Atomic positions near interfaces and defects are required to assess their physical properties. Their electronic properties can be calculated only after fixing the positions of atoms. The determination of atomic positions consists of three parts: (1) Theoretical calculations of atomic positions with appropriate interatomic potentials, (2) simulation of positions of atoms in the electron microscope, and (3) comparison of experimental results with the calculations. We have performed these three operations to determine atomic structures of coherent and semicoherent interfaces in Si/Ge systems. A coherent Si/Ge interface is simulated using a computer program. An edge dislocation is introduced at this interface with the help of elasticity theory. Energy minimization calculations are then carried out using interatomic potentials for germanium and silicon. The positions of atoms at the interface are thus determined. Critical phenomena in coherent and semicoherent interfaces are examined in relation to the strain energy of the system. For semicoherent interface containing dislocations, we can determine the critical thickness at which dislocations are generated. Energy minimization computations are found to play a major role in establishing critical phenomena. A model is also developed for the distribution of boron atoms near this dislocation. Isotropic elasticity theory is used for boron-dislocation interaction with correction factors inside the core to avoid singularities. Occupation probabilities of the atomic sites in the computational cell are calculated using the Fermi-Dirac distribution function. Interaction between boron atoms is neglected in the present analysis. Two configurations: 1. Si/Ge interface with a impurity free dislocation, and 2. the dislocation with boron impurities are then used to simulate high resolution images using the SHRLI computer program.