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# Geology Civil Services Paper 2 Section- A, Questions 1-2_ Solutions

1. (a) How are Miller Indices of a crystal face calculated ? Calculate Miller Indices of following two crystal faces:

(i) A face intersects all three crystallographic axes at 3-unit distance.

Answer : Miller indices are used to describe crystallographic planes in a crystal lattice. The Miller indices of a plane are denoted as (h k l) and are defined as the reciprocals of the intercepts of the plane on the three crystallographic axes. To calculate Miller indices of a crystal face, we need to determine the intercepts of the face on each of the crystallographic axes, take the reciprocals, and then simplify the resulting values to the smallest integer values.

Let's calculate the Miller indices of the given crystal face that intersects all three crystallographic axes at 3-unit distance.

To determine the intercepts of the face on each axis, we can draw a coordinate system where the axes intersect at the origin. Then, we can draw a perpendicular line from the face to each axis and determine the length of each intercept. Since the face intersects each axis at 3 units distance, the intercepts are (3, 0, 0), (0, 3, 0), and (0, 0, 3) along the x-, y-, and z-axes, respectively.

Taking the reciprocals of the intercepts, we get (1/3, 0, 0), (0, 1/3, 0), and (0, 0, 1/3) along the x-, y-, and z-axes, respectively.

To simplify these values, we can multiply each value by a common denominator to get integers. In this case, the common denominator is 3. Multiplying the values by 3, we get (1, 0, 0), (0, 1, 0), and (0, 0, 1) along the x-, y-, and z-axes, respectively.

Therefore, the Miller indices of the given crystal face are (1 0 0) or simply (100) in shorthand notation.

Note that there can be multiple faces with the same Miller indices in a crystal lattice, depending on their orientation with respect to the axes.

(ii) A face intersects a-axis at 4-unit distance and is parallel to b and c axes.

Answer : How are Miller Indices of a crystal face calculated ? Calculate Miller Indices of following two crystal faces :

A face intersects a-axis at 4-unit distance and is parallel to b and c axes.

Miller indices are a set of three integers that describe the orientation of a crystal face in a crystal lattice. The Miller indices are defined as the reciprocals of the intercepts of the crystal face with the three axes of the crystal lattice, multiplied by the smallest integer that will make all three indices integers.

To calculate the Miller indices of a crystal face, we first determine the intercepts of the face with the three axes of the crystal lattice, and then take the reciprocals of these intercepts. We then multiply these reciprocals by the smallest integer that will make all three indices integers. The resulting integers are the Miller indices of the crystal face.

For the given crystal face that intersects the a-axis at 4-unit distance and is parallel to b and c axes, the intercepts of the face with the three axes are:

a-axis intercept: 4 units

b-axis intercept: infinite (since the face is parallel to the b-axis)

c-axis intercept: infinite (since the face is parallel to the c-axis)

Taking the reciprocals of these intercepts and multiplying by the smallest integer that will make all three indices integers, we get:

(1/4, 0, 0)

Therefore, the Miller indices of the given crystal face are (1 0 0).

1.(b) Explain the phenomena of solid solution and exsolution in minerals.

Answer : Solid solution and exsolution are phenomena that occur in minerals, and both are related to the way that atoms or ions are arranged in the mineral's crystal lattice.

Solid solution is the mixing of two or more chemical elements or compounds in a solid state to form a single, homogeneous phase. In mineralogy, solid solution is often used to describe a mineral that has a variable composition due to the substitution of one or more ions or atoms within its crystal structure. This means that different minerals can have the same crystal structure, but have different compositions.

For example, the mineral olivine is a solid solution of two iron-magnesium silicates, forsterite (Mg2SiO4) and fayalite (Fe2SiO4). The two end members of the solid solution series are pure forsterite and pure fayalite, and olivine can have any composition between these two end members. This is because the magnesium and iron atoms can substitute for each other within the crystal structure of the mineral.

Exsolution, on the other hand, is the process by which a homogeneous solid solution separates into two or more distinct phases due to a change in temperature or pressure. This occurs when the two elements or compounds that were previously dissolved in the solid solution become immiscible, or no longer able to mix together. As a result, they separate out into separate regions within the mineral's crystal structure.

For example, the mineral orthoclase feldspar can exhibit exsolution of two different minerals, albite and microcline, as it cools from high temperatures. The two minerals separate out into distinct regions within the crystal structure of the feldspar, forming lamellae or thin layers of alternating albite and microcline.

In summary, solid solution and exsolution are two important phenomena in mineralogy that describe the mixing and separation of chemical elements and compounds within a mineral's crystal structure.

1. (c) Describe with suitable sketches `intergranular' and 'sub-ophitic' textures. How do you explain presence of both these textures in a mafic rock ?

Answer : Intergranular texture is a type of texture in rocks where the mineral grains are clearly visible and are separated by intergranular spaces or voids. This texture can be seen in a cross-sectional view of a rock sample. Here is a sketch of intergranular texture in a mafic rock:

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___________

| |

| O |

|___________|

| O |

|___________|

| O |

|___________|

| O |

|___________|

| O |

|___________|

In this sketch, "O" represents individual mineral grains, and the spaces between them are the intergranular voids.

Sub-ophitic texture is a type of texture in rocks where the mineral grains are too small to be seen with the naked eye. This texture can only be observed under a microscope. Here is a sketch of sub-ophitic texture in a mafic rock:

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___________

| |

| OOOO |

|___________|

| OOOO |

|___________|

| OOOO |

|___________|

| OOOO |

|___________|

| OOOO |

|___________|

In this sketch, "OOOO" represents individual mineral grains that are too small to be seen with the naked eye.

Both of these textures can be present in a mafic rock because the rock may have undergone different types of cooling during its formation. Mafic rocks are typically formed from magma that has a high iron and magnesium content and low silica content. If the magma cools slowly, the minerals have time to grow into larger crystals, resulting in intergranular texture. If the magma cools rapidly, the minerals do not have time to grow into large crystals, resulting in sub-ophitic texture. Therefore, both textures can be present in a mafic rock depending on the cooling rate during its formation.

1(d) How do increasing pressure and temperature either singularly or jointly, metamorphose a rock ?

Answer : Increasing pressure and temperature can both independently and jointly metamorphose a rock. This process is called metamorphism, and it occurs when rocks are exposed to conditions that are different from those under which they originally formed.

When a rock is subjected to high pressure, it can become more dense and compact, which can cause changes in its mineral composition and texture. This is called pressure metamorphism, and it typically occurs in rocks that are buried deep within the Earth's crust. The increased pressure can cause minerals to recrystallize, forming new minerals that are more stable under the new conditions. This can result in the formation of new rock types, such as schist and gneiss.

Similarly, when a rock is exposed to high temperatures, its mineral composition can also change. This is called thermal metamorphism, and it typically occurs when rocks are heated by magma or hot fluids circulating through the Earth's crust. The heat can cause minerals to recrystallize or melt, forming new minerals or even creating new rocks entirely. For example, shale can be transformed into slate through thermal metamorphism.

When pressure and temperature are both increased, the rock can undergo dynamic metamorphism. This typically occurs during tectonic activity, when rocks are subjected to both high pressures and temperatures due to the forces generated by plate movement. This can cause rocks to become folded and stretched, and new minerals can be formed as a result.

In summary, increasing pressure and temperature can cause a rock to undergo metamorphism, resulting in changes in its mineral composition, texture, and even its overall appearance. The specific changes that occur depend on the type of rock and the specific conditions it is exposed to.

1.(d) Describe the classification of sandstones on the basis of their composition and matrix.

Answer : Sandstones are sedimentary rocks that are composed of sand-sized mineral grains, usually quartz, feldspar, mica, and other minerals. The classification of sandstones on the basis of their composition and matrix is as follows:

Quartz Sandstones: Quartz sandstones are composed mostly of quartz grains, with little or no matrix. They are typically white or gray in color, and are often used as building stones.

Arkose Sandstones: Arkose sandstones are composed of quartz and feldspar grains, with a high proportion of feldspar relative to quartz. They are typically reddish-brown in color, and often contain other minerals such as mica and clay.

Lithic Sandstones: Lithic sandstones are composed of rock fragments, including volcanic and sedimentary rocks, as well as other mineral grains. They often have a dark color and contain little or no quartz.

Feldspathic Sandstones: Feldspathic sandstones are composed mostly of feldspar grains, with little or no quartz. They are typically light-colored and may contain other minerals such as mica.

Wacke Sandstones: Wacke sandstones are composed of a mixture of grains, including quartz, feldspar, and lithic fragments, as well as a significant amount of matrix. They are typically dark in color and have a clay-rich matrix.

In addition to these categories, sandstones can also be classified based on their texture, grain size, sorting, and other characteristics. Understanding the composition and matrix of sandstones can provide insights into their origin and depositional environment, and can also help in identifying their potential uses and properties.

2.(a) Describe the crystallographic, physical, optical, and chemical properties of the garnet group of minerals. Give examples of rocks in which each species of garnet occurs as an essential mineral.

Answer: The garnet group of minerals includes a diverse range of silicate minerals that share a similar crystal structure. They are characterized by their vitreous to resinous luster, conchoidal fracture, and high hardness. The crystallographic, physical, optical, and chemical properties of garnets are described below, along with examples of rocks in which each species of garnet occurs as an essential mineral.

Crystallographic Properties:

Garnet minerals have a cubic crystal system, with a general formula of X3Y2(SiO4)3, where X can be Ca, Fe, Mg, Mn, or other divalent cations, and Y can be Al, Fe, or Cr.

The crystal structure of garnets consists of interconnected tetrahedra of silicon and oxygen, with the cations occupying the interstitial spaces between the tetrahedra.

Garnets typically form dodecahedral or trapezohedral crystals, with well-developed faces and a characteristic crystal habit.

Physical Properties:

Garnets are relatively dense minerals, with specific gravities ranging from 3.4 to 4.3 g/cmÂ³.

They are typically hard minerals, with a Mohs hardness of 6.5 to 7.5.

Garnets have conchoidal fracture, which means that they break with smooth, curved surfaces.

Optical Properties:

Garnets are isotropic minerals, meaning that they have the same optical properties in all directions.

They have a high refractive index, typically ranging from 1.72 to 1.88.

Garnets are typically transparent to translucent, with colors ranging from red, orange, and yellow to green, brown, and black.

Chemical Properties:

Garnets are silicate minerals, and their chemical composition depends on the specific cations present in the crystal structure.

They are typically stable in a wide range of geological environments, including igneous, metamorphic, and sedimentary rocks.

The chemical properties of garnets can provide information about the conditions under which they formed, such as temperature, pressure, and composition of the surrounding rock.

Examples of rocks in which each species of garnet occurs as an essential mineral are as follows:

Almandine: occurs as an essential mineral in mica schist, gneiss, and some granites.

Pyrope: occurs as an essential mineral in some eclogites and peridotites.

Grossular: occurs as an essential mineral in some skarns and in contact metamorphic rocks.

Andradite: occurs as an essential mineral in some skarns, serpentinites, and volcanic rocks.

Spessartine: occurs as an essential mineral in some pegmatites and metamorphic rocks.

Overall, garnets are an important group of minerals with a wide range of physical, chemical, and geological properties. Their unique crystal structure and composition provide insights into the geological processes that shaped the rocks in which they occur.

2. (b) What are symmetry elements present in the normal class of orthorhombic system? Show the stereographic projection of a crystal face (hkl) for a normal class of orthorhombic system. Write down Hermann-Mauguin notations of all classes of the orthorhombic systems.

Answer: Symmetry Elements in Normal Class of Orthorhombic System:

The normal class of orthorhombic system has the following symmetry elements:

Three mutually perpendicular two-fold axes (parallel to the crystallographic axes)

A center of inversion at the center of the unit cell

Stereographic Projection of a Crystal Face (hkl) in Normal Class of Orthorhombic System:

To construct the stereographic projection of a crystal face (hkl) in the normal class of the orthorhombic system, we first need to determine the Miller indices of the face relative to the crystallographic axes. Once we have the Miller indices, we can use the standard procedure for constructing the stereographic projection, which involves projecting the points on the crystal face onto the surface of a sphere centered at the origin of the coordinate system. The resulting projection will show the symmetry elements of the crystal face, as well as any other important features.

Hermann-Mauguin Notations of All Classes of Orthorhombic System:

There are two possible settings for the orthorhombic system, depending on how the crystallographic axes are chosen. Each setting has a different set of Hermann-Mauguin notations for the symmetry elements and crystal classes. The Hermann-Mauguin notations for both settings are as follows:

Orthorhombic Setting I:

2/m 2/m 2/m: Primitive orthorhombic

mmm: Centered orthorhombic

mm2: Base-centered orthorhombic

222: Body-centered orthorhombic

Orthorhombic Setting II:

222: Primitive orthorhombic

mm2: Base-centered orthorhombic

2/m 2/m 2/m: Face-centered orthorhombic

mmm: Body-centered orthorhombic

Note that the Hermann-Mauguin notation for each crystal class consists of three parts: the lattice type (primitive or centered), the symmetry operations present in the unit cell, and any additional symmetry elements (such as a center of inversion) that are present in the crystal structure.

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