Infrared and Raman spectroscopic characterization of the phosphate mineral leucophosphite - K(Fe3+)2(PO4)2(OH)·2(H2O)

The phosphate mineral leucophosphite K(Fe2)3þ(PO4)2(OH) · 2H2O has been characterized by SEM-EDS, Raman, and infrared spectro- scopic measurements. The mineral is predominantly a K and Fe phosphate with some minor substitution of Al in the Fe3þ site. Raman bands at 994 and 1058 cm-1 are assigned to the symmetric stretching modes of PO3- and HPO2- units. The Raman bands at 1104, 1135, and 1177 cm-1 are assigned to the PO3- and HPO2- antisymmetric stretching modes. Raman and infrared spectra in the 2600–3800 cm-1 region show a complex set of overlapping bands, which may be resolved into the component bands. The Raman bands observed at 3325, 3355, and 3456 cm-1 are attributed to water stretching vibrations, and in the infrared spectrum, bands at 3237, 3317, and 3453 cm-1 are assigned to water stretching bands.

Infrared and Raman spectroscopic characterization of the silicate-carbonate mineral carletonite – KNa4Ca4Si8O18(CO3)4(OH,F) H2O

Abstract An assessment of the molecular structure of carletonite a rare phyllosilicate mineral with general chemical formula given as KNa4Ca4Si8O18(CO3)4(OH,F)·H2O has been undertaken using vibrational spectroscopy. Carletonite has a complex layered structure. Within one period of c, it contains a silicate layer of composition NaKSi8O18·H2O, a carbonate layer of composition NaCO3·0.5H2O and two carbonate layers of composition NaCa2CO3(F,OH)0.5. Raman bands are observed at 1066, 1075 and 1086 cm−1. Whether these bands are due to the CO32- ν1 symmetric stretching mode or to an SiO stretching vibration is open to question. Multiple bands are observed in the 300–800 cm−1 spectral region, making the attribution of these bands difficult. Multiple water stretching and bending modes are observed showing that there is much variation in hydrogen bonding between water and the silicate and carbonate surfaces.

Spectral approximations to the fractional integral and derivative

In this paper, the spectral approximations are used to compute the fractional integral and the Caputo derivative. The effective recursive formulae based on the Legendre, Chebyshev and Jacobi polynomials are developed to approximate the fractional integral. And the succinct scheme for approximating the Caputo derivative is also derived. The collocation method is proposed to solve the fractional initial value problems and boundary value problems. Numerical examples are also provided to illustrate the effectiveness of the derived methods.

Comment on "Local accumulation times for source, diffusion, and degradation models in two and three dimensions" [J. Chem. Phys. 138, 104121 (2013)]

In a recent paper, Gordon, Muratov, and Shvartsman studied a partial differential equation (PDE) model describing radially symmetric diffusion and degradation in two and three dimensions. They paid particular attention to the local accumulation time (LAT), also known in the literature as the mean action time, which is a spatially dependent timescale that can be used to provide an estimate of the time required for the transient solution to effectively reach steady state. They presented exact results for three-dimensional applications and gave approximate results for the two-dimensional analogue. Here we make two generalizations of Gordon, Muratov, and Shvartsman’s work: (i) we present an exact expression for the LAT in any dimension and (ii) we present an exact expression for the variance of the distribution. The variance provides useful information regarding the spread about the mean that is not captured by the LAT. We conclude by describing further extensions of the model that were not considered by Gordon,Muratov, and Shvartsman. We have found that exact expressions for the LAT can also be derived for these important extensions...

The molecular structure of the phosphate mineral väyrynenite : a vibrational spectroscopic study

We have studied the mineral väyrynenite from the Viitaniemi pegmatite, located in the Eräjärvi area, Finland using a combination of electron microscopy electron microprobe and vibrational spectroscopic techniques. Chemical analysis shows the formula of the mineral to be (Mn0.88,Fe0.08,Mg0.01)∑0.97Be1.02(PO4)1.00(OH)1.02. Vibrational spectroscopy enables an assessment of the molecular structure of väyrynenite to be assessed. An intense Raman band at 1004 cm−1 is to the ν1 symmetric stretching mode. The observation of multiple bands in the phosphate stretching region, offers support for the concept of different phosphate units in the väyrynenite structure. Infrared spectroscopy confirms this multiplicity of vibrational bands. Multiple bands are observed in the phosphate bending region.

Characterization of the sulphate mineral amarantite Fe3 2 3+ (SO4)O 7H2O using infrared, Raman spectroscopy and thermogravimetry

The mineral amarantite Fe23+(SO4)O∙7H2O has been studied using a combination of techniques including thermogravimetry, electron probe analyses and vibrational spectroscopy. Thermal analysis shows decomposition steps at 77.63, 192.2, 550 and 641.4°C. The Raman spectrum of amarantite is dominated by an intense band at 1017 cm-1 assigned to the SO42- ν1 symmetric stretching mode. Raman bands at 1039, 1054, 1098, 1131, 1195 and 1233 cm-1 are attributed to the SO42- ν3 antisymmetric stretching modes. Very intense Raman band is observed at 409 cm-1 with shoulder bands at 399, 451 and 491 cm-1 are assigned to the v2 bending modes. A series of low intensity Raman bands are found at 543, 602, 622 and 650 cm-1 are assigned to the v4 bending modes. A very sharp Raman band at 3529 cm-1 is assigned to the stretching vibration of OH units. A series of Raman bands observed at 3025, 3089, 3227, 3340, 3401 and 3480 cm-1 are assigned to water bands. Vibrational spectroscopy enables aspects of the molecular structure of the mineral amarantite to be ascertained.

Vibrational spectroscopy of the mineral meyerhofferite CaB3O3(OH)5·H2O – An assessment of the molecular structure

Meyerhofferite is a calcium hydrated borate mineral with ideal formula: CaB3O3(OH)5�H2O and occurs as white complex acicular to crude crystals with length up to �4 cm, in fibrous divergent, radiating aggregates or reticulated and is often found in sedimentary or lake-bed borate deposits. The Raman spectrum of meyerhofferite is dominated by intense sharp band at 880 cm�1 assigned to the symmetric stretching mode of trigonal boron. Broad Raman bands at 1046, 1110, 1135 and 1201 cm�1 are attributed to BOH in-plane bending modes. Raman bands in the 900–1000 cm�1 spectral region are assigned to the antisymmetric stretching of tetrahedral boron. Distinct OH stretching Raman bands are observed at 3400, 3483 and 3608 cm�1. The mineral meyerhofferite has a distinct Raman spectrum which is different from the spectrum of other borate minerals, making Raman spectroscopy a very useful tool for the detection of meyerhofferite in sedimentary and lake bed deposits.

Analysis of stream cipher based authenticated encryption schemes

Authenticated Encryption (AE) is the cryptographic process of providing simultaneous confidentiality and integrity protection to messages. This approach is more efficient than applying a two-step process of providing confidentiality for a message by encrypting the message, and in a separate pass providing integrity protection by generating a Message Authentication Code (MAC). AE using symmetric ciphers can be provided by either stream ciphers with built in authentication mechanisms or block ciphers using appropriate modes of operation. However, stream ciphers have the potential for higher performance and smaller footprint in hardware and/or software than block ciphers. This property makes stream ciphers suitable for resource constrained environments, where storage and computational power are limited. There have been several recent stream cipher proposals that claim to provide AE. These ciphers can be analysed using existing techniques that consider confidentiality or integrity separately; however currently there is no existing framework for the analysis of AE stream ciphers that analyses these two properties simultaneously. This thesis introduces a novel framework for the analysis of AE using stream cipher algorithms. This thesis analyzes the mechanisms for providing confidentiality and for providing integrity in AE algorithms using stream ciphers. There is a greater emphasis on the analysis of the integrity mechanisms, as there is little in the public literature on this, in the context of authenticated encryption. The thesis has four main contributions as follows. The first contribution is the design of a framework that can be used to classify AE stream ciphers based on three characteristics. The first classification applies Bellare and Namprempre's work on the the order in which encryption and authentication processes take place. The second classification is based on the method used for accumulating the input message (either directly or indirectly) into the into the internal states of the cipher to generate a MAC. The third classification is based on whether the sequence that is used to provide encryption and authentication is generated using a single key and initial vector, or two keys and two initial vectors. The second contribution is the application of an existing algebraic method to analyse the confidentiality algorithms of two AE stream ciphers; namely SSS and ZUC. The algebraic method is based on considering the nonlinear filter (NLF) of these ciphers as a combiner with memory. This method enables us to construct equations for the NLF that relate the (inputs, outputs and memory of the combiner) to the output keystream. We show that both of these ciphers are secure from this type of algebraic attack. We conclude that using a keydependent SBox in the NLF twice, and using two different SBoxes in the NLF of ZUC, prevents this type of algebraic attack. The third contribution is a new general matrix based model for MAC generation where the input message is injected directly into the internal state. This model describes the accumulation process when the input message is injected directly into the internal state of a nonlinear filter generator. We show that three recently proposed AE stream ciphers can be considered as instances of this model; namely SSS, NLSv2 and SOBER-128. Our model is more general than a previous investigations into direct injection. Possible forgery attacks against this model are investigated. It is shown that using a nonlinear filter in the accumulation process of the input message when either the input message or the initial states of the register is unknown prevents forgery attacks based on collisions. The last contribution is a new general matrix based model for MAC generation where the input message is injected indirectly into the internal state. This model uses the input message as a controller to accumulate a keystream sequence into an accumulation register. We show that three current AE stream ciphers can be considered as instances of this model; namely ZUC, Grain-128a and Sfinks. We establish the conditions under which the model is susceptible to forgery and side-channel attacks.

Vibrational spectroscopy of the phosphate mineral kovdorskite – Mg2PO4(OH)⋅3H2O

The mineral kovdorskite Mg2PO4(OH)�3H2O was studied by electron microscopy, thermal analysis and vibrational spectroscopy. A comparison of the vibrational spectroscopy of kovdorskite is made with other magnesium bearing phosphate minerals and compounds. Electron probe analysis proves the mineral is very pure. The Raman spectrum is characterized by a band at 965 cm�1 attributed to the PO3� 4 m1 symmetric stretching mode. Raman bands at 1057 and 1089 cm�1 are attributed to the PO3�4 m3 antisymmetric stretching modes. Raman bands at 412, 454 and 485 cm�1 are assigned to the PO3�4 m2 bending modes. Raman bands at 536, 546 and 574 cm�1 are assigned to the PO3�4 m4 bending modes. The Raman spectrum in the OH stretching region is dominated by a very sharp intense band at 3681 cm�1 assigned to the stretching vibration of OH units. Infrared bands observed at 2762, 2977, 3204, 3275 and 3394 cm�1 are attributed to water stretching bands. Vibrational spectroscopy shows that no carbonate bands are observed in the spectra; thus confirming the formula of the mineral as Mg2PO4(OH)�3H2O.

Raman spectroscopic study of the mineral qingheiite Na2(Mn2+,Mg,Fe2+)2(Al,Fe3+)(PO4)3, a pegmatite phosphate mineral from Santa Ana pegmatite, Argentina

The pegmatite mineral qingheiite Na2(Mn2+,Mg,Fe2+)2(Al,Fe3+)(PO4)3 has been studied by a combination of SEM and EMP, Raman and infrared spectroscopy. The studied sample was collected from the Santa Ana pegmatite, Argentina. The mineral occurs as a primary mineral in lithium bearing pegmatite, in association with beausite and lithiophilite. The Raman spectrum is characterized by a very sharp intense Raman band at 980 cm�1 assigned to the PO3�4 symmetric stretching mode. Multiple Raman bands are observed in the PO3�4 antisymmetric stretching region, providing evidence for the existence of more than one phosphate unit in the structure of qingheiite and evidence for the reduction in symmetry of the phosphate units. This concept is affirmed by the number of bands in the m4 and m2 bending regions. No intensity was observed in the OH stretching region in the Raman spectrum but significant intensity is found in the infrared spectrum. Infrared bands are observed at 2917, 3195, 3414 and 3498 cm�1 are assigned to water stretching vibrations. It is suggested that some water is coordinating the metal cations in the structure of qingheiite.

The molecular structure of the phosphate mineral senegalite Al2(PO4)(OH)3⋅3H2O – A vibrational spectroscopic study

We have studied the mineral senagalite, a hydrated hydroxy phosphate of aluminium with formula Al2(PO4)(OH)3⋅3H2O using a combination of electron microscopy and vibrational spectroscopy. Senegalite crystal aggregates shows tabular to prismatic habitus and orthorhombic form. The Raman spectrum is dominated by an intense band at 1029 cm−1 assigned to the PO43- ν1 symmetric stretching mode. Intense Raman bands are found at 1071 and 1154 cm−1 with bands of lesser intensity at 1110, 1179 and 1206 cm−1 and are attributed to the PO43- ν3 antisymmetric stretching vibrations. The infrared spectrum shows complexity with a series overlapping bands. A comparison is made with spectra of other aluminium containing phosphate minerals such as augelite and turquoise. Multiple bands are observed for the phosphate bending modes giving support for the reduction of symmetry of the phosphate anion. Vibrational spectroscopy offers a means for the assessment of the structure of senagalite.

Vibrational spectroscopic characterization of the phosphate mineral kulanite Ba(Fe2+,Mn2+,Mg)2(Al,Fe3+)2(PO4)3(OH)3

The mineral kulanite BaFe2Al2(PO4)3(OH)3, a barium iron aluminum phosphate, has been studied by using a combination of electron microscopy and vibrational spectroscopy. Scanning electron microscopy with EDX shows the mineral is homogenous with no other phases present. The Raman spectrum is dominated by an intense band at 1022 cm−1 assigned to the PO43-ν1 symmetric stretching mode. Low intensity Raman bands at 1076, 1110, 1146, 1182 cm−1 are attributed to the PO43-ν3 antisymmetric stretching vibrations. The infrared spectrum shows a complex spectral profile with overlapping bands. Multiple phosphate bending vibrations supports the concept of a reduction in symmetry of the phosphate anion. Raman spectrum at 3211, 3513 and 3533 cm−1 are assigned to the stretching vibrations of the OH units. Vibrational spectroscopy enables aspects on the molecular structure of kulanite to be assessed.

Half metallicity in a zigzag double-walled nanotube nanodot : an Ab initio prediction

Ab initio density functional calculations were performed to study finite-length zigzag (7, 0) @ (16, 0) double-walled carbon nanotubes (DWCNTs) with H-termination at the open ends. We find that such a DWCNT nanodot displays a very large magnetic moment at the zigzag edges and the ground state displays symmetric anti-ferromagnetic coupling. When an external electric field is applied along the direction of tube axis, a gap is opened for one spin channel, whereas another spin channel remains metallic, i.e. half metallicity occurs. Our results suggest an important new avenue for the development of CNT-based spintronic materials with enhanced properties.

Vibrational spectroscopy of the phosphate mineral lazulite – (Mg, Fe)Al2(PO4)2·(OH)2 found in the Minas Gerais, Brazil

This research was done on lazulite samples from the Gentil mine, a lithium bearing pegmatite located in the municipality of Mendes Pimentel, Minas Gerais, Brazil. Chemical analysis was carried out by electron microprobe analysis and indicated a magnesium rich phase with partial substitution of iron. Traces of Ca and Mn, (which partially replaced Mg) were found. The calculated chemical formula of the studied sample is: (Mg0.88, Fe0.11)Al1.87(PO4)2.08(OH)2.02. The Raman spectrum of lazulite is dominated by an intense sharp band at 1060 cm-1 assigned to PO stretching vibrations of of tetrahedral [PO4] clusters presents into the HPO2/4- units. Two Raman bands at 1102 and 1137 cm-1 are attributed to both the HOP and PO antisymmetric stretching vibrations. The two infrared bands at 997 and 1007 cm-1 are attributed to the m1 PO3/4- symmetric stretching modes. The intense bands at 1035, 1054, 1081, 1118 and 1154 cm-1 are assigned to the v3PO3/4- antisymmetric stretching modes from both the HOP and tetrahedral [PO4] clusters. A set of Raman bands at 605, 613, 633 and 648 cm-1 are assigned to the m4 out of plane bending modes of the PO4, HPO4 and H2PO4 units. Raman bands observed at 414, 425, 460, and 479 cm-1 are attributed to the m2 tetrahedral PO4 clusters, HPO4 and H2PO4 bending modes. The intense Raman band at 3402 and the infrared band at 3403 cm-1 are assigned to the stretching vibration of the OH units. A combination of Raman and infrared spectroscopy enabled aspects of the molecular structure of the mineral lazulite to be understood.

Thermal analysis and vibrational spectroscopic characterization of the boro silicate mineral datolite – CaBSiO4(OH)

The objective of this work is to determine the thermal stability and vibrational spectra of datolite CaBSiO4(OH) and relate these properties to the structure of the mineral. The thermal analysis of datolite shows a mass loss of 5.83% over a 700–775 °C temperature range. This mass loss corresponds to 1 water (H2O) molecules pfu. A quantitative chemical analysis using electron probe was undertaken. The Raman spectrum of datolite is characterized by bands at 917 and 1077 cm−1 assigned to the symmetric stretching modes of BO and SiO tetrahedra. A very intense Raman band is observed at 3498 cm−1 assigned to the stretching vibration of the OH units in the structure of datolite. BOH out-of-plane vibrations are characterized by the infrared band at 782 cm−1. The vibrational spectra are based upon the structure of datolite based on sheets of four- and eight-membered rings of alternating SiO4 and BO3(OH) tetrahedra with the sheets bonded together by calcium atoms.