Covalent Solids

Covalent Solids

In this lecture, we will talk about covalent solids and ionic solids.

So, let me recap what we have studied so far. We looked at the structure of metals in past few lectures. So, structure of metals typically is of three types most metals are FCC structured, or you can say cubic close-packed (CCP) structured or hexagonal close-packed and BCC structured. There is only one example of simple cubic metal which is polonium.

FCC based materials like gold, Cu, nickel, etc, HCP based materials are magnesium, cadmium, etc. and then BCC based materials are titanium, tungsten, molybdenum, etc. Most metals do not exist in pure form, and we also use an impure form for improving their properties, for example, iron is used as an alloy of iron and carbon because carbon is intentionally put to make iron stronger. So, the question arises is where does carbon go?

Similarly, brasses and bronzes, which are solid solutions of Sn or Cu and Zn. And there are three famous examples of materials that we use in developing applications. So, where do these atoms go for example, where does Zn go? where does Sn go? where this carbon go? So, it is determined by the size of the atom, it is determined by the size difference between the host lattice and the impurity atom, it is determined by the valence difference, the structural difference, and so on.

So, it turns out that carbon and iron will make an interstitial solid solution, whereas Zn and Sn will make a substitutional solid solution because the size of Zn and Sn are larger than the size of interstitials that occur in these solids. So, carbon prefers to go to interstitial size because is smaller atom. So, whether it is a γ-iron or α-iron depending upon the temperature it goes in interstitial sites so solid solubility limit, and they make a solid substitution solution, and then we also saw some examples of compounds which are line compounds which have fixed composition intermetallics. Intermetallics can often be similar also, and then we also looked at electron compounds. So, these were 3 compounds which form when you mix two metals, and they tend to have fixed composition and for example, electron compounds they have fixed electron to atom ratio.

So, Fe3C, for example, is a line compound with a fixed composition you have intermetallics like Ni3Al, CuZn and so on. Electron compounds we looked at some Cu Zn type of compounds system which has electron, specifical electron to atom ratios. So, these are all materials that are metallically bonded materials predominantly, although intermetallics and line compounds may have some fraction of covalent ionic bonding, predominantly these are metallically boundary materials. So, now, we will look at the case of what we call as covalently bonded materials.

And this is again an important class of materials because there are a lot of materials which have covalent bonded, for example, you take group-VII B, basically halogens right. So, your Cl2, Br2, F2, I2 in solid-state, are covalently bonded, and they make a particular crystal structure which is based on covalent bonding.

Similarly, if you look at group-VI B will have molecules like S8 or even H2O. So, H2O will make, for example, hexagonal ice crystal. So, these are also covalently bonded materials this not something that we use in basis group-V elements, such as phosphorus, arsenic, bismuth, antimony also have strong covalent character, and they basically have this sheet-like layered structure in which each atom has three neighbors.

So, it is a layered structure, each atom having three neighbors. The group-IV contains silicon, carbon. Silicon carbide, solid solution of silicon and compound made by silicon and carbon, are all diamond cubic structured materials, and they are covalently bonded very strongly covalently bonded.

So, compounds, for example, you have 4-4 compound which is silicon of carbide, then, we have 3-5 compounds things like aluminum phosphide, aluminum arsenide, gallium arsenide, these are all famous semiconductors. The 3-5 semiconductors are strongly covalent in nature. The 2-6 compounds such as ZnO and ZnS are also strongly covalent, then we have 1-7 compounds; these are CuCl or AgI, and so on. The covalent bonding typically takes place by, so the theory which is about covalent bonding is called a valence bond theory.

The valence bond theory started with people like Linus Pauling, a famous physicist or chemistry. So, a covalent bond would form when the orbitals on the atoms would interact with each other. So, for example, if you take this orbital will depend upon how they align with each other, for example, in case of hydrogen, so when orbitals interact now this valence bond theory has undergone several modifications, the reason for that is earlier atomic this orbital interaction was fine, but there was no concept of orbital hybridization.

So, it is it was reasonably straightforward for spherical orbitals to interact or linear orbitals to interact, but when it came to things like silicon, methane, the question was why would something having two electrons in the outer shell make four nearest neighbors, and that would not be possible until you have SP3 kind of hybridization in the system, so hybridization concept came later. So, this modified, and I can write here valence bond theory and modifications, which were based on hybridization. So it is not only just orbital interaction, it is also orbital hybridization, which leads to better orbital interaction if you take the example of hydrogen.

So, hydrogen you know we know H atom is 1S, and another H atom is again 1S, and if you put these two together they form, so there is this overlap of orbitals, but when they interact with each other, one spin would be up another spin would be down. So, this would be H, and they would form what we call as H2 molecule, which is covalently molecule, and you can see that orbitals can interact with each other because they are spherical orbitals symmetric orbitals and they have to share one electron each.

For example, if you take the case of hydrogen fluoride has one H atom here, but the problem with F atom has P orbitals, through which it has to interact why does interact with a P orbital, so it will interact with a P orbit or something like that. So, you have this center F, and this will be another orbital, so this would be F, and then you have this axis x, y, and z-axis here total of 6 orbitals right. I am not drawing all the orbitals, but if I put them in different colors, so this would be ok. So, you will have a spin, so if you just put on this spin, they will be one spin up another spin down, and this would make HF, this is again a covalently bonded molecule. Similar examples you can give for fluorine, for example, F2 gas.

So, F2 gas has one orbital on this side, another orbital on this side and it will interact with the neighboring fluorine atom which will have P orbital like this and orbital like this, of course, you will have other two axes as well, and this will give you F2 molecule. So, this is fine, but the problem arose with silicon or let us say CH4 or methane is a good example.

In CH4, Carbon has a configuration of 1S2 2S2 2P2, and we know that in CH4, carbon will make four bonds, the question is why it will make four bonds? And how will the orbitals align with each other, and the measured angles bond angles are 109.50?

In this 4-fold coordination coordinated structure, for example, if you look at the top view this is carbon you do not have hydrogen sitting like that, they do not make if you if you look at the top view this angle would be 900, they do not make 900. So, this is like 900 according to valence bond theory this should be 900, but then if it was 900 then how come it is making four bonds because four bonds mean carbon will have to share the four electrons, where do those four electrons come from? So, these were the questions that led to sort of modified theory, So, this is what gave rise to questions, the questions were how could carbon make bonds with 4 neighbors? how could one have bond angle of 109.50? So, these were the questions they led to the answers in what we call as now hybridization.

So there are various kinds of hybridization that occur. So, for example, it is S and P-type of hybridization. So, you can have SP hybridization, and you can have SP2 hybridization, SP3 hybridization, the hybridized S, and P orbitals give you enough number of electrons. So that you can have sufficient number of neighbors to make that particular structure, for example, the covalently bonded structure. So, in case of methane the structure looks something like this, so you have this carbon atom sitting here; the hydrogen atom is here, one hydrogen atom is here, next hydrogen atom is here, another hydrogen atom is here.

So, this is hydrogen this is basically what they make is a tetrahedral kind of structure, so basically this is a tetrahedral kind of coordination. So, essentially what happens is that you have 1S orbital, this is 2S orbital, you can have 2P orbitals, for example, if this is my x-axis I can have 1P here, this is along the x, I can have another P along y, and then another P can be along z. So this is 2Px, 2Py, and 2Pz. If you look at the energetics, this is, for example, the energy scale, the isolated carbon atom so this is 2S of isolated carbon atom, this has spins like this is satisfied all right. So, whereas, in case of P we have three orbitals, this is up, this is up, and this is empty, so this is x this is y this is z, and this is 2 P all of them are 2P 2Px 2Py 2Pn.

So, In case of hybridization, what happens is that you make SP3 kind of hybridized orbital like this. So, this is we say as SP3 orbital, and this what you form is basically for SP3 orbitals. So, you have four electrons here. Each of them remains unpaired, and this is what is orbital hybridization. So, essentially what you will have is now you will have one hydrogen will come and attach to it, so this is another hydrogen will come in attached to this hydrogen will come very attached to this. This is how you will make a methane molecule. So, methane will now interact in such a fashion, so that you will have one central atom here.

Methane, carbon, and this will have a bond with one here, I mean I am showing the top view; another would be somewhere here, and they will make an angle such a fashion. So, that the angle between each of them will be 109.50, so these are all tetrahedral bonds. So this is basically you can say it is SP3 hybridization in CH4 molecules, this is what same happens in diamond, which makes silicon.

So, in case of a diamond, in silicon also, so in case of methane this would be carbon this would be hydrogen, this would be hydrogen, and this would be hydrogen, in case of silicon you will have a tetrahedron. So, this is tetrahedral that we can have, this is one silicon, this is another silicon, this is another silicon, this is another silicon, and one silicon will be sitting somewhere in the center. So, this is again silicon, and again they make tetrahedral coordination by SP3 hybridization, which would not be possible just by orbital overlap.

Can we understand this hybridization in terms of energetic? There is an energetic, of course, it leads lowering of energy, but I am not covering in this course because it is too extensive. But any basic book on, for example, a book by Atkins should be.

Now, but there are a few books which can deal with this any chemistry undergraduate books will give you the introduction, and there are a lot of theories, you have valence bond theory which is modified then you have molecular or orbital theory, there are lot of theories and covalent bonding.

So, this is the vertical one which will interact with one hydrogen, this is another one which will interact another hydrogen, and at the center you will have C, and all of these will have angles 109.50. So, these are all hybridized SP3 orbitals. They are not exactly P orbital; these are all hybridized orbitals.

So, what you see here this one this is a hybridized orbital. So, you can have other cases as well you can have, for example SP hybridization also, you can have SP2 hybridization, for example, graphite will not have SP3 hybridization and graphite has only SP2 hybridization and there are some other materials which will have SP3 hybridization. The bond which forms between these is called a σ-bond, and σ-bond is a very strong bond. There is another kind of bond which forms in molecules, which is called a covalent bond, especially in polymeric materials. So, you can have if you look at, so you can have these P-type of loops.

So, suppose you have these P-type of loops along the chains of a poly bar like this, the bond which forms between these and the neighboring ones is called π-bond or pi bond is a weak bond, and σ-bond is a strong bond. So, there are these are the two terms that you will come across π-bonds σ-bonds and π-bond, strong basically along the axis, and these are weak you can say these are basically at the periphery alright. So, typically, you will see if you have SP hybridization then the configuration will be linear.

So, SP will lead to linear configuration. If you have SP2 you will have triangular. So, the angles will be 1200. So, for example, in graphite you have tetrahedral then it is SP3. So, that I showed you have one loop here, another loop here, and these angles would be 109.550. As well as you can have SP3d and SP3d2, which I am not going to get into the details, and they are more complicated to draw. So, these are some examples, so this is the basis of covalent bonding.

So, there are the covalent the solids now when we come to materials, the covalent solids that we come across we start with. For example, graphite, graphite, is a form of carbon it has these hexagonal sheets. So, you have these hexagonal sheets of graphite, so you can see that each is having how many neighbors.

So, if you look at this, it has three neighbors, it makes an angle of it. So, this is SP2 hybridized structure and each of these layers, so when you put these layers, so if you now look at the cross-section, so these are the layers. So, this is one carbon layer, this is another carbon layer, so within the plane they are covalently bonded, and between the plane they are van der walls bonded. That is why graphite has this. So, graphite makes a unit cell whose C-axis is length 0.67nm. So, within the plane, you have SP2 bonds, and between the layers, you have a Van der Waals bond, as result, graphite has this very nice tendency to make slippery compounds. So, that is why graphite is used as a lubricant because graphite can be shared easily because the Van Der Waals bonding. So, within the sheet is strong it makes strong covalent bonds, but sheets themselves are not bonded strongly with respect to each other. So, shear very easily, and that is why it is used as a lubricant.

Now, in the next lecture there, we will discuss another form of carbon, which is again a covalently bonded solids, and that is diamond, which is SP3 hybridized material, and perhaps we will also look at some other structures of carbon if possible.

For the Previous Lecture Click below

Part III:- Solid Solution and Alloys 

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