You are here: Material Science/Chapter 1/Bonding

Crystal Structure

Before we talk about bonding, let’s introduce the concept of crystal structure very briefly.  What exactly is crystal structure?  Let’s back up a bit.  We’re going to be talking about materials.  Materials are made up of atoms.  A crystalline material (liquid or solid) has crystal structure.  And the crystal structure is just the way the atoms are arranged.  If a material is crystalline, then the atoms will be arranged very specifically – they are highly ordered, and a pattern of atoms will appear throughout the material.  In other words, the placement of atoms isn’t just random.  Take a look at Figure 1, with the spheres representing individual atoms.  That is a crystal structure (just an illustration, not any particular crystal structure).

A little more detail: a crystal structure is just a certain arrangement of atoms repeated throughout the structure.  Not all crystal structures are the same.  Different crystal structures have atoms in different arrangements.   So when we’re talking about crystal structure, it is useful to break it down into smaller, manageable units.   How can we do this?  By looking at the smallest repeating pattern that makes up the broader structure.  In the 2D pattern in Figure 2, the smallest repeating pattern is the part shown on the left.  If we know what that looks like, then we can simply repeat this many times to create the overall pattern.  It’s exactly the same thing with a crystal structure, except that it’s 3D instead of 2D and atoms instead of shapes.

Unit Cell

This smallest repeating unit is called the unit cell.  Let’s use another analogy for explaining crystal structure.  Think of a moving van with boxes of your stuff packed in the back. Obviously, you want to minimize the number of trips you need to make, so the boxes aren’t haphazardly thrown in – they’re ordered and structured to make efficient use of the space.  The boxes are the smallest repeating thing that you’re putting the van.  Now imagine that in each box, there is a certain arrangement of atoms.  Maybe there’s an atom in the middle, and one at each corner.  Each group of atoms, contained within the moving box, is the unit cell.  Say you have many of these boxes full of atoms, all identical.  Now let’s say you stack these boxes in each direction to create a larger box made up of these smaller boxes.  Take the box away, so that only the atoms remain, and you’ve just created a crystalline material.

Lattice Parameters

Now all we need a way of describing the shape of these unit cells.  Back to the moving boxes for a second: if a friend asked you how big the boxes were, you’d simply tell them the dimensions of the box -e.g 3’x3’x3′.  For describing unit cells, it is very similar: we do by using what are called lattice parameters. Fancy name, but really just describes the dimensions of the unit cell.  The parameters a, b and c describe the box edge lengths, and the parameters alpha, beta, and gamma describe the angles between these lines. Of course, for our cubic moving boxes, a, b, and c will be equal and all angles between the lines will be 90 degrees, since it is a box.  We’ll be discussing lattice parameters more on the next page.

Atomic Bonds

Now that you have as simple understanding of unit cells, we can talk about what is holding the atoms in these unit cells together: atomic bonds.  Let’s do a bit of review here, from high school chemistry,  Atoms all have an atomic number, which is designated by the letter Z, which is the number of protons that the atom contains. Hydrogen has an atomic number of Z=1, which means it contains a single proton. As you move along the periodic table, each element has one more proton than the previous one. The atomic number is unique, and can be used to identify the element.  Now, let’s explain what a neutral atom is, because this is important. A neutral atom has a neutral charge – a net of zero. For that to happen, it needs the same amount of positively charged particles and negatively charged particles. Since protons are positively charged, a neutral atom needs the same amount of electrons, which are negative. All this means is that for a neutral atom, the atomic number is also equal to the number of electrons.

The Bohr Model

The chemical properties of the element are directly a result of the number of electrons that are orbiting the atom.   According to the Bohr model, electrons orbit the nucleus of the atom at discrete energy levels called shells.

Disclaimer: Before going further, just a note about the Bohr model and the following explanation of bonding.  The Bohr model is very intuitive and commonly taught since it is useful for explaining the chemical bonding and reactivity of elements.  But it doesn’t actually accurately describe where the electrons are or how they are distributed around the nucleus.  In reality, electrons don’t just orbit the nucleus like the earth orbits the sun – instead, there are regions in which electrons are likely to be found at any given time (we can’t say for sure at a given moment where an electron will be located, but we can mathematically calculate where it is likely to be).  These regions, known as electron orbitals, are often complex shapes.  Knowing all this, just accept the simplified Bohr model for now, since we are trying to learn about material science, not quantum mechanics, and that level of detail won’t concern us.

In the example shown below, which is the Bohr model for aluminum, there are two electrons in the first energy shell, n=1, which is the maximum number of electrons that can be in the first shell for any atom.  N=2 can have up to 8 atoms, which aluminum does.  The outermost shell in this case, n=3, has 3 electrons.  (Note that this shell can have up to 8 electrons, just like n=2).  So the total number of electrons is 13.  The atomic number is also 13, which means there are 13 protons.  Since the number of protons and electrons is the same, then this is a neutral atom.

 

A bit more detail on the energy levels of electrons. The energy levels are quantized – just a fancy word for discrete or specific. It’s like saying that an electron can have an energy level of either 1 or 2, but nothing in-between. One or the other. So as electrons orbit the nucleus, they do so in different energy levels, which are specific levels of energy. Think of the rings of a tree trunk; there are only rings are discrete distances as you travel further away from the centre. Same idea with electrons – the rings of the tree turns represent the discrete energy levels.

Valence Electrons

What is important is the outmost shell of the atom – the electrons located here are termed the valence electrons. These electrons are key to bonding.  A stable electron configuration occurs when the valence shell is completely filled (the shell contains the maximum number of electrons).  When the outer shell of an electron is not completely filled is when the interesting things begin happening, as this forms the basis for chemical reactions.  Atoms want to have a stable electron configuration, and so if the valence shell is not full, they will try to achieve a stable configuration by either gaining or losing electrons (to form charged ions) or they will share an electron with another atom.  The life goal of an atom wanting it’s outer shell to be perfect is why we have chemical reactions and atomic bonding. It’s all about finding equilibrium, about finding that perfect, poetic balance. It’s the driving nature of nearly everything, really.

Back to the aluminum model in Figure 4.  The third energy level could have up to 8 electrons, but there are only 3 electrons, so the outer shell is not completely filled.  In some cases, aluminum will give up its 3 valence electrons, so that it can have a filled n=2 shell (8 electrons).  Note that some atoms naturally have a stable electron configuration  – this means that the outermost shell is completely filled.  Since these atoms are content, they are extremely boring and interactive – the noble gases.

Ionic Bonding

Ionic bonding is common, and luckily it’s fairly easy to understand and visualize. First, as an example, take a nonmetallic and a metallic element, at horizontal extremes of the periodic table. Now, let the metallic metal give up electrons to the non-metallic. The metallic loses an electron, the non-metallic gains one. There is a reason they did this: both atoms have now inert gas configurations. They both have full outer shells. But they are no longer neutral atoms. In both atoms, the number of protons no longer matches the number of electrons, since some electrons were shifted from one atom to another. This means that both of these atoms are not longer chargeless – they indeed have an electrical charge, and now we have to call them ions.  Now, the two ions are oppositely charged and are attracted to each other. And there it is: ionic bonding. Of course, it can be more complex than just a metallic and nonmetallic element.  This type of electron transfer is known as electrovalence (there’s also covalence, which we’ll see in a second).

 

Usually when ionic bonds form, we can’t really discuss two individual atoms being bonded together.  Instead, when these bonds form, its usually many, many atoms that come together, and so it is more of a group or collective bond – like a ‘glue’ holding everything together.  This differs from covalent bonding, where we can more explicitly say that atom X is bonded to atom Y.  Another interesting fact about ionic bonding: the bonding is nondirectional – the attraction is equal in all directions around the ion. What results is a positive ion being surrounded by negative ions, which are all surrounded by positive ions, and so on.  This results in tightly packed ions that use up space efficiently.

Covalent Bonding

Whereas atoms give up and receive electrons in ionic bonding, covalent bonding is all about electrons sharing.  There’s two key points:

• 1) electrons are shared by adjacent atoms;
• 2) two atoms covalently bonded can share one or more electrons. These electrons belong to both atoms.

 

 

Why do they share the electron?  You guessed it – to obtain a full outer shell, to become just like that noble gas they idolize. This type of electron transfer is know as covalence. ‘Co’ just means together, and ‘valent’, as in valence electrons in the outer shell.   What types of elements covalently bond?  Quite a few types!  Nonmetallic elements of the same kind can join together, such as H2, shown in Figure 5. Or, dissimilar atoms such as hydrogen and oxygen can share electrons as well – to make water!

Ionic or Covalent?

How do you know whether atoms will share or transfer electrons?  How do you know whether it will be covalent or ionic bonding?  What matters is the electronegativities of the atoms. All that the electronegativity describes is how attracted electrons are to an atom or molecule. This will depend mainly on a couple of things: the number of protons (more protons, more positive charges, more pull on the electrons) and the distance at which the valence electrons are from the atoms nucleus.  If the valence electrons are far away in some distant energy shell, then the pull towards the nucleus will be less. If the electronegativity is high, then the electrons are really attracted to the nucleus.

For the bonding to be purely covalent – the electron shared (shared meaning that it spends its time, on average, halfway between the two atoms) – the atoms would have to be equally attractive to that electron, so the electronegativities with be equal or very similar.  If there is a big discrepancy between atoms in terms of electronegativity, then the electron will just go to that more attractive atom, which is ionic bonding, not covalent bonding. In the H2 case, the electronegativity of both hydrogen atoms is exactly the same, so the electrons are shared, not transferred. What about the H2O case?  The electronegativities of hydrogen and oxygen are different, so what happens?  Is the water molecule held together by ionic or covalent bonding?

Well, although the electronegativities of hydrogen and oxygen are different, they still bond covalently. But what happens is that the relationship of sharing the atom is unequal; one of the atoms is a bit more attractive, and so everything isn’t perfect. The unequal relationship is know as a polar covalent bond – polar referring to how there is some polarity, as in north-south type stuff.  This is because the shared electron might be pulled closer to the atom with higher electronegativity, and so that side becomes a little more negative, because the electron is a bit more on that side.  And on the other side, the molecule is a little bit more positive. This is effect is demonstrated with the drawing below of the water molecule:

Metallic Bonding

Stating the obvious, but metals are important in engineering. Metallic bonding is found in metals and their alloys. Metals usually have one, two or sometimes three valence electrons (such as aluminum). So the metal atoms make an agreement: these electrons won’t belong to any one atom in particular – let them drift around throughout the metal, some here, some there, like a sea of electrons. An expression you’ll hear a lot is an electron cloud. The metal is clouded with these free electrons, we’ll say. Now what we have remaining is ion cores – these are all the atoms that have lost their valence electrons to the electron sea. And since they have lost electrons, the ions are positive. Positive ion cores sounded by a sea of electrons. Okay, but where and how does the actual bonding take place?  Well, the sea of electrons, which are the free valence electrons floating around aimlessly between the positive ion cores – they hold everything together like glue. All of the positive ion cores are attracted to them, and things are squeezed tight. Like so:

Mechanical properties can often be explained by examining what types of bonds the material contains. We’ll see all this later!  A preview: metals are good conductors of heat and electricity due to their electron clouds. Conversely, ionic and covalently bonded materials are terrible at conducting, because all of the electrons are spoken for. This concept will be discussed more later, in the circuits chapter.

That’s it on bonding for now.  Don’t worry if some of this isn’t entirely clear, or you’re finding that there is gaps in your knowledge, as the coverage of these concepts has been brief. But remember that this knowledge is not all that important when it comes to materials science for the average engineer – at least, the average mechanical engineer. But it is interesting, and useful, to know what’s happening down there on the smallest level.  Because ultimately, everything begins and ends there.

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