279 resultados para Symmetric Kravchuk polynomials
Resumo:
Plumbogummite PbAl3(PO4)2(OH,H2O)6 is a mineral of environmental significance and is a member of the alunite-jarosite supergroup. The molecular structure of the mineral has been investigated by Raman spectroscopy. The spectra of different plumbogummite specimens differ although there are many common features. The Raman spectra prove the spectral profile consisting of overlapping bands and shoulders. Raman bands and shoulders observed at 971, 980, 1002 and 1023 cm−1 (China sample) and 913, 981, 996 and 1026 cm−1 (Czech sample) are assigned to the ν1 symmetric stretching modes of the (PO4)3−, at 1002 and 1023 cm−1 (China) and 996 and 1026 cm−1 to the ν1 symmetric stretching vibrations of the (O3POH)2− units, and those at 1057, 1106 and 1182 (China) and at 1102, 1104 and 1179 cm−1 (Czech) to the ν3 (PO4)3− and ν3 (PO3) antisymmetric stretching vibrations. Raman bands and shoulders at 634, 613 and 579 cm−1 (China) and 611 and 596 cm−1 (Czech) are attributed to the ν4 (δ) (PO4)3− bending vibrations and those at 507, 494 and 464 cm−1 (China) and 505 and 464 cm−1 (Czech) to the ν2 (δ) (PO4)3− bending vibrations. The Raman spectrum of the OH stretching region is complex. Raman bands and shoulders are identified at 2824, 3121, 3249, 3372, 3479 and 3602 cm−1 for plumbogummite from China, and at 3077, 3227, 3362, 3480, 3518 and 3601 cm−1 for the Czech Republic sample. These bands are assigned to the ν OH stretching modes of water molecules and hydrogen ions. Approximate O–H⋯O hydrogen bond lengths inferred from the Raman spectra vary in the range >3.2–2.62 Å (China) and >3.2–2.67 Å (Czech). The minority presence of some carbonate ions in the plumbogummite (China sample) is connected with distinctive intensity increasing of the Raman band at 1106 cm−1, in which may participate the ν1 (CO3)2− symmetric stretching vibration overlapped with phosphate stretching vibrations.
Resumo:
Henmilite is a triclinic mineral with the crystal structure consisting of isolated B(OH)4 tetrahedra, planar Cu(OH)4 groups and Ca(OH)3 polyhedra. The structure can also be viewed as having dimers of Ca polyhedra connected to each other through 2B(OH) tetrahedra to form chains parallel to the C axis. The structure of the mineral has been assessed by the combination of Raman and infrared spectra. Raman bands at 902, 922, 951, and 984 cm−1 and infrared bands at 912, 955 and 998 cm−1 are assigned to stretching vibrations of tetragonal boron. The Raman band at 758 cm−1 is assigned to the symmetric stretching mode of tetrahedral boron. The series of bands in the 400–600 cm−1 region are due to the out-of-plane bending modes of tetrahedral boron. Two very sharp Raman bands are observed at 3559 and 3609 cm−1. Two infrared bands are found at 3558 and 3607 cm−1. These bands are assigned to the OH stretching vibrations of the OH units in henmilite. A series of Raman bands are observed at 3195, 3269, 3328, 3396, 3424 and 3501 cm−1 are assigned to water stretching modes. Infrared spectroscopy also identified water and OH units in the henmilite structure. It is proposed that water is involved in the structure of henmilite. Hydrogen bond distances based upon the OH stretching vibrations using a Libowitzky equation were calculated. The number and variation of water hydrogen bond distances are important for the stability off the mineral.
Resumo:
Vibrational spectroscopy has been used to assess the structure of kotoite a borate mineral of magnesium which is isostructural with jimboite. The mineral is orthorhombic with point group: 2/m 2/m 2/m. The mineral has the potential as a new memory insulator material. The mineral has been characterised by a combination of Raman and infrared spectroscopy. The Raman spectrum is dominated by a very intense band at 835 cm−1, assigned to the symmetric stretching mode of tetrahedral boron. Raman bands at 919, 985 and 1015 cm−1 are attributed to the antisymmetric stretching modes of tetrahedral boron. Kotoite is strictly an hydrous borate mineral. An intense Raman band observed at 3559 cm−1 is attributed to the stretching vibration of hydroxyl units, more likely to be associated with the borate mineral hydroxyborate. The lack of observation of water bending modes proves the absence of water in the kotoite structure.
Resumo:
The presence of arsenic in the environment is a hazard. The accumulation of arsenate by a range of cations in the formation of minerals provides a mechanism for the remediation of arsenate contamination. The formation of the crandallite group of minerals provides a mechanism for arsenate accumulation. Among the crandallite minerals are philipsbornite, arsenocrandallite and arsenogoyazite. Raman spectroscopy complimented with infrared spectroscopy has enabled aspects of the structure of philipsbornite to be studied. The Raman spectrum of philipsbornite displays an intense band at around 840 cm−1 attributed to the overlap of the symmetric and antisymmetric stretching modes. Raman bands observed at 325, 336, 347, 357, 376 and 399 cm−1 are assigned to the ν2 (AsO4)3− symmetric bending vibration (E) and to the ν4 bending vibration (F2). The observation of multiple bending modes supports the concept of a reduction in symmetry of the arsenate anion in philipsbornite. Evidence for phosphate in the mineral is provided. By using an empirical formula, hydrogen bond distances for the OH units in philipsbornite of 2.8648 Å, 2.7864 Å, 2.6896 Å cm−1 and 2.6220 were calculated.
Resumo:
The objective of this work is to analyze ludlamite (Fe,Mn,Mg)3(PO4)2⋅4H2O from Boa Vista mine, Galiléia, Brazil and to assess the molecular structure of the mineral. The phosphate mineral ludlamite has been characterized by EMP-WDS, Raman and infrared spectroscopic measurements. The mineral is shown to be a ferrous phosphate with some minor substitution of Mg and Mn. Raman bands at 917 and 950 cm−1 are assigned to the symmetric stretching mode of and units. Raman bands at 548, 564, 599 and 634 cm−1 are assigned to the ν4 bending modes. Raman bands at 2605, 2730, 2896 and 3190 cm−1 and infrared bands at 2623, 2838, 3136 and 3185 cm−1 are attributed to water stretching vibrations. By using a Libowitzky empirical function, hydrogen bond distances are calculated from the OH stretching wavenumbers. Strong hydrogen bonds in the structure of ludlamite are observed as determined by their hydrogen bond distances. The application of infrared and Raman spectroscopy to the study of ludlamite enables the molecular structure of the pegmatite mineral ludlamite to be assessed.
Resumo:
Zanazziite is the magnesium member of a complex beryllium calcium phosphate mineral group named roscherite. The studied samples were collected from the Ponte do Piauí mine, located in Itinga, Minas Gerais. The mineral was studied by electron microprobe, Raman and infrared spectroscopy. The chemical formula can be expressed as Ca2.00(Mg3.15,Fe0.78,Mn0.16,Zn0.01,Al0.26,Ca0.14)Be4.00(PO4)6.09(OH)4.00⋅5.69(H2O) and shows an intermediate member of the zanazziite–greinfeinstenite series, with predominance of zanazziite member. The molecular structure of the mineral zanazziite has been determined using a combination of Raman and infrared spectroscopy. A very intense Raman band at 970 cm−1 is assigned to the phosphate symmetric stretching mode whilst the Raman bands at 1007, 1047, 1064 and 1096 cm−1 are attributed to the phosphate antisymmetric stretching mode. The infrared spectrum is broad and the antisymmetric stretching bands are prominent. Raman bands at 559, 568, 589 cm−1 are assigned to the ν4 out of plane bending modes of the PO4 and HPO4 units. The observation of multiple bands supports the concept that the symmetry of the phosphate unit in the zanazziite structure is reduced in symmetry. Raman bands at 3437 and 3447 cm−1 are attributed to the OH stretching vibrations; Raman bands at 3098 and 3256 are attributed to water stretching vibrations. The width and complexity of the infrared spectral profile in contrast to the well resolved Raman spectra, proves that the pegmatitic phosphates are better studied with Raman spectroscopy.
Resumo:
The secondary phosphate mineral sigloite Fe3+Al2(PO4)2(OH)3·7H2O is the exception to the rule that phosphate mineral paragenesis is related to the final phase of hydrothermal mineralization at low temperatures. Sigloite was formed as an oxidation pseudomorph after paravauxite, during the last supergene paragenetic stage. We have studied the secondary phosphate mineral sigloite Fe3+Al2(PO4)2(OH)3·7H2O using vibrational spectroscopic techniques. Because the mineral is a phosphate mineral, it is readily studied by spectroscopic techniques as the phosphate and hydrogen phosphate units are readily measured. Indeed, sigloite shows the presence of both phosphate and hydrogen phosphate units in its structure. Raman bands at 1009 cm−1 with shoulders at 993 and 1039 cm−1 are assigned to stretching vibrations of and units. The Raman band at 993 cm−1 is assigned to the ν1 symmetric stretching mode of the POH units, whereas the Raman band at 1009 cm−1 is assigned to the ν1 symmetric stretching mode. Raman bands observed at 506, 528, 571, 596, 619 and 659 cm−1 are attributed to the ν4 out of plane bending modes of the PO4 and H2PO4 units. The Raman bands at 2988, 3118 and 3357 cm−1 are assigned to water stretching vibration. The series of bands at 3422, 3449, 3493, 3552 and 3615 cm−1 are assigned to the OH stretching vibrations of the hydroxyl units. The observation of multiple bands gives credence to the non-equivalence of the OH units in the sigloite structure.
Resumo:
The mineral tooeleite Fe6(AsO3)4SO4(OH)4�4H2O is secondary ferric arsenite sulphate mineral which has environmental significance for arsenic remediation because of its high stability in the regolith. The mineral has been studied by X-ray diffraction (XRD), infrared (IR) and Raman spectroscopy. The XRD result indicates tooeleite can form more crystalline solids in an acid environment than in an alkaline environment. Infrared spectroscopy identifies moderately intense band at 773 cm�1 assigned to AsO3� 3 symmetric stretching vibration. Raman spectroscopy identifies three bands at 803, 758 and 661 cm�1 assigned to the symmetric and antisymmetric stretching vibrations of AsO3� 3 and As-OH stretching vibration respectively. In addition, the infrared bands observed at 1116, 1040, 1090, 981 and 616 cm�1, are assigned to the m3, m1 and m4 modes of SO2� 4 . The same bands are observed at 1287, 1085, 983 and 604 cm�1 in the Raman spectrum. As3d band at binding energy of 44.05 eV in XPS confirms arsenic valence of tooeleite is +3. These characteristic bands in the IR and Raman spectra provide useful basis for identifying the mineral tooeleite.
Resumo:
Papagoite is a silicate mineral named after an American Indian tribe and was used as a healing mineral. Papagoite CaCuAlSi2O6(OH)3 is a hydroxy mixed anion compound with both silicate and hydroxyl anions in the formula. The structural characterization of the mineral papagoite remains incomplete. Papagoite is a four-membered ring silicate with Cu2+ in square planar coordination. The intense sharp Raman band at 1053 cm−1 is assigned to the ν1 (A 1g) symmetric stretching vibration of the SiO4 units. The splitting of the ν3 vibrational mode offers support to the concept that the SiO4 tetrahedron in papagoite is strongly distorted. A very intense Raman band observed at 630 cm−1 with a shoulder at 644 cm−1 is assigned to the ν4 vibrational modes. Intense Raman bands at 419 and 460 cm−1 are attributed to the ν2 bending modes. Intense Raman bands at 3545 and 3573 cm−1 are assigned to the stretching vibrations of the OH units. Low-intensity Raman bands at 3368 and 3453 cm−1 are assigned to water stretching modes. It is suggested that the formula of papagoite is more likely to be CaCuAlSi2O6(OH)3 · xH2O. Hence, vibrational spectroscopy has been used to characterize the molecular structure of papagoite.
Resumo:
We have characterized anapaite Ca2Fe2+(PO4)2·4(H2O), a rare Ca and Fe phosphate, using a combination of electron microscopy and vibrational spectroscopy. The mineral occurs in soils and lacustrine sediments and is usually related to the diagenetic process in phosphorous rich sediments. The phosphate anion is characterized by its Raman spectrum with an intense sharp band at 943 cm-1, attributed to the ν1 PO4 3- symmetric stretching mode. Three bands at 992, 1039 and 1071 cm-1 are attributed to ν3 PO4 3-antisymmetric stretching modes. The infrared spectrum of anapaite shows complexity with a series of overlapping bands. Water in the structure of anapaite is observed by OH stretching vibrations at 2777, 3022 and 3176 cm-1 (Raman) and 2744, 3014 and 3096 cm-1 (infrared). The position of these bands provides evidence for the strong hydrogen bonding of water in the anapaite structure and contributes to the stability of the mineral.
Resumo:
This research was undertaken on phosphophyllite sample from the Hagendorf Süd pegmatite, Bavaria, Germany. Chemical analysis was carried out by Scanning Electron Microscope in the EDS mode and indicates a zinc and iron phosphate with partial substitution of manganese, which partially replaced iron. The calculated chemical formula of the studied sample was determined to be: Zn2(Fe0.65, Mn0.35)P1.00(PO4)2- �4(H2O). The intense Raman peak at 995 cm�1 is assigned to the m1 PO3� 4 symmetric stretching mode and the two Raman bands at 1073 and 1135 cm�1 to the m3 PO3� 4 antisymmetric stretching modes. The m4 PO3� 4 bending modes are observed at 505, 571, 592 and 653 cm�1 and the m2 PO3� 4 bending mode at 415 cm�1. The sharp Raman band at 3567 cm�1 attributed to the stretching vibration of OH units brings into question the actual formula of phosphophyllite. Vibrational spectroscopy enables an assessment of the molecular structure of phosphophyllite to be assessed.
Resumo:
The arrojadite-(KFe) mineral has been analyzed using a combination of scanning electron microscopy and a combination of Raman and infrared spectroscopy. The origin of the mineral is Rapid Creek sedimentary phosphatic iron formation, northern Yukon. The formula of the mineral was determined as K2.06Na2Ca0.89Na3.23(Fe7.82Mg4.40Mn0.78)Σ13.00Al1.44(PO4)10.85(PO3OH0.23)(OH)2. The complexity of the mineral formula is reflected in the spectroscopy. Raman bands at 975, 991 and 1005 cm−1 with shoulder bands at 951 and 1024 cm−1 are assigned to the View the MathML source ν1 symmetric stretching modes. The Raman bands at 1024, 1066, 1092, 1123, 1148 and 1187 cm−1 are assigned to the View the MathML source ν3 antisymmetric stretching modes. A series of Raman bands observed at 540, 548, 557, 583, 604, 615 and 638 cm−1 are attributed to the ν4 out of plane bending modes of the PO4 and H2PO4 units. The ν2 PO4 and H2PO4 bending modes are observed at 403, 424, 449, 463, 479 and 513 cm−1. Hydroxyl and water stretching bands are readily observed. Vibrational spectroscopy enables new information about the complex phosphate mineral arrojadite-(KFe) to be obtained.
Resumo:
Vibrational spectroscopy enables subtle details of the molecular structure of cyrilovite to be determined. Single crystals of a pure phase from a Brazilian pegmatite were used. Cyrilovite is the Fe3+ member of the wardite group. The infrared and Raman spectroscopy were applied to compare the structure of cyrilovite with that of wardite. The Raman spectrum of cyrilovite in the 800–1400 cm−1 spectral range shows two intense bands at 992 and 1055 cm−1 assigned to the ν1View the MathML source symmetric stretching vibrations. A series of low intensity bands at 1105, 1136, 1177 and 1184 cm−1 are assigned to the ν3View the MathML source antisymmetric stretching modes. The infrared spectrum of cyrilovite in the 500–1300 cm−1 shows much greater complexity than the Raman spectrum. Strong infrared bands are found at 970 and 1007 cm−1 and are attributed to the ν1View the MathML source symmetric stretching mode. Raman bands are observed at 612 and 631 cm−1 and are assigned to the ν4 out of plane bending modes of the View the MathML source unit. In the 2600–3800 cm−1 spectral range, intense Raman bands for cyrilovite are found at 3328 and 3452 cm−1 with a broad shoulder at 3194 cm−1 and are assigned to OH stretching vibrations. Sharp infrared bands are observed at 3485 and 3538 cm−1. Raman spectroscopy complimented with infrared spectroscopy has enabled the structure of cyrilovite to be ascertained and compared with that of wardite.
Resumo:
The mineral weloganite Na2Sr3Zr(CO3)6·3H2O has been studied by using vibrational spectroscopy and a comparison is made with the spectra of weloganite with other carbonate minerals. Weloganite is member of the mckelveyite group that includes donnayite-(Y) and mckelveyite-(Y). The Raman spectrum of weloganite is characterized by an intense band at 1082 cm−1 with shoulder bands at 1061 and 1073 cm−1, attributed to the View the MathML source symmetric stretching vibration. The observation of three symmetric stretching vibrations is very unusual. The position of View the MathML source symmetric stretching vibration varies with mineral composition. The Raman bands at 1350, 1371, 1385, 1417, 1526, 1546, and 1563 cm−1 are assigned to the ν3 (CO3)2− antisymmetric stretching mode. The observation of additional Raman bands for the ν3 modes for weloganite is significant in that it shows distortion of the carbonate anion in the mineral structure. The Raman band observed at 870 cm−1 is assigned to the (CO3)2− ν2 bending mode. Raman bands observed for weloganite at 679, 682, 696, 728, 736, 749, and 762 cm−1 are assigned to the (CO3)2− ν4 bending modes. A comparison of the vibrational spectra is made with that of the rare earth carbonates decrespignyite, bastnasite, hydroxybastnasite, parisite, and northupite.
Resumo:
The mineral creedite is a fluorinated hydroxy hydrated sulphate of aluminium and calcium of formula Ca3Al2SO4(F,OH)·2H2O. The mineral has been studied by a combination of electron probe analysis to determine the molecular formula of the mineral and the structure assessed by vibrational spectroscopy. The spectroscopy of creedite may be compared with that of the alums. The Raman spectrum of creedite is characterised by an intense sharp band at 986 cm−1 assigned to the View the MathML source ν1 (Ag) symmetric stretching mode. Multiple bands of creedite in the antisymmetric stretching region support the concept of a reduction in symmetry of the sulphate anion. Multiple bands are also observed in the bending region with the three bands at 601, 629 and 663 cm−1 assigned to the View the MathML source ν4 (Ag) bending modes. The observation of multiple bands at 440, 457 and 483 cm−1 attributed to the View the MathML source ν2 (Bg) bending modes supports the concept that the symmetry of the sulphate is reduced by coordination to the water bonded to the Al3+ in the creedite structure. The splitting of the ν2, ν3 and ν4 modes is attributed to the reduction of symmetry of the SO4 and it is proposed that the sulphate coordinates to water in the hydrated aluminium in bidentate chelation.