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Raman spectra of the products It is well-known that Raman spectra are an important tool for identifying the lattice dynamics and the crystal electric field splitting of rare-earth hexaborides¡£ Fig 8 shows Raman spectra of RB6 nanocubes and nanoparticles,respectively¡£According to group theory, the hexaboridess tructure has a Pm3m cubic symmetry,which contains A1g+Eg+T1g+T2g+2T1u+T2u vibrational modes, where A1g, Eg, and T2g are Raman activephonons¡£The A1g and Eg modes originate from the stretching vibration of B¨CB bonds and T2g is due to the valence angle bending of B¨CB¨CB in the boron lattice¡£ It can be seen that the sespectra are shifted along the vertical direction,and the order corresponds to the decrease of the lattice constants of RB6 from the top to bottom¡£ However,the peaks of Raman spectra of the same compound of RB6 nanocubes and nanoparticles remain unchanged in the present experiment¡£The three expected main peaksare observed around680cm_1 (T2g), 1140cm_1 (Eg) and1260cm_1 (A1g), which are inagreement with earlier reports [32¨C34], and they completelysatisfy the polarization selection rule in the cubic symmetry¡£ These three prominent peaks are additional confirmation for the formation of hexaborides because the peaks obey these lection rule for the hexaborides¡¯cubic symmetry¡£ Abroad peak around 1400cm-1, labeled as *, is commonly observed with a relatively strong intensity for trivalent and intermediate-valent crystals¡£ For trivalentcase,twice the energy of T2g is slightly lower than the peak energy,however,the peak energy systematically follows twice the energy of T2g¡£ In LaB6, the peak energy is far from twice the energy of T2u and that of T2g is very close to the peak energy¡£For SmB6 the energy coincidence is very good¡£Thus it can be concluded that the peak observed in the trivalent case originates from these cond-order process of T2g¡£ |
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Raman spectra of the products ÑùÆ·µÄÀÂü¹âÆ×Ñо¿ It is well-known that Raman spectra are an important tool for identifying the lattice dynamics and the crystal electric field splitting of rare-earth hexaborides¡£ ÖÚËùÖÜÖª£¬ÀÂü¹âÆ×·ÖÎöÊÇʶ±ðÏ¡ÍÁÁù½ÇÅð»¯Îï¾§Ì嶯Á¦Ñ§ºÍ¾§³¡·ÖÁѵÄÖØÒªÊֶΡ£ Fig 8 shows Raman spectra of RB6 nanocubes and nanoparticles,respectively¡£ ͼ8·Ö±ð¸ø³öÁËRB6ÄÉÃ׹ܺÍÄÉÃ׿ÅÁ£µÄÀÂü¹âÆ×¡£ According to group theory, the hexaboridess tructure has a Pm3m cubic symmetry,which contains A1g+Eg+T1g+T2g+2T1u+T2u vibrational modes, where A1g, Eg, and T2g are Raman activephonons¡£ ¸ù¾ÝȺÂÛ£¬Åð»¯Îï½á¹¹¾ßÓÐÁ¢·½¶Ô³ÆµÄPm3m¿Õ¼äµãȺ£¬°üÀ¨A1g+Eg+T1g+T2g+2T1u+T2uÕâÑùһЩÕñ¶¯Ä££¬ÆäÖÐA1g, Eg, and T2gÊÇÀÂü»îÐÔµÄÉù×ÓÄ£¡£ The A1g and Eg modes originate from the stretching vibration of B¨CB bonds and T2g is due to the valence angle bending of B¨CB¨CB in the boron lattice¡£ A1gºÍEgÄ£À´Ô´ÓÚB-B¼üµÄÀÉìÕñ¶¯£¬T2gÀ´Ô´ÓÚÅ𾧸ñÖÐB-B-B¼ü½ÇµÄÍäÇúÕñ¶¯¡£ It can be seen that the sespectra are shifted along the vertical direction,and the order corresponds to the decrease of the lattice constants of RB6 from the top to bottom¡£ ´ÓͼµÄÉÏÃæÍùÏ¿´£¬ÀÂüÆ×ÔÚÊúÖ±·½ÏòÉÏ·¢ÉúÒÆ¶¯£¬ÆäÒÆ¶¯³Ì¶È¶ÔÓ¦ÓÚRB6¾§¸ñ³£ÊýµÄ¼õС However,the peaks of Raman spectra of the same compound of RB6 nanocubes and nanoparticles remain unchanged in the present experiment¡£ µ«ÊÇ£¬ÊµÑéÖУ¬RB6ÄÉÃ׹ܺÍÄÉÃ׿ÅÁ£µÄÀÂü·åȴûÓз¢Éú±ä»¯¡£ The three expected main peaksare observed around680cm_1 (T2g), 1140cm_1 (Eg) and1260cm_1 (A1g), which are inagreement with earlier reports [32¨C34], ÕýÈçËùÆÚ´ýµÄÄÇÑù£¬Èý¸öÖ÷ÒªµÄÀÂü·å³öÏÖÔÚ 680 m_1 (T2g), 1140cm_1 (Eg) and1260cm__1 (A1g)£¬ÕâºÍÔçÏȵÄÎÄÏ×±¨µÀÒ»Ö¡£ and they completelysatisfy the polarization selection rule in the cubic symmetry¡£ ²¢ÇÒËûÃÇÍêÃÀÎǺÏÁ¢·½¶Ô³Æ½á¹¹µÄ¼«»¯Ñ¡Ôñ¹æÔò¡£ These three prominent peaks are additional confirmation for the formation of hexaborides because the peaks obey these lection rule for the hexaborides¡¯cubic symmetry¡£ ÕâÈý¸öÍ»³öµÄ·å£¬¸ü¼Ó֤ʵÁËÁù½ÇÅð»¯Îï½á¹¹µÄÐγɣ¬ÒòΪÕâЩ·å×ñ´ÓÕâЩÁù½ÇÁ¢·½¶Ô³ÆÐÔµÄÑ¡Ôñ¶¨Ôò Abroad peak around 1400cm-1, labeled as *, is commonly observed with a relatively strong intensity for trivalent and intermediate-valent crystals¡£ ¶ÔÓÚ3¼Û»òÖмä¼ÛλµÄ¾§Ì壬ͨ³£ÔÚÔÚ1400cm-1,±ê¼ÇΪ *µÄµØ·½Í¨³£»á³öÏÖÒ»¸ö½ÏÇ¿µÄ¿í·å¡£ For trivalentcase,twice the energy of T2g is slightly lower than the peak energy,however,the peak energy systematically follows twice the energy of T2g¡£ ¶ÔÓÚ3¼ÛÇé¿ö£¬T2gµÄË«±¶ÄÜÁ¿±ÈÆð¸Ã·åµÄÄÜÁ¿ÉÔС£¬Õâ¸ö·åÄÜÁ¿ÏµÍ³µØ½ôËæT2gÄÜÁ¿µÄÁ½±¶Öµ¡£ In LaB6, the peak energy is far from twice the energy of T2u and that of T2g is very close to the peak energy¡£ ÔÚLaB6ÖУ¬·åÄÜÁ¿±ÈÆðT2uµÄ2±¶ÄÜÁ¿ÒªÐ¡ºÜ¶à¡£µ«ÊÇT2gµÄ2±¶ÄÜÁ¿È¥ºÜ½Ó½ü·åÄÜÁ¿¡£ For SmB6 the energy coincidence is very good¡£Thus it can be concluded that the peak observed in the trivalent case originates from these cond-order process of T2g¡£ ¶ÔÓÚSmB6£¬ÄÜÁ¿µÄ·ûºÏÒ²·Ç³£ºÃ¡£Òò´Ë£¬¿ÉÒԵóö½áÂÛ£¬ÔÚ3¼ÛÇé¿öϹ۲쵽µÄ·åÀ´Ô´ÓÚT2gµÄcond-order¹ý³Ì¡£ |
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