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Melilite-type oxide SrGdGa3O7: bulk crystal growth and theoretical studies upon both chemical bonding theory of single crystal growth and DFT methods Yan Wang, Congting Sun, Chaoyang Tu, and Dongfeng Xue Cryst. Growth Des., Just Accepted Manuscript • DOI: 10.1021/acs.cgd.7b01555 • Publication Date (Web): 24 Jan 2018 Downloaded from http://pubs.acs.org on January 29, 2018

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Crystal Growth & Design

Figure 1. Thermodynamic morphology of SGGM single crystal calculated on the basis of chemical bonding theory of single crystal growth: (a) along c-axis, (b) along a-axis. 256x140mm (96 x 96 DPI)

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Crystal Growth & Design 1 2 3 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 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. XRD patterns of SGGM polycrystalline and single crystal 289x299mm (150 x 150 DPI)


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Figure 3. Photoes of the whole (a), top (b), surface (c) and bottom (d) of the as-grown SGGM crystal. 213x151mm (96 x 96 DPI)



Figure 4. The rocking curve of the (200) diffraction plane for the SGGM crystal. 203x143mm (300 x 300 DPI)


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Figure 5. 3D map of the optical homogeneity for the SGGM crystal. 165x87mm (96 x 96 DPI)



Figure 6. View of crystal structure of SGGM: on the a-c plane (a), a-b plane (b) and a-c plane (c). 567x155mm (120 x 120 DPI)


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Figure 7. The calculated band structure of SrGdGa3O7. 289x203mm (150 x 150 DPI)



Figure 8. Electronic DOS of SrGdGa3O7. 289x300mm (300 x 300 DPI)


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For Table of Contents Use Only 274x100mm (96 x 96 DPI)



Melilite-type oxide SrGdGa3O7: bulk crystal growth and theoretical studies upon both chemical bonding theory of single crystal growth and DFT methods Yan Wang,† Congting Sun,‡ Chaoyang Tu,†,* and Dongfeng Xue‡ †

Key Laboratory of Optoelectronic Materials Chemistry and Physics, Fujian

Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou City, Fujian Province, 350002, P. R. China ‡

State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of

Applied Chemistry, Chinese Academy of Sciences, Changchun City, Jilin Province, 130022, P. R. China ABSTRACT: The chemical bonding theory of single crystal growth has been applied to SrGdGa3O7 (SGGM) Czochralski growth system and the optimized growth parameters were calculated. These optimized growth parameters were applied to the Czochralski growth system of SGGM, and the bulk crystal with dimensions of Φ 35×150 mm was obtained successfully. The crystal structure of SGGM was demonstrated. The theoretical calculations based on density functional theory (DFT) methods were carried out on SGGM crystal. Its band structure and density of state were presented. The present work deepens our understanding of the mesoscale process in SGGM Czochralski growth system and the structures of SGGM crystal. It can be concluded that this crystal is a good candidate of all-solid-laser host material.

1. INTRODUCTION Solid oxide fuel cells (SOFCs) are an efficient and low-polluting energy transfer technology. These devices require materials that exhibit good oxide-ion conductivity, among which layered gallium oxides with ABC3O7 melilite structure have been proposed as good candidates. 1-4 ABC3O7 (A= Ca, Sr, Ba; B=Y, La−Gd; C=Al, Ga) crystals belong 1


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to tetragonal system with space group P 4 21m, which are usually made of anionic layers of five-membered rings of CO4 tetrahedra, separated by sheets of A and B cations located above the five-ring centers, and the A2+ and B3+ ions are randomly distributed in one position producing a disordered structure.5 The disordered crystals of them have attracted a lot of attention because they can combine excellent thermomechanical features and relatively broad emission lines, which have been widely investigated owing to their lasing possibilities.6 SrGdGa3O7 (SGGM) is one member of ABC3O7 family, which melts congruently at 1600 C and can be obtained in a single crystal formed by the Czochralski method.7 The earliest crystal growth of SGGM might begin in 1989 by Verdun et al.,8 then the rare earth ions such as Nd3+、Tm3+、Ho3+ singly doped and Tm3+/Ho3+ co-doped SGGM crystals have been developed for the design of all-solid-state lasers.9-15 The growth and spectroscopy of chromium ions doped SGGM crystals were carried out,16 and the authors proved the presence of Cr2+, Cr3+ and Cr4+ ions in the grown Cr3+:SGGM crystals.17 In 2011, the crystal-field analysis and energy levels calculations for Tm3+ ions doped into SGGM crystal were presented.18 In 2012, Prof. Zhang’s group obtained SGGM crystal with length up to 50 mm, then determined and analyzed its piezoelectric, elastic and dielectric constants, which shows that SGGM exhibits excellent piezoelectric properties.19 The optical and fluorescence properties of planar and channel waveguides in Nd: SGGM by carbon ion implantation was studied.20 Kaminskii et al. has discovered and investigated the third nonlinear optical potential of SGGM crystal, and concluded that it can be applied as SRS-active material.21 In 2012, the operation of spontaneous mode locking in a diode-pumped Nd:SGGM crystal laser was explored, the maximum output power was 415 mW at a pump power of 6.1 W, and 80 GHz pulse train with a pulse duration as short as 616 fs was observed.22 In 2013, the researches on the broad band, near infrared emission in ABC3O7 crystals doped with rare earth and transition metals were carried out systematically.23 In our previous work, Er3+ activated and several kinds of rare earth ions sensitized SGGM crystals have been reported as 2.7~3 µm laser gain media, 24, 25 which are proved to be excellent candidates for mid-infrared waveband lasers, especially beneficial for the Q-switched or ultra fast laser output. However, the obtainment of this crystal with 2



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high-optical-quality is very difficult, owing to the disordered and layered structure of SGGM, as well as the evaporation of Ga2O3 during the crystal growth. In this work, we use the chemical bonding theory of single crystal growth to direct the growth of the title crystal, and finally a large-sized SGGM single crystal was obtained by the Czochralski method, and the first-principles calculations of this crystal were carried out.

2. CALCULATION METHODOLOGY During the crystal growth of SGGM single crystal from the melt, the crystal constituents of SGGM single crystal undergoes the phase transition from the melt to the crystalline state, and the phase transition at the growing interface promotes the crystal growth. In such a phase transition process, the anisotropic chemical bonding energy density acts as the essential driving force for the phase transition from liquid to crystalline solid, and the chemical potential of crystal constituents decreases thermodynamically.26-28 Moreover, crystal growth is also a multi-factor influenced phase transition process, which depends on the mass transfer process, temperature gradient in three-dimensional space, liquid fluid flow in the melt, and so on. On the basis of chemical bonding theory of single crystal growth, the chemical bonding architecture at the growing interface is identified as the critical parameter that dominates the anisotropic growth of SGGM single crystal. On the basis of the anisotropic structure, we can establish the relationship between the growth rate along the [uvw] direction and the anisotropic chemical bonding energy density. The anisotropic growth rate can be expressed by29-31 Ruvw

Bond E uvw K Auvw  d uvw

(1).

Bond where Euvw is the chemical bonding energy of the interface along the [uvw] direction,

Auvw is the projection area of SGGM growth unit along the [uvw] direction at the growth interface, duvw is the increased height on the (hkl) surface when the growth units incorporated into the lattice along [uvw] direction, and K is the function of growth parameters, which is a constant for any [uvw] directions when we calculate the Bond thermodynamic morphology. Euvw , Auvw and duvw are used to calculate the anisotropic

Bond chemical bonding energy density. The value of Euvw depends on the selected area and

3


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Bond thickness of the interface. Different Auvw and duvw result in different Euvw , however,

Bond /(Auvwduvw) is a fixed value for [uvw] direction in the calculation of thermodynamic Euvw

morphology. Starting from the anisotropic chemical bonding architectures at the interface along [uvw] direction, the anisotropic growth rate can be calculated in terms of Eq. (1). Consequently, the thermodynamic crystal morphology of SGGM single crystal can be obtained, as shown in Figure 1. By combining the pulling direction, the thermodynamic morphology and the anisotropic growth rates, we can further obtain the numerical solution of thermodynamically preferred growth rate for SGGM single crystal that grows along [uvw] pulling direction. In Cz crystal growth system, the growth along the radial directions finally leads to the growth along axial direction, i.e., the pulling direction. Therefore, the growth rate along the pulling direction depends on the growth rate along the radial directions. On the basis of the thermodynamic morphology, we can confirm both the radial and axial directions. The growth rates of these radial directions can be calculated by the chemical bonding theory of single crystal growth, which are used to obtain the growth rate along the pulling direction. The pulling direction which has a lower growth rate in calculation is the preferred pulling direction. The growth parameters were calculated and optimized through the above calculations, and the optimized growth parameters were used in the following CZ growth system.

3. EXPERIMENTAL SECTION Reagents. SrCO3 (Alfa Aesar Chemical Reagent Co. Ltd., China, purity 99.8%), Gd2O3 (Changchun Highpurity Chemical Reagent Co. Ltd., China, purity 99.99%) and Ga2O3 (Shanghai Mingqing Chemical Reagent Co. Ltd., China, purity 99.99%) powders. Polycrystalline Synthesis. Polycrystalline samples of SGGM were synthesized by the traditional solid-state reaction techniques. The starting materials were weighed accurately by mixing the oxide powders according to the following reaction formula, with an excess of Ga2O3 (1.0 wt %) added to the starting components for compensation for the evaporation of Ga2O3 during the growth process: 2SrCO3+Gd2O3+3Ga2O3=2SrGdGa3O7+2CO2↑ The mixtures with total weight of 1400 g were pressed into tablets and put in a Pt 4



crucible, then heated to 1000 ℃ at the rate of 200 ℃/h in a Muffle furnace (KSL1800X, KMT Furnace Co., China), maintaining at this temperature for 14 h to decompose the SrCO3 completely, and then heated to 1200 ℃ at the rate of 100 ℃/h and maintained for 24 h. After that, the furnace was cooled down to room temperature at the rate of 200 ℃/h. The calcined powders were taken out, milled and mixed carefully again, which were then pressed into tablets and sintered at 1250 ℃ for 24 h to synthesize the polycrystalline compounds. Generally, the above processes were carried out continuously and confirmed by X-ray diffraction until the pure-phase polycrystalline was obtained. Single Crystal Growth. The obtained ceramic-like polycrystalline tablets were then loaded into Φ80×60 mm2 iridium (Ir) crucible in Czochralski instrument (XT600-LT200, CETC, China). Nitrogen gas with 99.99% purity was flowed into the furnace as protection atmosphere with the pressure of 0.04 Mpa. Then the Ir crucible was frequency-inductive heated to melt the polycrystalline materials with a computer controller (CRMY, CETC, China). The melt materials were kept for 2 h at a temperature 50 ℃ above the melting point, to ensure homogeneity of the melt. When the melt reached a thermal equilibrium, one a-cut Nd:SGGM crystal seed was lowered to the surface of the melt, and the seeding temperature was located around 1600 ℃. Then the growth of crystal was proceeding by pulling upward SGGM seed slowly from the melt surface, going through the three stages including shoulder-extending, equivalence-diameter and tail. During the Cz growth process, the SGGM single crystal grew with the phase transition at the melt and crystal interface when it was pulled out of the melt vertically. On the basis of chemical bonding theory of single crystal growth, the optimized growth parameters were set as follows: the pulling rate was set at 0.8~1.0 mm/h in the shoulder-extending stage, and then the pulling rate was set as 1.6 mm/h in the equivalence-diameter and tail stage, with a rotation rate of 5.0 r.p.m for the whole processes of crystal growth. After growth was completed, the crystal was cooled down slowly to room temperature at a rate of 10~35 C/h. Finally, one large-sized SGGM crystal with high optical quality was obtained successfully. Powder X-ray Diffraction. Powder X-ray diffraction of the obtained polycrystalline and the as-grown crystal of SGGM were performed on a Miniflex600 X-ray diffractometer, which is equipped with a diffracted beam monochromator set for CuKα 5


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radiation (λ=1.54056 Å) in the 2θ range 10-70º with a step size of 0.02º and a step time of 0.4s at room temperature. Crystal Quality Measurement. One sample was cut from the middle of the grown crystal and polished in the level of optical standards for crystal quality tests. The crystal quality was measured by Bruker D8-advance high-resolution X-ray diffractometer (HRXRD), which is equipped with a four-crystal Ge (220) monochromator set for Cuka radiation (λ=1.5406 Å). The voltage and current of the generator were adopted to be 40 kV and 20 mA, respectively. The step time and step size were set to be 0.1 s and 0.001°, respectively. The optical homogeneity of as-grown SGGM crystal was measured by using ZYGO GPI XP optical interferometer equipped with a He-Ne laser (632.8 nm). The Zygo MetroPro software was used to record and analyze the results. Single Crystal X-ray Diffraction. A colorless SGGM prism crystal of 0.3×0.25×0.1 mm3 was selected for single-crystal XRD analysis. The diffraction data were collected with the use of graphite-monochromatized MoKα radiation (λ=0.71073 Å) at 293.15K on a Mercury CCD diffractometer. The collection of the intensity data, cell refinement and data reduction were carried out with the program of CrystalClear (Rigaku Inc., 2008). The structure was solved by the direct method with program Olex2 (Dolomanov, 2009) and refined with the least-squares program ShelXL (Sheldrick, 2015). Final refinement includes anisotropic displacement parameters. The structure was verified by using the ADDSYM algorithm from the program PLATON17 and no higher symmetries were found. The Flack factor is close to zero as 0.0465, which indicates that the absolute structure is correct. Details of crystal parameters, data collection, and structure refinement are summarized in Table 1. Table 1. Crystal data and structure refinement for SrGdGa3O7 formula sum formula weight (g/mol) crystal system space group unit cell dimensions (Å) V(Å3) Z μ (mm−1) F(000) Dc/g·cm-3

SrGdGa3O7 566.03 tetragonal P 4 21m (No.113) a=7.9467(3) b=7.9467(3) c=5.2458(4) 331.27(3) 2 29.901 502 5.675 6



2660/0/36 data/restraints/parameters R(int) 0.0789 2 GOF (F ) 1.094 flack parameter 0.0465 final R indices [Fo 2 >2σ(Fc 2)]a R1 = 0.0291, wR2 = 0.0652 a final R indices (all data) R1 = 0.0313, wR2 = 0.0664 a wR2=[Σ[w(Fo2−Fc2)2]/Σ[w(Fo2)2]]1/2 for Fo2>2σ(Fc2) R1= Σ||Fo| − |Fc||/Σ|Fo|; 4. FIRST-PRINCIPLES CALCULATIONS Single crystal structural data of SGGM was used for the theoretical calculations. The electronic structures including band structure and density of states (DOS) calculations were performed by using CASTEP, a plane-wave pseudopotential total energy package based on density functional theory (DFT).32 The exchange and correlation effects were treated by Perdew−Burke−Ernzerhof (PBE) in the generalized gradient approximation (GGA). The interactions between the ionic cores and the valence electrons were described by the norm-conserving pseudopotential. The following valence-electron configurations were considered in the computation: Sr-4s24p65s2, Gd-4f75s25p65d16s2, Ga-3d104s24p1 and O-2s22p4. Kinetic cut-off energy is 820 eV. The other parameters were the default values of the CASTEP code. The convergence tests shows that the choice of the above computational parameters is sufficiently accurate for this study.

5. RESULTS AND DISCUSSION Chemical Bonding Calculations of SGGM Crystal Growth. Owing to their unique electron structures (4f0145d016s2), rare earth elements show multiple chemical bonding characteristics.33 Rare earth elements can mainly generate three types of chemical bonding, depending on different orbital electrons that participate in the formation of chemical bond.34-36 In SGGM single crystal, the coordination number of Gd3+ is 8, indicating the 4f electrons in Gd3+ that do not participate in the chemical bonding. Therefore, Gd3+ and Sr2+ occupy the identical lattice sites in the chemical bonding calculations. On the basis of chemical bonding theory of single crystal growth, the layer structure of SGGM single crystal along c-axis leads to the slower rate of [001] growing Bond interface (Figure 1a). Specially, Euvw /(Auvwduvw) along [121], [001], [100], [110] and

[111] directions are calculated to be 7.93, 5.27, 7.46, 11.63 and 7.86 kJmol1Å3, 7


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respectively. The chemical bonding theory of single crystal growth indicates that the ratio of pulling rate to axial rotation rate is a key parameter to preferentially select practical pulling parameters such as pulling direction. It is notable that the crystal rotates in the whole Cz growth process, resulting in the isotropic mass transfer. The anisotropic chemical bonding architecture in thermodynamics and isotropic mass transfer in kinetics will compete with each other and influence crystal growth. In order to coordinate the thermodynamic and kinetic controls, a more isotropic geometry viewed down along pulling direction is needed. Therefore, both [100] and [001] pulling directions are preferred in Cz growth according to the thermodynamic morphology of SGGM. In fact, the growth along the radial directions finally leads to the growth along pulling direction in Cz crystal growth system. Figure 1b shows the projection of SGGM viewed along a-axis. When [100] acts as the pulling direction, the radial directions are [010], [001], and [021] that need slower growth rates. Moreover, once the [001] serves as the pulling direction, the radial directions are [100] and [120] that need faster growth rates. For high quality growth of SGGM single crystal, we conclude that [100] direction is better than [001] direction owing to a lower growth rate. On the basis of these anisotropic chemical bonding architectures, the size-dependent pulling rates will be further obtained.

Figure 1. Thermodynamic morphology of SGGM single crystal calculated on the basis of chemical bonding theory of single crystal growth: (a) along c-axis, (b) along a-axis.

Crystal Growth and Crystal Quality. Figure 2 shows XRD patterns of the polycrystalline and the as-grown crystal of SGGM, both of them are well consistent with 8



the standard JCPDF file [No. 50-1835] for SGGM. The pure-phase polycrystalline is the basis of the obtainment of the high optical-quality crystal growth. With the guiding of chemical bonding theory of single crystal growth, we obtain high-quality SGGM crystal successfully. The photo of the as-grown SGGM crystal with dimension of Φ35×150 mm2 is shown in Figure 3(a), in which the length of equal-diameter part is 110 mm. There aren’t any obvious scatter particles within the crystal when we light the crystal with He-Ne laser, and this proves that the optical quality of this crystal is very good. The detailed parts of the grown crystal including the top, surface and bottom are shown in Figure 3(b), 3(c) and 3(d). As seen from Fig. 3(c), the surface of the crystal is a little unsmooth, owing to the negative effect of the evaporation of Ga2O3 during the process of crystal growth, which doesn’t affect the quality of the inner crystal. The crystal quality of as-grown SGGM crystal was characterized by the HRXRD and optical interferometry measurements. The rocking curve of the (200) diffraction plane, shown in Figure 4, is characterized by a full width at half maximum (FWHM) of 28.8″, which means a good crystalline quality. The optical interferometry measurement was carried out as shown in Figure 5 and the 3D map confirms the high optical homogeneity of the sample, and the homogeneity RMS value is 1.24×10-5.

Figure 2. XRD patterns of SGGM polycrystalline and single crystal.

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Figure 3. Photoes of the whole (a), top (b), surface (c) and bottom (d) of the as-grown SGGM crystal.

Figure 4. The rocking curve of the (200) diffraction plane for the SGGM crystal.

Figure 5. 3D map of the optical homogeneity for the SGGM crystal.

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Crystal Structure. Good properties are closely related to the structure of the crystal, here the structure of SGGM is analyzed as shown in Figure 6. As seen from it, the crystal structure is constructed from layers of large polyhedra alternating along c-axis, forming five-fold coordination rings from GaO45- tetrahedra linked at each corner. And between the layers, Gd3+ and Sr2+ ions are distributed randomly with a ratio of 1:1, and the large size-disparity of Gd3+ and Sr2+ leads to a significant lattice distortion. In the unit cell (Z=2) of SGGM, Sr2+ and Gd3+ atoms occupy only the 4e positions, and the crystallographic sites of Sr2+ and Gd3+ with 6-fold coordination are the same. Half of the 4e sites are expected to be filled by Gd atoms, the other half by Sr atoms. There are two different types of GaO45- tetrahedra in the lattice: one has S4 symmetry, the other has mirror symmetry, among which the tetrahedra are distorted and linked to each other at one corner, forming pairs of pyramids and having one vertex along the optical axis. These tetrahedra are subjected to a dominant C3v distortion and a weak perturbation would reduce the local symmetry to Cs. Once rare earth ions such as Er3+ was doped into SGGM crystal, three kinds of ions including Er3+, Gd3+ and Sr2+ are situated in one crystal lattice, producing a more disordered structure and thus a large inhomogeneous broadening of absorption & emission spectra, as presented in our previous work. The broadening of absorption band is beneficial for diode pumping, and the broadening of emission band is favorable for achievements of tunable or ultra fast laser output.

Figure 6. View of crystal structure of SGGM: on the a-c plane (a), a-b plane (b) and a-c plane (c).

Electronic Structure. To gain further insight of the bonding interactions in SGGM, theoretical calculations were made based on DFT methods. The band structure of SGGM along high-symmetry points of the first Brillouin zone is calculated and plotted in Figure

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7. It is clear that both the lowest conduction band and the highest valence band are localized at the same point G, hence SGGM is direct band gap semiconductor. The calculated band gap of it is 3.080 eV, which is a little lower than that of SLGO crystal (3.265 eV).37 The bands can be assigned according to the total and partial DOS, as shown in Figure 8. As seen in it, the peak localized around −13.5 eV is mostly contributed by Sr-4p and Ga-3d states. And the peaks localized around −5.0 and 3.3 eV are mostly contributed by O-2p and Gd-4f states. While the peak localized around −17.0 eV is mainly contributed by O-2s and Gd-5p states. In the vicinity of the Fermi level, namely, from −6.2 to 0 eV in the valence band and from 2.8 to 7.6 eV in the conduction band, the O-2p and Gd-4f5d states are mainly involved and overlapped, indicative of the strong covalent interactions of Gd−O bonds. As discussed above, the single-crystalline structure of SGGM is mainly composed of GaO4 tetrahedra, therefore, the bonding orbitals of Ga-O bonds contribute mainly to the Valence bands. As seen in Figure 8, the valence band is mainly occupied by O-2p states, and the conduction band is mainly contributed by the 5d orbitals of Gd. The present first-principles study of the electronic structures of SGGM host can provide valuable guidance for future experiments in rare earth ions doped SGGM for luminescent or laser materials.

Figure 7. The calculated band structure of SrGdGa3O7.

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Figure 8. Electronic DOS of SrGdGa3O7.

6. CONCLUSION In conclusion, the chemical bonding theory of single crystal growth has been applied to SGGM crystal growth, and the high optical quality SGGM single crystal with dimension of Φ35×150mm2 was grown successfully by using the Czochralski technique. The structure of SGGM is demonstrated and analyzed. The theoretical calculations based on DFT methods were performed on SGGM crystal, and the electronic structures including the band structure and electronic DOS of SGGM crystal were presented and discussed. The present work can deepen our understanding of the mesoscale process in SGGM growth system and the structures of SGGM crystal, which is helpful to promote the growth of large size ABC3O7 melilite family single crystals effectively, also reveals that SGGM crystal can be employed as candidate of all-solid-laser host material.

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▇ AUTHOR INFORMATION Corresponding Author *E-mail: [email protected] ▇ ACKNOWLEDGMENTS This work is supported by National Nature Science Foundation of China (51472240, 61675204),

National

Key

Research

and

Development

Program

of

China

(2016YFB0701002), Strategic Priority Research Program of Chinese Academy of Scienc es (XDB20010200). The authors also thank Dr. Jianghe Feng and Dr. Chensheng Lin of FJIRSM for helpful discussions in the crystal structure and theoretical calculations.

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For Table of Contents Use Only

Melilite-type oxide SrGdGa3O7: bulk crystal growth and theoretical studies upon both chemical bonding theory of single crystal growth and DFT methods Yan Wang,† Congting Sun,‡ Chaoyang Tu,†,* and Dongfeng Xue‡ †

Key Laboratory of Optoelectronic Materials Chemistry and Physics, Fujian

Institute of Research on the Structure of Matter, Chinese Academy of Sciences, Fuzhou City, Fujian Province, 350002, P. R. China ‡

State Key Laboratory of Rare Earth Resource Utilization, Changchun Institute of

Applied Chemistry, Chinese Academy of Sciences, Changchun City, Jilin Province, 130022, P. R. China

The chemical bonding theory of single crystal growth has been applied to SrGdGa3O7 (SGGM) Czochralski growth system and the high-quality crystal of it was grown successfully. Its structure was analyzed, the band structure and density of state were calculated by using DFT methods. The present work deepens our understanding of the mesoscale process in the growth system and the structures of SGGM crystal.

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Bulk Crystal Growth and Theoretical Studies upon Bo - ACS Publications

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