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1.
Artigo em Inglês | MEDLINE | ID: mdl-23995604

RESUMO

Manganese minerals ardenite, alleghanyite and leucopoenicite originated from Madhya Pradesh, India, Nagano prefecture Japan, Sussex Country and Parker Shaft Franklin, Sussex Country, New Jersey respectively are used in the present work. In these minerals manganese is the major constituent and iron if present is in traces only. An EPR study of on all of the above samples confirms the presence of Mn(II) with g around 2.0. Optical absorption spectrum of the mineral alleghanyite indicates that Mn(II) is present in two different octahedral sites and in leucophoenicite Mn(II) is also in octahedral geometry. Ardenite mineral gives only a few Mn(II) bands. NIR results of the minerals ardenite, leucophoenicite and alleghanyite are due to hydroxyl and silicate anions which confirming the formulae of the minerals.


Assuntos
Espectroscopia de Ressonância de Spin Eletrônica , Manganês/química , Minerais/química , Silicatos/química , Espectroscopia de Luz Próxima ao Infravermelho , Índia
2.
Spectrochim Acta A Mol Biomol Spectrosc ; 81(1): 308-12, 2011 Oct 15.
Artigo em Inglês | MEDLINE | ID: mdl-21782499

RESUMO

The mineral sphalerite (Zn,Fe)S has been characterized by a combination of X-ray diffraction, EPR and NIR spectroscopy. The optical absorption spectrum of mineral sphalerite is due to an iron impurity only, which is in a distorted octahedral environment. The g=2.2 is attributed to iron and g and A value observed in the spectrum 1.999 and 6.0 mT are assigned to Mn(II) impurity in the mineral. These results indicate that iron and Mn(II) impurity have entered the lattice by substitution. The EPR results confirm the presence of manganese in a distorted octahedral environment. It is evident from the chemical analysis that iron is present in higher concentrations. NIR results are due to the presence of water and sulphide fundamentals which also support the formula of the mineral. No sulphate in the sphalerite mineral was observed.


Assuntos
Sulfetos/química , Compostos de Zinco/química , Absorção , Espectroscopia de Ressonância de Spin Eletrônica , Ferro/química , Manganês/química , Minerais/química , Rotação Ocular , Espectroscopia de Luz Próxima ao Infravermelho , Difração de Raios X
3.
Artigo em Inglês | MEDLINE | ID: mdl-19926334

RESUMO

Optical absorption and EPR studies of the mineral tenorite, a cupric oxide which originated from Mexico and contains 54.40 wt% of CuO. EPR spectral results indicate two Cu(II) closely interacting ions to give a d(2) type structure. The calculated spin Hamiltonian at room temperature and liquid nitrogen temperature is g=2.160 and D=125 G. The intensity of resonance line is not the same in low and high field regions. The optical absorption spectrum is due to Cu(II) in which three sets of energies indicating Cu(II) in two independent tetragonal C(4v) symmetry, in addition to d(2) structure of octahedral coordination. The octahedral and tetragonal field parameters are compared with those reported for several other copper containing minerals.


Assuntos
Cobre/química , Espectroscopia de Ressonância de Spin Eletrônica/métodos , Minerais/química , Óptica e Fotônica/métodos , Oligoelementos/química , Absorção , Temperatura , Termodinâmica
4.
Artigo em Inglês | MEDLINE | ID: mdl-19010719

RESUMO

Descloizite mineral originated from Grootfontein, South West Africa, is used in the present work. The chemical analysis of this mineral reveals the presence of V(2)O(5)=20.94 wt%, CuO=0.45 wt%, FeO in traces. An EPR study of sample confirms the presence of VO(II) and Fe(III). Optical absorption spectrum of descloizite indicates that VO(II) is present in distorted octahedral environment. NIR results are due to water fundamentals.


Assuntos
Minerais/química , Vanadatos/química , Absorção , Espectroscopia de Ressonância de Spin Eletrônica , Espectroscopia de Luz Próxima ao Infravermelho , Análise Espectral , Temperatura
5.
Spectrochim Acta A Mol Biomol Spectrosc ; 71(1): 31-8, 2008 Nov 01.
Artigo em Inglês | MEDLINE | ID: mdl-18280774

RESUMO

Leaves of bhringaraj and guduchi herb of Kadapa district of Andhra Pradesh, India, are dried and powdered. ICP-MS analysis of samples indicates that copper is present in both the samples. An EPR study of guduchi sample also confirms the presence of Fe(III) whereas Eclipta alba confirms the presence of Fe(III), Mn(II) and Cu(II). Optical absorption spectrum of guduchi indicates that Cu(II) is present in rhombically distorted octahedral environment. NIR and IR results are due to carbonate fundamentals.


Assuntos
Espectroscopia de Ressonância de Spin Eletrônica/métodos , Ferro/análise , Espectrometria de Massas/métodos , Extratos Vegetais/análise , Plantas Medicinais/metabolismo , Espectrofotometria Infravermelho/métodos , Cobre/análise , Manganês/análise , Óptica e Fotônica , Extratos Vegetais/química , Espectrofotometria/métodos , Espectroscopia de Luz Próxima ao Infravermelho/métodos , Temperatura , Oligoelementos
6.
Spectrochim Acta A Mol Biomol Spectrosc ; 71(1): 45-52, 2008 Nov 01.
Artigo em Inglês | MEDLINE | ID: mdl-18221911

RESUMO

Thermal decomposition studies of the free polyhedral oligomeric silsesquioxane, POSSh, and when this compound has been impregnated with Cp2ZrCl2 (Cp = eta5-C5H5) or immobilized on SiO2 were conducted using infrared emission spectroscopy (IES) over a 100-1000 degrees C temperature range and by thermogravimetric analysis (TGA). The organic groups in POSS(h) apparently decompose thermally into Si-CH3, Si-H and other fragments. Upon impregnation with Cp2ZrCl2, however, a different thermal decomposition pathway was followed and new infrared emission bands appeared in the 1000-900 cm(-1) region suggesting the formation of Si-O-Zr moieties. When immobilized on SiO2 and subjected to thermal decomposition, the POSSh compound lost its organic groups and the inorganic structure remaining was incorporated into the SiO2 framework.


Assuntos
Compostos Organometálicos/química , Dióxido de Silício/química , Espectrofotometria/métodos , Catálise , Química/métodos , Temperatura Alta , Modelos Químicos , Compostos de Organossilício/química , Compostos de Amônio Quaternário/química , Espectrofotometria Infravermelho/métodos , Temperatura , Termogravimetria/métodos
7.
Artigo em Inglês | MEDLINE | ID: mdl-17600761

RESUMO

Pelecypod shell originated from Kolleru lake of Andhra Pradesh is used in the present work. It contains Mn(II) and Fe(III) in traces. The EPR spectrum of the compound is due to Mn(II) which is in three independent sites. The three g values are evaluated with slight differences. The hyperfine component varies from 9.33 to 9.49mT. The zero field splitting parameter is also ranges from 43.8(1) to 44.1(1)mT. Using the covalence parameter the number of ligands around metal is estimated as 20. In EPR spectrum Fe(III) is identified. The optical absorption spectrum is attributed to Mn(II) in octahedral geometry. Further 10 Dq band is attributed to Fe(II) in the optical absorption spectrum. NIR spectral results are due to water fundamentals, whereas IR and Raman spectrum is due to carbonate ion fundamentals.


Assuntos
Bivalves/anatomia & histologia , Bivalves/química , Espectroscopia de Ressonância de Spin Eletrônica/métodos , Espectrofotometria/métodos , Análise Espectral Raman/métodos , Animais , Vibração
8.
Artigo em Inglês | MEDLINE | ID: mdl-17428726

RESUMO

The behaviour of transition metal ions in beaverite mineral has been studied by spectroscopic techniques such as electron paramagnetic resonance and absorption spectroscopy in the UV-vis and NIR regions. The ground state of Cu(II) ion in beaverite is confirmed as (2)B(1g) since g(parallel)>g(perpendicular) (2.42>2.097). A resonance noticed at g=2.017 is ascribed to Fe(III) impurity. Two sets of three characteristic bands observed in the optical absorption spectra are assigned to the same transitions, (2)B(1g)-->(2)A(1g), (2)B(1g)-->(2)B(2) and (2)B(1g)-->(2)E(g) of Cu(II) ion in tetragonal field. The presence of Fe(III) bands is supportive evidence for iron impurity in the mineral. Mid infrared spectrum is due to overtones and combination tones of water and hydroxyl groups.


Assuntos
Cobre/química , Minerais/química , Óptica e Fotônica , Espectroscopia de Ressonância de Spin Eletrônica , Espectrofotometria Ultravioleta , Espectroscopia de Luz Próxima ao Infravermelho , Temperatura , Termodinâmica
9.
Spectrochim Acta A Mol Biomol Spectrosc ; 65(5): 1227-33, 2006 Dec.
Artigo em Inglês | MEDLINE | ID: mdl-16815088

RESUMO

Apjohnite, a naturally occurring Mn-bearing pseudo-alum from Terlano, Bolzano, Italy, has been characterized by EPR, optical, IR and Raman spectroscopy. The optical spectrum exhibits a number of electronic bands around 400 nm due to Mn(II) ion in apjohnite. From EPR studies, the parameters derived, g=2.0 and A=8.82 mT, confirm MnO(H(2)O)(5) distorted octahedra. The presence of iron impurity in the mineral is reflected by a broad band centered around 8400 cm(-1) in the NIR spectrum. A complex band profile appears strongly both in IR and Raman spectra with four component bands around 1100 cm(-1) due to the reduction of symmetry for sulphate ion in the mineral. A strong pair of IR bands at 1681 and 1619 cm(-1) with variable intensity is a proof for the presence of water in two states in the structure of apjohnite.


Assuntos
Compostos de Alúmen/química , Compostos de Manganês/química , Minerais/química , Sulfatos/química , Absorção , Espectroscopia de Ressonância de Spin Eletrônica , Espectrofotometria Infravermelho , Espectroscopia de Luz Próxima ao Infravermelho
10.
Spectrochim Acta A Mol Biomol Spectrosc ; 64(2): 448-53, 2006 May 15.
Artigo em Inglês | MEDLINE | ID: mdl-16434228

RESUMO

Raman spectroscopy has been used to investigate raw cotton acetylation using acetic anhydride/4-dimethylaminopyridine (DMAP) catalyst blend without solvent. The Raman data further confirm successful acetylation as shown by FTIR that was demonstrated previously to be highly sensitive for determining the level of acetylation. However, the Raman peaks are much weaker than the FTIR bands. Nevertheless, the variations of the extent of acetylation estimated from both Raman and FTIR spectra with weight percent gain due to acetylation (WPG) were observed to follow the same pattern. The degrees of acetylation calculated from Raman data were also found to increase linearly with that calculated from the more sensitive FTIR technique. Raman technique is thus suitable for further development as an analytical tool for determining the acetylation level of natural cellulose fibres. Raman data have also shown that the acetylation reaction reduces the crystallinity of cotton.


Assuntos
Fibra de Algodão , Análise Espectral Raman , Acetilação , Celulose/química , Espectroscopia de Infravermelho com Transformada de Fourier , Vibração
11.
Nature ; 438(7069): 779-84, 2005 Dec 08.
Artigo em Inglês | MEDLINE | ID: mdl-16319830

RESUMO

Saturn's largest moon, Titan, remains an enigma, explored only by remote sensing from Earth, and by the Voyager and Cassini spacecraft. The most puzzling aspects include the origin of the molecular nitrogen and methane in its atmosphere, and the mechanism(s) by which methane is maintained in the face of rapid destruction by photolysis. The Huygens probe, launched from the Cassini spacecraft, has made the first direct observations of the satellite's surface and lower atmosphere. Here we report direct atmospheric measurements from the Gas Chromatograph Mass Spectrometer (GCMS), including altitude profiles of the constituents, isotopic ratios and trace species (including organic compounds). The primary constituents were confirmed to be nitrogen and methane. Noble gases other than argon were not detected. The argon includes primordial 36Ar, and the radiogenic isotope 40Ar, providing an important constraint on the outgassing history of Titan. Trace organic species, including cyanogen and ethane, were found in surface measurements.


Assuntos
Atmosfera/química , Meio Ambiente Extraterreno/química , Cromatografia Gasosa-Espectrometria de Massas/instrumentação , Voo Espacial , Argônio/análise , Carbono/análise , Carbono/química , Isótopos/análise , Metano/análise , Metano/química , Nitrogênio/análise , Nitrogênio/química , Voo Espacial/instrumentação
12.
Spectrochim Acta A Mol Biomol Spectrosc ; 59(2): 321-8, 2003 Jan 15.
Artigo em Inglês | MEDLINE | ID: mdl-12685906

RESUMO

Infrared and Raman spectroscopy have been used to characterise synthetic hydrotalcites of formula Cu(x)Zn(6 - x)Al2(OH)16(CO3) x 4H2O. The spectra have been used to assess the molecular assembly of the cations in the hydrotalcite structure. The spectra may be conveniently subdivided into spectral features based (a) upon the carbonate anion (b) the hydroxyl units (c) water units. The Raman spectra of the hydroxyl-stretching region enable bands to be assigned to the CuOH, ZnOH and AlOH units. It is proposed that in the hydrotalcites with minimal cationic replacement that the cations are arranged in a regular array. For the Cu(x)Zn(6 - x)Al2(OH)16(CO3) x 4H2O hydrotalcites, spectroscopic evidence suggests that 'islands' of cations are formed in the structure. In a similar fashion, the bands assigned to the interlayer water suggest that the water molecules are also in a regular well-structured arrangement. Bands are assigned to the hydroxyl stretching vibrations of water. Three types of water are identified (a) water hydrogen bonded to the interlayer carbonate ion (b) water hydrogen bonded to the hydrotalcite hydroxyl surface and (c) interlamellar water. It is proposed that the water is highly structured in the hydrotalcite as it is hydrogen bonded to both the carbonate anion and the hydroxyl surface.


Assuntos
Hidróxido de Alumínio/química , Alumínio/análise , Cobre/análise , Hidróxido de Magnésio/química , Zinco/análise , Alumínio/química , Hidróxido de Alumínio/análise , Cobre/química , Hidrogênio , Hidróxido de Magnésio/análise , Espectrofotometria Infravermelho , Análise Espectral Raman , Água/análise , Água/química , Zinco/química
13.
Spectrochim Acta A Mol Biomol Spectrosc ; 59(6): 1195-204, 2003 Apr.
Artigo em Inglês | MEDLINE | ID: mdl-12659888

RESUMO

The Raman spectroscopy of selected minerals of the corrosion products has been measured including nantokite, eriochalcite, claringbullite, atacamite, paratacamite, clinoatacamite and brochantite and related minerals. The free energy of formation shows that each mineral is stable relative to copper metal. The mineral, which is formed in copper corrosion, depends on the kinetics and conditions of the reaction. Raman spectroscopy clearly identifies each mineral by its characteristic Raman spectrum. The Raman spectrum is related to the mineral structure and bands are assigned to CuCl stretching and bending modes and to SO stretching modes. Clinoatacamite is identified as the polymorph of atacamite and not paratacamite. Paratacamite is a separate mineral with a similar but different structure to that of atacamite.


Assuntos
Cobre/química , Análise Espectral Raman/métodos , Cloretos/química , Corrosão , Cinética , Minerais/química
14.
Spectrochim Acta A Mol Biomol Spectrosc ; 58(13): 2849-59, 2002 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-12477029

RESUMO

The modification of kaolinite surfaces through mechanochemical treatment has been studied using a combination of mid-IR and near-IR spectroscopy. Kaolinite hydroxyls were lost after 10 h of grinding as evidenced by the 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 observed. The mechanochemical activation (dry grinding) causes destruction in the crystal structure of kaolinite by the rupture of the O-H, Al-OH, Al-O-Si and Si-O bonds. Evidence of this destruction may be followed using near-IR spectroscopy. Two intense bands are observed in the spectral region of the first overtone of the hydroxyl-stretching vibration at 7065 and 7163 cm(-1). These two bands decrease in intensity with mechanochemical treatment and two new bands are observed at 6842 and 6978 cm(-1) assigned to the first overtone of the hydroxyl-stretching band of water. Concomitantly the water combination bands observed at 5238 and 5161 cm(-1) increase in intensity with mechanochemical treatment. The destruction of the kaolinite surface may be also followed by the loss of intensity of the two hydroxyl combination bands at 4526 and 4623 cm(-1). Infrared spectroscopy shows that the kaolinite surface has been modified by the removal of the kaolinite hydroxyls and their replacement with water adsorbed on the kaolinite surface. NIR spectroscopy enables the determination of the optimum time for grinding of the kaolinite. Further NIR allows the possibility of continual on-line analysis of the mechanochemical treatment of kaolinite.


Assuntos
Caulim/química , Espectrofotometria Infravermelho , Hidróxidos/química , Estresse Mecânico
15.
Spectrochim Acta A Mol Biomol Spectrosc ; 58(5): 967-81, 2002 Mar 15.
Artigo em Inglês | MEDLINE | ID: mdl-11942403

RESUMO

Fourier transform infrared microscopy has been used to investigate in situ dehydroxylation of goethite to form hematite. The characterisation was based on the behaviour of hydroxyl units, which were observed in the hydroxyl stretching and hydroxyl deformation and water bending regions, and the Fe-O vibrations of the newly formed hematite during the thermal dehydroxylation process. Two hydroxyl stretching modes (v1 and v2), and three bending (V(bending-1, 2, 3)) and two deformation (V(deformation-1, 2)) modes were observed for goethite. The characteristic vibration at 916 cm(-1) was observed together with the residuals of the v1 and v2 bands in hematite spectrum. The structural transformation between goethite and hematite through thermal dehydroxylation was interpreted in order to provide criteria that can be used for the characterisation of thermally activated bauxite and their conversion to activated alumina phases.


Assuntos
Compostos Férricos/análise , Compostos de Ferro/análise , Espectrofotometria Infravermelho/métodos , Espectroscopia de Infravermelho com Transformada de Fourier/métodos , Óxido de Alumínio/análise , Fenômenos Biofísicos , Biofísica , Minerais , Modelos Químicos , Temperatura
16.
Artigo em Inglês | MEDLINE | ID: mdl-11905533

RESUMO

Dehydroxylation of goethite as affected by aluminium substitution was investigated using Fourier transform infrared spectroscopy (FT-IR) in conjunction with X-ray diffraction (XRD), thermogravimetric analysis (TGA) and differential thermogravimetric analysis (DTGA). The band intensities of hydroxyl vibrations were indicative of the degree of dehydroxylation and the changes in band parameters due to aluminium substitution were observed. The effect of aluminium substitution on band parameters of FT-IR spectra of goethite and its partially and fully dehydroxylated products, the mixture of goethite/hematite and hematite, were interpreted. The results of this study have confirmed that aluminium substituted goethite is thermally more stable than non-substituted goethite and is in harmony with the results of XRD and DTGA. A larger amount of non-stoichiometric hydroxyl units is associated with a higher aluminium substitution. A shift to a higher wavenumber of bending and hydroxyl stretching vibrations is attributed to the effects of aluminium substitution associated with non-stoichiometric hydroxyl units on the a-b plane relative to the b-c plane of goethite. The results provide information for the characterisation of activated bauxite containing hematite and goethite.


Assuntos
Compostos de Ferro/química , Espectrofotometria Infravermelho/métodos , Alumínio/química , Compostos Férricos/química , Gravitação , Minerais , Espectroscopia de Infravermelho com Transformada de Fourier , Temperatura , Difração de Raios X
17.
Spectrochim Acta A Mol Biomol Spectrosc ; 58(2): 265-72, 2002 Jan 15.
Artigo em Inglês | MEDLINE | ID: mdl-11808732

RESUMO

Far-infrared spectroscopy (FIR) has been used to distinguish alumina phases boehmite, diaspore, gibbsite and bayerite. The pellets of samples were prepared by mixing alumina phases with polyethylene at a ratio of 1:50, and the spectra were recorded between 50 and 400 cm(-1). The spectrum of boehmite resembles that of diaspore in the 300-400 cm(-1) region. Boehmite has two characteristic FIR bands at 366 and 323 cm(-1), while diaspore has five at 354, 331, 250, 199 and 158 cm(-1). The spectrum of gibbsite resembles that of bayerite in the 230-300 cm(-1) region. Gibbsite shows three characteristic FIR bands at 371, 279 and 246 cm(-1), whereas bayerite shows six at 383, 345, 326, 296, 252 and 62 cm(-1). The overlapping bands were resolved, and the spectra were manipulated appropriately using band analysis techniques. The FIR spectra are in harmony with the FT-Raman spectra. Far-infrared spectroscopy allows the study and differentiation of the stretching of AlO4 units to characterize these four alumina phases. Far-IR spectroscopy complements the mid-IR and near-IR for distinguishing alumina phases in bauxites.


Assuntos
Hidróxido de Alumínio/química , Óxido de Alumínio/química , Espectrofotometria Infravermelho
18.
Spectrochim Acta A Mol Biomol Spectrosc ; 57(3): 603-9, 2001 Mar 01.
Artigo em Inglês | MEDLINE | ID: mdl-11300571

RESUMO

Raman microscopy has been used to study low and high defect kaolinites and their potassium acetate intercalated complexes at 298 and 77 K. Raman spectroscopy shows significant differences in the spectra of the hydroxyl-stretching region of the two types of kaolinites, which is also reflected in the spectroscopy of the hydroxyl-stretching region of the intercalation complexes. Additional bands to the normally observed kaolinite hydroxyl stretching frequencies are observed for the low and high defect kaolinites at 3605 and 3602 cm(-1) at 298 K. Upon cooling to liquid nitrogen temperature, these bands are observed at 3607 and 3604 cm(-1), thus indicating a weakening of the hydrogen bond formed between the inner surface hydroxyls and the acetate ion. Upon cooling to liquid nitrogen temperature, the frequency of the inner hydroxyls shifted to lower frequencies. Collection of Raman spectra at liquid nitrogen temperature did not give better band separation compared to the room temperature spectra as the bands increased in width and shifted closer together.


Assuntos
Caulim/química , Acetato de Potássio/química , Análise Espectral Raman , Temperatura
19.
Artigo em Inglês | MEDLINE | ID: mdl-11209858

RESUMO

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.


Assuntos
Caulim/química , Cristalização , Modelos Moleculares , Conformação Molecular , Análise Espectral Raman , Termodinâmica
20.
Spectrochim Acta A Mol Biomol Spectrosc ; 57(13): 2575-86, 2001 Nov.
Artigo em Inglês | MEDLINE | ID: mdl-11765784

RESUMO

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.


Assuntos
Compostos Férricos/química , Compostos de Ferro/química , Cristalografia por Raios X , Compostos de Ferro/síntese química , Minerais , Espectroscopia de Infravermelho com Transformada de Fourier
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