Prediction of multilocus identity-by-descent

Previous studies have enabled exact prediction of probabilities of identity-by-descent (IBD) in randommating populations for a few loci (up to four or so), with extension to more using approximate regression methods. Here we present a precise predictor of multiple-locus IBD using simple formulas based on exact results for two loci. In particular, the probability of non-IBD X ABC at each of ordered loci A, B, and C can be well approximated by XABC = XABXBC/XB and generalizes to X123. . .k = X12X23. . .Xk-1,k/ Xk-2, where X is the probability of non-IBD at each locus. Predictions from this chain rule are very precise with population bottlenecks and migration, but are rather poorer in the presence of mutation. From these coefficients, the probabilities of multilocus IBD and non-IBD can also be computed for genomic regions as functions of population size, time, and map distances. An approximate but simple recurrence formula is also developed, which generally is less accurate than the chain rule but is more robust with mutation. Used together with the chain rule it leads to explicit equations for non-IBD in a region. The results can be applied to detection of quantitative trait loci (QTL) by computing the probability of IBD at candidate loci in terms of identity-by-state at neighboring markers.

A vibrational spectroscopic study of philipsbornite PbAl3(AsO4)2(OH)5⋅H2O-molecular structural implications and relationship to the crandallite subgroup arsenates

The presence of arsenic in the environment is a hazard. The accumulation of arsenate by a range of cations in the formation of minerals provides a mechanism for the remediation of arsenate contamination. The formation of the crandallite group of minerals provides a mechanism for arsenate accumulation. Among the crandallite minerals are philipsbornite, arsenocrandallite and arsenogoyazite. Raman spectroscopy complimented with infrared spectroscopy has enabled aspects of the structure of philipsbornite to be studied. The Raman spectrum of philipsbornite displays an intense band at around 840 cm−1 attributed to the overlap of the symmetric and antisymmetric stretching modes. Raman bands observed at 325, 336, 347, 357, 376 and 399 cm−1 are assigned to the ν2 (AsO4)3− symmetric bending vibration (E) and to the ν4 bending vibration (F2). The observation of multiple bending modes supports the concept of a reduction in symmetry of the arsenate anion in philipsbornite. Evidence for phosphate in the mineral is provided. By using an empirical formula, hydrogen bond distances for the OH units in philipsbornite of 2.8648 Å, 2.7864 Å, 2.6896 Å cm−1 and 2.6220 were calculated.

A vibrational spectroscopic study of the phosphate mineral zanazziite - Ca2(MgFe2+)(MgFe2+Al)4Be4(PO4)6⋅6(H2O)

Zanazziite is the magnesium member of a complex beryllium calcium phosphate mineral group named roscherite. The studied samples were collected from the Ponte do Piauí mine, located in Itinga, Minas Gerais. The mineral was studied by electron microprobe, Raman and infrared spectroscopy. The chemical formula can be expressed as Ca2.00(Mg3.15,Fe0.78,Mn0.16,Zn0.01,Al0.26,Ca0.14)Be4.00(PO4)6.09(OH)4.00⋅5.69(H2O) and shows an intermediate member of the zanazziite–greinfeinstenite series, with predominance of zanazziite member. The molecular structure of the mineral zanazziite has been determined using a combination of Raman and infrared spectroscopy. A very intense Raman band at 970 cm−1 is assigned to the phosphate symmetric stretching mode whilst the Raman bands at 1007, 1047, 1064 and 1096 cm−1 are attributed to the phosphate antisymmetric stretching mode. The infrared spectrum is broad and the antisymmetric stretching bands are prominent. Raman bands at 559, 568, 589 cm−1 are assigned to the ν4 out of plane bending modes of the PO4 and HPO4 units. The observation of multiple bands supports the concept that the symmetry of the phosphate unit in the zanazziite structure is reduced in symmetry. Raman bands at 3437 and 3447 cm−1 are attributed to the OH stretching vibrations; Raman bands at 3098 and 3256 are attributed to water stretching vibrations. The width and complexity of the infrared spectral profile in contrast to the well resolved Raman spectra, proves that the pegmatitic phosphates are better studied with Raman spectroscopy.

Vibrational spectroscopic study of the mineral penkvilksite Na2TiSi4O11·2H2O – a mineral used for the uptake of radionuclides

We have used vibrational spectroscopy to study the formula and molecular structure of the mineral penkvilksite Na 2TiSi 4O 11·2H 2O. Penkvilksite is a mineral which may be used in the uptake of radioactive elements. Both Raman and infrared spectroscopies identify a band at 3638 cm−1 attributed to an OH-stretching vibration of hydroxyl units. The inference is that OH units are involved in the structure of penkvilksite. The formula may be well written as Na 2TiSi 4O 10(OH)2·H 2O. The mineral is characterised by a very intense Raman band at 1085 cm−1 and a broad infrared band at 1080 cm−1 assigned to SiO-stretching vibrations. Raman bands at 620, 667 and 711 cm−1 are attributed to SiO and TiO chain bonds. Water-stretching vibrations are observed as Raman bands at 3197, 3265, 3425 and 3565 cm−1. Vibrational spectroscopy enables aspects of the molecular structure of the mineral penkvilksite to be ascertained. Penkvilksite is a mineral which can incorporate actinides and lanthanides from radioactive waste.

Effect of rehydration on structure and surface properties of thermally treated palygorskite

Palygorskite has a fibrous like morphology with a distinctive layered appearance. The simplified formula of palygorskite (Mg5Si8O20(OH)2(OH2)4 nH2O) indicates that two different types of water are present. The dehydration and rehydration of palygorskite have been studied using thermogravimetry and H2O-tem- perature programmed desorption. X-ray diffractograms, NH3 adsorption profiles, and NH3 desorption profiles were obtained for thermally treated palygorskite as a function of temperature. The results proved water molecules were mainly derived from Si–OH units. In addition, five kinds of acid sites were found for palygorskite. The number of acid sites of external surfaces was larger than that of the internal sur- faces. Bonding on the internal surface acid sites was stronger than the bonding of the external surfaces. Rehydration restored the folded structure of palygorskite when thermal treatment temperature was lower than 300 oC.

A vibrational spectroscopic study of the so-called ‘healing’ mineral papagoite CaCuAlSi2O6(OH)3

Papagoite is a silicate mineral named after an American Indian tribe and was used as a healing mineral. Papagoite CaCuAlSi2O6(OH)3 is a hydroxy mixed anion compound with both silicate and hydroxyl anions in the formula. The structural characterization of the mineral papagoite remains incomplete. Papagoite is a four-membered ring silicate with Cu2+ in square planar coordination. The intense sharp Raman band at 1053 cm−1 is assigned to the ν1 (A 1g) symmetric stretching vibration of the SiO4 units. The splitting of the ν3 vibrational mode offers support to the concept that the SiO4 tetrahedron in papagoite is strongly distorted. A very intense Raman band observed at 630 cm−1 with a shoulder at 644 cm−1 is assigned to the ν4 vibrational modes. Intense Raman bands at 419 and 460 cm−1 are attributed to the ν2 bending modes. Intense Raman bands at 3545 and 3573 cm−1 are assigned to the stretching vibrations of the OH units. Low-intensity Raman bands at 3368 and 3453 cm−1 are assigned to water stretching modes. It is suggested that the formula of papagoite is more likely to be CaCuAlSi2O6(OH)3 · xH2O. Hence, vibrational spectroscopy has been used to characterize the molecular structure of papagoite.

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.

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 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.

SEM-EDX, Raman and infrared spectroscopic characterization of the phosphate mineral frondelite (Mn2+)(Fe3+)4(PO4)3(OH)5

We have analyzed a frondelite mineral sample from the Cigana mine, located in the municipality of Conselheiro Pena, a well-known pegmatite in Brazil. In the Cigana pegmatite, secondary phosphates, namely eosphorite, fairfieldite, fluorapatite, frondelite, gormanite, hureaulite, lithiophilite, reddingite and vivianite are common minerals in miarolitic cavities and in massive blocks after triphylite. The chemical formula was determined as (Mn0.68, Fe0.32)(Fe3+)3,72(PO4)3.17(OH)4.99. The structure of the mineral was assessed using vibrational spectroscopy. Bands attributed to the stretching and bending modes of PO4 3- and HOPO3 3- units were identified. The observation of multiple bands supports the concept of symmetry reduction of the phosphate anion in the frondelite structure. Sharp Raman and infrared bands at 3581 cm−1 is assigned to the OH stretching vibration. Broad Raman bands at 3063, 3529 and 3365 cm−1 are attributed to water stretching vibrational modes.

Stichtite : a review

Stichtite is a naturally occurring layered double hydroxide (LDH) with the ideal chemical formula Mg6Cr2CO3(OH)16·4H2O. It has received less attention in the literature than other LDHs and is often described as a rare mineral; however, abundant deposits of the mineral do exist. In this article we aim to review a number of significant publications concerning the mineral stichtite, including papers covering the discovery, geological origin, synthesis and characterizsation of stichtite. Characterization techniques reviewed include powder X-ray diffraction (XRD), infrared spectroscopy (IR), near infrared spectroscopy (NIR), Raman spectroscopy (Raman), thermogravimetry (TG) and electron microprobe analysis.

Infrared and Raman spectroscopic characterisation of the sulphate mineral creedite – Ca3Al2SO4(F,OH)·2H2O – and in comparison with the alums

The mineral creedite is a fluorinated hydroxy hydrated sulphate of aluminium and calcium of formula Ca3Al2SO4(F,OH)·2H2O. The mineral has been studied by a combination of electron probe analysis to determine the molecular formula of the mineral and the structure assessed by vibrational spectroscopy. The spectroscopy of creedite may be compared with that of the alums. The Raman spectrum of creedite is characterised by an intense sharp band at 986 cm−1 assigned to the View the MathML source ν1 (Ag) symmetric stretching mode. Multiple bands of creedite in the antisymmetric stretching region support the concept of a reduction in symmetry of the sulphate anion. Multiple bands are also observed in the bending region with the three bands at 601, 629 and 663 cm−1 assigned to the View the MathML source ν4 (Ag) bending modes. The observation of multiple bands at 440, 457 and 483 cm−1 attributed to the View the MathML source ν2 (Bg) bending modes supports the concept that the symmetry of the sulphate is reduced by coordination to the water bonded to the Al3+ in the creedite structure. The splitting of the ν2, ν3 and ν4 modes is attributed to the reduction of symmetry of the SO4 and it is proposed that the sulphate coordinates to water in the hydrated aluminium in bidentate chelation.

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.

The molecular structure of the phosphate mineral chalcosiderite – a vibrational spectroscopic study

The mineral chalcosiderite with formula CuFe6(PO4)4(OH)8⋅4H2O has been studied by Raman spectroscopy and by infrared spectroscopy. A comparison of the chalcosiderite spectra is made with the spectra of turquoise. The spectra of the mineral samples are very similar in the 1200–900 cm−1 region but strong differences are observed in the 900–100 cm−1 region. The effect of substitution of Fe for Al in chalcosiderite shifts the bands to lower wave numbers. Factor group analysis (FGA) implies four OH stretching vibrations for both the water and hydroxyl units. Two bands ascribed to water are observed at 3276 and 3072 cm−1. Three hydroxyl stretching vibrations are observed. Calculations using a Libowitzky type formula show that the hydrogen bond distances of the water molecules are 2.745 and 2.812 Å which are considerably shorter than the values for the hydroxyl units 2.896, 2.917 and 2.978 Å. Two phosphate stretching vibrations at 1042 and 1062 cm−1 in line with the two independent phosphate units in the structure of chalcosiderite. Three bands are observed at 1102, 1159 and 1194 cm−1 assigned to the phosphate antisymmetric stretching vibrations. FGA predicts six bands but only three are observed due to accidental degeneracy. Both the ν2 and ν4 bending regions are complex. Four Raman bands observed at 536, 580, 598 and 636 cm−1 are assigned to the ν4 bending modes. Raman bands at 415, 420, 475 and 484 cm−1are assigned to the phosphate ν2 bending modes. Vibrational spectroscopy enables aspects of the molecular structure of chalcosiderite to be assessed.

Calculation of dose kernels for radiotherapy applications using the GEANT 4 Monte Carlo toolkit

Dose kernels may be used to calculate dose distributions in radiotherapy (as described by Ahnesjo et al., 1999). Their calculation requires use of Monte Carlo methods, usually by forcing interactions to occur at a point. The Geant4 Monte Carlo toolkit provides a capability to force interactions to occur in a particular volume. We have modified this capability and created a Geant4 application to calculate dose kernels in cartesian, cylindrical, and spherical scoring systems. The simulation considers monoenergetic photons incident at the origin of a 3 m x 3 x 9 3 m water volume. Photons interact via compton, photo-electric, pair production, and rayleigh scattering. By default, Geant4 models photon interactions by sampling a physical interaction length (PIL) for each process. The process returning the smallest PIL is then considered to occur. In order to force the interaction to occur within a given length, L_FIL, we scale each PIL according to the formula: PIL_forced = L_FIL 9 (1 - exp(-PIL/PILo)) where PILo is a constant. This ensures that the process occurs within L_FIL, whilst correctly modelling the relative probability of each process. Dose kernels were produced for an incident photon energy of 0.1, 1.0, and 10.0 MeV. In order to benchmark the code, dose kernels were also calculated using the EGSnrc Edknrc user code. Identical scoring systems were used; namely, the collapsed cone approach of the Edknrc code. Relative dose difference images were then produced. Preliminary results demonstrate the ability of the Geant4 application to reproduce the shape of the dose kernels; median relative dose differences of 12.6, 5.75, and 12.6 % were found for an incident photon energy of 0.1, 1.0, and 10.0 MeV respectively.