{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,21]],"date-time":"2026-04-21T06:43:23Z","timestamp":1776753803256,"version":"3.51.2"},"reference-count":32,"publisher":"MDPI AG","issue":"14","license":[{"start":{"date-parts":[[2023,7,11]],"date-time":"2023-07-11T00:00:00Z","timestamp":1689033600000},"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>The introduction of the notion of energy change resulting from the ion exchange in apatites leads to the question: how can some simple isomorphic series be described using the mentioned idea? We concentrated on the simple isomorphic series of compounds: apatite, bioapatite, calcite, aragonite, celestine, K-, Zn- and Cu-Tutton\u2019s salts. It was demonstrated in all the series, except Tutton\u2019s salts, that the change in energy and the change in the crystal cell volume are, in a simple way, dependent on the change in the ionic radii of the introduced ions. The linear relationships between the variations in energy and in the universal crystallographic dimension d were derived from the earlier equations and proven based on available data. In many cases, except the Tutton\u2019s salts, linear dependence was discovered between the change in energy and the sinus of universal angle \u0398, corresponding to the change in momentum transfer. In the same cases, linear dependencies were observed between the energy changes and the changes in the volumes of crystallographic cells, and mutually between changes in the crystallographic cell volume V, crystallographic dimension d, and diffraction angle \u0398.<\/jats:p>","DOI":"10.3390\/ijms241411324","type":"journal-article","created":{"date-parts":[[2023,7,12]],"date-time":"2023-07-12T00:50:41Z","timestamp":1689123041000},"page":"11324","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Quantitative Description of Isomorphism in the Series of Simple Compounds"],"prefix":"10.3390","volume":"24","author":[{"given":"Andrzej","family":"Kuczumow","sequence":"first","affiliation":[{"name":"Lab 196, Radawiec Du\u017cy 196, 21-030 Motycz, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Mieczys\u0142aw","family":"Gorzelak","sequence":"additional","affiliation":[{"name":"Department of Orthopedics and Rehabilitation, Medical University of Lublin, 20-059 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1700-0317","authenticated-orcid":false,"given":"Jakub","family":"Kosi\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Orthopedics and Rehabilitation, Medical University of Lublin, 20-059 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3654-3042","authenticated-orcid":false,"given":"Agnieszka","family":"Lasota","sequence":"additional","affiliation":[{"name":"Chair and Department of Jaw Orthopedics, Medical University of Lublin, Chod\u017aki 6, 20-093 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Anna","family":"Szabelska","sequence":"additional","affiliation":[{"name":"Department of Dental Techniques with the Lab of Modern Technologies, Medical University of Lublin, Chod\u017aki 6, 20-093 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9747-8817","authenticated-orcid":false,"given":"Tomasz","family":"Blicharski","sequence":"additional","affiliation":[{"name":"Department of Orthopedics and Rehabilitation, Medical University of Lublin, 20-059 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jacek","family":"G\u0105ga\u0142a","sequence":"additional","affiliation":[{"name":"Department of Orthopedics and Traumatology, Medical University of Lublin, K. Jaczewskiego 8, 20-090 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6720-891X","authenticated-orcid":false,"given":"Jolanta","family":"Wawrzyniak","sequence":"additional","affiliation":[{"name":"Faculty of Food Science and Nutrition, Pozna\u0144 University of Life Sciences, 60-624 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"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 Science, 60-637 Pozna\u0144, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Miros\u0142aw","family":"Jab\u0142o\u0144ski","sequence":"additional","affiliation":[{"name":"Department of Orthopedics and Rehabilitation, Medical University of Lublin, 20-059 Lublin, Poland"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,7,11]]},"reference":[{"key":"ref_1","unstructured":"Murdzek, J. 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