A least squares based finite volume method for the Cahn-Hilliard and Cahn-Hilliard-reaction equations

A vertex-centred finite volume method (FVM) for the Cahn-Hilliard (CH) and recently proposed Cahn-Hilliard-reaction (CHR) equations is presented. Information at control volume faces is computed using a high-order least-squares approach based on Taylor series approximations. This least-squares problem explicitly includes the variational boundary condition (VBC) that ensures that the discrete equations satisfy all of the boundary conditions. We use this approach to solve the CH and CHR equations in one and two dimensions and show that our scheme satisfies the VBC to at least second order. For the CH equation we show evidence of conservative, gradient stable solutions, however for the CHR equation, strict gradient-stability is more challenging to achieve.

The persistence of phase-separation in LiFePO4 with two-dimensional Li+ transport : the Cahn-Hilliard-reaction equation and the role of defects

We examine the solution of the two-dimensional Cahn-Hilliard-reaction (CHR) equation in the xy plane as a model of Li+ intercalation into LiFePO4 material. We validate our numerical solution against the solution of the depth-averaged equation, which has been used to model intercalation in the limit of highly orthotropic diffusivity and gradient penalty tensors. We then examine the phase-change behaviour in the full CHR system as these parameters become more isotropic, and find that as the Li+ diffusivity is increased in the x direction, phase separation persists at high currents, even in small crystals with averaged coherency strain included. The resulting voltage curves decrease monotonically, which has previously been considered a hallmark of crystals that fill homogeneously.

Vibrational spectroscopic characterization of the phosphate mineral phosphophyllite – Zn2Fe(PO4)2·4H2O, from Hagendorf Süd, Germany and in comparison with other zinc phosphates

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.

Removal of phosphorus using NZVI derived from reducing natural goethite

Nano zero valent iron (NZVI) prepared by reducing natural goethite in hydrogen at 550 °C was used to remove phosphate. The effect of particle size, reaction time, NZVI dose, pH, initial phosphorus concentration, and oxygen amount in reaction system on phosphorus removal was investigated. The characterization of X-ray fluorescence (XRF), X-ray diffraction (XRD), N2 adsorption and desorption (BET analysis), transmission electron microscope (TEM), field emission scanning electron microscope with a energy dispersive X-ray detector (FESEM/EDS) and X-ray photoelectron spectroscopy (XPS) indicated that nanoscale of iron (around 80–150 nm length and 5–30 nm width) was prepared successfully with high dispersion and relative large surface area around 22 m2/g. The results of batch experiments and XPS analysis suggested that this kind of NZVI had a good performance on removal of phosphate (over 99%) despite in slightly acidic media as the initial concentration of P was 5 mg/L. The reason was ascribed to the effective corrosion of this NZVI under the function of proton and dissolved oxygen in spite of the existence of thin passive films.

External pressure in the hardening of phosphate in tribofilm on iron surfaces

Purpose: In the present work we consider our (in progress) spectroscopy study of zinc and iron phosphates under the influence external high pressure to determine zinc ion change coordination from tetrahedral to octahedral (or hexahedral) structure.----- Design/methodology/approach: The standard equipment is the optical high pressure cell with diamond (DAC). The DAC is assembled and then vibrational or electronic spectra are collected by mounting the cell in an infrared, Raman, EXAFS or UV-visible spectrometer.----- Findings: Mechanism by which zinc and iron methaphosphate material is transformed to glassy meta-phosphate is enhancing mechanical properties of tribofilm. The two decades of intensive study demonstrates that Zn (II) and Fe (III) ions participate to cross-link network under friction, hardening the phosphate.----- Research limitations/implications: Transition metal atoms with d orbital have flexible coordination numbers, for example zinc acts as a cross-linking agent increasing hardness, by changing coordination from tetrahedral to octahedral. Perhaps the external pressure effect on the [Zn–(O-P-)4 ] complex causes a transformation to an [Zn –(O-P-)6] grouping.----- Originality/value: This paper analyses high-pressure spectroscopy which has been applied for the investigation of 3D transition metal ions in solids. When studying pressure effects on coordination compounds structure, we can expect changes in ground electronic state (spin-crossovers), electronic spectra due to structural distortions (piezochromism), and changes in the ligand field causing shifts in the electronic transitions.

Chemistry, Raman and infrared spectroscopic characterization of the phosphate mineral reddingite: (MnFe)3(PO4)2(H2O,OH)3, a mineral found in lithium-bearing pegmatite

Detailed investigation of an intermediate member of the reddingite–phosphoferrite series, using infrared and Raman spectroscopy, scanning electron microcopy and electron microprobe analysis, has been carried out on a homogeneous sample from a lithium-bearing pegmatite named Cigana mine, near Conselheiro Pena, Minas Gerais, Brazil. The determined formula is (Mn1.60Fe1.21Ca0.01Mg0.01)∑2.83(PO4)2.12⋅(H2O2.85F0.01)∑2.86 indicating predominance in the reddingite member. Raman spectroscopy coupled with infrared spectroscopy supports the concept of phosphate, hydrogen phosphate and dihydrogen phosphate units in the structure of reddingite-phosphoferrite. Infrared and Raman bands attributed to water and hydroxyl stretching modes are identified. Vibrational spectroscopy adds useful information to the molecular structure of reddingite–phosphoferrite.

Vibrational spectroscopic characterization of the phosphate mineral ludlamite (Fe,Mn,Mg)3(PO4)2⋅4H2O – a mineral found in lithium bearing pegmatites

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.

Vibrational spectroscopic characterization of the phosphate mineral hureaulite – (Mn, Fe)5(PO4)2(HPO4)2·4(H2O)

This research was done on hureaulite samples from the Cigana claim, a lithium bearing pegmatite with triphylite and spodumene. The mine is located in Conselheiro Pena, east of Minas Gerais. Chemical analysis was carried out by Electron Microprobe analysis and indicated a manganese rich phase with partial substitution of iron. The calculated chemical formula of the studied sample is: (Mn3.23, Fe1.04, Ca0.19, Mg0.13)(PO4)2.7(HPO4)2.6(OH)4.78. The Raman spectrum of hureaulite is dominated by an intense sharp band at 959 cm−1 assigned to PO stretching vibrations of HPO42− units. The Raman band at 989 cm−1 is assigned to the PO43− stretching vibration. Raman bands at 1007, 1024, 1047, and 1083 cm−1 are attributed to both the HOP and PO antisymmetric stretching vibrations of HPO42− and PO43− units. A set of Raman bands at 531, 543, 564 and 582 cm−1 are assigned to the ν4 bending modes of the HPO42− and PO43− units. Raman bands observed at 414, and 455 cm−1 are attributed to the ν2 HPO42− and PO43− units. The intense A series of Raman and infrared bands in the OH stretching region are assigned to water stretching vibrations. Based upon the position of these bands hydrogen bond distances are calculated. Hydrogen bond distances are short indicating very strong hydrogen bonding in the hureaulite structure. A combination of Raman and infrared spectroscopy enabled aspects of the molecular structure of the mineral hureaulite to be understood.

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.

Lithium release from ß-tricalcium phosphate inducing cementogenic and osteogenic differentiation for both hPDLCs and hBMSCs

It is accepted that the accelerated differentiation of tissue cells on bioactive materials is of great importance to regenerate the lost tissues. It was previously reported that lithium (Li) ions could enhance the in vitro proliferation and differentiation of retinoblastoma cells and endometrium epithelia by activating the Wnt canonical signalling pathway. It is interesting to incorporate Li ions into bioactive ceramics, such as β-tricalcium phosphate (Li-β-TCP), in order to stimulate both osteogenic and cementogenic differentiation of different stem cells for the regeneration of bone/periodontal tissues. Therefore, the aim of this study was to investigate the interactions of human periodontal ligament cells (hPDLCs) and human bone marrow stromal cells (hBMSCs) with Li-β-TCP bioceramic bulks and their ionic extracts, and further explore the osteogenic and cementogenic stimulation of Li-β-TCP bioceramics and the possible molecular mechanisms. The results showed that Li-β-TCP bioceramic disks supported the cell attachment and proliferation, and significantly enhanced bone/cementum-related gene expression, Wnt canonical signalling pathway activation for both hPDLCs and hBMSCs, compared to conventional β-TCP bioceramic disks without Li. The release of Li from Li-β-TCP powders could significantly promote the bone/cementum-related gene expression for both hPDLCs and hBMSCs compared to pure β-TCP extracts without Li release. Our results suggest that the combination of Li with β-TCP bioceramics may be a promising method to enhance bone/cementum regeneration as Li-β-TCP possesses excellent in vitro osteogenic and cementogenic stimulation properties by inducing bone/cementum-related gene expression in both hPDLCs and hBMSCs.

The phosphate mineral arrojadite-(KFe) and its spectroscopic characterization

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.

Vibrational spectroscopic characterization of the phosphate mineral series eosphorite–childrenite–(Mn,Fe)Al(PO4)(OH)2·(H2O)

The phosphate mineral series eosphorite–childrenite–(Mn,Fe)Al(PO4)(OH)2·(H2O) has been studied using a combination of electron probe analysis and vibrational spectroscopy. Eosphorite is the manganese rich mineral with lower iron content in comparison with the childrenite which has higher iron and lower manganese content. The determined formulae of the two studied minerals are: (Mn0.72,Fe0.13,Ca0.01)(Al)1.04(PO4, OHPO3)1.07(OH1.89,F0.02)·0.94(H2O) for SAA-090 and (Fe0.49,Mn0.35,Mg0.06,Ca0.04)(Al)1.03(PO4, OHPO3)1.05(OH)1.90·0.95(H2O) for SAA-072. Raman spectroscopy enabled the observation of bands at 970 cm−1 and 1011 cm−1 assigned to monohydrogen phosphate, phosphate and dihydrogen phosphate units. Differences are observed in the area of the peaks between the two eosphorite minerals. Raman bands at 562 cm−1, 595 cm−1, and 608 cm−1 are assigned to the �4 bending modes of the PO4, HPO4 and H2PO4 units; Raman bands at 405 cm−1, 427 cm−1 and 466 cm−1 are attributed to the �2 modes of these units. Raman bands of the hydroxyl and water stretching modes are observed. Vibrational spectroscopy enabled details of the molecular structure of the eosphorite mineral series to be determined.

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.

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.

Raman and infrared spectroscopic characterization of the phosphate mineral Lithiophilite—LiMnPO4

The metal lithium is very important in industry, including lithium batteries. An important source of lithium besides continental brines is granitic pegmatites as in Australia. Lithiophilite is a lithium and manganese phosphate with chemical formula LiMnPO4 and forms a solid solution with triphylite, its Fe analog, and belongs to the triphylite group that includes karenwebberite, natrophilite, and sicklerite. The mineral lithiophilite was characterized by chemical analysis and spectroscopic techniques. The chemical is: Li1.01(Mn0.60, Fe0.41, Mg0.01, Ca0.01)(PO4)0.99 and corresponds to an intermediate member of the triphylite-lithiophilite series, with predominance of the lithiophilite member. The mineral lithiophilite is readily characterized by Raman and infrared spectroscopy.