In a cubic crystal the (111) and (222) reflections are observed but no...
**Bravais Lattice and Reflections**
The Bravais lattice refers to the arrangement of lattice points in a crystal. It determines the symmetry and packing of atoms or ions in the crystal structure. The Bravais lattices can be categorized into 14 different types, including simple cubic, body-centered cubic (BCC), face-centered cubic (FCC), and side-centered cubic (SCC).
**Understanding Reflections**
In crystallography, reflections refer to the diffraction of X-rays by the crystal lattice. When X-rays interact with the crystal lattice, they are diffracted in different directions depending on the arrangement of atoms or ions. The diffracted X-rays create a pattern that can be observed as reflections.
**Observation of Reflections**
The (hkl) notation is used to represent different crystallographic planes in a crystal lattice. The numbers h, k, and l correspond to the Miller indices, which represent the orientation and spacing of the crystal planes. The presence or absence of reflections can provide information about the crystal structure.
In this case, the (111) and (222) reflections are observed, but the (001) reflection is not observed. This suggests that the crystal lattice is not cubic, as cubic lattices should exhibit reflections for all possible Miller indices.
**Determining the Bravais lattice**
To determine the Bravais lattice based on the observed reflections, we can analyze the Miller indices of the observed reflections.
- The (111) reflection indicates the presence of a lattice plane with Miller indices (111). This suggests a cubic lattice, as the Miller indices are all the same.
- The (222) reflection also indicates the presence of a lattice plane with Miller indices (222). Again, this suggests a cubic lattice.
Since both reflections indicate cubic symmetry, the crystal lattice must be cubic. However, the absence of the (001) reflection suggests that the crystal lattice is not simple cubic (SC), as the (001) reflection is expected in an SC lattice.
Therefore, the only remaining cubic lattices are body-centered cubic (BCC) and face-centered cubic (FCC).
**Conclusion**
Based on the observations, we can conclude that the crystal lattice is either body-centered cubic (BCC) or face-centered cubic (FCC). Further experiments or analysis may be required to determine the specific Bravais lattice and to distinguish between BCC and FCC.