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10. STORAGE OF SPENT NUCLEAR FUEL

10.4. Safety issues in a storage facility for SNF

10.5.2. User requirement UR1: Robustness of design during normal

(X = Br, Cl)

Por outro lado, foi investigado a dependência das características principais dos modos vibracionais dos compostos multiferróicos isoestruturais, brometo de cobre (CuBr2) e cloreto de cobre (CuCl2) anidros em função da temperatura.

Os espectros Raman em temperatura ambiente conrmam os três modos vibra- cionais previstos pela teroria de grupo, já a análise realizada a cerca da frequência e largura a meia altura dos fônons sob variação de temperatura mostram desvios do comportamento anarmônico previsto por Balkanski, que sugerem uma mudança de fase magnética e são esperados em compostos que apresentam o acoplamento spin-fônon. Uma análise mais aprofundada do desvio dos fônons relacionados com o comportamento magnético foi utilizada. Baseada na composição da susceptibilidade magnética como sendo formada por dois fatores, uma contribuição da susceptibili- dade devido ao ordenamento magnético de longo alcance e outra sendo a contribui- ção devido a interação de baixa dimensão (intra e inter cadeias), com resultados que evidenciam boa concordância com os modelos propostos, mas não em toda faixa de temperatura onde o ordenamento antiferromagnético existe. Essa abordagem é in- teressante e útil quando a magnetização da amostra não é determinada apenas pelo ordenamento de longo alcance, mas também por sistemas de baixa dimensionalidade (intra e inter cadeias).

REFERÊNCIAS BIBLIOGRÁFICAS

[1] Melvin M Vopson. Fundamentals of multiferroic materials and their possible applications. Critical Reviews in Solid State and Materials Sciences, 40(4):223 250, 2015.

[2] Shanghui Ye, Yunqi Liu, Kun Lu, Weiping Wu, Chunyan Du, Ying Liu, Hong- tao Liu, Ti Wu, and Gui Yu. An alternative approach to constructing solution processable multifunctional materials: Their structure, properties, and appli- cation in high-performance organic light-emitting diodes. Advanced Functional Materials, 20(18):31253135, 2010.

[3] Hans Schmid. Magnetic ferroelectric materials. Bulletin of Materials Science, 17(7):14111414, 1994.

[4] Dmitry V Efremov, Jeroen Van Den Brink, and Daniel I Khomskii. Bond- versus site-centred ordering and possible ferroelectricity in manganites. Nature materials, 3(12):853, 2004.

[5] G Lawes and GJPDAP Srinivasan. Introduction to magnetoelectric coupling and multiferroic lms. Journal of Physics D: Applied Physics, 44(24):243001, 2011.

[6] Silvia Picozzi and Claude Ederer. First principles studies of multiferroic mate- rials. Journal of Physics: Condensed Matter, 21(30):303201, 2009.

REFERÊNCIAS BIBLIOGRÁFICAS 40 [7] Kun Cao, RD Johnson, Feliciano Giustino, Paolo G Radaelli, GC Guo, and Lixin He. First-principles study of multiferroic rbfe (moo 4) 2. Physical Review B, 90(2):024402, 2014.

[8] Z Czapla, J Janczak, O Czupi«ski, J Przesªawski, and M Crofton. Structural phase transition and ferroelasticity in (h2nnh3) 3cdbr5 crystal. Journal of Physics and Chemistry of Solids, 124:9499, 2019.

[9] Giorgio Bertotti and Isaak D Mayergoyz. The science of hysteresis: Hysteresis in materials, volume 3. Gulf Professional Publishing, 2006.

[10] Nicola A Hill. Why are there so few magnetic ferroelectrics? Journal of physics and chemistry B, 104(29):66946709, 2000.

[11] L Fuentes, M Garca, J Matutes-Aquino, and D Ros-Jara. Magnetoelectricity via crystallography. Journal of alloys and compounds, 369(1-2):1013, 2004. [12] Manfred Fiebig. Revival of the magnetoelectric eect. Journal of physics D:

applied physics, 38(8):R123, 2005.

[13] VF Freitas, DZ Montanher, TGM Bonadio, VL Mazzocchi, J Mestnik-Filho, CBR Parente, D Garcia, JA Eiras, LF Cótica, and IA Santos. Intrinsic features of the magnetoeletric coupling mechanism in displacive multiferroics. Journal of Applied Physics, 114(13):134102, 2013.

[14] MM Vopson, YK Fetisov, G Caruntu, and G Srinivasan. Measurement tech- niques of the magneto-electric coupling in multiferroics. Materials, 10(8):963, 2017.

[15] M Balkanski, RF Wallis, and E Haro. Anharmonic eects in light scattering due to optical phonons in silicon. Physical Review B, 28(4):1928, 1983.

[16] E Granado, A Garcia, JA Sanjurjo, C Rettori, I Torriani, F Prado, RD Sánchez, A Caneiro, and SB Osero. Magnetic ordering eects in the Raman spectra of La1−x Mn1−x O3. Physical Review B, 60(17):11879, 1999.

REFERÊNCIAS BIBLIOGRÁFICAS 41 [17] John MD Coey. Magnetism and magnetic materials. Cambridge University

Press, 2010.

[18] Neil W Ashcroft and N David Mermin. Solid state physics (holt, rinehart and winston, new york, 1976), volume 403. 2005.

[19] DJ Lockwood and MG Cottam. The spin-phonon interaction in fef2 and mnf2 studied by raman spectroscopy. Journal of Applied Physics, 64(10):58765878, 1988.

[20] W Baltensperger and JS Helman. Inuence of magnetic order in insulators on optical phonon frequency. Helvetica physica acta, 41(6-7):668+, 1968.

[21] BS Araújo, AM Arévalo-López, JP Atteld, CWA Paschoal, and AP Ayala. Spin-phonon coupling in melanothallite cu2ocl2. Applied Physics Letters, 113(22):222901, 2018.

[22] MN Iliev, MM Gospodinov, MP Singh, J Meen, KD Truong, P Fournier, and S Jandl. Growth, magnetic properties, and raman scattering of la 2 nimno 6 single crystals. Journal of Applied Physics, 106(2):023515, 2009.

[23] RB Macedo Filho, DAB Barbosa, H Reichlova, X Marti, AS de Menezes, AP Ayala, and CWA Paschoal. Role of rare-earth ionic radii on the spin phonon coupling in multiferroic ordered double perovskites. Materials Research Express, 2(7):075201, 2015.

[24] RX Silva, H Reichlova, X Marti, DAB Barbosa, MW Lufaso, BS Araujo, AP Ayala, and CWA Paschoal. Spin-phonon coupling in gd (co1/2mn1/2) o3 perovskite. Journal of Applied Physics, 114(19):194102, 2013.

[25] Pierre Toulemonde, Pierre Bordet, Pierre Bouvier, and Jens Kreisel. Single- crystalline bimno 3 studied by temperature-dependent x-ray diraction and raman spectroscopy. Physical Review B, 89(22):224107, 2014.

[26] Sudipta Mahana, Bipul Rakshit, Raktima Basu, Sandip Dhara, Boby Joseph, U Manju, Subhendra D Mahanti, and D Topwal. Local inversion symmetry

REFERÊNCIAS BIBLIOGRÁFICAS 42 breaking and spin-phonon coupling in the perovskite gdcro 3. Physical Review B, 96(10):104106, 2017.

[27] E Aytan, B Debnath, F Kargar, Y Barlas, MM Lacerda, JX Li, RK Lake, J Shi, and AA Balandin. Spin-phonon coupling in antiferromagnetic nickel oxide. Applied Physics Letters, 111(25):252402, 2017.

[28] MA Prosnikov, AN Smirnov, V Yu Davydov, RV Pisarev, NA Lyubochko, and SN Barilo. Magnetic dynamics and spin-phonon coupling in the antiferromagnet ni 2 nbbo 6. Physical Review B, 98(10):104404, 2018.

[29] Raimundo Bezerra Macedo Filho, Alejandro Pedro Ayala, and Carlos Wil- liam de Araujo Paschoal. Spin-phonon coupling in y2nimno6 double perovskite probed by raman spectroscopy. Applied Physics Letters, 102(19):192902, 2013. [30] Rosivaldo X Silva, Manoel C Castro Júnior, Susana Yáñez-Vilar, Manuel Sán- chez Andújar, Jorge Mira, María Antonia Señarís-Rodríguez, and Carlos Wil- liam A Paschoal. Spin-phonon coupling in multiferroic y2comno6. Journal of Alloys and Compounds, 690:909915, 2017.

[31] MN Iliev, H Guo, and A Gupta. Raman spectroscopy evidence of strong spin- phonon coupling in epitaxial thin lms of the double perovskite la 2 ni mn o 6. Applied physics letters, 90(15):151914, 2007.

[32] AB Sushkov, O Tchernyshyov, W Ratcli II, SW Cheong, and HD Drew. Pro- bing spin correlations with phonons in the strongly frustrated magnet zncr 2 o 4. Physical review letters, 94(13):137202, 2005.

[33] Tsuyoshi Kimura, T Goto, H Shintani, K Ishizaka, T-h Arima, and Y Tokura. Magnetic control of ferroelectric polarization. nature, 426(6962):55, 2003. [34] T Kimura, S Ishihara, H Shintani, T Arima, KT Takahashi, K Ishizaka, and

Y Tokura. Distorted perovskite with e g 1 conguration as a frustrated spin system. Physical Review B, 68(6):060403, 2003.

REFERÊNCIAS BIBLIOGRÁFICAS 43 [35] J Laverdiere, S Jandl, AA Mukhin, V Yu Ivanov, VG Ivanov, and MN Iliev. Spin-phonon coupling in orthorhombic r mn o 3 (r= pr, nd, sm, eu, gd, tb, dy, ho, y): A raman study. Physical Review B, 73(21):214301, 2006.

[36] Peter C Burns and Frank C Hawthorne. Tolbachite, cucl2, the rst example of cu2+ octahedrally coordinated by cl-. American Mineralogist, 78(1-2):187189, 1993.

[37] Lindsay Helmholz. The crystal structure of anhydrous cupric bromide. Journal of the American Chemical Society, 69(4):886889, 1947.

[38] O Oeckler and A Simon. Redetermination of the crystal structure of cop- per dibromide, cubr2. Zeitschrift für Kristallographie-New Crystal Structures, 215(1):1313, 2000.

[39] MG Banks, RK Kremer, C Hoch, A Simon, B Ouladdiaf, J-M Broto, H Rakoto, C Lee, and M-H Whangbo. Magnetic ordering in the frustrated heisenberg chain system cupric chloride cucl 2. Physical Review B, 80(2):024404, 2009.

[40] Li Zhao, Tsu-Lien Hung, Ching-Chien Li, Yang-Yuan Chen, Maw-Kuen Wu, Reinhard K Kremer, Michael G Banks, Arndt Simon, Myung-Hwan Whangbo, Changhoon Lee, et al. Cubr2a new multiferroic material with high critical temperature. Advanced Materials, 24(18):24692473, 2012.

[41] JW Stout and RC Chisholm. Heat capacity and entropy of cucl2 and crcl2 from 11 to 300 k. magnetic ordering in linear chain crystals. The journal of chemical physics, 36(4):979991, 1962.

[42] S Seki, T Kurumaji, S Ishiwata, H Matsui, H Murakawa, Y Tokunaga, Y Ka- neko, T Hasegawa, and Y Tokura. Cupric chloride cucl 2 as an s= 1 2 chain multiferroic. Physical Review B, 82(6):064424, 2010.

[43] C. Lee, Jia Liu, M. H. Whangbo, H. J. Koo, R. K. Kremer, and A. Simon. Investigation of the spin exchange interactions and the magnetic structure of the high-temperature multiferroic CuBr 2. Physical Review B - Condensed Matter and Materials Physics, 86(6):15, 2012.

REFERÊNCIAS BIBLIOGRÁFICAS 44 [44] SW Peterson and Henri A Levy. Proton positions in cucl2· 2h2o by neutron

diraction. The Journal of Chemical Physics, 26(1):220221, 1957.

[45] Sydney Brownstein, Nam Fong Han, Eric Gabe, and Yvon LePage. A redeter- mination of the crystal structure of cupric chloride dihydrate. Zeitschrift für Kristallographie-Crystalline Materials, 189(1-4):1316, 1989.

[46] IR Beattie, TR Gilson, and GA Ozin. Single-crystal raman spectroscopy of `square-planar'and `tetrahedral'cucl 4 2ions, of the zncl 4 2ion, and of cucl 2, 2h 2 o. Journal of the Chemical Society A: Inorganic, Physical, Theoretical, pages 534541, 1969.

[47] A Engberg. An x-ray renement of the crystal structure of copper (ii) chloride dihydrate. Acta Chem. Scand, 24(10):35103526, 1970.

[48] Marcin Wojdyr. Fityk: a general-purpose peak tting program. Journal of Applied Crystallography, 43(5-1):11261128, 2010.

[49] I Vasilef. Qtiplot: data analysis and scientic visualization. Version 0.9, 8, 2011.

[50] Denis L Rousseau, RPSPS Porto Bauman, and SPS Porto. Normal mode de- termination in crystals. Journal of Raman Spectroscopy, 10(1):253290, 1981. [51] H Tanaka, J Henning, HD Lutz, and G Kliche. Infrared and raman spectra

of cucl2· 2 (h, d) 2o and k2cucl4· 2 (h, d) 2o. vibrational modes, assignment and coupling of the water librations. Spectrochimica Acta Part A: Molecular Spectroscopy, 43(3):395400, 1987.

[52] Gwen H Thomas, Michael Falk, and Osvald Knop. Infrared studies of wa- ter in crystalline hydrates: K2cucl4ˆ 2h2o. Canadian Journal of Chemistry, 52(7):10291041, 1974.

[53] Chong Wang, Daiwei Yu, Xiaoqiang Liu, Rongyan Chen, Xinyu Du, Biaoyan Hu, Lichen Wang, Kazuki Iida, Kazuya Kamazawa, Shuichi Wakimoto, et al.

REFERÊNCIAS BIBLIOGRÁFICAS 45 Observation of unusual magnetoelastic eects in a quasi-1d spiral magnet. arXiv preprint arXiv:1512.07120, 2015.

[54] Derek Albert Long and DA Long. Raman spectroscopy, volume 276. McGraw- Hill New York, 1977.

[55] Michael E Fisher. Relation between the specic heat and susceptibility of an antiferromagnet. Philosophical Magazine, 7(82):17311743, 1962.

[56] JN McElearney, S Merchant, and RL Carlin. Isotropic magnetic exchange in magnesium dichloride dihydrate, mncl2. 2h2o, a chemical linear chain. Inorga- nic Chemistry, 12(4):906908, 1973.

[57] William E Hateld. New magnetic and structural results for uniformly spa- ced, alternatingly spaced, and ladder-like copper (ii) linear chain compounds. Journal of Applied Physics, 52(3):19851990, 1981.

ÍNDICE REMISSIVO

A

acoplamento spin-fônon, 4 Air Products and Chemicals, 15 aproximação de campo médio, 9 B

Bruker AXS, 16 Bruker Optics, 15 C

ciência dos materiais, 1 coeciente magnetoelétrico, 3 curvas lorentzianas, 26 E Edwards, 16 espectroscopia Raman, 11 F

física do estado sólido, 1 ferro/antiferromagnetismo, 1 ferroelasticidade, 1

ferroeletricidade, 1

função escalar de correlação de spin, 5

H

Heisenberg, 5

Horiba Jobin Yvon, 14 Horiba Jobin-Yvon, 15 I

integral de troca, 4 L

Linkan Scientic instruments, 15 LynxEye, 16 M magnetoeletricidade, 2 materiais multiferróicos, 1 materiais multifuncionais, 1 modelo de Balkanski, 4 multiferróico magnetoelétrico, 2 N Netzsch, 15 Nikon, 15 O Olympus, 15 46

ÍNDICE REMISSIVO 47 T

tensor de acoplamento spin-fônon, 7 tensor de ligação iônica, 7

tensor potêncial elástico da rede, 7