How to view unit cells along crystallographic axes

A 3D unit cell looks different from every direction. This post shows you how to choose the direction in Crystal Lab.

You will learn the Look along controls, two step-by-step routines, and the mistakes to avoid.

Why the viewing direction matters

A unit cell is the smallest repeating box of a crystal. Its three edges define the axes a, b and c. Looking along an axis means your eye sits on that axis, so the axis points straight at you.

Seen this way, the cell flattens into a pattern. Atoms that lie one behind another on the same line overlap. The 3D cell then reads like a 2D drawing.

This helps you in three ways:

• You see the symmetry of the pattern, for example a square arrangement.
• You see which atoms sit directly behind others.
• You can match a textbook figure, which is usually drawn from one fixed direction, with the real 3D cell.

A freely tilted view hides all this. So fix the direction first, and rotate only afterwards.

Where the controls are

Open Crystal Lab. Choose a structure with Select structure, or press Random. You can also type a name, formula or element in Search structures.

The View panel holds the controls you need:

You can also drag the cell with the mouse to rotate it by hand. Use the Look along buttons first, because they give an exact direction. Your hand cannot.

Step by step: view a cell along an axis

Take face-centred cubic (fcc) copper as the example. You will find it under Elements and packing.

1. Pick the structure from Select structure, or search for it.
2. Press Reset so you start from a clean view.
3. Switch Cell on, so the box edges are drawn. Without the edges you cannot tell where the axes are.
4. Under Look along, press c. The c axis now points at you.
5. Note the pattern. In a cubic cell the three axes are equal, so a, b and c give the same picture.
6. Press a and then b. Check that the pattern repeats.
7. Press Reset before you move to another structure.

Now try a structure that is not cubic, such as hexagonal close-packed magnesium. Its c axis is different from a and b. Looking along c gives a different picture from looking along a. That is the point of the exercise: the direction changes what you see.

Step by step: view along a diagonal

A body diagonal joins one corner of the cell to the opposite corner and passes through the centre. In fcc and hcp, the close-packed layers are closely linked to the diagonal direction in the cubic case, so it is a useful view when you study close packing.

Crystal Lab gives two diagonal options:

• diagonal → viewer: the diagonal points at you. You look straight down it.
• diagonal vertical: the diagonal stands upright on the screen. You see it from the side.

Follow this routine:

1. Load fcc copper and press Reset.
2. Switch Cell on.
3. Press diagonal → viewer. The cell now shows a very different outline from the axis views.
4. Under Colour, choose Layer. Atoms are now coloured by layer.
5. Look at how the colours repeat. Then press diagonal vertical to see the layers stacked up the screen.
6. Switch on Build layers and watch the layers appear one by one.

The first view shows the pattern when you look down onto the layers. The second shows how the layers sit above each other. Use both when you study close packing.

Make the view easier to read

Other controls in the View panel help once the direction is set.

• Cells: choose 2×2×2 or 3×3×3 to see the pattern repeat. A single cell can look sparse.
• Atoms: switch between Ball and Touching. Touching shows atoms in contact, so you see how tightly they pack.
• Colour: Element colours by element. Layer colours by layer.
• Opacity: lower it to see atoms hidden behind others.
• Atom size: shrink the atoms if they cover each other.
• Bonds: switch bonds on to see which atoms are joined.
• CN: click an atom to see its coordination number, which is the count of its nearest neighbours.
• PNG: save the view as an image for your notes.

Change one control at a time. If you change everything together, you will not know what caused the change.

Common mistakes

• Rotating by hand and calling it an axis view. A hand-dragged view is almost never exactly along an axis. Use the Look along buttons.
• Forgetting to press Reset. The next structure then starts from an odd angle. Press Reset first.
• Keeping the cell edges off. You then cannot tell which edge is a, b or c.
• Assuming a, b and c always look the same. This is true only when the axes are equivalent, as in a cubic cell. For other systems, check all three.
• Counting atoms from a flat view. Overlapping atoms hide each other. Use the sharing rule instead: a corner atom is shared by 8 cells, an edge atom by 4, a face atom by 2, and an interior atom belongs wholly to the cell.
• Reading a diagonal view as a cell face. In diagonal → viewer, the outline is not a square face. Do not compare it with a face drawing from your book.

Key takeaways

Frequently asked questions

What does Look along mean in Crystal Lab?

It turns the cell so that the chosen axis or diagonal points toward you. You then see the cell as it appears down that direction.

Can I still rotate after choosing an axis?

Yes. Drag the cell to rotate it, or use the Rotate control. Press Reset to come back to the starting view.

Why do a, b and c look the same for some structures?

In a cubic cell the three axes are equal, so the cell looks the same from each. In lower-symmetry systems the axes differ, so the views differ.

Which structures can I try this on?

Crystal Lab lists simple cubic, body-centred cubic, face-centred cubic, hexagonal close-packed, rock salt, caesium chloride, fluorite, rutile and perovskite, among others. Try the same routine on each and compare.

How do I keep the view for my notes?

Use the PNG button to save the current view as an image.