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# Formula unit

About: Formula unit is a(n) research topic. Over the lifetime, 1331 publication(s) have been published within this topic receiving 29304 citation(s).

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TL;DR: In this article, a simple general equation is presented for estimating the Fe 3 § concentrations in ferromagnesian oxide and silicate minerals from microprobe analyses, assuming that iron is the only element present with variable valency.

Abstract: A simple general equation is presented for estimating the Fe 3 § concentrations in ferromagnesian oxide and silicate minerals from microprobe analyses. The equation has been derived using stoichiometric criteria assuming that iron is the only element present with variable valency and that oxygen is the only anion. In general, the number of Fe 3 + ions per X oxygens in the mineral formula, F, is given by; F = 2X(1 - T/S) where T is the ideal number of cations per formula unit, and S is the observed cation total per X oxygens calculated assuming all iron to be Fe 2 § Minerals for which this equation is appropriate include pyralspite and ugrandite garnet, aluminate spinel, magnetite, pyroxene, sapphirine and ilmenite. The equation cannot be used for minerals with cation vacancies (e.g. micas, maghemite) unless, as in the case of amphiboles, the number of ions of a subset of elements in the formula can be fixed. Variants of the above equation are presented for some of the numerous published schemes for the recalculation of amphibole formulae. The equation is also inappropriate for minerals showing SP += 4H § substitution (e.g. staurolite, hydrogarnet), minerals containing an unknown proportion of an unanalysed element other than oxygen (e.g. boron-bearing kornerupine) and minerals containing two or more elements with variable valency.

1,556 citations

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TL;DR: In this paper, a multi-component Rietveld analysis of the powder diffraction pattern with the mass and volume of the unit cell is proposed to determine the weight of a phase in a mixture.

Abstract: The weight of a phase in a mixture is proportional to the product of the scale factor, as derived in a multi-component Rietveld analysis of the powder diffraction pattern, with the mass and volume of the unit cell. If all phases are identified and crystalline, the weight fraction W of phase p is given by W_{p} = S_{p}(ZMV)_{p}/\sum_{i}S_{i}(ZMV)_{i},where S, Z, M and V are, respectively, the Rietveld scale factor, the number of formula units per unit cell, the mass of the formula unit and the unit-cell volume. This is the basis of a method providing accurate phase analyses without the need for standards or for laborious experimental calibration procedures. The method is demonstrated by measurements on binary mixtures of rutile, corundum, silicon and quartz.

1,040 citations

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TL;DR: In this paper, the R2Ni17 and R2Fe17C intermetallic compounds were found to absorb approximately two atoms of nitrogen per formula unit on heating in ammonia or nitrogen.

Abstract: The R2Fe17 and R2Fe17C intermetallic compounds are found to absorb approximately two atoms of nitrogen per formula unit on heating in ammonia or nitrogen. The interstitial nitrides retain the original Th2Ni17 or Th2Zn17 structures, but with a large increase in unit cell volume (≈ = 7%). Curie temperatures of 420 °C are found when R = Y and 470 °C when R = Sm. There are also substantial increases in magnetisation and anisotropy field (when R = Sm). These new interstitia nitrides have excellent intrinsic magnetic properties for permanent magnet applications.

1,026 citations

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TL;DR: In this article, the reaction of M(II) acetate hydrate (M = Co, Ni, and Zn) with 1,3,5-benzenetricarboxylic acid yields a material formulated as M3(BTC)2·12H2O.

Abstract: The reaction of M(II) acetate hydrate (M = Co, Ni, and Zn) with 1,3,5-benzenetricarboxylic (BTC) acid yields a material formulated as M3(BTC)2·12H2O. These compounds are isostructural as revealed by their XRPD patterns and a single crystal structure analysis performed on the cobalt containing solid [monoclinic, space group C2, a = 17.482 (6) A, b = 12.963 (5) A, c = 6.559 (2) A, β = 112.04°, V = 1377.8 (8) A, Z = 4]. This solid is composed of zigzag chains of tetra-aqua cobalt(II) benzenetricarboxylate that are hydrogen-bonded to yield a tightly held 3-D network. Upon liberating 11 water ligands per formula unit a porous solid results, M3(BTC)2·H2O, which was found to reversibly and repeatedly bind water without destruction of the framework. The proposed 1-D channels of the monohydrate have a pore diameter of 4 × 5 A, which is typical of those observed in zeolites and molecular sieves. The successful inclusion of ammonia into the porous solid was demonstrated. Larger molecules and others without a reactiv...

708 citations

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TL;DR: In this paper, Na2Ti3O7 is found to reversibly uptake 2 Na ions per formula unit (200 mA h/g) at an average potential of 0.3 V and is hence a very promising negative electrode material for building sodium ion bat...

Abstract: Na2Ti3O7 is found to reversibly uptake 2 Na ions per formula unit (200 mA h/g) at an average potential of 0.3 V and is hence a very promising negative electrode material for building sodium ion bat...

655 citations