An approach to investigate the crystallographic unit cell of human tooth enamel

Human tooth enamel (HTE) is the hardest tissue in the human body and its structural organization shows a hierarchical composite material. At the nanometric level, HTE is composed of approximately 97% hy­droxy­apatite [HAP, Ca₁₀(PO₄)₆(OH)₂] as inorganic phase, and of 3% as organic phase and water. However, it is still controversial whether the hexagonal HAP phase crystallizes in P6₃/m or another space group. The observance in HTE of Ca²⁺, Mg²⁺ and Na⁺ ions using X-ray characteristic energy-dispersive spectroscopy in the scanning electron microscope has been explained by substitutions in the HAP unit cell. Thus, Ca²⁺ can be replaced by Na⁺ and Mg²⁺ ions; the PO₄³⁻ group can be replaced by CO₃²⁻ ions; and the OH⁻ ions can also be replaced by CO₃²⁻. A unit-cell model of the hexagonal structure of HTE is not fully defined yet. In this work, density functional theory calculations are performed to study the hexagonal HAP unit cell when substitution by OH⁻, CO₃²⁻, Mg²⁺ and Na⁺ ions are carried out. An approach is presented to study the crystallographic unit cell of HTE by examining the changes resulting from the inclusion of these different ions in the unit cell of HAP. Enthalpies of formation and crystallographic characteristics of the electron diffraction patterns are analysed in each case. The results show an enhancement in structural stability of HAP with OH defects, atomic substitution of Mg²⁺, carbonate and interstitial Na⁺. Simulated electron diffraction patterns of the generated structures show similar characteristics to those of human tooth enamel. Hence, the results explain the indiscernible structural changes shown in experimental X-ray diffractograms and electron diffraction patterns.

Computing details

(I)

Crystal data

P1	α = 90.364365°
a = 9.817578 Å	β = 91.753616°
b = 9.642835 Å	γ = 120.151657°
c = 6.829235 Å	V = 558.61 Å^3

Data collection

h = →	l = →
k = →

Fractional atomic coordinates and isotropic or equivalent isotropic displacement parameters (Ų)

	x	y	z	Uiso*/Ueq
Ca1	0.715284	0.341537	0.483745	?*
Ca2	0.265017	0.970315	0.240970	?*
Ca3	0.993057	0.246446	0.251990	?*
Ca4	0.718477	0.719065	0.246649	?*
Ca5	0.767613	0.005480	0.756687	?*
Ca6	0.995221	0.726650	0.748964	?*
Ca7	0.163539	0.139432	0.817084	?*
Ca8	0.668047	0.350383	0.971994	?*
Ca9	0.317051	0.661064	0.455160	?*
O1	0.354956	0.519800	0.172766	?*
O2	0.509046	0.848889	0.227700	?*
O3	0.138302	0.687122	0.232752	?*
O4	0.667863	0.518505	0.714872	?*
O5	0.514301	0.166934	0.705883	?*
O6	0.886392	0.411643	0.757133	?*
O7	0.555682	0.436179	0.270653	?*
O8	0.537338	0.129914	0.203798	?*
O9	0.881595	0.408809	0.214212	?*
O10	0.427116	0.554254	0.658626	?*
O11	0.491831	0.902300	0.818643	?*
O12	0.178587	0.605567	0.824097	?*
O13	0.406401	0.333069	0.948632	?*
O14	0.752103	0.082381	0.077507	?*
O15	0.882089	0.642140	0.061558	?*
O16	0.696579	0.773068	0.570880	?*
O17	0.330410	0.899945	0.533346	?*
O18	0.091524	0.417547	0.535736	?*
O19	0.946973	0.925105	0.877749	?*
O20	0.717465	0.094694	0.437524	?*
O21	0.894064	0.626327	0.425916	?*
O22	0.259746	0.230725	0.259029	?*
O23	0.268124	0.959955	0.875951	?*
O24	0.056746	0.301291	0.886651	?*
O25	0.620419	0.713233	0.926682	?*
O26	0.112755	0.964773	0.520021	?*
O27	0.955536	0.962553	0.271822	?*
O28	0.994985	0.108388	0.544633	?*
P1	0.392728	0.380989	0.159284	?*
P2	0.626917	0.034328	0.235537	?*
P3	0.957106	0.595124	0.234096	?*
P4	0.605452	0.637963	0.718261	?*
P5	0.400950	0.982776	0.734510	?*
P6	0.054716	0.430373	0.752817	?*
H1	0.941408	0.909723	0.019325	?*
C1	0.018069	0.008183	0.446771	?*
Mg1	0.400345	0.694198	0.966815	?*
Na1	0.414138	0.326398	0.565945	?*