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Hydroxyapatite is a crystalline calcium phosphate whose ideal composition is $\mathrm{C}{\mathrm{a}}_{10}(\mathrm{P}{\mathrm{O}}_4{)}_6(\mathrm{OH}{)}_2$, equivalently $\mathrm{C}{\mathrm{a}}_5(\mathrm{P}{\mathrm{O}}_4{)}_3\mathrm{OH}$. The formula describes an extended ionic solid, not a discrete hydroxyapatite molecule. Its ideal calcium-to-phosphorus molar ratio is $10/6=5/3$. NIST uses hydroxyapatite reference powder to evaluate physical and chemical measurements of apatites.^[ref]

The ideal composition is electrically neutral: ten calcium ions contribute charge $+20$, six phosphate ions contribute $-18$ and two hydroxide ions contribute $-2$. Changing a subscript changes this composition; it is not the same operation as multiplying the whole chemical formula by a coefficient.

An original composition calculation uses approximate molar masses $40.078$ for calcium, $30.974$ for phosphorus, $15.999$ for oxygen and $1.008$ for hydrogen, in grams per mole. The full formula has molar mass about $1004.62\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$, with ideal calcium mass fraction about $39.89\%$ and phosphorus mass fraction about $18.50\%$. Their mass-fraction ratio is about $2.157$, whereas their mole ratio is $1.667$. An elemental mass ratio cannot be compared directly with the stoichiometric mole ratio.

Identity also needs structural evidence. NIST characterized its reference powder by elemental analysis and powder X-ray diffraction, comparing diffraction positions with the hydroxyapatite pattern. Its certificate distinguishes certified composition values from supplementary diffraction information.^[ref] A measured Ca/P ratio near $5/3$ alone does not establish that every part of a specimen is a single hydroxyapatite phase: a mixture can reproduce an overall elemental ratio. Composition, phase identification and the properties of a biological composite material answer related but different questions.

In the electron-count estimate $f_{\mathrm{Ga}}\simeq 31$, $f_{\mathrm{As}}\simeq 33$, the structure factors are $F_{111}=4(31-33i)$ and $F_{200}=4(31-33)$. Thus a single-directed-reflection estimate isA powder X-ray diffraction peak collects all equivalent reflections. The powder diffraction multiplicities are eight for $\{111\}$ and six for $\{200\}$, so the multiplicity-and-electron-count estimate isAt $(200)$ the two sublattice amplitudes are opposite in phase and nearly cancel; at $(111)$ their relative phase is a quarter cycle, so this cancellation does not occur. In silicon, the two atomic scattering factors are identical and the diamond cubic structure has an exactly forbidden $(200)$ reflection, while $(111)$ remains allowed in the kinematic approximation.

The numerical ratio neglects the angular dependence of the atomic scattering factors, the Lorentz-polarization factor and thermal-motion corrections. No wavelength or measurement geometry is supplied to refine those factors. This is therefore a stated structural estimate, rather than a unique precision ratio of measured peak areas.

Use temperature-dependent X-ray diffraction, with the crystal in a controlled heating stage and a detector measuring diffracted directions. A reflection occurs when the scattering wavevector matches a reciprocal lattice vector, or equivalently when Bragg's law $2d_{hkl}\sin \theta =\lambda$ is satisfied. Record peak positions and intensities while heating to infer changes in lattice spacings and structure.

A monatomic conventional BCC cell has nonzero crystal basis structure factor only when $h+k+l$ is even. For FCC the indices must be all even or all odd. The change in reflection selection and peak positions therefore distinguishes the phases. For instance, BCC starts with a $(110)$ family whereas FCC starts with $(111)$, when indexed in their own conventional cells.

The transformation can create multiple orientation variants, grains, strain and phase coexistence. A reciprocal point that formerly satisfied the diffraction geometry may disappear or move off a fixed detector; a loss of one spot alone does not identify the new phase. Thermal expansion shifts peaks, thermal motion weakens coherent intensities, and hot iron may oxidize without a protective atmosphere.

After transformation, scan crystal angle and scattering angle or use an area detector to locate the new reflections. If single-crystal order has been lost, powder X-ray diffraction or a sufficiently broad orientation survey collects rings or many grain reflections instead of relying on the original alignment. Index several new peaks using the FCC selection rule and fit their common lattice parameter; this probes the new structure even when the original crystal orientation is no longer usable.

Powder X-ray diffraction measures X-ray diffraction from many crystal grains with different orientations. For each allowed set of lattice spacings, suitable grains satisfy Bragg's law and produce a cone of diffracted directions, seen as a ring on an area detector or a peak in an angular scan. Several peak positions and systematic absences can identify a crystal structure even when a sample no longer retains one single-crystal orientation. Preferred orientation, strain and phase coexistence can complicate interpretation.