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Unable to Resist
Published in Sharon Ann Holgate, Understanding Solid State Physics, 2021
The dotted line in Figure 6.11a shows the E-k relationship from the Pauli model. By contrast, the E-k curve for the nearly free-electron model, with its missing portions, shows there are values of energy that electrons in solids cannot occupy. These can be represented by a “band diagram,” which is shown in Figure 6.11b, and would normally be displayed without the E-k curve overlaid. (See figure caption for more details.) The “forbidden” bands of levels, known as bandgaps or “energy gaps,” are indicated by the plain white regions. These correspond to the areas in the crystal where the electron wavelength satisfies the Bragg condition, and so the Bragg reflections from the lattice ions are preventing electrons with energies within the bandgaps from travelling along. Electrons with all other values of energy in conjunction with any of the values of wave vector, k, that fit on the broken E-k curve can travel through the crystal, and the regions representing these allowed energy states in band diagrams are known as energy bands—here represented by dotted shading.
Introduction to optical materials
Published in John P. Dakin, Robert G. W. Brown, Handbook of Optoelectronics, 2017
The one-dimensional, nearly free electron model demonstrates that the periodicity of a crystal results in electrons being confined to bands separated by energy gaps. It also enables the dynamics of the electron to be analyzed. The free electron equations may be used provided that the electron mass is replaced by an effective mass. This effective mass takes account of the interaction between the electrons and the lattice (see, for example, [3, Chapter 4]). The effective mass of an electron is given by
Simulation of the crystal structure formation from the small lithium clusters
Published in Molecular Physics, 2019
Lithium is one of the most studied alkali metals. It has a simple electronic configuration of just one valence electron, which makes it possible to implement the nearly free electron model. Therefore, a success achieved in the study of crystalline lithium. And the first work on the structural properties of small lithium clusters was published relatively recently. The structures of Li3 and Li4 were studied first in [1] and Lin clusters (n = 3–6) – in [2]. The first systematic study of the cluster geometry dependence on the electronic structure was carried out in [3]. Further research was aimed to clarify the previously discovered structures and searching for new ones [4–9]. It was shown that lithium metal clusters are similar to simple molecules in their electronic structure [10]. Thus, electronic states and chemical bonding of Li4, Li10 and Li8 clusters were similar to those in F2, N2, and CH4 molecules, respectively. The paper [11] presents a detailed review of various methods of theoretical studies on lithium clusters. It gives additional information in understanding the processes of formation and stabilisation of individual lithium clusters. But there is no information about the formation mechanism of crystalline lithium from clusters in literature. In the present work, we consider the formation process of crystalline lithium from individual small clusters.