In X-ray crystallography, the diffraction pattern obtained from a crystal can provide valuable information about its atomic structure. Diamond cubic is a common crystal structure, and X-ray diffraction (XRD) analysis of this structure reveals characteristic peaks associated with different crystallographic planes. This response aims to explain the number of XRD peaks below a 64-degree angle for the (311) plane in diamond cubic.


The diamond cubic structure is a highly symmetric arrangement of atoms commonly found in materials like diamond, silicon, and germanium. It consists of a face-centered cubic (FCC) lattice with two interpenetrating face-centered tetrahedral sub-lattices.


X-ray diffraction is a technique used to study the arrangement of atoms in a crystal lattice. When X-rays are incident on a crystal, they undergo constructive interference due to scattering from the crystal's planes of atoms. This interference produces a diffraction pattern characterized by distinct peaks.


The (311) plane in diamond cubic is one of the crystallographic planes that can diffract X-rays. The diffraction pattern of this plane is characterized by a peak at an angle of 64 degrees. However, it is important to note that in XRD analysis, there can be multiple peaks below a given angle. The number of peaks below 64 degrees for the (311) plane depends on various factors, including the lattice spacing and the wavelength of X-rays used.


1. Lattice Spacing: The lattice spacing of the crystal is a crucial factor influencing the number of XRD peaks. Different crystallographic planes have different lattice spacings, which determine the angles at which the peaks appear in the diffraction pattern. The lattice spacing can vary for different materials with the diamond cubic structure, such as diamond, silicon, or germanium.

2. X-ray Wavelength: The wavelength of X-rays used in the diffraction experiment also affects the number of peaks. According to Bragg's law, the angle of diffraction is inversely proportional to the X-ray wavelength. Therefore, changing the wavelength can alter the diffraction pattern and the number of peaks observed.


In the case of the (311) plane in the diamond cubic structure, the XRD peak at 64 degrees corresponds to the primary diffraction peak. However, there can be multiple peaks below this angle, depending on factors such as lattice spacing and X-ray wavelength. The exact number of peaks below 64 degrees for the (311) plane would require the specific details of the crystal being analyzed, including its lattice spacing and the experimental setup.