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The three primitive lattice translation vectors join a cube corner to the three adjacent face centres. Thus the Bravais lattice is a face-centered cubic lattice, with conventional cubic side $a$.

Write the given primitive lattice translation vectors as ${\mathbf{a}}_1,{\mathbf{a}}_2,{\mathbf{a}}_3$. Their primitive unit cell volume isThe reciprocal lattice convention ${\mathbf{a}}_i\cdot {\mathbf{b}}_j=2\pi {\delta }_{ij}$ then givesEach reciprocal lattice vector has units ${\mathrm{m}}^{-1}$ when $a$ is in metres. Integer combinations generate a body-centered cubic lattice of conventional cubic side $4\pi /a$; the point $(2\pi /a)(1,1,1)$ is its body centre. Directly taking the nine dot products checks the signs and the $2\pi$ normalization.

Write the particle volume fraction as $\eta =(4\pi a^3/3)n_p$. In a stable, repulsion-dominated colloid, low $\eta$ gives a disordered fluid. Increasing $\eta$ makes the interaction between neighboring particles important and can produce an ordered crystal, separated from the fluid by a phase coexistence curve. Increasing the Debye–Hückel screening length at fixed charge strengthens the repulsion at a given separation and allows freezing at smaller geometrical volume fraction.

The geometric intuition is that particles behave as though they occupy more than their bare diameter: roughly, an effective exclusion diameter $d_{\mathrm{eff}}$ extends out to the separation where $U_{\mathrm{el}}$ is of order $k_{B}T$. A hard sphere comparison then uses ${\eta }_{\mathrm{eff}}\sim \eta [d_{\mathrm{eff}}/(2a){]}^3$. This explains the trend; it is not an exact freezing criterion.

At short Debye–Hückel screening length and negligible attraction, the diagram approaches hard sphere fluid–crystal coexistence. For longer-ranged soft repulsion, body-centered cubic lattice and face-centered cubic lattice crystals can both be stable, with the former often appearing towards the softer, lower-density freezing boundary. Screened-Coulomb simulations exhibit both these crystal structures.^[ref]

No universal quantitative diagram follows from $(\eta ,{\lambda }_D)$ alone: the charge, Hamaker constant and surface conditions must also be fixed. If salt suppresses the stabilizing barrier enough for Van der Waals force attraction to dominate, a colloid-poor/colloid-rich separation or aggregation can replace part of this repulsive reference diagram. Dense colloidal glasses or colloidal gels may also be observed after kinetic arrest; they should not be mistaken for additional thermodynamic equilibrium thermodynamic phases.

The reciprocal lattice of a body-centered cubic lattice is face-centred cubic, and that of a face-centered cubic lattice is body-centred cubic. In both cases its conventional cubic side is $4\pi /a$ if the direct conventional side is $a$. Thus a direct BCC-to-FCC phase transition reverses the reciprocal lattice types. The reciprocal primitive cell volume is $(2\pi {)}^3/\Omega$, so thermal expansion contracts reciprocal spacings, while a discontinuous change in direct primitive unit cell volume gives an inverse change in reciprocal cell volume.

A first-order structural transition need not continuously deform one perfect reciprocal array into another. Phase coexistence, new orientation variants, domains and loss of single-crystal alignment can produce two sets of diffraction peaks or many differently oriented sets. The two endpoint lattice types alone do not specify the transformation path or orientation relationship.