This chapter is dedicated to the first step in solving a crystal structure: determining the true unit cell, a task made challenging by the fact that the experimental data represent a one-dimensional projection of the three-dimensional reciprocal lattice. This step is unavoidable, as further structural characterization is not possible without knowing the true unit cell. Therefore, this chapter discusses in detail unit cell indexing using the manual approach (high-symmetry cases only) and automatic ab initio indexing algorithms, indexing reliability and figures of merit, and related topics. Finally, the refinement of precise lattice parameters is covered, along with the basics of the linear least-squares method and unit cell reduction algorithms. The chapter also includes a review of existing indexing software, followed by several examples illustrating the use of such software to solve common indexing problems.

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Determination and Refinement of the Unit Cell

  • Peter Zavalij,
  • Vitalij Pecharsky

摘要

This chapter is dedicated to the first step in solving a crystal structure: determining the true unit cell, a task made challenging by the fact that the experimental data represent a one-dimensional projection of the three-dimensional reciprocal lattice. This step is unavoidable, as further structural characterization is not possible without knowing the true unit cell. Therefore, this chapter discusses in detail unit cell indexing using the manual approach (high-symmetry cases only) and automatic ab initio indexing algorithms, indexing reliability and figures of merit, and related topics. Finally, the refinement of precise lattice parameters is covered, along with the basics of the linear least-squares method and unit cell reduction algorithms. The chapter also includes a review of existing indexing software, followed by several examples illustrating the use of such software to solve common indexing problems.