Solid Solution of Metals: With Diagram | Metallurgy

Solid Solution of Metals: With Diagram | Metallurgy

In this article we will discuss about:- 1. Introduction to Solid Solution of Metals 2. Types of Solid Solutions 3. Hume Rothery’s Rules for Primary Substitutional Solid Solubility.

Introduction to Solid Solution:

The liquid solution of the two-metal solution has formed, when it crystallizes and the solid phase of only one single crystal structure. This is when two-metal atoms are able to combine a given crystal structure (normally of a solvent metal) to ensure that both types of atoms are present in proportion to their concentration in one unit cell of this crystalline solid, Fig. (c) 2.2. So there is a single crystal structure in the solid solution of two (or more) elements that constitutes one single step.

Both metals, at least to some extent in their solid state, are mutually soluble. For example, without breaking the FCC crystalline lattice, copper can be dissolved to 38.4 per cent by weight by zinc and copper can dissolve to aluminium (FCC) at up to 5.5 per cent by weight.

A solid solution typically needs a more special obligation between water and solvent than a liquid solution, since the crystal structure of the material is less suitable. However, other metals such as copper and nickel have a strong solvability of up to 100% copper to 100% nickel, i.e. they are soluble in each other in any way to give the same FCC crystal structure (with different proportions).

These are classified as solid solutions expanded. Fig.-Fig. 2.3 shows three of them with three compositions (190% Cu, 10% Ni, 50, 50% Cu, 50% Ni, 10% Cu, and 90% Ni), each of which is composed of three compositions: In all three cases, the crystal structure is FCC with a sight decrease in the nickel content parameter (as nickel lattice is lower).

Alloy systems (Au-Ag) (both FCC) and Fe-Cr (both BCC), Mg-Cd (both HCP) are also strongly soluble. The solid solutions were obtained through a variety of compositions mainly based on the nature of the metal bond (attraction between ions and free moving electrons). This relation is largely indifferent to the exact proportion and precision of the element atoms in the crystalline array of nuclear sites.

Types of Solid Solutions:

There are two main types of solid solutions:

(i) Substitutional solid solutions.

(ii) Interstitial solid solutions.

(i) Substitutional Solid Solutions:

Two elements (or more) form a solid substitute as atoms of the solvent component (also known as matrix atoms) in its crystal structure replace the atoms of the solvent. Atoms share a common set of nuclear sites. Fig.-Fig. 2.2 (c) shows a Cu-Ni solid solution unit cell in which three Copper unit cell copper atoms have been randomly but replaced with three Nickel atoms. During freezing these three copper atoms have to be added to the grid elsewhere.

Since the solvents and the solute atoms always vary in their size and electronic structure, the solvent metal's crystal grid is always distorted as long as a solid solution is formed. The parameter for grinding either increases or decreases (if a solution atom is greater than a solvent atom, only if a copper is in nickel grid or when a solvent atom is in the intersttial site).
The figure shows this. [ 2.4 ]. This distortion interferes with dislocation motion on sliding designs, thus increasing alloy power. This is the main cause of a metal by alloying.
A certain order of the arrangement of solute or solvent atoms takes place in many substitutive solid solutions, that is, a well organized solution is formed at a certain fixed ratio of solvent and solvent atoms (particularly at lower temperatures).
An ordered solid solution is a solid replacement solution whereby the atoms ideally organize themselves, that is, the two species are arranged in a regular pattern of alternative arrangements as shown in the figure. 2.3 (b), but Fig. (b) 2.3 (a) indicates a random solid solution in which atom replacement occurred at a random rate.
This preference to form unlike pair of atoms to form an ordered solid solution is expressed as:

where, EXY is the energy of an unlike-bond, and EXX and EYY are the energies of like-bonds between X – X and Y – Y atoms respectively. If EXY, the energy of the unlike bonds is very much smaller, then a long range order, i.e., an order over large distances, may take place. To illustrate this point in a unit ceil, let us take the case of beta-brass, which is BCC.
In BCC, two effective atoms per unit cell are present, one because of the atoms in the corner and the other because the atom of the body is centered. If the mass solution has equivalent atomic ratios of copper and zinc atoms, we have a stoichiometer composition where zinc atoms will occupy all of the corner points of the cells of the BCC system and all of the copper atoms are concentrated in the body (ratio1:1).
As illustrated in Fig, a perfect order is generated. a] 2.5. Each zinc atom consists of eight copper atoms, and each copper atom consists of eight zinc atoms. The alloy is subject to a switch from a disorderly (random) to a specified state in which it is refreshed below a critical ordering temperature (470 ° C in this case).
Only a critical and simple proportion of two atom groups, i.e. 1 to 1 or 3 to 1, is feasible for a perfect super grid. The figure shows this. 2.5 (b) and (c), respectively. Here, such solid solution can be applied to the formula for a chemical compound such as CuAu and Cu3Au. The solid solution ordered is different from a chemical compound, as the liquid metal crystal structure is preserved and the solution gets disordered over critical temperature.

(ii) Interstitial Solid Solution:

Solvent atoms here are far smaller than solvent atoms and therefore occupy the arbitrarily interstitial region (interatomic space) in the crystal lattice of solvent between solvent atoms. As shown in Fig., the solute atoms do not occupy grids. (b) 2.2. In FCC-iron (gamma-iron) carbon atoms, for example, dissolves by occupying the interstitial space in the iron structure of FCC-gamma.
Picture. 2.6 exposes one of these space-octahedral interstitial vacuum in which carbon is contained. There is a better fit of small carbon atom but the distortion of the glaze is still sufficient to prevent the position of carbon atoms at any interstitial site under FCC-Iron, as shown in 2.6(b).
The crystal structure of the solvent always increases in an interstitial solid solution. Such solutions are referred to in 2.6(b) as interstitial and solid solutions. Atoms with only few elements, as interstitial solutes in metals, are small enough. Table 2.1 lists atoms that form interstitial solid solutions with their atomic radii. Each of them has less than 1 A atomic radius.
Some atoms from the alloy elements may substitutively dissolve while others, such as carbon interstitially, are used in multicomponent alloys. Manganese atoms replace iron atoms in manganese steel at the points of lattice or carbon atom entries at the interstice, as shown in fig. As shown above. The second is 2.7.

Hume Rothery’s Rules for Primary Substitutional Solid Solubility:

The pioneering work of Hume Rothery on a number of alloy systems led to the formulation of conditions that favour extensive primary substitutional solid solubility.

These empirical conditions are called Hume Rothery’s rules (there are numerous exceptions to these rules):

1. Atomic-Size Factor:

The larger the difference in the base atom and solvent is the strong solubility. The size factor must be less than 8% for full strong solubility. It has more than 15 percent of atomic diameters, undesirable volume and small solid solubility.
Metals such as silver and gold have a difference of 0.2%; nickel and copper have a maximum solid solubility of 2.7%. However the difference between copper and zinc is 4.2% and its peak solubility 38.4% Zn. Cadmium in copper with a difference in size of 16.5% has a good solubility of 1.7 wt.% (other conditions are less favorable).
The size factor comes into play due to the elastic strains caused in the crystal lattice around a misfitting solute atom. The atoms of the solvent are pushed out or pulled in accordingly as the solute atom is larger or smaller than the solvent atom (or crystal site) as illustrated in Fig. 2.4 (a) and (b).
This change in the interatomic spacing from the ideal value increases the energy of the crystal. As the difference in sizes becomes more, more are then the lattice strains, lesser becomes the solubility of the solute.
Since the effect of the size factor differentiates from the isomorpher system Cu-Ni to the eutectic system Cu-Ag with partial solid solubility, if the other three factors are favorable, to 15 per cent, the equilibrium diagram changes. If the size factor is helpful, other factors should be weighed to assess the possible degree of solid solubility.

2. Electro-Chemical Factor:

When one solid solution is electropositive and the other component is more electronegative, a compound is more likely than a solid solution and solid solubility is lower. Electromegativity values can be used to quantify electro-chemical behavior.
As seen in table 2.2, traditional metal components typically have much fewer values and form solid solutions. A non-metallic element such as sulphur however has a value of 2,5 and therefore tries to form sulfides rather than dissolve into atoms. The compounds P, As, Sb and Bi are generally made of metals like Mg and Li. But there is some solubility if the variable sizes are favorable with lesser electropositive metals, including Cu and Ag.

3. Crystal-Structure Factor:

To achieve complete solid solubility, the crystal structure of the solute and the solvent metal should be the same. The crystal lattice parameter of each metal must be constantly changed to the other metal with an increase in the solute metal concentration.

4. Relative-Valency Effect:

A metal with a lower valence is more likely to disintegrate the high valence metal than vice versa, because other variables are similar. Both elements are better equally valid. The rule applies especially to copper, silver or gold alloys. The resistance of metal bonds to changes in electron concentration is expressed in this element.
It is generally found that an excess of electrons is readily tolerated rather than a deficiency of valence electrons. For example, zinc (divalent) dissolves up to 38.4 wt. % in copper (monovalent), whereas copper dissolves up to only about 3 weight % in zinc.
If the mutual solid solubility is restricted (as in Cu-Ag system) to only those portions of the phase diagram that are linked to the pure elements, the solid solutions formed are called as primary (or terminal) solid solutions, which have same crystal structure as of solvent metals. If other phases are present in the system, they are usually called intermediate phases, or intermetallic phases, having different crystal structure than either of the two elements. Such an intermediate phase having a range of solubility is called secondary solid solution.


From the following data, predict whether aluminium, nickel or chromium as solute metal shall form extensive substitutional solid solubility in solvent copper.

All solute metals have ± 15% radius difference but Al has a difference of more than ± 8%, which reduces the probability of 100% solubility. While Ni has greater similarity than other values, electro negative values are not greatly different. In contrast to copper FCC, the crystal structure of Cr is BCC which decreases the degree of solubility.
Ni in copper thus has the same glass structure, similar electronegativity and just–2.3% atomic radius differences. There is a good possibility of significant solubility. The difference in copper between atomic radius and electronegativity is important, and the same crystal structure that give about 10% solid solubility. Cr has a small percent differential of radius, little more electronegativity differential (the Ni) but different structures of crystal can lead to low solid solubility.

The observed experimental values are:

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