What Are the Key Features of the Monoclinic Crystal System?
The monoclinic system is the structural category of crystalline solids. Well, crystalline solids can be categorized according to the structure of crystals. In the monoclinic system, crystals are referred to mainly three axes, a, b, and c, where axes a is perpendicular to axes b and c, but simultaneously, a and b are not perpendicular to each other. Suppose atom groups or atoms in crystalline solids are represented by points and lattices when points are connected with each other. The monoclinic unit cell is differentiated by a single axis called two-fold symmetry, where the monoclinic unit cell can be rotated by 180 degrees without disturbing appearance. Some of the solids that belong to the monoclinic crystal system are borax, gypsum, beta-sulfur, orthoclase, muscovite, kaolin, clinoamphibole, azurite, jadeite, and spodumene.
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What is Crystallography and its Types?
Crystallography is the study of the arrangement of bonds of atoms in crystalline solids. In this system, mainly atoms arrangement is studied based on the crystal lattice. In modern days, DNAs and minerals are examined through crystallography. Well, many kinds of crystal systems are used nowadays. All the structure is defined based on three factors: how many axes used, length, and angles of the axis.
Six different crystal systems are isometric system, tetragonal system, orthorhombic system, monoclinic system, triclinic system, hexagonal system, trigonal subsystem. All these systems have three axes, and the direction of the axis indicates the sides. The longest axis is C, and the shortest axis is A, and axis B is also there; in some systems, you can see axis D.
Monoclinic Crystal Shape And Monoclinic Crystal Angles
In crystallography, the monoclinic crystal system is one of the practical crystal systems. Three vectors describe a crystal system. In the monoclinic system, the quartz is described by vectors of inequitable lengths, as in the orthorhombic system forming a rectangular type prism with a parallelogram base. Hence two combinations of vectors are perpendicular (join at right angles), while the third pair forms an angle other than 90°.
Orientation of a crystal has few constraints – where b is the only fixed axis by symmetry.
Axis C is generally chosen based on cleavage and habit.
α and γ = 90
In some cases, the b axis will be 90 degrees that result in pseudo- orthorhombic form.
Symmetry operation in a monoclinic system, the unprecedented operation is 2/m – a twofold axis of rotation with a mirror plane.
The axis b is the rotation, while c and a lie in the mirror plane
Monoclinic crystals have two forms: pinacoids and Monoclinic shape crystals have two shapes: pinacoidal and prisms.
Common monoclinic rock-forming crystals include clinopyroxene, orthoclase, mica, and titanite.
Orthorhombic System In Crystallography
As we have discussed, crystallography has many types, and the orthorhombic system is one of them. Orthorhombic lattices are formed by extending cubic lattices with two orthogonal pairs by two different factors. While raising the cubic lattice with the two factors, a rectangular prism is formed, and axis a and b form the rectangular prism base. Axis c determines the height of the prism in the orthorhombic system in crystallography. Here all three-axis a, b, and c are different and intersect each other at the rectangle. Hence, all the three orthorhombic lattice vectors remain mutually orthogonal.
In Orthorhombic crystallography, all the three-axis are of a distinct length that is mutually perpendicular to each other.
Convention has it that a crystal is oriented so that c is the most significant axis and a minor axis.
In such a case, b is taken as unity, and after that, you can calculate ratios.
The unique symmetry operation in an orthorhombic system is The special symmetry operation in an orthorhombic system is 2/m 2/m 2/m – Three twofold axes of rotation coinciding with the three crystallographic axes.
There are three types of patterns in the class: prisms, pinacoids, and dipyramids.
Common orthorhombic rock-forming minerals incorporate andalusite and sillimanite, olivine, orthopyroxene, and topaz.
Forms of Orthorhombic System in Crystallography
The orthorhombic system has two types of forms, unique form, and general form. A possible form has the maximum number of faces of any pattern in its crystal class. Particular forms may appear in any crystal class of the system. In general form, three-axis a, b, and c intersect with each other at a specific angle, and it will never be zero. Different forms are pyramid, prisms, domes, disphenoid, sphenoid, pedion, pinacoids, and dipyramid.
FAQs on Monoclinic System in Physics: Complete Guide
1. What is a monoclinic crystal system?
A monoclinic crystal system is one of the seven fundamental crystal systems used to classify crystalline solids. It is defined by a unit cell with three unequal axes (a ≠ b ≠ c). In this system, two of the axes (a and c) are inclined to each other at an angle (β) that is not 90°, while both are perpendicular to the third axis (b). This results in the characteristic axial relationship: α = γ = 90°, but β ≠ 90°.
2. What are the defining axial lengths and angles for a monoclinic system?
The defining parameters for a monoclinic system are based on the lengths of its crystallographic axes and the angles between them. These conditions are:
- Axial Lengths: The lengths of the three axes are unequal. This is represented as a ≠ b ≠ c.
- Axial Angles: Two of the angles between the axes are right angles (90°), while the third angle is oblique (not 90°). This is represented as α = γ = 90°, and β > 90°. The non-90° angle, β, is the angle between the 'a' and 'c' axes.
3. What are some common examples of substances that crystallise in the monoclinic system?
The monoclinic system is very common in minerals and chemical compounds. Some well-known examples include:
- Gypsum (CaSO₄·2H₂O)
- Orthoclase Feldspar (KAlSi₃O₈)
- Monoclinic Sulphur (also known as β-Sulphur)
- Borax (Na₂[B₄O₅(OH)₄]·8H₂O)
- Muscovite Mica
- Ferrous Sulphate (FeSO₄·7H₂O)
- Sucrose (table sugar)
4. How many Bravais lattices are associated with the monoclinic system?
There are two Bravais lattices associated with the monoclinic crystal system. These describe the possible arrangements of lattice points within the unit cell:
- Primitive (or Simple) Monoclinic: In this lattice, the points are located only at the corners of the unit cell.
- Base-Centred (or End-Centred) Monoclinic: This lattice has points at all corners of the unit cell, plus two additional points at the centre of two opposite faces (typically the 'C' faces).
5. How does the monoclinic system differ from the orthorhombic and triclinic systems?
The key difference lies in their symmetry, specifically their axial angles. While all three systems have unequal axial lengths (a ≠ b ≠ c), their angles distinguish them:
- Orthorhombic System: All three axes intersect at 90°. It has high symmetry with α = β = γ = 90°.
- Monoclinic System: This system has lower symmetry. Only two angles are 90°, while one is oblique. Its condition is α = γ = 90°, β ≠ 90°. It's like an orthorhombic system that has been sheared along one plane.
- Triclinic System: This is the least symmetric system. All three axes are of unequal length, and none of the angles are 90°. The condition is a ≠ b ≠ c and α ≠ β ≠ γ ≠ 90°.
6. What are the symmetry elements present in the monoclinic system?
The monoclinic system has a relatively low degree of symmetry. Its characteristic symmetry elements include a single two-fold axis of rotation (which means the crystal appears the same after a 180° rotation) and/or a single mirror plane. The axis of rotation is typically aligned with the 'b' crystallographic axis, and the mirror plane is perpendicular to it. It does not possess any three-fold or four-fold rotation axes, which are found in more symmetric crystal systems.
7. Why is the monoclinic crystal system so common, especially among minerals?
The monoclinic system is very common because its lower symmetry requirements are easier to satisfy for complex molecules or ionic arrangements. While high-symmetry systems like cubic require all axes and angles to be perfectly equal and perpendicular, the monoclinic system is more flexible. It only requires one axis to be perpendicular to the plane of the other two. This structural flexibility allows a wider variety of atoms and molecules of different shapes and sizes to pack efficiently, making it one of the most frequently observed crystal structures in nature.
8. How does the unique geometry of the monoclinic system influence a crystal's physical properties like cleavage?
The unique geometry, specifically the oblique angle (β ≠ 90°), directly influences physical properties. In terms of cleavage—the tendency of a mineral to break along flat planes—the monoclinic system often exhibits cleavage in one or two directions. Because the underlying atomic planes are not at right angles in every direction, the resulting cleavage planes are often inclined to one another. For example, the mineral gypsum shows perfect cleavage in one direction and distinct cleavage in two others, none of which are mutually perpendicular, reflecting the internal atomic asymmetry.
