Influence of Octahedral Site Chemistry on the Elastic Properties of Biotite

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Highlights

Inﬂuence of Octahedral Site Chemistry on the Elastic Properties of Biotite

Dillon F. Hanlon, G. Todd Andrews, Roger A. Mason

•Elastic properties of natural biotite crystals are functions of octahedral site

chemistry.

•Elastic stability of biotite shows dramatic decrease with increasing iron con-

tent.

•Elastic properties and elastic stability of a biotite can be estimated if iron

content is known.

arXiv:2210.10915v1 [cond-mat.mtrl-sci] 19 Oct 2022

Inﬂuence of Octahedral Site Chemistry on the Elastic

Properties of Biotite

Dillon F. Hanlona, G. Todd Andrewsa, Roger A. Masonb

aDepartment of Physics and Physical Oceanography, Memorial University, St. John’s, NL,

Canada, A1B 3X7

bDepartment of Earth Sciences, Memorial University, St. John’s, NL, Canada, A1B 3X5

Abstract

Brillouin light scattering spectroscopy was used along with detailed composition

information obtained from electron probe microanalysis to study the inﬂuence of

octahedral site chemistry on the elastic properties of natural biotite crystals. Elas-

tic wave velocities for a range of directions in the ac and bc crystallographic planes

were obtained for each crystal by application of the well-known Brillouin equa-

tion with refractive indices and phonon frequencies obtained from the Becke line

test and spectral peak positions, respectively. In general, these velocities increase

with decreasing iron content, approaching those of muscovite at low iron concen-

trations. Twelve of thirteen elastic constants for the full monoclinic symmetry

were obtained for each crystal by ﬁtting analytic expressions for the velocities as

functions of propagation direction and elastic constants to corresponding exper-

imental data, while the remaining constant was estimated under the approxima-

tion of hexagonal symmetry. Elastic constants C11,C22, and C66 are comparable

to those of muscovite and show little change with iron concentration due to the

strong bonding within layers. In contrast, nearly all of the remaining constants

show a pronounced dependence on iron content, a probable consequence of the

weak interlayer bonding. Similar behaviour is displayed by the elastic stability,

which exhibits a dramatic decrease with increasing iron content, and by the elas-

tic anisotropy within the basal cleavage plane, which decreases as the amount of

iron in the crystal is reduced. This systematic dependence on iron content of all

measured elastic properties indicates that the elasticity of biotite is a function of

octahedral site chemistry and provides a means to estimate the elastic constants

and relative elastic stability of most natural biotite compositions if the iron or,

equivalently, magnesium, concentration is known. Moreover, the good agreement

between the elastic constants of Fe-poor (Mg-rich) biotite and those of phlogopite

Preprint submitted to Elsevier October 21, 2022

obtained from ﬁrst-principles calculation based on density functional theory indi-

cates that the latter approach may be of use in predicting the elastic properties of

biotites.

Keywords: Biotite, Elastic Properties, Octahedral Site Chemistry, Brillouin light

scattering, Electron Probe Microanalysis

1. Introduction

Micas are common rock-forming phyllosilicate minerals displaying mono-

clinic symmetry and comprising approximately 5-12% of the continental crust

[1]. The perfect {001}cleavage and platy habit of the mica group lead to preferred

orientation of their grains. In sedimentary rocks preferred orientation arises as

a depositional or diagenetic feature. In shales, composed predominantly of clay

minerals, which are closely related in structure to micas, such preferred orienta-

tion leads to their ﬁssility. In metamorphic rocks preferred orientation of micas

(and other minerals) is a response to crystallisation (or recrystallisation) in a stress

ﬁeld, causing the development of a foliation (or schistosity) perpendicular to the

direction of the primary stress. At the highest temperatures of metamorphism, and

in the presence of an anisotropic stress ﬁeld, compositional segregation, combined

with foliation, may lead to the development of very strongly layered gneisses

(gneissosity).

The presence of ﬁssility, foliation, or gneissosity causes anisotropy in the ve-

locity of seismic waves through the Earth. This was recognised in the nineteenth

century and with the development of improved instrumentation and processing

techniques has become a tool that is used both in exploration geophysics and deep

Earth studies [2, 3, 4].

The anisotropy of rocks can provide information on rock microstructure and

crystal anisotropy bears on eﬀorts to use inclusions of one mineral in another to

obtain measures of pressure at the time of inclusion [5]. Complete and accurate

characterization of the elastic properties of rocks and the minerals that compose

them is therefore important to understanding the composition and structure of the

Earth. On a microscopic scale, knowledge of the elasticity of sheet silicates like

micas provides insight into the nature of bonding and acoustic wave behaviour

in layered materials. Moreover, the use of micas in applications such as ﬂexible

electronic devices also requires that the elastic properties be known [6, 7].

1.1. The Micas

The silicates are, volumetrically, the most important mineral group in the

Earth’s crust. Their structures are based on tetrahedra, i.e. sites in which each

central cation (commonly Si or Al) is coordinated by four oxygen atoms arrayed

at the apices of a tetrahedron. Sharing of the apical oxygens between adjacent

tetrahedra, together with substitution or larger cations on sites that arise between

tetrahedra give rise to a wide variety of silicate structures and symmetries.

A key determinant of structure type is the number of oxygens per tetrahe-

dron that are shared with adjacent tetrahedra. In the sheet silicates three of the

four oxygen atoms of each tetrahedral site are shared, giving rise to the (Si, Al)-O

tetrahedral sheet as the common structural characteristic of these minerals. Within

the sheet silicates the micas form a large and important group. Their distinguish-

ing feature is a structure based on a double sheet of tetrahedra between which

is sandwiched a layer of octahedral sites (coordination number six, see Fig. 1)

in which four of the six apices of each octahedron are coordinated to the oxy-

gens of the tetrahedra and two to sites that can be occupied by hydroxyl, ﬂuorine

or chlorine. There are two tetrahedral sheets per octahedral sheet and the com-

bined tetrahedral-octahedral-tetrahedral layer is often called a TOT sheet. The

TOT sheets carry a net negative charge that is compensated by large cations (K,

Na, etc.) lying between them. Various stacking sequences of the TOT sheets are

possible but the most common gives rise to monoclinic symmetry. Figure 1 was

created using VESTA [8] software along with data publicly available through the

American Mineralogist database [9] for biotite [10] and muscovite [11].

1.2. Biotite and Muscovite

Biotite (K2(Mg,Fe)6[Si6Al2O20](OH,F,Cl)4) is trioctahedral with three octahe-

dral sites per formula unit (six in the conventional unit cell, which we use here)

completely or almost completely ﬁlled (see left panel of Fig. 1). Muscovite

(K2Al4[Si6Al2O20](OH,F,Cl)4) is dioctahedral, meaning that one of every three

octahedra is vacant (see right panel of Fig. 1). In biotite, substitution of trivalent

(Fe3+, Al3+) or quadrivalent (Ti4+) cations on octahedral sites can be compensated

by either octahedral vacancies or by replacement of Si by Al on tetrahedral sites

beyond the ideal one out of four and there can be extensive solid solution towards

siderophyllite (an end member with Fe and Al mixing on octahedral sites). Simi-

larly, in muscovite altervalent substitution on the octahedral sites can be compen-

sated by changing the composition of the tetrahedra, although such substitutions

are less common than in biotite. The chemical diversity of the micas accounts for

Figure 1: Crystal structures of biotite and muscovite. a) Biotite structure [10] with two T=Si, Al

tetrahedral layer shown with light grey spheres which sandwich an octahedral layer. Mg (or Fe)

octahedral layer shown with medium grey spheres. Interlayer potassium cations shown with black

spheres. b) Muscovite structure [11] with interlayer cations shown with black spheres, tetrahedral

cations shown with light grey spheres, and octahedral cations shown with medium grey spheres.

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HighlightsInuenceofOctahedralSiteChemistryontheElasticPropertiesofBiotiteDillonF.Hanlon,G.ToddAndrews,RogerA.MasonˆElasticpropertiesofnaturalbiotitecrystalsarefunctionsofoctahedralsitechemistry.ˆElasticstabilityofbiotiteshowsdramaticdecreasewithincreasingironcon-tent.ˆElasticpropertiesandelasticsta...

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