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Journal articles on the topic 'Crystal field energy'

Author: Grafiati
Published: 4 June 2021
Last updated: 1 February 2022

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1

Brik, M. G., and A. A. Chaykin. "Comparative crystal field study of Ni2+ energy levels and crystal field effects in CsCdBr3 and CsMgBr3 crystals." Journal of Luminescence 145 (January 2014): 563–68. http://dx.doi.org/10.1016/j.jlumin.2013.08.037.

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2

Ryu, Sun Young, In Hwan Oh, Sang Jin Cho, Shin Ae Kim, and Hyun Kyu Song. "Enhancing Protein Crystallization under a Magnetic Field." Crystals 10, no. 9 (September 16, 2020): 821. http://dx.doi.org/10.3390/cryst10090821.

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High-quality crystals are essential to ensure high-resolution structural information. Protein crystals are controlled by many factors, such as pH, temperature, and the ion concentration of crystalline solutions. We previously reported the development of a device dedicated to protein crystallization. In the current study, we have further modified and improved our device. Exposure to external magnetic field leads to alignment of the crystal toward a preferred direction depending on the magnetization energy. Each material has different magnetic susceptibilities depending on the individual direction of their unit crystal cells. One of the strategies to acquire a large crystal entails controlling the nucleation rate. Furthermore, exposure of a crystal to a magnetic field may lead to new morphologies by affecting the crystal volume, shape, and quality.
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3

Su, Ping, and Wen-Chen Zheng. "Crystal field energy levels of the laser crystal Gd3Ga5O12: Nd3+." Optik 123, no. 22 (November 2012): 2025–27. http://dx.doi.org/10.1016/j.ijleo.2011.09.038.

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4

BRIK, M. G. "ON THE CRYSTAL FIELD ANALYSIS OFCr4+ENERGY LEVELS INRb2CrF6." Modern Physics Letters B 20, no. 17 (July 30, 2006): 1007–14. http://dx.doi.org/10.1142/s0217984906011712.

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Optical absorption spectrum of Cr4+ion in Rb2CrF6is analyzed using the exchange charge model of crystal field theory. The crystal field parameters acting on the optical electrons of Cr4+are calculated using the crystal structure data; a good agreement between the calculated and observed energy levels of Cr4+in the title host is demonstrated. The crystal field strength Dq=2159 cm-1and Racah parameters B=639 cm-1, C=3605 cm-1were evaluated from the experimental spectrum.
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5

Muñoz-Santiuste, J. E., A. Lorenzo, L. E. Bausá, and J. García Solé. "Crystal field and energy levels of centres in." Journal of Physics: Condensed Matter 10, no. 34 (August 31, 1998): 7653–64. http://dx.doi.org/10.1088/0953-8984/10/34/018.

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6

Day, Graeme. "Insight from energy surfaces: structure prediction by lattice energy exploration." Acta Crystallographica Section A Foundations and Advances 70, a1 (August 5, 2014): C28. http://dx.doi.org/10.1107/s2053273314099719.

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A long-standing challenge for the application of computational chemistry in the field of crystallography is the prediction of crystal packing, given no more than the chemical bonding of the molecules being crystallised. Recent years have seen significant progress towards reliable crystal structure prediction methods, even for traditionally challenging systems involving flexible molecules and multi-component solids [1]. These methods are based on global searches of the lattice energy surface: a search is performed to locate all possible packing arrangements, and these structures are ranked by their calculated energy [2]. One aim of this lecture is to provide an overview of advances in methods for crystal structure prediction, focussing on molecular organic crystals, and highlighting strategies that are being explored to extend the reach of these methods to more complex systems. A second aim is to discuss the range applications of crystal structure prediction calculations, which have traditionally included solid form screening, particularly of pharmaceutically active molecules, and structure determination. As energy models become more reliable at correctly ranking the stability order of putative structures, and the timescale required for structure searching decreases, crystal structure prediction has the potential for the discovery of novel molecular materials with targeted properties. Prospects for computer-guided discovery of materials will be discussed.
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7

Diao, Xin-Feng, Li-Ke Gao, Yu Xie, Tian-Yu Tang, and Yan-Lin Tang. "Ferromagnetic and Antiferromagnetic Properties of Perovskite Solar Cell Materials." Journal of Nanoelectronics and Optoelectronics 16, no. 3 (March 1, 2021): 434–43. http://dx.doi.org/10.1166/jno.2021.2943.

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This paper provides an intriguing electronic and magnetic properties of the Perovskite solar cell materials (MAPbI3, CsGeI3) which are analyzed by using density functional theory, where MAPbI3 is the abbreviation of CH3NH3PbI3. Herein, we mainly discuss the influence of ferromagnetism and antiferromagnetism on the crystal structure, band gap and electronic density of states of perovskite (MAPbI3) (CsGeI3). The magmom values of the applied magnetic field are from −6 μB to 6 μB, respectively (The negative sign here represents the opposite direction of the original magnetic field). The lattice parameters and volume of the crystal under different magnetic fields are obtained. It can be seen from the free energy that the stability of the crystal is compared with non-magnetic field, when the applied magnetic fields are at 4 μB and 5 μB, the free energy of the crystal is the lowest and its relative stability is better. At the same time, the magnetic field of CsGeI3 increases from −5 μB to 5 μB. The results show that the density of states of CsGeI3 moves towards the direction of higher energy, and the change of MAPbI3 crystal is more obvious. Similarly, we should pay attention to that when applying a magnetic field to the crystals, it is found that the band gap of both MAPbI3 and CsGeI3 decreases obviously after increasing the magnetic field, which avoids the situation of spin up and spin down overlap of MAPbI3, which is helpful to adjust the band gap size. From the perspective of crystal spectral absorption characteristics, when considering the ferromagnetic effect on CsGeI3 with the magnetic moment of a single atom is set to (1 μB, 2 μB, 3 μB, 4 μB, 5 μB, 6 μB), the width of absorption spectrum tends to decrease, but the impact on MAPbI3 is small.
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8

Elking, Dennis M., Laszlo Fusti-Molnar, and Anthony Nichols. "Crystal structure prediction of rigid molecules." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 72, no. 4 (August 1, 2016): 488–501. http://dx.doi.org/10.1107/s2052520616010118.

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A non-polarizable force field based on atomic multipoles fit to reproduce experimental crystal properties andab initiogas-phase dimers is described. The Ewald method is used to calculate both long-range electrostatic and 1/r6dispersion energies of crystals. The dispersion energy of a crystal calculated by a cutoff method is shown to converge slowly to the exact Ewald result. A method for constraining space-group symmetry during unit-cell optimization is derived. Results for locally optimizing 4427 unit cells including volume, cell parameters, unit-cell r.m.s.d. and CPU timings are given for both flexible and rigid molecule optimization. An algorithm for randomly generating rigid molecule crystals is described. Using the correct experimentally determined space group, the average and maximum number of random crystals needed to find the correct experimental structure is given for 2440 rigid single component crystals. The force field energy rank of the correct experimental structure is presented for the same set of 2440 rigid single component crystals assuming the correct space group. A complete crystal prediction is performed for two rigid molecules by searching over the 32 most probable space groups.
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9

Nakamura, Satoshi, Keiichirou Shinohara, Nobuo Kieda, and Kimihiro Yamashita. "Polarization Energy Effect of Electrovector Hydroxyapatite on Bonelike Crystal Growth in SBF." Key Engineering Materials 309-311 (May 2006): 145–48. http://dx.doi.org/10.4028/www.scientific.net/kem.309-311.145.

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An electrovector effect of the polarized hydroxyapatite (HA) on crystal growth in a simulated body fluid was clarified to discuss the role of the polarization energy in the effect. The polarization of the HA carried out in high dc field at 300-600°C was confirmed by thermally stimulated depolarization current measurements. The dependence of the thickness of the crystal grown layer on the induced charge was remarkably indicated in the modification of the growth rates. The growth rate under an optimum polarization condition was estimated to be almost 3 times of that by the biomimetic method. At the early stage of the crystal growth, the grown crystals were spherical and their sizes were dependent on the field strength and time for polarization. The polarization is therefore considered to effect the nucleation as well as the crystal growth.
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10

Zhong, Z., M. Hasnah, A. Broadbent, E. Dooryhee, and M. Lucas. "Phase-space matching between bent Laue and flat Bragg crystals." Journal of Synchrotron Radiation 26, no. 6 (October 23, 2019): 1917–23. http://dx.doi.org/10.1107/s1600577519010774.

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Through phase-space analysis of Dumond diagrams for a flat Bragg crystal, a single bent Laue crystal and a monochromator consisting of double-bent Laue crystals, this work shows that it is possible to match the flat Bragg crystal to both the single-crystal and double-crystal Laue monochromators. The matched system has the advantage that the phase space of the bent crystal's output beam is much larger than that of the flat crystal, making the combined system stable. Here it is suggested that such a matched system can be used at synchrotron facilities to realize X-ray dark-field imaging, analyzer-based imaging and diffraction-enhanced imaging at beamlines using double-Laue monochromators.
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11

Christianson, A. D., J. M. Lawrence, P. S. Riseborough, N. O. Moreno, P. G. Pagliuso, E. D. Bauer, J. L. Sarrao, et al. "Crystal Field Effects in CeIrIn 5." Journal of Neutron Research 13, no. 1-3 (March 1, 2005): 179–82. http://dx.doi.org/10.1080/10238160412331299942.

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12

Heber, J., M. Lange, M. Altwein, B. Z. Malkin, and M. P. Rodionova. "Local lattice structure, crystal field and energy level patterns in CsCdBr3:Tm3+ crystals." Journal of Alloys and Compounds 275-277 (July 1998): 181–85. http://dx.doi.org/10.1016/s0925-8388(98)00299-0.

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13

Mazurak, Z., and J. B. Gruber. "Energy levels and crystal field parameters of Nd3+and Er3+in LiRP4O12single crystals." Journal of Physics: Condensed Matter 4, no. 13 (March 30, 1992): 3453–58. http://dx.doi.org/10.1088/0953-8984/4/13/009.

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14

Kebaïli, I., M. Dammak, E. Cavalli, and M. Bettinelli. "Energy levels and crystal-field analysis of Tm3+ in YAl3(BO3)4 crystals." Journal of Luminescence 131, no. 9 (September 2011): 2010–15. http://dx.doi.org/10.1016/j.jlumin.2011.04.029.

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15

Guo Chang-Xin, Tan Xiao-Liang, Liu Wen-Peng, Yin Shao-Tang, Jiang Hai-He, Xiao Jin, Xia Shang-Da, Zhang Qing-Li, and Zhou Wen-Long. "Crystal field energy-levels of Nd3+:Gd3Sc2Al3O12 and fitting." Acta Physica Sinica 59, no. 10 (2010): 7306. http://dx.doi.org/10.7498/aps.59.7306.

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16

Fournier, J. M., A. Blaise, G. Amoretti, R. Caciuffo, J. Larroque, M. T. Hutchings, R. Osborn, and A. D. Taylor. "High-energy-neutron spectroscopy of crystal-field excitations inNpO2." Physical Review B 43, no. 1 (January 1, 1991): 1142–45. http://dx.doi.org/10.1103/physrevb.43.1142.

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17

Devic�, S. D., Z. V. Popovic�, A. Breitschwerdt, G. Dhalenne, and A. Revcolevschi. "Optical Energy Gap and Crystal Field Excitations in CuGeO3." physica status solidi (b) 203, no. 2 (October 1997): 579–84. http://dx.doi.org/10.1002/1521-3951(199710)203:2<579::aid-pssb579>3.0.co;2-x.

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18

Brik, M. G., N. M. Avram, and C. N. Avram. "Crystal Field Analysis of Cr3+Energy Levels in LiGa5O8Spinel." Acta Physica Polonica A 112, no. 5 (November 2007): 1055–60. http://dx.doi.org/10.12693/aphyspola.112.1055.

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19

Sun, Gang, Alexander Hawken, and Peter Harrowell. "The displacement field associated with the freezing of a melt and its role in determining crystal growth kinetics." Proceedings of the National Academy of Sciences 117, no. 7 (February 3, 2020): 3421–26. http://dx.doi.org/10.1073/pnas.1915806117.

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The atomic displacements associated with the freezing of metals and salts are calculated by treating crystal growth as an assignment problem through the use of an optimal transport algorithm. Converting these displacements into timescales based on the dynamics of the bulk liquid, we show that we can predict the activation energy for crystal growth rates, including activation energies significantly smaller than those for atomic diffusion in the liquid. The exception to this success, pure metals that freeze into face-centered cubic crystals with little to no activation energy, are discussed. The atomic displacements generated by the assignment algorithm allows us to quantify the key roles of crystal structure and liquid caging length in determining the temperature dependence of crystal growth kinetics.
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20

Xueyuan, Chen, and Luo Zundu. "Crystal-field analysis of the energy levels and spectroscopic characteristics of in crystal." Journal of Physics: Condensed Matter 10, no. 23 (June 15, 1998): 5147–60. http://dx.doi.org/10.1088/0953-8984/10/23/015.

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21

Gao, Jinyun, Qingli Zhang, Dunlu Sun, Jianqiao Luo, Wenpeng Liu, and Shaotang Yin. "Energy levels fitting and crystal-field calculations of Nd3+ doped in GYSGG crystal." Optics Communications 285, no. 21-22 (October 2012): 4420–26. http://dx.doi.org/10.1016/j.optcom.2012.06.050.

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22

Gao, J. Y., D. L. Sun, Q. L. Zhang, X. F. Wang, W. P. Liu, J. Q. Luo, G. H. Sun, and S. T. Yin. "Experimental investigation and crystal-field modeling of Er3+ energy levels in GSGG crystal." Journal of Alloys and Compounds 671 (June 2016): 389–95. http://dx.doi.org/10.1016/j.jallcom.2016.01.178.

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23

Yang, Wei-Qing, and Wen-Chen Zheng. "Spin-Hamiltonian Parameters of Gd3+ Ion in the Room Temperature Tetragonal Phase of BaTiO3." Zeitschrift für Naturforschung A 69, no. 10-11 (November 1, 2014): 606–10. http://dx.doi.org/10.5560/zna.2014-0057.

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AbstractThe spin-Hamiltonian parameters (g factors g||, g⊥, and zero-field splittings b02 , b04 , b44 , b06 , b46 ) of the 4f7 Gd3+ ion in the tetragonal phase of a BaTiO3 crystal are calculated through the diagonalization (of energy matrix) method based on the one-electron crystal field mechanism. In the calculations, the crystal field parameters are estimated from the superposition model with the structural data of the studied crystal. It is found that by using three adjustable intrinsic parameters Āk(R0) (k=2, 4, 6) in the superposition model, the seven calculated spin-Hamiltonian parameters are in good agreement with the experimental values, suggesting that the diagonalization method based on one-electron crystal field mechanism is effective in the studies of spin-Hamiltonian parameters for 4f7 ions in crystals.
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24

Brik, M. G., and N. M. Avram. "Crystal Field Analysis and Electron-phonon Coupling in Sc2O3:Cr3+." Zeitschrift für Naturforschung A 59, no. 11 (November 1, 2004): 799–803. http://dx.doi.org/10.1515/zna-2004-1113.

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Crystal field analysis of the energy level structure of the Cr3+ ion in the Sc2O3 crystal is performed, using the exchange charge model of the crystal field theory. The crystal field parameters acting on the optical electrons of the Cr3+ ion at the sites with C2 and C3i symmetry are calculated from the crystal structure data. On the basis of the comparison between experimental absorption and emission spectra and theoretically calculated energy levels of Sc2O3:Cr3+, the conclusion is made that the spectroscopic properties of the title host are determined by the Cr3+ ion at the positions of C2 local symmetry. The Stokes shift S = 4.32 and the energy of the phonons effectively interacting with an impurity center h̅ω = 499 cm−1 are derived from the experimental spectra of absorption and emission
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25

Duan, Mei Ling, Jin Hong Li, and Xiao Feng Yang. "Energy-Level Splitting of Cs2NaYCl6 Crystal Doped with Praeseodymium." Advanced Materials Research 634-638 (January 2013): 11–14. http://dx.doi.org/10.4028/www.scientific.net/amr.634-638.11.

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The 91×91 complete energy matrix of 4f2 configuration ion praeseodymium in octahedral cubic crystal field has been constructed based upon the combination of Racah’s group-theoretical consideration with Slater’s wavefunctions. The energy levels of praseodymium (Pr3+) in hexachloride elpasolite crystals Cs2NaYCl6 have been calculated. The calculated results display a good agreement with the experimental values, which implies that the complete energy matrix method can be received as a recommendable tool to perform a theoretical analysis to the doped crystal.
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26

Hu, Chengpeng, Xiangda Meng, Mao-Hua Zhang, Hao Tian, John E. Daniels, Peng Tan, Fei Huang, et al. "Ultra-large electric field–induced strain in potassium sodium niobate crystals." Science Advances 6, no. 13 (March 2020): eaay5979. http://dx.doi.org/10.1126/sciadv.aay5979.

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Electromechanical coupling in piezoelectric materials allows direct conversion of electrical energy into mechanical energy and vice versa. Here, we demonstrate lead-free (KxNa1−x)NbO3 single crystals with an ultrahigh large-signal piezoelectric coefficient d33* of 9000 pm V−1, which is superior to the highest value reported in state-of-the-art lead-based single crystals (~2500 pm V−1). The enhanced electromechanical properties in our crystals are realized by an engineered compositional gradient in the as-grown crystal, allowing notable reversible non-180° domain wall motion. Moreover, our crystals exhibit temperature-insensitive strain performance within the temperature range of 25°C to 125°C. The enhanced temperature stability of the response also allows the materials to be used in a wider range of applications that exceed the temperature limits of current lead-based piezoelectric crystals.
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27

Brandenburg, Jan Gerit, and Stefan Grimme. "Organic crystal polymorphism: a benchmark for dispersion-corrected mean-field electronic structure methods." Acta Crystallographica Section B Structural Science, Crystal Engineering and Materials 72, no. 4 (August 1, 2016): 502–13. http://dx.doi.org/10.1107/s2052520616007885.

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We analyze the energy landscape of the sixth crystal structure prediction blind test targets with variousfirst principlesandsemi-empiricalquantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pairwise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko–Scheffler (TS) method, and the density-dependent dispersion correction dDsC. Recent methodological progress includes higher-order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod–Teller–Muto type three-body contribution, the TS based many-body dispersion (MBD), and the nonlocal van der Waals density functional (vdW-DF2). The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As a computationally less demanding method, we test our recently presented minimal basis Hartree–Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.
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28

Brik, M. G., N. M. Avram, and C. N. Avram. "Comparative crystal field study of Ni2+ energy levels in NiCl2, NiBr2, and NiI2 crystals." Physica B: Condensed Matter 371, no. 1 (January 2006): 43–49. http://dx.doi.org/10.1016/j.physb.2005.09.034.

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29

Zhuang, Qingqu, Shuying Zhai, and Zhifeng Weng. "Efficient numerical algorithms for the phase field crystal equation." International Journal of Modeling, Simulation, and Scientific Computing 12, no. 05 (April 17, 2021): 2150042. http://dx.doi.org/10.1142/s1793962321500422.

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In this paper, based on the Lagrange Multiplier approach in time and the Fourier-spectral scheme for space, we propose efficient numerical algorithms to solve the phase field crystal equation. The numerical schemes are unconditionally energy stable based on the original energy and do not need the lower bound hypothesis of the nonlinear free energy potential. The unconditional energy stability of the three semi-discrete schemes is proven. Several numerical simulations in 2D and 3D are demonstrated to verify the accuracy and efficiency of our proposed schemes.
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30

Huang, Yidong, and Zundu Luo. "Energy Levels and Crystal-Field Calculation of Nd3+ Ions in YAl3 (BO3)4 Crystal." physica status solidi (b) 167, no. 2 (October 1, 1991): K117—K120. http://dx.doi.org/10.1002/pssb.2221670246.

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31

Rukmini, E., C. K. Jayasankar, and M. F. Reid. "Correlation-crystal-field analysis of Nd3+(4f3) energy-level structures in various crystal hosts." Journal of Physics: Condensed Matter 6, no. 30 (July 25, 1994): 5919–36. http://dx.doi.org/10.1088/0953-8984/6/30/011.

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32

Gruber, John B., John R. Quagliano, Michael F. Reid, Frederick S. Richardson, Marian E. Hills, Michael D. Seltzer, Sally B. Stevens, Clyde A. Morrison, and Toomas H. Allik. "Energy levels and correlation crystal-field effects inEr3+-doped garnets." Physical Review B 48, no. 21 (December 1, 1993): 15561–73. http://dx.doi.org/10.1103/physrevb.48.15561.

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33

Brik, M. G., I. Tanaka, T. Ishii, K. Ogasawara, A. Nakamura, and S. Watanabe. "Crystal field analysis of energy level structure of LaF3:Eu3+." Journal of Alloys and Compounds 408-412 (February 2006): 753–56. http://dx.doi.org/10.1016/j.jallcom.2004.11.078.

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34

Antic-Fidancev, E., P. J. Deren, and J. C. Krupa. "Energy levels and crystal field calculations of Er3+ in LaAlO3." Journal of Alloys and Compounds 380, no. 1-2 (October 2004): 376–79. http://dx.doi.org/10.1016/j.jallcom.2004.03.063.

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35

Kinoshita, Toyohiko, Yasutaka Takata, Tokuo Matsukawa, Hirofumi Aritani, Shigehiro Matsuo, Takashi Yamamoto, Masao Takahashi, et al. "Performance of the YB66 soft X-ray monochromator crystal at the wiggler beamline of the UVSOR facility." Journal of Synchrotron Radiation 5, no. 3 (May 1, 1998): 726–28. http://dx.doi.org/10.1107/s0909049597017159.

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Soft X-ray spectra have been measured using a pair of YB66(400) monochromator crystals at the double-crystal monochromator beamline BL7A of the UVSOR facility, where the wiggler radiation has a magnetic field of 4 T. Deformation of the YB66 crystal due to heat load from the synchrotron radiation is almost negligible. The photon flux is about 108 photons s−1 (100 mA)−1 in the energy region 1.2–2 keV and the energy resolution is 0.7 ± 0.1 eV around hν = 1.5 keV. These results show that the YB66 crystal is suitable for use as a monochromator crystal. Its application to soft X-ray spectroscopy is discussed.
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36

Williams, D. E., and D. Gao. "Intermolecular Force-Field Parameters for Boron Hydrides." Acta Crystallographica Section B Structural Science 54, no. 1 (February 1, 1998): 41–49. http://dx.doi.org/10.1107/s0108768197012147.

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Intermolecular atom–atom force-field parameters of the (exp-6-1) type for B and H atoms in boron hydrides were determined. They were obtained by full-weighted least-squares minimization of 116 forces in 15 observed crystal structures of boranes, the heat of sublimation of B10H14 and data from ab initio wavefunction calculations for diborane. Net atomic charges were obtained by fitting them to molecular electric potentials calculated from ab initio wavefunctions. Charges of terminal hydrogens were usually negative and those of bridging hydrogens usually positive. Repulsion-energy calculations for the B2H6 dimer provided the exponential dependence of H...H repulsion. Using the resulting force field, minimum-energy crystal structures were found with structural parameter values close to those of the observed structures. For diborane, energy minimization beginning with randomly oriented molecules placed initially in an 8 × 8 × 8 body-centered orthogonal cell led to the observed crystal structure and monoclinic space group.
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37

Brik, Mikhail G. "Crystal Field Analysis, Electron-Phonon Coupling and Spectral Band Shape Modeling in MgO:Cr3+." Zeitschrift für Naturforschung A 60, no. 6 (June 1, 2005): 437–43. http://dx.doi.org/10.1515/zna-2005-0609.

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A crystal field analysis of the energy level structure of Cr3+ in MgO crystal is performed, using the exchange charge model of the crystal field theory. The crystal field parameters acting on the optical electrons of Cr3+ are calculated from the crystal structure data; good agreement between the calculated and observed energy levels of Cr3+ in the title host is demonstrated. The Stokes shift S=5.9 and the energy of the phonons effectively interacting with the impurity center ħω =405 cm−1 are derived from the experimental spectra of absorption and emission. The obtained values of S and ħω were used for the computer modeling of the Cr3+4T2g → 4A2g emission and 4A2g → 4T2g absorption bands. From this modeling, the zero-phonon energy for the considered transitions was estimated to be 14,000 cm−1.
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38

KADIVAR, ERFAN. "DIRECTOR FIELD OF DISCLINATION LINE IN UNIAXIAL NEMATIC LIQUID CRYSTAL IN THE PRESENCE OF MAGNETIC FIELD." International Journal of Modern Physics B 25, no. 01 (January 10, 2011): 153–58. http://dx.doi.org/10.1142/s0217979211056901.

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Using the Oseen–Zöcher–Frank theory, in the steady state, I study the distortion energy of a disclination line in nematic liquid crystal in the presence of an external magnetic field. The director field around a disclination line is exactly calculated by minimizing the total free energy. The behavior of total free energy as a function of magnetic field for two kinds of nematic material (positive and negative magnetic anisotropy) are discussed. In the short distance limit, the total free energy per unit length is calculated. In this case, the magnetic dependence of total free energy is discussed.
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39

Warsono, Y. Yusuf, Pekik Nurwantoro, and Kamsul Abraha. "Theoretical Studies of the Effects of Magnetic Field on the Phase Transition of Swollen Liquid Crystal Elastomers." Advanced Materials Research 1123 (August 2015): 46–54. http://dx.doi.org/10.4028/www.scientific.net/amr.1123.46.

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The effect of magnetic fields on the swelling of liquid crystal elastomers (LCE) dissolved in liquid crystal (LC) solvent have been studied. The Flory-Huggins model used to calculate the free energy of an isotropic mixing and the Maier-Saupe model used to calculate the free energy of a nematic mixing. Numerical integration method used to calculate the orientational order parameter and the total free energy of system (consists of : nematic free energy, elastic free energy, isotropic mixing free energy and magnetic free energy) and the calculation results graphed as a function of temperatures for various magnetic fields and as function of magnetic fields for various of temperatures. We find that the magnetic field shifts the transition points towards higher temperatures, increases the energy transition, and induces an isotropic phase to paranematic phase.
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40

Brik, M. G., A. El-Korashy, and M. Almokhtar. "Exchange charge model calculations of crystal field parameters and crystal field energy levels for [N(CH3)4]2CoCl4 and [N(CH3)4]2MnCl4 single crystals." Journal of Alloys and Compounds 459, no. 1-2 (July 2008): 71–77. http://dx.doi.org/10.1016/j.jallcom.2007.05.040.

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41

Mei, Yang, Wen-Chen Zheng, and Yu-Guang Yang. "Studies of the crystal field energy levels and g factors for Ce3+ in LiYF4 crystal." Optik 124, no. 19 (October 2013): 3949–50. http://dx.doi.org/10.1016/j.ijleo.2012.11.047.

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42

Duan, Mei Ling, Jin Hong Li, and Xiao Feng Yang. "Theoretical Study of Energy-Level Splitting of Cs2NaPrCl6 Crystal." Applied Mechanics and Materials 268-270 (December 2012): 11–14. http://dx.doi.org/10.4028/www.scientific.net/amm.268-270.11.

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The 91×91 complete energy matrix of 4f2 configuration ion Pr3+ in octahedral cubic crystal field has been constructed based upon the combination of Racah’s group-theoretical consideration with Slater’s wavefunctions. The energy levels of the neat hexachloride elpasolite crystals Cs2NaPrCl6 containing rare earth Pr3+ ion have been calculated. The results imply that the diagonalization to the complete energy matrix can be received as an effective method of performing a theoretical calculation to the rare earth compounds.
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43

Kirova, N., and M. H. Bussac. "Polarons at the field-effect junctions." Journal de Physique IV 12, no. 9 (November 2002): 99–100. http://dx.doi.org/10.1051/jp4:20020370.

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We consider the interface of a molecular crystal with a polar dielectrics. Coulomb interaction of free electrons in the crystal with surface polar phonons of the dielectrics can lead to self-trapping of carriers. For typical parameters of field effect transistors the binding energy is found to be high enough t o allow for formation of a strongly coupled polaron. The effect is further enhanced at presence of the bias electric filed.
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44

Filippini, G., A. Gavezzotti, and J. J. Novoa. "Modelling the crystal structure of the 2-hydronitronylnitroxide radical (HNN): observed and computer-generated polymorphs." Acta Crystallographica Section B Structural Science 55, no. 4 (August 1, 1999): 543–53. http://dx.doi.org/10.1107/s0108768199001202.

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The crystal structures of two polymorphs of 4,4,5,5-tetramethyl-4,5-dihydro-1H-imidazol-1-oxyl 3-oxide (the 2-hydronitronylnitroxide radical, HNN) are analyzed by packing energy criteria. Other unobserved polymorphic crystal structures are generated using a polymorph predictor package and three different force fields, one of which is without explicit Coulomb-type terms. The relative importance of several structural motifs (hydrogen-bonded dimers, shape-interlocking dimers or extended hydrogen-bonded chains) is discussed. As usual, many crystal structures within a narrow energy range are generated by the polymorph predictor, confirming that ab initio crystal-structure prediction is still problematic. Comparisons of powder patterns generated from the atomic coordinates of the X-ray structure and from computational crystal structures confirm that although the energy ranking depends on the force field used, the X-ray structure of the \alpha polymorph was found to be among the most stable ones produced by the polymorph predictor, even using the chargeless force field.
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45

Philippe, T., H. Henry, and M. Plapp. "A regularized phase-field model for faceting in a kinetically controlled crystal growth." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 476, no. 2241 (September 2020): 20200227. http://dx.doi.org/10.1098/rspa.2020.0227.

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At equilibrium, the shape of a strongly anisotropic crystal exhibits corners when for some orientations the surface stiffness is negative. In the sharp-interface problem, the surface free energy is traditionally augmented with a curvature-dependent term in order to round the corners and regularize the dynamic equations that describe the motion of such interfaces. In this paper, we adopt a diffuse interface description and present a phase-field model for strongly anisotropic crystals that is regularized using an approximation of the Willmore energy. The Allen–Cahn equation is employed to model kinetically controlled crystal growth. Using the method of matched asymptotic expansions, it is shown that the model converges to the sharp-interface theory proposed by Herring. Then, the stress tensor is used to derive the force acting on the diffuse interface and to examine the properties of a corner at equilibrium. Finally, the coarsening dynamics of the faceting instability during growth is investigated. Phase-field simulations reveal the existence of a parabolic regime, with the mean facet length evolving in t , with t the time, as predicted by the sharp-interface theory. A specific coarsening mechanism is observed: a hill disappears as the two neighbouring valleys merge.
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46

S., Laachir, Moussetad M., Adhiri R., and Fahli A. "Crystal-Field Energy Levels of Trivalent Erbium Ion in Cubic Symmetry." Zeitschrift für Naturforschung A 66a (2011): 457. http://dx.doi.org/10.5560/zna.2011.66a0457.

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47

Yin Chun-Hao, Han Kui, and Ye Shi-Wang. "Ground-state energy and zero-field splitting parameters in GeFe2O4 crystal." Acta Physica Sinica 52, no. 9 (2003): 2280. http://dx.doi.org/10.7498/aps.52.2280.

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48

Guo, Can, Jincheng Wang, Zhijun Wang, Junjie Li, Yaolin Guo, and Yunhao Huang. "Interfacial free energy adjustable phase field crystal model for homogeneous nucleation." Soft Matter 12, no. 20 (2016): 4666–73. http://dx.doi.org/10.1039/c6sm00774k.

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49

Chen, Xia, Shang Yuan Ren, and John D. Dow. "Splitting of angular momentum energy levels in a tetrahedral crystal field." Philosophical Magazine B 79, no. 1 (January 1999): 177–204. http://dx.doi.org/10.1080/13642819908206792.

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50

Laachir, Said, Mohamed Moussetad, and Rahma Adhiri. "Crystal-Field Energy Levels of Trivalent Erbium Ion in Cubic Symmetry." Zeitschrift für Naturforschung A 66, no. 6-7 (July 1, 2011): 457–60. http://dx.doi.org/10.1515/zna-2011-6-711.

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This paper describes a scheme for the numerical calculation of crystal field (CF) energy levels and at the same time wave functions of the trivalent erbium ion in cubic symmetry. The 16-fold degenerate term 4I15=2 of the trivalent erbium ion splits into three Stark quartets Γ8 and two different doublets Γ6 and Γ7 (irreducible representations). The CF energy matrix of the Er3+ ion has been constructed and calculated from the complete diagonalization method, and the corresponding wave functions were used to calculate the ground state g-values. This method is outlined and illustrated by the examples of the Si:Er for comparison. The calculated g-factors are g = 6:8 and g = 6:0 for Γ6 and Γ7, respectively
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