Class Notes - Minerals

States of Matter

Anything that has mass and occupies space is matter. The following classification will help define the states in which matter can occur.
• Solid - rigid substance that retains its shape unless distorted by a force
  • Crystalline Solid - as above and the structure (distribution of the components) is highly regular and repetitive - long range order

  • Non-Crystalline Solid - as above but the structure exhibits a short range order - glass is an non crystalline or amorphous solid

• Liquid - flows and conforms to the shape of its container - short range order

• Gas - flows easily and expands to fill its container - disordered structure

A Mineral:
• is a crystalline solid

• is naturally occurring

• is inorganic - not formed as part of a life process

• has a fixed chemical composition or a composition that varies over a known extent

Structure of an Atom

All matter is made up of chemical elements, each of which is made up of particles called atoms. A rather crude, but useful, picture of an atom is that of a rigid sphere. The radii of these atoms are a few angstroms (where an angstrom is 10^-10 cm. There are 92 so-called naturally occurring elements of which 90 can be detected on Earth at this time. What happened to the "missing 2" will be left for you to think about.

These spheres contain a central nucleus which contains two types of particles:

• protons which carry a positive charge and
  
• neutrons which are neutral (no charge)

  For our purposes we will ignore quarks and other particles that we would encounter if this were a upper level physics course.

The atomic number is the number of protons in the nucleus of the atom. The atomic mass number is the number of protons plus neutrons in the nucleus. All atoms of an element have the same number of protons - hence the same atomic number; for example all atoms of hydrogen have one proton in the nucleus. Each element is assigned a symbol - H for hydrogen. You should learn the symbols for the eight most abundant elements in the Earth's crust [Oxygen (O), Silicon (Si), Aluminum (Al), Calcium (Ca), Iron (Fe), Magnesium (Mg), Sodium (Na), and Potassium (K)] .

Calcium is atomic number 20. Therefore,

There are 20 neutrons in the nucleus of a Calcium atom
There are 20 protons in the nucleus of a Calcium atom
A Calcium atom weighs 20 atomic mass units


If we could weigh individual atoms of calcium we would find some variation in their mass; this must be due to variations in the number of neutrons in their nucleus as all must have the same number of protons - 20. Atoms which have the same atomic number but different mass numbers are isotopes. For example, all calcium atoms have an atomic number of 20 but there are three isotopes of calcium - 39, 40, and 42. (How many neutrons does each isotope possess?)

A calcium atom is found with a mass of 42. Therefore,

there are 20 protons and 22 neutrons in its nucleus
there are 20 neutrons and 22 protons in its nucleus
there are 20 protons and 42 neutrons in its nucleus


In addition to the particles in the nucleus, there are negatively charged particles - electrons which "orbit" the central nucleus. Recognition that the distribution of electrons around the nucleus is not random was one of the great accomplishments of physicists in the 1920s - quantum mechanics.

Electrons occupy "levels" which are separated from each by some volume of space which electrons can pass through but not remain. In fact, much of the volume of an atom consists of empty space. [I remember that this is how Superman was able to pass through solid objects!] Electrons are "attracted" to the nucleus (positive and negative charges attract).

The primary division of these levels is called the principal quantum number. The first level (K) is closest to the nucleus. As the principal number increases 1...2....3....4 the number of electrons that can reside in the level increases.

Level	Electrons
K	2
L	8
M	18
N	32

The maximum occupancy = 2n² where n is the level ... 1, 2, 3, 4, etc.

In a neutral atom the number of negative particles equals the number of positive particles (electrons = protons).

A atom of calcium has 20 neutrons. Therefore,

its mass number is 40
there are 20 protons in its nucleus
there are 20 electrons surrounding is nucleus
all of the above are correct


A useful exercise is to start with the first element (Hydrogen) with its one proton and one electron and add protons and electrons to build up the remaining chemical elements. The build-up process works as follows. Start with a single electron - it occupies the empty level closest to the nucleus. The second electron goes into the first level (atomic Helium) and the shell K) is filled. Actually, there are sub levels within the main level (except for the K-shell).

Sub Shell	Max Electrons
s	2
p	6
d	10
f	14

For element 11 (Sodium - Na) there are 11 electrons and 11 protons. Two electrons are in the K shell, 8 in the L shell and one in the M shell. The outer most electron(s) are termed the valence electrons.
If one electron is removed from a sodium atom

there is one more negative charge than positive charge : -1
there is one more positive charge than negative charge : +1


Main Level	Orbitals
K	1s (max = 2) Total = 2
L	2s (max = 2), 2p (max = 6) Total = 8
M	3s (max = 2), 3p (max = 6), 3d (max = 10) Total = 18

An ion is a charged atom; that is, there is an excess of positive (cation) or negative charge (anion). If an electron is removed a cation is formed. If an electron is added an anion is formed. Of the eight most abundant elements in the Earth's crust only Oxygen forms anions; the rest form cations by loosing one or more electrons. When there are 8 outer most electrons in the s and p sub shells the atom has a tendency to resist change and ions are formed with great difficulty if at all.

An atom of element Z has 40 protons. Therefore, the outer most, valence electrons are in which main shell?

K
L
M
N


How many of the 40 electrons are in the outer most level?

12
10
22
40


Chemical Bonding

Most elements in the Earth react to form compounds although there are a few which are stable as elements (gold, for example). There are several "bonding models" which need to be summarized.
• Ionic Bonding - Element 11 (Sodium) has a single valence electron which can be relatively easily lost as it is relatively far from the positive charges in the nucleus. Oxygen needs (atomic number 8) needs two electrons to give it full s and p subshells. The compound Na₂O consists of two Sodium cations and one Oxygen anion. Each Sodium contributes a single electron to the Oxygen giving the Oxygen a charge of -2. This compound is "held together" by ionic bonds.

• Covalent Bonding - Carbon contains 6 electrons and 4 of them are in the outer most level (the L level). Two carbons could bond by sharing their four electrons which would create the full s and p subshells in the L main shell. Covalent bonding involves sharing electrons.

• Metallic Bonding - Metals are known for their ability to conduct the flow of electrons. Metallic Bonding involves a "smearing out" of the valence electrons of the metal atoms. These electrons are easily displaced.

• van der Waals Bonding The carbon atoms in graphite are covalently bonded to form sheets of carbon atoms. The sheets are held together by weak attractive forces.

The Periodic Table provides a framework in which to place the chemical elements so that their similarities are recognized. Look at the properties of Oxygen and Silicon - the two most abundant elements in the Earth's crust - by clicking on their symbols on the Periodic Table.

The recognition that the elements could be arranged in a systematic way so as to emphasize relationships between elements, was a major break through in the history of chemistry. For example, all of the elements in the first column (the alkali metals) have a single outermost electron in its outermost sub shell (an s sub shell). All of these elements can lose a single electron forming a cation with a +1 charge. All of the elements in the column on the far right (inert or Nobel gases) have two s electrons and eight p electrons in their outermost level (called the valence level). Note that the Periodic Table has the shape of a distorted "H". The vertical bars (sides of the H) contain the A group elements. The central bar contains the "transition" elements. Down at the bottom of the page are two rows - the "Lanthanides" and the "Actinides". Look to see where these rows fit into the "H". If these rows which shown in proper position the Periodic Table would be less compact.

The Chemical Composition of the Continental Crust

Eight elements make up about 99% of the weight of the continental crust
1. Oxygen ~ 50%
2. Silicon ~ 25%
3. Aluminum
4. Iron
5. Calcium
6. Sodium
7. Magnesium
8. Potassium

Mineral Structures

Think about the statement that oxygen occupies 95% of the volume of the Earth's crust. If oxygens were cubes they could be packed together to fill up space. However, the oxygens are presumed to be spheres and you cannot pack equal sized spheres to fill up all space; some open spaces will remain inside of the framework produced by the oxygens. Other ions fit into these open spaces. In general, these spaces are "regular".

One common type of space is that created when there are three oxygens on the bottom and one on the top. This is called a "tetrahedral void". (A tetrahedron is a regular solid consisting of four faces, each of which is an equilateral triangle.) The larger the ion the larger the preferred site.

The coordination number of a cation is the number of nearest neighbor anions. Silicon, with one exception, prefers to "sit" in a tetrahedral void formed by packing Oxygen anions together. Thus, silicon usually has a coordination number of 4. Coordination numbers are used to produce a structural formula.

Remember that the subscripts give the number of ions in one formula unit and the numbers above the chemical symbols given the coordination numbers.

Quartz				
4
SiO2

Stishovite
6
SiO2

Quartz and Stishovite are polymorphs (many forms). They have identical chemical compositions but differ in structure and hence in physical properties. An increase in pressure favors a larger coordination number. Temperature has the reverse effect. If a large meteorite were to impact quartz then stishovite might form (if the pressure were sufficiently high).

Other polymorphs are:

• diamond and graphite (both carbon)
  
• calcite and aragonite (both calcium carbonate)

  

  Calcite and aragonite differ in structure in that in calcite each calcium ion is surrounded by 6 nearest neighbor oxygens. This is an octahedral structure. In aragonite each calcium ion is surrounded by 9 nearest neighbor oxygens. Which of these two minerals has the highest density?

  aragonite
  calcite
  

In the definition of a mineral it was noted that a mineral has a fixed composition (like quartz) or a composition that is variable within a limit. Consider the two minerals Forsterite and Fayalite.

Forsterite				
6   4
Mg2SiO4

Fayalite
6   4
Fe2SiO4

Note that the two minerals differ chemically in that one has Mg (magnesium) and the other Fe (iron). The rest of the chemical formulas are identical. Note that both Mg and Fe sit in 6 fold sites (octahedral). The sizes of these two ions are nearly identical, the charge on both is +2 and the Mg-O and Fe-O bonds are dominately ionic in nature. When such similarities occur the ions may substitute for each other forming a solid solution series. The series between these two end members is called the olivine series. Compositions range from pure Forsterite to pure Fayalite. Not all solid solution series are complete; some exhibit a limited amount of substitution.

Almost all of the common minerals we will work with are solid solution series. Quartz is the notable exception.

Classification of Minerals

The broadest classification of the nearly 3,500 known minerals is based on chemical composition. Thus, we recognize Native Elements (individual chemical elements), Carbonates (containing the CO₃ group, Silicates (containing Silicon and Oxygen) and other broad chemical groups.

Chemically, the silicates are very complicated and not much progress was made in understanding until a structural classification was devised. The most common "structural element" is the silicon/oxygen tetrahedron. The simplest structural class of silicates consists of those compounds (minerals) which consist of isolated single tetrahedra - the Nesosilicates. Tetrahedra can share oxygens between themselves. Two, three and four oxygens per tetrahedron can be shared and in some structures two or more sharing schemes exist. The most common minerals are listed below. (keep in mind that all of these contain Si and O and many also contain Al).

Mineral	Structural Type	Composition
Olivine	Isolated	Fe and Mg rich
Pyroxene	Single Chains	Ca, Fe, and Mg rich
Amphibole	Double Chains	Ca, Fe, Mg and K rich (with "OH")
Mica	Sheet Silicates	K, Na rich (with "OH")
Plagioclase	Tectosiicates	Ca and Na rich
Alkali Feldspar	Tectosilicates	Na and K rich
Quartz	Tectosilicates	Si

In addition, the following mineral groups are important - especially in the sedimentary rocks

Carbonates
Sulfates
Salts

Silicate Structural Classification. [then return to this page]

Questions

Use the section on Properties to help answer the following questions.

• Distinguish between fracture and cleavage

• What is luster?

• What is specific gravity? The specific gravity of the continental crust is about 2.7 whereas the specific gravity of the oceanic crust is 3.0.

• Quartz and Feldspar are the two most abundant minerals in the Earth's crust. How does this fit with the list of most abundant elements in the Earth's crust?
  • Continental Crust - Alkali Feldspar
    
  • Oceanic Crust - Plagioclase

Hardness

Mineralogists usually measure hardness using a relative scale devised by Frederick Mohs. Mohs scale ranges from Talc with a value of 1 to Diamond with a value of 10. Diamond is NOT 10 times harder than Talc.

Quartz has a hardness of 7 and Talc has a hardness of 1. Is Quartz seven times harder than Talc? Explain what type of scale Moh's Scale is and how to use it. How is a diamond "cut"?

The following interactive problem is modified from the National Association of Geoscience Teachers.

An ionic bonded material consists of anions and cations which exert a force of electrical attraction toward each other. The value of this attraction is proportional to the product of the charges (C) on the two ions divided by the square of the distance between them:

Force of Attraction = C_cation*C_anion/Distance²

We will assume that the cations and anions just "touch" so that the distance is given by the sum of their radii.

We will take the absolute value of the calculated force - that is, the force must be a positive number.

Cations are positively charged.

True
False


Ion	Ionic Radius	Charge
Calcium - Ca	1.00 A	+2
Chlorine - Cl	1.80A	-1
Fluorine - F	1.40A	-1
Magnesium - Mg	0.7A	+2
Sodium - Na	1.00A	+1

Calculate the force of attraction for CaF₂.

0.83
0.35
0.50


Calculate the force of attraction for NaF.

0.18
0.42
0.50


From your calculations above, CaF₂ is harder than NaF.

True
False


Therefore, when the distances of separation are equal, the compound with the highest charged ions will be the softest.

True
False


Calculate the force of attraction for NaCl.

0.35
0.12
1.66


Compare NaCl with NaF. Which of the two should be harder?

NaF
NaCl
they have the same hardness


Therefore, when two compounds have ions of the same charge, the one with the smaller ion is the hardest.

True
False


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Copyright by John C. Butler, July 29, 1995

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