Рис.1. Основные типы кристаллических решеток:
а – объемно-центрированная кубическая; б – гранецентрированная кубическая; в – гексагональная плотноупакованная.
Band theory of a metal from the side of its crystal lattice.
The main problem is that using X-rays, the types of crystal lattices of different metals were determined, and why they are such and not others is not yet known. For example, copper crystallizes in the fcc lattice, and iron in the bcc lattice, which, when heated, becomes fcc and this transition is used in heat treatment of steels. Usually in the literature, the metallic bond is described as carried out through the socialization of the outer electrons of the atoms and does not possess the property of directionality. Although there are attempts (see below) to explain the directional metal bond since the elements crystallize into a specific type of lattice. The main types of crystal lattices of metals are body-centered cubic; face-centered cubic; hexagonal close-packed. It is still impossible in the general case to deduce the crystal structure of a metal from the electronic structure of the atom from quantum-mechanical calculations, although, for example, Ganzhorn and Delinger pointed out a possible connection between the presence of a cubic body-centered lattice in the subgroups of titanium, vanadium, chromium and the presence of valence d in the atoms of these metals. -orbitals. It is easy to see that the four hybrid orbitals are directed along the four solid diagonals of the cube and are well suited for connecting each atom with its 8 neighbors in a body-centered cubic lattice. In this case, the remaining orbitals are directed to the centers of the unit cell faces and, possibly, can take part in the bond of the atom with its six second neighbors. The first coordination number (K.CH.1) \ "8 \" plus the second coordination number (K.CH.2) \ "6 \" in total is \ "14 \". Let us show that the metallic bond in the closest packing (HEC and FCC) between a centrally selected atom and its neighbors, in the general case, is presumably carried out through 9 (nine) directional bonds, in contrast to the number of neighbors equal to 12 (twelve) the first (coordination number) ... The second (K.P. 2 \ '' 6 \ '' in total is \ '' 18 \ ''.
In the literature, there are many factors affecting crystallization, so I decided to remove them as much as possible, and the metal model in the article, let's say, is ideal, i.e. all atoms are the same (pure metal), crystal lattices without inclusions, without interstices, without defects, etc. Using the Hall effect and other data on properties, as well as calculations by Ashcroft and Mermin, for me the main factor determining the type of lattice turned out to be the outer electrons of the core of an atom or ion, which resulted from the transfer of some of the outer electrons to the conduction band. It turned out that the metallic bond is due not only to the socialization of electrons, but also to the outer electrons of the atomic cores, which determine the direction or type of the crystal lattice.
How did I start to build models of ideal single crystals of pure metals? https://zen.yandex.ru/media/id/5ff97bc2aed88a7c9be811b5/band-theory-of-a-metal-from-the-side-of-its-crystal-lattice-61bf25c648334379189b62c2
Band theory of a metal from the side of its crystal lattice.
ReplyDeleteThe main problem is that using X-rays, the types of crystal lattices of different metals were determined, and why they are such and not others is not yet known. For example, copper crystallizes in the fcc lattice, and iron in the bcc lattice, which, when heated, becomes fcc and this transition is used in heat treatment of steels. Usually in the literature, the metallic bond is described as carried out through the socialization of the outer electrons of the atoms and does not possess the property of directionality. Although there are attempts (see below) to explain the directional metal bond since the elements crystallize into a specific type of lattice. The main types of crystal lattices of metals are body-centered cubic; face-centered cubic; hexagonal close-packed. It is still impossible in the general case to deduce the crystal structure of a metal from the electronic structure of the atom from quantum-mechanical calculations, although, for example, Ganzhorn and Delinger pointed out a possible connection between the presence of a cubic body-centered lattice in the subgroups of titanium, vanadium, chromium and the presence of valence d in the atoms of these metals. -orbitals. It is easy to see that the four hybrid orbitals are directed along the four solid diagonals of the cube and are well suited for connecting each atom with its 8 neighbors in a body-centered cubic lattice. In this case, the remaining orbitals are directed to the centers of the unit cell faces and, possibly, can take part in the bond of the atom with its six second neighbors. The first coordination number (K.CH.1) \ "8 \" plus the second coordination number (K.CH.2) \ "6 \" in total is \ "14 \". Let us show that the metallic bond in the closest packing (HEC and FCC) between a centrally selected atom and its neighbors, in the general case, is presumably carried out through 9 (nine) directional bonds, in contrast to the number of neighbors equal to 12 (twelve) the first (coordination number) ... The second (K.P. 2 \ '' 6 \ '' in total is \ '' 18 \ ''.
In the literature, there are many factors affecting crystallization, so I decided to remove them as much as possible, and the metal model in the article, let's say, is ideal, i.e. all atoms are the same (pure metal), crystal lattices without inclusions, without interstices, without defects, etc. Using the Hall effect and other data on properties, as well as calculations by Ashcroft and Mermin, for me the main factor determining the type of lattice turned out to be the outer electrons of the core of an atom or ion, which resulted from the transfer of some of the outer electrons to the conduction band. It turned out that the metallic bond is due not only to the socialization of electrons, but also to the outer electrons of the atomic cores, which determine the direction or type of the crystal lattice.
How did I start to build models of ideal single crystals of pure metals? https://zen.yandex.ru/media/id/5ff97bc2aed88a7c9be811b5/band-theory-of-a-metal-from-the-side-of-its-crystal-lattice-61bf25c648334379189b62c2