Short-distance order

We find the concept of local composition in solid solutions, just as it is found for liquid solutions. Because of the existence of an exchange energy, we can imagine that if a molecule of A and a molecule of B experience a greater force of attraction than two molecules of A or two molecules of B, a molecule of A will tend to be surrounded by molecules of B and therefore the composition of the immediate environment of the molecule of A will not be the same as the overall composition of the solution the immediate vicinity is richer in molecules of B. The opposite effect is obtained if the molecules A and B attract each other less strongly than do two molecules of A or two molecules of B. This is the concept of local composition, which was first put forward by Wilson. 

To describe this concept of local composition, we use a nomenclature which enables us to clearly distinguish, every time, between the central molecule and its nearest surrounding molecules. 

We use the notation Nij to speak of the number of molecules of / immediately neighboring a molecule of j. The probability of finding a molecule of / immediately neighboring a molecule of j is given by the 

This number also represents the local molar fraction of the atoms of i around an atom of j. 

For a solution containing molecules i and j, Warren and Cowley defined an order parameter 77 as  

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Volkov, V. V. et al., Long- and short-distance ordering of the metal cores of giant Pd clusters, J. Cryst. 

In an ionic melt, coulombic forces between charges of opposite sign lead to relative short-distance ordering of ions, with anions surrounded by cations and vice versa. The probability of finding a cation replacing an anion in such ordering is effectively zero and, from a statistical point of view, the melt may be considered as a quasi-lattice, with two distinct reticular sites that we will define as anion matrix and cation matrix. 

In the glassy state the molecular structure is disorderly, and comparable to that of a liquid. This is clearly demonstrated by X-ray diffraction patterns, in which only a diffuse ring is visible, which indicates some short-distance order in contrast to to the sharp reflections found with crystals as a result of long-distance order. 

Researchers have confirmed the existence of BP III, the structure of which is predicted to be more amorphous with the short-distance order of double twist alone. However, further details of this phase have yet to be cleared. 

Under the assumption of a continuous random network distribution [8,10], the short-distance order (up to 3 A) is made of basic structural units determined by the properties of the chemical bonds (coordination number, bond length, bond angles). The medium distance order (up to 5-10 A) describes the sequence of the basic structural units (Fig. 11). 

As the temperature increases, the short-distance order decreases, because of two mutually complementary phenomena the exchange energies decrease and the thermal agitation increases. The solution then tends toward random distribution. 

This notion of short-distance order comes into play in certain solution models, and is encountered in the quasi-chemical model (see section 2.3.4). 

Essentially, we are looking at the solubility of metals in other metals - i.e. monophase metal alloys. The most commonly used solution models are the models with similar atomic volumes, which give us the perfect solution, the infinitely-dilute solution and the strictly-regular solution. Thus, we will then look at Guggenheim s quasi-chemical model, which includes the notion of short-distance order. 

Note.- As we continue to use the hypothesis of a random distribution of the molecules of A and B, this hypothesis appears to conflict with the existence of an exchange energy that means the minimum of the Helmholtz energy cannot correspond exactly to the random distribution. In other words, we circumvent the contradiction by accepting that the short-distance order, which would be introduced by the exchange energy, is annihilated by the thermal agitation. That is we accept the condition ... 

We suppose that there is no short-distance order in the alloy, and therefore all of the configurational partition function is due to the long-distance order. 

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