Kʿun Huang

Bio: Kʿun Huang is an academic researcher. The author has contributed to research in topics: Cauchy–Born rule. The author has an hindex of 1, co-authored 1 publications receiving 7417 citations.

Dynamical Theory of Crystal Lattices

Abstract: Although Born and Huang's classic work on the dynamics of crystal lattices was published over thirty years ago, the book remains the definitive treatment of the subject. It begins with a brief introduction to atomic forces, lattice vibrations and elasticity, and then breaks off into four sections. The first section deals with the general statistical mechanics of ideal lattices, leading to the electric polarizability and to the scattering of light. The second section deals with the properties of long lattice waves, the third with thermal properties, and the fourth with optical properties.

Phonons and related crystal properties from density-functional perturbation theory

Abstract: This article reviews the current status of lattice-dynamical calculations in crystals, using density-functional perturbation theory, with emphasis on the plane-wave pseudopotential method. Several specialized topics are treated, including the implementation for metals, the calculation of the response to macroscopic electric fields and their relevance to long-wavelength vibrations in polar materials, the response to strain deformations, and higher-order responses. The success of this methodology is demonstrated with a number of applications existing in the literature.

The mathematical theory of equilibrium cracks in brittle fracture

Abstract: Publisher Summary In recent years, the interest in the problem of brittle fracture and, in particular, in the theory of cracks has grown appreciably in connection with various technical applications. Numerous investigations have been carried out, enlarging in essential points the classical concepts of cracks and methods of analysis. The qualitative features of the problems of cracks, associated with their peculiar nonlinearity as revealed in these investigations, makes the theory of cracks stand out distinctly from the whole range of problems in terms of the theory of elasticity. The chapter presents a unified view of the way basic problems in the theory of equilibrium cracks are formulated and discusses the results obtained thereby. The object of the theory of equilibrium cracks is the study of the equilibrium of solids in the presence of cracks. However, there exists a fundamental distinction between these two problems, The form of a cavity undergoes only slight changes even under a considerable variation in the load acting on a body, while the cracks whose surface also constitutes a part of the body boundary can expand even with small increase of the load to which the body is subjected.

The structure of suspended graphene sheets

Abstract: Graphene — a recently isolated one-atom-thick layered form of graphite — is a hot topic in the materials science and condensed matter physics communities, where it is proving to be a popular model system for investigation. An experiment involving individual graphene sheets suspended over a microscale scaffold has allowed structure determination using transmission electron microscopy and diffraction, perhaps paving the way towards an answer to the question of why graphene can exist at all. The 'two-dimensional' sheets, it seems, are not flat, but wavy. The undulations are less pronounced in a two-layer system, and disappear in multilayer samples. Learning more about this 'waviness' may reveal what makes these extremely thin carbon membranes so stable. Investigations of individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or in air reveal that the membranes are not perfectly flat, but exhibit an intrinsic waviness, such that the surface normal varies by several degrees, and out-of-plane deformations reach 1 nm. The recent discovery of graphene has sparked much interest, thus far focused on the peculiar electronic structure of this material, in which charge carriers mimic massless relativistic particles1,2,3. However, the physical structure of graphene—a single layer of carbon atoms densely packed in a honeycomb crystal lattice—is also puzzling. On the one hand, graphene appears to be a strictly two-dimensional material, exhibiting such a high crystal quality that electrons can travel submicrometre distances without scattering. On the other hand, perfect two-dimensional crystals cannot exist in the free state, according to both theory and experiment4,5,6,7,8,9. This incompatibility can be avoided by arguing that all the graphene structures studied so far were an integral part of larger three-dimensional structures, either supported by a bulk substrate or embedded in a three-dimensional matrix1,2,3,9,10,11,12. Here we report on individual graphene sheets freely suspended on a microfabricated scaffold in vacuum or air. These membranes are only one atom thick, yet they still display long-range crystalline order. However, our studies by transmission electron microscopy also reveal that these suspended graphene sheets are not perfectly flat: they exhibit intrinsic microscopic roughening such that the surface normal varies by several degrees and out-of-plane deformations reach 1 nm. The atomically thin single-crystal membranes offer ample scope for fundamental research and new technologies, whereas the observed corrugations in the third dimension may provide subtle reasons for the stability of two-dimensional crystals13,14,15.

Necessary and sufficient elastic stability conditions in various crystal systems

Abstract: While the Born elastic stability criteria are well known for cubic crystals, there is some confusion in the literature about the form they should take for lower-symmetry crystal classes Here we present closed form necessary and sufficient conditions for elastic stability in all crystal classes, as a concise and pedagogical reference to stability criteria in noncubic materials

A combined quantum mechanical and molecular mechanical potential for molecular dynamics simulations

Abstract: A combined quantum mechanical (QM) and molecular mechanical (MM) potential has been developed for the study of reactions in condensed phases. For the quantum mechanical calculations semiempirical methods of the MNDO and AM1 type are used, while the molecular mechanics part is treated with the CHARMM force field. Specific prescriptions are given for the interactions between the QM and MM portions of the system; cases in which the QM and MM methodology is applied to parts of the same molecule or to different molecules are considered. The details of the method and a range of test calculations, including comparisons with ab initio and experimental results, are given. It is found that in many cases satisfactory results are obtained. However, there are limitations to this type of approach, some of which arise from the AM1 or MNDO methods themselves and others from the present QM/MM implementation. This suggests that it is important to test the applicability of the method to each particular case prior to its use. Possible areas of improvement in the methodology are discussed.