• Title/Summary/Keyword: triangular numbers

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Crystallographic Studies of $Ag^+$-and $Ca^{2+}$- Exchanged Zeolite A Reacting with Rubidium Vapor (루비듐 증기와 반응한 $Ag^+$ 이온과 $Ca^{2+}$ 이온으로 치환된 제올라이트 A의 결정학적 연구)

  • Han, Young-Wook;Song, Seong-Hwan;Kim, Yang
    • Journal of the Mineralogical Society of Korea
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    • v.4 no.1
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    • pp.22-31
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    • 1991
  • Three crystal structures of dehydrated $Ag^+$-and $Ca^{2+}$- exchanged zeolite $A(Ag_4Ca_4-A,\;Ag_^Ca_3-A,\;and\;Ag_8Ca_2-A)$ treated at 250${\circ}C$ with 0.1 Torr of Rb vapor have been determined by single-crystal x-ray diffraction techniques in the cubic space group Pm3m at 21(1)${\circ}C$ (a=12,271(1)${\AA}$, 12.255(1)${\AA}$, and 12.339(1)${\AA}$, respectively). Their structures were refined to the final error indices. R(weighted) of 0.072 with 130 reflections, 0.050 with 110 reflections, and 0.083 with 86 reflections, respectively, for which $I>3{\rho}(I)$. In each structure, Rb species are found at three different crystallographic sites:3$Rb^+$+ions per unit cell are located at 8-ring centers, ca. 5.6 to 6.4 $Rb^+$ ions are found opposite 6-rings on threefold axes in the large cavity, and ca. 2.5 to 3.0 $Rb^+$ ions are found on threefold axes in the sodalite unit. Also, Ag species are found at two different crystallographic stites: ca. 0.7 to 2.1 $Ag^+$ lie opposite 4-rings and ca. 2.2 to 4.8 Ag atoms are located near the center of the large cavity. In these structures, the numbers of Ag atoms per unit cell are 2.2, 2.4, and 4.8, respectively, and these may form hexasilver clusters at the centers of the large cavities. The $Rb^+$ ions, by blocking 8-rings, may have prevented silver from migrating out of the structure. Each hexasilver cluster is stabilized by coordination to up to 13 $Rb^+$ions. An excess absorption of about 0.8 Rb atom per unit cell indicates that the presence of a triangular symmetric $(Rb_3)2^{+}$ cation in sodalite cavity. At least one large-cavity six-ring $Rb^+$ ion must necessarily approach this cluster and may be viewed as a member of it to give $(Rb)_4^{3+}$, $(Rb)_5^{4+}$ or $(Rb)_6^{5+}$.

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