Solid solution

Solid solutions are phases of variable composition in which atoms of various elements are located in a common crystal lattice .

Content

1 Classification
2 Regular mortar model
3 notes
4 See also
5 Literature

Classification

They can be disordered (with a random arrangement of atoms), partially or completely ordered. Experimentally, ordering is determined mainly by X-ray structural analysis .

The ability to form solid solutions is common to all crystalline solids . In most cases, it is limited by narrow concentration limits, but systems with a continuous series of solid solutions are known (for example, Cu - Au , Ti - Zr , Ga As - Ga P ). In essence, all crystalline substances considered to be pure are solid solutions with a very low content of impurities.

There are three types of solid solutions:

solid substitution solutions ;
interstitial solid solutions ;
solid solutions of subtraction .

According to the Hume-Rosery semi-empirical rules ^[1] , a continuous series of substitutional solid solutions in metal systems are formed only by elements that, firstly, have atomic radii of similar size (differing by no more than 15%) and, secondly, are not too far from each other in the electrochemical series of voltages . In this case, the elements must have the same type of crystal lattice. In solid solutions based on semiconductors and dielectrics, due to more “friable” crystal lattices, the formation of substitutional solid solutions is possible even with a larger difference in atomic radii.

If the atoms of the components vary significantly in size or electronic structure, the introduction of atoms of one element into the interstices of the lattice formed by another element is possible. Such solid solutions are often formed upon the dissolution of nonmetals ( B , H ₂ , O ₂ , N ₂ , C ) in metals ^[2] .

Subtraction solid solutions arising due to the appearance of vacant sites in the crystal lattice are formed when one of the components is dissolved in a chemical compound and is characteristic of non-stoichiometric compounds.

Natural minerals are often solid solutions (see Crystal Isomorphism ). The formation of solid solutions during the alloying of elements and compounds is of great importance in the production of alloys, semiconductors , ceramics, and ferrites .

Solid solutions are the basis of all the most important structural and stainless steels , bronzes , brass , aluminum and magnesium alloys of high strength. The properties of solid solutions are controlled by their composition, thermal or thermomechanical treatment. Doped semiconductors and many ferroelectrics , which are the basis of modern solid-state electronics , are also solid solutions.

During the decomposition of solid solutions, alloys acquire new properties. The most valuable qualities are possessed by alloys with a very fine inhomogeneity - the so-called dispersion hardening, or aging solid solutions. Dispersion hardening can also be observed during the decomposition of solid solutions based on compounds, for example, non-stoichiometric spinels .

Regular Solution Model

To study the properties of real solid solutions, a regular solution model can be used.
This model is more rigorous in comparison with the model of ideal solutions.

The model is based on the following approximations:

Quasi-chemical approximation. According to this approximation, the interaction between atoms is independent of the composition of the solution. This leads to the fact that the length of the bonds is also independent of the composition. It is easy to verify that for such a case the mixing volume is zero and the mixing enthalpy coincides with the internal mixing energy. When calculating the potential part of the internal energy, as a rule, they are limited only by the nearest neighbors.
The distribution of atoms is considered random. The interaction between atoms is considered small and cannot affect their distribution. Therefore, the configurational entropy of the regular solution coincides with that for the ideal. The validity of this approximation in real solutions increases with temperature.

Consider the formation of a regular solution using the example of mixing two samples with atoms of type A and B. The potential energy of the samples:

E=P_{AA}E_{AA}+P_{BB}E_{BB}

{\ displaystyle E = P_ {AA} E_ {AA} + P_ {BB} E_ {BB}}

,

Where $P_{AA},E_{AA}$ ${\ displaystyle P_ {AA}, E_ {AA}}$ - the number of bonds between atoms and their energy in sample A.

After mixing:

E=P_{AA}E_{AA}+P_{BB}E_{BB}+P_{AB}E_{AB}

{\ displaystyle E = P_ {AA} E_ {AA} + P_ {BB} E_ {BB} + P_ {AB} E_ {AB}}

If $z$ ${\ displaystyle z}$ Is the coordination number, then for the number of bonds you can write the following expressions:

P_{AA}=(zN_{A}-P_{AB})/2,P_{BB}=(zN_{B}-P_{AB})/2,

{\ displaystyle P_ {AA} = (zN_ {A} -P_ {AB}) / 2, P_ {BB} = (zN_ {B} -P_ {AB}) / 2,}

Where $N_{A}$ ${\ displaystyle N_ {A}}$ Is the number of atoms of type A.

After substitution, we obtain for E:

E=zN_{A}E_{AA}/2+zN_{B}E_{BB}/2+P_{AB}(E_{AB}-(E_{AA}+E_{BB})/2)

{\ displaystyle E = zN_ {A} E_ {AA} / 2 + zN_ {B} E_ {BB} / 2 + P_ {AB} (E_ {AB} - (E_ {AA} + E_ {BB}) / 2 )}

,

where the last term describes the change in energy during mixing.

Using the fact that the atoms in the solution are randomly distributed, we find $P_{AB}$ ${\ displaystyle P_ {AB}}$ . Each atom of B has $z$ ${\ displaystyle z}$ neighbors. The average number of A atoms around the B atom should be proportional to the concentration of A atoms in the system.

Then we have:

n=zX_{A}

{\ displaystyle n = zX_ {A}}

Number of AB links:

P_{AB}=nN_{B}=zX_{A}N_{B}=zNX_{A}X_{B}

{\ displaystyle P_ {AB} = nN_ {B} = zX_ {A} N_ {B} = zNX_ {A} X_ {B}}

,

Where $N=N_{A}+N_{B}$ ${\ displaystyle N = N_ {A} + N_ {B}}$ .

Finally, we have an expression for the potential mixing energy of a regular solution:

\Delta E=(E_{AB}-zN(E_{AB}-(E_{AA}+E_{BB})/2X_{A}X_{B})

{\ displaystyle \ Delta E = (E_ {AB} -zN (E_ {AB} - (E_ {AA} + E_ {BB}) / 2X_ {A} X_ {B})}

Notes

↑ Hume-Rosery, 1965 .
↑ Hume-Rosery, 1965 , p. 92-94.

Literature

Indenbaum G.V. Chemical Encyclopedic Dictionary. Ch. ed. I.L. Knunyants. - Moscow: Soviet Encyclopedia, 1983.- 792 p.
Khachaturian A.G. Theory of phase transformations and the structure of solid solutions. - Moscow: Metallurgy, 1974.
W. Hume-Rothery. Introduction to physical metallurgy. - Per. from English V. M. Glazova and S. N. Gorin. - Moscow: Metallurgy, 1965 .-- 203 p.
J. D. Fast. The interaction of metals with gases. - Per. from English L.P. Emelianenko and A.I. Rogov, ed. L. A. Schwartzman. - Moscow: Metallurgy, 1975 .-- 350 p.

[_0629618b743a3c1e-1] Hume-Rosery, 1965 .

[_ed0fe68315ebf623-2] Hume-Rosery, 1965 , p. 92-94.