Influence of doping on band structure, optical, non-linear optical and dielectric results for Ca12Al14O33 (C12A7) single crystals which prepared by grown using Traveling-Solvent Floating Zone (TSFZ) methodAbstractCa12Al14O33 (C12A7) single crystals were grown using (TSFZ), to avoid the bubbles and cracks which may be formed during preparation of the ingot material. The structure of both Ca12Al14O33 and Ca12Al14O33 doped with Yttrium (Y- C12A7) was investigated using X-ray diffraction (XRD) and Laue picture.
Optical measurements such as transmission and reflection had been carried out for C12A7 and Y- C12A7 single crystals, in order to calculate the optical parameters such as optical energy gap (Eg), refractive index, oscillating energy, dispersion energy, Volume Energy Loss Function (VELF), Surface Energy Loss Function (SELF) and finally third-order nonlinear optical susceptibility (3). The results have been discussed with effect of Y-doping on the C12A7 single crystals for optical applications.Key words: single crystals, Y-doping, C12A7, structure, optical properties, dielectric results, nonlinear optical properties.
IntroductionBecause of their importance in electronics applications and modern technology in other common uses [1-3], such as luminescent materials [4″6]. Calcium aluminates glasses had had investigated widely because of their unique properties [7-9], due to their properties these materials are widely used for many electronics applications [10-11]. The crystal structure of Ca12Al14O33 (C12A7) is cubic (a0 = 11.982 … . As these oxide ions are conductive, C12A7 is known as an oxygen ionic conductor .There are many methods for preparing Ca12Al14O33 crystals (C12A7), including; (SFZM)  that gives high quality single crystals, self-propagating combustion method, solid state reaction , and another methods [16-17]. Many authors had studied structure of C12A7 they reported that, C12A7 had only one crystal structure, which had 4 positive charges with anions, O2 [18-20]. On the other hand, some authors had studied the C12A7, they found that, C12A7 crystals have body-centered cubic structure with I-43d space group [21″22] with cell parameter 11.99 …. Moreover, the defect structure of C12A7 was studied [23″25]. The physical properties of C12A7 have been studied including; electric properties , thermodynamic  and optical properties . Wang, et al,  had studied the doping effect for 12Ca7Al on both of structure and Raman spectra, while phase transformation effect optical properties on the of Ca”Al”O system had studied . the optical properties of doped 12CaO.7Al2O3 thin films , monoclinic CaAl2O4:Er3+ , and Ca12Al10.6Si3.4O32Cl5.4  had been studied, moreover, Eu effected the optical emission spectra for CaAl2O4 samples . The physical properties dependence on temperature for doped CaAl4O7 was studied . While the influence of doping with different rare earth on physical properties of (C12A7) had been studied [36-40] In this paper, We study the structure of single crystal of C12A7 and Y-doped C12A7 using XRD. Optical measurements such as transmission and reflection had been carried out for C12A7 and Y-doped C12A7 single crystals, in order to determine (Eg), refractive index, Eo, Ed, (VELF), (SELF) and (3). The results have been discussed with effect of Y-doping on the C12A7 single crystals for optical applications.3. Results and discussion3.1. structure 3.1.1. X-Ray Diffraction (XRD) analysis (XRD) patterns of a Ca12Al14O33 (C12A7) and Y-Ca12A7 single crystals are shown in Fig. 1. It was noticed that, the doping had affected on both of the peak intensity anda full width at half maximum (FWHM) of these peaks. The crystallite size (Cs) of these crystals has been calculated using Sherrer’s formula  (1)where ” is the wavelength of the X-ray used, is the Bragg’s angle and І (the FWHM of the peak) is expressed in radians. While the dislocation density () was determine as follow : (2)The lattice strain (Ls) was calculated as follows  (3)The number of crystallites per unit area (N) of the studied crystals has been determined using the following equation  (4)where t is the crystal thickness. The calculate values for these studied crystals are shown in Table (1). 3.2. Optical resultsBoth of optical transmittance (T) and reflectance (R) for these crystals are shown in Figs. 2 (a,b). From Fig. 2a it is clear that (T) behavior is the same for these samples, on the other hand, Fig. 2b shows that, the behavior of (R) for these crystals are completely different from each other and the (Y-Ca12A7) single crystals had a lower reflectance value than Ca12A7, this could be attributed, that the Yttrium (Y) is an element which had a dark-gray color which gives the probability of decrease a reflection. The optical energy gap (Eg) is determined using the equation : (5)Where ± is the absorption coefficient, A is a constant, Ѕ is the frequency of the incident radiation and h is Plank’s constant. the (±) of these studied thin crystals were determined as follow  (6)where d is the film thickness. (±) dependence on the photon energy (h…) for these studied crystals is shown in Fig. 2d. For these crystals, it is found that, Egdirc had a values of 3.00 and 3.80 eV for (C12A7) and (Y-Ca12A7) respectively, this could be attributed to, that the electron mobility for (C12A7) crystals is higher than the electron mobility of (Y-Ca12A7) single crystals, these electrons mobility affected on the conductivity of these studied samples, which finally decrease the direct optical energy gap.The extinction coefficient for all films were calculated from the relation: – (7)The dependence of k of these crystals on photon energy (hЅ) is shown in Fig. 5a. The refractive index (n) for these crystals were calculated as follow  (8)Fig. 3b shows the dependence of (n) on wave length for these investigated samples, from this Fig. it is clear that, the (C12A7) single crystals had a higher value of (n) than (Y-Ca12A7) single crystals. The concept of the single oscillator of these crystals were studied from the dispersion of (n) for (C12A7) and (Y-Ca12A7) single crystals, which can be expressed by the Wemple”DiDomenico relationship  (9)where E is the photon energy, The values of Eo and Ed are determined as the intercept and the slope resulting from the extrapolation of the line of Fig. 3(c). The values of E0 and Ed for all samples are shown in Table. 2. From this table it was seen that the value of Eo~ 2Eg. On the basis of the above-mentioned model, the M-1 and M-3 moments of µ/ (hЅ) optical spectrum  can be derived from the relations: (10) (11)Table 2. shows the values of the first order moment (M-1) and third order moment ( M-3) for (C12A7) single crystals and (Y-Ca12A7) single crystals. Another important parameter called the oscillator strength (f) which was calculated as follow  (12)The value of (f) is shown in Table 1. The relation between (n)2 and (“)2 for the studied samples is shown in Fig. 4c. The ratio of the free carrier concentration / effective mass (N/m*) for these studied samples were determined optically from this Figure as follow  (13)Where µL is the lattice dielectric constant, µo is the permittivity of free space, e is the charge of electron, N is the free carrier concentration and c is the speed of light. From this figure the slope of the gotten line equal to the value of (e.N/4c2µ0m*), so the ratio of free carrier concentration / effective mass (N/m*) for these crystals were calculated as shown in Table. 2. From Fig. 3c the value of µL for these thin films was determined by the extend line will intercept with the y-axis at value of (n2) .Another important parameters such as dielectric loss (µ) and dielectric tangent loss(µ\) were determined optically  (14) (15)Figs. 4 (a, b) shows the dependence of both (µ) and (µ\) on photon energy for the investigated samples. From Fig. 6a, it is clear that, the behavior of (µ) and (µ\) is completely inverse each other. (VELF) and (SELF) for these films were determined optically as follow :- (16) (17)The relation between VELF/SELF for these crystals is shown in Fig. 4c. From this figure the values of VELF/SELF for Ca12Al14O33 single crystals decrease with photon energy, while the values of VELF/SELF for Y-Ca12Al14O33 single crystals increase with photon energy. As a result of its optical application in electronic devices, Another important parameter had been determined optically for these crystal, it is the degree of nonlinearities is the third-order nonlinear optical susceptibility (3). Which is depends mainly on thy photon energy (hЅ) and both of oscillator energy (Eo) and dispersion energy (Ed) : (18)The relation between (3) and (hЅ)is shown in Fig. 4d. From this Fig. it was noticed that, the both crystals had the same (3) behavior with (hЅ), but the values of (3) for (Y-Ca12A7) single crystals is higher than Ca12A7 single crystals. 4. Conclusion A high quality Ca12Al14O33 (C12A7) single crystal was prepared using Traveling-Solvent Floating Zone (TSFZ) method. The doping was achieved for this crystal using Y-element. The doing affected on the structure parameters such as number of defects, lattice strain and number of crystallites, and the doping plays an important rule for changing the measured optical parameters such as transmittance and reflectance. The direct optical energy gap increases with doping, because of changing the electron mobility and conductivity. Another optical result such as oscillating and depression energy, oscillating strength had affected by doping. The ratio free carrier concentration / effective mass (N/m*) decreased by on order of magnitude by doing because of increase the electrons number, on the other hand the doping process had affected strongly on the dielectric results, where the behavior for the dielectric loss and dielectric tangent loss had completely inversed for these crystals. While the third-order nonlinear optical susceptibility (3) valued had increased by doping. Finally, our results confirmed the doping of Y-ion in C12A7 can be good candidate for optical applications. Acknowledgements. We thank Dr. Park at Korean standard and measurements institute for XRD and Laue Experiments., This Project supported from BK21 (Korean Government) through Yonsei University. Table 1:(Y-Ca12A7) single crystals (C12A7) single crystalsLattice strain Ls Thenumber of crystallites per unit area (N) / cm2 Dislocation density () line/cm2 Grain size Cs (nm) І(FWHM) Lattice strain Ls The number of crystallites per unit area (N) / cm2 Dislocation density () line/cm2 Grain size Cs (nm) І (FWHM) ґ0.90 6.70E+18 2.00E+15 45.00 0.06 2.40 3.20E+15 5.20E+8 44.00 0.060 11.560.02 1.80E+16 3.00E+20 170.00 0.03 2.80 3.20E+13 3.10E+8 120.00 0.030 14.140.64 3.70E+18 6.70E+15 81.00 0.025 0.68 5.70E+14 2.40E+8 72.00 0.028 18.081.31 4.40E+18 4.70E+15 68.00 0.023 0.25 9.30E+14 2.50E+8 69.00 0.023 21.580.33 2.00E+18 2.40E+16 154.00 0.013 0.48 8.10E+13 9.30E+7 100.00 0.020 25.90.10 8.00E+17 1.43E+17 378.00 0.022 3.40 5.50E+12 8.20E+7 346.00 0.024 30.020.04 3.30E+17 8.20E+17 906.00 0.03 14.10 4.00E+11 1.10E+8 906.00 0.030 33.040.16 1.20E+18 6.50E+16 254.00 0.013 0.71 1.80E+13 1.80E+7 236.00 0.014 33.440.16 1.20E+18 6.10E+16 246.00 0.013 0.79 2.00+13 2.90E+7 200.00 0.016 35.660.24 1.70+18 3.20E+16 178.00 0.015 0.58 5.30E+13 3.80E+7 178.00 0.015 41.840.66 2.60E+18 1.40E+16 117.00 0.014 0.20 1.90E+14 8.10E+7 109.00 0.015 47.610.55 3.10E+18 9.10E+15 95.00 0.021 0.50 3.40E+14 1.10E+8 95.00 0.021 49.500.14 1.20E+18 6.80E+16 260.00 0.024 2.60 1.70E+13 1.40E+7 250.00 0.025 55.201.10 2.20E+18 1.83E+16 135.00 0.011 0.10 1.20E+14 6.50E+7 125.00 0.012 56.302.20 3.30E+18 8.45E+15 92.00 0.016 0.01 3.70E+14 1.50E+8 82.00 0.018 56.400.26 1.70E+18 3.10E+16 177.00 0.013 0.40 5.40E+13 3.20E+7 177.00 0.013 57.400.19 1.30E+18 5.40E+20 233.00 0.011 0.44 2.40E+13 2.10E+7 215.00 0.012 57.504.67 8.10E+18 1.40E+15 37.00 0.04 0.21 5.60E+15 7.30E+8 37.00 0.040 59.48 .Crystal type Oscillator energy (Eo) (eV) Dispersion energy (Ed) (eV) First order of moment (M-1) Third order of moment (M-3) oscillator strength (f) (eV)2 N/m* (gm-1.cm-3) lattice dielectric constant(µL)Ca12Al14O33 8.00 15.00 11.00 4.00 120.00 1.40E+49 12.80Y-Ca12Al14O33 8.50 18.00 12.00 3.00 153.00 7.20E+48 11.40