A Computational Tool for the Prediction of Crystalline Phases

glasses or glass ceramics, systematically sampling the ratios of the ions in different portions of the simulation box and comparing them to the stoich...
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J. Phys. Chem. B 2005, 109, 21586-21592

A Computational Tool for the Prediction of Crystalline Phases Obtained from Controlled Crystallization of Glasses Gigliola Lusvardi, Gianluca Malavasi, Ledi Menabue, M. Cristina Menziani,* Alfonso Pedone, and Ulderico Segre Department of Chemistry and SCS center, UniVersity of Modena and Reggio Emilia, Via G. Campi 183, 41100 Modena, Italy ReceiVed: August 19, 2005; In Final Form: September 20, 2005

An automatic tool (named CLUSTER) for the prediction of the most probable crystal phases that can separate from glasses has been developed. The program analyzes the output of molecular dynamics simulations of glasses or glass ceramics, systematically sampling the ratios of the ions in different portions of the simulation box and comparing them to the stoichiometric ratio of compositionally equivalent crystalline phases retrieved from a crystal structure database. The efficacy of the similarity index elaborated has been judged by comparing the results obtained with the crystal phases identified by XRD analysis after thermal treatment in a series of multicomponent potential bioactive glasses and glass ceramics for which the advantages of rational-designed erosion-controlled release is straightforward.

Introduction Crystal nucleation is a fundamental issue in the development of advanced glass ceramics for novel applications. In the field of bioactive materials, this phenomenon is particularly interesting since it can be exploited to tailor a great range of properties and of linking speed to the tissues.1 In the presence of body fluids, and depending upon the rate of ion release and resorption, bioglass and bioglass ceramics create chemical gradients which promote, early in the implantation period, the formation of a layer of biologically active bonelike apatite at the interface. Bone-producing cells, that is, osteoblasts, can preferentially proliferate on the apatite and differentiate to form new bone that bonds strongly to the implant surface.2 The decomposition and conversion rate that results in the rapid connection to the tissues is the major characteristic of these materials as well as their greater disadvantage. In fact, it determines their low mechanical properties compared to human cortical bone, limiting their use as bone restoration with loadbearing functions. However, composites with mechanical properties comparable to the properties of cortical bone can be obtained by controlled crystallization of bioactive glasses.3 An exact theory for the prediction of the specific crystalline phases that an ionic mixture could form on the basis of its chemical composition is, as of yet, not available; however, a relationship between the short-range order around the cations and the crystal nucleation tendency has been recently demonstrated for silicate glasses by means of extended X-ray absorption fine spectroscopy and 29Si MAS NMR.4,5 The main assumption advocated by the authors is that if the local structure of a glass and its isochemical crystal are similar, then only a few interfacial rearrangements will be necessary for crystal nucleation, which then can take place easily, even in the glass volume. If these rearrangements are substantial, then nucleation can only occur on the external surfaces, assisted by unsaturated * To whom correspondence should be addressed. E-mail: menziani@ unimo.it. Tel.: +39 059 2055091. Fax: +39 059 373543.

bonds and solid impurities at the surface, or in the volume, only with the aid of nucleating agents. Molecular dynamics (MD) simulations of multicomponent silicate glasses show that during cooling of the melt, ions do not rearrange homogeneously into the simulation box. Segregation zones for specific ions are observed depending on the chemical nature of the glass constituents.6,7 This behavior can be considered a generalization of the modified random network theory put forward by Greaves,8 who first realized that in silicate glasses the alkali ions are not uniformly distributed through the tetrahedral network but rather clustered inhomogeneously forming alkali-rich and silica-rich regions. On the basis of the assumption that the nucleating tendency depends on the structural similarity between the glass and its isochemical crystals,4,5 this paper aims at investigating the medium-scale organization of atoms in a molecular dynamics simulation box and predicting the most probable crystal phases that could separate from glasses. To this purpose, we have developed a program (named CLUSTER) able to identify clusters of ions in the simulation box and compare their numerical ratios with the stoichiometry ratio of compositionally equivalent crystalline solids stored in a database. The efficacy of the similarity index elaborated has been judged by comparing the results obtained with the crystal phases identified by XRD analysis after thermal treatment in this and previous works.7 Although the program has a general applicability and utility, we show here its application to a series of multicomponent potential bioactive glasses and glass ceramics for which the advantages of rationaldesigned erosion-controlled release are straightforward. Methods Glass Preparation and Characterization. We have synthesized five different batch compositions (Table 1) as reported in ref 7. The samples H, HZ20, and HP6.5 were obtained as transparent homogeneous glasses, while HP8 and SZ6 showed an opaque effect due to partial crystallization.

10.1021/jp0546857 CCC: $30.25 © 2005 American Chemical Society Published on Web 10/22/2005

Computational Tool for Predication of Crystalline Phases

J. Phys. Chem. B, Vol. 109, No. 46, 2005 21587

TABLE 1: Molar Composition of the Simulated Glasses glass

SiO2

Na2O

CaO

P2O5

H HP6.5 HP8a SZ6a HZ20

46.2 42.2 40.0 43.5 38.8

24.3 24.4 24.4 25.4 20.5

26.9 26.9 26.9 25.4 22.6

2.6 6.5 8.7

a

2.2

ZnO

5.7 15.9

Partially crystallized.

The crystallization temperature of the glass systems were identified by DSC measurements, and they were performed in air with a NETZSCH DSC 4 instrument by using ≈30 mg of sample previously finely milled to 108-125 µm particle size range; the scan rate was 10 °C/min and the temperature range 25-1400 °C. X-ray diffraction (XRD) analyses were performed on as quenched glass ceramics and after thermal treatment (2.5 h) on all glass and glass-ceramics samples with a Philips PW3710based automated diffractometer, using Ni-filtered CuKR radiation (λ ) 1.540 60 Å). The conditions for data collections were 5 < 2θ < 60° range, with a time step of 8 s and a step size 0.03°. Computational Procedure. MD simulations were performed with the DL_POLY package9 using Cerius210 as the graphical interface. The input structures of the glass compositions simulated in this work were obtained by adding randomly the appropriate number (2800-3000 atoms) and type of atoms into a simulation box with ∼35 Å edge length. Several tests were carried out by varying the dimensionality of the systems studied; the number of atoms finally chosen represents a good compromise between the agreement of the results obtained with the experimental data and the computational effort. The starting volume of the system was increased up to 30% to account for the estimated thermal expansion coefficient and then scaled to reproduce the experimental density (H, 2.719 g/cm3; HP6.5, 2.687 g/cm3; HP8, 2.772 g/cm3; SZ6, 2.880 g/cm3, HZ20, 3.075 g/cm3; mean error, (0.002 g/cm3) at the final simulation temperature during the quenching procedure. The initial structures were melted at 12 000 K to remove possible memory effects and then cooled sequentially to 10 000, 8000, 6000, 3000, 1500, and finally to 300 K, using a quench rate of 4 × 1013 K/s. At each temperature, a 20 000 time steps relaxation was allowed at a time step of 2 fs. The velocity was scaled at every time step during the first 6000 of these 20 000 time steps. Velocity scaling every 40 time steps was performed during the second 6000 time steps, and finally, during the last 8000 time steps, no velocity scaling was applied. The canonical ensemble NVT (Evans thermostat) was used. Data collections were performed every 50 time steps during the last 10 000 of 35 000 time steps using the microcanonical ensemble NVE. As usual, in the Born model, the ions were treated as point charges (whose values in this work correspond to their formal oxidation state charge), with short-range forces acting between them. The short-range interactions between cation-anion and anion-anion were modeled by a Buckingham potential

Uij(rij) ) Aij exp(-rij/Fij) - Cij/rij

6

(1)

where Uij(rij) is the short-range potential energy between pairs with a separation of rij. The parameters Aij, Cij, and Fij are listed in Table 2. To account for the covalency of the P-O and Si-O bonds, we have used the three-body screened harmonic

TABLE 2: Empirical Parameters Used in the Buckingham Potential eq 1 interacting pair

Aij (eV)

Cij (eVA-6)

Fij (Å)

ref

Si-O P-O Zn-O Ca-O Na-O O-O

1036.9 1273.4 700.3 1228.9 1226.8 3116130.6

0 0 0 0 0 61.3916

0.3259 0.3227 0.3372 0.3118 0.3060 0.1515

11 12 13 11 11 11

TABLE 3: Empirical Parameters Used in the Screened Harmonic Potential eq 2 O-Si-O O-P-O

kjik (eV)

θ0 (deg)

F1 (Å)

F2 (Å)

ref

0.1444703 0.652436

109.47 109.47

2.0 2.0

2.0 2.0

12 12

function described by Sauer12

Φij(θijk) )

kjik (θ - θ0)2 exp[- (rij/F1 + rik/F1)] 2 jik

(2)

Table 3 lists the parameters used. The long-range electrostatic potential was evaluated by the Ewald summation method with the cutoff distance set at 13.0 Å and precision set to 10-6. The short-range cutoff distance was set at 7.6 Å. Outline of the CLUSTER Algorithm. Our aim is to check whether clusters of ions with numerical ratios close to the stoichiometric ratio of known isochemical crystal phases can be localized into the simulation box. The program performs the following steps: 1. The crystal phase (A) is chosen from the Inorganic Crystal Structure Database,14 and its stoichiometric ratios are stored in a reference vector, ordering the ions forming the glass arbitrarily. Let us consider, for instance, a phosphosilicate glass composed by Si, P, Na, Ca, and O ions. We order the ion symbols in the sequence [Na, Ca, P, O, Si], and we want to check whether some clusters in the sample have an ionic ratio similar to the stoichiometry of the β-NaCaPO4 crystal phase. In this case, the reference vector is

[]

1 1 RA ) 1 4 0

The vector RA is the constraint for the stoichiometric coefficients. 2. The simulation box is mapped by a sphere of variable r, with the maximum value of r corresponding approximately to 1/ of the edge of the box. The program computes the ratios of 4 the ions lying inside the sphere and stores the minima “stoichiometry coefficients” of the cluster in vector χ having the same dimensions as RA. As an example let us consider a cluster cointaining 3 Na, 3 Ca, 4 P, and 13 O ions. In this case, vector χA with the minima “stoichiometry coefficients” is

[]

1 1 χA ) 1.33 4.33 0

The components of χA are functions of the radius r. The probing sphere must move smoothly in the sampled space, therefore,

∆(r) r (Å) β-NaCaPO4 Na3PO4 Ca3(PO4)2 NaPO3 Ca(PO3)2 Na4P2O7 Ca2P2O7 Na2Ca4(PO4)2SiO4 Na2CaSi2O6 Na2.2Ca1.9Si3O9 Na2Ca2Si3O9 Na2CaSi5O12 Na2Ca3Si6O16 Na2Ca3Si3O10 CaSiO3 Ca2SiO4 Na2SiO3 Na4SiO4 H

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 ∆ h (r)

0.50 0.33 0.50 1.00 1.13 1.33 1.47 1.68 1.64 1.68 1.12

0.40 0.50 0.86 1.06 1.33 1.70 1.95 2.04 2.31 2.38 1.45

1.00 2.09 3.12 4.20 4.48 5.00 5.00 5.38 5.88 6.10 4.22

0.50 1.00 1.20 1.48 1.67 1.63 1.63 1.80 1.80 1.92 1.46

0.75 1.50 3.14 3.46 3.71 3.57 3.88 4.07 4.31 4.52 3.29

0.80 1.50 1.27 2.05 3.20 3.73 4.06 4.34 4.99 5.14 3.11

1.08 1.45 3.12 3.39 3.55 4.18 4.44 4.40 4.77 4.97 3.54

1.00 1.00 0.88 1.91 2.74 3.30 3.57 3.71 4.31 4.65 2.71

0 0 0.22 0 0 0 0.02 0 0 0.02 0.08

0.30 0.30 0.30 0.24 0.17 0.23 0.26 0 0 0.28 0.21

0 0 0 0.22 0.25 0.31 0.15 0.24 0.25 0.28 0.17

0.80 0 0.47 0.91 0.67 1.12 1.11 1.61 1.84 2.50 1.10

1.00 0.81 0.89 1.00 0.87 0.70 0.68 1.19 1.00 1.65 0.98

0.86 0 0.35 0.35 0.30 0.43 0.44 0.45 0.44 0.52 0.42

0.20 0 0.25 0.32 0.30 0.50 0.56 0.58 0.67 0.72 0.41

0 0.20 0.25 1.00 1.12 1.20 1.49 1.41 1.79 1.68 1.01

0 0.20 0.14 0.28 0.38 0.79 0.81 0.85 0.81 0.92 0.52

0 0.55 1.29 0.87 1.67 2.29 2.50 2.59 2.66 2.76 1.72

HP6.5 3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 ∆ h (r)

0 0.23 0.29 0.39 0.57 0.55 0.72 0.87 0.94 1.09 0.57

0 0.40 0.29 0.44 1.08 1.70 2.08 2.28 2.29 2.43 1.30

0 0.60 1.00 1.48 2.63 3.48 3.81 4.73 4.77 5.17 2.77

0.33 0.50 0.60 0.95 1.04 1.22 1.27 1.26 1.37 1.42 1.00

0.33 1.46 1.67 2.04 2.41 2.67 2.65 3.26 3.31 3.50 2.33

0 1.10 2.00 2.65 2.30 3.03 3.72 3.89 3.94 4.43 2.71

0.78 1.08 1.66 1.67 2.25 2.83 3.27 3.77 3.91 4.15 2.54

1.00 0 0.33 0.71 1.43 1.21 1.75 2.60 2.65 3.26 1.49

0 0 0.20 0.14 0. 0.23 0.20 0.24 0.24 0.31 0.16

0.11 0.30 0.45 0.24 0.42 0.15 0.48 0.39 0.48 0.47 0.34

0 0 0.36 0.22 0.33 0.25 0.39 0.41 0.70 0.64 0.33

0.80 0 0.59 0.46 0.50 0.77 0.79 1.35 2.31 2.12 0.97

1.00 1.00 1.00 0.56 0.50 1.40 1.55 1.50 2.16 2.44 1.31

0.86 0 0.67 0 0.85 1.25 1.08 1.02 0.96 1.22 0.79

0.29 0 0.33 0.36 0.62 0.89 0.91 0.97 1.07 1.12 0.66

0.33 0.33 1.00 0.80 1.43 1.68 1.68 1.81 1.92 2.09 1.31

0.29 0.25 0.38 0.43 0.46 0.42 0.73 1.00 1.12 1.24 0.63

0 1.00 1.00 1.50 2.28 2.00 2.49 2.57 2.75 2.81 1.84

HP8

0.43 0 0.25 0.52 0.43 0.46 0.63 0.65 0.89 1.13 0.54

0 0.67 0.75 1.27 1.60 1.95 2.18 2.76 2.86 3.13 1.72

1.00 1.31 1.70 2.09 2.68 3.00 3.62 3.50 4.10 4.52 2.75

0.29 0.38 0.64 0.63 1.03 0.98 1.08 1.26 1.32 1.42 0.90

0.75 1.00 1.88 1.78 1.94 2.14 2.56 2.94 3.07 3.22 2.13

0 0.80 1.06 1.23 1.80 2.41 2.82 3.83 4.00 4.48 2.24

1.16 0.82 1.65 1.52 2.00 2.25 2.79 2.69 3.21 3.58 2.17

1.00 0 1.00 1.08 0.82 1.29 1.37 1.85 1.75 2.72 1.29

0.33 0 0.20 0.14 0.40 0.33 0.32 0.25 0.46 0.66 0.31

0.30 0.30 0.30 0.42 0.67 0.85 0.72 0.90 1.14 0.96 0.66

0 0 0 0.44 0.68 0.75 0.75 1.03 1.18 1.25 0.61

0.79 0 0.59 0.76 0.58 1.12 1.00 1.85 2.48 2.73 1.19

1.00 0.82 0.73 1.00 1.86 2.16 1.72 2.19 3.37 3.83 1.87

0.85 0 0.67 0.42 0.90 1.05 1.29 1.58 1.75 1.84 1.04

0.33 0.38 0.29 0.60 0.70 0.91 1.04 1.05 1.26 1.35 0.79

0.33 0.33 1.00 1.17 1.55 1.54 1.90 1.98 2.21 2.20 1.42

0.28 0 0.14 0.40 0.60 0.83 1.12 1.19 1.08 1.34 0.70

0 0 1.57 1.88 2.11 2.67 2.81 2.81 3.05 3.08 2.00

3.5 4.0 4.5 5.0 5.5 6.0 6.5 7.0 7.5 8.0 ∆ h (r)

21588 J. Phys. Chem. B, Vol. 109, No. 46, 2005

TABLE 4: Clusters Analysis of the H, HP6.5, and HP8 Glasses and Glass Ceramic

TABLE 5: Clusters Analysis of the SZ6 Glass Ceramic and HZ20 Glass

∆ h (r)a

Na2ZnSiO4

Na4Zn2Si3O10

Zn2SiO4

CaZn2Si2O7

Zn2(PO4)3

Zn(PO3)2

Na2CaSi2O6

Na2Ca2Si3O9

Na2Ca3Si5O12

Na2Ca3Si6O16

Na2Ca3Si3O10

CaSiO3

Ca2SiO4

Na2SiO3

Na4SiO4

0.80 0.88

1.65 0.64

2.87 1.77

2.63 1.43

5.40

3.72

0.11 0.29

0.32 0.44

1.81 1.77

1.57 1.73

0.56 0.68

0.57 0.57

1.31 1.17

0.45 0.56

1.56 1.56

a∆ h (r) is the average of the dissimilarity index ∆(r) over 10 values of the radius of the sphere analyzed. It represents the distance between the ionic ratios in the cluster recognized by the program and the stoichiometric ratio of the isochemical crystal phase.

Lusvardi et al.

SZ6 HZ20

∆ h (r)a

Computational Tool for Predication of Crystalline Phases

J. Phys. Chem. B, Vol. 109, No. 46, 2005 21589

the center of the sphere is located on the oxygen ions which are distributed more homogeneously than the other atoms. 3. If the cluster has the same composition of the A phase, then the two vectors χA(r) and RA are equal and the angle between them is zero. We have chosen the Hamming distance ∆(r) between the components of the two vectors as a measure of the deviation of the cluster composition from the A phase n

∆(r) )

|χjA - RjA| ∑ j)1

(3)

where n represents the order of the vectors. The value of the Hamming distance15 is calculated for the spheres with radius r centered on all oxygen ions, and the sphere with the minimum ∆(r) value is chosen. This is the cluster whose ionic ratio is closest to the stoichiometric ratio of the crystal phase A. ∆(r) defines the distance or dissimilarity between the ionic ratio in the cluster and in the crystal phase and ranges from 0 to ∞; for ∆(r) ) 0, the exact stoichiometry of the A crystal phase is found. 4. The value of the radius r is changed, and the computation is performed again. Obviously, χA(r) will tend to the stoichiometric ratio of the glass when r tends to the half-box length. 5. The final result is a list of the minimum ∆A(r) values for each A crystal phases chosen from the database. Criteria for Crystal Phase Selection. In principle, all the crystalline phases stored in the database constituted by ions present in the glasses and glass ceramics of interest could be checked for evaluating the similarity with the clusters identified by the program. In practice, we have selected a subset of crystals according to the following criteria: (a) the ion coordination number is the same in the crystal phase and in the glass, and (b) the presence of MO4-n isolated units, M2O7-n dimers, MO3-n-based rings, or linear polymers, which ensure the maximum coverage of the known crystal phases’ space. Results and Discussion MD simulations have been carried out for the reference glass7 Bioglass (45S5, named H hereafter), two glasses (HZ207 and HP6.5), and two glass ceramic (HP87 and SZ6) synthesized and characterized in our laboratory in the context of a wider study aimed at highlighting the determinants for bioactivity. Their molar compositions are reported in Table 1. The analysis of the medium-scale structural evolution of the multicomponent glasses and glass ceramics simulated by means of MD revealed a clear tendency of the constituting cations to segregate in the network giving origin to zones of different scales enriched in specific species.6,7 The low concentration of P in the H glass allows the random dissemination of isolated monophosphate (Q0)16 units in the silicon network, in agreement with 31P MAS NMR findings.7 Islets characterized by the presence of P, Na, and Ca are progressively formed in the HP6.5 and HP8 simulated systems by increasing the concentration of P. Zinc in the HZ20 glass promotes the participation of P to the glass network by forming a highly ramified backbone of interconnected Si-Zn-P tetrahedra, with an average value of the phosphorus Qn species of 1.78.7 Segregation zones for the Ca ions are observed in close proximity to Si and P, whereas Na is almost uniformly distributed. Finally, pairs of cornersharing ZnO4 tetrahedra are formed giving rise to zinc-rich regions, where long strips of [(ZnO4)n-(SiO4)N]m tetrahedra surrounded by Na ions are found. Although to a lower extent, this phenomenon can be observed also in the SZ6 glass ceramics.

It has been proposed4,5 that for glasses which nucleate in the volume, the local structure of network-forming and modifier cations is similar to the short-range order in the corresponding isochemical crystal phases. In this perspective, the phenomenon of microsegregation in multicomponent glasses can be considered a preorganization step of crystal nucleation. To support the structural picture derived by the visual analysis of the simulated glasses and give a quantitative description of the phenomenon, we developed an algorithm capable of systematically sampling the ratios of the ions in different portions of the simulation box and comparing them to the stoichiometric ratio of isocompositional crystalline phases retrieved from the Inorganic Crystal Structure Database (ICSD), NIST.14 Among all the possible crystal phases containing some or all of the glass constituents, we have restricted the comparison to those which satisfied the criteria enounced in the previous paragraph. The data values of the distance (dissimilarity index) ∆(r) between the ionic ratios in the cluster recognized by the program and the stoichiometric ratio of the isochemical crystal phase are listed in Table 4 for the H and HP6.5 glasses and HP8 glass ceramic. The value of ∆(r) ranges from 0 to ∞, and for ∆(r) ) 0, the exact stoichiometry of the crystal phase is found in the cluster. The ∆ h (r)data values, which represent the average of ∆(r) over the 10 values of the radius of the sphere analyzed, are listed in the last row to facilitate the comparison. For the zinc-containing glass and glass ceramic (HZ20 and SZ6), only the ∆ h (r) data values are listed in Table 5 for brevity (see Supporting Information for the complete set of data). The CLUSTER algorithm clearly recognizes zones in the simulation box of the H glass (Table 4) in which the ratios among the ions are very close to those found in the Na2CaSi2O6, Na2Ca2Si3O9, and Na2.2Ca1.9Si3O19 crystal phases. In fact, in these cases, the ∆ h (r) score shows the lowest value (0.08, 0.17, and 0.21, respectively) among all the silicate phases analyzed. The Na and Ca cations are found almost uniformly disseminated in the glass, therefore, binary silicate phases are less probable. Moreover, since the stoichiometric ratio of the Na, Ca, and Si ions in the Na2CaSi2O6 crystal is the most similar to the ionic ratio in the glass (Table 1), this is the most favored phase whatever cluster radius is chosen. Among the orthophosphate phases analyzed, by increasing the P content in the H, HP6.5, HP8 series, the program identifies β-NaCaPO4 as the most probable phase that segregates in the P-enriched glasses. Besides showing the lowest ∆ h (r) value, this phase is characterized by a significant decrement of the ∆ h (r) values in HP6.5 and HP8 with respect to H (Table 4). Visual analysis of the clusters found by the program reveals P-rich islets containing five to seven orthophosphate unities at r ) 5.0 Å of the HP6.5 glass and r ) 6.0 Å of the HP8 glass, respectively, as shown in Figure 1a. The ions are arranged in strips of isolated PO4 units which share Na ions among faces; Ca ions coronate the strips. Although disordered, this spatial arrangement is reminiscent of the mutual ion positions into the β-NaCaPO4 crystalline phase (Figure 1b), which is formed by a strip of alternating Na atoms and discrete [PO4] tetrahedra and one made up of Ca atoms. The results obtained for the Zn-containing SZ6 glass (Table 5) reveal an inhomogeneous distribution of the Ca ions, which are segregated in silica-rich regions. In fact, clusters with an ionic ratio similar to the stoichiometric ratio of Na2ZnSiO4 are found as the most probable among the zinc-silicate phases considered, and Na2CaSi2O6 is the favorite zinc-free phase. Similarly, in the five-component HZ20 glass, the CLUSTER program highlights wide zones in which only Na, Si, and Zn ions are found. In these zones, of a radius up to 5.5 Å, the ionic

21590 J. Phys. Chem. B, Vol. 109, No. 46, 2005

Lusvardi et al.

Figure 1. (a) Snapshot of a cluster of Na, Ca, P, and O found in the HP8 simulated glass: blue spheres represent Ca ions and cyan ones Na and purple tetrahedra represent [PO4] units. (b) Rearrangement of ions into the β-NaCaPO4 crystal phase.

ratio is almost identical to the stoichiometry of the Na4Zn2Si3O10 phase that is therefore indicated as the most probable among the zinc-containing silicate phases. The structure of Na4Zn2Si3O10, not yet determined, is described in the literature17 as a β-cristobalite type structure where the 3D network is built by alternate SiO4 and ZnO4 tetrahedra with a Si/Zn ratio of 3:2. A similar network is observed in the simulated glass, as shown in Figure 2. Five- to seven-membered rings with a Si/Zn ratio close to 1.5, as in the Na4Zn2Si3O10 crystal, are formed. The rings are surrounded mainly by Na ions acting as a charge compensator. A good test for the validation of the results obtained by the CLUSTER program consists of the comparison with the crystal phases identified by XRD analysis of the glasses and glass ceramic after thermal treatment. These are reported in Table 6. In general, a very satisfactory agreement between the theoretical and experimental data is achieved. In fact, ternary sodiumcalcium-silicates such as Na2CaSi2O6, Na4.4Ca2.8Si6O18, and Na4Ca4Si6O18 are identified as forming the main phase in the XRD patterns of H and HP6.5 after 2.5 h of thermal treatment. The 3D structure of these crystal phases are very similar, all being part of the solid solution, Na6-2xCa3+xSi6O18; the main differences are in the occupancy of the Na and Ca ion sites. β-NaCaPO4 is also identified in the HP6.5 after 2.5 h, whereas it has been detected in the as-quenched HP8. The presence of ZnO in the HZ20 glass leads to the formation of Na4Zn2Si3O10 as the main crystal phase after 2.5 h of thermal treatment; other

TABLE 6: Crystal Phases, Relative Intensities (I/I0), and Counts of the Principal Peaks Identified by XRD Analysis of the Glasses glass H HP6.5 HP8b HZ20 SZ6b

crystal phases Na2CaSi2O6a Na2CaSi2O6a β-NaCaPO4 β-NaCaPO4 Na2CaSi2O6 Na4Zn2Si3O10 Na2CaSi2O6 Zn2SiO4 Na2ZnSiO4 Na4Zn2Si3O10 Na2CaSi2O6

no thermal treatments I/I0 % counts

100

3174

100

1245

2.5 h I/I0 % counts 100 100 65 100c 72c 100 14 7 70

5013 4200 2820 8046c 5788c 9643 1369 625 2800

100

4000

a

Quantitave XRD analysis (Rietweld-R.I.R. method) shows a small percent of Na4.4Ca2.8Si6O18 (x ) 0.8) and Na4Ca4Si6O18 (x ) 1). The ratios among the phases (in mass %) Na2CaSi2O6/Na4.4Ca2.8Si6O18/ Na4Ca4Si6O18 are 4:1:0.3 and 2.5:1:0 for H and HP6.5, respectively. b Glass partially crystallized. c Five hour thermal treatment.

minor phases found were Na2CaSi2O6, and Zn2SiO4. The material obtained by quenching the SZ6 melted glass presents the signals characteristic of the crystal phases Na2ZnSiO4 and Na4Zn2Si3O10; after 2.5 h of thermal treatment, Na2CaSi2O6 was also found. Moreover, a further argument in support of the hypothesis that the homogeneous nucleation tendency depends on the

Computational Tool for Predication of Crystalline Phases

J. Phys. Chem. B, Vol. 109, No. 46, 2005 21591 TABLE 8. Bond Distances, Bond Angles, and Coordination Number (CN) of the Crystal Phases Identified by XRD Analysis of the Glasses Na2ZnSiO4 β-NaCaPO4 Na2CaSi2O6 Na4Zn2Si3O10 (ref 18) (ref 19) (ref 17)

Zn2SiO4 (ref 20)

bond length (Å) Si-O SiBO SiNBO P-O PNBO Zn-O Ca-O Na-O

SiBO(Zn) 1.60-1.64

1.63-1.64

1.93-1.97

1.95

1.63 1.59 1.54 1.48-1.61 2.47 2.54

2.59-2.72 2.35-2.47

2.29-2.99

bond angle (deg) O-Si-O

108.8-113

BO-Si-BO BO-Si-NBO NBO-Si-NBO BO-P-BO 109.4 O-Zn-O

Figure 2. Cluster found in the HZ20 glass whose ionic ratio is similar to the Na4Zn2Si3O10 stoichiometry: yellow tetrahedra represent [SiO4], light blue tetrahedral [ZnO4], and cyan balls Na ions.

TABLE 7: Bond Distances, Bond Angles, and Coordination Numbers (CN) of the Simulated Glasses (the width at half-maximum of the bond angle distribution is reported in parentheses) H Si-O Si-BO Si-NBO P-O PNBO Zn-O Ca-O Na-O

1.58 1.63 1.52 1.51 1.49

O-Si-O BO-Si-BO BO-Si-NBO NBO-Si-NBO O-P-O O-Zn-O BO-Zn-BO Si-O-Si Si-O-Zn Zn-O-Zn

109 (14) 106 (13) 108 (13) 112 (16) 109 (13)

2.25 2.46

HP6.5

HP8

bond length (Å) 1.58 1.58 1.62 1.63 1.53 1.53 1.51 1.51 1.50 1.50 2.27 2.45

2.26 2.47

bond angle (deg) 109 (15) 109 (15) 105 (13) 106 (16) 109 (14) 109 (16) 112 (16) 112 (14) 109 (13) 109 (13)

154 (33)

154 (33)

154 (35)

4.0 4.0

4.0 4.0

4.0 4.0

5.0 7.4

5.0 7.4

5.1 7.7

HZ20 1.57 1.59 1.54 1.51 1.50 1.93 2.24 2.46 109 (14) 108 (11) 109 (12) 111 (12) 109 (14) 104 (30) 103 (25) 154 (35) 130 (31) 89, 106

SZ6 1.57 1.62 1.55 1.93 2.27 2.49 109 (21) 105 (21) 108 (20) 110 (20) 101 (39) 101 (40) 150 (39) 132 (51) 95 (60)

CN Si P Zn Ca Na

4.0 4.0 4.0 4.9 7.5

4.0 4.1 5.5 8.1

structural similarity between the parent glass and the phases crystallized from such glass4,5 is given by the comparison of the structural parameters obtained from the simulated multicomponent glasses and the crystal phases found after thermal treatment (Tables 7-8). In general, the local environment of the ion in the clusters found in the glasses is in good agreement with the experimental values of the crystals phases that separate from these glasses, with the main differences being observed in the wide distribution of the O-Si-O angle in the simulated glasses and the Ca-O and Na-O distances.

BO-Zn-BO Si-O-Si Si-O-Zn Zn-O-Zn Si P Zn Ca Na

109 (106-111)

109.4 111.7 119.2 106.6 (103-110) 106.7-112.9 159.2 127.0-129.0 117.6-132.6 109.7-112.3 CN 4.0

4.0

4.0

4.0

4.0

4.0 5.3 7.7

5.0 6.5

6.0

Conclusions The results obtained by analyzing the molecular simulations trajectories of several potential bioglasses and glass ceramics by means of the CLUSTER program show that the tool developed is able to highlight the main feature of the nucleation process encoded in the simulate glasses. The chemical composition, the content of the crystals, and the morphology of the glass ceramics are the important factors that determine the properties of the materials. Therefore, the prediction of the most probable crystal phases that can separate from a glass on the basis of their medium-range structure similarity has outstanding consequences for the engineering of new composite materials with improved mechanical and biological properties with respect to the parent glass. A particularly interesting task will be to challenge the program’s performances in tailoring rationally the separation of crystal phases at a high bioactive index, the dissolution rates and cellular reactions, and the release of optimal concentrations of dopant with important effect on health and diseases. Notwithstanding, this program constitutes a fast automatic tool for the prediction of the most probable crystal phases that could separate from glasses; in particular, a few aspects have to be considered carefully: (a) the size of the simulation box should be chosen in relation to the molar composition of the glasses. In fact, no appreciable segregation of a minor glass component is observed in boxes containing 1000 to 1500 ions; segregation becomes apparent by analyzing the trajectories obtained on bigger boxes due to improvement in their statistical distribution. Moreover, larger samples discourage artificial crystal nucleation induced by the application of a cubic periodic boundary condition.21 (b) The cooling rate typically used in the

21592 J. Phys. Chem. B, Vol. 109, No. 46, 2005 simulations is many orders of magnitude larger than the one used in laboratory, thus it might favor the formation of metastable crystal phases not observed experimentally. This does not seem to happen in this work, since the annealing procedure has been optimized to reproduce several experimental data.6,7 (c) Finally, it has to be taken into account that misleading results could be obtained when the optimum sphere lies in a zone of the boundary between two segregation zones. Therefore, a graphical visualization of the clusters found is always necessary for checking the resemblance of the ion arrangements with the crystal symmetry. The code is available on request from the authors ([email protected]), at the web site of the CCP5 Program Library (http://www.ccp5.ac.uk/librar.shtml) and through the DL_POLY distribution. Acknowledgment. This work was supported by Ministero dell’Istruzione, Universita`’ e Ricerca (MIUR, Grant 2003032158_005). Supporting Information Available: Table A: Clusters analysis of SZ6 glass ceramic. The dissimilarity index ∆(r) represents the distance between the ionic ratios in the cluster recognized by the program and the stoichiometric ratio of the isochemical crystal phase. The value of ∆(r) ranges from 0 to ∞, and for ∆(r) ) 0, the exact stoichiometry of the crystal phase is found in the cluster. ∆ h (r) is the average of ∆(r) over 10 values of the radius of the sphere analyzed. Table B: Clusters analysis of HZ20 glass. The dissimilarity index ∆(r) represents the distance between the ionic ratios in the cluster recognized by the program and the stoichiometric ratio of the isochemical crystal phase. The value of ∆(r) ranges from 0 to ∞, and for ∆(r) ) 0, the exact stoichiometry of the crystal phase is found in the cluster. ∆ h (r) is the average of ∆(r) over 10 values of the

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