Plane angle between lattice planes

One is also occasionally interested in computing the angle between planes. If cp is the angle between the plane with Miller indices (h, fc, /,) and the plane with Miller indices h, k, ), then the basic equation to calculate this angle is (see coefficients s in Table D.24)  

---

Table D.23. Plane angle between lattice planes...

The Bragg equation describes the relationship between the impinging X-radiation, the diffraction angle, and the separation between lattice planes in the crystal under study. The Bragg equation is generally written as... 

The dot product is also useful for calculating the angle between a plane normal and any direction in a direct lattice. In general, the angle between any two directions, specified... 

Derive the expression for the angle between a plane normal and any direction in an orthorhombic lattice. 

A space lattice is defined by either the three unit lattice vectors a, b, and c or the set of the six lattice parameters a, b,c, a, fi, and where the last three quantities represent the plane angles between the cell edges. The International Union of Crystallography (lUCr) has now standardized the notation and definition of space lattice parameters and this international standard nomenclature is listed below ... 

The rhombohedral unit cell is defined by three equal-length unit translations a, and the plane angle between them, a. The rhombohedral lattice parameters can be converted to hexagonal by using the following equations ... 

We found that without any exception in all of our simulations Bain s lattice correspondence actually applies, i.e. one set of (110) planes of the bcc structure corresponds to a set of fee (111) planes, while the bcc [001] direction lying in these planes is transformed into the [110] direction of the fee phase. Moreover, these directions are exactly parallel to each other. This would correspond to a Nishiyama-Wassermann orientational relationship if the (110) and (111) planes would also be parallel to each other. But this is not the case. These planes are rotated around [001] by an angle between 0 and 9 during the transformation. This angle differs between the simulations in a non-systematic way. 

Figure 4.4. X-rays scattered by atoms in an ordered lattice interfere constructively in directions given by Bragg s law. The angles of maximum intensity enable one to calculate the spacings between the lattice planes and allow furthermore for phase identification. Diffractograms are measured as a function of the angle 26. When the sample is a...

If planes of identical atoms in a crystal structure are considered as lattice planes, a relation exists between the diffraction angle (20) and the distance (d) between identical lattice planes. This relation is known as the Bragg equation ... 

---