Forces, attractive interatomic

To obtain a metallurgical bond between two metals, the atoms of each metal must be brought sufficiently close so that their normal forces of interatomic attraction produce a bond. The surfaces of metals and alloys must not be covered with films of oxides, nitrides, or adsorbed gases. When such films are present, metal surfaces do not bond satisfactorily (see Metal surface treatments). 

It is possible also to use eqn. (xxiv) to take account of attractive interatomic forces such as arise from hydrogen bonds or the interactions between a cation and atoms of its coordination shell, and to maintain the distances between the atoms involved near prescribed standards. This is achieved by... 

Chemists have historically employed various means of representating molecular structure. Two-dimensional drawings of atoms connected by lines are some of the most common molecular representations. Each line represents a chemical bond that, in the simplest case, is a pair of electrons shared between the connected atoms, resulting in a very strong attractive interatomic force. The various interatomic forces define the structure or shape of a molecule, while its chemistry is dependent on the distribution of electrons. A chemical reaction involves a change in the electron distribution, i.e., a change in bonding. 

The van der Waals or residual bond, a weak force of interatomic attraction operating between all atoms and ions in all solids. 

There are three basic regions of interaction between the probe and surface (i) free space, (ii) attractive region, and (iii) repulsive region. At short distances, the cantilever mainly senses interatomic forces the very short range ( 0.1 nm) repulsive forces, and the longer-range (up to 10 nm) van der Waals forces. Attractive forces near the surface ean arise from a layer of contamination present on all surfaces in ambient air. The eontamination is typically an aerosol composed of water vapor and hydrocarbons. On the other hand, the repulsive force occurs between any two atoms or molecules that approach so closely that... 

Inside an atom, the nucleus carries a positive charge. Negatively charged electrons are located at off-centre and fluctuating positions relative to the nucleus. This asymmetry gives rise to attractive interatomic electromagnetic forces. In some cases, the asymmetry extends to the molecular scale (polar molecules), but the effect is globally the same. All forces of this kind are known as London-van der Waals forces. 

Now consider just two atoms in equilibrium with each other as shown in Fig. 2,22. Application of a tensile force, Fj, will induce an attractive force. Fa, between the two atoms in order to maintain equilibrium. Application of a compressive force will induce a repulsive force, Fr, between the two atoms to maintain equilibrium. These attractive and repulsive forces will vary depending upon the separation distance. It is to be noted that the attractive forces in interatomic bonds are largely electrostatic in nature. For example. Coulomb s law for electrostatic charges indicates that the force is inversely proportional to the square of the spacing. The repulsive forces are caused by the interactions of the electron shells of the atoms and is somewhat difficult to estimate directly. 

When two atoms approach each other so closely that their electron clouds interpenetrate, strong repulsion occurs. Such repulsive van der Waals forces follow an inverse 12th-power dependence on r (1/r ), as shown in Figure 1.13. Between the repulsive and attractive domains lies a low point in the potential curve. This low point defines the distance known as the van der Waals contact distance, which is the interatomic distance that results if only van der Waals forces hold two atoms together. The limit of approach of two atoms is determined by the sum of their van der Waals radii (Table 1.4). 

The van der Waals forces are present universally, regardless of the species and polarity of the interacting atoms or molecules. The forces can be attractive or repulsive, but mostly attractive and long-range, effective from a distance longer than 10 nm down to the equilibrium interatomic distance (about 0.2 nm). 

Both of the above approaches rely in most cases on classical ideas that picture the atoms and molecules in the system interacting via ordinary electrical and steric forces. These interactions between the species are expressed in terms of force fields, i.e., sets of mathematical equations that describe the attractions and repulsions between the atomic charges, the forces needed to stretch or compress the chemical bonds, repulsions between the atoms due to then-excluded volumes, etc. A variety of different force fields have been developed by different workers to represent the forces present in chemical systems, and although these differ in their details, they generally tend to include the same aspects of the molecular interactions. Some are directed more specifically at the forces important for, say, protein structure, while others focus more on features important in liquids. With time more and more sophisticated force fields are continually being introduced to include additional aspects of the interatomic interactions, e.g., polarizations of the atomic charge clouds and more subtle effects associated with quantum chemical effects. Naturally, inclusion of these additional features requires greater computational effort, so that a compromise between sophistication and practicality is required. 

Parameters Bi , ai - and Ci - for light atoms have been listed by Gavezzoti [63], Examples of the resulting potential functions are shown in Fig. 5.1. The minimum point in each graph corresponds to the interatomic equilibrium distance between two single atoms. In a crystal shorter distances result because a molecule contains several atoms and thus several attractive atom-atom forces are active between two molecules, and because attractive forces with further surrounding molecules cause an additional compression. All attractive forces taken together are called van der Waals forces. 

The effectiveness of these forces differs and, furthermore, they change to a different degree as a function of the interatomic distance. The last-mentioned repulsion force is by far the most effective at short distances, but its range is rather restricted at somewhat bigger distances the other forces dominate. At some definite interatomic distance attractive and repulsive forces are balanced. This equilibrium distance corresponds to the minimum in a graph in which the potential energy is plotted as a function of the atomic distance ( potential curve , cf. Fig. 5.1, p. 42). 

Figure 11.6 Variation of bond energy with interatomic distance for the hydrogen molecule. If the two hydrogen nuclei are close together mutual repulsion occurs, and at greater distances the attractive force becomes weaker. The equilibrium bond length and bond energy occur at the energy minimum.

Figure 2.2 Illustrative plot of the Lennard-Jones-Devonshire interatomic potential showing the force and the modulus curve for the pair interaction. Positive values indicate repulsion and negative values indicate attraction...

Laplace could not express any opinion on the absolute values of the attraction assumed by him. At present, our knowledge of interatomic, interionic, and analogous forces is much greater than 170 years ago, and attempts to calculate surface energies and surface tensions are possible. 

Inert Gases. The calculation of 7 should be relatively straightforward for crystals of inert gases, in which only one kind of interaction may be expected. These crystals have a face-centered cubic structure. If each atom is treated as a point source of attractive and repulsive forces, only the forces between the nearest pairs of atoms are considered, the zero point energy is neglected, and no re-arrangement of atoms in the surface region is permitted, then the calculated 7 still depends on the equation selected to represent the interatomic potential U. 

V. As a convention, the norm out of the sample surface is denoted as the positive z direction. From an experimental point of view, there is another zero point that is directly measurable the equilibrium distance or equilibrium point. We may consider an STM as a giant molecule consisting of two parts, the tip and the sample. At a relatively large (absolute) distance, for example, 5 A, the force between these two parts is attractive. At very short distances, for example, 2 A, the force between these two parts is repulsive. Between these two extremes, there is a well-defined position where the net force between the tip and the sample is zero. We define it as the equilibrium distance. On the microscopic scale, the equilibrium distance is approximately equal to the interatomic distance in the material under investigation, which is 2-3 A. Thus, the normal tip-sample distance in STM experiments is 4-7 A on the microscopic distance scale. 

This fundamental relation can be extended to the many-body case, and a correlation between the interatomic force in the attractive-force regime and the tunneling conductance can be established. For metals, an explicit equation between two sets of measurable quantities is derived. Of course, the simple relation between the measured force and measured tunneling conductance is not valid throughout the entire distance range. First, the total force has three components, namely, the van der Waals force, the resonance force, and the repulsive force. Second, the actual measurement of the force in STM and... 

EXAMPLE 10.2 The Dispersion Force and Nonideality of Gases. The nonideality of gases arises from the repulsive and attractive forces between atoms. As a consequence, the deviation of the properties of a gas from ideal gas behavior can be traced to the interatomic or intermolec-ular forces. Assume that methane follows the van der Waals equation of state at sufficiently low densities. It is known from experiments that (see Israelachvili 1991)... 

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