See images below.Ĭonventional unit cell - BCC: Photo- credit: click link to left. This is a primitive unit cell different from the conventional cell. Photo- credit: click on link to left.īody centered cubic: Lattice point at origin is connected to lattice point at body centers of 3 cubes whose intersection is origin. Home-work: you should try to understand the primitive cells of other types of crystals. 3 most important lattice types, the simple cubic (sc), the body centered cubic (bcc) and the face centered cubic (fcc) types Parameter Now in the following table we will summarize the properties of the 3 most important lattice types, the simple cubic (sc), body centered cubic (bcc) and face centered cubic (fcc) types. The following table shows the 14 types of special lattice types with their various properties. basic lattices in 2-dimensional plane: rectangular and centered rectangular lattices, showing primitive and non-primitive cell type. The figure below shows rectangular and centered rectangular lattices. basic lattices in 2-dimensional plane: Oblique, square and hexagonal. The first figure shows oblique, square and hexagonal lattice. When conditions are imposed on primitive lattice vectors - read lecture - I, II, linked here, to know how we define them, that is relations are established that restrict their size and the angle between the various dimensions, the resulting lattices are known as special lattice types, in 2-dimension there are 5 and in 3-dimension there are 14. Reflection symmetry: Its transformed through a plane about which a reflection or mirror image of all points retain their symmetry of the lattice. All other lattice points given by are transformed to so that lattice - translational symmetry, is preserved. Inversion symmetry: A lattice point is taken as origin. The 5-fold symmetry is not possible and 1-fold symmetry is trivial. A rotation is a transformation through angles of only, about an axis passing through a lattice point so that the lattice symmetry - translational that is, is preserved. There are only 230 such fundamental symmetry operations. These symmetry are referred to as “ point group symmetry” and together with obedience to translational symmetry referred as “ space group symmetries“. There are further symmetry operations that non-Bravais lattices such as “ lattices with a basis” must satisfy. reflection about a plane passing through a lattice pointor.Thus in 3-dimensional lattices the 14 classes of Bravais lattices are categorized into 7 types or systems of fundamental lattices. In 3-dimensional geometry there are a total of 14 classes of lattices. This means in 2-dimensional lattice constructs we have only 5 types of lattices which satisfy additional symmetry operations. But due to the constraint of translational symmetry the total number of symmetry operations that the lattices can satisfy is reduced to a minimum. Lattices satisfy additional symmetry operations. In our last two lectures, here, - we saw that all lattices must satisfy a translational symmetry given by the lattice displacement vectors which qualifies them to be known as Bravais lattice. Based on their properties we will classify them into various types and classes. In this lecture we will follow through our basic knowledge gained in the last lecture, - lecture - I, II, and shed light on the most interesting properties of crystal lattices, viz. A representative structure for symmetry as would be exhibited by eg a lattice. Expect some refinement, add-ons, content expansion etc, in the web version. It was delivered to the same class on 26th July 2017. This article is purported to serve as an introduction to a solid state physics course for the 3 year degree physics honors class. All articles in this series can be found here.
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