Meaning: Walter Kohn was a prominent physicist who made significant contributions to the field of condensed matter physics. The quote you provided highlights one of his notable achievements in the study of energy thresholds for the permanent displacement of nuclei within a crystalline lattice. This work has had a profound impact on our understanding of the behavior of materials at the atomic level.

Kohn's research focused on understanding the fundamental properties of materials, particularly in relation to their atomic and electronic structures. His work on the energy threshold for permanent displacement of nuclei from their regular lattice positions speaks to the intricate interplay between energy levels and atomic arrangements within a material.

The concept of a "reasonably accurate energy threshold" refers to the minimum amount of energy required to permanently displace a nucleus from its regular lattice position. In the context of crystalline materials, the regular lattice structure is a key characteristic that defines the material's properties. Displacing a nucleus from its regular position can have profound effects on the material's behavior, such as altering its mechanical, electrical, or thermal properties.

Kohn's assertion that the energy threshold for permanent displacement is "substantially smaller than had been previously presumed" underscores the significance of his findings. Prior to his work, the scientific community held certain assumptions about the energy required to induce permanent displacements in atomic lattices. Kohn's research challenged these assumptions, revealing that the energy threshold was lower than previously thought. This discovery has far-reaching implications for our understanding of material behavior under various conditions, such as mechanical stress, temperature changes, or irradiation.

Understanding the energy threshold for permanent displacement of nuclei is crucial for numerous applications in materials science and engineering. For instance, it has implications for the design and development of structural materials, semiconductors, and other advanced materials. By accurately determining the energy required to induce permanent displacements, researchers and engineers can better predict and control the mechanical and electronic properties of materials, leading to advancements in fields such as nanotechnology, electronics, and energy storage.

Kohn's work in this area also sheds light on the fundamental interactions between atoms within a crystalline lattice. The energy thresholds for permanent displacement are intimately linked to the bonding forces between atoms, as well as the overall stability of the material's structure. By elucidating the energy landscape governing these processes, Kohn's research has deepened our understanding of the atomic-scale mechanisms that underpin the behavior of materials.

In conclusion, Walter Kohn's investigation of the energy threshold for permanent displacement of nuclei from their regular lattice positions has had a profound impact on the field of condensed matter physics and materials science. His findings have challenged previous assumptions and provided valuable insights into the fundamental behavior of materials at the atomic level. This work has not only expanded our theoretical understanding of materials but also has practical implications for the design and engineering of advanced materials for various technological applications.