{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,30]],"date-time":"2026-07-30T17:09:36Z","timestamp":1785431376282,"version":"3.56.0"},"reference-count":53,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T00:00:00Z","timestamp":1746489600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IJMS"],"abstract":"<jats:p>Apatites are very important compounds of mineralogical and biological meaning. Apatites originated from the calcium hydroxy compound 3Ca3(PO4)2\u00b7Ca(OH)2 and potentially might form three series of isomorphic salts, derived from cationic substitutions in the positions of Ca(I) and Ca(II) ions in the core compound; anionic substitutions of phosphates; and substitutions of anions and very simple chemical entities instead of the hydroxyl group in channel locations. The energies coupled with the ion exchanges inside those three locations were studied using our original method resulting from the transformation of Braggs\u2019 law. The energy changes resulting from the ion exchanges were studied in connection with either the ionic radii for the cations or ionic volumes for the anions. The same series were observed when the variabilities of energy were confronted with the variabilities in the sinus of diffraction angle \u0398 showing changes in momentum transfer. In particular, the relationships between the energy changes and the coupled changes in the universal crystallographic parameter d showed the surprising uniformity of all ion exchanges in the apatites. The incremental change in the Braggs\u2019 d-parameter always demands the same change in the energy, with good approximation, independently of the location of the ion exchange. So, the isomorphism of the apatites is not triple but a uniform one at the energy level. Such an approach enables the estimation of the volume of the ion-\u25a1 (\u25a1-vacancies) agglomerates. The introduction of ions with greater volumes exerts the phenomenon of swelling of apatite cells, which can be quantitatively estimated. The dependence of diffraction spectra on the temperature allows for the determination of minimal values of crystallographic cell volumes and d parameters at the temperature of 0 K. In sum, the study of energies connected with the change of Bragg dimension d is a new and valuable method of insight into the behaviour of apatite crystals.<\/jats:p>","DOI":"10.3390\/ijms26094397","type":"journal-article","created":{"date-parts":[[2025,5,6]],"date-time":"2025-05-06T05:54:43Z","timestamp":1746510883000},"page":"4397","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Implications of Isomorphism in the Family of Apatite Compounds"],"prefix":"10.3390","volume":"26","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3654-3042","authenticated-orcid":false,"given":"Agnieszka","family":"Lasota","sequence":"first","affiliation":[{"name":"Department of Jaw Orthopaedics, Medical University of Lublin, 20-093 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Mieczys\u0142aw","family":"Gorzelak","sequence":"additional","affiliation":[{"name":"Department of Orthopaedics and Rehabilitation, Medical University of Lublin, 20-059 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0043-0011","authenticated-orcid":false,"given":"Emanuela","family":"Bis","sequence":"additional","affiliation":[{"name":"Student Research Group at the Chair and Department of Oral Medicine, Medical University of Lublin, Chod\u017aki 6, 20-093 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8247-4343","authenticated-orcid":false,"given":"Przemys\u0142aw","family":"Bili\u0144ski","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Health Promotion, The President Stanis\u0142aw Wojciechowski University of Kalisz, 62-800 Kalisz, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Krzysztof","family":"Gieburowski","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Health Promotion, The President Stanis\u0142aw Wojciechowski University of Kalisz, 62-800 Kalisz, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Wojciech","family":"K\u0142ape\u0107","sequence":"additional","affiliation":[{"name":"Department of Orthopaedics and Rehabilitation, Medical University of Lublin, 20-059 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Barbara","family":"Tymczyna-Borowicz","sequence":"additional","affiliation":[{"name":"Department of Conservative Dentistry with Endodontics, Medical University of Lublin, 20-093 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9897-3174","authenticated-orcid":false,"given":"Micha\u0142","family":"\u0141obacz","sequence":"additional","affiliation":[{"name":"Department of Oral Surgery, Medical University of Lublin, Chod\u017aki 6, 20-093 Lublin, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Jaros\u0142aw","family":"Pawlicz","sequence":"additional","affiliation":[{"name":"Department of Orthopedics and Traumatology, Poznan University of Medical Sciences, 28 Czerwca 1956 135\/147, 61-545 Pozna\u0144, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9832-9274","authenticated-orcid":false,"given":"Maciej","family":"Jarz\u0119bski","sequence":"additional","affiliation":[{"name":"Department of Physics and Biophysics, Pozna\u0144 University of Life Sciences, 60-637 Pozna\u0144, Poland"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4867-195X","authenticated-orcid":false,"given":"Marek","family":"Wieruszewski","sequence":"additional","affiliation":[{"name":"Department of Wood-Based Materials, Faculty of Forestry and Wood Technology, Pozna\u0144 University of Life Sciences, Wojska Polskiego 28, 60-627 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