Application of a continuum theory to vertical vibrations of a layer of granular material

Many interesting phenomena have been observed in layers of granular materials subjected to vertical oscillations; these include the formation of a variety of standing wave patterns, and the occurrence of isolated features called oscillons, which alternately form conical heaps and craters oscillating at one-half of the forcing frequency. No continuum-based explanation of these phenomena has previously been proposed. We apply a continuum theory, termed the double-shearing theory, which has had success in analyzing various problems in the flow of granular materials, to the problem of a layer of granular material on a vertically vibrating rigid base undergoing vertical oscillations in plane strain. There exists a trivial solution in which the layer moves as a rigid body. By investigating linear perturbations of this solution, we find that at certain amplitudes and frequencies this trivial solution can bifurcate. The time dependence of the perturbed solution is governed by Mathieu’s equation, which allows stable, unstable and periodic solutions, and the observed period-doubling behaviour. Several solutions for the spatial velocity distribution are obtained; these include one in which the surface undergoes vertical velocities that have sinusoidal dependence on the horizontal space dimension, which corresponds to the formation of striped standing waves, and is one of the observed patterns. An alternative continuum theory of granular material mechanics, in which the principal axes of stress and rate-of-deformation are coincident, is shown to be incapable of giving rise to similar instabilities.

Confirmation of the assignment of vibrations of goethite: An ATR and IES study of goethite structure

Transmission electron microscopy (TEM), field emission scanning electron microscopy (FE-SEM/EDS) and X-ray diffraction (XRD) were used to characterize the morphology of synthetic goethite. The behavior of the hydroxyl/water molecular units of goethite and its thermally treated products were characterized using Fourier transform-infrared emission spectroscopy (FT-IES) and attenuated total reflectance–Fourier transform infrared (ATR–FTIR) spectroscopy. The results showed that all the expected vibrational bands between 4000 and 650 cm−1 including the resolved bands (3800–2200 cm−1) were confirmed. A band attributed to a new type of hydroxyl unit was found at 3708 cm−1 and assigned to the FeO–H stretching vibration without hydrogen bonding. This hydroxyl unit was retained up to the thermal treatment temperature of 500 °C. On the whole, seven kinds of hydroxyl units, involving three surface hydroxyls, a bulk hydroxyl, a FeO–H without hydrogen bonding, a nonstoichiometric hydroxyl and a reversed hydroxyl were observed, and three kinds of adsorbed water were found in/on goethite.

Hydraulic instability onset detection in Kaplan turbines by monitoring shaft vibrations

Design of hydraulic turbines has often to deal with hydraulic instability. It is well-known that Francis and Kaplan types present hydraulic instability in their design power range. Even if modern CFD tools may help to define these dangerous operating conditions and optimize runner design, hydraulic instabilities may fortuitously arise during the turbine life and should be timely detected in order to assure a long-lasting operating life. In a previous paper, the authors have considered the phenomenon of helical vortex rope, which happens at low flow rates when a swirling flow, in the draft tube conical inlet, occupies a large portion of the inlet. In this condition, a strong helical vortex rope appears. The vortex rope causes mechanical effects on the runner, on the whole turbine and on the draft tube, which may eventually produce severe damages on the turbine unit and whose most evident symptoms are vibrations. The authors have already shown that vibration analysis is suitable for detecting vortex rope onset, thanks to an experimental test campaign performed during the commissioning of a 23 MW Kaplan hydraulic turbine unit. In this paper, the authors propose a sophisticated data driven approach to detect vortex rope onset at different power load, based on the analysis of the vibration signals in the order domain and introducing the so-called "residual order spectrogram", i.e. an order-rotation representation of the vibration signal. Some experimental test runs are presented and the possibility to detect instability onset, especially in real-time, is discussed.

Spectroscopic vibrations of austinite (CaZnAsO4⋅OH) and its mineral structure : Implications for identification of secondary arsenic-containing mineral

Austinite (CaZnAsO4⋅OH) is a unique secondary mineral in arsenic-contaminated mine wastes. The infrared and Raman spectroscopies were used to characterize the austenite vibrations. The IR bands at 369, 790 and 416 cm−1 are assigned to the ν2, ν3 and ν4 vibrations of AsO43− unit, respectively. The Raman bands at 814, 779 and 403 cm−1 correspond to the ν1, ν3 and ν4 vibrations of AsO43− unit respectively. The sharp bands at 3265 cm−1 for IR and 3270 cm−1 both reveals that the structural hydroxyl units exist in the austenite structure. The IR and Raman spectra both show that some SO4 units isomorphically replace AsO4 in austinite. X-ray single crystal diffraction provides the arrangement of each atom in the mineral structure, and also confirms that the conclusions made from the vibrational spectra. Micro-powder diffraction was used to confirm our mineral identification due to the small quantity of the austenite crystals.

The'cave' mineral oxammite: a high resolution thermogravimetry and Raman spectroscopic study

The thermal decomposition of natural ammonium oxalate known as oxammite has been studied using a combination of high resolution thermogravimetry coupled to an evolved gas mass spectrometer and Raman spectroscopy coupled to a thermal stage. Three mass loss steps were found at 57, 175 and 188°C attributed to dehydration, ammonia evolution and carbon dioxide evolution respectively. Raman spectroscopy shows two bands at 3235 and 3030 cm-1 attributed to the OH stretching vibrations and three bands at 2995, 2900 and 2879 cm-1, attributed to the NH vibrational modes. The thermal degradation of oxammite may be followed by the loss of intensity of these bands. No intensity remains in the OH stretching bands at 100°C and the NH stretching bands show no intensity at 200°C. Multiple CO symmetric stretching bands are observed at 1473, 1454, 1447 and 1431cm-1, suggesting that the mineral oxammite is composed of a mixture of chemicals including ammonium oxalate dihydrate, ammonium oxalate monohydrate and anhydrous ammonium oxalate.

Towards a single crystal Raman spectrum of kaolinite at 77 K

The Raman spectra at 77 K of the hydroxyl stretching of kaolinite were obtained along the three axes perpendicular to the crystal faces. Raman bands were observed at 3616, 3658 and 3677 cm−1 together with a distinct band observed at 3691 cm−1 and a broad profile between 3695 and 3715 cm−1. The band at 3616 cm−1 is assigned to the inner hydroxyl. The bands at 3658 and 3677 cm−1 are attributed to the out-of-phase vibrations of the inner surface hydroxyls. The Raman spectra of the in-phase vibrations of the inner-surface hydroxyl-stretching region are described in terms of transverse and longitudinal optic splitting. The band at 3691 cm−1 is assigned to the transverse optic and the broad profile to the longitudinal optic mode. This splitting remained even at liquid nitrogen temperature. The transverse optic vibration may be curve resolved into two or three bands, which are attributed to different types of hydroxyl groups in the kaolinite.

Electronic and vibrational spectra of gaspeite

Visible, near-infrared, IR and Raman spectra of magnesian gaspeite are presented. Nickel ion is the main source of the electronic bands as it is the principal component in the mineral where as the bands in IR and Raman spectra are due to the vibrational processes in the carbonate ion as an entity. The combination of electronic absorption and vibrational spectra (including near-infrared, FTIR and Raman) of magnesian gaspeite are explained in terms of the cation co-ordination and the behaviour of CO32– anion in the Ni–Mg carbonate. The electronic absorption spectrum consists of three broad and intense bands at 8130, 13160 and 22730 cm–1 due to spin-allowed transitions and two weak bands at 20410 and 30300 cm–1 are assigned to spin-forbidden transitions of Ni2+ in an octahedral symmetry. The crystal field parameters evaluated from the observed bands are Dq = 810; B = 800 and C = 3200 cm–1. The two bands in the near-infrared spectrum at 4330 and 5130 cm–1 are overtone and combination of CO32– vibrational modes. For the carbonate group, infrared bands are observed at 1020 cm–1(1 ), 870 cm–1 (2), 1418 cm–1 (3) and 750 cm–1 (4), of which3, the asymmetric stretching mode is most intense. Three well resolved Raman bands at 1571, 1088 and 331 cm–1 are assigned to 3, 1 and MO stretching vibrations.

Raman microscopic study of the Li amphibole holmquistite, from the Martin Marietta Quarry, Bessemer City, NC, USA

The Raman spectrum of holmquistite, a Li-containing orthorhombic amphibole from Bessemer City, USA has been measured. The OH-stretching region is characterized by bands at 3661, 3646, 3634 and 3614 cm–1 assigned to 3 Mg–OH, 2 Mg + Fe2+–OH, Mg + 2Fe2+–OH and 3 Fe2+–OH, respectively. These Mg and Fe2+ cations are located at the M1 and M3 sites and have a Fe2+/(Fe2+ + Mg) ratio of 0.35. The 960–1110 cm–1 region represents the antisymmetric Si–O–Si and O–Si–O stretching vibrations. For holmquistite, strong bands are observed around 1022 and 1085 cm–1 with a shoulder at 1127 cm–1 and minor bands at 1045 and 1102 cm–1. In the region 650–800 cm–1 bands are observed at 679, 753 and 791 cm–1 with a minor band around 694 cm–1 attributed to the symmetrical Si–O–Si and Si–O vibrations. The region below 625 cm–1 is characterized by 14 vibrations related to the deformation modes of the silicate double chain and vibrations involving Mg, Fe, Al and Li in the various M sites. The 502 cm–1 band is a Li–O deformation mode while the 456, 551 and 565 cm–1 bands are Al–O deformation modes.

The Behavior of Hydroxyl Units of Synthetic Goethite and its Dehydroxylated Product Hematite

The behavior of the hydroxyl units of synthetic goethite and its dehydroxylated product hematite was characterized using a combination of Fourier transform infrared (FTIR) spectroscopy and X-ray diffraction (XRD) during the thermal transformation over a temperature range of 180-270 degrees C. Hematite was detected at temperatures above 200 degrees C by XRD while goethite was not observed above 230 degrees C. Five intense OH vibrations at 3212-3194, 1687-1674, 1643-1640, 888-884 and 800-798 cm(-1), and a H2O vibration at 3450-3445 cm(-1) were observed for goethite. The intensity of hydroxyl stretching and bending vibrations decreased with the extent of dehydroxylation of goethite. Infrared absorption bands clearly show the phase transformation between goethite and hematite: in particular. the migration of excess hydroxyl units from goethite to hematite. Two bands at 536-533 and 454-452 cm(-1) are the low wavenumber vibrations of Fe-O in the hematite structure. Band component analysis data of FTIR spectra support the fact that the hydroxyl units mainly affect the a plane in goethite and the equivalent c plane in hematite.

Vibrational spectroscopy of phthalocyanine and naphthalocyanine in sandwich-type (na)phthalocyaninato and porphyrinato rare earth complexes : (Part 10) The infrared and Raman characteristics of phthalocyanine in heteroleptic bis(phthalocyaninato) rare earth complexes with decreased molecular symmetry

The infrared (IR) spectroscopic data for a series of eleven heteroleptic bis(phthalocyaninato) rare earth complexes MIII(Pc)[Pc(α-OC5H11)4] (M = Sm–Lu, Y) [H2Pc = unsubstituted phthalocyanine, H2Pc(α-OC5H11)4 = 1,8,15,22-tetrakis(3-pentyloxy)phthalocyanine] have been collected with 2 cm−1 resolution. Raman spectroscopic properties in the range of 500–1800 cm−1 for these double-decker molecules have also been comparatively studied using laser excitation sources emitting at 632.8 and 785 nm. Both the IR and Raman spectra for M(Pc)[Pc(α-OC5H11)4] are more complicated than those of homoleptic bis(phthalocyaninato) rare earth analogues due to the decreased molecular symmetry of these double-decker compounds, namely C4. For this series, the IR Pc√− marker band appears as an intense absorption at 1309–1317 cm−1, attributed to the pyrrole stretching. With laser excitation at 632.8 nm, Raman vibrations derived from isoindole ring and aza stretchings in the range of 1300–1600 cm−1 are selectively intensified. In contrast, when excited with laser radiation of 785 nm, the ring radial vibrations of isoindole moieties and dihedral plane deformations between 500 and 1000 cm−1 for M(Pc)[Pc(α-OC5H11)4] intensify to become the strongest scatterings. Both techniques reveal that the frequencies of pyrrole stretching, isoindole breathing, isoindole stretchings, aza stretchings and coupling of pyrrole and aza stretchings depend on the rare earth ionic size, shifting to higher energy along with the lanthanide contraction due to the increased ring-ring interaction across the series. The assignments of the vibrational bands for these compounds have been made and discussed in relation to other unsubstituted and substituted bis(phthalocyaninato) rare earth analogues, such as M(Pc)2 and M(OOPc)2 [H2OOPc = 2,3,9,10,16,17,23,24-octakis(octyloxy)phthalocyanine].

Mechanochemical treatment of kaolinite

Kaolinite surfaces were modified by mechanochemical treatment for periods of time up to 10 h. X-ray diffraction shows a steady decrease in intensity of the d(001) spacing with mechanochemical treatment, resulting in the delamination of the kaolinite and a subsequent decrease in crystallite size with grinding time. Thermogravimetric analyses show the dehydroxylation patterns of kaolinite are significantly modified. Changes in the molecular structure of the kaolinite surface hydroxyls were followed by infrared spectroscopy. Hydroxyls were lost after 10 h of grinding as evidenced by a decrease in intensity of the OH stretching vibrations at 3695 and 3619 cm−1 and the deformation modes at 937 and 915 cm−1. Concomitantly an increase in the hydroxyl stretching vibrations of water is found. The water-bending mode was observed at 1650 cm−1, indicating that water is coordinating to the modified kaolinite surface. Changes in the surface structure of the OSiO units were reflected in the SiO stretching and OSiO bending vibrations. The decrease in intensity of the 1056 and 1034 cm−1 bands attributed to kaolinite SiO stretching vibrations were concomitantly matched by the increase in intensity of additional bands at 1113 and 520 cm−1 ascribed to the new mechanically synthesized kaolinite surface. Mechanochemical treatment of the kaolinite results in a new surface structure.

An infrared spectroscopic study of the some Autunite minerals

A series of selected autunites with phosphate as the anion have been studied using infrared spectroscopy. Each autunite mineral has its own characteristic spectrum. The spectra for different autunites with the same composition are different. It is proposed that this difference is due to the structure of water and hydrated cations in the interlayer region between the uranyl phosphate sheets. This structure is different for different autunites. The position of the water hydroxyl stretching bands is related to the strength of the hydrogen bonds as determined by hydrogen bond distance. The highly ordered structure of water is also observed in the water HOH bending modes where a high wavenumber bands are observed. The phosphate and uranyl stretching vibrations overlap and are obtained by curve resolution.

The effect of mechanochemical activation upon the intercalation of a high-defect kaolinite with formamide

The effect of mechanochemical activation upon the intercalation of formamide into a high-defect kaolinite has been studied using a combination of X-ray diffraction, thermal analysis, and DRIFT spectroscopy. X-ray diffraction shows that the intensity of the d(001) spacing decreases with grinding time and that the intercalated high-defect kaolinite expands to 10.2 A. The intensity of the peak of the expanded phase of the formamide-intercalated kaolinite decreases with grinding time. Thermal analysis reveals that the evolution temperature of the adsorbed formamide and loss of the inserting molecule increases with increased grinding time. The temperature of the dehydroxylation of the formamide-intercalated high-defect kaolinite decreases from 495 to 470oC with mechanochemical activation. Changes in the surface structure of the mechanochemically activated formamide-intercalated high-defect kaolinite were followed by DRIFT spectroscopy. Fundamentally the intensity of the high-defect kaolinite hydroxyl stretching bands decreases exponentially with grinding time and simultaneously the intensity of the bands attributed to the OH stretching vibrations of water increased. It is proposed that the mechanochemical activation of the high-defect kaolinite caused the conversion of the hydroxyls to water which coordinates the kaolinite surface. Significant changes in the infrared bands assigned to the hydroxyl deformation and amide stretching and bending modes were observed. The intensity decrease of these bands was exponentially related to the grinding time. The position of the amide C&unknown;O vibrational mode was found to be sensitive to grinding time. The effect of mechanochemical activation of the high-defect kaolinite reduces the capacity of the kaolinite to be intercalated with formamide.

Raman spectroscopic characteristics of phthalocyanine and naphthalocyanine in sandwich-type phthalocyaninato and porphyrinato rare earth complexes Part 5. – Raman spectroscopic characteristics of naphthalocyanine in mixed [tetrakis(4-tert-butylphenyl)porphyrinato]-(naphthalocyaninato) rare earth double-deckers

Raman spectra were recorded in the range 400–1800 cm−1 for a series of 15 mixed \[tetrakis(4-tert-butylphenyl)porphyrinato](2,3-naphthalocyaninato) rare earth double-deckers M(TBPP)(Nc) (M = Y; La–Lu except Pm) using laser excitation at 632.8 and 785 nm. Comparisons with bis(naphthalocyaninato) rare earth counterparts reveal that the vibrations of the metallonaphthalocyanine M(Nc) fragment dominate the Raman features of M(TBPP)(Nc). When excited with radiation of 632.8 nm, the most intense vibration appears at about 1595 cm−1, due to the naphthalene stretching. These complexes exhibit the marker Raman band for Nc•− as a medium-intense band in the range 1496–1507 cm−1, attributed to the coupling of pyrrole and aza stretching, while the marker Raman band of Nc2− in intermediate-valence Ce(TBPP)(Nc) appears as a strong band at 1493 cm−1 and is due to the isoindole stretchings. By contrast, when excited with radiation of 785 nm that is in close resonance with the main Q absorption band of the naphthalocyanine ligand, the ring radial vibrations at ca 680 and 735 cm−1 for MIII(TBPP)(Nc) are selectively intensified and are the most intense bands. For the cerium double-decker, the most intense vibration also acting as the marker Raman band of Nc2− appears at 1497 cm−1 with contributions from both pyrrole CC and aza CN stretches. The same vibrational modes show weak to medium intensity scattering at 1506–1509 cm−1 for MIII(TBPP)(Nc) and this is the marker Raman band of Nc•− when thus excited. The scatterings due to the Nc breathings, ring radial vibration, aza group stretchings, naphthalene stretchings, benzoisoindole stretchings and the coupling of pyrrole CC and aza CN stretchings in MIII(TBPP)(Nc) are all slightly blue shifted along with the decrease in rare earth ionic radius, confirming the effects of increased ring–ring interactions on the Raman characteristics of naphthalocyanine in the mixed ring double-deckers.