What are crystal structures? How to determine crystal structure by x-ray diffraction?

Introduction:

Crystal is a periodic representation of atoms in 3D lattice space. There are seven crystal systems. They are cubic, tetragonal, hexagonal, rhombohedral, orthorhombic, monoclinic, and triclinic. Very often students and researchers get into trouble at the beginning of their research to determine crystal structures. They can not judge their findings properly. One of the tools to investigate the crystal of a crystal specimen is XRD.

2theta-Omega scanning:

When we carry out the XRD 2theta-Omega to study the epitaxial growth. After the measurement, we can easily relate the angle theta with the lattice spacing along the c-axis. Hence from the measured data, with the help of the lattice relation with the d-value, we can find the information about the lattice parameters and hence about the corresponding crystal structure. The detail of the lattice relation of the seven-crystal is shown in figure 1. 

Figure 1: Seven crystal system and their lattice relation

However, only 2theta-omega scanning can not give information about the detail of the crystal system. Figure 2 shows peaks from the planes parallel to the c-axis of the substrate. From this measurement, we can also calculate the lattice mismatch of the crystal system. Please check our primitive discussion.

Figure2. 2theta-omega scanning by symmetric x-ray diffraction technique

Along with the measurement, there is phi-scanning which gives information about the symmetry of the crystal. The symmetry in this case is mainly we call rotational symmetry.  Figure 3 shows the rotational symmetry of MnAs/InAs/GaAs epitaxial growth. Here, hexagonal MnAs (six-fold) with 3-fold rotational symmetry of InAs and GaAs. 

Figure 3: Phi-scanning to see the symmetry of the MnAs/InAs/GaAs hetero-structure.

Besides, we also carry out omega or theta scanning only to judge the displacement of the c-axis of the epitaxial film from the c-axis of the substrate. This gives information about the tilting of the grown film. Figure 4 shows omega scanning which reveals the relation between substrate and film distribution on the substrate along the c-axis. Tilting is usually visible in the case of large lattice mismatch growth i.e hetero-epitaxial growth. The Gaussian distribution theoretically also represents the distribution of the film c-axis with the substrate. 

Figure 4: Omega scanning to judge the tilt of the film c-axis with respect to the substrate 

Please check the measurement configuration in the earlier discussion.