Bravais Lattice

14 Bravais Lattice are described with examples of from 6 crystal system

1. Bravais Lattice Sujan Raj Pandey/ 05 M.Sc. 1 st Semester, 2077

2. Crystal Structure = Lattice + Motif Lattice is an imaginary framework , resembling a 3-dimensional periodic array of points or an atomic arrangement on which a crystal is built. Lattice points have identical surroundings. Motif is the building block or group of atoms which are located upon the points of lattice which when repeated forms a crystal structure. Lattice points Motif Crystal Structure

3. Bravais Law Crystal faces develop along planes defined by the points in the lattice. In other words, all crystal faces must intersect atoms or molecules that make up the points. In 1850, Auguste Bravais found that, “ A face is more commonly developed in a crystal if it intersects a larger number of lattice points .” This is known as the Bravais Law. In general, the line that connects most of the lattice points decides the faces. For example, in the plane lattice shown at the right, faces will be more common if they develop along the lattice planes labeled 1, somewhat common if they develop along those labeled 2, and less and less common if they develop along planes labeled 3, 4, and 5.

4. Bravais Lattice Bravais lattices are the foundation for crystal structures Bravais lattices move a specific motif by translation symmetry so that it lines up to an identical motif and divides the lattice into number of identical blocks or unit cell. In 1850,Bravais showed that identical points can be arranged spatially to produce 14 types of unit cell. Thus, a Bravais lattice refer that only these 14 types of unit cells are compatible with the orderly arrangements of atoms found in crystals . The 14 Bravais lattice are distributed within the six crystal system with each crystal system having four different types of centering.

5. Different kind of centering's 1 .Primitive(P): The smallest-possible unit cell is called the “primitive” unit cell or if a unit cell is considered to have lattice points only at its vertices it is a Primitive (P). 2. Body Centered (I): If a unit cell is considered to have lattice points at its vertices and a lattice point at its centered it is a body centered (I). 3 . Face- Centered (F): If a unit cell is considered to have lattice points at its vertices and lattice points at each face, it is a face-centered (F). 4. End- Centered (C): If a unit cell is considered to have lattice points at its vertices plus lattice points at the top and bottom bases then it is a end- centered (C).

6. 14 Bravais Lattice Isometric or Cubic Crystal System: In Bravais lattices with cubic systems, the following relationships can be observed. a = b = c; 𝛂 = 𝞫 = 𝝲 = 90 ° Primitive (or Simple) Cubic Cell (P) Face-Centered Cubic Cell (F) Body-Centered Cubic Cell (I) e.g : Polonium e.g : Lead , Nickel, Copper, Gold, Silver and Aluminum. e.g : Magnetite , Tungsten Chromium , and Potassium.

7. 14 Bravais Lattice 2. Orthorhombic Crystal System: R elationships: a ≠ b ≠ c ; 𝛂 = 𝞫 = 𝝲 = 90° Primitive Orthorhombic ( P) Face-Centered Orthorhombic ( F) Body-Centered Orthorhombic(I ) End-Centered Orthorhombic (C) e.g : Iron Carbide, Rhombic Sulphur e.g : Potassium Nitrate e.g : B arite e.g : Epsomite

8. 14 Bravais Lattice 3 . Tetragonal Crystal System: R elationships: a = b ≠ c ; 𝛂 = 𝞫 = 𝝲 = 90° Primitive Tetragonal (P ) Body-Centered Tetragonal (I ) e.g : C assiterite e.g:Rutile

9. 14 Bravais Lattice 4. Monoclinic Crystal System: R elationships: a ≠ b ≠ c; 𝞫 = 𝝲 = 90 o  and 𝛂 ≠ 90 o Primitive Monoclinic (P ) End-Centered Monoclinic (C) 5 . Triclinic Crystal System: Relationships: a ≠ b ≠ c; 𝛂 ≠ 𝞫 ≠ 𝝲 ≠ 90 o Primitive Triclinic (P ) e.g : 𝞫- Sulphur, Nickel Titanium e.g : Tenorite , sodium sulfate e.g : Plagioclase, Microcline, K yanite

10. 14 Bravais Lattice 6 a . Hexagonal Crystal System: R elationships: a = b ≠ c 𝛂 = 𝞫 = 90 o  and 𝝲 = 120 o Primitive (P) 6 b. Rhombohedral (R): Relationship: a = b = c 𝛂 = 𝞫 = 𝝲 ≠ 90 o Rhombohedral (R ) e.g : Quartz, Calcite, Hematite , Nitratine e.g : Zincite , Beryl, Emerald, Apatite, Aquamarine