What are Bravais Lattices?
Bravais Lattice refers to the 14 different 3-dimensional configurations into which atoms can be arranged in crystals. The smallest group of symmetrically aligned atoms which can be repeated in an array to make up the entire crystal is called a unit cell.
There are several ways to describe a lattice. The most fundamental description is known as the Bravais lattice. In words, a Bravais lattice is an array of discrete points with an arrangement and orientation that look exactly the same from any of the discrete points, that is the lattice points are indistinguishable from one another.
Out of 14 types of Bravais lattices some 7 types of Bravais lattices in three-dimensional space are listed in this subsection. Note that the letters a, b, and c have been used to denote the dimensions of the unit cells whereas the letters 𝛂, 𝞫, and 𝝲 denote the corresponding angles in the unit cells.
How to Calculate Interplanar Angle for Hexagonal System?
Interplanar Angle for Hexagonal System calculator uses Interplanar Angle = acos(((Miller Index along plane 1*Miller Index h along plane 2)+(Miller Index k along Plane 1*Miller Index k along Plane 2)+(0.5*((Miller Index along plane 1*Miller Index k along Plane 2)+(Miller Index h along plane 2*Miller Index k along Plane 1)))+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*Miller Index l along plane 1*Miller Index l along plane 2))/(sqrt(((Miller Index along plane 1^2)+(Miller Index k along Plane 1^2)+(Miller Index along plane 1*Miller Index k along Plane 1)+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*(Miller Index l along plane 1^2)))*((Miller Index h along plane 2^2)+(Miller Index k along Plane 2^2)+(Miller Index h along plane 2*Miller Index k along Plane 2)+((3/4)*((Lattice Constant a^2)/(Lattice Constant c^2))*(Miller Index l along plane 2^2)))))) to calculate the Interplanar Angle, The Interplanar angle for Hexagonal system is the angle between two planes (h1, k1, l1) and (h2, k2, l2) in a Hexagonal system. Interplanar Angle is denoted by θ symbol.
How to calculate Interplanar Angle for Hexagonal System using this online calculator? To use this online calculator for Interplanar Angle for Hexagonal System, enter Miller Index along plane 1 (h_{1}), Miller Index h along plane 2 (h_{2}), Miller Index k along Plane 1 (k_{1}), Miller Index k along Plane 2 (k_{2}), Lattice Constant a (a_{lattice}), Lattice Constant c (c), Miller Index l along plane 1 (l_{1}) & Miller Index l along plane 2 (l_{2}) and hit the calculate button. Here is how the Interplanar Angle for Hexagonal System calculation can be explained with given input values -> 180.2041 = acos(((5*8)+(3*6)+(0.5*((5*6)+(8*3)))+((3/4)*((1.4E-09^2)/(1.5E-09^2))*16*25))/(sqrt(((5^2)+(3^2)+(5*3)+((3/4)*((1.4E-09^2)/(1.5E-09^2))*(16^2)))*((8^2)+(6^2)+(8*6)+((3/4)*((1.4E-09^2)/(1.5E-09^2))*(25^2)))))).