lecture 6_crystal growth

8/13/2019 Lecture 6_crystal Growth

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Schedule

Date Topic Reading

9/26 Introduction to Earth Materials Ch. 1 [WB]; Ch. 1-3 [M]

9/28 Elements, minerals and cosmochemistry Ch. 2 pp. 12-22; [WB]

10/3 Atoms and crystals

ionic radii and Paulings rules Ch. 2; pp. 23-31 [WB]

10/5 Atoms and crystals

symmetry and crystal structure Ch. 3 pp. 32-44 [WB]

10/10 Crystal growth and habit Ch. 5 [WB]

10/12 Physical and mechanical properties of crystals

Ch. 8,11,13 [WB skim]

10/17 Identifying minerals (classification) Ch. 14 [WB]; Ch. 7 [M]

10/19 MIDTERM I

10/24 Minerals in hand specimen Ch. 15 [WB]

10/26 Mineral genesis Ch. 16 [WB]

10/31 Introduction to igneous systems Ch. 18 [WB]

11/6 Igneous rocks and minerals Ch. 19;35 [WB]

11/7 Introduction to sedimentary minerals Ch. 21-23 [WB]


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11/9 MIDTERM II

11/14 Sulfides and related minerals Ch. 24 [WB]

11/16 Metamorphic environments Ch. 26 [WB]

11/21 Practical mineralogy soil minerals & cement

Ch. 27, 32 [W] skim

11/23 THANKSGIVING

11/28 Practical mineralogy gemstones Ch. 30-31 [WB];

Ch. 9-10 [M]

11/30 MIDTERM III

12/9 PAPER DUE BY THE END OF EXAM WEEK

NOTE: Initials in brackets refer to the text book: WB is Wenk and BulakhMineralogy and

M is Murray Evidence from the Earth

Lecture 1

Earth Materials - Minerals and Rocks

Overview Details
http://darkwing.uoregon.edu/~cashman/GEO311/311pages/L1-Intro_pic.htmhttp://darkwing.uoregon.edu/~cashman/GEO311/311pages/L1-Intro_pic.htmhttp://darkwing.uoregon.edu/~cashman/GEO311/311pages/L1-Intro_pic.htmhttp://darkwing.uoregon.edu/~cashman/GEO311/311pages/L1-Intro_pic.htm


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Minerals: basic compounds of the solid earth. ~ 3000 known; these 3000 contain all of the

chemical elements of which the earth is made.

Rocks: physical mixtures of minerals. Most of the rocks that make up the earth are composed of

only ~ 50 of the known minerals

Why study? Minerals occur in nearly all inorganic materials of everyday life, and are thus important

economically, aesthetically and scientific terms.

Definition of a mineral:

A mineral is a naturally occurring, inorganic, homogeneous solid with a definite chemical

composition and an ordered atomic arrangement

The crystalline state of matter is the most fundamental property of minerals

Aspects of Earth Materials that we will cover this term:

- crystal chemistry - the chemical nature of minerals

- crystallography - the study of symmetry and the internal order of crystals

- mineral physics - the physical properties of minerals

- petrology the study of rocks and the minerals that form them

Lecture 1


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Earth Materials - Minerals and Rocks

Minerals: basic compounds of the solid earth. ~ 3000 known; these 3000 contain all of thechemical elements of which the earth is made.

Rocks: physical mixtures of minerals. Most of the rocks that make up the earth are composed of

only ~ 50 of the known minerals

Why study? Minerals occur in nearly all inorganic materials of everyday life, and are thus important

economically, aesthetically and scientific terms.

ECONOMIC Many minerals have economic value - early on were used for pigments, gemstones forornamentation, clay for bricks, iron for utensils. Not until the 19th century, however, were metals minedand extracted.

ore minerals - minerals from which valuable metallic elements can be extracted

industrial minerals - nonmetallic materials used manufacturing (EX: insulators, ceramics, glass,

cement, fertilizers, etc.)

gangue minerals - those minerals not considered useful but which must be mined anyway

Some minerals are now considered "strategic" - [ex. Al and Cr in WWII]

Synthetic minerals are now important in materials science (Ex. high-T superconductors)

AESTHETIC Gemstones have been important throughout the history of most cultures, and preciousmetals, prized for their aesthetic values, form the basis of most economies.


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SCIENTIFIC Minerals are the building blocks of all solid parts of the universe, and are thereforefundamental to all aspects of the geological sciences. Some examples:

- petrologists use individual minerals that form under restricted conditions of pressure and

temperature to map physical conditions within the Earth

- geophysicists studying the Earth's interior need to understand how minerals behave under

pressure, and how they transmit seismic waves

- geochemists use changes in water chemistry to understand processes of weathering and

contamination by interaction with mineral surfaces

Minerals are also important to a number of related scientific disciplines, including

- agricultural sciences (soils)

- hydrology (important for understanding development of aquifers and aquitards)

- materials science (development of synthetic minerals with specific properties)

- medical science (e.g., asbestos)

- biological sciences (may have been important as templates for the origin of life)

Definition of a mineral:

A mineral is a naturally occurring, inorganic, homogeneous solid with a definite chemical

composition and an ordered atomic arrangement

- naturally occuring - this modifier in the definition is considered superfluous by some, but is an

important distinction to others (especially gemologists)

- homogeneous solid- a single, solid substance (phase) that cannot be physically

separated into distinct compounds; this distinguishes minerals from rocks that can be

disaggregated into individual mineral constituents


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- definite chemical composition -al'>ineral is a chemical element or compound whose

composition can be represented by a chemical formula (e.g., SiO 2). The compositions of minerals

are either fixed, or vary within specified limits (EX: the mineral olivine may vary in composition

from Mg 2SiO 4 to Fe 2SiO 4). The composition dictates the mineral structure, which in turn controls

the physical properties of the mineral

- ordered atomic arrangement - nearly all minerals are crystalline. It means that the internal

structure is characterized by periodic or predictable arrays of atoms, ions, or molecules ... this

ordered arrangement of atoms is often expressed in the symmetry of the external form. It also

means that different minerals may have the same composition but different structures (EX:

graphite and diamond).

The crystalline state of matter is the most fundamental property of minerals

In fact, the word 'crystal' is an anglicized version of the Greek word for ice, and was generally

employed through the Middle Ages for describing quartz - 'rock crystal' - as quartz was

considered to be permanently solidified water. The word has persisted for any quartz clear

enough for ornaments (e.g., New Age uses) or glass.

Aspects of Earth Materials that we will cover this term:

- crystal chemistry - the chemical nature of minerals

- crystallography - the study of symmetry and the internal order of crystals

- mineral physics - the physical properties of minerals

- petrology -al'> study of rocks and the minerals that form them


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A bit of history

Very early man recognized natural pigments and used them in cave paintings. Stone Age

man knew something about the hardness of minerals, and about mineral cleavage (how they

break) - jadeite commonly used as tools. The mining and smelting of minerals for iron, copper,bronze, lead, silver probably dates back to > 4000 yrs. However, there is no written record of any

of this.

300 BC Theophrastus (pupil of Aristotle) wrote On Stones

23-79 AD Pliny the Elder recorded a great deal of natural history, and described a number of

minerals mined as gemstones, ores, and pigments. His are the earliest comments on crystal form

and the quality of crystal faces. Books 33-37 of his volume on Natural History cover such topics

as prec ious m e tals (not only mining and uses but also man's greed and exploitation of mineral

resources); use of minerals for pigments and pa in t ing ; mining and m e tal lu rgy ; marble and other

materials used in sculpture; and prec ious s tones .

1556 AD Georgius Agricola (Georg Bauer; German physician) published De Re Metallica , in

which "I have omitted all those things which I have not myself seen, or have not read or heard of

from persons upon whom I can rely." He is considered the founder of geology as a discipline, and

his work contributed to the fields of mining geology, metallurgy, mineralogy, structural geology

and paleontology. This book became a handbook of mining practices for the next two centuries,

and laid the framework of stratigraphic principles. In other books he developed a classification

systems for minerals based on their physical properties, gave them standardized names and

recorded where they could be found.

1611 AD Kepler speculated on the planar arrangement of spheres as an explanation for the

symmetry of snowflakes.


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1669 Nicolaus Steno recognized that the interfacial angles of quartz crystals were the

same regardless of the size or shape of the crystal. This led to his hypothesis of the constancy of

interfacia l angles , with the basis that there is an underlying pattern of symmetry to crystal forms.

He concluded that processes of crystal growth may allow different faces to dominate under

different growth conditions - this results in crystals of the same composition having very different

external forms. SIGNIFICANCE OF CRYSTAL FORM

1768 AD Carolus Linnaeus developed a mineral classification based primarily on external

form. Throughout 18th century, studies of chemistry and mineralogy closely linked, as chemists

worked with minerals as their raw materials. Saw the discovery of many new minerals and, with

that, identification of many new elements (cobalt, nickel, manganese, tungsten, molybdenum,

uranium ...)

1784 AD The French mineralogist Rene Hauy recognized that the perfection of external

form, the symmetry possessed by crystals, and the existence of perfect cleavage must be

manifestations of the internal structure of minerals (involving planes of atoms). In his study of

calcite crystals Hauy defined axes of reference for a few crystals, and recognized that all faces on

a crystal cut those axes at simple multiples - this led to his conception of crystal structures made

up of identical "integral molecules" ... turns out that this concept is similar to the modern concept

of a space lattice. RELATIONSHIP BETWEEN CRYSTALLOGRAPHY AND MINERALOGY

1830 AD Johan Hessel proved that geometric constraints limit the number of crystal classes

to 32, and that only 2-, 3-, 4-, and 6-fold axes of rotational symmetry are possible in minerals.

1837 AD James D Dana (Yale) completed the 1st edition of A Sys tem of Mine ra logy , a book

which, in the 4th edition, introduced the chemically based classification system that we still use.


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1848 Auguste Bravais proposed the existence of 32 crystal classes He also proposed that there

were only 14 space lattices (that is, he demonstrated that only 14 regular patterns in space can

result form the periodic arrangement of points) - his work was the forerunner of space group

theory. He also perceived that the 14 space lattices consisted of 7 different lattice symmetries,

which correspond to 7 crystal systems.

1870 AD Petrographic (polarizing) microscope invented in mid-1800s ... brought to this

country by G. Huntington Williams (Johns Hopkins). This allowed determination of the optical

properties of minerals, and also made possible the study of fine-grained rocks...

1862-1870 AD Periodic table developed first by a geologist and mineralogist Alexandre Beguyer

de Chancourtois (1862), who published a list of all of the known elements in order of their atomic

weights. He also recognized that some elements had the same physical properties, thus

introducing the idea of periodicity. In 1868 Dmitri Mendeleev expanded on the idea that there was

a periodic repetition of elements with similar physical and chemical properties. Ex. atoms

numbered 3,11,19,37,55 (Li, Na, K, Rb, Cs) all soft, silvery white metals. All these elements are

reactive, and form perfect cubes when combined with chlorine. The resulting compounds (LiCl,

NaCl, KCl, RbCl and CsCl) are all colorless and display perfect cubic cleavage. In fact, the

symmetry of his table was so compelling that he recognized absence of elements where not yet

discovered ...

1895 AD Wilhelm Roentgen discovered xrays; he showed that xrays were able to pass

through materials that are opaque to light, invisible to the human eye, and could be recorded on

photographic paper. For this work Roentgen was awarded the first Nobel Prize in physics in 1901.

1912 AD The physicist Max von Laue first demonstrated that xrays were diffracted by a

crystal structure (in his case, copper sulphate). The implications of this observation were that the

wavelengths of xrays were comparable with the spacing between atoms in crystals. This was the

start of an entire field devoted to the determination of crystal structure.


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1913 AD The father-son team W. Lawrence and W. Henry Bragg used diffraction to analyze

the first crystal structure, that is, the precise position of atoms in the structure was ascertained,

along with the distances and angles between atoms. This work allowed inferences about atomicsize and bond strengths, and thus won the Braggs the Nobel Prize in 1915.

The twentieth century has seen a dramatic increase in the 'tools' available for studying minerals -

XRD, XRF, electron microprobe, electron microscope, spectroscopic techniques, and, most

recently, computer-assisted tomography, TEM and atomic force microscopy, where individual

atoms can be imaged...

We now realize that the internal structure of any mineral can be described as a 3-D array of

positive (cations) and negative (anions) ions built up by a regular repetition of the unit cell.

Symmetry and form of a crystal are determined by the shape of that unit cell. The chemica l

f o r m u l a of a mineral expresses the relative proportions of its constitutive elements.

Lecture 2 - Atoms and Elements

1862-1870 Periodic table developed first by a geologist and

mineralogist Alexandre Beguyer de Chancourtois (1862), who published

a list of all of the known elements in order of their atomic weights. He

also recognized that some elements had the same physical properties,

thus introducing the idea of periodicity. In 1868 Dmitri Mendeleev

expanded on the idea that there was a periodic repetition of elements

with similar physical and chemical properties. Ex. atoms numbered

3,11,19,37,55 (Li, Na, K, Rb, Cs) all soft, silvery white metals. All these

elements are reactive, and form perfect cubes when combined with


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chlorine. The resulting compounds (LiCl, NaCl, KCl, RbCl and CsCl) are all colorless and

display perfect cubic cleavage. In fact, the symmetry of his table was so compelling that he

recognized absence of elements where not yet discovered ...

1897 J.J. Thompson discovered electrons; soon after Rutherford recognized that atoms had a

small nucleus composed of protons and neutrons (to explain charge and mass).

Bohr model of the atom: Bohr introduced the concept of energylevels, known as quantum numbers. He believed that these

levels were arranged as spherical shells, a geometry now known

to be too restrictive

SUMMARY OF QUANTUM NUMBERS

1. The principle quantum number (n) determines the major energy level. n = 1-7, with each

level also designated by a le to Q, with K (n=1) being the lowest energy level and Q (n=7) thehighest.: K is equivalent to (n=1). When an electron moves from a higher energy level to a lower

one, energy is released as electromagnetic radiation (usually x-rays); this forms the basis for

many of our analytical techniques. The maximum number of electrons allowed at any one level

is 2n 2.


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2. The angular momentum quantum number (l)

represents 'subshells' or orbitals , within each energy level.

l varies from 0 to n-1, with higher values of l correspondingto higher angular momentum. The corresponding orbitals

are s, p, d, and f for l = 0-3; these may hold up to 2,6,10

and 14 electrons, respectively. Electrons fill orbitals from

lowest to highest energy. The outermost electrons are

called the alence

electrons

3. The magnetic quantum number (m) relates to the magnetic field generated by an electron

with angular momentum and may be 1, 1

4. The spin quantum number relates to the intrinsic magnetism of the electron itself, and maybe either -1/2 or +1/2

Modern periodic table

1. Periods are rows; the number of the period indicates the orbitals occupied by electrons.

EX: elements in 1 st period contain electrons in 1 s orbital; elements in 2 nd period have

electrons in 2 s and 2 p orbitals; elements in 3 rd period have electrons in 3 s and 3 p 4 th


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to 7 th periods have 10 extra elements with electrons in d -orbitals. 6 th and 7 th periods

have additional 14 elements with electrons in f -orbitals [listed separately at the bottom of

the table includes rare earth elements and actinide series]

2. Groups -orbitals that are readily given up to produce cations . Elements near the right hand

side of the table have nearly full orbitals and thus easily acquire additional electrons;these elements become nions. Properties of elements in the middle of the table (the

transition elements ) are less predictable. Important groups are the alkalis (I), the alkali

earths (II), the halogens (VII), and the transition elements (partially filled d- and f-orbitals,

and therefore may have unpredictable behavior).

IONS

Atoms are most stable if electrons completely fill energy

levels and sublevels. For this reason, many atoms will either give

up or accept extra electrons in order to stabilize their

configuration, thereby creating ions . The number of electrons

gained or lost is referred to as the valence , or valence state . The

process of losing an electron is called oxidation , while gaining

an electron is reduction . When one or more electrons are lost from the electron configuration ofthe atom, a cation is formed. When electrons are added, an anion is formed.

Energy required to removed the most weakly held electron is known as the first ionization

potential . Note that the noble (inert) elements have the highest ionization energy, while the

alkalis (row 1 of the periodic table) have the lowest. However, a more common measure is that


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of the ability of an atom in a crystal structure or molecule to attract electrons to its outer shell -

calculated from known bonds strengths, and known as electronegativity (concept developed by

Pauling). Atoms with different electronegativity form ionic bonds with one another, and

elements of periodic table can be divided into two groups, electron donors (the metals , in the

left-hand side of the periodic table) and electron acceptors (the nonmetals , on the righthand sideof the periodic table). Elements with similar electronegativities form covalent bonds (C).

Additionally, several elements are found in more than one valence state. EX: Fe can occur in a

divalent state Fe 2+ (ferrous iron) or Fe 3+ (ferric iron).

Sizes of io ns

Anions are formed when atoms gain 1 or more electrons

Cations are formed when atoms lose 1 or more electrons

Anions are thus generally larger than cations, and crystal structures can be envisaged as largespheres packed around small spheres in such a way that the space between spheres isminimized, and positive and negative charges are balanced. Thus the chemical classificationsystem that we use is based primarily on the anion or anion group.

Atomic number and mass

Atomic number is the number of protons in an element's nucleus ( Z ) and, in a neutral

atom, is also equal to the number of electrons. It is also close to the number of electrons in

most ions. Most important in controlling elemental properties .

Atomic mass (A) is the number of protons ( Z ) + number of neutrons ( N ). Most elements

have several different isotopes (same Z different N). Although chemists don't worry much about

isotopes, very important in geology as climate tracers and for radioactive dating of geologicmaterials.

A mole of an element is defined as the amount of that element that has its weight in

grams equal to its atomic weight. Given by Avogadro's number (N): one mole of an element or

compound always has 6.022 x 10 23 atoms.


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EX: Box 1.2 What is a mole of quartz?

SiO2 = 28.0855 + 2(15.994) = 60.0843 grams

Bonding in minerals

A chemical bond exists when the forces acting between two elements are sufficient to

form a new aggregate or molecule. There are four primary types of chemical bonds:

Covalent bonds involve shared electrons in outer shell; this means that an electron pair

occupies two different orbitals simultaneously; such bonds are directional because of this orbital

control. Covalent bonds are strong (diamond) and molecules with these bonds tend to be

electrical insulators .

Ionic Metallic bonds are al'>acteristic of native metals, which are elements that easily

lose their outer electrons. In a metal there are more bond sites (empty orbitals) than there are

electron pairs to fill them. Detached electrons mover freely through the structure, thus metals

are good electrical conductors .

Van der Waals ; not important in most minerals (except graphite).

Type of bonding in minerals determines both the symmetry and the physical properties of minerals; the most important bond in manyminerals that we will examine is the Si-O bond, which is partly ionicand partly covalent (called polar cov alent ); directionality of covalent

part of bond is preserved.

Effec ts of s ize

As important asvalence state is the relative size of the two ions


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( ion ic rad ius ), which dictates their separation. Note that the attractive force increases as theatoms approach each other, with a maximum when they are just touching. As soon as theirelectron clouds overlap, repulsive forces become strong (counteracts attractive energy). Theminimum energy configuration occurs where the distance between centers of ions is equal tothe sum of their ionic radii ( closes t packing ).

Lecture 2 - Atoms and Elements

Overview Details

A. Bohr model of the atom

B. Quantum numbers

1. The principle quantum number (n) determines the major energy level. n = 1-7, with

each level also designated by a letter: K - Q, with K (n=1) being the lowest energy

level and Q (n=7) the highest.

2. The angular momentum quantum number (l) represents 'subshells' or orbitals ,

within each energy level. l varies from 0 to n-1, with higher values of l

corresponding to higher angular momentum. The corresponding orbitals are s, p,

d, and f for l = 0-3; these may hold up to 2,6,10 and 14 electrons, respectively.

Electrons fill orbitals from lowest to highest ene

3. The magnetic quantum number (m) relates to the magnetic field generated by an

electron with angular momentum; may be 1, 1

4. The spin quantum number relates to the intrinsic magnetism of the electron itself,and may be either -1/2 or +1/2
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C. Modern periodic table

1. Periods - rows; the number of the period indicates the orbitals occupied by

electrons

2. Groups - columns; have valence electrons in similar orbitals, and hence they

have similar chemical properties.

D. Ions

Anions are formed when atoms gain 1 or more electrons

Cations are formed when atoms lose 1 or more electrons

Anions are thus generally larger than cations, and crystal structures can be envisaged aslarge spheres packed around small spheres in such a way that the space betweenspheres is minimized, and positive and negative charges are balanced.

E. Atomic number and mass

Atomic number is the number of protons in an element's nucleus ( Z ) - mostimportant in controlling elemental properties.

Atomic mass (A) is the number of protons ( Z ) + number of neutrons ( N ).

A m o l e of an element is defined as the amount of that element that has its weight in

grams equal to its atomic weight. Given by Avogadro's number (N): one mole of an

element or compound always has 6.022 x 10 23 atoms.

F. Bonding in minerals

Covalent - shared electrons in outer shell


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Ionic -bond between a cation and an anion where complete electron transfer has

occurred

Metallic - detached electrons move freely through the structure

Van der Waals

Effec ts of s ize - The minim um energy co nfigura t ion o ccurs w here the d is tance be tweencenters of ions is equal to the sum of the ir ion ic rad i i (c loses t packing) .

Cosmochemistry

1. Origin of the elements and Earth

Big Bang First determined by E Hubble, who measured the speed at which somegalaxies were moving away from the Earth. He then recognized that the universeseemed to be expanding, and that he could use the measured velocities of expansion tofigure out the time of origin.

Radiometric dating of meteorites indicates that the solar system began to form about4.56 Ga BP as the solar nebula , consisting mostly of molecular H 2 plus He and minor Be and Li(the only products of the Big Bang). About 2% estimated to be heavier dust created by nuclearsynthesis reactions in early stars and supernovae.

The first 100,000 years: The nebular cloud began to collapse because of gravitationalinteractions. Also flattened into a disk because of rotation (centrifugal forces), with 1-10% ofmass constituting the central disk. Most of the mass gradually lost angular momentum andcollapsed into the center to form the sun . Planetesimals (kilometer-size bodies) began to form

by accretion, and gravitational collapse provided heat that eventually permitted nuclearsynthesis (fusion) of hydrogen to helium.

The next 10 million years: known as the T-Tauri stage ; during this stage the solar wind began to emanate radially outward from the and the nebula lost about 1/2 of its initial massduring this stage. Of the remaining material, 99.9% of the mass collapsed to form thesun; the other 0.1% remained in the disk. The disk material had sufficient mass tocontract to the median plane, where it aggregated into the planets. Planet formation


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took place under conditions of strong gradients in T and P generated by the early sun. As a result, the more volatile elements evaporated in the inner, hotter portion, werestripped off by the solar winds, and condensed to solids further outward where thetemperatures were sufficiently low. The actual condensation temperatures dependedon the elements/compounds involved. Only the most refractory elements condensed in

the innermost zone; with the more volatile elements condensed in the outermost zone. As a result, the nebula experienced chemical differentiation, with refractory oxides(Al2O3, CaO, TiO2) concentrated in the innermost portions of the solar system, and Fe-Ni alloys, Fe-Mg-Ni silicates, alkali metals and silicates, sulfides, hydrous silicates, H2O,and solids of ammonia & methane concentrated progressively outward.

Condensed solids then began to accrete as planetesimals. The terrestrial (Earth-like)planets (Mercury, Venus, Earth, Mars) formed from the more refractory materials, as well as theparent bodies that produced asteroids and meterorites. In the outer portions, the large gaseous planets formed (Saturn, Jupiter, Uranus, Neptune). [Pluto is anomalous in orbit and probablycomposition; may actually be an escaped moon]

IF YOU'D LIKE TO KNOW MORE ABOUT THE SOLAR SYSTEM...

THUS the Earth's composition is a product of its accretion history. However, as the process ofchemical differentiation was not perfectly efficient, the Earth contains some of every stableelement (not just those elements that were condensable at our distance from the sun). Thatsaid, only 7 elements comprise 97% of Earth: O (50.7%), Mg (15.3%), Fe (15.2%), Si (14.4%),S (3.0%), Al (1.4%), Ca (1.0%), consistent with solar abundances and condensates anticipatedfor Earth's position.

2. Differentiation of the Earth

Differentiation may have started during accretion; continued afterward because ofintense heating by gravitational collapse, impacts, and radioactive heat. Eventually part of theEarth melted, which increased mobility such that dense melts moved inward and light meltsmoved to the surface. Gravitational energy released by this process may have melted the entireEarth ( magma ocean ), with the possible exception of the outermost surface. The result was alayered Earth structure.

Goldschmidt (1937) proposed that Earth's elements separate into different phases; thisconcept gave rise to the terms:

lithophile (stone-loving) elements form the light silicate phases

chalcophile (copper-loving) elements form an intermediate sulfur phase
http://seds.lpl.arizona.edu/nineplanets/nineplanets/intro.htmlhttp://seds.lpl.arizona.edu/nineplanets/nineplanets/intro.htmlhttp://seds.lpl.arizona.edu/nineplanets/nineplanets/intro.html


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gravitational constant - use to calculate Earth's mass (average density), whichis 5.52 g/cm 3. Density of surface rocks rarely > 3, therefore the Earth must contain a largeproportion of very dense material.

nebular composition e material the comprises the solar system can bemeasured using various types of spectroscopy (emission of characteristic light spectra). H byfar the most abundant, as it made up most of original nebula. All other elements except He, thenext most abundant, were synthesized from H in the sun and other stars. Together H & Hecomprise > 99% of all atoms in solar system. Decrease in abundance with increasing Z reflectsincreasing synthesis difficulty. Also evident is

(1) relatively low abundance of some elements such as Li, Be, B, Sc is a consequenceof their formation only by spallation by cosmic rays, supernova explosions and because of theirconsumption in subsequent fusion processes;

(2) sawtooth pattern "Oddo-Harkins rule", which says that atoms with even numbersare more stable because their nuclei are more tightly bound.

(3) Fe is particularly stable because its nucleus is tightly bound

Note abundance of Fe (plus Mg, Ni) in solar system relative to Earth's crust; used to inferthat these components must constitute much of the Earth's core. Fe is also denseenough to satisfy density requirement.

seismic studies locities of P and S waves in various materials can be measuredand compared with known seismic velocities. Reflection and refraction of seismic wavesat discontinuities provides direct evidence for layered structure, while absence of shearwave transmission indicates the liquid nature of the outer core.

mantle rocks ophiolites, xenoliths

3. Meteorites

Solid extraterrestrial objects that strike the Earth; many are likely fragments derived fromcollisions of larger bodies (particularly asteroid belt between Mars and Jupiter). Believed torepresent early stages in development of the solar nebula, and thus provide information aboutstate of early solar system. Classification:

irons -composed of Fe-Ni alloy

stones - composed of silicates (can be difficult to tell from terrestrial rocks, but comprise about94% of meteorites)

chondrites contain chondrules (spherical silicate inclusions that appear to haveformed as droplets of glass); considered to be "undifferentiated" meteorites most primitive


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achondrites do not contain chondrules

stony-irons - contain subequal amounts of each

TO SEE PICTURES OF METEORITES...

Chondrite Earth Model (CEM) - average composition assumed to represent original compositionof the Earth. However, Earth is denser, and has a higher Fe/Si ratio, than provided byCEM.

Cosmochemistry

Details

1. Origin of the elements and Earth

Big Bang (~15 Ga)

Solar system (~ 4.56 Ga)

The first 100,000 years

The next 10 million years

BOTTOM LINE: the Earth's composition is a product of its accretion history. However, as theprocess of chemical differentiation was not perfectly efficient, the Earth contains some of everystable element (not just those elements that were condensable at our distance from the sun).That said, only 7 elements comprise 97% of Earth: O (50.7%), Mg (15.3%), Fe (15.2%), Si(14.4%), S (3.0%), Al (1.4%), Ca (1.0%), consistent with solar abundances and condensatesanticipated for Earth's position.
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2. Differentiation of the Earth

Goldschmidt (1937) proposed that Earth's elements separate into different phases thisconcept gave rise to the terms:

lithophile ("stone-loving") elements form the light silicate phases

chalcophile ("copper-loving") elements form an intermediate sulfur phase

siderophile ("iron-loving") elements form a dense metallic phase

These three layers do not correspond to the three layers of the Earth. The core issiderophile, but chalcophile component likely dissolved in siderophile core and was never aseparate phase. Mantle is the lithophile phase; Earth's crust had not yet formed.

Most common lithophile components of early Earth (and mantle):

olivine (Mg,Fe) 2SiO 4

orthopyroxene (Mg, Fe)SiO 3

clinopyroxene Ca(Mg,Fe)Si 2O 6

3. How do we know this?

gravitational - use to calculate Earth's mass (average density), which is5.52 g/cm 3. Density of surface rocks rarely > 3, therefore the Earth must contain a largeproportion of very dense material.

nebular composition -Together H & He comprise > 99% of all atoms in solarsystem. Decrease in abundance with increasing Z reflects increasing synthesisdifficulty. Also evident is

(1) relatively low abundance of some elements - Li, Be, B, Sc consequence offormation only by spallation by cosmic rays, supernova explosions and because of theirconsumption in subsequent fusion processes, and

(2) "sawtooth" pattern "Oddo-Harkins rule", which says that atoms with evennumbers are more stable because their nuclei are more tightly bound.

(3) Fe is particularly stable because its nucleus is tightly bound


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ANISOTROPY AND PHYSICAL PROPERTIES

Many physical properties are anisotropic , such that their magnitude depends on the direction inthe crystal. An easy way to picture this is by a mechanical analogue with springs of differentstiffness in different directions net displacement is the result of the vector sum of thecomponents, thus the direction of displacement is not necessarily the same as the direction ofthe applied force.

DIRECTIONAL PROPERTIES

thermal conductivity relateds heat flow to temperature gradient

electrical conductivity relates electrical current density to electric field

diffusivity relates atomic flux to concentration gradient

elastic properties relate strain (extent of deformation) to applied stress

seismic properties relate to velocity of seismic wave propagation (related todensity, rigidity, bulk modulus)

optical properties relate to refractive index variations

Examples: calcite shows double refraction

ulexite is a natural fiber optic


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carbonates [with anion complex CO 32-]

native elements

sulfides [with anion S 2-]


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Classification of silicates

In most silicates, Si 4+ exists in 4-fold coordination with O 2-. The subclasses are classifiedaccording to how the tetrahedral are linked (see Table 2.6 in your text); because the linkagedetermines the number of Si per O, each subclass has its own distinctive Si:O ratio. The mostcommon subclasses of silicates are:

Framework silicates (including quartz and feldspar, the mostabundant elements in the Earths crust); Si:O ratio is 2:1,although in many framework silicates Si is replaced to someextent by Al (as in the feldspars). Framework silicates aresubdivided by groups shown in Table 2.7

Sheet silicates this group includes serpentines, clays andmicas. Sheet silicates consist of sheets of SiO4- tetrahedral(arranged as joined 6-fold rings) separated by octahedral layersthat contain cations (commonly either Al 3+ or Mg 2+). The Si:O ratioin these minerals is 2:5 (which often appears in the mineralformula as 4:10). The tetrahedral and octahedral layers can then

be stacked in different ways for example, serpentine andkaolinite have alternating T and O layers, while pyrophyllite andtalc have TOT sequences that are loosely joined to each other byvan der Waals bonds (hence the softness of talc)


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Single chain silicates the single chain silicate group contains all of the pyroxenes, withstructures based on chains of SiO4- tetrahedral linked by shared (often called bridging)oxygens. The Si:O ratio is 1:3 (often written as 2:6). The most common pyroxenes involve solidsolutions between Mg, Fe and Ca, but other forms may include Na (jadeite) and Li

(spodumene). In the image below diopside is the paleblue mineral more commonly, however, it is green.Chrome diopside is a beautiful dark green gemstone.

Jadeite isonemineralknown as

jade,althoughnephrite(anamphibol

e) is also called jade (andtends to be a darker green incolor).

Double chain silicates these structures are intermediate between the pyroxenes and thesheet silicates in having linked chains of tetrahedral, separated by octahedral layers. Thecharacteristic Si:O ratio is 4:11 (8:22). This group includes all of the amphiboles and thepyroxenoids.

Isolated tetrahedra this group contains some important minerals, many of which you alreadyknow. First there are the olivines, with Si:O ratios of 1:4. Also in this group are thealuminosilicates (sillimanite, kyanite, and andalusite) with fairly invariant formulas of Al 2SiO 5.


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Finally, there are some other distinctive minerals such as staurolite (whose name meanscross), titanite (CaTiSiO 5), topaz, and zircon (ZrSiO 5).

HOMEWORK

Id like you to try to work through the process of normalizing a mineral analysis (that is,converting a chemical analysis to a mineral formula) between now and Thursdays class. I willnot require you to hand your work in instead, bring it with you and I will go over it at the startof class.

Analytical instruments can be used to obtain chemical analyses. The resulting data are generallyreported in weight percent of the major oxides in the mineral. Use the following chemicalanalysis and the instructions below to determine the specific mineral formula and the identity ofthe unknown mineral. Be sure to show all your work! Using a spreadsheet program like Excelmakes these calculations easier, although this particular analysis can be done pretty quickly byhand as well. A similar set of instructions appears in Box 1.5 (p. 22) of your text.

Analysis

SiO 2 38.05%

FeO 20.38%

MgO 41.57%


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Total 100 %

(Assume the known total number of oxygen atoms per formula unit is 4)

Mineral formula_______________________________________

What mineral is this?________________________________


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Steps for determining a specific mineral formula:

1) Convert oxide wt.% into molecular proportion of each oxide. This is done by dividing the wt.% of each oxide by the molecular weight of the oxide. This gives the molecular proportion ofeach oxide. (The molecular weight for each is calculated from their atomic weights.)

2) Multiply the molecular proportion for each oxide by the # of oxygen atoms present in eachoxide. This gives the O atomic proportion.

3) Sum the O atomic proportion column.

4) Divide the known total # of Oxygen atoms per unit cell in the mineral by the sum of the Oatomic proportion. (e.g. Olivine is know to have 4 oxygen atoms in its mineral formula,Feldspars have 8). This operation gives you a normalization factor.

5) Next, normalize the O atomic proportions from each oxide by multiplying each entry by thisnormalization factor. This gives the number of anions based on the known number in themineral formula.

6) Determine the number of cations associated with the oxygens by dividing the number ofanions determined in step 5 by the number of oxygens in the reported oxide. (e.g. SiO2 has 2O per 1 Si, Al2O3 has 1.5 O per 1 Al).

7) The number you obtain after doing step six is the number of cations that are in the finalmineral formula.


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EXAMPLE:

Olivine:

s tep 1 s tep 2 s tep 4 s tep 5 s tep 6 s tep 7 Element Oxide

wt. % Molec.Wt.

Molec.Prop.

#Oxygen

O atomic Normaliza. # of Anions

Oxygen Cations

of oxides proportion factor percation

SiO2 31.85 60.074 0.530179 2 1.060368 1.90543 2.02043 2 1.0102 FeO 58.64 71.841 0.816247 1 0.816247 1.90543 1.5553 1 1.5553

MnO 0.85 70.937 0.011982 1 0.011982 1.90543 0.02283 1 0.02283 MgO 8.49 40.299 0.210675 1 0.210675 1.09543 0.04142 1 0.40142

(step 3) Total 2.09926 Normalizationfactor=

4Oxygens/2.09926

Formula: (Fe 1.555 Mg 0.401 Mn 0.023 ) Si 1.01 O 4

Lecture 5

Classification of Minerals; Crystal growth

Review from last time - Paulings Rules:

1. The Coordination (radius ratio) Principle a coordination polyhedron of anions surroundseach cation. The cation-anion distance is determined by the sum of the cation and anion radiiand the number of anions coordinating with the cation is determined by the relative size of thecation and anion.

2. Electrostatic Valency Principle in a stable ionic structure, the total strength of the valencybonds that reach an anion from all neighboring cations is equal to the charge of the anion.


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minor elements are present in small amounts (up to a few %), usually as substitutes formajor elements

trace elements are present in extremely small amounts but are often responsible formineral color.


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Structural formula VIFe 2IVZnO 4

Often, a structural site may be interchangeably occupied by different cations as part of a solidsolution series. In this case, the interchangeable cations are grouped within parentheses. Thespinel formula shown above can be modified to show that the octahedral sites can hold eitherFe 3+ or Mn 3+ ions and the tetrahedral sites can hold either Zn 2+ or Fe 2+ ions.

General formula ( Fe, Mn) 2(Zn,Fe)O 4

Note that in this formula, the cations in parentheses are conventionally assumed to be listed inorder of decreasing abundance that is, Fe is mo re likely than Mn to occupy the octahedral

site, while Zn is more likely than Fe to occupy the tetrahedral site.

Using certain analytical techniques, it is possible to determine the proportion or relativeabundance of each type of cation occupying a substitution site in a given sample. Thisinformation yields the samples specific mineral formula , which could look something like this:

Specific formula ( Fe 1.4 Mn 0.6 )(Zn 0.8 Fe 0.2 )O 4

In this example, Fe 3+ ions proportionally across the structure occupy 1.4 of every two filledoctahedral sites, while Mn 3+ ions occupy the remaining 0.6 of every two filled octahedral sites.Similarly, Zn 2+ ions proportionally occupy 0.8 of every filled tetrahedral site, while Fe 2+ ionsoccupy 0.2 of every filled tetrahedral site.

HOMEWORK

Solid Solutions

The discussion above leads directly to a discussionof substitutions of one element foranother within the stable mineral structure called isostructural substitutions . This process isknown as solid solution , defined in a mineral structure as specific atomic sites that areoccupied in variable proportions by two or more different chemical elements.

Three main fac tors de termine whether or not so l id so lu t io n is poss ib le :
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1. Comparative size of ions (atoms, molecules) that are substituting for oneanother This results directly from Paulings first rule of radius ratios, in that ions that substitutemust be able to occupy the same interstitial site. Generally, for this to happen the radius ratiosmust be within 15%; substitution is unlikely when the radii differ by > 30%.

2. The valence state (charge) of the ions involved in the substitution . Thisstipulation relates to Paulings second rule, which involves electrical neutrality. If thesubstituting elements have the same charge (Fe 2+ and Mg 2+; Na + and K +), then neutrality will bemaintained. If the charges are different (Al 3+ and Si 4+; Na + and Ca 2+), then another ionicsubstitution must take place to maintain neutrality this is called a coupled substitution, forexample Ca 2+ Al3+ for Na +Si 4+

3. The temperature at which the substitution takes place . Substitution of ions ofdifferent size is favored by elevated temperatures, where the structure is expanded and there isgreater tolerance for size variation.

Types of subst i tu t ion

Simple cationic/anionic: Ions of similar size and charge substitute for each other.Examples:

K = Na KCl NaCl (sylvite - halite);

KAlSi3O 8-NaAlSi 3O 8 (orthoclase albite) Mg = Fe (= Mn) Mg2SiO 4 Fe 2SiO 4 Mn 2SiO 4 (forsterite fayalite - tephroite;

olivine)

MgSiO 3 FeSiO 3 (enstatite ferrosilite; pyroxene) Cl - Br KCl - KBr Fe = Zn (Zn, Fe)S (sphalerite)

Depending on the relative sizes of the ions involved, the solid solution may be either partial (K =Na; ionic radii 1.46:1.08 in 6-fold coordination) or complete (Mg = Fe; ionic radii 0.77:0.80 in 6-fold coordination).

Coupled substitution: For electrical neutrality to be maintained, substitution of twoelements requires an additional substitution. Examples:


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Fe 2+ + Ti 4+ = 2Al 3+ (Al, Ti) 2O 3 (corundum, var. sapphire) Ca 2+ Al3+ = Na +Si 4+ CaAl 2Si 2O 8-NaAlSi 3O 8 (plagioclase) Mg2+ + 2Al 3+ = 2Fe 2+ + Ti 4+ (Mg, Fe)(Al, Ti) 2O 4 (spinel group)

Interstitial substitution: Between some ions or ionic groups there may exist structuralvoids. Particularly where these have the form of channels (as in beryl and some zeolites), theymay be partially filled. Example:

BERYL Be 3 Al2Si 6O 18 may contain substantial amounts of Li, Na, K, Rb through coupledsubstitutions involving Si 4+ and Al 3+

Vacancy solid solution: remember that close packing of anions often creates morecation sites than can be filled. Partial filling of these sites forms another type of substitution. Acommon example is the mineral amphibole, which has the end member

TREMOLITE [] Ca 3Mg5Si 8O 22(OH) 2

where [] represents a vacant site that may be filled using the coupled substitution

[] + Si 4+ = Na + Al3+

Omission solid solution: this is the opposite of filling a vacancy, that is, creating one. An example is the substitution of the large Pb 2+ cation for the equally large K + cation as

K+ + K + = Pb 2+ + []

The result of these substitutions is a wide variety of mineral and mineral formulas!!!


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Crystallization and polymorphs

So how, and why, do crystals form?

Crystals typically form from a supersaturated solution, as we experimented with in lab. Thatsolution may be an aqueous phase, a magma, or a gas. During metamorphism we also seeexamples of solid state crystallization (that is, one crystal growing from another solid).

We may create a supersaturated solution by changing the temperature, changing the pressure,

or changing the composition (by either adding or subtracting components). We usually showmineral stability fields using phase diagrams , as shown below for the system SiO 2.


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Lecture 5 - OVERVIEW

Classification of Minerals; Crystal growth

Details

Review from last time - Paulings Rules:



3. Sharing of Polyhedral Elements I the existence of edges (and particularly faces) commonto coordination polyhedra decreases the stability of ionic structures

4. Sharing of Polyhedral Elements II in a crystal containing different cations, those withlarge valence and small coordination number tend not to share polyhedral elements with eachother.

5. Principle of Parsimony the number of essentially different kinds of constituents in a crystaltends to be small.
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Chemical Variation in Minerals

This raises an issue of terminology:

major elements are fundamental to the mineral, control its structure and gross physicalproperties

minor elements are present in small amounts (up to a few %), usually as substitutes formajor elements

trace elements are present in extremely small amounts but are often responsible formineral color.


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We also need to introduce the idea of mineral formulas , which is how we describe mineralcompositions.

Idealized formula Fe 2ZnO 4

Structural formula VIFe 2IVZnO 4

General formula ( Fe, Mn) 2(Zn,Fe)O 4

Specific formula ( Fe 1.4 Mn 0.6 )(Zn 0.8 Fe 0.2 )O 4

Solid Solutions

The discussion above leads directly to a discussion of substitutions of one element foranother within the stable mineral structure called isostructural substitutions . This process isknown as solid solution , defined in a mineral structure as specific atomic sites that areoccupied in variable proportions by two or more different chemical elements.

Three main fac tors de termine whether or not so l id so lu t io n is poss ib le :

1. Comparative size of ions (atoms, molecules) that are substituting for oneanother

2. The valence state (charge) of the ions involved in the substitution .

3. The temperature at which the substitution takes place


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Types of subst i tu t ion

Simple cationic/anionic: Ions of similar size and charge substitute for each other.Examples:

K = Na KCl NaCl (sylvite - halite);

KAlSi3O 8-NaAlSi 3O 8 (orthoclase albite) Mg = Fe (= Mn) Mg2SiO 4 Fe 2SiO 4 Mn 2SiO 4 (forsterite fayalite - tephroite;

olivine)

MgSiO 3 FeSiO 3 (enstatite ferrosilite; pyroxene) Cl - Br KCl - KBr

Fe = Zn (Zn, Fe)S (sphalerite)

Coupled substitution: For electrical neutrality to be maintained, substitution of twoelements requires an additional substitution. Examples:

Fe 2+ + Ti 4+ = 2Al 3+ (Al, Ti) 2O 3 (corundum, var. sapphire) Ca 2+ Al3+ = Na +Si 4+ CaAl 2Si 2O 8-NaAlSi 3O 8 (plagioclase) Mg2+ + 2Al 3+ = 2Fe 2+ + Ti 4+ (Mg, Fe)(Al, Ti) 2O 4 (spinel group)

Interstitial substitution: Between some ions or ionic groups there may exist structuralvoids.

Vacancy solid solution: remember that close packing of anions often creates more

cation sites than can be filled.

Omission solid solution: this is the opposite of filling a vacancy, that is, creating one.


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The result of these substitutions is a wide variety of mineral and mineral formulas!!!

Crystallization and polymorphs

Lecture 6

Crystal growth, Physical properties of minerals

Crystallization

Crystallization involves nucleation of a seedcrystal and subsequent growth of that crystal. Nucleationinvolves competition between the supersaturation drivingcrystallization and the surface energy created byformation of a new phase. For this reason, highsupersaturations (a large driving force) promotesnucleation. In contrast, once nuclei exist, they may growat smaller supersaturations.

The figure below illustrates the different supersaturationregimes anticipated for different locations of magmacooling. Slow cooling (low supersaturation) of rockswithin the Earths crust is often invoked to explain thelower number density, but larger size, of crystals in


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plutonic rocks relative to volcanic rocks that cool on the Earths surface.

Differences in nucleation and growth behavior can also explain the difference between the saltand alum crystals that you grew in lab.


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Crystal growth

Processes of crystal growth arent perfect for example,crystals that grow rapidly may develop skeletal or dendriticforms. Such a crystal is shown in the photo on the right. Thisis a scanning electron microscope image where backscatteredelectrons are collected to yield an image that tells us aboutcomposition. You can see many different features in thisimage. First, the crystal appears to have a hole in the middle this is the texture that we call skeletal . Second, note thatthe structures at the corners of the crystals are decoratedwith the onset of dendritic overgrowths. Finally, note that the

crystal is zoned in gray scale, which represents compositional zoning (discussed below).

And most crystals have some sort of imperfection (many of which are diagnostic of that crystal).Which leads to a discussion of:

Crystal imperfections - defects

Defects important in that they increase crystal reactivity ...

Point defects

All crystals above absolute zero contain some defects ... increases energy of system,thus more at high temperatures

1. Impurity defect results from the presence of a foreign atom, either replacing onenormally in the str ucture or filling a vacancy.

2. Paired vacancies Anion vacancies are regions where there is more positive charge -

may trap nearby electron ... transitions between energy levels may be invisible range - colorcenter For this reason, can induce colors using radiation (Pleichroic halos around zirconinclusions) Vacancies are important for process of diffusion, that is, moving ions through thecrystal structure.

3. Line defects - happen when rock is stressed. Most easily understood with referenceto simple cubic lattice. dislocations - extra plane of atoms.


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Physical properties of minerals

Well look at two different aspects of physical properties those that are important for diagnosticidentification of minerals (mostly scalar), and those that dictate the physical behavior ofminerals (those that often show directionality, that is they are vector properties).

HAND SPECIMEN PROPERTIES

As these properties are best learned in lab, I will just present an overview in class.

1. Appearance

LUSTER general appearance orsheen examples include metallic, vitreous,adamantine (diamond-like). Metallic luster isthe result of near-complete reflection of light bythe mineral surface. The adamantine luster ofdiamond is a consequence of its high index ofrefraction

DIAPHENITY refers to a minerals ability to transmit light(transparent, translucent, opaque). Most opaque minerals have metallicluster.


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COLOR often useful for quick ID (particularly when color is distinctive), but can be verymisleading. Color is controlled by chromophores and is a consequence of the interaction oflight with electrons in the crystal.

Allochromatic minerals have color caused by elements that are present in trace amounts, likethe Cr that causes the green color of beryl to the right (emerald), or the Ti that gives corundumthe blue that we call sapphire.


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In contrast, idiochromatic minerals have color as an intrinsic property, sometimes on thatchanges with solid solution composition, and thus may be

diagnostic not only of mineraltype but also end membercomposition (as in garnet).Examples of idiochromaticminerals include Cu-bearingminerals (which are typically blueor green) and Mn-bearingminerals, which are typically pink.

Color can also be created by electron vacancies to form color centers (particularly common influorite).

STREAK the color of finely powdered mineral; useful for distinguishing oxides andsulfides

LUMINESCENCE any emission of light that is not the direct result of incandescence;includes properties such as fluorescence and phosphorescence . Luminescence of minerals isanother property that may be controlled by trace amounts of an element.

COLOR PLAY refers to properties of light scattering, as seenin the star sapphire in the picture. In this case the star of light iscreated by light scattering from small inclusions that are arranged alongthe three principle crystallographic directions.

Other examples of color play include theiridescence that is characteristic of labradorite;here the scattering is the result of very fine-scaleexsolution.

Opalescence is probably one of the best examples of color play opalescence is the result of silica precipitation as tiny sphericalbodies that are able to scatter light.


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2. Crystal shape

Called crystal habit theappearance of minerals, either as singlecrystals or as aggregates; includesterms such as the fibrous growth ofcerussite (Pb carbonate) crystals to theleft, or the botryoidal habit ofsmithsonite (Zn carbonate) to the right.

3. Strength related primarily to bonding

TENACITY cohesiveness, or resistance to breaking. Terms to describe tenacityinclude brittle (ionic bonding); malleable (metallic bonding), flexible (characteristic of sheetsilicates like mica)

CLEAVAGE, FRACTURE, PARTING reaction of crystal (strain) to an external force(stress). Cleavage is the tendency of minerals to break along certain planes (EX: graphite).When minerals break along planes of weaknes they have parting; weakness may be twinning,pressure solution. When minerals do not have a dominant plane of we akness they fracture inpatterns that may be described as conchoidal, fibrous, hackly.

HARDNESS resistance of a smooth surface to scratching. Hardness is probably aconsequence of weakest bond in structure.

4. Density (specific gravity)

Ratio of the weight of a substance and the weight of an equal volume of water.Determined as


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Specific gravity (the ratio) can be measured by a Jolly balance; density requires a pycnometer.The density can be calculated from the mineral formula if you know the dimensions of the unitcell and the number of formula units per unit cell.

5. Magnetism

Magnetite and pyrrhotite are the only common minerals with a magnetic signature.


Many physical properties are anisotropic , such that their magnitude depends on the direction inthe crystal. An easy way to picture this is by a mechanical analogue with springs of differentstiffness in different directions net displacement is the result of the vector sum of th ecomponents, thus the direction of displacement is not necessarily the same as the direction ofthe applied force.


thermal conductivity relateds heat flow to temperature gradient





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Examples: calcite shows double refraction

ulexite is a natural fiber optic

Each of these properties is controlled by the crystal structure, such that

the directional variation in the value of a physical property must be consistent with thepoint group symmetry of the crystal

since physical properties can always be broken i nto three mutually perpendicularcomponents, the symmetry of physical properties may be greater than the symmetry of thecrystal itself

Physical properties may be

isotropic uniform in all directions (isometric crystals)

uniaxial similar in two directions and different in the third (hexagonal and tetragonalcrystals)

biaxial different in all three directions (orthorhombic, monoclinic, trigonal crystals)

Lecture 6 OVERVIEW

Details

Crystal growth, Physical properties of minerals

Crystallization
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Crystal nucleation

Crystal growth

Crystal imperfections

Defects

Point defects

Impurity defects

Paired vacancies

Line defects

edge dislocation

screw dislocation

Stacking faults

Zoning

Twinning

simple twins

multiple twins

contact twins

penetration twins

Physical properties of minerals


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HAND SPECIMEN PROPERTIES

1. Appearance

LUSTER

DIAPHENITY

COLOR

Allochromatic minerals

Idiochromatic minerals

STREAK

LUMINESCENCE

COLOR PLAY

2. Crystal shape

3. Strength related primarily to bonding

TENACITY

CLEAVAGE, FRACTURE, PARTING

HARDNESS

4. Density (specific gravity)


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5. Magnetism



thermal conductivity relates heat flow to temperature gradient






Physical properties may be

isotropic uniform in all directions (isometric crystals)

uniaxial similar in two directions and different in the third (hexagonal and tetragonalcrystals)

biaxial different in all three directions (orthorhombic, monoclinic, trigonal crystals)


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Lecture 4 Radius ratios and Pauling's Rules

As we have discussed, the outward symmetry of crystals is an expression of internal ordering ofatoms and ions in the crystal structure. This in turn reflects the intrinsic symmetry of thepacking of atoms, and their interaction with neighboring atoms...

The ultimate reason for a particular arrangement of atoms in a mineral structure lies in thenature of the cohesive forces that hold atoms together. In theory, we should be able to predict amineral structure from the chemical composition, but in reality the problem rapidly becomes toocomplex to solve.

We'll be discussing the subject of crystal chemistry for the next few weeks - defined as theelucidation of the relationship between chemical composition, internal structure and physicalproperties of crystalline material.

A reminder: the chemical composition of the Earth's crust - 8 elements make up ~99 wt% of thecrust ("major elements") ... O and Si are most abundant, thus most common minerals aresilicates and oxides .

Ionic radii

Size of atoms difficult to define, let alone measure. Determined be maximum chargedensity, which itself is a function of the type and number of nearest neighbor atoms. Thereforeit is possible to assign each ion a radius such that the sum of the radii of two adjacent ions iseach to the interatomic (separation) distance. Thus we can determine effective radii bymeasuring bond lengths in crystals.


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Within a given period (say, the alkalis), the radius increases with atomic number. (Table13.1)

Radii also vary systematically across a row, being smaller at the center (cation chargeincreases) and largest to the right (the anions; Table 13.2).


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Ionic radii depend strongly upon the valencestate of the ion, with larger sizes for negative ions andsmaller sizes for positive ions (Table 13.3, 13.4).

EX:

S +6: radius = 0.6 A

S: radius = 1.04 A

S -2 radius = 1.7A

Finally, the size of an ion is dependent on its coordination number .

Coordination number

Many simple mineral structures can be viewed as close packing of large anions, withsmaller cations in interstitial sites. The anions are packed in a regular structure, while thecations fit in between. The number of anions t o which a particular cation bonds is the cationscoordination number . EX: Si +4 typically bonds to 4 O atoms, and therefore has a coordinationnumber of 4.


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The size of the interstices depends how the anions are packed different in 2- and 3-dimensions.

EXAMPLES

We give coordination arrangements geometrical names:

2-fold linear

3-fold triangular

4-fold tetrahedral

6-fold octahedral


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8-fold cubic

12-fold dodecahedral


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Closest packing

What is the most economical way to pack spheres?

2D: If spheres of equal size are packed together as closeas possible in a plane, they arrange themselves as follows:

Center of spheres are at the corners of equilateraltriangles; each sphere is in contact with 6 others. Notethat within this layer there are 3 close-packed directions,each at 60 o. Unit cell is hexagonal, with lattice parameter


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Let's add a third layer. Again, we have two choices. If third layer goes above A position: ABABABABA

simplest form of close packing - hexagonal closest packing (has underlying hexagonal lattice) this is true for Na metal

If third layer goes in the C position, stacking sequence would be ABCABCABC.

cubic closest packing

(has underlying cubic lattice). In both of these closestpacking sequences, each atom has twelve equidistant nearestneighbors, six in its own plane, and three each in the layer aboveand the layer below. Examples include Au (shown to the left), Ag,and Cu.

This simple structure means that metal atoms of similar sizecan easily substitute for each other, thus allowing for alloys ofmetals like silver and gold. Because of the close packing, metalsare dense; they are also malleable and good electrical conductors.


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Other minerals that have a cubic closest packed structure are

sphalerite halite

ZnS NaCl

Most minerals are not formed by metallicbonds, and thus do not have this simplestructure. For example, the covalent bonds ofdiamond are strongly directional, whichprevents the atoms from adopting a close-packed structure. As a consequence,

diamond has a lower specific gravity than atypical metal.


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Ion ic Bond ing

One of the most successful models for predicting crystal structure is to treat crystals aspacking of anions and cations as different sized spheres these rules are collectively known asPaulings Rule and can be summarized as follows:



3. Sharing of Polyhedral Elements I the existence of edges (and particularly faces) commonto coordination polyhedra decreases the stability of ionic structures

4. Sharing of Polyhedral Elements II in a crystal containing different cations, those withlarge valence and small coordination number tend not to share polyhedral elements with eachother.

5. Principle of Parsimony the number of essentially different kinds of constituents in a crystaltends to be small.


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Well look at each rule separately.

Coordination (radius ratio) Principle:

This principle states that the number of anions with which a cation coordinates isdetermined by the ratio of their radii r c/r a .

Bottom line: most stable configuration is achieved when oppositely charged ions (e.g.Na+ and Cl-) are as close together as possible without overlapping. Inter-ionic distancedetermined by the balance of electrostatic attractive forces between outer electron charges, andrepulsive forces between nuclei. Thus in 3 dimensions, ions with positions that follow principlesof ionic bonding form highly symmetric polyhedra ( coordination polyhedra) that have sameinter-ionic distances - will control where certain cations fit into crystal structures. Tetrahedra

and octahedra are most common structural types, but triangles, cubes, and other formsimportant. These coordination polyhedra link together in various ways to form the polyhedral-frame structures. Include all of rock-forming silicates, as well as many borates, sulfates,phosphates, tungstates, oxides, hydroxides.

To reiterate, a coordination polyhedron of anions is formed about each cation, the cation-anion distance being determined by the radius sum and the coordination number of the cationby radius ratio. Thus when bonding dominantly ionic, each cation in the structure will tend toattract, or coordinate, as many anions as will fit around it.

NaCl

Appropriate radii:

Na + = 0.097nm

Cl- = 0.181nm (almost twice as large)

r c/r a = 0.54

If we imagine these as rigid spheres, how closely can we packthem?


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First lets look at 2 dimensions. If the radius of the cation is very small relative to the cation, thecation can fit into small space between three close-packed anions. As the cation becomeslarger, the anions move farther apart. At some ratio of ionic radii, closest packing switches toone in which the cation is surrounded by 4 anions (this is the case for NaCl)

From trigonometry:

r c / r a = .414

Thus the radius ratio between anions and cations tells us how thespheres can be packed. For smaller ratios, all 4 anions would nottouch the cations, and distances would not be minimized. Forlarger ratio, distance between anions > 2ra, and eventually a newconfiguration becomes stable.

What about the third dimension? In order to maintain r c/r a = .414 (minimum separation = closestpacking), we must add two additional anions, one above and one below. Thus each cation is in6-fold (octahedral) coordination.

In general:

R c /R a Expected coordination of cation C.N.


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0.22

0.22-0.41

ideal tetrahedral

tetrahedral

4

0.41

0.41-0.73

ideal octahedral

octahedral

6

0.73

0.73-1.0

ideal cubic

cubic

8

1.0

> 1.0

ideal dodecahedral

dodecahedral

12

Lets return to our model of close -packed spheres. As you determined in lab, stacking ofclose-packed layers of spheres generates two kinds of interstices:

tertrahedral site between 4 close-packed atoms. Thus any small atom occupying thissite will be tetrahedrally-coordinated with its neighbors. Tetrahedral sites form in two distinctorientations - apex pointing up or apex pointing down. For this reason, there are twice as manytetrahedral sites as there are close-packed ions (one above and one below).

octahedral site is larger - has 3 atoms below and 3 above.


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SOME CONSEQUENCES:

A. Geometrical and electrical stability - (Ex. fluorite, CaF 2). Each Ca has8 fluorine neighbors, while each fluorine has only four Ca neighbors.

rCa = .99A rF = 1.33A rc/ra = .74

Even though relative sizes would allow closest packing, charge balancerequires the 2:1 ratio, and thus determines the structure.

Fluorite and halite illustrate another consequence of rule 2, which is that when all ionic bondshave the same strength , anions pack together in a highly symmetrical arrangement, thus theseminerals are highly symmetric. Minerals with uniform bond strengths include the oxides,fluorides, chlorides , etc.

In contrast, when there are nonuniform bond strengths , crystal structures have lowersymmetry. This is true when structures include small cations of high charge (C 4+, S 6+ , P 5+, Si 4+).

Additionally, this rule means that the number and kinds of coordination polyhedra that can meettogether at a point are severely limited. For example, no more than 2 Si 4+ tetrahedra can sharea common oxygen, even though the radius ratio considerations alone would permit three, four ormore ... each Si-O bond contributes an electrostatic strength of 4/4 = 1, so that two Si-O bondswill just satisfy the -2 charge of the oxygen. Similarly, exactly three divalent cation octahedrawill share a common oxygen with a Si 4+ tetrahedron. Mineral groups included in this categoryare the carbonates, sulfates, phosphates and silicates .


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3) Sharing of polyhedral elements. I. The existence of edges, and particularly of faces,common to two anion polyhedra in a coordinated structure decreases its stability. Directoutgrowth of electrostatic forces... Most stable configuration is when two polyhedra share only acorner, because then the two central cations are as far apart as possible.

The figure above shows that the more anions shared between polyhedra, the closer thepositively charged cations. This reduces stability, particularly when the cations are highlycharged (e.g., Si 4+).

4) Sharing of polyhedral elements II. In a crystal containing different cations, those of highvalency and small coordination number tend not to share polyhedral elements with each other.Corollary of rule three - emphasizes the fact that highly charged cations will be as far apart fromeach other as possible. Effect stronger if coordination number is low. Ex. - no silicate mineralshave edge-sharing or face-sharing Si tetrahedra. However, edge-shared octahedra arecommon (TiO 2, or, as shown in the diagram below, NaCl), and even face-shared octahedra arefound (Fe 2O 3).


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Summary:

It is possible to regard a crystal as being made up of AXn groups that are joined together bysharing corners, edges or faces of coordination polyhedra rather than as individual ions... we'llsee a lot more of these. Coordination polyhedra commonly distorted.

1. polyhedral framework structures

Most of rock-forming minerals in this category, especially silicates. All structures aredirect consequence of predominantly ionic bonds between constituent ions. As result ofbonding, anions tend to group around cations in highly symmetric manner to define coordinationpolyhedra.

Ex: silica tetrahedron (SiO 4)-4

divalent cation octahedra (MgO 6)-10

By sharing apical oxygens, polyhedra link together to define a structural frame that possesses atleast half of the total bonding energy of the mineral - resulting frame is relatively strong and hasimportant influence on most physical and chemical properties.

2. Symmetrically packed structures

Either bonds between atoms are nondirectional or bond directions are highlysymmetrical .

Ex. metallic bond, also many examples of covalent and ionic.

Atoms form highly symmetrical structures in which atoms packed together in symmetrical ways:

a) monatomic (native metals) - if atoms are in contact in and between sheets - highlyefficient packing called closest packing . If atoms lose contact within sheets but retain contactbetween sheets - close-packed.

b) mulitatomic - both cations and anions... many oxides, sulfides, halides and most ofimportant silicates considered as framework are in this category. Anions are in symmetricallypacked sites, and cation soccupy voids between. symmetry of anion packing is basiccharacteristic.


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Sheet silicates

Single chain silicates

Double chain silicates

Isolated tetrahedra

Lecture 8 OVERVIEW

Details

Composition space

Two-component systems (linear composition space)

FeO SiO 2

Fe 2SiO 4 Mg 2SiO 4

Three component systems (planar triangle)

FeO-MgO-SiO2

MgSiO 3-FeSiO 3-CaSiO 3
http://darkwing.uoregon.edu/~cashman/GEO311/311pages/Lecture%208.htmhttp://darkwing.uoregon.edu/~cashman/GEO311/311pages/Lecture%208.htmhttp://darkwing.uoregon.edu/~cashman/GEO311/311pages/Lecture%208.htm


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Chemical reactions between different mineral phases. EX:

The minerals that we find together in a given rock are a function of (1) which mineral orcombination of minerals is stable, and (2) the bulk composition of the rock.

One more ternary example: CaO-SiO 2-Al2O 3

Mineral MolesCaO

MolesAl2O 3

MolesSiO 2

% CaO % Al 2O 3 %SiO 2

anorthite 1 1 2 25 25 50 grossular 3 1 3 43 14 43 wollastonite 1 1 kyanite 1 1

v

lecture 6_crystal growth

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