a0, ∆b/b0, and ∆c*/c0* are the thermal expansion ratios that were previously calculated. The density can therefore be calculated using the following equation:
)
The angle φ can be calculated using the following equation:27
2|a31| tan 2φ ) ) 1.15 f φ ) 24.51° a33 - a11
(
(3)
F) (2)
)
∆a ∆b ∆c* b ) b0 × 1 + c* ) c/0 × 1 + a0 b0 c0
)
m a · b · c* m ∆a ∆b ∆c* a0b0c/0 1 + 1+ 1+ / a0 b0 c
(
(
)(
)(
0
F0 ∆a ∆b ∆c* 1+ 1+ 1+ / a0 b0 c
)(
)(
0
)
) (4)
where F0 is the density of the crystal at T0, F0 was measured using the buoyancy method with a value of 7.555 g/cm3 at 305.15 K. The density versus temperature curve is shown in Figure 7. The density exhibits an almost linear decrease as the temperature increases.
Figure 7. Density and the specific heat of crystalline KYbW versus temperature.
3982 Crystal Growth & Design, Vol. 8, No. 11, 2008
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Figure 8. Thermal diffusion coefficients of crystalline KYbW vs temperature. Table 3. The Principal Axis Thermal Diffusion Coefficients at Different Temperatures T (°C)
λx (mm2/s)
λy (mm2/s)
λz (mm2/s)
Φ (°)
30 60 90 120 150 180 210 240 290
0.991 0.908 0.841 0.795 0.746 0.708 0.674 0.648 0.623
0.682 0.637 0.58 0.577 0.566 0.54 0.516 0.493 0.476
1.015 0.922 0.854 0.806 0.754 0.716 0.680 0.653 0.628
33.4 34.8 31.8 31.8 31.1 27.6 26.9 21.7 20.7
D. Specific Heat. Figure 7 shows the curve of the specific heat vs temperature. The specific heat value reaches 0.362, 0.397, and 0.429 J/gK at 50, 100, and 150 °C, respectively. It is smaller than that of KGd(WO4)2 (0.502 J/gK) at 100 °C,34 but larger than that exhibited by the KLuW series (0.365 J/gK for Yb: KLuW and 0.38 J/gK for Yb, Tm: KLuW at 90 °C).33,35 The molar mass of KYbW is 707.818 g · mol-1, so the molar specific heat (Cp) is 239.242 J · K-1 · mol-1 at 20 °C. According to the Dulong-Petit law and Kopp’s law, the specific heat can be calculated as Cv ) 25 + 25 + 25 × 2 + 16.7 × 8 ) 233.6 J · K-1 · mol-1.36,37 The calculated value of Cv agrees with the measured value of Cp. E. Thermal Diffusivity and Thermal Conductivity. Thermal diffusivity is one of the most important properties used for evaluating the effectiveness of laser crystals. Figure 8 shows elements of the thermal diffusivity tensor of crystalline KYbW plotted against temperature. The thermal diffusivity tensor [λij] is diagonal like the thermal expansion tensor [Rij]. The thermal diffusivity tensor elements are 0.828, 0.932, 0.682, and 1.095 mm2/s along the a, a*, b and c directions, respectively. The thermal diffusivity coefficients are λ22 and λb in the direction of the b-axis. The principal axis thermal diffusivity coefficient elements were calculated using the same method as was used in the calculation of the thermal expansion. The values of the principal thermal diffusivity coefficients λ1, λ2, λ3 are 0.831, 0.682 and 1.178 mm2/s. The angle φ is the counterclockwise angle measured from the λ3 to the c-axis and is calculated to be 34.0°. Table 3 shows the calculated principal axis parameters. The thermal conductivity was calculated using the equation: k ) λFCp, where k, λ, F and Cp denote the principal thermal conductivity, thermal diffusivity, density and specific heat of crystalline KYbW, respectively. The thermal conductivity
Figure 9. Thermal conductivity of crystalline KYbW vs temperature.
coefficients are calculated to be 2.17, 2.44, 1.78, 2.82, 2.87 W/mK at 30 °C along the a, a*, b, c and c* directions, respectively. Figure 9 shows the plots of thermal conductivity vs temperature. All of the curves are nearly linear and indicate a large degree of anisotropy.
V. Conclusion In conclusion, we report that monoclinic KYbW has been successfully grown using the TSSG method. Since the refractiveindex coordinates (ng, nm, np) are relevant for determination of the direction of light propagation, we choose the physical coordinates (X, Y, Z) to study the lattice vibrations. The polarized Raman and infrared transmission spectra were recorded. The holosymmetric vibrations were ascribed to the six modes of the WO6 octahedron. Some extraneous peaks were recorded because of instrumental deficiencies. ν6, which is a silent mode, was observed and is caused by the distortion of the WO6 octahedron. The DTA/TG, high-temperature X-ray diffraction patterns, thermal expansion, thermal diffusivity and thermal conductivity were studied in detail. The results indicate that crystalline KYbW has a phase transition below the melting point and it shows a large anisotropy similar to the other members of the KReW family of crystals. In view of the structure of KYbW, the thermal expansion coefficient is small along the b-axis because of the rigid joining of the WO6 and YbO6 polyhedra along the b-axis. By contrast, because of the elastic joining of the flexible zigzag double WO6 chains along the c-axis, the thermal diffusion along the c-axis is large. Acknowledgment. This work is supported by NSFC, No. 50590401/E01.
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CG800021H
