Part II:- Solid Solution and Alloys

 Part II:- Solid Solution and Alloys

In this lecture, we will talk about Solid solutions in the Metallic Context and Alloys, which are formed by mixing one or two or more elements. So, let me recap the initial the last lecture first [Part I:- Solid Solution and Alloys]. 

So, in the last class, we learned about Interstices. Interstices are nothing but voids that are present in the crystal structures. And there are two types of voids that we are concerned about, one is tetrahedral, and second is octahedral.

So, the tetrahedral void is characterized by 4-fold coordination because it is a body with the four corners. So, as a result the impurity that sits inside has four neighbors. Whereas octahedral is 6-fold coordinated void and if you have a regular tetrahedron and regular octahedron, in case of FCC and HCP structures, the size of an atom that can fit in tetrahedral in void is 0.225 of radius of the host atom. This is without distorting the tetrahedral void.

Similarly, roct is 0.414r. So, this is the maximum size of the atom that can fit in octahedral, tetrahedral impurities without distorting the octahedral or tetrahedral. Also we saw that in FCC and HCP, you have two tetrahedral voids per atom and one octahedral void per atom. Things are different for BCC, you do not have a regular octahedral or tetrahedral, but you do have octahedral and tetrahedral voids and whose location and numbers are different.

So, you were asked to count the numbers of octahedral and tetrahedral voids in BCC. So, I will leave it to you, that at that as home exercise, that is what the location of tetrahedral octahedral voids in BCC structure is? And what is their number?.

And you can also calculate, what is the size of the atom that can fit in there? You have to be a little careful there because the sites of tetrahedral and octahedral are different, they are not regular. As a result, you need to lo at the minimum size, the minimum side length. So, now, in this lecture, we will talk about Solid solutions.

Solid solutions are just like liquid solutions. They are the solution of two or more atoms into each other. So, what basically what does it mean? So, you have a lattice of some structure, let me first draw the 2-D diagram without getting into 3D. So, you have these atoms of host lattice. Now, of course, this is going very dilated, but it is not that dilated in reality. So, the impurity atom can go either here, a smaller impurity atom or the impurity atom can go here.

The question is, how do you arrange? Although, in some sense, Solid solutions are just like liquid solutions and analogous to such as when you mix two liquids or sugar in water or salt in water. So, salt molecules dissolving in the water or sugar molecules dissolve in the water, but since water itself is amorphous structure or it does not have periodicity where atoms go, it also of little consequence.

And water is generally a loosely structured phase. As a result, the impurity atoms salt atoms or some other atoms have plenty of spaces to go into, however, you as you notice in case of salt as well and you put. So, there is a saturation limit beyond, excess salt does not dissolve into the liquid. You can see that the excess salt and remains as solid within the water because the empty spaces within the water phase are already filled. So, it is saturated. So, then you go beyond saturation. Similarly, same thing happens with solids as well. Solids also can dissolve only a certain amount of solute. So, you have solute, and you have solvent. So, solvent is the host phase, and solute is the impurity phase. So, they can only dissolve a certain amount of solute in most cases.

There are some cases in which two elements can be put into each other, and they still remain the same single phase. In solids, what happens is that since atoms are periodically arranged. Sometimes you will see structures in which the impurity atoms also adopt structures that are ordered. So, there are various types of Solid solutions, and we will define them in now.

So, the first Solid solution is called as a substitutional solid solution. And the second solid solution is called an Interstitial solid solution. A substitutional solid solution means that the solute or impurity atom goes to host atom site. So, it replaces or occupies the same site as the host atom.

However, the manner in which it can do, that could be random. So, it can randomly go anywhere, or it could be ordered. So, this will be determined by various factors. So, for example, thermodynamics plays an important role, the configuration entropy will play important role in determining where will go, and temperature plays a very important role. So, it is a combination of enthalpy, entropy and temperature which will determine free energy of which structure will be minimum. So, you know that Δ𝐺=Δ𝐻−𝑇Δ𝑆.

So, there is enthalpy of mixing, there is entropy of mixing, and then there is a temperature term. These three terms together will determine whether the substitution will be random or whether the substitution will be ordered. Because, in the end, free energy has to be minimized. So, I will not get into the details of free energy of mixing, but I will recommend you to go through any basic book on thermodynamics, such as Phase Transformations by Porter Easterling and Materials. The second chapter of that book is very useful to understand mixing of two elements.

So, and the second Solid solution is Interstitial solid solutions. We know that the interstices may go to Tetrahedral site or Octahedral site. So, depending upon the size of the atom and the structure of the host phase whether FCC, BCC, HCP, the impurity atom might decide to go to any of these sites.

So, for example, let me make a little closer structure. So, this is let us say your B atom, and this is your A atom. So, A is the host phase, and B is the solute. In terms of chemistry, you call it a solvent phase host lattice. So, this is a random substitutional solid solution. So, here, you can see that your solid solution is random, and you can construct a lattice here, but your lattice has changed now. Because if you remember your primitive, non-primitive lattice concept, the lattice, in this case, is no longer a small blue square, rather it has become a the bigger this has become the lattice. So, this is called ordered substitutional solid solution. This typically happens when the impurity concentration is a little larger. 

So, random solid solutions form at lower concentrations, typically within the solubility limit. And ordered substitutions typically form at higher concentrations, and they form different phases altogether different structure altogether. And the Interstitial example could be like this. So, your interstitial atom may go here, for example, somewhere randomly. These are your interstitial sites. Now interstitial sites and reality may lead to distortion. So, the atom may be slightly smaller or slightly bigger than the interstitial site. So, it may create tensile or compressive stresses depending upon the size. So, in real situations they do create stresses. Similarly, insufficient solid solution they do create stresses because the size of the atom is not going to be exactly similar; there is got to be some difference. So, whether it is a difference of 1 %, 5 %, and 10 %, will determine eventually whether the solid solution will form or not.

But if the solid solution does form, then there are stresses in the structure. So, this is called interstitial solid solution. You can have ordered interstitial sites, as well. As we will see in case of silicon carbide or zinc sulfide, but it typically happens in the case of ionically or covalently bonded solids. In case of metallic solids, typically interstitial solid solutions are random in nature. So, random interstitial sites are randomly occupied, but we do have intermetallics, we do have ordered solid solutions in which you will have ordering of impurity at even at interstitial sites, but it is typically more common in compounds where covalent or ionic character is stronger.

Copper-Zinc is an example of Substitutional solid solution. Copper-Nickel is another example of Substitutional solid solution. Copper-Tin is also an al example of solid substitution solution. So, these are some examples of Substitutional solid solution. Your Interstitial Solid solution says Carbon and Iron is an Interstitial Solid solution. So, this is basically a steel right. Steel has a ferrite phase, which is α-ferrite, α-phase or α-iron. So, it is basically BCC iron with carbon atoms in interstitial sites. So, there are plenty of more examples in metallic systems, because most metals are impure, then even if you say it is 99.99 % pure, I mean there is 0.1 % impurity sitting there, and that impurity may go to interstitial or substitution sites.

So, let us look at the example of Copper-Zinc alloy first. This is with the Cu:Zn = 50:50. So, above 4700C, it makes a BCC structure. You can see that the structure is not same as Copper or Zinc. It makes a BCC structure, which is disordered. Below 4700C, it makes an ordered Structure. So, below 4700C, it loses something like this. So, these are your atoms. You do not know which one is Copper and which one is Zinc. So, there is an equal probability. So, this is above, above 4700C, it is possible that you know this atom will be Copper, some other will be Zinc, as a result, this is a disordered structure, and it is a BCC structure because each atom is 50% Copper, 50% Zinc. Below 4700C what happens is that there is a specific preference for sites. So, you can see that Copper makes one sublattice, Zinc makes another sublattice, and both of these sublattices are primitive cubic in nature.

        So, these are two interpenetrating cubic lattices of Copper and Zinc into each other, which are very ordered. So, this is below 4700C, and why this happens is that, if you look at this case, where there is a random distribution of Copper and Zinc, there is no preference for Copper-Copper bonds or Copper-Zinc bonds or Zinc-Zinc bonds. So, there is no preference for any particular kind of neighbor. In this case, below 4700C, Copper prefers to have Zinc as a neighbor, and Zinc prefers to have Copper as a neighbor because this changes the enthalpy. Enthalpy is depending upon the number and type of nearest neighbors.

             So, this is determined by thermodynamics, which will be stable. So, this is disordered, and this is the ordered solid solution. In disordered solid solution, you cannot say this is Copper atom, or this is the Zinc atom.There is a probability, but in case of ordered structure, you can make a difference, and this is very clearly seen in X-ray diffraction pattern. When you do the X-ray diffraction, it will show you a pattern for disordered structure same as a BCC material, which is very different for a cubic structure, primitive cubic, which is for ordered copper. Because here, you will see two superlattices, one of Copper, one of Zinc. So, they will have their effect on it. can we have this disordered structure at room temperature?

        Of course, you can have a disordered structure room temperature. Any dilute solid solutions are disordered. This is a very high disordered concentration; this is 50:50, but if you have 1% Zinc in Copper or for example, Copper-Nickel very good example, Copper-Nickel all the way it is FCC. So, you cannot distinguish which is Copper, and which is Nickel. So, at any concentration, each atom is a mixture of Copper and Nickel. The probability of each site being occupied by Copper and Nickel is determined by their fraction. So, if Copper-Nickel, 50:50, each atom is copper 50 % Copper and 50 % Nickel. I mean it is not real it will be either Copper or Nickel, but probability wise it is 50 % Copper, 50 % Nickel.

If it is 25 % Copper, 75 % Nickel, it will be 25 % Copper, 75 %. So, this is the disordered solid solution, which remains FCC even at room temperature.

The atoms are put in intentionally to improve the properties, second phases are, or other elements are added. So, it is intentional in many cases. In some cases, it is unintentional because we cannot remove the impurity, but in most cases, that is intentional like examples steel, which is Iron-Carbon alloys with up to 2% Carbon. Then, you have Brass, and Brass is Copper-Zinc alloy up to about 50 wt.% Zinc. And then, you have Bronze, which is a copper-tin alloy, which has up to about 12 wt.%. Now, here one interesting thing is copper has a structure which is FCC, Zinc has which is if HCP, Copper again has FCC, here Tin has HCP or which is it depending upon, but it is HCP. So the question is, what is the structure that the eventual alloys are going to take place, are there any guidelines? So, there are certain guidelines that are called Hume-Rothery rules.

Extensive solid solubility occurs when the size difference between two atoms is less than 15%, and there should be smaller difference in the electronegativity, which means they should not be very far apart in the Periodic Table; otherwise, they will make ionic bond. So, there should be smaller difference in electronegativity. The third is their valences similar. Now, these are not the only rules or guidelines because there are violations that are there, but by and large they are followed in most metallic systems. And fourth is the crystal structures should be similar.

    So, element with higher valence is likely to resolve in the element of lower valence. And if electronegativity difference is large, then instead of making alloy, it tends to make an ordered compound, it could be intermetallic, it is called a line compound. It has a higher high ionic or covalent character than metallic bonding because of the large difference in electronegativity.

So, these are certain guidelines that are to be followed when you form the structures. Deviations typically lead to lower solid solubility. If you have deviations from these rules they lead to lower solid solubility which means you cannot dissolve a large amount of impurity in the host phase, if there is a large size difference, if there is a large valence difference, there is a large change in the crystal structure because you know they are not compatible with each other as such.

So, let me give you some examples. For the first example, let us say Silver-Gold. So, we can see that Silver here has FCC structure, Gold has again FCC structure, Silver has a radius of 1.44Å, gold has a radius of 1.44 Å, it has a valence of 1, it has electronegative 19, it has electronegativity of 2.4. So they make a solid solution, which is extensive, extended solid solution. Similarly, Copper-Nickel, And the reason for that is Copper is FCC, Nickel is FCC, Copper has a radius of 1.28, Nickel has a radius of 1.25, their valence is a not similar by the way, Copper could be plus 1, electronegativities are fairly identical and they make extended solid solutions all the way from Copper to Nickel.

        And then Silicon-Germanium is another system which is a very well known system. So, Silicon-Germanium both are diamond cubic. I will come to diamond cubic structure, later on, Silicon radius is 1.22, this is 1.18, valence is 4 for both of them, electronegativity is same, so they make the extended solid solution.

        On the other hand, when you make Cu-Zn, Copper is FCC, Zinc is HCP. As a result of solid solubility is limited, you can only put 35 % Zinc in Copper. And nearly 1 % Copper in Zinc without making a second phase. It makes a Solid solution up to 35 Zinc on the copper side. And it makes a Solid solution only up to 1 % Copper on the Zinc side. If you are between these two ranges, then they make second phases that are not solid, which may or may not be solid solutions, but there are different phases because it cannot accommodate more Zinc or more Copper in it.

 

For the Previous Lecture Click below

Part I:- Solid Solution and Alloys

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