Solid state — crystalline vs amorphous; unit cell, Bravais lattices: Question bank

True or false — justify

Glass is a solid with long-range order.

False — glass has only short-range order; it is an amorphous "supercooled liquid" that softens over a temperature range, so it is not crystalline.

Amorphous solids are isotropic.

True — their random arrangement makes every direction statistically identical, so measured properties (refractive index, conductivity) are the same in all directions.

Crystalline solids are isotropic because their pattern is regular.

False — regularity is exactly what makes them anisotropic; slicing along dense rows versus gaps gives different properties per direction.

A crystalline solid melts over a range of temperature.

False — all bonds sit in identical environments and break at the same temperature, giving one sharp melting point.

Every corner atom of a unit cell contributes a whole atom to that cell.

False — a corner is shared by 8 cells, so it contributes only

\frac{1}{8}

of an atom to any one cell.

The unit cell is always the smallest possible chunk that contains one atom.

False — the unit cell is the smallest repeating block; e.g. FCC has

Z = 4

atoms yet is still one unit cell.

There are 14 crystal systems.

False — there are 7 crystal systems (box shapes) and 14 Bravais lattices (shapes plus centring); do not swap the numbers.

A hexagonal system has three edges all equal in length.

False — hexagonal has

a = b \neq = c

with angles

9 0^{\circ}, 9 0^{\circ}, 12 0^{\circ}

; only cubic and rhombohedral force

a = b = c

All seven crystal systems allow face-centred (F) Bravais lattices.

False — most centrings are redundant for a given shape; only cubic and orthorhombic actually keep a distinct F lattice.

Amorphous solids have a definite, sharp heat of fusion.

False — because bonds break over a range, the energy to melt is spread out, so the heat of fusion is not sharply defined.

Spot the error

"FCC has

Z = 6

because a cube has 6 faces."

Wrong — each face atom is shared by 2 cells and counts as

\frac{1}{2}

, so faces give

6 \times \frac{1}{2} = 3

; adding corners

8 \times \frac{1}{8} = 1

yields

Z = 4

"BCC has

Z = 1

because the body-centre atom is shared."

Wrong — the body-centre atom lies entirely inside one cell, is shared by nobody, and counts as a full

1

; with corners this gives

Z = 2

"Rubber is crystalline because you can stretch it into a solid shape."

Wrong — the ability to hold shape is not long-range order; rubber lacks a repeating lattice and softens gradually, so it is amorphous.

"The lattice already includes the atoms."

Wrong — a space lattice is an abstract array of points; you must place a basis (atom/ion/molecule) on each point to build the real crystal.

"Triclinic has one

9 0^{\circ}

angle."

Wrong — triclinic has no right angles and all three edges unequal (

a \neq = b \neq = c

α \neq = β \neq = γ

, none

= 9 0^{\circ}

); it is the least symmetric system.

"Edge atoms contribute

\frac{1}{8}

just like corners."

Wrong — an edge is shared by 4 cells, not 8, so an edge atom contributes

\frac{1}{4}

; corners contribute

\frac{1}{8}

"Cubic has only one Bravais lattice."

Wrong — cubic has three: primitive (P), body-centred (I), and face-centred (F).

Why questions

Why does a crystalline solid cleave along clean flat faces while amorphous ones break irregularly?

The regular planes of atoms give preferred weak directions that split cleanly, whereas random amorphous structure has no preferred plane so it fractures unevenly.

Why do we bother defining a unit cell instead of describing every atom?

Because the pattern repeats forever, storing one repeating block plus "copy in three directions" fully describes an infinite crystal with finite information.

Why does the same set of atoms give different

Z

for simple, BCC, and FCC cubes?

They differ in how many extra lattice points (none / body / faces) are added, so the counted atoms per cell change to

1

2

, and

4

respectively.

Why are amorphous solids called supercooled liquids?

Their particles were frozen in a liquid-like disordered arrangement before crystallising, so they retain a liquid's randomness in a rigid state.

Why can't every shape have a base-centred (C) lattice as a distinct entry?

Adding base-centring to some shapes reproduces a lattice already counted under another shape, so Bravais discarded those duplicates, leaving only 14.

Edge cases

Is a single perfect atom sitting alone a "unit cell"?

No — a unit cell only means something as the repeating unit of a lattice; without translation in three directions there is no crystal to describe.

If a crystal is heated to just below melting, does it become amorphous?

No — it keeps long-range order until it melts; increased vibration alone does not destroy the periodic lattice.

What is

Z

for a primitive cubic cell in the limit where you keep only the 8 corners?

Z = 8 \times \frac{1}{8} = 1

; the eight shared corner fractions assemble into exactly one whole atom.

Does an amorphous solid ever show a sharp X-ray diffraction pattern?

No — Bragg diffraction needs repeating planes; amorphous solids give broad diffuse halos, not sharp spots.

Can two different crystal systems share the same edge lengths yet differ?

Yes — cubic and rhombohedral both have

a = b = c

, but cubic forces all angles

9 0^{\circ}

while rhombohedral has all angles equal and

\neq = 9 0^{\circ}

Is a body-centre atom ever fractionally shared in any cubic lattice?

No — by definition it lies wholly inside its cell, so it always contributes a full

1

regardless of the surrounding structure.

Recall One-line survival kit

Long-range order → crystalline, sharp melt, anisotropic; no order → amorphous, range melt, isotropic. Sharing = corner $\frac{1}{8}$ , edge $\frac{1}{4}$ , face $\frac{1}{2}$ , body $1$ . Seven shapes, fourteen Bravais lattices.