Absolute quantification by powder X-ray diffraction of complex mixtures of crystalline and amorphous phases for applications in the Earth sciences
-
Denis G. Rancourt
and
Mei-Zhen Dang
Abstract
Many natural surface-environment samples, such as soils and marine and lacustrine sediments, are complex mixtures involving several mineral phases (both petrogenic and authigenic), several amorphous and nanoparticulate inorganic phases (usually authigenic or pedogenic), and a heterogeneous amorphous component of “organic matter” (OM). The main inorganic amorphous and crystalline components are often operationally separated and quantified by various selective or sequential chemical extraction methods that are subject to various artifacts and that can be significantly affected by the presence of OM. Here we develop a general method of absolute quantification based on powder X-ray diffraction (pXRD) measurements that are obtained using standard θ-θ or θ-2θ type diffractometers. The method does not require calibration or the use of standards and does not require instrument parameter determinations but relies instead on exact normalization conditions that we prove. In particular, we develop a .general integrated intensity formula. (GIIF) for X-ray diffraction. All relevant sampleradiation interaction phenomena are considered, including polarization, mass absorption, Compton scattering, and resonance absorption re-emission. We show that the mole fraction of any given phase (crystalline, amorphous, quasicrystalline, or nanophase) is exactly given by the collection sphere integrated intensity of the resolved phase-specific contribution to the Compton corrected and electron unit normalized diffraction pattern, T(θ), divided by the wavevector (q) integrated average squared atomic form factor of the phase. Electron unit calibration is achieved by a global normalization that directly gives the product A⊥Io of the effective cross sectional area (A⊥) of the incident (and outgoing) beam and the effective incident beam intensity (Io), including counter efficiency, beam path losses, etc. The problem of incomplete collection sphere integration (including the q = 0 region) is resolved by showing that all the results hold for a given Bragg angle range of measurement for a sufficiently large range. We evaluate the accuracy of the method by application to synthetic binary amorphous-crystalline mixtures of (1) a rock standard, that provides an assembly of crystalline phases, (2) a certified OM standard, and (3) a synthetic inorganic amorphous phase (silica gel). We expect that the method will be particularly useful in surface sediment and environmental geochemistry applications.
© 2015 by Walter de Gruyter Berlin/Boston
Articles in the same Issue
- Presidential Address To The Mineralogical Society Of Amrica, Boston, November 6, 2001: Some Precambrian Banded Iron-Formations (BiIFs) From Around The World: Their Age, Geologic Setting, Mineralogy, Metamorphism, Geochemistry, And Origin
- Effects of high pressure and high temperature on cation ordering in magnesioferrite, MgFe2O4, using in situ synchrotron X-ray powder diffraction up to 1430 K and 6 GPa
- Raman spectroscopy and vibrational analyses of albite: From 25 °C through the melting temperature
- A new occurrence of xitieshanite [Fe3+(SO4)Cl⋅6H2O] crystals in acid-mine seepways, Green Valley, Vigo County, Indiana, U.S.A.
- Effect of A-site cation radius on ordering of BX6 octahedra in (K,Na)MgF3 perovskite
- Crystal chemistry of NaMgF3 perovskite at high pressure and temperature
- Hyperfine electric field gradient tensors at Fe2+ sites in octahedral layers: Toward understanding oriented single-crystal Mössbauer spectroscopy measurements of micas
- Does the bazhenovite structure really contain a thiosulfate group? A structural and spectroscopic study of a sample from the type locality
- Light-induced degradation dynamics in realgar: in situ structural investigation using single-crystal X-ray diffraction study and X-ray photoelectron spectroscopy
- Absolute quantification by powder X-ray diffraction of complex mixtures of crystalline and amorphous phases for applications in the Earth sciences
- Detrital illite crystals identified from crystallite thickness measurements in siliciclastic sediments
- High-temperature density of lanthanide-bearing Na-silicate melts: Partial molar volumes for Ce2O3, Pr2O3, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb2O3, Dy2O3, Ho2O3, Er2O3, Tm2O3, and Yb2O3
- Coupled dichotomies of apatite and fluid composition during contact metamorphism of siliceous carbonate rocks
- The effect of zoned garnet on metapelite pseudosection topology and calculated metamorphic P-T paths
- Low-pressure and low-temperature K-bearing kosmochloric diopside from the Osayama serpentinite mélange, SW Japan
- Dehydration of natural stilbite: An in situ FTIR study
- Structural changes accompanying the phase transformation between leadhillite and susannite: A structural study by means of in situ high-temperature single-crystal X-ray diffraction
- Optic properties of centimeter-sized crystals determined in air with the spindle stage using EXCALIBRW
- Zoltaiite, a new barium-vanadium nesosubsilicate mineral from British Columbia: Description and crystal structure
- Mn-tourmaline from island of Elba (Italy): Crystal chemistry
- Letter: An infrared study of carbon-oxygen bonding in magnesite to 60 GPa
- Letter: Metals in quartz-hosted melt inclusions: Natural facts and experimental artifacts
- Letter: A high-pressure phase transition of calcite-III
- Letter: Experimental observation of an interface-controlled pseudomorphic replacement reaction in a natural crystalline pyrochlore
- Letter: A natural scandian garnet
Articles in the same Issue
- Presidential Address To The Mineralogical Society Of Amrica, Boston, November 6, 2001: Some Precambrian Banded Iron-Formations (BiIFs) From Around The World: Their Age, Geologic Setting, Mineralogy, Metamorphism, Geochemistry, And Origin
- Effects of high pressure and high temperature on cation ordering in magnesioferrite, MgFe2O4, using in situ synchrotron X-ray powder diffraction up to 1430 K and 6 GPa
- Raman spectroscopy and vibrational analyses of albite: From 25 °C through the melting temperature
- A new occurrence of xitieshanite [Fe3+(SO4)Cl⋅6H2O] crystals in acid-mine seepways, Green Valley, Vigo County, Indiana, U.S.A.
- Effect of A-site cation radius on ordering of BX6 octahedra in (K,Na)MgF3 perovskite
- Crystal chemistry of NaMgF3 perovskite at high pressure and temperature
- Hyperfine electric field gradient tensors at Fe2+ sites in octahedral layers: Toward understanding oriented single-crystal Mössbauer spectroscopy measurements of micas
- Does the bazhenovite structure really contain a thiosulfate group? A structural and spectroscopic study of a sample from the type locality
- Light-induced degradation dynamics in realgar: in situ structural investigation using single-crystal X-ray diffraction study and X-ray photoelectron spectroscopy
- Absolute quantification by powder X-ray diffraction of complex mixtures of crystalline and amorphous phases for applications in the Earth sciences
- Detrital illite crystals identified from crystallite thickness measurements in siliciclastic sediments
- High-temperature density of lanthanide-bearing Na-silicate melts: Partial molar volumes for Ce2O3, Pr2O3, Nd2O3, Sm2O3, Eu2O3, Gd2O3, Tb2O3, Dy2O3, Ho2O3, Er2O3, Tm2O3, and Yb2O3
- Coupled dichotomies of apatite and fluid composition during contact metamorphism of siliceous carbonate rocks
- The effect of zoned garnet on metapelite pseudosection topology and calculated metamorphic P-T paths
- Low-pressure and low-temperature K-bearing kosmochloric diopside from the Osayama serpentinite mélange, SW Japan
- Dehydration of natural stilbite: An in situ FTIR study
- Structural changes accompanying the phase transformation between leadhillite and susannite: A structural study by means of in situ high-temperature single-crystal X-ray diffraction
- Optic properties of centimeter-sized crystals determined in air with the spindle stage using EXCALIBRW
- Zoltaiite, a new barium-vanadium nesosubsilicate mineral from British Columbia: Description and crystal structure
- Mn-tourmaline from island of Elba (Italy): Crystal chemistry
- Letter: An infrared study of carbon-oxygen bonding in magnesite to 60 GPa
- Letter: Metals in quartz-hosted melt inclusions: Natural facts and experimental artifacts
- Letter: A high-pressure phase transition of calcite-III
- Letter: Experimental observation of an interface-controlled pseudomorphic replacement reaction in a natural crystalline pyrochlore
- Letter: A natural scandian garnet
