# Steering of Crystal Cell Volumes in Apatites and Bioapatites

## TL;DR

This paper explores how different organisms use specific apatite crystal structures in their hard tissues, and how these structures can be influenced by environmental factors.

## Contribution

The paper introduces a reformulated version of Bragg’s law to classify apatite biomaterials and steer crystal cell volumes.

## Key findings

- Organisms select specific apatites for hard tissues based on environmental adaptation.
- Volume expansion in apatites is linearly coupled with the expansion of Bragg’s d parameter.
- Different modes of change in Bragg’s dimension d were identified and quantified.

## Abstract

The biological variability of apatites in different hard tissues of organisms was the starting point for this investigation. Materials such as whale rostrums, ganoine, and some fish bones were analyzed. It has been proven that different organisms select specific kinds of apatites for the construction of their hard organs at the level of the crystal cell. This probably results from the long-lasting adaptation of the construction to their environmental needs. The materials are characterized by the parameters Δd and ΔE, being the real and apparent deviations from Bragg’s dimension d and the energy of excitation in XRD—E. This study is based on previously published, verified results from a number of researchers and research groups. The derivation of expressions was possible due to an original approach to Bragg’s equation, finally finished in the reformulation of the law, which describes the interplay between the absolute value of the probing excitation energy E and the crystal cell’s internal volume V. It enabled the classification of apatite biomaterials in living and fossil organisms, as well as the classification of the apatite excretions. In addition, the following different possible modes of changes in Bragg’s dimension d were illustrated—spontaneous geometrical expansion, thermal action, pressurization, and single- and multiple-ion exchanges. The contributions of such expansions were estimated. We can steer the cell volume of apatites in various ways. It has been proven that the volume expansion is linearly coupled with the expansion of Bragg’s d parameter in the hexagonal system.