Crystal Lattice — Structure & Formation

What Is A Crystal Lattice?

A crystal or crystalline solid is a solid with a highly organized structure. The molecules, ions, or atoms that make up the crystal are arranged in ordered patterns throughout the solid called a crystal lattice. The crystal structure is a description of the ordered arrangement within a crystal. This order occurs throughout the entire crystal and because it is so extensive, it can be visible by eyesight. Crystalline solids will have distinct angles, lines, and faces.

Formation Of Crystals

When crystals are formed the process is known as crystallization. There are various ways this can occur such as:

• Precipitation: solid crystals can form by manipulating a solution. This can be done by concentration, evaporation, adding other solvents, and more. A common example is salt water. Salt crystals form out of the solution when the water evaporates.

• Freezing: since crystals are solids, they can be formed when energy is removed from a higher energy phase. An example of this is snowflakes. When precipitation becomes cold enough, the water turns to ice. Snowflakes are examples of crystalline solids.

Once a small amount of solid begins to form, it is called a nucleation site. More layers of atoms/molecules/ions are added to the nucleation point. The layering forms defined, consistent shapes, or the crystal lattice. The more time and substance available, the larger the crystal can grow.

Crystal Structures

The organized structure of crystals has repeating patterns throughout. The smallest repeating pattern of the crystal is called a unit cell. The symmetry within crystal structures can be described by space groups. Space groups describe the three dimensional symmetry within the crystal related to the unit cell and overall shape.

(Video) Lattice Structures in Ionic Solids

by Professor Dave Explains

In this video, Professor Dave shows you different types of crystal lattices. He uses a program called ChemDoodle to show you each variety. Dave starts with two examples of a simple cubic: polonium metal and cesium chloride. Next, he demonstrates two face-centered cubics: zinc sulfide and calcium fluoride. Finally, you'll see an aluminum oxide configuration with a rhombohedral unit cell. If you're looking for a deeper understanding of crystal lattices, this video can help you visualize the lattices.

When we learned about bonding, everything was easy. In ionic bonds, a metal and nonmetal transfer electrons to create ions. Why? Because of the immense electronegativity difference. The electrostatic interactions hold the two ions together. In covalent bonds, the electronegativity differences are much less. So, they share electrons between them. Soon, we learned about molecular geometry. Covalent compounds can form unique shapes based on they're bonding. We can predict those shapes with VSEPR theory.

We've spent a lot of time on covalent compounds. But we glossed over ionic compounds. It turns out that they also have a geometry classification system.

Ionic Lattices

When we think of ionic compounds, we think of crystals. The first one that comes to my mind is sodium chloride. That's table salt. But how do ionic compounds form crystals? When you examine a crystal, it looks uniform. They often have flat faces and sharp edges. Why? Because the atoms are in a very orderly arrangement. The microscopic structure produces macroscopic properties. The atoms create a repeating pattern that extends throughout the whole crystal. We call the repeating pattern a unit cell. It's the smallest repeating unit. The shape of the unit cell correlates to the geometry.

The simplest unit cell is a cubic. Like it sounds, the atoms arrange in a cube shape. Unfortunately, polonium is the only pure element that is cubic. But, many compounds are simple cubics. The best example is sodium chloride. The cubic geometry also had two derivatives. The first is the body-centered cubic. The atoms form a cube, but there is an extra atom at the cube's center. The most complex is the face-centered cubic. In it, additional atoms sit at the center of each side of the cube. There are many other unit cell geometries, like octahedral and rhomboidal. But, you don't typically study them unless you take inorganic chemistry.

Covalent Lattices

Sometimes, covalent compounds will assemble into crystals. We call them network covalents. Why? Because they form massive substances interconnected by covalent bonds. The most common example is diamond. In diamond, each carbon atom single bonds with a neighboring carbon. So, it has a tetrahedral VSEPR geometry. Another example is graphite. It's composed of repeating hexagonal rings. Each bond alternates between a single and double bond. So, we have delocalized pi bonding! It has opposite properties compared to diamond. For example, it is soft, malleable, and conductive. They consist of the same element. But, the bonding changes everything!

Another standard network covalent is silicon dioxide. You might even have a chunk in your home. It's probably from a random family vacation. Rock shops often sell it at tourist sites. The common name is quartz! In silicon dioxide, the silicon atoms form four single bonds. Two with oxygens and two others with silicon atoms. Again, the tetrahedral geometry repeats throughout the crystal.

Molecular and Atomic Crystals

Ionic and covalent crystals consist of bonds. But, we can also form crystals from Van der Waal's forces. The most common example is ice or snow. Water creates unique crystals. But, the molecules get held together by hydrogen bonds. We can also generate crystals from atoms. For example, you can look up pictures of solid xenon. It looks like ice. But, the atoms interact via dispersion forces. That's why its freezing temperature is -170 celsius!

How Do We Know?

Are you wondering how we know the shape of a crystal? Analytical chemists use x-ray crystallography. X-rays have unbelievably minuscule wavelengths. When they hit an atom's electrons, they get deflected. Often, the deflected x-rays destructively interfere. But sometimes, they constructively interfere. With constructive interference, we can apply Bragg's law. It's $n\lambda=2dsin{(\theta)}$.

In the equation...

• $\lambda$ is the wavelength.
• $\theta$ is the deflection angle.
• d is the distance between planes.
• n is an integer. It connects the wavelength with the deflection angle.

But what does Bragg's law tell us? Basically, atoms that are along the same angle will have the same $\theta$ value. But, d changes based on the atom's depth. Imagine two atoms along a diagonal line. The x-ray will scatter off both at the same angle. But, one is below the other. So, d is the distance between them.

Polymorphism

Sometimes, compounds can have the same elements but different shapes. We call this polymorphism. It's a type of allotropy. For example, consider calcium carbonate ($CaCO_{3}$). Two of its polymorphs are calcite and vaterite. Both are common geological minerals. In calcite, each calcium atom interacts with six oxygens. So, it has an octahedral geometry. But vaterite, forms sheets of alternating calcium atoms and carbonate ions. They have the same chemical formula. But, they have different molecular geometries. So, they're polymorphs!

(Video) How Do Crystals Work?

by TED-Ed

In this short video, TED-Ed explains crystals. You'll learn about where crystals come from, their geometry, their atomic structure, and why they sometimes have defects. It's a great video if you want to know more about crystals.