A lattice or a crystal lattice is the formation of an asymmetrical 3D structural arrangement of ions, atoms, and molecules to form a unit cell. The significant and distinct geometrical shape of a unit cell defines the type of crystal lattice.
The features of a crystal structure are:
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In a unit cell of a crystal structure, every ion, atom, or molecule represents a point in a 3D space. It means all the constituent particles in that unit can be considered points.
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Every point in a crystal structure is defined as a lattice point or lattice site.
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Two or more lattice points can be joined to form a straight line depending on the shape of a unit cell.
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When two or more straight lines are joined, it will form a 3D unit cell design representing a crystal structure. This arrangement of lattice points in a 3D space is called Bravais Lattices.
What is a Unit Cell?
The smallest unit of a solid crystal structure is called a unit cell. It can be defined as the structural unit of a solid crystal, and a lattice is generated by its repetition in a particular format.
To identify a unit cell of a crystalline structure, the following parameters are considered.
The angles between these edges can vary. When high-energy electromagnetic waves are passed through a crystal, the unit cells absorb and send signals. These signals can be interpreted to understand the shape of a unit cell. Hence, the mutual arrangements of multiple unit cells can be identified, leading to the expression of a crystal structure.
Types of Lattice Structures
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Primitive Unit Cells
In this arrangement, the constituent lattice points hold the corner positions only.
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Centered Unit Cells
In this arrangement, the particles occupy the centre along with the corner positions. They are of the following types.
This is a typical lattice structure where the atomic planes or lattice planes lie within the gaps of the lower planes of the respective atoms. In this type, the unit cell is shaped like a cube. It means that one atom is directly in contact with eight other atoms or lattice points. This type of arrangement can be found in vanadium, tungsten, and chromium.
The superposed atoms or lattice points create gaps where the underlying plane can fit into the upper one. The atomic levels are closely packed, creating a hexagonal closest packed (HCP) lattice structure. Metals like cobalt, zinc, titanium, and magnesium show such types of lattice arrangement. A point is connected with 12 neighbouring points making its coordination number 12.
This lattice structure also packs the maximum number of atomic planes in a stacking sequence. The second layer of atoms is primarily stacked following the HCP structure in the underlying layer gaps. The third layer, on the contrary, lies in the free gaps. The metals like copper, lead, and nickel shows such types of solid crystal lattice arrangements. The coordination number of this crystal structure is 12.
Types of Crystal Systems
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Triclinic System
In this system, all three axes are inclined to each other and share the same length. Based on their inclination angles, the shape of the crystals varies. Example – kyanite, amazonite, feldspar, etc.
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Monoclinic System
In this crystalline structure, there are three axes. Two of them are perpendicular to each other, whereas the 3rd one is inclined to form a different angle. The best examples of monoclinic systems are gypsum, petalite, diopside, etc.
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Orthorhombic System
The crystal lattice structure of this type comprises three axes that are perpendicular to each other but the lengths of these axes vary. Examples of this lattice structure are topaz, iolite, zoisite, etc.
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Trigonal Structure
The unit cell of this system is basically a three-sided pyramid. It can also attend to shapes like rhombohedral and scalenohedral. Examples are calcite, ruby, agate, etc.
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Hexagonal System
Now that we know what crystal structure is, this system seems a little different from the rest. It has four axes where three of them share the same length. The 4th one intersects these three at right angles. The examples are beryl, apatite, etc.
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Tetragonal System
This system also consists of three axes. Only the main axis varies in dimension. The other two are of the same length. An example of this system is perovskite.
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Cubic System
This is a lattice system where all three angles are at right angles to each other with the same length. This crystal structure of metals can be found in gold and silver. Among nonmetals, diamond shows this characteristic crystal shape.
Crystal shape
Crystal refers to a regular shape that some substances take up when they solidify, like salt and snowflake. One of the most beautiful crystals in nature are snowflakes, which are just water condensed around a dust particle. Snowflakes are one of the most amazing aspects of nature. Each snowflake is different in the way that its crystalline structure is unique.
Crystal-ware
Crystal, when used in our common language, is a beautiful and precious piece of utensil made of transparent glass that is more refractive than normal glass. Crystal vases and glasses add to the beauty of a house. What makes crystal stand out is the way it refracts light, quite striking. When held up to the light, it creates a rainbow prism effect, thus distinguishing it from glass. When tapped, a crystal glass sounds a musical ringing echo but a normal glass does not create such sounds.
Crystallography
Science studies crystals and their lattices in great detail with numerous applications. The study of crystals is called Crystallography. It can be defined as the experimental and applied study of crystalline structures and how their atoms are arranged. The word Crystallography uses two Latin words: crystallon and graphein. Crystallon means a ‘frozen drop’. Graphein means ‘to write’. It can be noted that the suffix -graphy forms the end part of many kinds of studies, like Geography (Study of the Earth), Cartography (Study of Maps), or Stenography (The skill of shorthand, typewriting, and transcription).
Lattice: The Framework
Just as crystals have a set shape, the framework of these crystals is called a lattice. This framework of a crystal is three-dimensional, like the skeleton of a wooden box. Lattice is also the pattern created by weaving strips in a criss-cross fashion, alternating between the X and Y-axis. A common example of such a lattice would be a lattice pie crust or the weaving of a bamboo basket.
Lattice in Studies
Lattice is used in various subjects to refer to a three-dimensional framework or structure, like Chemistry, Physics, Mathematics, Biology, and interrelated fields like Biophysics. Chemistry uses lattice to describe the structure of molecules. Maths uses lattices in abstract algebra. Condensed matter physics uses lattice to represent atoms. Biology uses lattices to represent structures of DNA or protein.
Understanding Lattice
In basic crafts, making a dice out of paper or cardboard would be a good practice to understand a lattice. Understanding a lattice requires spatial understanding. This is the understanding of the size or position of any object or point in space. People with good spatial understanding and orientation can figure out directions and routes. Those with good spatial reasoning can see in their minds where an object or objects are placed in relation to other objects around them in three dimensions. Those with exceptional spatial understanding and spatial-visual memory are excellent Rubic’s cube solvers.