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Theoretical analysis of hydroxylapatite and its main precursors by quantum mechanics and HREM image simulation
Computational Materials Science 25 (2002) 413–426 www.elsevier.com/locate/commatsci
Theoretical analysis of hydroxylapatite and its main precursors by quantum mechanics and HREM image simulation J.A. Ascencio
a,b,*
, V. Rodrıguez-Lugo c, C. Angeles a, T. Santamarıa d, V.M. Casta~ no e
a
b
Coordinaci on del Programa de Ductos, Instituto Mexicano del Petr oleo, L azaro C adenas 152, San Bartolo Atepehuac an, CP 07730, M exico DF, Mexico Facultad de Quımica, Universidad Aut onoma del Estado de M exico, Paseo Tollocan Esq. Paseo Col on, Toluca 50180, Mexico c Instituto de Fısica, Benem erita Universidad Aut onoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico d Instituto Tecnol ogico de Cd. Guzm an, Domicilio Conocido, Carretera al Fresnito, Ciudad Guzm an, Jalisco 49050, Mexico e Instituto de Fısica, Universidad Nacional Aut onoma de M exico, AP 1-1010 Quer etaro 76000, Mexico Received 10 September 2000; received in revised form 6 February 2002; accepted 24 March 2002
Abstract The possibility to produce hydroxylapatite, for biomaterials applications, from different kind of precursors has motivated many efforts. In this work we have analyzed several common precursors, mainly calcium based systems. Quantum mechanics calculations, by density-functional theory and semi-empirical approximations, were used to study the characteristic crystals and the particular behavior of the PO3 4 molecules interaction, both by the electronic distributions in order to give a new possibility for the study of these materials and for improving new synthesis methods. High resolution electron microscopy images are also calculated, by a multislice method, to confirm our approaches and also to show a easy way to distinguish this materials experimentally as is proved in this work. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Earlier studies of biocompatible materials have identified the main elements and crystalline systems present in animal and, more specifically *
Corresponding author. Address: Coordinaci on del Programa de Ductos, Instituto Mexicano del Petr oleo, Lazaro C adenas 152, San Bartolo Atepehuacan, CP 07730, Mexico DF, Mexico. E-mail address: [email protected] (J.A. Ascencio).
human bones and teeth [1–5], these materials involve the family of Ca-apatites and other calciumderived materials. Multiple analyses have demonstrated that those minerals have the proper spatial structure that in turn contributes to the biocompatibility in human bones and teeth [6,7]. Accordingly, in order to synthesize materials that could act as prosthesis, many authors have reported different technologies which make use of this kind of material by using diverse techniques [1–5,8–11].
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 2 ) 0 0 2 4 3 - 4
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Biomaterials based on hydroxylapatite and other apatites have become a productive technology, where the composition, structure and chemical properties are very important. In order to identify the biocompatibility [1], adhesion properties [5] and also to determine the optimal conditions for the synthesis [10], multiple experimental studies have been carried out by using several characterization techniques [9,11]. However these studies have been rarely accompanied by theoretical analysis. On the other hand, molecular simulation techniques have gained strength amongst the scientific community during the last two decades, both for molecular and crystal systems, and by classical and quantum mechanics approximations. Computational materials science can be used as a virtual laboratory, where the electronic structure, charge distribution and atomic configuration is analyzed by quantum mechanics calculations [12–14], using both semi-empirical [15] and density functional theory based approaches [16,17], that allow the identification of reaction conditions [18], molecular selectivity [14] and to predict macroscopic properties [19]. In this sense it is important to either confirm or to refine the models and the corresponding predictions through a comparison between theoretical and experimental analytical data [11,20–22]. This also makes easier the interpretation and identification of small details from the studied materials particularly in such cases as the high resolution electron microscopy (HREM) images, which could be really complicated, especially when more than one crystalline matrix exists [21] or when the particles are nanometric and any tilting or focusing changes could lead to misinterpretation of the image [22]. In this work, a comprehensive analysis is done for hydroxylapatite and the common precursors involved in its synthesis [9], by applying quantum mechanics calculations and by simulating the corresponding crystal morphology and HREM images. 2. Methods 2.1. Computer simulations The crystal models were built after experimental parameters from the most usual precursors ob-
served in the hydroxylapatite production reaction (CaCO3 , CaO, CaOH and CaHPO4 , named calcite, calcium oxide, portlandite and monetite respectively) and the hydroxylapatite (Ca5 ðPO4 Þ3 OH), which are also corroborated by previous reports [23–26] for these materials. In Table 1, the crystalline lattice, space group, cell dimensions and angles, and the fundamental atomic positions to build the crystals, are summarized. The CASTEP method [27], which is based in the density functional theory (DFT) using plane waves to represent the electronic density, and a gradient correction approach [17], was applied to calculate two different items: first, to analyze the precision of our models, the geometry optimization was obtained for each of the unit cell, with no restriction whatsoever in lattice parameter, and atomic position. A second analysis, on the system energy, was made to calculate the wave function to obtain the electron distribution, charge density and electrostatic potential iso-surfaces distribution for each crystal structure model. In the DFT based calculations, we used self-optimized pseudo-potentials and with a 3 3 3 MP grid, while the value of the energy cutoff was 200 eV. A molecular orbital calculation method (MOPAC), based on the semi-empirical approximation [15], was used to study the molecular orbital behavior for one and two PO3 4 ion with no calcium atoms present. The analysis was focused to study the minimal energy configuration; the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), the charge density distribution and electrostatic potential iso-surfaces. The analysis of both crystal and molecular calculations, is done in order to identify the reaction conditions and the corresponding changes over the characteristics for precursors and final material. Aiming to achieve a full characterization, the precursors and the hydroxylapatite crystalline habits based on the atomistic distribution and crystalline characteristics were calculated by means of the Donnay method [28]. Because of the importance of HREM images to analyze local atomic and crystal distribution, these images were calculated using the multislice method [22] and a 200 kV TEM parameter, which was used in the experi-
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Table 1 Unit cell data used for the quantum calculation Crystal
Crystalline lattice
Space group
Cell vectors
Cell angles
Fundamental positions
Calcite (CaCO3 ) [23]
Trigonalhexagonal
R-3 2/c
a ¼ b ¼ 4:990 A c ¼ 17:059 A
a ¼ b ¼ 90° c ¼ 120°
Calcium oxide (CaO) Portlandite (CaOH) [24]
FCC
F 4/m-3 2/m
a ¼ 4:811 A
a ¼ 90°
Trigonalhexagonal
P-3 2/m 1
a ¼ b ¼ 3:592 A c ¼ 4:906 A
a ¼ b ¼ 90° c ¼ 120°
Monetite (CaHPO4 ) [25]
Triclinic
P-1
a ¼ 6:190 A b ¼ 6:660 A c ¼ 7:020 A
a ¼ 96:10° b ¼ 103:90° c ¼ 89:20°
Hydroxylapatite (Ca5 (PO4)2 OH) [26]
Hexagonal
P 63/m
a ¼ b ¼ 9:430 A c ¼ 6:880 A
a ¼ b ¼ 90° c ¼ 120°
Ca (0, 0, 4.265) C (0, 0, 0) O (1.038, 0.599, 4.265) O (0, 0, 0) Ca (2.405, 2.405, 2.405) Ca (0, 0, 0) O (1.037, 1.796, 1.149) H (1.037, 1.796, 2.084) Ca1 (1.767, 2.855, 1.163) Ca2 (1.052, 5.523, 3.827) P1 (1.249, 2.497, 4.475) P2 (1.781, 6.234, 0.362) O1 (1.935, 2.209, 5.846) O2 (2.085, 3.213, 3.539) O3 (0.817, 1.202, 3.852) O4 (0.228, 3.461, 4.810) O5 (1.989, 5.486, 0.976) O6 (2.764, 0.656, 1.376) O7 (0.577, 0.430, 0.962) O8 (1.724, 5.198, 1.466) Ca1 (2.722, 4.715, 0.007) Ca2 (2.009, 8.204, 1.720) P (3.267, 1.594, 1.720) O1 (2.687, 3.013, 1.720) O2 (4.810, 1.617, 1.720) O3 (2.842, 0.802, 0.502) O4 (0.000, 0.000, 1.720)
mental analysis for the sample characterization [7,9]. The images were calculated, for a 5 5 5 unit cell model, in the [0,0,1] orientation and rotating the model each 15° over the h1; 0; 0i, h0; 1; 0i and h1; 1; 0i axes until 90° that changes just for the fcc CaO model because of its symmetry. The calculations were made with the crystal builder, CASTEP, MOPAC, morphology, crystal diffraction and HREM modules from the Cerius2 software of Molecular Simulation Inc. [29]. To compare the simulated models with actual experimental results, samples of CaCO3 and CaO crystal precursors and the corresponding hydroxylapatite crystals were prepared by depositing crystal powder on a copper grid coated with amorphous carbon and observed in a Jeol 2010 microscope to obtain HREM images at Scherzer conditions [30,31].
The HREM images were digitalized using a SensysColor low noise CCD. The digital images were processed by obtaining their fast fourier transform (FFT) and then applying filters in frequencies space to reduce the noise and to enhance their corresponding crystalline structure [31]. 2.2. Experimental Synthesis of hydroxylapatite from a marine skeleton (sea star), namely Mellite eduardo Barroso sp. Nov. has been described elsewhere [7,9]. It basically consists in applying a thermal treatment at 800 °C for 2 h, which produces calcium oxide (CaO) in a first stage, which is used with the monetite (CaHPO4 ) as the precursor material to obtain the hydroxylapatite.
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Thus, the first stage of the reaction is CaCO3 ! CaO þ CO2 "
ð1Þ
procedure, the calcium hydroxide must be present as another precursor for the hydroxylapatite synthesis.
where the calcite produces calcium oxide. Moreover, the main possible reactions to be analyzed are
3. Results
2CaO þ 3CaHPO4 ! Ca5 ðPO4 Þ3 ðOHÞ þ H2 O
3.1. Precursors ð2Þ
2CaðOHÞ þ 3CaHPO4 ! Ca5 ðPO4 Þ3 ðOHÞ þ 3H2 O ð3Þ 2CaCO3 þ 3CaHPO4 ! Ca5 ðPO4 Þ3 OH þ H2 O ð4Þ that produce the hydroxylapatite from the calcium oxide and the calcium phosphate anhydride. However, even when there are only two precursors involved in this reaction, because of the reaction
To better understand the reaction conditions, the different models for the precursor, can be observed in the Fig. 1, where the main orientation corresponding to each one of the four precursors involved in the reaction is illustrated. These models were built based on the data of the Table 1, which are also corroborated with reported data in the literature for the different materials [23–26], where the crystalline parameters and the fundamental positions are listed for each unit cell. It is clear, from the atomistic distribution in the models how the reaction must produce an atomic
Fig. 1. Crystal models for the different precursor materials: (a) CaCO3 in [0,0,1] and [0,1,0] orientations, (b) CaO in [0,0,1] and [0,1,1] orientations, (c) CaOH and (d) CaHPO4 in the [0,0,1] and [0,1,0] orientations.
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redistribution from the calcite to the hydroxylapatite, including all the precursors. It is important to understand the electrostatic behavior and charge influence over the atomistic changes because there is no evidence of breaking or forming of chemical bonds, so then all the crystal changes must be just a function of the energy contribution to the local and global system. Even when the calcium in all the precursors can be considered as a common characteristic, the different precursors have particular environments for the calcium atoms. Calcite, for instance, has Ca2þ cations surrounded by hexagons formed by oxygen atoms over the a–b cell planes, and these planes have carbon atoms between them as can be seen in Fig. 1a. The calcium oxide presents a threedimensional regular Ca–O atom distribution, so the Ca2þ cations have always the same kind of oxygen coordination environment as can be observed in Fig. 1b. The calcium hydroxide present a rhombohedral periodicity of its Ca2þ cations, which are basically identified in planes over the a– b cell planes while in the middle position (in the c
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vector) OH anions are polarized, as shown in Fig. 1c. The last precursor involves PO3 4 anions with tetrahedral configuration; these molecules are regularly distributed with the Ca2þ cations (Fig. 1d). In Fig. 2, the electrostatic potential distributions for each precursor are shown. In the calcite calculation (Fig. 2a), the direct influence produced by the Ca, C and O atoms generate multiple isosurfaces that cover the full cell regularly in spherical shapes, produced mainly because of the atomsÕ electronic distribution. In this cell analysis it is impossible to identify any way to produce a simple electrostatic carbon interchange. The electrostatic potential calculation for the calcium oxide presents, in Fig. 2b, a well defined iso-surface distribution, this configuration is found in the interstitial spaces, showing symmetric shapes conformed by the charge equilibrium between the oxygen and calcium atoms. It is clear how the instabilities can affect this configuration when extra energy is applied to the crystalline system.
Fig. 2. Electrostatic potential distribution for the calcium precursors: (a) CaCO3 in [0,0,1] and [0,1,0] orientations, (b) CaO in [0,0,1] and [0,1,1] orientations, (c) CaOH and (d) CaHPO4 in the [0,0,1] and [0,1,0] orientations.
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In case of calcium hydroxide (Fig. 2c), the isosurfaces are fixed mainly in two wave configurations with curvature defined by the Ca2þ cations mainly and just distorted in the OH anions position, these iso-potential surfaces determine a region of low charge density in the middle of the cell that shows a possible route to convert from the hydroxide to phosphate via an easier process than for any other precursor. Fig. 2d shows the electrostatic iso-potential surfaces that presents a homogeneous distribution, mainly determined by the Ca2þ cations and PO3 4 anions, which are symmetrically distributed keeping constant the corresponding distances and producing surfaces with high curvature and complicated vacuum spaces of the inter-cell sites. It is possible to identify a relation between electrostatic contribution from the PO3 4 anions over the field produced from the Ca2þ cations producing a total electrostatic potential neutralization in the unit cell. From the different precursor analysis, the calcium behavior can be well understood. However
the PO4 role in the reaction is not still clear, so then it is important to study the PO4 molecules behavior, when the Ca atoms are not present, to identify the stable configuration, charge distribution and molecular orbital conditions for one and two PO4 molecules. 3 3.2. PO3 4 –PO4 interaction
In order to understand the PO4 –PO4 interaction, a couple of calculations were made, for the 3 cases of a single PO3 4 and two PO4 anions with no influence from other atomic species. The minimum energy configuration was determined using a semi-empirical molecular optimization, which also produces the molecular orbital (HOMO and LUMO), charge density and electrostatic potential distribution as can be seen in Fig. 3a for just one PO3 4 anion. In the single PO3 4 anion analysis, the model of minimum energy configuration (MEC) is observed in Fig. 3a, where the angles and distances for the oxygen atoms generate a well-defined tetrahedral
3 Fig. 3. Quantum chemical semi-empirical calculation for (a) single PO3 4 anion molecule and (b) two PO4 anion molecules. MEC, with its frontier orbitals HOMO, LUMO, ChD and EPIS are shown for each case.
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form. Also the two frontier orbitals, HOMO and LUMO, are shown; both are regular and symmetrically distributed mainly around the oxygen atoms. The charge density distribution (ChD) and electrostatic potential iso-surfaces (EPIS) are regularly distributed with an external shell shape for the charge density graph, while the electrostatic potential is observed as a shape inverse to that of the charge distribution. It is also clear that the oxygen atoms produce the main influence. Two perpendicular orientations are shown. The two PO3 4 molecules analysis, shown in Fig. 3b, began with a random configuration where the PO3 4 molecules are at the same distances as in the CaHPO4 crystal. However, on geometry optimization, the molecules tend to reduce the distance between them, mainly between one oxygen atom of each molecule, as can be observed in the figure. The P–P distance is reduced from the original distance to the final distance of 2.34 A . 4.71 A Similarly, the influence over the HOMO and LUMO orbitals is observed in the figure, where it is also clear that the HOMO localization decreases in the oxygen atoms that are in the region between the molecules. While the LUMO density is increased in those atoms and its localization is reduced strongly in the external oxygen atoms. Finally, the electrostatic potential is shown, with strong influence from the external region atoms, and presenting a small region of influence in the middle region of the two-molecule configuration. 3.3. Hydroxylapatite as final product To study the atomic and the electron distribution influence for the final product, the hydroxylapatite crystal was analyzed with a similar method to the above cases, calculating its minimum energy unit cell and its corresponding electrostatic potential distribution. In Fig. 4a the hydroxylapatite crystal structure for the two main orientations, and also a polygon presentation is shown to aid in the identification of the atomic distribution. It is clear that the PO3 4 anions in the interstices form the tetrahedron figure and these molecules are periodically distributed with Ca2þ cations and OH anions in the
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middle spaces; the model shows how the distances remain constant. The electrostatic iso-potential are observed in the Fig. 4b for the two above directions. In this scheme, the calcium atoms present surfaces that denote how these atoms affect the interaction fixing the distances by repulsion, while the OH anions produce smaller radius iso-potential surfaces. However, the electrostatic system homogeneity shows that the system has electrostatic equilibrium in function of the atomic charge distribution. 3 Obviously the PO3 4 –PO4 interaction does not correspond to the calculated one in the last section because of the presence of the calcium atoms. So then, there are many significant differences produced by the charge compensation between the different species in the crystalline systems. 3.4. Analytical data calculation The different models were also used to calculate three of the main analytical data patterns: crystalline morphology, electron diffraction patterns, and HREM images. These electron microscopy characteristic patterns were calculated for a mapping that includes the main orientations, which were selected depending on the crystal lattice. In Fig. 5, the calculated habits are shown for the precursors and the hydroxylapatite crystals. The calcite characteristic morphology is defined as aggregates in Fig. 5a, with regular hexagon faces observed in the [0,0,1] orientation, while irregular hexagonal and rectangular faces are identified in the [0,1,0] orientation. The corresponding morphology to calcium oxide is observed in Fig. 5b, where the hexagonal and square faces are shown in the [0,0,1] and [1,1,1] orientation respectively. Hexagonal faces in the h0; 0; 1i axis determine the calcium hydroxide crystal habit whereas rectangular shapes are observed in the other faces of the Fig. 5c. The morphology corresponding to the CaHPO4 crystal (Fig. 5d) shows rectangular, irregular hexagon and rhombic faces as can be observed in the [0,0,1] and [1,1,1] orientation. The final productÕs characteristic morphology are shown in Fig. 5e, hydroxylapatite is clearly characterized by a hexagonal fiber shape that grows in
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Fig. 4. Hydroxylapatite crystal model (a) in the [0,0,1], [0,1,0] and a polygonal scheme where it is possible to identify the tetrahedron distribution, and its corresponding electrostatic iso-potential surfaces calculation (b) for the [0,0,1] and [0,1,0] orientations.
Fig. 5. Calculated crystalline habits for (a) calcite, (b) calcium oxide, (c) portlandite, (d) monetite and (e) hydroxylapatite.
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Fig. 6. HREM simulated image mapping for the calcite model with steps for each 15° and the corresponding FFT for the main orientations. The three main orientations are marked in both (a) image and (b) diffraction pattern.
the h0; 0; 1i axis direction as can be seen in figure in the corresponding [0,0,1] and [1,1,1] orientations. A full image mapping is observed for the calcite in Fig. 6a, with the corresponding FFT in Fig. 6b; generally the hexagonal periodicity is observed, even when only the [0,0,1] orientation is present 60° between reflections. It is similar to the HREM image contrast of white dots that correspond to
the atom columns are mainly produced by the Ca2þ cations, which have a much bigger scattering factor than the carbon and oxygen atoms. Fig. 7 shows the corresponding mapping of images and the FFT for the calcium oxide model, where the 90° angles in the FFT and white dot contrast are clear in the [0,0,1] orientation. Also, the irregular and regular hexagon characteristic to the [0,1,1]
Fig. 7. (a) HREM simulated image mapping for the calcium oxide model with steps for each 15° (the 35° is also included to obtain the [1,1,1] orientation) and (b) the corresponding FFTs.
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and [1,1,1] orientations respectively can be seen in the figures. The HREM image mapping and the main FFT calculations, of calcium hydroxide and CaHPO4 respectively are shown in Figs. 8 and 9. The hexagonal order for the [0,0,1] orientation and linear contrast for the orientations [0,1,0] and [1,0,0] of
the CaOH model can clearly be seen. In the case of CaHPO4 , [0,0,1] orientation shows distorted hexagons while there are multiple orientations that generates linear and zigzag like contrasts. The analysis of hydroxylapatite results is shown in the Fig. 10. The hydroxylapatite HREM mapping calculations produces for the [0,0,1] orienta-
Fig. 8. HREM simulated image mapping for the portlandite model with steps for each 15° and the corresponding FFT.
Fig. 9. HREM simulated image mapping for the monetite model with steps for each 15° and the corresponding FFT for the main orientations.
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Fig. 10. HREM simulated image mapping for the hydroxylapatite model with steps for each 15° and the corresponding FFT for the main orientations.
tion a particular contrast, with a hexagonal preference as can be seen in the FFT, while the [0,1,0] and [1,0,0] orientations can be characterized because of their special 90° periodic contrast and FFT.
3.5. Experimental HREM images Fig. 11 shows a well-defined HREM contrast characteristic of the CaCO3 crystal from the sample edges where the thickness is smaller, the
Fig. 11. HREM experimental image for a calcite sample and its calculated FFT that corresponds to a 45° rotation over the h0; 0; 1i axis.
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Fig. 12. HREM experimental image for a calcium oxide sample. A full view is observed in (a) while selected areas show small sections in (b), where several crystalline orientation are shown: [0,1,1] in I, and [0,0,1] in III, while in II and IV, rotations around 15° over the h1; 0; 0i axis and 35° over h0; 1; 0i are shown.
contrast and the corresponding FFT match directly to the theoretical calculations. While in Fig. 12, a HREM image shows the characteristic contrast for the CaO sample. In the image it is possible to distinguish the four main orientations with their corresponding FFT, which correspond to the predicted contrast for this crystal. These two figures present a crystal characterization way by HREM, which is based in the dispersion of a electron beam over the sample. Obviously, while the elements are heavier the contrast is increased, and in these cases the main atomic evidences correspond to the calcium arrays, which also denote the crystalline symmetry. The crystalline geometry is also identified from the FFT, which shows in the space of frequencies the periodicity of a particular geometry. A general view of the experimental image of the hydroxylapatite sample is observed in Fig. 13 with its corresponding FFT. Four different sections from the full image, which were processed, are
presented with their corresponding FFT to analyze local sections where the crystals show small tilts and structural changes. These changes can also be interpreted as produced by the influence of the electron beam as reported previously [11].
4. Conclusions From the analysis presented in this paper, it is identified that there are no bond change processes in this kind of reaction, and the main conditions to produce the hydroxylapatite from these precursors are electrostatic interactions. That implies a direct dependence between the calcium saturation in the system to obtain the hydroxylapatite structure. The quantum mechanics calculation and the analytical data prediction provide a basis to further analysis in the biomaterials involved in this work. Also that the experimental and theoretical contrast match clearly corroborating the exacti-
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Fig. 13. Analysis of hydroxylapatite by HREM image where it is possible to observe selected areas with their corresponding FFT that denotes small differences in the contrast and periodicity.
tude of the used models. It is clear how this Atlas of images can help to provide a full and easier characterization by means of a direct comparison between experimental and theoretical images in the different orientations.
Acknowledgements Authors are indebted to Raquel Cruz, Ignacio Sandoval, Thelma Falcon and Juan Bonifacio for their technical assistance, and particularly to Maria Eufemia Fernandez for her support in the theoretical calculations. Also we are indebted to CONACYT for grants within the project ‘‘Desarrollo de materiales cer amicos para aplicaciones biomedicas’’ 32605-U and ‘‘Coloides Cu anticos, Puntos Cu anticos y Nanopartıculas’’.
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Theoretical analysis of hydroxylapatite and its main precursors by quantum mechanics and HREM image simulation J.A. Ascencio
a,b,*
, V. Rodrıguez-Lugo c, C. Angeles a, T. Santamarıa d, V.M. Casta~ no e
a
b
Coordinaci on del Programa de Ductos, Instituto Mexicano del Petr oleo, L azaro C adenas 152, San Bartolo Atepehuac an, CP 07730, M exico DF, Mexico Facultad de Quımica, Universidad Aut onoma del Estado de M exico, Paseo Tollocan Esq. Paseo Col on, Toluca 50180, Mexico c Instituto de Fısica, Benem erita Universidad Aut onoma de Puebla, Apartado Postal J-48, Puebla 72570, Mexico d Instituto Tecnol ogico de Cd. Guzm an, Domicilio Conocido, Carretera al Fresnito, Ciudad Guzm an, Jalisco 49050, Mexico e Instituto de Fısica, Universidad Nacional Aut onoma de M exico, AP 1-1010 Quer etaro 76000, Mexico Received 10 September 2000; received in revised form 6 February 2002; accepted 24 March 2002
Abstract The possibility to produce hydroxylapatite, for biomaterials applications, from different kind of precursors has motivated many efforts. In this work we have analyzed several common precursors, mainly calcium based systems. Quantum mechanics calculations, by density-functional theory and semi-empirical approximations, were used to study the characteristic crystals and the particular behavior of the PO3 4 molecules interaction, both by the electronic distributions in order to give a new possibility for the study of these materials and for improving new synthesis methods. High resolution electron microscopy images are also calculated, by a multislice method, to confirm our approaches and also to show a easy way to distinguish this materials experimentally as is proved in this work. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Earlier studies of biocompatible materials have identified the main elements and crystalline systems present in animal and, more specifically *
Corresponding author. Address: Coordinaci on del Programa de Ductos, Instituto Mexicano del Petr oleo, Lazaro C adenas 152, San Bartolo Atepehuacan, CP 07730, Mexico DF, Mexico. E-mail address: [email protected] (J.A. Ascencio).
human bones and teeth [1–5], these materials involve the family of Ca-apatites and other calciumderived materials. Multiple analyses have demonstrated that those minerals have the proper spatial structure that in turn contributes to the biocompatibility in human bones and teeth [6,7]. Accordingly, in order to synthesize materials that could act as prosthesis, many authors have reported different technologies which make use of this kind of material by using diverse techniques [1–5,8–11].
0927-0256/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 7 - 0 2 5 6 ( 0 2 ) 0 0 2 4 3 - 4
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Biomaterials based on hydroxylapatite and other apatites have become a productive technology, where the composition, structure and chemical properties are very important. In order to identify the biocompatibility [1], adhesion properties [5] and also to determine the optimal conditions for the synthesis [10], multiple experimental studies have been carried out by using several characterization techniques [9,11]. However these studies have been rarely accompanied by theoretical analysis. On the other hand, molecular simulation techniques have gained strength amongst the scientific community during the last two decades, both for molecular and crystal systems, and by classical and quantum mechanics approximations. Computational materials science can be used as a virtual laboratory, where the electronic structure, charge distribution and atomic configuration is analyzed by quantum mechanics calculations [12–14], using both semi-empirical [15] and density functional theory based approaches [16,17], that allow the identification of reaction conditions [18], molecular selectivity [14] and to predict macroscopic properties [19]. In this sense it is important to either confirm or to refine the models and the corresponding predictions through a comparison between theoretical and experimental analytical data [11,20–22]. This also makes easier the interpretation and identification of small details from the studied materials particularly in such cases as the high resolution electron microscopy (HREM) images, which could be really complicated, especially when more than one crystalline matrix exists [21] or when the particles are nanometric and any tilting or focusing changes could lead to misinterpretation of the image [22]. In this work, a comprehensive analysis is done for hydroxylapatite and the common precursors involved in its synthesis [9], by applying quantum mechanics calculations and by simulating the corresponding crystal morphology and HREM images. 2. Methods 2.1. Computer simulations The crystal models were built after experimental parameters from the most usual precursors ob-
served in the hydroxylapatite production reaction (CaCO3 , CaO, CaOH and CaHPO4 , named calcite, calcium oxide, portlandite and monetite respectively) and the hydroxylapatite (Ca5 ðPO4 Þ3 OH), which are also corroborated by previous reports [23–26] for these materials. In Table 1, the crystalline lattice, space group, cell dimensions and angles, and the fundamental atomic positions to build the crystals, are summarized. The CASTEP method [27], which is based in the density functional theory (DFT) using plane waves to represent the electronic density, and a gradient correction approach [17], was applied to calculate two different items: first, to analyze the precision of our models, the geometry optimization was obtained for each of the unit cell, with no restriction whatsoever in lattice parameter, and atomic position. A second analysis, on the system energy, was made to calculate the wave function to obtain the electron distribution, charge density and electrostatic potential iso-surfaces distribution for each crystal structure model. In the DFT based calculations, we used self-optimized pseudo-potentials and with a 3 3 3 MP grid, while the value of the energy cutoff was 200 eV. A molecular orbital calculation method (MOPAC), based on the semi-empirical approximation [15], was used to study the molecular orbital behavior for one and two PO3 4 ion with no calcium atoms present. The analysis was focused to study the minimal energy configuration; the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO), the charge density distribution and electrostatic potential iso-surfaces. The analysis of both crystal and molecular calculations, is done in order to identify the reaction conditions and the corresponding changes over the characteristics for precursors and final material. Aiming to achieve a full characterization, the precursors and the hydroxylapatite crystalline habits based on the atomistic distribution and crystalline characteristics were calculated by means of the Donnay method [28]. Because of the importance of HREM images to analyze local atomic and crystal distribution, these images were calculated using the multislice method [22] and a 200 kV TEM parameter, which was used in the experi-
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Table 1 Unit cell data used for the quantum calculation Crystal
Crystalline lattice
Space group
Cell vectors
Cell angles
Fundamental positions
Calcite (CaCO3 ) [23]
Trigonalhexagonal
R-3 2/c
a ¼ b ¼ 4:990 A c ¼ 17:059 A
a ¼ b ¼ 90° c ¼ 120°
Calcium oxide (CaO) Portlandite (CaOH) [24]
FCC
F 4/m-3 2/m
a ¼ 4:811 A
a ¼ 90°
Trigonalhexagonal
P-3 2/m 1
a ¼ b ¼ 3:592 A c ¼ 4:906 A
a ¼ b ¼ 90° c ¼ 120°
Monetite (CaHPO4 ) [25]
Triclinic
P-1
a ¼ 6:190 A b ¼ 6:660 A c ¼ 7:020 A
a ¼ 96:10° b ¼ 103:90° c ¼ 89:20°
Hydroxylapatite (Ca5 (PO4)2 OH) [26]
Hexagonal
P 63/m
a ¼ b ¼ 9:430 A c ¼ 6:880 A
a ¼ b ¼ 90° c ¼ 120°
Ca (0, 0, 4.265) C (0, 0, 0) O (1.038, 0.599, 4.265) O (0, 0, 0) Ca (2.405, 2.405, 2.405) Ca (0, 0, 0) O (1.037, 1.796, 1.149) H (1.037, 1.796, 2.084) Ca1 (1.767, 2.855, 1.163) Ca2 (1.052, 5.523, 3.827) P1 (1.249, 2.497, 4.475) P2 (1.781, 6.234, 0.362) O1 (1.935, 2.209, 5.846) O2 (2.085, 3.213, 3.539) O3 (0.817, 1.202, 3.852) O4 (0.228, 3.461, 4.810) O5 (1.989, 5.486, 0.976) O6 (2.764, 0.656, 1.376) O7 (0.577, 0.430, 0.962) O8 (1.724, 5.198, 1.466) Ca1 (2.722, 4.715, 0.007) Ca2 (2.009, 8.204, 1.720) P (3.267, 1.594, 1.720) O1 (2.687, 3.013, 1.720) O2 (4.810, 1.617, 1.720) O3 (2.842, 0.802, 0.502) O4 (0.000, 0.000, 1.720)
mental analysis for the sample characterization [7,9]. The images were calculated, for a 5 5 5 unit cell model, in the [0,0,1] orientation and rotating the model each 15° over the h1; 0; 0i, h0; 1; 0i and h1; 1; 0i axes until 90° that changes just for the fcc CaO model because of its symmetry. The calculations were made with the crystal builder, CASTEP, MOPAC, morphology, crystal diffraction and HREM modules from the Cerius2 software of Molecular Simulation Inc. [29]. To compare the simulated models with actual experimental results, samples of CaCO3 and CaO crystal precursors and the corresponding hydroxylapatite crystals were prepared by depositing crystal powder on a copper grid coated with amorphous carbon and observed in a Jeol 2010 microscope to obtain HREM images at Scherzer conditions [30,31].
The HREM images were digitalized using a SensysColor low noise CCD. The digital images were processed by obtaining their fast fourier transform (FFT) and then applying filters in frequencies space to reduce the noise and to enhance their corresponding crystalline structure [31]. 2.2. Experimental Synthesis of hydroxylapatite from a marine skeleton (sea star), namely Mellite eduardo Barroso sp. Nov. has been described elsewhere [7,9]. It basically consists in applying a thermal treatment at 800 °C for 2 h, which produces calcium oxide (CaO) in a first stage, which is used with the monetite (CaHPO4 ) as the precursor material to obtain the hydroxylapatite.
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Thus, the first stage of the reaction is CaCO3 ! CaO þ CO2 "
ð1Þ
procedure, the calcium hydroxide must be present as another precursor for the hydroxylapatite synthesis.
where the calcite produces calcium oxide. Moreover, the main possible reactions to be analyzed are
3. Results
2CaO þ 3CaHPO4 ! Ca5 ðPO4 Þ3 ðOHÞ þ H2 O
3.1. Precursors ð2Þ
2CaðOHÞ þ 3CaHPO4 ! Ca5 ðPO4 Þ3 ðOHÞ þ 3H2 O ð3Þ 2CaCO3 þ 3CaHPO4 ! Ca5 ðPO4 Þ3 OH þ H2 O ð4Þ that produce the hydroxylapatite from the calcium oxide and the calcium phosphate anhydride. However, even when there are only two precursors involved in this reaction, because of the reaction
To better understand the reaction conditions, the different models for the precursor, can be observed in the Fig. 1, where the main orientation corresponding to each one of the four precursors involved in the reaction is illustrated. These models were built based on the data of the Table 1, which are also corroborated with reported data in the literature for the different materials [23–26], where the crystalline parameters and the fundamental positions are listed for each unit cell. It is clear, from the atomistic distribution in the models how the reaction must produce an atomic
Fig. 1. Crystal models for the different precursor materials: (a) CaCO3 in [0,0,1] and [0,1,0] orientations, (b) CaO in [0,0,1] and [0,1,1] orientations, (c) CaOH and (d) CaHPO4 in the [0,0,1] and [0,1,0] orientations.
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redistribution from the calcite to the hydroxylapatite, including all the precursors. It is important to understand the electrostatic behavior and charge influence over the atomistic changes because there is no evidence of breaking or forming of chemical bonds, so then all the crystal changes must be just a function of the energy contribution to the local and global system. Even when the calcium in all the precursors can be considered as a common characteristic, the different precursors have particular environments for the calcium atoms. Calcite, for instance, has Ca2þ cations surrounded by hexagons formed by oxygen atoms over the a–b cell planes, and these planes have carbon atoms between them as can be seen in Fig. 1a. The calcium oxide presents a threedimensional regular Ca–O atom distribution, so the Ca2þ cations have always the same kind of oxygen coordination environment as can be observed in Fig. 1b. The calcium hydroxide present a rhombohedral periodicity of its Ca2þ cations, which are basically identified in planes over the a– b cell planes while in the middle position (in the c
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vector) OH anions are polarized, as shown in Fig. 1c. The last precursor involves PO3 4 anions with tetrahedral configuration; these molecules are regularly distributed with the Ca2þ cations (Fig. 1d). In Fig. 2, the electrostatic potential distributions for each precursor are shown. In the calcite calculation (Fig. 2a), the direct influence produced by the Ca, C and O atoms generate multiple isosurfaces that cover the full cell regularly in spherical shapes, produced mainly because of the atomsÕ electronic distribution. In this cell analysis it is impossible to identify any way to produce a simple electrostatic carbon interchange. The electrostatic potential calculation for the calcium oxide presents, in Fig. 2b, a well defined iso-surface distribution, this configuration is found in the interstitial spaces, showing symmetric shapes conformed by the charge equilibrium between the oxygen and calcium atoms. It is clear how the instabilities can affect this configuration when extra energy is applied to the crystalline system.
Fig. 2. Electrostatic potential distribution for the calcium precursors: (a) CaCO3 in [0,0,1] and [0,1,0] orientations, (b) CaO in [0,0,1] and [0,1,1] orientations, (c) CaOH and (d) CaHPO4 in the [0,0,1] and [0,1,0] orientations.
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In case of calcium hydroxide (Fig. 2c), the isosurfaces are fixed mainly in two wave configurations with curvature defined by the Ca2þ cations mainly and just distorted in the OH anions position, these iso-potential surfaces determine a region of low charge density in the middle of the cell that shows a possible route to convert from the hydroxide to phosphate via an easier process than for any other precursor. Fig. 2d shows the electrostatic iso-potential surfaces that presents a homogeneous distribution, mainly determined by the Ca2þ cations and PO3 4 anions, which are symmetrically distributed keeping constant the corresponding distances and producing surfaces with high curvature and complicated vacuum spaces of the inter-cell sites. It is possible to identify a relation between electrostatic contribution from the PO3 4 anions over the field produced from the Ca2þ cations producing a total electrostatic potential neutralization in the unit cell. From the different precursor analysis, the calcium behavior can be well understood. However
the PO4 role in the reaction is not still clear, so then it is important to study the PO4 molecules behavior, when the Ca atoms are not present, to identify the stable configuration, charge distribution and molecular orbital conditions for one and two PO4 molecules. 3 3.2. PO3 4 –PO4 interaction
In order to understand the PO4 –PO4 interaction, a couple of calculations were made, for the 3 cases of a single PO3 4 and two PO4 anions with no influence from other atomic species. The minimum energy configuration was determined using a semi-empirical molecular optimization, which also produces the molecular orbital (HOMO and LUMO), charge density and electrostatic potential distribution as can be seen in Fig. 3a for just one PO3 4 anion. In the single PO3 4 anion analysis, the model of minimum energy configuration (MEC) is observed in Fig. 3a, where the angles and distances for the oxygen atoms generate a well-defined tetrahedral
3 Fig. 3. Quantum chemical semi-empirical calculation for (a) single PO3 4 anion molecule and (b) two PO4 anion molecules. MEC, with its frontier orbitals HOMO, LUMO, ChD and EPIS are shown for each case.
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form. Also the two frontier orbitals, HOMO and LUMO, are shown; both are regular and symmetrically distributed mainly around the oxygen atoms. The charge density distribution (ChD) and electrostatic potential iso-surfaces (EPIS) are regularly distributed with an external shell shape for the charge density graph, while the electrostatic potential is observed as a shape inverse to that of the charge distribution. It is also clear that the oxygen atoms produce the main influence. Two perpendicular orientations are shown. The two PO3 4 molecules analysis, shown in Fig. 3b, began with a random configuration where the PO3 4 molecules are at the same distances as in the CaHPO4 crystal. However, on geometry optimization, the molecules tend to reduce the distance between them, mainly between one oxygen atom of each molecule, as can be observed in the figure. The P–P distance is reduced from the original distance to the final distance of 2.34 A . 4.71 A Similarly, the influence over the HOMO and LUMO orbitals is observed in the figure, where it is also clear that the HOMO localization decreases in the oxygen atoms that are in the region between the molecules. While the LUMO density is increased in those atoms and its localization is reduced strongly in the external oxygen atoms. Finally, the electrostatic potential is shown, with strong influence from the external region atoms, and presenting a small region of influence in the middle region of the two-molecule configuration. 3.3. Hydroxylapatite as final product To study the atomic and the electron distribution influence for the final product, the hydroxylapatite crystal was analyzed with a similar method to the above cases, calculating its minimum energy unit cell and its corresponding electrostatic potential distribution. In Fig. 4a the hydroxylapatite crystal structure for the two main orientations, and also a polygon presentation is shown to aid in the identification of the atomic distribution. It is clear that the PO3 4 anions in the interstices form the tetrahedron figure and these molecules are periodically distributed with Ca2þ cations and OH anions in the
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middle spaces; the model shows how the distances remain constant. The electrostatic iso-potential are observed in the Fig. 4b for the two above directions. In this scheme, the calcium atoms present surfaces that denote how these atoms affect the interaction fixing the distances by repulsion, while the OH anions produce smaller radius iso-potential surfaces. However, the electrostatic system homogeneity shows that the system has electrostatic equilibrium in function of the atomic charge distribution. 3 Obviously the PO3 4 –PO4 interaction does not correspond to the calculated one in the last section because of the presence of the calcium atoms. So then, there are many significant differences produced by the charge compensation between the different species in the crystalline systems. 3.4. Analytical data calculation The different models were also used to calculate three of the main analytical data patterns: crystalline morphology, electron diffraction patterns, and HREM images. These electron microscopy characteristic patterns were calculated for a mapping that includes the main orientations, which were selected depending on the crystal lattice. In Fig. 5, the calculated habits are shown for the precursors and the hydroxylapatite crystals. The calcite characteristic morphology is defined as aggregates in Fig. 5a, with regular hexagon faces observed in the [0,0,1] orientation, while irregular hexagonal and rectangular faces are identified in the [0,1,0] orientation. The corresponding morphology to calcium oxide is observed in Fig. 5b, where the hexagonal and square faces are shown in the [0,0,1] and [1,1,1] orientation respectively. Hexagonal faces in the h0; 0; 1i axis determine the calcium hydroxide crystal habit whereas rectangular shapes are observed in the other faces of the Fig. 5c. The morphology corresponding to the CaHPO4 crystal (Fig. 5d) shows rectangular, irregular hexagon and rhombic faces as can be observed in the [0,0,1] and [1,1,1] orientation. The final productÕs characteristic morphology are shown in Fig. 5e, hydroxylapatite is clearly characterized by a hexagonal fiber shape that grows in
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Fig. 4. Hydroxylapatite crystal model (a) in the [0,0,1], [0,1,0] and a polygonal scheme where it is possible to identify the tetrahedron distribution, and its corresponding electrostatic iso-potential surfaces calculation (b) for the [0,0,1] and [0,1,0] orientations.
Fig. 5. Calculated crystalline habits for (a) calcite, (b) calcium oxide, (c) portlandite, (d) monetite and (e) hydroxylapatite.
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Fig. 6. HREM simulated image mapping for the calcite model with steps for each 15° and the corresponding FFT for the main orientations. The three main orientations are marked in both (a) image and (b) diffraction pattern.
the h0; 0; 1i axis direction as can be seen in figure in the corresponding [0,0,1] and [1,1,1] orientations. A full image mapping is observed for the calcite in Fig. 6a, with the corresponding FFT in Fig. 6b; generally the hexagonal periodicity is observed, even when only the [0,0,1] orientation is present 60° between reflections. It is similar to the HREM image contrast of white dots that correspond to
the atom columns are mainly produced by the Ca2þ cations, which have a much bigger scattering factor than the carbon and oxygen atoms. Fig. 7 shows the corresponding mapping of images and the FFT for the calcium oxide model, where the 90° angles in the FFT and white dot contrast are clear in the [0,0,1] orientation. Also, the irregular and regular hexagon characteristic to the [0,1,1]
Fig. 7. (a) HREM simulated image mapping for the calcium oxide model with steps for each 15° (the 35° is also included to obtain the [1,1,1] orientation) and (b) the corresponding FFTs.
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and [1,1,1] orientations respectively can be seen in the figures. The HREM image mapping and the main FFT calculations, of calcium hydroxide and CaHPO4 respectively are shown in Figs. 8 and 9. The hexagonal order for the [0,0,1] orientation and linear contrast for the orientations [0,1,0] and [1,0,0] of
the CaOH model can clearly be seen. In the case of CaHPO4 , [0,0,1] orientation shows distorted hexagons while there are multiple orientations that generates linear and zigzag like contrasts. The analysis of hydroxylapatite results is shown in the Fig. 10. The hydroxylapatite HREM mapping calculations produces for the [0,0,1] orienta-
Fig. 8. HREM simulated image mapping for the portlandite model with steps for each 15° and the corresponding FFT.
Fig. 9. HREM simulated image mapping for the monetite model with steps for each 15° and the corresponding FFT for the main orientations.
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Fig. 10. HREM simulated image mapping for the hydroxylapatite model with steps for each 15° and the corresponding FFT for the main orientations.
tion a particular contrast, with a hexagonal preference as can be seen in the FFT, while the [0,1,0] and [1,0,0] orientations can be characterized because of their special 90° periodic contrast and FFT.
3.5. Experimental HREM images Fig. 11 shows a well-defined HREM contrast characteristic of the CaCO3 crystal from the sample edges where the thickness is smaller, the
Fig. 11. HREM experimental image for a calcite sample and its calculated FFT that corresponds to a 45° rotation over the h0; 0; 1i axis.
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Fig. 12. HREM experimental image for a calcium oxide sample. A full view is observed in (a) while selected areas show small sections in (b), where several crystalline orientation are shown: [0,1,1] in I, and [0,0,1] in III, while in II and IV, rotations around 15° over the h1; 0; 0i axis and 35° over h0; 1; 0i are shown.
contrast and the corresponding FFT match directly to the theoretical calculations. While in Fig. 12, a HREM image shows the characteristic contrast for the CaO sample. In the image it is possible to distinguish the four main orientations with their corresponding FFT, which correspond to the predicted contrast for this crystal. These two figures present a crystal characterization way by HREM, which is based in the dispersion of a electron beam over the sample. Obviously, while the elements are heavier the contrast is increased, and in these cases the main atomic evidences correspond to the calcium arrays, which also denote the crystalline symmetry. The crystalline geometry is also identified from the FFT, which shows in the space of frequencies the periodicity of a particular geometry. A general view of the experimental image of the hydroxylapatite sample is observed in Fig. 13 with its corresponding FFT. Four different sections from the full image, which were processed, are
presented with their corresponding FFT to analyze local sections where the crystals show small tilts and structural changes. These changes can also be interpreted as produced by the influence of the electron beam as reported previously [11].
4. Conclusions From the analysis presented in this paper, it is identified that there are no bond change processes in this kind of reaction, and the main conditions to produce the hydroxylapatite from these precursors are electrostatic interactions. That implies a direct dependence between the calcium saturation in the system to obtain the hydroxylapatite structure. The quantum mechanics calculation and the analytical data prediction provide a basis to further analysis in the biomaterials involved in this work. Also that the experimental and theoretical contrast match clearly corroborating the exacti-
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Fig. 13. Analysis of hydroxylapatite by HREM image where it is possible to observe selected areas with their corresponding FFT that denotes small differences in the contrast and periodicity.
tude of the used models. It is clear how this Atlas of images can help to provide a full and easier characterization by means of a direct comparison between experimental and theoretical images in the different orientations.
Acknowledgements Authors are indebted to Raquel Cruz, Ignacio Sandoval, Thelma Falcon and Juan Bonifacio for their technical assistance, and particularly to Maria Eufemia Fernandez for her support in the theoretical calculations. Also we are indebted to CONACYT for grants within the project ‘‘Desarrollo de materiales cer amicos para aplicaciones biomedicas’’ 32605-U and ‘‘Coloides Cu anticos, Puntos Cu anticos y Nanopartıculas’’.
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