• Title/Summary/Keyword: Sigma Space

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Crystal Structure of Fully Dehydrated Partially Ag$^+$-Exchanged Zeolite 4A, $Ag_{7.6}Na_{4.4}$-A. Ag$^+$ Ions Prefer 6-Ring Sites. One Ag$^+$ Ion is Reduced

  • Kim, Yang;Han, Young-Wook;Seff, Karl
    • Bulletin of the Korean Chemical Society
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    • v.7 no.3
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    • pp.190-193
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    • 1986
  • The structure of partially $Ag^+$-exchanged zeolite 4A, $Ag_{7.6}Na_{4.4}-A$, vacuum dehydrated at $370^{\circ}C$, has been determined by single-crystal x-ray diffraction techniques in the cubic space group, Pm3m (a = 12.311(1)${\AA}$) at $24(1)^{\circ}}C$. The structure was refined to the final error indices $R_1$ = $R_2$ (weighted) = 0.064 using 266 independent reflections for which $I_0$>$3{\sigma}(I_0)$. Three $Na^+$ ions occupy the 3 8-ring sites, and the remaining ions, 1.4 $Na^+$ and 6.6 $Ag^+$, fill the 8 6-ring sites; each $Ag^+$ ion is nearly in the [111] plane of its 3 O(3) ligands, and each $Na^+$ ion is 0.9${\AA}$ from its corresponding plane, on the large-cavity side. One reduced silver atom per unit cell was found inside the sodalite unit. It was presumably formed from the reduction of a $Ag^+$ ion by an oxide ion of a residual water molecule or of the zeolite framework. It may be present as a hexasilver cluster in 1/6 of the sodalite units, or, most attractively among several alternatives, as an isolated Ag atom coordinated to 4 Ag ions in each sodalite unit to give $(Ag_5)^{4+}$, symmetry 4mm.

Crystal Structure of Dehydrated Partially Ag$^+$-Exchanged Zeolite A, Ag$_{4.6}Na_{7.4}$-A, Treated with Hydrogen at 350${^{\circ}C}$

  • Kim Yang;Seff Karl
    • Bulletin of the Korean Chemical Society
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    • v.6 no.4
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    • pp.202-206
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    • 1985
  • The crystal structure of The crystal structure of $Ag^+$-Exchanged Zeolite A, $Ag_{4.6}Na_{7.4}-A$, dehydrated, treated with $H_2$, and evacuated, all at $350^{\circ}C$, has been determined by single crystal x-ray diffraction methods in the cubic space group Pm3m at $24(1)^{\circ}C;$ a = $12.208(2)\AA.$ The structure was refined to the final error indices R1 = 0.088 and R2 (weighted) = 0.069 using 194 independent reflections for which II_0$ > $3{\sigma}(I_0)$. On threefold axes near the centers of 6-oxygen rings, $7.4 Na^+$ ions and $0.6 Ag^+$ ions are found. Two non-equivalent 8-ring $Ag^+$ ions are found off the 8-ring planes, each containing about $0.6 Ag^+$ ions. Three non-equivalent Ag atom positions are found in the large cavity, each containing about 0.6 Ag atoms. This crystallographic analysis may be interpreted to indicate that $0.6 (Ag_6)^{3+}$ clusters are present in each large cavity. This cluster may be viewed as a nearly linear trisilver molecule $(Ag_3)^0$ (bond lengths, 2.92 and 2.94 $\AA;$ angle, $153^{\circ})$ stabilized by the coordination of each atom to a Ag^+$ ion at 3.30, 3.33, and 3.43 $\AA$, respectively. In addition, one of the silver atoms approaches all of the 0(1) oxygens of a 4-ring at $2.76\AA.$ Altogether $7.4 Na^+$ ions, $1.8 Ag^+$ ions, and 1.8 Ag atoms are located per unit cell. The remaining $1.0 Ag^+$ ion has been reduced and has migrated out of the zeolite framework to form silver crystallites on the surface of the zeolite single crystal.

Crystal Structure of Dehydrated Partially Ag$^+$-Exchanged Zeolite A treated with Cesium Vapor at 250${^{\circ}C}$

  • Kim, Duk-Soo;Song, Seong-Hwan;Kim, Yang
    • 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.

Application of Back Analysis for Tunnel Design by Modified In Situ Rock Model (현장암반 모델을 적용한 터널의 역해석)

  • Kim, Hak-Mun;Lee, Bong-Yeol;Hwang, Ui-Seok;Kim, Tae-Hun
    • Journal of Korean Tunnelling and Underground Space Association
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    • v.2 no.3
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    • pp.25-36
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    • 2000
  • The purpose of this research work is to propose an analytical method of tunnel design based on reasonable site data. Therefore the proposed design method consists of monitoring data and Modified In Situ Rock Model. Also the Rock Mass Rating for very poor quality rock is very difficult to estimate, the balances between the ratings may no longer gives a reliable basis for the rock mass strength. But in reality Rock Mass Rating is only the property which can be obtained from face mapping records of the exposed tunnel face during construction stage. Evaluation of rock parameters for the actual design prior to tunnel construction should be corrected during tunnelling process in particularly complex ground conditions. This study intends to investigate application of in-situ rock model to soft rock tunnelling (weathered rock) by face mapping results and site measurement data that are obtained at the costraction site of Seoul Subway Tunnel. For the preparation of more reliable ground parameters, the Rock Mass Rating values for the weathered rocks were modified and readjusted in accordance with the measurement data. The modified input parameters obtained by the proposed method are used for the prediction of the tunnel behavior at subsequent construction stages. The results of this study revealed that more reasonable feed back tunnel analysis can be possible as suggested. Ample measurement data would be able to confirm the new proposed technique in this research work.

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The Far-ultraviolet Spectrum Study of Comet C/2001 Q4 (NEAT)

  • Lim, Yeo-Myeong;Min, Kyoung-Wook;Feldman, Paul D.;Han, Wanyong;Edelstein, Jerry
    • The Bulletin of The Korean Astronomical Society
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    • v.39 no.1
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    • pp.68.1-68.1
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    • 2014
  • We present the results of far-ultraviolet (FUV) observations of comet C/2001 Q4 (NEAT) obtained with Far-ultraviolet Imaging Spectrograph (FIMS) on board the Korean microsatellite STSAT-1, which operated at an altitude of 700 km in a sun-synchronous orbit. FIMS is a dual channel imaging spectrograph (S-channel 900-1150 ${\AA}$, L-channel 1350-1710 ${\AA}$, and ${\lambda}/{\Delta}{\lambda}$ ~ 550 for both channels) with large image fields of view (S-channel $4.0^{\circ}{\times}4.6^{\prime}$, L-channel $7.5^{\circ}{\times}4.3^{\prime}$, and angular resolution ~ $5-10^{\prime}$) optimized for the observation of diffuse emission of astrophysical radiation. Comet C/2001 Q4 (NEAT) were made in two campaigns during its perihelion approach between May 8 and 15, 2004. Based on the scanning mode observations in the wavelength band of 1400-1700 ${\AA}$, we have constructed an image of the comet with an angular size of $5^{\circ}{\times}5^{\circ}$, which corresponds to the central coma region. Several important fluorescence emission lines were detected including S I multiplets at 1429 and 1479 ${\AA}$, C I multiplets at 1561 and 1657 ${\AA}$, and the CO $A^1{\Pi}-X^1{\Sigma}^+$ Fourth Positive system; we have estimated the production rates of the corresponding species from the fluxes of these emission lines. The estimated production rate of CO was $Q_{CO}=(2.65{\pm}0.63){\times}10^{28}s^{-1}$, which is 6.2-7.4% of the water production rate and is consistent with earlier predictions. The average carbon production rate was estimated to be $Q_C={\sim}1.59{\times}10^{28}s^{-1}$, which is ~60% of the CO production rate. However, the observed carbon profile was steeper than that predicted using the two-component Haser model in the inner coma region, while it was consistent with the model in the outer region. The average sulfur production rate was $Q_S=(4.03{\pm}1.03){\times}10^{27}s^{-1}$, which corresponds to ~1% of the water production rate.

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Dependency of Tangential Friction Angle and Cohesion of Non-linear Failure Criteria on the Intermediate Principal Stress (비선형 암석 파괴조건식의 접선 마찰각과 점착력의 중간주응력 의존성)

  • Lee, Youn-Kyou;Choi, Byung-Hee
    • Tunnel and Underground Space
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    • v.23 no.3
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    • pp.219-227
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    • 2013
  • Although Mohr-Coulomb failure criterion has limitations in that it is a linear criterion and the effect of the intermediate principal stress on failure is ignored, this criterion has been widely accepted in rock mechanics design. In order to overcome these shortcomings, the Hoek-Brown failure criterion was introduced and recently a number of 3-D failure criteria incorporating the effect of the intermediate principal stress on failure have been proposed. However, in many rock mechanics designs, the possible failure of rock mass is still evaluated based on Mohr-Coulomb criterion and most of practitioners are accustomed to understanding the strength of rock mass in terms of the internal friction angle and cohesion. Therefore, if the equivalent Mohr-Coulomb strength parameters of the advanced failure criteria are calculated, it is possible to take advantage of the advanced failure criteria in the framework of the Mohr-Coulomb criterion. In this study, a method expressing the tangential Mohr-Coulomb strength parameters in terms of the stress invariant is proposed and it is applied to the generalized Hoek-Brown criterion and the HB-WW criterion. In addition, a new approach describing the geometric meaning of the ${\sigma}_2$-dependency of failure criteria in 3-D principal stress space is proposed. Implementation examples of the proposed method show that the influence of the intermediate principal stress on the tangential friction angle and cohesion of the HB-WW criterion is considerable, which is not the case for the 2-D failure criterion.

Two Anhydrous Zeolite X Crystal Structures, $Pd_{18}Ti_{56}Si_{100}Al_{92}O_{384} and Pd_{21}Tl_{50}Si_{100}Al_{92}O_{384}$

  • Yun, Bo Yeong;Song, Mi Gyeong;Lee, Seok Hui;Kim, Yang
    • Bulletin of the Korean Chemical Society
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    • v.22 no.1
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    • pp.30-36
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    • 2001
  • The crystal structures of fully dehydrated $Pd^{2+}$ - and $TI^{+}$ -exchanged zeolite X, $Pd_{18}TI_{56}Si_{100}Al_{92}O_{384}(Pd_{18}TI_{50-}X$, a = $24.935(4)\AA$ and $Pd_{21}TI_{50}Si_{100}Al_{92}O_{384}(Pd_{21}TI_{50-}X$ a = $24.914(4)\AA)$, have been determined by single-crystal X-ray diffraction methods in the cubic space group Fd3 at $21(1)^{\circ}C.$ The crystals were prepared using an exchange solution that had a $Pd(NH_3)_4Cl_2\;:TINO_3$ mole ratio of 50 : 1 and 200 : 1, respectively, with a total concentration of 0.05M for 4 days. After dehydration at $360^{\circ}C$ and 2 ${\times}$$10^{-6}$ Torr in flowing oxygen for 2 days, the crystals were evacuated at $21(1)^{\circ}C$ for 2 hours. They were refined to the final error indices $R_1$ = 0.045 and $R_2$ = 0.038 with 344 reflections for $Pd_{18}Tl_{56-}X$, and $R_1$ = 0.043 and $R_2$ = 0.045 with 280 reflections for $Pd_{21}Tl_{50-}X$; I > $3\sigma(I).$ In the structure of dehydrated $Pd_{18}Tl_{56-}X$, eighteen $Pd^{2+}$ ions and fourteen $TI^{+}$ ions are located at site I'. About twenty-seven $TI^{+}$ ions occupy site II recessed $1.74\AA$ into a supercage from the plane of three oxygens. The remaining fifteen $TI^{+}$ ions are distributed over two non-equivalent III' sites, with occupancies of 11 and 4, respectively. In the structure of $Pd_{21}Tl_{50-}X$, twenty $Pd^{2+}$ and ten $TI^{+}$ ions occupy site I', and one $Pd^{2+}$ ion is at site I. About twenty-three $TI^{+}$ ions occupy site II, and the remaining seventeen $TI^{+}$ ions are distributed over two different III' sites. $Pd^{2+}$ ions show a limit of exchange (ca. 39% and 46%), though their concentration of exchange was much higher than that of $TI^{+}$ ions. $Pd^{2+}$ ions tend to occupy site I', where they fit the double six-ring plane as nearly ideal trigonal planar. $TI^{+}$ ions fill the remaining I' sites, then occupy site II and two different III' sites. The two crystal structures show that approximately two and one-half I' sites per sodalite cage may be occupied by $Pd^{2+}$ ions. The remaining I' sites are occupied by $TI^{+}$ ions with Tl-O bond distance that is shorter than the sum of their ionic radii. The electrostatic repulsion between two large $TI^{+}$ ions and between $TI^{+}$ and $Pd^{2+}$ ions in the same $\beta-cage$ pushes each other to the charged six-ring planes. It causes the Tl-O bond to have some covalent character. However, $TI^{+}$ ions at site II form ionic bonds with three oxygens because the super-cage has the available space to obtain the reliable ionic bonds.

RADARSAT SAR Investigations of Lineament and Spring Water in Cheju Island (RADARSAT SAR 자료를 이용한 제주도 선구조 연구 및 용천 특성 연구)

  • 원중선;류주형;지광훈
    • Korean Journal of Remote Sensing
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    • v.14 no.4
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    • pp.325-342
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    • 1998
  • Two RADARSAT SAR images with different modes acquired by Canadian Space Agency to test the effectiveness of geological lineament extraction and spring water detection over the Cheju Island. Geological lineaments are poorly developed this basalt dominant volcanic island, but more linear features can be extracted when SAR and TM images are simultaneously analyzed than when TM image alone is used. This results mainly owe to the facts that RADARSAT SAR systems are able to provide data with different frequencies, azimuth, and incidence angles. Distribution of spring water along coast is poorly correlated with geological lineaments or drainage pattern, but those in middle range of mountain region are developed along geological lineaments. Detection of spring water using remotely sensed images are turned out to be very difficult to achieve. Radial shaped sea surface temperature anomaly derived from TM thermal band should be the best candidate for spring water, but the resolution is not high enough. We also investigate the normalized radar cross section (or sigma naught) converted from RADARSAT and ERS-1 SAR data but to discriminate the spring water effectively except where relatively large water mass is observed on land side. Speckle noise and irregularity in physical sea surface condition are the serious obstacles for this application. ERS-1 SAR image acquired in low incidence angle was more useful for geological lineament estimation and water body study than RADARSAT SAR images with high incidence angles. Therefore the selection of incidence angle is critical in geological and spring water applications of SAR images, and low incidence angles less than about 30$^{\circ}$ are recommended to monitor the Cheju volcanic island.

Two Crystal Structures of Dehydrated Calcium and Silver Exchanged Zeolite A, $Ag_{12-2x}Ca_x-A (x = 2.5 and 5.0)$ (칼슘 및 은 이온으로 치환한 제올라이트 A, $Ag_{12-2x}Ca_x-A (x = 2.5$$5.0)$ 의 탈수한 결정구조)

  • Seung Hwan Song;Jong Yul Park;Kim, Eun Sik;Yang Kim
    • Journal of the Korean Chemical Society
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    • v.33 no.5
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    • pp.452-458
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    • 1989
  • The crystal structures of vacuum-dehydrated $Ag^+\;and\;Ca^{2+}$ exchanged zeolite A, Ag_7Ca_{2.5}-A(a = 12.310(1){\AA})$ and $Ag_2Ca_5-A(a = 12.287(2){\AA})$ have been determined by single-crystal X-ray diffraction methods in the cubic space group Pm3m at $21(1)^{\circ}C$. The crystals of $A_7Ca_{2.5}-A\;and\;Ag_2Ca_5-A$ were prepared by flow method using exchange solutions in which mole ratios of $AgNO_3\;and\;Ca(NO_3)_2$ were 1:50 and 1:1000, respectively, with total concentration of 0.05 M. Full-matrix least-squares refinement converged to the final error indices of R1 = 0.056 and R2 = 0.059 for $Ag7Ca2.5-A$, and R1 = 0.054 and R2 = 0.082 for $Ag2Ca5-A$ using 306 and 348 reflections, respectively, for which I >3 {\sigma}$ (I). 5.5 $Ag^+$ ions and 2.5 Ca^{2+}$ ions for $Ag_7Ca_{2.5}-A\;and\;2\;Ag^+$ ions and 5 $Ca^{2+}$ ions for $Ag_2Ca_5-A$ lie on two crystallographically nonequivalent threefold axes on the 6-rings. Both structures indicate that smaller Ca2+ ions preferentially occupy 6-ring sites and larger $Ag+$ ions occupy 8-ring sites when total number of cations per unit cell is more than 8.

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Three Crystal Structures of Dehydrated $Ag_{12-x}Na_x-A$ (x = 4, 6, and 8) Treated with Rubidium Vapor (탈수한 $Ag_{12-x}Na_x-A$ (x = 4, 6, 및 8)를 루비듐 증기로 처리한 세가지 결정구조)

  • Lee, Hyeon Do;Kim, Un Sik;Park, Jong Yeol;Kim, Yang
    • Journal of the Korean Chemical Society
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    • v.38 no.3
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    • pp.186-196
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    • 1994
  • Three fully dehydrated partially $Ag^+$-exchanged zeolite A(Ag_4Na_8-A, Ag_6Na_6-A, and Ag_8Na_4-A) were treated at $250^{\circ}C$ with 0.1 torr Rb vapor at 4 h. Their structures were determined by singlecrystal X-ray diffraction methods in the cubic space group $Pm{\bar3}m$ (a = 12.264(4) $\AA$, a = 12.269(1) $\AA$, and a= 12.332(3) $\AA$, respectively) at $22(1)^{\circ}C$, and were refined to the final error indices, R(weighed), of 0.056 with 131 reflections, 0.068 with 108 reflections, and 0.070 with 94 reflections, respectively, for which I > $3\sigma(I).$ In these structures, Rb species are found at three different crystallographic sites; three $Rb^+$ ions per unit cell are located at 8-ring centers, ca. 6.0∼6.8 $Rb^+$ ions are found opposite 6-rings on threefold axes in the large cavity, and ca. 2.5 $Rb^+$ ions are found on three fold axes in the sodalite unit. Also, Ag species are found at two different crystallographic sites; ca. 0.6∼1.0 $Ag^+$ ion lies opposite 4-rings and about 1.8∼4.2 Ag atoms are located near the center of the large cavity. In these structures, the numbers of Ag atoms per unit cell are 1.8, 3.0, and 4.2, respectively, and these are likely to form hexasilver clusters at the centers of the large cavities. The $Rb^+$ ions, by blocking 8-rings, may have prevented silver atoms from migrating out of the structure. Each hexasilver cluster is stabilized by coordination to 6-ring, 8-ring $Rb^+$ ions, and also by coordination to a 4-ring $Ag^+$ ion.

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