Methods utilizing relatively simple mathematical operations during physical analyses to enable the visualization of otherwise invisible correlations and effects are of particular appeal to researchers and students in pedagogical settings. At the same time, discerning the amorphous phase from its crystalline counterpart in materials is challenging with the use of vibrational spectroscopy and is nowhere as straightforward as in phase composition analytical methods such as X-ray diffraction. A method is demonstrated for the use of first- and second-order differentiation of Fourier transform infrared spectra of calcium phosphates to distinguish their amorphous states from the crystalline ones based on the exact line positioning rather than on comparatively vaguer band broadening and splitting effects. The study utilizes a kinetic approach, focusing on the comparison of spectral features of amorphous precursors annealed in air at different temperatures and aged for different periods of time in an aqueous solution until transforming to one or a mixture of crystalline phases, including hydroxyapatite and α- and β-tricalcium phosphate. One of the findings challenges the concept of the nucleation lag time preceding the crystallization from amorphous precursors as a "dead" period and derives a finite degree of constructive changes occurring at the atomic scale in its course. The differential method for highlighting spectral differences depending on the sample crystallinity allows for monitoring in situ the process of conversion of the amorphous calcium phosphate phase to its crystalline analogue(s). One such method can be of practical significance for synthetic solid state chemists testing for the chemical stability and/or concentration of the reactive amorphous phase in these materials, but also for biologists measuring the maturity of bone and medical researchers evaluating its phase composition and, thus, the state of metabolic and mechanical stability.

Keywords: Amorphous; Crystallization; Derivative Method; FTIR; Hydroxyapatite; Tricalcium phosphate; XRD.