基于DFT的描述符预测生物陶瓷的降解性

doi:10.15541/jim20240125

无机材料学报 ›› 2024, Vol. 39 ›› Issue (10): 1175-1181.DOI: 10.15541/jim20240125 CSTR: 32189.14.10.15541/jim20240125

基于DFT的描述符预测生物陶瓷的降解性

陈梦杰¹^,²(), 王倩倩¹^,², 吴成铁¹^,², 黄健¹^,²^,³()

1.中国科学院上海硅酸盐研究所高性能陶瓷和超微结构国家重点实验室, 上海 200050
2.中国科学院大学材料科学与光电技术中心, 北京 100049
3.上海大学材料基因组工程研究院, 上海 200444

收稿日期:2024-03-14 修回日期:2024-05-04 出版日期:2024-10-20 网络出版日期:2024-05-16
通讯作者: 黄健, 研究员. E-mail: huangj@shu.edu.cn
作者简介:陈梦杰(1998-), 男, 硕士研究生. E-mail: chenmengjie20@mails.ucas.ac.cn

Predicting the Degradability of Bioceramics through a DFT-based Descriptor

CHEN Mengjie¹^,²(), WANG Qianqian¹^,², WU Chengtie¹^,², HUANG Jian¹^,²^,³()

1. State Key Laboratory of High Performance Ceramics and Superfine Microstructure, Shanghai Institute of Ceramics, Chinese Academy of Sciences, Shanghai 200050, China
2. Center of Materials Science and Optoelectronics Engineering, University of Chinese Academy of Sciences, Beijing 100049, China
3. Materials Genome Institute, Shanghai University, Shanghai 200444, China

Received:2024-03-14 Revised:2024-05-04 Published:2024-10-20 Online:2024-05-16
Contact: HUANG Jian, professor. E-mail: huangj@shu.edu.cn
About author:CHEN Mengjie (1998-), male, Master candidate. E-mail: chenmengjie20@mails.ucas.ac.cn
Supported by:
National Key Research and Development Program of China(2023YFB3813000);National Natural Science Foundation of China(52272256);State Key Laboratory of Advanced Technology for Materials Synthesis and Processing (Wuhan University of Technology)(2022-KF-77)

摘要/Abstract

摘要：

生物陶瓷以其优异的生物活性和可降解性在骨缺损修复领域受到广泛关注。然而, 如何使生物陶瓷降解速率与新骨生成速率相匹配仍然存在挑战, 因此需要更深入地了解生物陶瓷的降解特性。本研究采用密度泛函理论(DFT)计算并探索硅酸盐生物陶瓷的电子结构。研究结果表明硅酸盐生物陶瓷价带顶电荷密度的最大值(VBM_Fmax)与其降解性之间存在线性相关性, 随后的降解实验验证了这种相关性。此外, 对磷酸盐生物陶瓷的研究也证实了该描述符可用于预测不同生物陶瓷的降解性。这一发现有助于更好地理解生物陶瓷的降解机制, 并有望加速可控降解生物陶瓷的设计和开发。

关键词: 生物陶瓷, 硅酸盐, 磷酸盐, 第一性原理, 降解

Abstract:

Bioceramics have attracted extensive attention for bone defect repair due to their excellent bioactivity and degradability. However, challenges remain in matching the rate between bioceramic degradation and new bone formation, necessitating a deeper understanding of their degradation properties. In this study, density functional theory (DFT) calculations was employed to explore the structural and electronic characteristics of silicate bioceramics. These findings reveal a linear correlation between the maximum isosurface value of the valence band maximum (VBM_Fmax) and the degradability of silicate bioceramics. This correlation was subsequently validated through degradation experiments. Furthermore, the investigation on phosphate bioceramics demonstrates the potential of this descriptor in predicting the degradability of a broader range of bioceramics. This discovery offers valuable insights into the degradation mechanism of bioceramics and holds promise for accelerating the design and development of bioceramics with controllable degradation.

Key words: bioceramics, silicate, phosphate, first principles, degradation

中图分类号:

TQ174

陈梦杰, 王倩倩, 吴成铁, 黄健. 基于DFT的描述符预测生物陶瓷的降解性[J]. 无机材料学报, 2024, 39(10): 1175-1181.

CHEN Mengjie, WANG Qianqian, WU Chengtie, HUANG Jian. Predicting the Degradability of Bioceramics through a DFT-based Descriptor[J]. Journal of Inorganic Materials, 2024, 39(10): 1175-1181.

图/表 10

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Name	Chemical formula	Mineralization ability
Wollastonite	CaSiO₃	▲▲▲▲*
Dicalcium silicate	Ca₂SiO₄	▲▲▲▲
Tricalcium silicate	Ca₃SiO₅	▲▲▲▲
Akermanite	Ca₂MgSi₂O₇	▲▲▲
Merrwinite	Ca₃MgSi₂O₈	▲▲▲
Diopside	CaMgSi₂O₆	▲▲
Monticellite	CaMgSiO₄	▲▲
Baghdadite	Ca₃ZrSi₂O₉	▲▲
Dimagnesium silicate	Mg₂SiO₄	▲
Magnesium silicate	MgSiO₃	▲
Zinc silicate	Zn₂SiO₄	▲
Hardystonite	Ca₂ZnSi₂O₇	▲
Sphene	CaTiSiO₅	▲
Strontium-akermanite	Sr₂MgSi₂O₇	▲
Strontium-hardystonite	Sr₂ZnSi₂O₇	▲

Name	Chemical formula	Mineralization ability
Wollastonite	CaSiO₃	▲▲▲▲*
Dicalcium silicate	Ca₂SiO₄	▲▲▲▲
Tricalcium silicate	Ca₃SiO₅	▲▲▲▲
Akermanite	Ca₂MgSi₂O₇	▲▲▲
Merrwinite	Ca₃MgSi₂O₈	▲▲▲
Diopside	CaMgSi₂O₆	▲▲
Monticellite	CaMgSiO₄	▲▲
Baghdadite	Ca₃ZrSi₂O₉	▲▲
Dimagnesium silicate	Mg₂SiO₄	▲
Magnesium silicate	MgSiO₃	▲
Zinc silicate	Zn₂SiO₄	▲
Hardystonite	Ca₂ZnSi₂O₇	▲
Sphene	CaTiSiO₅	▲
Strontium-akermanite	Sr₂MgSi₂O₇	▲
Strontium-hardystonite	Sr₂ZnSi₂O₇	▲

Bioceramic		a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	Cell volume/Å³	Density/ (g·cm^-3)	Void space/%
α-CaSiO₃	Calc.	11.9532	6.9367	10.6153	90	111.274	90	820.198	2.8224	58.32
α-CaSiO₃	Expt.	11.8322	6.8624	10.5297	90	111.245	90	796.878	N/A	N/A
β-CaSiO₃	Calc.	8.0250	7.3910	7.1500	90.083	95.531	103.437	410.433	2.8201	58.03
β-CaSiO₃	Expt.	7.9400	7.3200	7.0700	90.030	95.370	103.430	397.818	N/A	N/A
Ca₂SiO₄	Calc.	5.1234	11.3455	6.8071	90	90	90	395.748	2.8910	57.19
Ca₂SiO₄	Expt.	5.0910	11.3710	6.7820	90	90	90	392.608	N/A	N/A
Ca₃SiO₅	Calc.	11.7501	14.3209	13.7622	104.813	94.354	90.117	2231.821	3.0580	54.91
Ca₃SiO₅	Expt.	11.6700	14.2400	13.7200	105.500	94.330	90	2190.324	N/A	N/A
Ca₂MgSi₂O₇	Calc.	7.9073	7.9073	5.053	90	90	90	315.940	2.8661	57.30
Ca₂MgSi₂O₇	Expt.	7.8900	7.8900	5.0410	90	90	90	313.813	N/A	N/A
Ca₂ZnSi₂O₇	Calc.	7.9043	7.9043	5.0592	90	90	90	316.089	3.2961	57.87
Ca₂ZnSi₂O₇	Expt.	7.8279	7.8279	5.0138	90	90	90	307.226	N/A	N/A
Ca₃MgSi₂O₈	Calc.	9.8453	5.2925	13.7871	90	97.954	90	711.477	3.0690	54.41
Ca₃MgSi₂O₈	Expt.	9.9678	5.2693	13.6701	90	97.720	90	711.498	N/A	N/A
Ca₃ZrSi₂O₉	Calc.	7.4323	10.3145	10.5148	90	91.113	90	805.919	3.3927	56.03
Ca₃ZrSi₂O₉	Expt.	7.3603	10.1766	10.4514	90	90.875	90	782.748	N/A	N/A
CaMgSi₂O₆	Calc.	9.8690	9.0131	5.3152	90	106.122	90	454.197	3.1672	52.58
CaMgSi₂O₆	Expt.	9.7760	8.9790	5.2670	90	105.940	90	444.554	N/A	N/A
CaMgSiO₄	Calc.	5.2260	6.8631	9.1738	90	90	90	327.740	3.1714	52.65
CaMgSiO₄	Expt.	5.2408	6.8696	9.1348	90	90	90	328.869	N/A	N/A
CaTiSiO₅	Calc.	7.1294	8.7726	6.6609	90	114.041	90	380.457	3.4231	53.08
CaTiSiO₅	Expt.	7.0730	8.7180	6.5550	90	113.970	90	369.339	N/A	N/A
Ca₂Al₂SiO₇	Calc.	7.6773	7.6773	5.1888	90	90	90	305.833	2.9777	56.92
Ca₂Al₂SiO₇	Expt.	7.6764	7.6764	5.1908	90	90	90	305.878	N/A	N/A
Ca₅(PO₄)₂SiO₄	Calc.	6.8737	10.2116	15.4913	90	90	90	1087.357	2.9470	55.64
Ca₅(PO₄)₂SiO₄	Expt.	6.7370	10.1320	15.5080	90	90	90	1058.565	N/A	N/A
Mg₂SiO₄	Calc.	4.8043	10.3245	6.0475	90	90	90	299.970	3.1157	52.95
Mg₂SiO₄	Expt.	4.7630	10.2400	5.9990	90	90	90	292.590	N/A	N/A
MgSiO₃	Calc.	9.3655	8.8559	5.3797	90	90	90	446.190	2.9892	54.83
MgSiO₃	Expt.	9.2500	8.7400	5.3200	90	90	90	430.095	N/A	N/A
Na₂CaSiO₄	Calc.	7.5297	7.5297	7.5297	90	90	90	426.904	2.7719	53.91
Na₂CaSiO₄	Expt.	7.4800	7.4800	7.4800	90	90	90	418.509	N/A	N/A
Na₂Ca₂Si₃O₉	Calc.	10.6053	10.6053	13.3064	89.839	90.161	120.224	1293.145	2.7306	58.66
Na₂Ca₂Si₃O₉	Expt.	10.5989	10.5989	13.3074	89.720	90.280	120.203	1291.944	N/A	N/A
Sr₂MgSi₂O₇	Calc.	8.0962	8.0962	5.2249	90	90	90	342.478	3.5660	56.58
Sr₂MgSi₂O₇	Expt.	8.0107	8.0107	5.1636	90	90	90	331.355	N/A	N/A
Sr₂ZnSi₂O₇	Calc.	8.0954	8.0954	5.2322	90	90	90	342.897	3.9593	57.16
Sr₂ZnSi₂O₇	Expt.	8.0007	8.0007	5.1722	90	90	90	331.079	N/A	N/A
SrSiO₃	Calc.	12.4873	7.2366	10.9917	90	111.645	90	923.231	3.5335	58.61
SrSiO₃	Expt.	12.3330	7.1460	10.8850	90	111.570	90	892.131	N/A	N/A
Zn₂SiO₄	Calc.	14.1481	14.1481	9.4163	90	90	120	1632.331	4.0803	63.23
Zn₂SiO₄	Expt.	13.9710	13.9710	9.3340	90	90	120	1577.805	N/A	N/A
Li₂Ca₂Si₂O₇	Calc.	5.1459	5.1459	41.6617	90	90	120	955.403	2.7346	57.34
Li₂Ca₂Si₂O₇	Expt.	5.1471	5.1471	41.6291	90	90	120	955.116	N/A	N/A

Bioceramic		a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	Cell volume/Å³	Density/ (g·cm^-3)	Void space/%
α-CaSiO₃	Calc.	11.9532	6.9367	10.6153	90	111.274	90	820.198	2.8224	58.32
α-CaSiO₃	Expt.	11.8322	6.8624	10.5297	90	111.245	90	796.878	N/A	N/A
β-CaSiO₃	Calc.	8.0250	7.3910	7.1500	90.083	95.531	103.437	410.433	2.8201	58.03
β-CaSiO₃	Expt.	7.9400	7.3200	7.0700	90.030	95.370	103.430	397.818	N/A	N/A
Ca₂SiO₄	Calc.	5.1234	11.3455	6.8071	90	90	90	395.748	2.8910	57.19
Ca₂SiO₄	Expt.	5.0910	11.3710	6.7820	90	90	90	392.608	N/A	N/A
Ca₃SiO₅	Calc.	11.7501	14.3209	13.7622	104.813	94.354	90.117	2231.821	3.0580	54.91
Ca₃SiO₅	Expt.	11.6700	14.2400	13.7200	105.500	94.330	90	2190.324	N/A	N/A
Ca₂MgSi₂O₇	Calc.	7.9073	7.9073	5.053	90	90	90	315.940	2.8661	57.30
Ca₂MgSi₂O₇	Expt.	7.8900	7.8900	5.0410	90	90	90	313.813	N/A	N/A
Ca₂ZnSi₂O₇	Calc.	7.9043	7.9043	5.0592	90	90	90	316.089	3.2961	57.87
Ca₂ZnSi₂O₇	Expt.	7.8279	7.8279	5.0138	90	90	90	307.226	N/A	N/A
Ca₃MgSi₂O₈	Calc.	9.8453	5.2925	13.7871	90	97.954	90	711.477	3.0690	54.41
Ca₃MgSi₂O₈	Expt.	9.9678	5.2693	13.6701	90	97.720	90	711.498	N/A	N/A
Ca₃ZrSi₂O₉	Calc.	7.4323	10.3145	10.5148	90	91.113	90	805.919	3.3927	56.03
Ca₃ZrSi₂O₉	Expt.	7.3603	10.1766	10.4514	90	90.875	90	782.748	N/A	N/A
CaMgSi₂O₆	Calc.	9.8690	9.0131	5.3152	90	106.122	90	454.197	3.1672	52.58
CaMgSi₂O₆	Expt.	9.7760	8.9790	5.2670	90	105.940	90	444.554	N/A	N/A
CaMgSiO₄	Calc.	5.2260	6.8631	9.1738	90	90	90	327.740	3.1714	52.65
CaMgSiO₄	Expt.	5.2408	6.8696	9.1348	90	90	90	328.869	N/A	N/A
CaTiSiO₅	Calc.	7.1294	8.7726	6.6609	90	114.041	90	380.457	3.4231	53.08
CaTiSiO₅	Expt.	7.0730	8.7180	6.5550	90	113.970	90	369.339	N/A	N/A
Ca₂Al₂SiO₇	Calc.	7.6773	7.6773	5.1888	90	90	90	305.833	2.9777	56.92
Ca₂Al₂SiO₇	Expt.	7.6764	7.6764	5.1908	90	90	90	305.878	N/A	N/A
Ca₅(PO₄)₂SiO₄	Calc.	6.8737	10.2116	15.4913	90	90	90	1087.357	2.9470	55.64
Ca₅(PO₄)₂SiO₄	Expt.	6.7370	10.1320	15.5080	90	90	90	1058.565	N/A	N/A
Mg₂SiO₄	Calc.	4.8043	10.3245	6.0475	90	90	90	299.970	3.1157	52.95
Mg₂SiO₄	Expt.	4.7630	10.2400	5.9990	90	90	90	292.590	N/A	N/A
MgSiO₃	Calc.	9.3655	8.8559	5.3797	90	90	90	446.190	2.9892	54.83
MgSiO₃	Expt.	9.2500	8.7400	5.3200	90	90	90	430.095	N/A	N/A
Na₂CaSiO₄	Calc.	7.5297	7.5297	7.5297	90	90	90	426.904	2.7719	53.91
Na₂CaSiO₄	Expt.	7.4800	7.4800	7.4800	90	90	90	418.509	N/A	N/A
Na₂Ca₂Si₃O₉	Calc.	10.6053	10.6053	13.3064	89.839	90.161	120.224	1293.145	2.7306	58.66
Na₂Ca₂Si₃O₉	Expt.	10.5989	10.5989	13.3074	89.720	90.280	120.203	1291.944	N/A	N/A
Sr₂MgSi₂O₇	Calc.	8.0962	8.0962	5.2249	90	90	90	342.478	3.5660	56.58
Sr₂MgSi₂O₇	Expt.	8.0107	8.0107	5.1636	90	90	90	331.355	N/A	N/A
Sr₂ZnSi₂O₇	Calc.	8.0954	8.0954	5.2322	90	90	90	342.897	3.9593	57.16
Sr₂ZnSi₂O₇	Expt.	8.0007	8.0007	5.1722	90	90	90	331.079	N/A	N/A
SrSiO₃	Calc.	12.4873	7.2366	10.9917	90	111.645	90	923.231	3.5335	58.61
SrSiO₃	Expt.	12.3330	7.1460	10.8850	90	111.570	90	892.131	N/A	N/A
Zn₂SiO₄	Calc.	14.1481	14.1481	9.4163	90	90	120	1632.331	4.0803	63.23
Zn₂SiO₄	Expt.	13.9710	13.9710	9.3340	90	90	120	1577.805	N/A	N/A
Li₂Ca₂Si₂O₇	Calc.	5.1459	5.1459	41.6617	90	90	120	955.403	2.7346	57.34
Li₂Ca₂Si₂O₇	Expt.	5.1471	5.1471	41.6291	90	90	120	955.116	N/A	N/A

Bioceramic	Surrounding aqueous media	Weight loss	Total ion release in media after 7 d
α-CaSiO₃	SBF	31.27% (28 d)	N/A
α-CaSiO₃	SBF	16.58% (28 d)	Ca: ~3.58 mmol·L^-1/Si: ~0.67 mmol·L^-1
β-CaSiO₃	Tris-HCl	24.8% (28 d)	N/A
β-CaSiO₃	SBF	N/A	Ca: ~9.59 mmol·L^-1/Si: ~1.73 mmol·L^-1
Ca₂SiO₄	SBF	N/A	Ca: ~4.77 mmol·L^-1/Si: ~0.83 mmol·L^-1
Ca₃SiO₅	SBF	N/A	Ca: ~6.82 mmol·L^-1/Si: ~2.20 mmol·L^-1
Ca₂MgSi₂O₇	Tris-HCl	12.1% (28 d)	(2 d) Ca: ~13.51 mmol·L^-1/Si: ~0.26 mmol·L^-1/Mg: ~3.49 mmol·L^-1
	SBF	N/A	Ca: ~4.50 mmol·L^-1/Si: ~2.18 mmol·L^-1/Mg: ~2.15 mmol·L^-1
	SBF	N/A	Ca: ~2.38 mmol·L^-1/Si: ~0.91 mmol·L^-1/Mg: ~1.23 mmol·L^-1
Ca₂ZnSi₂O₇	Tris-HCl	8.4% (28 d)	(2 d) Ca: ~11.10 mmol·L^-1/Si: ~0.17 mmol·L^-1/Zn: ~0.06 mmol·L^-1
	Tris-HCl	N/A	Ca: ~2.68 mmol·L^-1/Si: ~0.47 mmol·L^-1/Zn: ~0.01 mmol·L^-1
	Tris-HCl	3.17% (28 d)	Ca: ~0.55 mmol·L^-1/Si: ~0.17 mmol·L^-1/Zn: ~0.02 mmol·L^-1
Ca₃MgSi₂O₈	Tris-HCl	3.05% (7 d)	N/A
Ca₃ZrSi₂O₉	SBF	N/A	Ca: ~2.55 mmol·L^-1/Si: ~1.52 mmol·L^-1/Zr: ~0.43 mmol·L^-1
Ca₃ZrSi₂O₉	SBF	N/A	Ca: ~9.15 mmol·L^-1/Si: ~1.55 mmol·L^-1
CaMgSi₂O₆	SBF	N/A	Ca: ~3.87 mmol·L^-1/Si: ~1.95 mmol·L^-1/Mg: ~2.01 mmol·L^-1
CaMgSi₂O₆	SBF	N/A	Ca: ~1.75 mmol·L^-1/Si: ~1.11 mmol·L^-1/Mg: ~0.85 mmol·L^-1
CaMgSiO₄	SBF	N/A	Ca: ~7.00 mmol·L^-1/Si: ~2.64 mmol·L^-1/Mg: ~3.29 mmol·L^-1
CaMgSiO₄	SBF	2.07% (7 d) 3.51% (14 d) 6.92% (28 d)	(2 d) Ca: ~13.17 mmol·L^-1/Si: ~0.06 mmol·L^-1/Mg: ~4.33 mmol·L^-1
CaTiSiO₅	Tris-HCl	N/A	Ca: ~0.23 mmol·L^-1/Si: ~0.05 mmol·L^-1
Ca₂Al₂SiO₇	SBF	N/A	Ca: ~2.64 mmol·L^-1/Si: ~0.21 mmol·L^-1/Al: ~0.12 mmol·L^-1
Ca₅(PO₄)₂SiO₄	SBF	N/A	Ca: ~7.10 mmol·L^-1/Si: ~3.88 mmol·L^-1/P: ~1.58 mmol·L^-1
Mg₂SiO₄	SBF	N/A	Ca: ~1.52 mmol·L^-1/Mg: ~2.78 mmol·L^-1
Mg₂SiO₄	PBS	0.11% (28 d)	N/A
MgSiO₃	Tris-HCl	7.31% (7 d) 10.77% (14 d)	N/A
Na₂CaSiO₄	PBS / SBF	2.49% (7 d) 2.86% (14 d) 1.72% (28 d)	Ca: ~5.68 mmol·L^-1/Si: ~0.46 mmol·L^-1
Na₂Ca₂Si₃O₉	Tris-HCl	4.32% (7 d)	N/A
Na₂Ca₂Si₃O₉	SBF	N/A	Ca: ~4.98/Si: ~0.87/Na: 172.57 (×10^-6 mmol·L^-1)
Sr₂MgSi₂O₇	N/A	N/A	(14 d) Sr: ~1.70 mmol·L^-1/Si: ~2.24 mmol·L^-1 / Mg: ~1.97 mmol·L^-1
Sr₂ZnSi₂O₇	N/A	N/A	(14 d) Sr: ~1.71 mmol·L^-1/Si: ~0.97 mmol·L^-1 / Zn: ~0.024 mmol·L^-1
Sr₂ZnSi₂O₇	Tris-HCl	1.19% (7 d) 1.70% (14 d) 2.26% (28 d)	N/A
SrSiO₃	SBF	N/A	Sr: ~8.27 mmol·L^-1/Si: ~2.35 mmol·L^-1
Zn₂SiO₄	N/A	N/A	Zn: ~0.012 mmol·L^-1/Si: ~0.015 mmol·L^-1
Li₂Ca₂Si₂O₇	SBF	N/A	Ca: ~3.12 mmol·L^-1/Si: ~2.33 mmol·L^-1/Li: ~0.82 mmol·L^-1

基于DFT的描述符预测生物陶瓷的降解性

Predicting the Degradability of Bioceramics through a DFT-based Descriptor

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Ca (Mg)/P molar ratio	Compounds and their typical abbreviations	Chemical formula	Solubility at 25 ℃ in SBF/(g·L^-1)
1.0	Dicalcium phosphate anhydrous (DCPA or DCP), mineral monetite	CaHPO₄	~0.048
1.33	Octacalcium phosphate (OCP)	Ca₈(HPO₄)₂(PO₄)₄·5H₂O	~0.0081
1.5	α-Tricalcium phosphate(α-TCP)	α-Ca₃(PO₄)₂	~0.0025
1.5	β-Tricalcium phosphate(β-TCP)	β-Ca₃(PO₄)₂	~0.0005
1.67	Hydroxyapatite (HA or HAP)	Ca₁₀(PO₄)₆(OH)₂	~0.0003
1.67	Fluorapatite (FA or FAP)	Ca₁₀(PO₄)₆F₂	~0.0002
1.67	Oxyapatite (OA、OAP or OXA), mineral voelckerite	Ca₁₀(PO₄)₆O	~0.087
1.5	Farringtonite	Mg₃(PO₄)₂	~0.00215
1.5	Bobierrite	Mg₃(PO₄)₂·8H₂O	~0.0062
1.5	Cattiite	Mg₃(PO₄)₂·22H₂O	~0.00146

Bioceramic		a/Å	b/Å	c/Å	α/(°)	β/(°)	γ/(°)	Cell volume/Å³	Density/ (g·cm^-3)	Void space/%
DCP	Calc.	6.7222	6.9771	7.1003	75.727	83.353	88.127	320.567	2.8192	55.11
DCP	Expt.	6.7205	6.9810	7.0970	75.716	83.359	88.176	320.503	N/A	N/A
OCP	Calc.	20.0539	9.6632	6.9266	90.376	93.188	110.180	1257.459	2.5951	58.04
OCP	Expt.	19.6920	9.5230	6.8350	90.150	92.540	108.650	1213.058	N/A	N/A
α-TCP	Calc.	5.2650	5.2650	7.2297	89.964	90.036	64.657	181.125	2.8437	57.68
α-TCP	Expt.	5.2719	5.2719	7.2338	89.713	90.287	64.441	181.367	N/A	N/A
β-TCP	Calc.	14.1827	14.1827	14.1827	43.823	43.823	43.823	1241.876	2.9033	75.04
β-TCP	Expt.	14.4070	14.4070	14.4070	43.443	43.443	43.443	1282.726	N/A	N/A
HAP	Calc.	9.5609	9.5609	6.9081	90	90	120	546.872	3.0505	55.17
HAP	Expt.	9.4240	9.4240	6.8790	90	90	120	529.086	N/A	N/A
FAP	Calc.	9.5015	9.5015	6.9174	90	90	120	540.833	3.0968	54.78
FAP	Expt.	9.3770	9.3770	6.8880	90	90	120	524.507	N/A	N/A
OAP	Calc.	9.6140	9.6140	6.8905	90	90	120	551.555	2.9704	56.88
OAP	Expt.	9.4320	9.4320	6.8810	90	90	120	530.139	N/A	N/A
Mg₃(PO₄)₂	Calc.	5.1226	8.3405	8.9544	90	120.550	90	329.469	2.6498	60.83
Mg₃(PO₄)₂	Expt.	5.1224	8.3404	8.9544	90	120.549	90	329.456	N/A	N/A
Mg₃(PO₄)₂·8H₂O	Calc.	8.4348	8.4348	4.6912	80.689	99.311	74.357	309.660	2.1825	59.26
Mg₃(PO₄)₂·8H₂O	Expt.	8.4235	8.4235	4.6942	80.788	99.212	74.232	309.059	N/A	N/A
Mg₃(PO₄)₂·22H₂O	Calc.	6.8362	7.0170	15.8842	87.185	94.670	118.362	668.225	1.6382	66.59
Mg₃(PO₄)₂·22H₂O	Expt.	6.9265	7.0204	15.9613	88.374	94.305	119.386	674.334	N/A	N/A

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