Simple Cubic

Viewer (top-left)

Left-click (or touch) and hold to rotate.
Use mouse wheel (or two-fingers scroll) to zoom in and out.
Double-click (or double-tap) to highlight a specific sphere, in all views except "Coordination" .
Holding shift while double-clicking (or double-tapping) allows highlighting of 2 to 4 spheres.
Holding space while double-clicking (or double-tapping) allows you to highlight interstitial sites.
If 2 (or 3 or 4) sphere are highlighted, an arrow (or plane or tetrahedron) is drawn to connect them.

Buttons (bottom-left)

Navigate to different views with the buttons.
Within the "Slice" view, use the arrow keys to move and rotate the slice plane. Holding shift while pressing the left or right arrow key will rotation the plane along the other axis.
The "Help" button shows this screen.

Controls (left)

Use the "Question #" input area to start, and later stop, an answer to a specific homework question.
Use the "Miller Index" input area to define a plane. (This will also be populated if you define a plane by double-clicking, or double-tapping).
Use the "Mirroring" input area to extend the model in the x,y and/or z directions.
Additional controls are also provided to turn on/off various aspects of the model.

Click anywhere to begin.

Credit: Aaron M. Geller - Northwestern IT / Jonathan Emery - Northwestern Materials Science and Engineering

Question #

Start

Lattice Position: q r s

Lattice Direction: [u v w]

Lattice Plane: (h k l)

Mirroring

Additional Controls

Tooltips On

Atoms On

Cubic Off

Atomic Positions:

$0 0 0$

Atoms touch along body diagonal:

Coordination

$= \color{maroon}{6}$

Atoms per unit cell:

$n = N_i + {N_f \over 2} + {N_c \over 8} = 0 + 0 + 1 = 1$

Lattice parameter:

$a = \color{red}{2 r_{\mathrm{SC}}}$

Atomic packing factor:

(APF) =

${n V_{\mathrm{atom}} \over V_{\mathrm{u.c}}} = \color{red}{0.52}$

Calculate density:

$\rho = {\color{green}{n} \color{maroon}{A} \over \color{darkcyan}{V_{\mathrm{u.c.}}} \color{purple}{N_{\mathrm{A}}}}$