Lattice Structures

Define Lattice Structure

If you zoom in on any material down to the atomic scale, you will find that the atoms are arranged in an orderly fashion. Imagine the carcass of a building. This arrangement of atoms is generally a repition of a basic arrangement of atoms. This "unit" which can make the entire structure of the material if repeated enough number of times is called the lattice structure of the material.

Types of lattice structures

Atoms or ions in a lattice can be arranged in multiple ways in 3D geometry.

Face-centred cubic (FCC) lattice structure

This is a cubic lattice, with an atom or ion at each of the 4 corners of the cube, plus an atom at the centre of each of the 6 faces of the cube. Hence, the name face-centred cubic lattice structure.

Body-centred cubic lattice structure

As you can deduce by the name, this lattice is a cubic lattice with an atom or ion at the centre of the cube. All the corners have an atom or ion, but not the faces.

Fig. 2: Body centered cubic lattice[1], Golart, CC BY-SA 3.0, via Wikimedia Commons

Hexagonal closest packed lattice structure

Now, the name of this lattice structure might not be painting a picture in your head right away. This lattice is not cubic like the previous two. The lattice can be divided in three layers, with the top and bottom layers having atoms arranged in a hexagonal manner. The middle layer has 3 atoms which are sandwiched between the two layers, with tthe atoms snugly fit in the gaps of the atoms in the two layers.

Imagine arranging 7 apples like the top or bottom layer of this lattice. Now try stacking 3 apples on top of these apples - how would you do it? You would put them in the gaps, which is precisely how the atoms in this lattice are arranged.

Examples Of Lattice Structures

Now that we know the arrangement that the atoms of a compound can exist in, let us look at some examples of these lattice structures.

Giant Ionic Lattice

You may remember from our articles on Bonding that Ionic Bonding occurs via the transfer of electrons from metals to non-metals. This causes metals to become charged by losing electrons, forming positively charged ions (cations). Non-metals, on the other hand, become negatively charged by gaining electrons. Ionic bonding, therefore, involves strong electrostatic forces forming between oppositely charged ions in a lattice structure.

These compounds can be arranged in giant ionic lattices called ionic crystals. They are referred to as “giant” as they are made up of large numbers of the same ions arranged in a repeating pattern.

An example of a giant ionic lattice is sodium chloride, NaCl. In the lattice of sodium chloride, the Na⁺ ions and Cl^- ions are all attracted to each other in opposite directions. The ions are packed together in a cubic shape with the negative ions being larger in size than the positive ions.

Fig. 3: Diagram of a giant ionic lattice of NaCl. StudySmarter Originals

Another example of a giant ionic lattice is Magnesium Oxide, MgO. Similar to the lattice of NaCl, Mg2+ ions and O2- ions are attracted to each other in its lattice. And also similar to the lattice of NaCl, they are packed together in a cubic lattice. Negative ions of Oxygen are larger than the positive ions of Magnesium.

Fig. 4: Lattice structure of magnesium oxide, MgO | Embibe

Covalent Lattices

Another important type of bond is Covalent Bond. Covalent bonding takes place between non-metals only.

There are two types of structures that can contain covalent bonding: giant covalent structures and simple covalent structures. The difference between them is that the electrostatic attraction holding giant structures together is stronger than the electrostatic attraction holding simple structures.

Simple Molecules

Some examples of simple molecular lattices would be iodine, buckminsterfullerene (C₆₀), and ice.

Buckminsterfullerene (C60) is an allotrope of carbon, which means its molecules only consist of carbon atoms. There are total 60 carbon atoms in buckminsterfullerene (C₆₀) which are arranged in 20 hexagonal rings, and 12 pentagonal rings. These rings form a spherical structure.

Fig.5: Diagram representing buckminsterfullerene (C60). StudySmarter Originals

When water freezes, the H2O molecules arrange themselves in a crystal lattice structure. Did you know that water expands when it freezes? That is because the water molecules get more space between them when arranged in a crystal structure than in liquid state. The red circles are oxygen atoms, and the yellow circles are hydrogen atoms.

Iodine is another simple molecule with its molecules arranged in a crystal lattice. Iodine molecules arrange themselves in a face-centric-cubic lattice. A face centric cubic lattice is a cube of molecules with other molecules on the centre of the faces of the cube.

Fig. 6: Iodine unit cell, shared under public domain, Wikimedia commons

Lattice of iodine can be a little hard to visualize even with an image. Look at the lattice from above - you'll see that molecules on the right and left side of the cube are aligned in the same way, while those in the middle are aligned the other way.

Giant covalent structures

Examples of giant molecular lattices are graphite, diamond, and silicon (IV) oxide.

Fig. 7: Shapes of the giant molecular lattices. StudySmarter Originals

Graphite is an allotrope of Carbon i.e., it is completely made up of carbon atoms. Graphite is a giant covalent structure because millions of carbon atoms can exist in a single molecule of graphite. Carbon atoms are arranged in hexagonal rings, and several rings are joined together to form a layer. Graphite consists of several of these layers stacked on top of each other.

Fig. 8: Structure of Graphite, shared under public domain, Wikimedia Commons.

The bonds shared by carbon atoms in a layer are strong covalent bonds. Each carbon atom makes 3 single covalent bonds with 3 other carbon atoms. There are weak intermolecular forces between layers (shown by dotted lines in the figure). Graphite is a unique material with some very interesting properties and uses, which you can read more about in an article dedicated to Graphite.

Diamond is yet another allotrope of carbon, and a giant covalent structure. Diamond and graphite both are made completely of carbon, but have completely different properties. This is because of the difference in the lattice structure of the two compounds. In diamond, carbon atoms are arranged in a tetrahedral structure. Each carbon atom makes 4 single covalent bonds with 4 other carbon atoms.

Fig. 9: Structure of Diamond | Carbons are arranged in a tetrahedral geometry | shared under public domain, Wikimedia Commons

This tetrahedral geometry makes diamond the hardest material in the world! You can read more about Diamond in an article dedicated to it.

Another example of a giant covalent structure is silicon (IV) oxide, also known as silica. Silica is the major constituent of sand. The chemical formula of silica is SiO₂. Like diamond, atoms in silica are also arranged in a tetrahedral geometry.

Fig. 10: Tetrahedral geometry of Silicon dioxide | Created using images from Wikimedia commons shared under public domain

Due to the tetrahedral structure, silicon (IV) oxide is very hard. Silica is also used in the formation of glass.

Metallic Lattices

When atoms of metals are closely packed together, they create a regular shape which we call a giant metallic lattice.

Within this lattice, there are free electrons in the outer shell of the metal atoms. These free electrons are also known as ‘delocalised’ electrons and they are free to drift around the structure allowing positive ions to form. This causes Metallic Bonding to occur.

An example of a metallic lattice is calcium, and its ions have a 2+ charge. Copper forms a face-centred-cubic (FCC) lattice. In an FCC lattice, there is an atom at each vertex of the cube, and there is an atom at the centre of each face of the cube. Metals form giant metallic structures as they consist of millions of atoms.

Characteristics Of Lattices

Ionic Lattices

Giant ionic lattices have very high melting and boiling points because of the strong attraction holding the ions together.

They conduct electricity but only when they are dissolved or molten. When ionic lattices are in a solid state, their ions are fixed in position and cannot move so electricity is not conducted.

Giant ionic lattices are soluble in water and polar solvents; however, they are insoluble in non-polar solvents. Polar solvents have atoms that have a large difference in Electronegativity. Non-polar solvents contain atoms with a relatively small difference in electronegativity.

Covalent Lattices

Simple covalent lattices:

Simple covalent lattices have low melting and boiling points because they have weak Intermolecular Forces between the molecules. Therefore, only a small amount of energy is required to break the lattice.

They do not conduct electricity in any of the states – solid, liquid, or gas as there are no ions or delocalised electrons to move around the structure and carry a charge.

Simple covalent lattices are more soluble in non-polar solvents and are insoluble in water.

Giant covalent lattices:

Giant covalent lattices have high melting and boiling points as a large amount of energy is required to break the strong bonds between the molecules.

Most of these compounds cannot conduct electricity because there are no free electrons available to carry a charge. However, graphite can conduct electricity because it has delocalised electrons.

These types of lattices are insoluble in water as they don’t contain any ions.

Metallic Lattices

Giant metallic lattices have moderately high melting and boiling points because of the strong metallic bonding.

These lattices can conduct electricity when solid or liquid as free electrons are available in both states and can drift around the structure carrying an electric charge.

They are insoluble in water due to the metallic bonds being very strong. However, they can be soluble in only liquid metals.

Lattice Parameters

Now that we have understood different types of lattice structures and their characteristics, we will now look into lattice parameters which will describe the geometry of a unit cell of a crystal.

Fig. 12: A unit cell of a simple cube with lattice parameters marked | Archana Tadimeti | StudySmarter Originals

Lattice parameters for this simple cube are a,b,c and angles \( \alpha , \beta , \gamma \). All of these are collectively called as lattice parameters which are the same for some other cubic systems like FCC or BCC.

For simple cubic, FCC and BCC, the dimensions a,b, and c are equal, i.e., \(a=b=c\) and the angles between them \( \alpha = \beta = \gamma = 90^ \circ \).

Lattice Constants

Lattice constant are unique for each crystal depending upon the structure of their unit cell. For example, the lattice constant, a of Polonium is 0.334 nm or 3.345 A^° . How has this been derived?

To understand this, let us have a look at how the polonium atoms are distributed in its simple cubic lattice.

Fig. 13: Simple Cubic crystal | Cdang,Samuel Dupré,Daniele Pugliesi CC BY-SA 3.0, via Wikimedia Commons[3]

Each Po atom sits on the corners of the cube. As you know that this cube is not alone but surrounded by unit cells three dimensionally. That is why this picture depicts only the parts of the atom (assumed as spheres) that are within this particular unit cell, hence drawn as if the atoms are 'chopped off', whose remaining spare parts are with other unit cells surrounding this one.

Now, let us get back to the length of each edge of this unit cell-represented by 'a' . Each atom at the edge has a radius of 'r'. Thus, the length of the edge, \(a = r + r = 2r \).

Now that we are clear that \( a = 2r\) , we will use this to calculate the lattice constant of Polonium.

From the periodic table, the atomic radius of polonium , \(r = 0.168\space nm \) . Therefore, the lattice constant of Polonium is \( 2 \times r = 2 \times 0.168 \space nm = 0.336\space nm \) .

Now that we have understood what a lattice constant is, let us jump into a few uses of studying lattice structures.

Uses of lattice structure

The lattice structure that the atoms of a compound form affects its physical properties such as ductility and malleability. When the atoms are arranged in a face-centred cubic lattice structure, the compound exhibits a high ductility. Compounds with an hcp lattice structure exhibit the lowest deformability. Compounds with bcc lattice structure lie between those with fcc and hcp in terms of ductility and malleability.

The properties affected by lattice structures are used in many materials applications. For example, atoms in graphite are arranged in an hcp lattice. Since the atoms are arranged with an offset to the atoms in the layers above and below, the layers can shift with respect to each other relatively easily. This property of graphite is used in pencil cores - the layers can shift and detach easily and be deposited on any surface, allowing a pencil to "write".