Abstract
A crystal is a highly organized arrangement of atoms in a solid, wherein a unit cell is periodically repeated to form the crystal pattern. A unit cell is composed of atoms that are connected to some of their first neighbors by chemical bonds. A recent rule, entitled the even-odd rule, introduced a new way to calculate the number of covalent bonds around an atom. It states that around an uncharged atom, the number of bonds and the number of electrons have the same parity. In the case of a charged atom on the contrary, both numbers have different parity. The aim of the present paper is to challenge the even-odd rule on chemical bonds in well-known crystal structures. According to the rule, atoms are supposed to be bonded exclusively through single-covalent bonds. A distinctive criterion, only applicable to crystals, states that atoms cannot build more than 8 chemical bonds, as opposed to the classical model, where each atom in a crystal is connected to every first neighbor without limitation. Electrical charges can be assigned to specific atoms in order to compensate for extra or missing bonds. More specifically the article considers di-atomic body-centered-cubic, tetra-atomic and dodeca-atomic single-face-centered-cubic crystals. In body-centered crystals, atoms are interconnected by 8 covalent bonds. In face-centered crystal, the unit cell contains 4 or 12 atoms. For di-element crystals, the total number of bonds for both elements is found to be identical. The neutrality of the unit cell is obtained with an opposite charge on the nearest or second-nearest neighbor. To conclude, the even-odd rule is applicable to a wide number of compounds in known cubic structures and the number of chemical bonds per atom is not related to the valence of the elements in the periodic table.
Highlights
In crystal structures, positions of atoms in the unit cell of a crystal are derived from experimental diffraction data [1]
The objective of the present paper is two-fold: to validate first an extension, of the procedure to cubic crystalline structures, during which we show that the number of bonds is not limited to the valence number; to propose alternative bonding configurations in well-known cubic structures while limiting the number of covalent bonds per atom to a maximum of eight
The limitations are: single covalent bonds only; atoms erect a number of bonds as allowed by the even-odd rule, depending on their charge and their even or odd character; no element can form more than 8 bonds; two atoms bearing the same charge, positive or negative, cannot be connected; in mono-element crystals, two atoms are connected when they are both neutral or with complementary charges; a unit cell with series of elements have connections only between different atoms; a unit cell with two series of elements have the same total number of bonds in each series; a unit cell containing charged atoms should be overall neutrally charged, or should be neutralized by the nearest neighbor or by the second nearest neighbor in the nearest unit cell
Summary
Positions of atoms in the unit cell of a crystal are derived from experimental diffraction data [1]. The coordination number of each atom, i.e. the number of its near neighbors can be evaluated [2]. This number indicates the number of bonds around the atom [3] [4]. Diffraction data do not give direct information to choose the nature of bonds in a solid [6]. There is no direct information about atoms charges
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