Earth Scientist Association (ESA)

About

The Earth Scientist Association (ESA), is the students and Professionals association of the Geoscientists, it is an organization with an academic profession

Mission

ESA organizes the following activities for its members:

Events (conferences, exhibitions, workshops)
Publications (journals, books)
Educational Programmes (short courses, lectures)
Student Programmes
Recruitment

Description

The aim of the ESA is to increase the profile of earth science in general by field trips, information and opportunities concerning jobs in earth sciences, and a common ground for students with common interests to interact and have fun.

Objectives:

The Association shall be to promote the development and application of geosciences related their subjects, to promote innovation and technical progress and to foster the communication, fellowship and cooperation between those working in, studying or otherwise being interested in this fields.ESA is committed to achieving and maintaining excellence in all aspects of its activities.
Encourage the participation of Member in the geosciences
Enhance the professional growth and advancement of Member in the geosciences

General Information

The ESA is a club by and for the students. IN order to establish our goals, the ESA makes available several activities during the semester, like seminars, field trips, excursions to companies and institutions, tutoring and fundraising.
The ESA consists of mainly earth scientists; however other students are encouraged to become members of the ESA.

Structural Geology

Lecture 19

Joint Patterns

(The orientation and spacing of joints, veins, and dikes)

Two parameters influence fracture patterns: the orientation of the the fractures and their frequencies.   Orientation of fractures is based on the state of stress within the rock -- both stress difference and orientation of the principal stresses.  In contrast, the frequency or spacing of fractures is based on the properties of the rocks in which the fractures have formed (Fig. 19-1).

Fig. 19-1

The solution to the fracture spacing problem is found by recalling that the critical stress intensity factor (KI) is

                                        KI  =  (s3)(πc)1/2                                                         

where c is the crack length.  Here stress intensity is a function of crack length and, thus, is independent of the lithology.  However, in a bedded quartzite-limestone sequence, we predict that a quartzite will have more closely spaced joints if a given extensional strain is responsible for generating larger tensile stress.  The Young’s Modulus for quartzite is greater than for limestone.  Hence, by applying Hooke’s law we predict that tensile stress in a quartzite bed might be larger for a given unit of strain.  If tensile stress increases as a consequence of the thermal cooling of rock the following equation for the development of thermal stresses might apply:

                                       

where E is the Young’s Modulus, a is the coefficient of thermal expansivity and DT is the change in temperature.  This equation also suggests that when quartzite and an adjacent limestone bed are subject to the same thermal change, tensile stress in the quartzite builds up faster because Young’s Modulus and thermal expansivity for quartz are larger, and hence,

                                        sqtz  >  sls                                                                     

So, the fracture intensity of the quartzite is larger and jointing will form on a closer spacing.

Fig. 19-2

Fracture nomenclature is in part tied to the type of rock in which the fractures have formed.  Orientation also plays a role in fracture nomenclature.  For example, Balk documented several types of fractures in granite bodies (Fig. 19-2).  The type of fractures are based on their relationship to the flow lines of the granite as well as the orientation of the surface of the granite body.   It is fair to assume that most joints in granites originate as extension fractures.   Sheeting joints for parallel to the topographic surface and are generally subhorizontal.  Longitudianl joints are steeply dipping which parallel the flow lines.  Cross joints in granites form perpendicular to flow lines. 

Granite quarries are laid out based on the direction in which the granite breaks in tension most easily.  The quarrymen call this direction of easy breaking the rift.  Flow lines and the longitudinal joints are ofter parallel to the rift of a granite.  The grain of a granite is the direction of next easiest breaking.  Sheeting joints may well parallel the grain of the granite.  In New England granites the orientation of the grain and rift may appear in the opposite orientation as described (i.e. sometimes the rift parallels the topography.   The hardway of the granite is the direction in which the granite is most difficult to break.  The hardway is vertical in all New England granites.

In sedimentary rocks the joint nomenclature depends on the orientation of local structures, most commonly the fold axis.  Stearns pointed out the folded sediments may have four fracture sets (Fig. 19-3).

(Fig. 19-3)

Each set may consist of up to three fractures: an extension fracture and conjugate shear fractures.  Conjugate shears form so that the acute angle between the shears faces s1.  Each of the sets has no particular name, however, the extension fractures may be referred to as either  cross joint (i.e. that group of joints perpendicular to the fold axis) or a strike joint (i.e. that group of joints parallel to the fold axis).  Here the term cross joint in a sedimentary rock refers to a different type of joint than that found in a granite.

A different set of nomenclature was developed for joints in flat-lying sedimentary rocks.  Hodgson observed that in the absence of shear fractures in sedimentary rocks there may be several joint patterns.  The most common three patterns are shown in Figure 18-4.

Extension joints are not one long discontinuity but rather several joints that form end-to-end in a joint zone.    Some authors preferred to restrict the term joint to extension fractures.  This is the case with Hodgson.  The line that an individual joint makes on the outcrop surface is called the joint trace.   Joint zones are often parallel to other zones within the outcrop.  These joint zones make up one joint set and are called systematic joints.   Often there are joints that form roughly perpendicular to the systematic joints.  If these latter joints are themselves systematic joints they may be called cross joints.  Otherwise they are non-systematic joints.  Here we see a third use of the term cross joint.

(Fig. 19-4)

(Fig. 19-5)

Conjugate shear fractures may be used to map s1is the vicinity of a fault zone.  For the Bonita Fault, a normal fault in New Mexico, the s1 is vertical as witnessed by the orientation of shear fractures in the fault zone  (Fig. 19-5).  Yet, as the fault is approached the local rocks are seen to drag into the fault zone.  Likewise, the conjugate shears rotate into the main Bonita Fault suggesting that the stress field was not homogeneous near the Bonita Fault.  In the case of the Bonita Fault each of conjugate shear fracture is inself a smaller normal fault.

Shear fractures in and around anticlines and synclines may vary in orientation.  For some limestones in Morocco, de Sitter showed that the acute angle of the conjugate shears faced parallel to the fold axes over anticlines yet faced perpendicular to the fold axes over the synclines (Fig. 19-6).

(Fig. 19-6)

On the New York portion of the Appalachian Plateau Engelder has used extension fractures to map the stress field during the Alleghanian Orogeny (Fig. 19-7).  Here there appear to be a conjugate set of shear fractures.  Yet, surface morphology studies and butting relationships show that all fractures are extension in origin.  These extension fractures may be called cross-fold joints.  The double pattern of cross-fold joints indicates that there were at least two phases of compression during the Alleghanian Orogeny.

 Evidence that joint sets are an accurate indicator of the maximum principal stress within the crust come from two areas.  Volcanic dikes may be thought of as equivalent to extension fractures.  In the Aleutian Peninsula of Alaska volcanic dikes parallel the direction of subduction of the Pacific Plate under North America (Fig.  19-8).  It is well known that the orientation of maximum principal stress in the lithosphere is parallel to subduction directions.

Dikes around the Spanish Peaks area of Colorado can also be used for stress markers at the time of injection.  Ordinarily the stress around a hole in an elastic plate would be radial.  However, if there is a tectonic stress in the vicinity of the hole then the stress trajectories is deflected away from this radial pattern.  The Sangre de Cristo Mountains served as a ram forcing the ß⁄ into the east-west direction.  This can be seen by the deflection of some of the dikes from the Spanish Peaks into the east-west orientation  (Fig. 19-9).

(Fig. 19-7)

(Fig. 19-8)

Fig. 19-9

Siderites or Iron Meteorites

Siderites or Iron Meteorites:

·         Iron Meteorite or siderites, found in 1864 in the Sahara Desert  weight about 500 kg. On display at Vulcania park in France.

·         Siderites are meteorites that consist of nickel–iron alloys.

·         The metal taken from these meteorites is known as meteoric iron and it was one of the earliest sources of usable iron available to humans.

·         Siderites are very dense and nonporous specimens, and are thus much heavier than most comparably-sized rocks found in the Earth's crust.

·         They also have metallic silver-colored interiors.

·         Siderites are thought to be the fragments of the core of larger ancient asteroids that have been shattered by impacts.

·         Only 6% of meteorites are iron meteorites in total numbers of meteorites in the solar system.

·         About 5% of meteorites that fall are iron meteorites with intergrowths of iron-nickel alloys, such as kamacite and taenite.

Principles of Crystal Chemistry

Principles of Crystal Chemistry

Our discussion of bonding led us to conclude that the bond character is determined primarily by the electronic configurations and electronegativity values of the combining elements, whereas the crystal structure (which controls the shape and system of the crystal) is a function of the plane lattice and the coordination number(s) (C.N.).

I- Coordination Number

1-      Is the number of nearest neighbors in a crystal structure. It depends on the radius ratio + type of hybridization in covalent ones (Table 1) and the radius ratio in ionic structures (Table 2).

2-      Whereas the C.N. is strongly controlled by the radius ratio, the radius of an ion (or atom) may (and usually does) change as a function of the C.N. (Fig. 1; Table 3). Other factors influencing the size of an ion are its charge, the atomic number of its element, and the “shielding” effect of some electrons, especially those of the penultimate shell. Of particular interest is the “lanthanide contraction”.

3-      Coordination numbers are usually 2, 3, 4, 6, 8, or 12. C.N.’s of 5, 7, 9, 10, or 11 are much less common, but can occur in some cases!

Some Examples of C.N. (Fig. 2)

Halite: NaCl

Na : Cl = 6 : 6

Sphalerite: ZnS

Zn : S = 4 : 4

Fluorite: CaF₂

Ca : F = 8 : 4

II- Structure Controls for minerals with metallic bonding:

·         Bonding takes place between electropositive elements of similar electronegativities.

·         Radii of the combining elements are also similar; radius ratio (r_A/r_B) @ 1.

·         Three types of packing (Fig. 3):

1.      Hexagonal close packing “HCP”: layers arranged in the pattern: ABAB. C.N. = 12.

2.      Cubic close packing “CCP”: layers arranged in the pattern: ABCABC. C.N. = 12.

3.      Body centered cubic packing: lower density structure; C.N. is always 8.

·     Close packing results in the high density observed for metals and alloys.

III- Structure controls for minerals with covalent bonding:

·         Hybridization of the orbitals forces this type of bonding to have a strong directional character.

·         Because of hybridization, the covalent radius of an element will be different from its ionic or metallic radii.

·         The structure of the mineral will be controlled by (i) the covalent radii of the elements; (ii) the type of hybrid resulting (Table 1); same factors that affect the C.N.!

IV- Structure controls for minerals with ionic bonding:

Pauling’s Rules for ionic compounds:

Rule 1:-

Cation – anion distance in a structure determined by radius sums, C.N.’s determined from r⁺/r^- (Table 1).

For this rule, the following points are very important:

1-      The r⁺/r^- limiting values for the different coordination numbers are derived by simple rules of geometry and trigonometry (Figs 4 & 5).

2-      If the r⁺/r^- falls very close to one of the limiting values (e.g. 0.414), then the same compound may have two different structures (in this case, one with a C.N. of 4; the other with 6). This may result in polymorphism.

3-      Because Oxygen is the most abundant element in the Earth’s crust, and because it is strongly electronegative, most of the common rock-forming minerals have a significant ionic character. Accordingly, relative to Oxygen, elements will have a fairly predictable size and coordination number. Common coordination numbers for some cations are listed in Table 3. Please make a strong effort to remember these!

Rule 2:

Electrostatic valency principle: The total strength of the valency bonds that reach an anion from all the neighboring cations is equal to the charge of the anion (Fig. 6).

Electrostatic valency = Z/C.N.                       (Where Z is the charge of the cation).

Strength of bond = sum of its electrostatic valencies.

This rule is useful for constraining the types of polyhedra in a crystal structure.

Example: Find the # of Ca²⁺ ions bonded to O in the structure of calcite, knowing that the C.N. of Ca²⁺ (to O) = 6. Use Pauling’s second rule knowing that the carbonate radical has a trigonal planar structure.

e.s.v. for CO₃^-2 = Z (for C)/ C.N. = 4/3

e.s.v. for Ca ²⁺ = 2/6 = 1/3

Let x be the # of Ca²⁺ linked to O in Calcite,

\x . 1/3 + 4/3 = 2

Þ x = 2.

Example 2:

e.s.v for Si – O = 4/4 = 1

            = ½ of 2 Þ (2 Si can link to one O)

\2 or more tetrahedra can become linked at their apex by sharing one of their oxygens.

This process, by which different tetrahedra are linked to each other, results in the formation of rings, chains, sheets or frameworks, and is known as polymerization.

Types of ionic compounds according to electrostatic bond strength:

1-      Isodesmic compounds: Crystals or compounds in which all bonds are of equal strength are known as isodesmic (Example: the Spinel group (MgAl₂O₄)). In the case of the spinels, there are 2 polyhedra. The contribution of oxygen to each of these two polyhedra is 2, which makes the mineral isodesmic. Isodesmic compounds are characterized by high symmetries, crystallizing in the cubic, tetragonal or hexagonal systems. Oxides, halides, and hydroxides are isodesmic.

2-      Anisodesmic compounds: Are ones that have different bonds with different bond strengths. Sulfates and carbonates are anisodesmic. Carbonates, phosphates and sulfates fall into this group.

3-      Mesodesmic compounds: Are ones in which one particular cation always accounts for half of the total bond strengths in the compound. Silicates are mesodesmic.

Rule 3:

Polyhedra are usually joined at their corners; joining at their edges is much less common, whereas joining by sharing faces is rare (Fig. 7). Sharing of faces among polyhedra generally decreases the stability of the structure, especially if the centers of these polyhedra are occupied by cations with high valency and small coordination numbers. This effect is especially large when the radius ratio approaches the lower stability limit of the polyhedron.

Rule 4:

In a crystal with different cations, those cations with high valency and small C.N. tend not to share polyhedral elements with each other. However, if they do, the polyhedra become distorted. This is necessary to minimize cation – cation repulsion.

Rule 5:

The number of essential sites in a crystal structure that are substantially different (i.e. with differences in size and coordination) tends to be small. On the other hand, many of these sites may be occupied by different ions, leading to the phenomenon of “isomorphism”. This is known as the “principle of parsimony”.

Example: Amphiboles are minerals that often contain 13 different elements (or more!), and are characterized by the formula:

A_0-1B₂C₅T₈O₂₂(OH,F,Cl)₂

Although this group of minerals has a large # of different sites (relative to most other minerals), there are only 5 such “different” sites:

A: occupied by K or Na in 8 or 12 coordination

B sites: filled with Na, Li, Ca, Fe²⁺, Mg and Mn²⁺ in six or 8 coordination

C sites: filled with Mg, Fe²⁺, Mn, Al, Fe³⁺, or Ti all in six coordination

T sites: filled with Si or Al, in 4 coordination; and finally,

Hydroxyl sites: where F and Cl may substitute.

IV- Calculation of the number of formula units per unit cell “f”:

Density of mineral = weight of unit cell/volume of unit cell (V)

Weight of the unit cell = molecular weight . # of formula units in the cell (f)/ # of formula units in 1 mole.

The # of formula units in 1 mole is Avogadro’s # (A = 6.023 . 10²³).

D = Mol. Wt . f/A. V

f = D . A . V/Mol. Wt.

V- Isostructuralism and Isotypism:

Isotypes: Two minerals are considered isotypes if they have the same structures (arising from similar C.N.’s and r⁺/r^- values), but otherwise have no chemical relations between them. Examples: Galena and Halite, NaNO₃ and CaCO₃, Stishovite and Rutile.

Isostructural groups: Minerals are considered isostructural if they have the same structures (same C.N.’s), and same anionic group (but obviously different cations, and hence different r⁺/r^- values. Examples are members of the aragonite group (aragonite, strontianite, witherite, and cerussite).

VI- Some important crystal structures

1-      Diamond (covalent): F 4₁/d  2/m; C.N = 4 (Fig. 8)

2-      Graphite (covalent): P 6₃/m m c; C.N. = 3 (Fig. 9)

3-      Sphalerite: F  3 m, C.N. = 4 (Fig. 10)

4-      Halite (ionic): F 4/m  2/m, C.N. = 6 (Fig. 11)

5-      Pyrite (ionic/metallic): P 2/m , C.N. = 12:6 (Fig. 12)

6-      CsCl (ionic): P 4/m  2/m, C.N. = 8 (Fig. 13)

7-      Fluorite (ionic): F 4/m  2/m, C.N. = 8:4 (Fig. 14)

8-      Calcite: P  2 m, C.N. = 6:6:2 (Fig. 15).

9-      Spinel: F 4₁/d  2/m, C.N.: Mg:O = 4:1, Al:O = 6:3, Mg:Al = 4:2 (Fig. 16)

10-    Perovskite: P 2₁/c 2₁/m 2₁/n, C.N.: Ca:O = 12:4, Ti:O = 6:2, Ca:Ti = 8:8 (Fig. 17)

VII- Structure of Silicates

·         The bond between Si and O has a mixed character, and is approximately 50% ionic and 50% covalent.

·         Remember, silicate structures are mesodesmic.

·         Si is tetravalent, whereas O is divalent. Therefore, if both elements are to form an electrically neutral compound, it would be SiO2 (equivalent mineral would be quartz or one of its polymorphs).

·         A Si atom may also combine with two more oxygens to form a negatively charged group (SiO4)-4. This group will always be tetrahedral as dictated by the radius ratio of Si to O. This is the basic building block of all silicate structures.

·         For this group to form an electrically neutral mineral, it needs to combine with two divalent cations, one monovalent and one trivalent cation, or four monovalent cations, of a specific size or size range. The most common minerals with this structure are olivines: (Fe,Mg)2SiO4 formed of single tetrahedra. Separate tetrahedra that are adjacent to one another may polymerize by sharing Oxygens, giving rise to more complex structures or networks of tetrahedra with different charges.

·         The reason for polymerization of tetrahedra can be understood from applying Pauling’s second rule; the e.s.v. between Si and O = 4/4 =1, which is equivalent to ½ the bonding strength of O^-2. Two tetrahedra may therefore be linked through a bridging or shared oxygen.

·         The degree of polymerization will depend on the conditions of formation or crystallization of the silicate mineral, and may be used to subdivide silicates into six groups (Fig. 18; Table 4).

Types of silicate structures:

(1) Nesosilicates (orthosilicates): with isolated tetrahedra linked by bonds sharing oxygen through cations. Example: olivine.

(2) Sorosilicates: consisting of two tetrahedra sharing one oxygen (Si2O7)-6. Example: hemimorphite Zn4Si2O7(OH)2.H2O

(3) Cyclosilicates: more polymerized, consisting of closed rings of 3, 4 or 6 tetrahedra each sharing 2 oxygens (Si3O9)-6, (Si4O12)-8, (Si6O18)-12. Example: tourmaline

(4) Inosilicates: consisting of single chains of tetrahedra, each sharing two oxygens (Si2O6)-4 (e.g. pyroxenes), or double chains of tetrahedra in which each tetrahedron shares three oxygens (Si4O11)-6 (e.g. amphiboles).

(5) Phyllosilicates: Continuous sheets of hexagonal networks of tetrahedra formed by sharing three oxygens (Si4O10)-4. Individual sheets are bonded to each other by the "interlayer cations", resulting in the minerals developing excellent cleavage which separates it into individual sheets. Example: micas.

(6) Tectosilicates: Three-dimensional networks of tetrahedra, each sharing all four of its oxygens (e.g. Feldspars).

It should be noted that Al+3 may substitute for Si+4 in many of the above structures, as both cations are of comparable sizes. This substitution increases the negative charge of the overall structural group, and must be compensated for in any mineral by another substitution that will increase the total number of positive charges to maintain electrical neutrality.