On the Calculation of the Relative Amounts of Endmember Constituents For Garnet

2021 ◽  
Author(s):  
Frank C. Hawthorne
Keyword(s):  
Unique Solution ◽  
General Formula ◽  
Simultaneous Equations ◽  
Mineral Species ◽  
Chemical Formula ◽  
Sequence Dependent ◽  
Definition Of

ABSTRACT It is commonly accepted that the calculation of the proportions of endmember constituents in garnet is dependent on the particular sequence of calculating the amounts of the endmembers, and this belief has been used to justify avoiding the use of endmembers in the definition of a mineral species. Calculating the amounts of endmember constituents to represent a specific mineral formula involves the solution of a set of simultaneous equations, and hence the idea that the solution is dependent on the order in which the amounts of endmember constituent are determined conflicts with the meaning of the term “simultaneous equations”. Here I examine the data on which these conclusions are based and show that these sequence-dependent results arise because of the use of non-stoichiometric formulae that are not electroneutral. If a garnet formula is adjusted slightly such that it exactly fits the general formula of a garnet, [8]X3[6]Y2[4]Z3O12, and is electroneutral, the simultaneous equations relating its chemical formula to a set of endmember constituents have a single unique solution. Thus, the argument that has been used to justify avoiding the use of endmembers in the definition of a mineral species is specious.

scholarly journals Nomenclature of the magnetoplumbite group

2020 ◽  
Vol 84 (3) ◽  
pp. 376-380 ◽  
Author(s):  
Dan Holtstam ◽  
Ulf Hålenius
Keyword(s):  
Crystal Structure ◽  
General Formula ◽  
Classification Scheme ◽  
Hierarchical Level ◽  
Mineral Species ◽  
New Mineral ◽  
Definition Of ◽  
Strong Order

AbstractA nomenclature and classification scheme has been approved by IMA–CNMNC for the magnetoplumbite group, with the general formula A[B12]O19. The classification on the highest hierarchical level is decided by the dominant metal at the 12-coordinated A sites, at present leading to the magnetoplumbite (A = Pb), hawthorneite (A = Ba) and hibonite (A = Ca) subgroups. Two species remain ungrouped. Most cations, with valences from 2+ to 5+, show a strong order over the five crystallographic B sites present in the crystal structure, which forms the basis for the definition of different mineral species. A new mineral name, chihuahuaite, is introduced and replaces hibonite-(Fe).

Vittinkiite, MnMn4[Si5O15], a member of the rhodonite group with a long history: definition as a mineral species

2020 ◽  
pp. 1-12
Author(s):  
Nadezhda V. Shchipalkina ◽  
Igor V. Pekov ◽  
Nikita V. Chukanov ◽  
Natalia V. Zubkova ◽  
Dmitry I. Belakovskiy ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Mineral Species ◽  
Crystal Chemical ◽  
Chemical Formula ◽  
Crystal Chemical Formula ◽  
Triclinic Space Group ◽  
Group Mineral ◽  
Coordination Numbers ◽  
The Relationship ◽  
Mn Oxides

Abstract The rhodonite-group mineral with the idealised, end-member formula MnMn4[Si5O15] and the crystal chemical formula VIIM(5)MnVIM(1–3)Mn3VIIM(4)Mn[Si5O15] (Roman numerals indicate coordination numbers) is defined as a valid mineral species named vittinkiite after the type locality Vittinki (Vittinge) mines, Isokyrö, Western and Inner Finland Region, Finland. Vittinkiite is an isostructural analogue of rhodonite, ideally CaMn4[Si5O15], with Mn2+ > Ca at the M(5) site. Besides Vittinki, vitiinkiite was found in more than a dozen rhodonite deposits worldwide, however, it is significantly less common in comparison with rhodonite. The mineral typically forms pink to light pink massive, granular aggregates and is associated with quartz, rhodonite, tephroite, pyroxmangite and Mn oxides. Vittinkiite is optically biaxial (+), with α = 1.725(4), β = 1.733(4), γ = 1.745(5) and 2Vmeas = 75(10)° (589 nm). The chemical composition of the holotype (wt.%, electron microprobe) is: MgO 0.52, CaO, 0.93, MnO 51.82, FeO 1.26, ZnO 0.11, SiO2 46.48, total 101.12. The empirical formula calculated based on 15 O apfu is Mn4.71Ca0.11Fe0.11Mg0.08Zn0.01Si4.99O15. Vittinkiite is triclinic, space group P $\bar{1}$ , with a = 6.6980(3), b = 7.6203(3), c = 11.8473(5) Å, α = 105.663(3), β = 92.400(3), γ = 94.309(3)°, V = 579.38(7) Å3 and Z = 2. The crystal structure is solved on a single crystal to R1 = 3.85%. Polymorphism of MnSiO3 (rhodonite-, pyroxmangite-, garnet- and clinopyroxene-type manganese metasilicates) is discussed, as well as the relationship between vittinkiite and pyroxmangite, ideally Mn7[Si7O21], and the application of infrared spectroscopy for the identification of manganese pyroxenoids.

scholarly journals Realization of the Landau definitions of effective Hamiltonian and nonequilibrium free energy in microscopic theory

2020 ◽  
Vol 28 (2) ◽  
pp. 63-74
Author(s):  
A. I. Sokolovsky
Keyword(s):  
Free Energy ◽  
Phase Transitions ◽  
General Formula ◽  
Correlation Functions ◽  
Nonequilibrium Thermodynamic ◽  
Microscopic Theory ◽  
Effective Hamiltonian ◽  
Equilibrium Fluctuations ◽  
Thermodynamic Potentials ◽  
Definition Of

Equilibrium fluctuations of some set of parameters in the states described by the canonical Gibbs distribution are investigated. In the theory of phase transitions of the second kind, these parameters are components of the order parameter. The microscopic realization of the Landau definition of the effective Hamiltonian of the system for studying the equilibrium fluctuations of the specified system of parameters is discussed in the terms of the probability density of their values. A general formula for this function is obtained and it is expressed through the equilibrium correlation functions of these parameters. An expression for the effective Hamiltonian in terms of deviations of the parameters from their equilibrium values is obtained. The deviations are considered small for conducting the calculations. The possibility of calculating the exact free energy of the system using the found effective Hamiltonian is discussed. In the microscopic theory, the implementation of the Landau definition of nonequilibrium thermodynamic potentials introduced in his phenomenological theory of phase transitions of the second kind is investigated. Nonequilibrium states of a fluctuating system described with some sets of parameters are considered. A general formula for nonequilibrium free energy expressed through the correlation functions of these parameters is obtained as for the effective Hamiltonian above. Like the previous case, the free energy expression via parameter deviations from the equilibrium values is obtained and small deviations are considered for calculations. The idea of the identity of the effective Hamiltonian of the system and its nonequilibrium free energy is discussed in connection with the Boltzmann distribution. The Gaussian approximation of both developed formalisms is considered. A generalization of the constructed theory for the case of spatially inhomogeneous states and the study of long-wave fluctuations are developed.

A New Definition of Non-Active Power

2006 ◽  
Vol 7 (4) ◽  
Author(s):  
Harnaak Khalsa ◽  
Jingxin Zhang
Keyword(s):  
Energy Transfer ◽  
Unique Solution ◽  
Single Phase ◽  
Active Power ◽  
Instantaneous Power ◽  
Unique Definition ◽  
Phase Systems ◽  
Definition Of

There is no unique definition of non-active power for nonsinusoidal systems. A new definition of non-active power is proposed in this paper. This definition is based on energy transfer and provides a unique solution for non-active power of single-phase systems under both sinusoidal and non-sinusoidal conditions. An example is used to illustrate the use of this new definition. Energy transfer calculated using the new definition provides the same energy transfer determined from the non-sinusoidal non-active instantaneous power. This is consistent with the existing definition of active power that is also based on energy transfer.

Recommended nomenclature for zeolite minerals: report of the subcommittee on zeolites of the International Mineralogical Association, Commission on New Minerals and Mineral Names

1998 ◽  
Vol 62 (04) ◽  
pp. 533-571 ◽  
Author(s):  
Douglas S. Coombs ◽  
Alberto Alberti ◽  
Thomas Armbruster ◽  
Gilberto Artioli ◽  
Carmine Colella ◽  
...  
Keyword(s):  
Structure Type ◽  
Group Symmetry ◽  
Mineral Species ◽  
Separate Species ◽  
Tetrahedral Framework ◽  
International Mineralogical Association ◽  
Mineralogical Association ◽  
Working Definition ◽  
Definition Of ◽  
Compositional Series

Abstract This report embodies recommendations on zeolite nomenclature approved by the International Mineralogical Association Commission on New Minerals and Mineral Names. In a working definition of a zeolite mineral used for this review, interrupted tetrahedral framework structures are accepted where other zeolitic properties prevail, and complete substitution by elements other than Si and Al is allowed. Separate species are recognized in topologically distinctive compositional series in which different extra-framework cations are the most abundant in atomic proportions. To name these, the appropriate chemical symbol is attached by a hyphen to the series name as a suffix except for the names harmotome, pollucite and wairakite in the phillipsite and analcime series. Differences in spacegroup symmetry and in order—disorder relationships in zeolites having the same topologically distinctive framework do not in general provide adequate grounds for recognition of separate species. Zeolite species are not to be distinguished solely on Si : Al ratio except for heulandite (Si : Al < 4.0) and clinoptilolite (Si : Al ⩾ 4.0). Dehydration, partial hydration, and over-hydration are not sufficient grounds for the recognition of separate species of zeolites. Use of the term ‘ideal formula’ should be avoided in referring to a simplified or averaged formula of a zeolite. Newly recognized species in compositional series are as follows: brewsterite-Sr, -Ba; chabazite-Ca, - Na, -K; clinoptilolite-K, -Na, -Ca; dachiardite-Ca, -Na; erionite-Na, -K, -Ca; faujasite-Na, -Ca, -Mg; ferrierite-Mg, -K, -Na; gmelinite-Na, -Ca, -K; heulandite-Ca, -Na, -K, -Sr; levyne-Ca, -Na; paulingite-K, -Ca; phillipsite-Na, -Ca, -K; stilbite-Ca, -Na. Key references, type locality, origin of name, chemical data, IZA structure-type symbols, space-group symmetry, unit-cell dimensions, and comments on structure are listed for 13 compositional series, 82 accepted zeolite mineral species, and three of doubtful status. Herschelite, leonhardite, svetlozarite, and wellsite are discredited as mineral species names. Obsolete and discredited names are listed.

On the empirical adequacy of terminological concept theories

Terminology ◽  
1994 ◽  
Vol 1 (2) ◽  
pp. 253-275 ◽  
Author(s):  
Britta E. Zawada ◽  
Piet Swanepoel
Keyword(s):  
Social Sciences ◽  
Pure Sciences ◽  
Concept Analysis ◽  
Empirical Adequacy ◽  
Mineral Species ◽  
Classical Concept ◽  
The Social ◽  
Definition Of

The main purpose of this paper is to demonstrate that classical concept theories and hybrids thereof are empirically inadequate for the terminological analysis and description of concepts in a number of sciences. Examples of the classification and definition of minerals in the field of mineralogy are used to illustrate that the defining features of mineral species are typically the attributes of prototype categories; i.e., they are, amongst others, culturally, perceptually, and bodily based, idealized and essentially interactional and functional in nature. Furthermore, it is argued that classification in mineralogy is founded on an experientialist rather than an objectivist epistemology. These factors strengthen the argument for a prototype approach to concept analysis not only in the humanities and the social sciences but also in the so-called natural and pure sciences.

scholarly journals Ontology, archetypes and the definition of ‘mineral species’

2021 ◽  
Vol 85 (2) ◽  
pp. 125-131
Author(s):  
Frank C. Hawthorne ◽  
Stuart J. Mills ◽  
Frédéric Hatert ◽  
Mike S. Rumsey
Keyword(s):  
Chemical Composition ◽  
Specific Property ◽  
Intrinsic Property ◽  
Mineral Species ◽  
General Definition ◽  
Intrinsic Properties ◽  
Space Group ◽  
Bond Topology ◽  
Definition Of ◽  
End Members

AbstractOntology deals with questions concerning what things exist, and how such things may be associated according to similarities and differences and related within a hierarchy. Ontology provides a rigorous way to develop a general definition of a mineral species. Properties may be divided into two principal groups: an intrinsic property is characteristic of the object and is independent of anything else; an extrinsic property depends on the relation between the object and other things. A universal is an entity that is common to all objects in a set. Here the objects are mineral samples, each entity is a specific property of these minerals, and the set of objects is all mineral samples of that mineral species. The key intrinsic properties of a mineral species are its name, its end-member formula and Z (the number of formula units in the unit cell), its space group and the bond topology of the end-member structure. These are also universals as they are common to all mineral samples belonging to that mineral species. An archetype is a pure form which embodies the fundamental characteristics of an object. Thus the archetype of a mineral species embodies the above set of universals. Real mineral samples of this mineral species are imperfect copies of that archetype, with a range of chemical composition defined by the boundaries between end-member formulae of this and other end members of the same bond topology. The result is a formal definition of a mineral species: A specific mineral species is the set of imperfect copies of the corresponding archetype and is defined by the following set of universals: name, end-member formula and Z, space group, and bond topology of the end-member structure, with the range of chemical composition limited by the compositional boundaries between end members with the same bond topology.

Structural and chemical characterization of dienerite, Ni3As, and its revalidation as a mineral species

2021 ◽  
Vol 59 (6) ◽  
pp. 1887-1898
Author(s):  
Paola Bonazzi ◽  
Luca Bindi
Keyword(s):  
Experimental Data ◽  
Chemical Analysis ◽  
Chemical Characterization ◽  
Mineral Species ◽  
Valid Species ◽  
Chemical Formula ◽  
History Museum ◽  
Cubic Structure ◽  
University Of Florence

ABSTRACT Dienerite, ideally Ni3As, was discovered in 1919 near Radstadt (Salzburg, Austria) and its description and chemical characterization date back to the 1920s. The paucity of reliable experimental data, as well as the absence of any other documented occurrences of such a mineral in over 80 years, led to the supposition of a typographic error in the transcription of the original chemical analysis, suggesting the mineral might in fact be nickelskutterudite [(Ni,Co,Fe)As3]. As a consequence, the mineral was discredited and deleted in the post-2006 IMA list of valid mineral species. Nonetheless, several minerals having a metal/As ratio close to 3:1 and a description fitting that of dienerite were reported after its discreditation. Here we report the discovery of minute inclusions in a sample of josephinite from Josephine Creek (Oregon, USA) exhibiting high optical and electron reflectance. Structural and chemical investigations unequivocally showed that a mineral having cubic structure [a = 9.6206(9) Å, sp. gr. I3d; R1 = 0.0353] and ideal chemical formula Ni3As does exist, suggesting that dienerite could in fact be a valid species. The proposal to revalidate dienerite has been approved by the Commission on New Minerals, Nomenclature and Classification (IMA-Proposal 19-E). The neotype is deposited in the mineralogical collections of the Natural History Museum, University of Florence, Italy, under catalogue number 3364/I.

On transfinite diameters in $\mathbb{C}^{d}$ for generalized notions of degree

2021 ◽  
Vol 127 (2) ◽  
pp. 337-360
Author(s):  
Norman Levenberg ◽  
Franck Wielonsky
Keyword(s):  
Convex Body ◽  
Unit Ball ◽  
General Formula ◽  
Plurisubharmonic Function ◽  
Integral Formula ◽  
Compact Set ◽  
Transfinite Diameter ◽  
Robin Function ◽  
Euclidean Unit Ball ◽  
Definition Of

We give a general formula for the $C$-transfinite diameter $\delta_C(K)$ of a compact set $K\subset \mathbb{C}^2$ which is a product of univariate compacta where $C\subset (\mathbb{R}^+)^2$ is a convex body. Along the way we prove a Rumely type formula relating $\delta_C(K)$ and the $C$-Robin function $\rho_{V_{C,K}}$ of the $C$-extremal plurisubharmonic function $V_{C,K}$ for $C \subset (\mathbb{R}^+)^2$ a triangle $T_{a,b}$ with vertices $(0,0)$, $(b,0)$, $(0,a)$. Finally, we show how the definition of $\delta_C(K)$ can be extended to include many nonconvex bodies $C\subset \mathbb{R}^d$ for $d$-circled sets $K\subset \mathbb{C}^d$, and we prove an integral formula for $\delta_C(K)$ which we use to compute a formula for $\delta_C(\mathbb{B})$ where $\mathbb{B}$ is the Euclidean unit ball in $\mathbb{C}^2$.

scholarly journals Shkatulkalite, a Rare Mineral from the Lovozero Massif, Kola Peninsula: A Re-Investigation

Minerals ◽  
2018 ◽  
Vol 8 (7) ◽  
pp. 303 ◽  
Author(s):  
Andrey Zolotarev ◽  
Ekaterina Selivanova ◽  
Sergey Krivovichev ◽  
Yevgeny Savchenko ◽  
Taras Panikorovskii ◽  
...  
Keyword(s):  
Crystal Structure ◽  
Kola Peninsula ◽  
General Formula ◽  
Interlayer Space ◽  
Mineral Species ◽  
Lovozero Massif ◽  
Structural Relations ◽  
Alkaline Massif

The crystal structure of shkatulkalite has been solved from the crystal from the Lovozero alkaline massif, Kola Peninsula, Russia. The mineral is monoclinic, P2/m, a = 5.4638(19), b = 7.161(3), c = 15.573(6) Å, β = 95.750(9)°, V = 606.3(4) Å3, R1 = 0.080 for 1551 unique observed reflections. The crystal structure is based upon the HOH blocks consisting of one octahedral (O) sheet sandwiched between two heteropolyhedral (H) sheets. The blocks are parallel to the (001) plane and are separated from each other by the interlayer space occupied by Na1 atoms and H2O groups. The Na2, Na3, and Ti sites are located within the O sheet. The general formula of shkatulkalite can be written as Na5(Nb1−xTix)2(Ti1−yMn2+y)[Si2O7]2O2(OH)2·nH2O, where x + y = 0.5 and x ≈ y ≈ 0.25 for the sample studied. Shkatulkalite belongs to the seidozerite supergroup and is a member of the lamprophyllite group. The species most closely related to shkatulkalite are vuonnemite and epistolite. The close structural relations and the reported observations of pseudomorphs of shkatulkalite after vuonnemite suggest that, at least in some environments, shkatulkalite may form as a transformation mineral species.

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