• Journal of the Korean Chemical Society
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• v.7 no.4
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• pp.293-298
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• 1963

The crystal structure of ethylenediamine dihydrochloride has been determined by the two-dimensional Patterson methods and refined by two-dimensional Fourier syntheses. The unit cell dimensions are a = 4.44${\pm}$0.02, b = 6.88${\pm}$0.02, c = 9.97${\pm}$0.02 ${\AA}$, ${\beta}$ = 92${\pm}$$1^{\circ}$. The space group is $P2_1_{/c}$. The carbon and nitrogen atoms in the ethylenediamine itself lie on one plane and its structure has a trans-form with a centre of symmetry in it, and C-C distance of 1.54 ${\AA}$, C-N distance of 1.48${\AA}$ and C-C-N bond angle of $109.07^{\circ}$. The molecules are linked by N-H${\cdots}$Cl hydrogen bonds with distance of 3.14, 3.16 and 3.22 ${\AA}$ forming three dimensional network. The values of reliability factor for F(okl), F(hol) and F(hko) are 0.11, 0.10 and 0.09 respectively.

• YAKHAK HOEJI
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• v.21 no.3
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• pp.146-158
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• 1977

N$_{1}$-cyclohexyl-$N_{2}$-(o-chlorobenzal) imino thiourea, $C_{14}$H$_{18}$N$_{3}$SCI, crystallizes in $C_{2}$/c, with a=19.68, b=7.74, c=20.42$\AA$, ${\beta}$=$92.$8^{\circ}$ and eight formula units in the unit cell. The structure was solved by the study of Patterson sections, calculated from three-dimensional film data, and was refined by block-diagonal least-squares methods to R=0.16 based on 1288 independent intensity data. The rest atoms of N$_{1}$-cyclohexyl-$_{2}$-(o-chlorobenzal) imino thiourea molecule excluding cyclohexan ring and chlorine atoms approximately lie on a plane. A pair of molecules related by the symmetry centers are connected directly with the N-H.......S hydrogen bonds. Apart from the hydrogen bonding system the structure is held together by the van der Waals forces.

• School Mathematics
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• v.7 no.4
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• pp.391-402
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• 2005

The purpose of this study is to resolve misunderstanding for centroid of a triangle and to clarify several logical problems in finding the centroid of a Polygon. The conclusions are the followings. For a triangle, the misunderstanding that the centroid of a figure is the intersection of two lines that divide the area of the figure into two equal part is more easily accepted caused by the misinterpretation of a median. Concerning the equilibrium of a triangle, the median of it has the meaning that it makes the torques of both regions it divides to be equal, not the areas. The errors in students' strategies aiming for finding the centroid of a polygon fundamentally lie in the lack of their understanding of the mathematical investigation of physical phenomena. To investigate physical phenomena mathematically, we should abstract some mathematical principals from the phenomena which can provide the appropriate explanations for then. This abstraction is crucial because the development of mathematical theories for physical phenomena begins with those principals. However, the students weren't conscious of this process. Generally, we use the law of lever, the reciprocal proportionality of mass and distance, to explain the equilibrium of an object. But some self-evident principles in symmetry may also be logically sufficient to fix the centroid of a polygon. One of the studies by Archimedes, the famous ancient Greek mathematician, gives a solution to this rather awkward situation. He had developed the general theory of a centroid from a few axioms which concerns symmetry. But it should be noticed that these axioms are achieved from the abstraction of physical phenomena as well.

• Proceedings of the Computational Structural Engineering Institute Conference
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• 1995.10a
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• pp.225-233
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• 1995

This paper presents an efficient numerical method for computation of eigenpair derivatives for the real symmetric eigenvalue problem with distinct and multiple eigenvalues. The method has very simple algorithm and gives an exact solution. Furthermore, it saves computer storage and CPU time. The algorithm preserves the symmetry and band of the matrices, allowing efficient computer storage and solution techniques. Thus, the algorithm of the proposed method will be inserted easily in the commercial FEM codes. Results of the proposed method for calculating the eigenpair derivatives are compared with those of Rudisill and Chu's method and Nelson's method which is efficient one in the case of distinct natural frequencies. As an example to demonstrate the efficiency of the proposed method in the case of distinct eigenvalues, a cantilever plate is considered. The design parameter of the cantilever plate is its thickness. For the eigenvalue problem with multiple natural frequencies, the adjacent eigenvectors are used in the algebraic equation as side conditions, they lie adjacent to the m (multiplicity of multiple natural frequency) distinct eigenvalues, which appear when design parameter varies. As an example to demonstrate the efficiency of the proposed method in the case of multiple natural frequencies, a cantilever beam is considered. Results of the proposed method fDr calculating the eigenpair derivatives are compared with those of Bailey's method (an amendation of Ojalvo's work) which finds the exact eigenvector derivatives. The design parameter of the cantilever beam is its height. Data is persented showing the amount of CPU time used to compute the first ten eigenpair derivatives by each method. It is important to note that the numerical stability of the proposed method is proved.

• Bulletin of the Korean Chemical Society
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• v.8 no.2
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• pp.69-72
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• 1987

The structures of dehydrated $Ag_9Cs_3$-A treated with hydrogen gas at three different temperatures have been determined by single-crystal X-ray diffraction techniques. Their structures were solved and refined in the cubic space group Pm3m at 23(1) $^{\circ}C$. All crystals were ion exchanged in flowing streams of aqueous $AgNO_3$/$CsNO_3$ with a mole ratio 1:3.0 to achieve the desired crystal composition. The structures treated with hydrogen at $23^{\circ}C(a=12.288(1)\;{\AA})\;and\;310^{\circ}C(a=12.291(2)\;{\AA})$ refined to the final error indices R1 = 0.091 and R2 = 0.079, and 0.065 and 0.073, respectively, using the 216 and 227 reflections, respectively, for which I >3${\sigma}$(I). In both of these structures, eight $Ag^+$ ions are found nearly at 6-ring centers, and three $Cs^+$ ions lie at the centers of the 8-rings at sites of $D_{4h}$ symmetry. One $Ag^{\circ}atom$, presumably formed from the reduction of a $Ag^+$ ion by an oxide ion of a residual water molecule or of the zeolite framework during the dehydration process, is retained within the zeolite, perhaps in a cluster. In these two structures hydrogen gas could not enter the zeolite to reduce the $Ag^+$ ions because the large $Cs^+$ ions blocked all the 8-windows. However, hydrogen could slowly diffuse into the zeolite and was able to reach and to reduce about half of the $Ag^+$ ions in the structure only at high temperature ($470^{\circ}C$). The silver atoms produced migrated out of the zeolite framework, and the protons generated led to substantial crystal damage.

• Bulletin of the Korean Chemical Society
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• v.5 no.3
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• pp.117-121
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• 1984

The structure of $CS_{7.3}Ag_{4.7}Si_{12}Al_{12}O_{48}$, vacuum dehydrated zeolite A with all Na+ ions replaced by $Cs^+$ and $Ag^+$ as indicated, has been determined by single-crystal x-ray diffraction techniques in the cubic space group, Pm3m (a = 12.282 (1) ${\AA}$). The structure was refined to the final error indices $R_1$$R_2$ (weighted) = 0.099 using 347 independent reflections for whind intlch $I_0\;>\;3{\sigma}(I_0)$. Although deydration occurred at $360^{\circ}C$, no silver atoms or clusters have been observed. The 8-ring sites are occupied only by $Cs^+$ ion, and the 4-ring sites only by a single $Ag^+$ ion. The 6-ring sites contain $Ag^+$ and $Cs^+$ ions with $Ag^+$ nearly in 6-ring planes and $Cs^+$ well off them, one on the sodalite unit side. With regard to the 6-rings, the structure can be represented as a superposition of two types of unit cells: about 70 % have $4Ag^+$ and $4Cs^+$ ions, and the remaining 30 % have $3Ag^+$ and $5Cs^+$. In all unit cells, $3Cs^+$ ions lie at the centers of the 8-rings at sites of D4h symmetry; these ions are approximately 0.3 ${\AA}$ further from their nearest framework-oxygen neighbors than the sum of the appropriate ionic radii would indicate. To minimize electrostatic repulsions, the $Cs^+$ ions at Cs(1) are not likely to occupy adjacent 6-rings in the large cavity; they are likely to be tetrahedrally arranged when there are 4.

• Bulletin of the Korean Chemical Society
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• v.10 no.3
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• pp.234-238
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• 1989

The crystal structure of partially $Ag^+$-exchanged zeolite A, $Ag_{3.2}Na_{8.8}$-A, vacuum dehydrated at $360^{\circ}C$ and then exposed to 0.1 torr of cesium vapor for 12 hours at $250^{\circ}C$ has been determined by single-crystal X-ray diffraction techniques in the cubic space group Pm3m (a = 12.262(2)${\AA})\;at\;21(1)^{\circ}C$. The structure was refined to the final error indexes $R_1=0.068\;and\;R_2=0.072$ by using 338 reflections for which $I_o\;>\;3{\sigma}(I_o)$ and the composition of unit cell is $Ag_{3.2}Cs_{8.8}-A.\;3\;Cs^+$ ions lie on the centers of the 8-rings at sites of D4h symmetry. Two crystallographycally different 6-ring $Cs^+$ ions were found: 1.5 $Cs^+$ ions at Cs(2) are located inside of sodalite cavity and 4.3 $Cs^+$ ions at Cs(3) are located in the large cavity. The fractional occupancies observed at Cs(2) and Cs(3) indicate that the existence of at least three types of unit cells with regard to the 6-ring $Cs^+$ ions. For example, 50% of unit cells may have two $Cs^+$ ions at Cs(2) and 4 $Cs^+$ ions at Cs(3). 30% of unit cells may have one Cs+ ion at Cs(2) and 5 $Cs^+$ ions at Cs(3). The remaining 20% would have one $Cs^+$ ion at Cs(2) and 4 $Cs^+$ ions at Cs(3). On threefold axes of the unit cell two non-equivalent Ag atom positions are found in the large cavity, each containing 0.64 and 1.92 Ag atoms, respectively. A crystallographic analysis may be interpreted to indicate that 0.64 $(Ag_5)^+$ clusters are present in each large cavity. This cluster may be viewed as a tetrasilver molecule $(Ag_4)^0$(bond length, 2.84${\AA}$) stabilized by the coordination of one $Ag^+$ ion.

• Bulletin of the Korean Chemical Society
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• v.13 no.4
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• pp.363-367
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• 1992

The crystal structure of (1,3,6,9,11,14-hexaazatricycol[12.2.1.$1^{6,9}$]octadecane)copper(Ⅱ) perchlorate, Cu($C_{12}H_{26}N_6$)$(ClO_4)_2$, has been determined by the X-ray diffraction methods. The crystal data are as follows: Mr=516.9, triclinic, ${\alpha}=8.572\;(2)$, b=8.499 (3), c=15.204 (3) ${\AA}$, ${\alpha}=80.42\;(5),\;{\beta}=73.57\;(3),\;{\gamma}=69.82\;(4)^{\circ},\;V=994.2\;{\AA}^3,\;D_C=1.726\;gcm^{-3}$, space group $P{\tilde{1}},\;Z=2,\;{\mu}=21.27\;cm^{-1}&, F(000)=534 and T=297 K. The structure was solved by direct methods and refined by full-matrix least-squares methods to and R value of 0.081 for 1608 observed reflections measured with graphite-mono-chromated Mo Ka radiation on a diffractometer. There are two independent complexes in the unit cell. The two copper ions lie at the special positions (1/2, 0, 0) and (0, 1/2, 1/2)and each complex possesses crystallographic center of symmetry. Each Cu ion is coordinated to four nitrogen donors if the hexaazamacrotricyclic ligand and weakly interacts with two oxygen atoms of the perchlorate ions to form a tetragonally distorted octahedral coordination geometry. The Cu_N (sec), Cu_N(tert) and Cu_O coordination distances are 1.985 (14), 2.055 (14) and 2.757 (13) ${\AA}$ for the complex A and 1.996 (10), 2.040 (11) and 2.660 (13) ${\AA}$ for the complex B, respectively. The macrocycles in the two independent cations assume a similar conformation with the average r.m.s. deviation of 0.073 ${\AA}$. Two 1,3-diazacyclopentane ring moieties of the hexaazamacrotricyclic ligand are placed oppositely and almost perpendicularly to the square coordination plane of the ruffled 14-membered macrocycle. The secondary N atoms are hydrogen-bonded to the perchlorate O atoms with distances of 3.017 (23) and 3.025 (19) ${\AA}$ for the complexes A and B, respectively.

• Journal of the Korean Chemical Society
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• v.37 no.2
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• pp.191-198
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• 1993

The crystal structures of $Cd_{6-}A$ evacuated at $2{\times}10^{-6}$ torr and $750^{\circ}C$ (a = 12.204(1) $\AA$) and dehydrated $Cd_{6-}A$ reacted with 0.1 torr of Cs vapor at $250^{\circ}C$ for 12 hours (a = 12.279(1) $\AA$) have been determined by single crystal X-ray diffraction techniques in the cubic space group Pm3m at $21(1)^{\circ}C.$ Their structures were refined to final error indices, $R_1=$ 0.081 and $R_2=$ 0.091 with 151 reflections and $R_1=$ 0.095 and $R_2=$ 0.089 with 82 reflections, respectively, for which I > $3\sigma(I).$ In vacuum dehydrated $Cd_{6-}A$, six $Cd^{2+}$ ions occupy threefold-axis positions near 6-ring, recessed 0.460(3) $\AA$ into the sodalite cavity from the (111) plane at O(3) : Cd-O(3) = 2.18(2) $\AA$ and O(3)-Cd-O(3) = $115.7(4)^{\circ}.$ Upon treating it with 0.1 torr of Cs vapor at $250^{\circ}C$, all 6 $Cd^{2+}$ ions in dehydrated $Cd_{6-}A$ are reduced by Cs vapor and Cs species are found at 4 crystallographic sites : 3.0 $Cs^+$ ions lie at the centers of the 8-rings at sites of $D_{4h}$ symmetry; ca. 9.0 Cs+ ions lie on the threefold axes of unit cell, ca. 7 in the large cavity and ca. 2 in the sodalite cavity; ca. 0.5 $Cs^+$ ion is found near a 4-ring. In this structure, ca. 12.5 Cs species are found per unit cell, more than the twelve $Cs^+$ ions needed to balance the anionic charge of zeolite framework, indicating that sorption of Cs0 has occurred. The occupancies observed are simply explained by two unit cell arrangements, $Cs_{12}-A$ and $Cs_{13}-A$. About 50% of unit cells may have two $Cs^+$ ions in sodalite unit near opposite 6-rings, six in the large cavity near 6-ring and one in the large cavity near a 4-ring. The remaining 50% of unit cells may have two Cs species in the sodalite unit which are closely associated with two out of 8 $Cs^+$ ions in the large cavity to form linear $(Cs_4)^{3+}$ clusters. These clusters lie on threefold axes and extend through the centers of sodalite units. In all unit cells, three $Cs^+$ ions fill equipoints of symmetry $D_{4h}$ at the centers of 8-rings.

• Journal of the Korean Chemical Society
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• v.33 no.1
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• pp.18-24
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• 1989

Two crystal structures of dehydrated $Ag^+$ and $Rb^+$ exchanged zeolite A, stoichiometries of $Ag_{9}Rb_{3}-A$ (a = 12.278(2)${\AA}$) and $Ag_{10}Rb_{2}-A$ (a = 12.286(2)${\AA}$) per unit cell, have been determined by single crystal x-ray diffraction techniques. Their structures were solved and refined in the cubic space group Pm3m at 21(1)$^{\circ}$C. The crystals of $Ag_{10}Rb_{2}-A$ and $Ag_{10}Rb_{2}-A$ were prepared by flow methods using exchanged solution in which mole ratios of AgNO$_3$ and RbNO$_3$ were 1:5 and 1:50, respectively, with the total concentration of 0.05 M. The structures of the dehydrated $Ag_{9}Rb_{3}-A$ and the $Ag_{10}Rb_{2}-A$ were refined to the final error indices, $R_1$ = 0.064 and $R_2$ = 0.060 with 291 reflections, and $R_1$ = 0.063 and $R_2$ = 0.080 with 416 reflections respectively, for which I >3${\sigma}$(I). In both structures, one reduced silver atom per unit cell was found inside the sodalite cavity. It may be present as a hexasilver cluster in 1/6 of the sodalite units or as an isolated Ag atom coordinated to 4 $Ag^+$ ions in each sodalite unit to give $(Ag_5)^{4+}$, symmetry 4 mm. In the structure of dehydrated $Ag_{9}Rb_{3}-A$, 8 $Ag^+$ ions lie on the threefold axis and each is nearly at the center of the 8-rings at the sites of $D_{4h}$ symmetry. In the structure of dehydrated $Ag_{10}Rb_{2}-A$, two crystallographically different eight 6-ring $Ag^+$ ions were found; $7Ag^+$ ions in the (111) planes of their O(3) framework oxygens and one $Ag^+$ ion inside of sodalite cavity. Two crystallographically different 8-ring cations were also found; two $Rb^+$ ions at the centers of the 8-oxygen rings and one $Ag^+$ ion into the large cavity. Both structures indicate that $Rb^+$ ions prefer to occupy the 8-ring sites, while $Ag^+$ ions prefer to occupy the 6-ring sites.