TEACHING EXPLORATION OF CRYSTALLINE RECIPROCAL SPACE TRANSFORMATION AND DIFFRACTION AND SCATTERING SPECTROSCOPY

In solid-state physics, reciprocal space is a fundamental concept for understanding crystal structures, diffraction phenomena, and spectroscopic behavior related to phonons and electrons. However, in undergraduate teaching, this concept is often introduced in an abstract mathematical form, making it difficult for students to connect it with concrete experiments and intuitive physical understanding. To address this pedagogical challenge, this paper proposes a teaching framework for undergraduate courses in solid-state physics and materials physics centered on reciprocal space. In this framework, reciprocal space is presented as the natural Fourier-space representation of crystal periodicity. Its mathematical foundation and physical significance are systematically explained and integrated into the teaching of diffraction and scattering spectroscopy. Starting from periodic structures in real space, typical experiments such as X-ray diffraction are introduced to clarify the role of reciprocal space in describing diffraction conditions and spectroscopic signals. By further incorporating reciprocal lattices, Brillouin zones, and energy-momentum representations, a unified and intuitive physical picture is established. This teaching design helps students connect crystal structures, experimental spectra, and theoretical analysis within a coherent framework of spatial transformation, thereby improving their understanding and application of modern condensed-matter experimental methods and spectroscopic analysis.