Nature of Interatomic Bonds

Atoms and even the PO4 unit in a phosphate crystal may be considered as spherical balls and stacked in various configurations. The PO4 unit is held together in solids by five types of bonds. These bonds, which hold the atoms at definite distances from each other, are formed by the electronic configuration of the atoms. The equilibrium distance between 

As seen in Chapters 4 and 5, aqueous cations and anions are formed by the dissolution of metal oxides and acid phosphates. Electrostatic (Coulomb) force attracts the oppositely charged ions to each other and stacks them in periodic configurations. That results in an ionic crystal structure. Thus, the ionic bond is one of the main mechanisms that is responsible for forming the acid-base reaction products. 

The crystals formed by ionic bonds are not very hard. Compared to other forms of crystal strucmres, they are more soluble in water and not very stable in a heat treatment. Most of the acid phosphates fall into this category. 

one or more electrons are shared between two atoms in such a manner that these electrons are attracted by the nuclei of both. This sharing creates a bond between the two atoms. The force of attraction is strong and leads to the formation of crystals that are hard, insoluble, and thermally stable. 

The bonding mechanism in most phosphate minerals is partly ionic and partly covalent, and depending on which bond is dominant, the mineral properties vary. Thus, the minerals with more covalent bonds, such as anhydrous phosphates are less soluble in water and are thermally stable. 

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Depending upon the nature of interatomic bonds established during its formation, solid elemental phosphorus could occur in three allotropic forms black, white (yellow), or red. Other forms of phosphorus are... 

Early atomistic simulations employed pair potentials, usually of the Morse or Lennard-jones type (Figure 11.6). Although such potentials have been and still are a useful model for fundamental studies of generic properties of materials, the agreement between simulation results and experiment can only be quantitative at best. While such potentials can be physically justified for inert elements and perhaps some ionic solids, they do not capture the nature of interatomic bonding even in simple metals, not to mention transition metals or covalent solids. 

The third and by far the largest class is that of structures with more parameters than bond lengths. A calculation of the structure must now include a consideration of non-bonded distances, and in favourable cases might be expected to provide insight into the relative importance of the different kinds of non-bonded interactions in the crystal (mainly repulsions). Even here, caution must be exercised. In a number of cases it has been shown that non-bonded repulsions can be successfully simulated by the simple device of maximising the crystal volume subject to the constraint of fixed bond lengths . Only when this ploy fails will it be necessary to enquire more closely into the nature of interatomic forces. 

Knowledge of the crystal structure permits determination of the coordination munber (the munber of nearest neighbors) for each kind of atom or ion, calculation of interatomic distances, and elucidation of other structural featmes related to the nature of chemical bonding and the imderstanding of physical properties in the solid state. 

The nature of plasticity is rupture and rearrangements of interatomic bonds which in crystalline objects involve peculiar mobile linear defects, referred to as dislocations. Temperature dependence of plasticity may significantly differ from that of Newtonian fluids. Under certain conditions (including the thermal ones) various molecular and ionic crystals, such as NaCl, AgCl, naphthalene, etc., reveal a behavior close to the plastic one. The values of x typically fall into the range between 10s and 109 N m 2. At the same time, plastic behavior is typical for various disperse structures, namely powders and pastes, including dry snow and sand. In this case the mechanism of plastic flow is a combination of acts involving the establishment and rupture of contacts between dispersed particles. Plastic object, in contrast to a liquid, maintains the acquired shape after removal of the stress. It is worth... 

The difference between the electronic and molecular rotational motions is in the radial function Rpx- In the molecular rotation motions, the radial function is assumed to be uninvolved in the quantum nature because of the typical deep potentials of interatomic bonds. However, this assumption is not appropriate for the electronic motions. Substituting Eq. (1.76) into Eq. (1.69) and (1.74) leads to the Schrodinger equation for the radial direction in polar coordinates (r, 0, [Pg.31]

The x-ray diffraction method has provided knowledge of the crystal structures of many crystals, including molecular crystals. The values of the interatomic distances provide information about the nature of the bonds between the adjacent atoms. The technique has become a very powerful one, and it is now sometimes used for determining the complete molecular structures of substances, in place of the older chemical methods of decomposing substances into simpler substances. 

Of all the physical characteristics of solids, the dynamical properties give a rather complete description of various aspects of the electronic ground state elasticity, phonon frequencies, dispersion, phase transformations, anharmonicity - they are all derived from the properties of interatomic bonds. Therefore it seems only natural to attempt to trace the origins of semiconductor dynamics back to the behavior of electrons, which ultimately reduces to electron - electron and electron - nuclei interactions. These are the starting point of "ab initio" theories. 

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