J. Phys. Chem. C 2008, 112, 10681–10687
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Structural and Energetic Analysis of MgxM1-x(OH)2 (M ) Zn, Cu or Ca) Brucite-Like Compounds by DFT Calculations Deyse G. Costa,† Alexandre B. Rocha,‡ Wladmir F. Souza,§ Sandra Shirley X. Chiaro,§ and Alexandre A. Leita˜o*,†,| Departamento de Quı´mica, UniVersidade Federal de Juiz de Fora, Campus UniVersita´rio, Juiz de Fora 36036-330 MG, Brazil, Instituto de Quı´mica, UniVersidade Federal do Rio de Janeiro, Ilha do Funda˜o, Rio de Janeiro, 21941-909, RJ, Brazil, PETROBRAS-CENPES, Ilha do Funda˜o, Rio de Janeiro, 21941-915 RJ, Brazil, DiVisa˜o de Metrologia de Materiais, Instituto Nacional de Metrologia, Normalizac¸a˜o e Qualidade Industrial, AV. Nossa Senhora das Grac¸as, 50, Xere´m, Duque de Caxias 25250-020, RJ, Brazil ReceiVed: February 25, 2008; ReVised Manuscript ReceiVed: April 29, 2008
Brucite-like mixed hydroxides of the general formula MgxM1-x(OH)2 for M ) Zn, Cu or Ca were studied by density functional theory within pseudopotential approximation, plane waves basis set, and periodic boundary conditions. Geometrical parameters and energy analysis were done for different compositions (different values of x in the previous formula). It is shown that substitution of magnesium by zinc and copper leads to stable species in several proportions, whereas a mixed hydroxide containing Mg2+ and Ca2+ is predicted not to be formed, at least in the range of molar ratio we have studied here; that is, 1/4-3/4. The species formed by copper substitution are paramagnetic and present Jahn-Teller distortion in the unit cell. Introduction Brucite, which is the mineral form of magnesium hydroxide, is a commonly occurring material. It presents a layered structure, in which magnesium cations are octahedrally coordinated to hydroxyl groups.1 The structure is shown in Figure 1, and its space group is P3jm1. Brucite is a precursor of two classes of technologically relevant materials, known as layered doubled hydroxides (LDH) and hydroxy double salts (HDS). LDHs can be formally obtained by substitution of the Mg2+ cation present in the brucite structure by a trivalent cation, resulting in a positively charged brucite-like layered compound. The charge compensation is achieved by the presence of an anion lying in the space between the layers. They have the general formula [M1-x2+Mex3+(OH)2]x+Ax/mm- · zH2O, where Am- represents the anion, and M2+ and Me3+ stand for the di- and trivalent cation, respectively. As the previous formula indicates, there are some water molecules accompanying the anions in the interlayer space. A naturally occurring example of LDH is hydrotalcite, whose constituents are Mg2+, Al3+, and CO32-. Hydroxy double salts have a structure similar to LDH. The main difference is that they present two kinds of divalent cations, which will be represented by M2+ and Me2+. Their general formula is [(M1-x2+Me1+x2+)(OH)3(1-y)]+A(1+3y)/nn- · zH2O. The presence of anions in this case is to compensate positive charge in the layer, which has its origin in the loss of a negative hydroxyl group. The common point among LDH and HDS structures is the presence of brucite-like layers intercalated by an essentially disordered layer containing the anions and water.2 As we have already mentioned, these materials have considerable technological importance. They are, for example, vastly used as catalysts or catalysts support due to their great surface area. Calcination of a LDH or HDS can lead to oxyhydroxide * Corresponding author. E-mail:
[email protected]. † Universidade Federal de Juiz de Fora. ‡ Universidade Federal do Rio de Janeiro. § PETROBRAS-CENPES. | Instituto Nacional de Metrologia.
or a double oxide, with a large surface area and a great number of basic sites.3 In the present work, we carried out a systematic investigation, based on density functional theory (DFT), of structure and stability of brucite and brucite-like compounds, obtained by isomorphic substitution of Mg2+ in the brucite structure by Cu2+, Ca2+, or Zn2+. The resulting compounds can be viewed as a HDS that has not lost a hydroxyl group, so there is no need for the presence of the compensating-charge anion. Information gained here is important not only to attest the possible formation of the brucite-like hydroxides but also to put a step forward into the knowledge of LDH and HDS compounds. Figure 2 shows examples of intralayer and interlayer admixtures in the brucite-like structures investigated. By “intralayer admixture”, we mean that there are two kinds of cation in the same layer, as can be seen in Figure 2A, whereas “interlayer admixture” means that there is just one kind of cation per layer (Figure 2B). Brucite has been studied by the periodic Hartree-Fock (HF) method by D’Arco et al. to investigate the interlayer interaction.4 Baranek et al. have calculated structural and vibrational properties of brucite and portlandite, Ca(OH)2, at different levels; that is, HF and DFT with different descriptions of exchange and correlation energy.5 Finally, the vibrational spectrum of Mg(OH)2 was also studied by Pascale et al. at different levels (HF, DFT/LDA, DFT/GGA, and DFT/hybrid).6 The latter work presents an estimation of anharmonic effects on OH modes. We present in this paper discussions about the composition and configurational structure for mixed brucite-like compounds based on calculated formation energies and geometry optimizations. Description of Used Supercells To investigate the composition effect on MgxM1-x(OH)2 (M ) Ca, Cu, or Zn) brucite-like compounds, we built 14 supercells, shown in Table 1 and Figure 3. Their total energies and structures are compared to the pure brucite-like structures of Mg(OH)2, Ca(OH)2, Cu(OH)2, and Zn(OH)2.
10.1021/jp8016453 CCC: $40.75 2008 American Chemical Society Published on Web 06/28/2008
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Figure 1. Two views of brucite fragments. A is the (1000) view, and B is the (0001) view.
With this procedure, the layered structure was forced for the Cu(OH)2 and Zn(OH)2.
Figure 2. Examples of admixtures in brucite type compounds. A is an intralayer mixture, and B is an interlayer mixture.
TABLE 1: Mg Molar Ratio and Shape of Model Super Cellsa supercell Or Tr H1 H2 H3 H4 H5 H6 H7 H8 H9 H10 H11 H12 a
Mg molar ratio
supercell shape
1/2 1/2 1/4 1/4 1/3 1/3 1/2 1/2 1/2 1/2 2/3 2/3 3/4 3/4
orthorrombic triclinic 2×2×1 4×1×1 3 × 3 × 1 1×1×3 2×1×2 2×2×1 4×1×1 1×1×2 3 × 3 × 1 1×1×3 2×2×1 4×1×1
Labels refer to structures in Figure 3.
The calculations of total energy and geometry optimizations, including a and c lattice parameters, for pure hydroxides brucite, portlandite, Cu(OH)2, and Zn(OH)2 were done by using primitive cells containing only five atoms (brucite structure discussed below). The cell shapes were optimized but, only for these fiveatoms unit cells, the symmetry group was constrained to P3jm1.
There was a sequence of ideas to choose supercells. Considering the brucite-like morphology, the cell constant a (or a and b for lower symmetries) is related to intralayer bond structure, and any growth or atomic modification on these directions would result in some changes in the layer. These changes are probably much more important than interlayer modification, since interlayer interaction is weak. Previous calculations using the Hartree-Fock method predict that this energy is ∼1.2 kcal/mol.4 Before going on the mixture calculations, we did calculations on pure hydroxides to verify whether the weak interlayer interaction hypothesis is confirmed. The interlayer interaction energy was determined by increasing the c lattice parameter of hexagonal brucite and brucite-like compounds up to reach the asymptotic limit for the total energy difference. The weak interaction hypothesis was confirmed, and for that reason, we selected more unit cells representing the intralayer mixtures than cells for interlayer configurations, since the former are expected to be more important. Supercells were adopted to reach a more comprehensive description of the admixtures. The brucite original structure was the base of the construction of the supercells. This cell corresponds to our optimized DFT-GGA structure, whose cell parameters are a ) 3.171 Å, c ) 4.815 Å, R ) β ) 90°, γ ) 120°, with five atoms in the following reduced positions: Mg 0, 0, 0; O 1/3, 2/3, 0.2154; H 1/3, 2/3, 0.4151; O 2/3, 1/3, -0.2154; H 2/3, 1/3, -0.4151. The supercells Or and Tr kept the brucite morphology but the arrangements of the vectors are more complex. The cell named Or (orthorrombic) has angles R ) β ) γ ) 90° and the lattice parameters a ) 3.224 Å, b ) 4.773 Å, and c ) 5.585 Å. The a, b, and c vectors are parallel to y, x, and z, respectively. The cell Tr (triclinic) has the lattice parameters a ) b ) c ) 5.760 Å and the angles R ) 147.5°, β ) 122.0°, γ ) 68.1°. The other supercells were built from a × a × c hexagonal brucite original cell, multiplying the lattice parameters by p, q, and r, respectively. Table 1 shows these supercells named H1 to H12 using p × q × r as notation for supercells according to the multiplication of the vectors from the original cell. The case of the supercells 3 × 3 × 1 is quite different. The original lattice vectors in the cations plane (the a vectors) were rotated by 30° first and after that, multiplied by 3.
Analysis of MgxM1-x(OH)2 Brucite-Like Compounds
J. Phys. Chem. C, Vol. 112, No. 29, 2008 10683
Figure 3. Schematic representation of supercells used in calculations.
Theoretical Methodology We performed ab initio calculations using periodic boundary conditions and based on DFT7,8 within the local density approximation (LDA) and generalized gradient approximation (GGA). We adopt the exchange-correlation functional parametrized by Perdew and Zunger9 and Perdew, Burke, and Ernzerhof10 from Ceperley and Alder’s11 data for correlation energy of the homogeneous electron gas for LDA and GGA approximation, respectively. The calculations were performed by using the ABINIT code,12,13 which is based on pseudopotentials and planewaves. It relies on an efficient fast Fourier transform algorithm14 for the conversion of wave functions between real and reciprocal space, on the adaptation to a fixed potential of the band-byband conjugate gradient method,15 and on a potential-based conjugate-gradient algorithm for the determination of the selfconsistent potential.16 The norm-conserving pseudopotentials have been generated by the FHI98PP code17 with the scheme of Troullier and Martins18 to generate soft norm conserving pseudopotentials. The semilocal pseudopotentials are further transformed into fully separable Kleinman-Bylander pseudopotentials,19 with the d potential chosen as the local potential. The considered valence configurations were 3s2, 4s2, 3d94s2, and 3d104s2 for Mg, Ca, Cu, and Zn, respectively. The cutoff radius used in channels s, p, and d were, respectively (in au), 2.14, 2.54, and 2.54 for Mg; 2.80, 3.01, and 2.60 for Ca; 2.13, 2.29, and 2.13 for Cu; and 2.06, 2.33, and 2.06 for Zn. For Mg and Ca, we have used nonlinear core corrections with 1.80 au and 2.60 au core radius, respectively. The wave functions are expanded in a plane wave basis set with maximum kinetic energy of 40 hartree (80 Ry). Brillouin-
Zone summations are carried out in Monkhorst-Pack strategy20 with about 0.04 Å-1 or less for k-point distance. The equilibrium lattice parameters and nuclei positions for all structures are found by minimizing the total energy. For each set of lattice parameters, the relative ion positions are relaxed until the forces are smaller than 0.01 eV/Å. For all the supercells, the lattice parameters a, b, and c and the unit cell angles R, β, and γ were optimized. The angles R, β, and γ were constrained only for the pure brucite-type structures (with x ) 0 or 1). To study the relative stability of layered hydroxide admixtures, it was assumed the formation reaction of the mixed hydroxides from pure brucite-like compounds.
xMg(OH)2 + (1 - x)M(OH)2 f MgxM(1-x)(OH)2 (1) where M ) Ca, Cu, or Zn. Therefore, the formation energy from layered brucite-type hydroxides is given by
Ef ) E{MgxM(1-x)(OH)2} - xE{Mg(OH)2} (1 - x)E{M(OH)2} (2) The terms E{MgxM(1-x)(OH)2}, E{Mg(OH)2}, and E{M(OH)2} are total electronic energies of MgxM(1-x)(OH)2, Mg(OH)2, and M(OH)2, respectively. The energy Ef is not a formation energy in the sense of prediction of formation of the mixed hydroxide directly, but only considering brucite-type layered structures with x ) 0 and x ) 1 as reactants. With the optimization of atomic positions, lattice parameters, and angles of the supercells, the layered structure could be broken. These cases are reported in the Discussion section. Results and Discussion The calculated geometrical parameters for Mg(OH)2 and Ca(OH)2 unit cells are presented in Table 2. Geometry
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TABLE 2: Experimental and Calculated Equilibrium Geometries (in Å) of Mg(OH)2 and Ca(OH)2 Respective Percent Errors with Different Exchange and Correlation Potential Approximations geometrical parameter
exptla
LDA
A C d (Mg-O) d (O-O) d (O-H) d (H-H)
3.150 4.770 2.100 2.779 0.958 1.997
A C d (Ca-O) d (O-O) d (O-H) d (H-H)
3.586 4.880 2.366 3.087 0.994 2.186
a
error LDA %
GGA
error GGA%
Mg(OH)2 3.125 -0.8 4.721 -1.0 2.099 0.0 2.784 0.2 0.993 3.7 1.933 -3.2
3.171 4.815 2.104 2.766 0.961 2.004
0.7 0.9 0.2 -0.5 0.3 0.4
Ca(OH)2 3.553 -0.9 4.644 -4.8 2.358 -0.3 3.101 0.5 0.976 -1.8 2.084 -4.7
3.667 4.998 2.417 3.151 0.964 2.242
2.3 2.4 2.2 2.1 -3.0 2.6
Figure 4. Energy as function of the interlayer distance. Zero level corresponds to DFT-PBE equilibrium geometry shown in Tables 2 and 3. The up triangles, squares, circles, and down triangles correspond to Mg(OH)2, Zn(OH)2, Cu(OH)2, and Ca(OH)2, respectively.
See reference 5.
TABLE 3: Equilibrium Geometry (in Å) of Cu(OH)2 and Zn(OH)2 Calculated Using DFT-GGA at Brucite Hexagonal P3jm1 Structurea d GGA
a
c
M-O
O-O
O-H
H-H
Cu(OH)2 Zn(OH)2
3.283 3.278
4.647 4.732
2.147 2.160
3.283 3.278
0.970 0.966
2.020 2.024
a
The cell constants (a and c) and atomic positions are fullyrelaxed but the angles R, β and γ were constrained during the calculations.
optimization was carried out within LDA and PBE approximation for exchange and correlation potential. As expected, GGA (PBE) approximation leads to a much better agreement with experimental values. As is well-known,21 Cu(OH)2 crystallizes with orthorhombic Cmcm structure, whereas Zn(OH)2 is orthorhombic,22 space group P212121. Our goal is to study not these species, but that formed by isomorphous substitution of Mg2+ ions in brucite by Cu2+, Zn2+. The optimized geometrical parameters are shown in Table 3. The numerical value for cell constant a is determined by intralayer interactions, whereas the value of c is a result of interlayer interactions. Total substitution of Mg2+ by Cu2+ or by Zn2+ results in two structures with a small difference in the a parameter. This is not unexpected, since they have similar ionic radius23 (0.74 Å for Zn2+ and 0.72 Å for Cu2+). On the other hand, the decrease in the c parameter can be attributed to an augmentation of interlayer interaction due to differences in the electronic density distribution resulting from cation exchange. Similar results were found when Mg2+ was substituted with Cu2+ and Fe2+ in hydrotalcite.24 This is an indication of the consistency of the results reported here. The ease of cleavage of brucite indicates that the interaction among its layers is very weak. Figure 4 shows the variation of energy as a function of the lattice parameter for brucite and brucite-like hydroxides containing Ca, Cu, and Zn. The four curves converge quickly to an asymptotic limit, which represents the separation energy. It can be noted that the minimum separation energy is 1.9 kcal/mol for Mg(OH)2, and the maximum energy is 2.2 kcal/mol for Ca(OH)2. These energies are very small and confirm the hypothesis of weak interaction among the layers in brucite-like compounds.
Figure 5. Formation energy of the Mg/Zn mixed hydroxides. The circles and squares are intralayer and interlayer mixtures, respectively. Labels refer to Figure 3.
Figure 6. Formation of Mg/Cu hydroxides calculated using spin polarization. The circles and squares are intralayer and interlayer mixtures, respectively. Labels refer to Figure 3.
Figures 5, 6, and 7 present the calculated formation energy (Ef) for the mixed hydroxides containing Mg/Zn, Mg/Cu, and Mg/Ca, respectively, as a function of the Mg molar ratio, x, defined in the chemical reaction of formation (equation 1). In Figure 5, we can see that the three structures with interlayer
Analysis of MgxM1-x(OH)2 Brucite-Like Compounds
J. Phys. Chem. C, Vol. 112, No. 29, 2008 10685 TABLE 5: Maximum and Minimum First Neighbor M-O Distances in Å (M ) Mg, Ca, Cu or Zn) for the MgxM1-x(OH)2 Admixtures That Kept Brucite-type Morphology distance
Figure 7. Formation energy of the Mg/Ca mixed hydroxides. The circles and squares are intralayer and interlayer mixtures, respectively. Labels refer to Figure 3.
TABLE 4: TSconf Energy in kcal/mol as a Function of Mg Molar Ratio and Temperature temp (K)
x ) 1/3
x ) 1/2
x ) 2/3
300 500 700
0.38 0.63 0.89
0.83 1.38 1.93
0.38 0.63 0.89
mixture (x ) 1/3, 1/2, and 2/3) have positive formation energies, but all configurations with intralayer mixture have negative formation energy. This result concerning interlayer mixture could be rationalized by regarding the difference of the a lattice parameter between Mg(OH)2 and Zn(OH)2. From data shown in Tables 2 and 3, this difference is 3.4%, and the layers formed by Zn(OH)2 and by Mg(OH)2 could be adjusted to an intermediate value for the a parameter with a small increase in the energy. In fact, the a parameters are 3.243, 3.225, and 3.206 Å for x values of 1/3, 1/2, and 2/3, respectively. Their formation energies were positive but up to 1.0 kcal/mol. This very small energy difference could be compensated for by the TS term (temperature times entropy) of formation free energy, which suggests a random occupation of the sites. Table 4 shows some values for the TS term of free energy as a function of molar ratio and temperature. S can be approximated by configurational entropy (Sconf) only and can be calculated in kcal/mol by the expression25
Sconf ) -R[x ln x + (1 - x) ln(1 - x)]
(3)
where R is the ideal gas constant. The idea of random occupation is reinforced by the very small difference for the first neighbors M--O (M ) Mg or Zn) distance in the different structures. Table 5 shows the extreme values for M-O first neighbor distances for brucite-type structures. Only for MgxCu1-x(OH)2 compounds were the distortions sufficiently large to break brucite-type morphology. For MgxZn1-x(OH)2 compounds, the maximum Mg-O and Zn-O distances for first neighbors are 2.15 and 2.17 Å, respectively. The minimum Mg-O and Zn-O distances are 2.10 and 2.14 Å, respectively. Therefore, the ensemble of completely geometry-optimized supercells exhibits a maximum difference of 0.07 Å for M-O distances that are very small and compatible with an idea of a disordered MgxZn1-x(OH)2 compound with minimum of free energy for x ) 1/2 due to configurational entropy. These results point to the formation of mixed structures with random occupation of cationic centers by Zn2+ or Mg2+,
max (supercell)
min (supercell)
d (Mg-O) d (Ca-O)
Compounds Mg/Ca 2.36 (H11) 2.09 (H10) 2.40 (H12) 2.32 (H6)
d (Mg-O) d (Cu-O)
Compounds Mg/Cu 2.19 (H2) 2.01 (H7) 2.43 (H2) 2.12 (H6)
d (Mg-O) d (Mg-Zn)
Compounds Mg/Zn 2.15 (H2) 2.10 (H3, H7, H9, H11) 2.17 (H2) 2.14 (10)
TABLE 6: Formation Energy for Some Mixed Mg2+/Cu2+ Hydroxides Calculated without Spin Polarization X
cell
Ef (kcal/mol)
mixture type
1/4 1/3 1/2 1/2 1/2
H11 H9 Tr Or H8
0.342 285 21 0.710 651 51 0.442 025 26 0.340 258 83 0.365 453 35
intra intra intra intra inter
especially at higher temperatures. Experimental data suggest the formation of these mixtures,26 as well. The same analysis was carried out for mixed hydroxides containing Mg and Cu, but no formation from pure hydroxides is predicted (Table 6). This sounds quite strange, since the formation of this kind of compound in hydrotalcite has already been reported.27 In fact, in case of copper substitution, spin polarization has to be considered, given that it is quite possible that the ground sate, in this case, is paramagnetic, so we have performed the calculations for Mg/Cu compounds allowing spin polarization. Results are shown in Figure 6. As can be seen, this lead to a quite different picture. The formation of mixed hydroxides from brucite and brucite-type Cu(OH)2 is predicted for all calculated molar ratios. As the examination of Figure 6 reveals, mixed hydroxides could easily be formed by interlayer admixtures. This reflects the minor difference predicted between Cu(OH)2 and Zn(OH)2 lattice parameters, as shown in Table 3. For x ) 1/2, even for 700 K, the entropic energy term -TS (-1.9 kcal) is greater than Ef (-4.7 kcal). In view of that, some order is expected in the mixture. For the other x values, the -TS term is even greater (less negative) than in x ) 1/2, but Ef values are around -1.0 to -2.0 kcal/mol. Other x ) 1/2 supercells but Or have an Ef around 2.0 kcal/mol, and these configurations would be accessible in a material with global x > 0.5. Then for samples with x > 0.5, a random occupation of cationic sites is expected. Figure 8 shows the supercell Or, which leads to the lowest total energy, after geometry optimization. A distortion from a perfect octahedron is clearly noted. This distortion could be predicted by the Jahn-Teller effect and is present in other optimized unit cells. Table 5 shows the largest distance differences for MgxM1-x(OH)2 hydroxides. The distortions are larger in the cells that have the lowest formation energy, and their x proportions are 1/2 (supercells Or and H5), 1/3 (supercells H3 and supercell H4), and 1/4 (supercell H2). Despite the maintenance of brucite-type morphology, the supercell H2 had a severe local octahedron distortion around the Cu2+ ion by 0.46 Å (difference between largest and smallest bonding distance). It is not coincidence that the Mg/(Mg + Cu) ratios are all j1 for the most distorted structures. EXAFS experiments have attested the existence of distorted octahedrons in hydro-
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Costa et al. TABLE 7: Distances of Mg-O and M-O (M ) Zn, Cu, or Ca) for the Ground State Structures (Å)a distance
Mg1/2Zn1/2(OH)2
d (Mg-O)
2.088 (2) 2.105 (2) 2.128 (2)
d (M-O)
2.142 (2) 2.164 (2) 2.179 (2)
Mg1/2Cu1/2(OH)2 2.067 2.071 2.090 2.093 2.112 2.121 1.962 (2) 2.041 2.044 2.925 2.942
Mg3/4Ca1/4(OH)2 2.082 (2) 2.134 2.141 2.143 (2) 2.348 2.353 2.358 2.360 2.381 2.387
a The values in parentheses correspond to the number of equivalent cation-oxygen distances.
Figure 8. Distorted local structure corresponding to the lowest energy for Mg/Cu mixture.
talcite-like compounds containing copper.27 A strategy to reduce the distortions is described by Vaccari26 and Khan28 and consists of formation of ternary hydrotalcite-like compounds containing Cu2+, Al3+, and M2+, where M2+ ) Mg2+, Co2+, or Zn2+. These works indicate that to minimize distortions caused by copper inclusions, the ratio Cu2+/M2+ must be kept equal to or less than 1. This behavior could have been predicted by our results with simulations using the simple layer hydroxides. The brucitelike structure was conserved for all structures with x > 1/2. For the Mg/Ca admixture, all the calculated formation energies, shown in Figure 7, are positive, and formation of brucite-like compounds containing Mg and Ca is not expected. Preparation of brucite-like or hydrotalcite-like compounds containing Mg and Ca has not been reported so far. This is commonly justified by the difference in radii3 between Mg2+ and Ca2+, but HDL structures with Ca and Al can be prepared with a hydrotalcite (Mg and Al) structure. In this case, the explanation based only on the ionic radius parameters is not complete because the Al3+ ionic radius is 0.51 Å, even shorter than Mg2+ (0.66 Å).24 Effects such as the capability of octahedron distortion (keeping the first neighbors) are very important and cannot be deduced by the radii. The ab initio calculations using the ensemble of supercells shows rigid structures with very different distances for Ca-O and Mg-O, as the example in Table 5. The compounds MgxCa(1-x)(OH)2 have the largest local distortion by 0.18 Å from octahedron for x ) 1/2 (supercell H5). This local distortion corresponds to the difference among the Ca-O bonding distances at the same cationic center. Due to the ionic ratio difference, it was expected that the largest distortion was the intralayer, with a 1:1 proportion between the Ca and Mg admixture, such as supercell H5. In Table 7, we gather together the results for calculated bond distances for the mixed compounds in their most stable composition. The difference between the largest and the smallest distance in the compound Mg1/2Zn1/2(OH)2 (supercell H5) is
0.09 Å. This same parameter is 0.16 Å in the Mg1/2Cu1/2(OH)2 structure (supercell Or) and 0.30 Å for the Mg3/4Ca1/4(OH)2 (supercell H2) structure. The distances 2.925 and 2.942 Å in Mg1/2Cu1/2(OH)2 were not considered in this analysis because they are so large that it would hardly correspond to any chemical bond. As expected, the largest difference is in the Mg/Ca compound. The structures have distinct Mg-O distances, as well, as a result of the perturbation caused by the presence of a different cation in the structure. Conclusions Mixed hydroxides, formed by isomorphous substitution of Mg2+ of brucite, Mg(OH)2, by divalent cations M2+ (M ) Zn, Cu, Ca) were studied by DFT. A detailed analysis of structure and energetics was carried out. Calculations were performed within the pseudopotential approximation, in a plane waves basis set and periodic boundary conditions. It was predicted that compounds of formula MgxZn1-x(OH)2 can be formed. The mixed hydroxides of the interlayer mixture are expected to be formed at higher temperatures; intralayer hydroxides would be formed even at room temperature. The same is true in the case of magnesium substitution by copper, which leads to formation of hydroxides with the formula MgxCu1-x(OH)2. Nevertheless, an important difference is found here. The calculations were done allowing spin polarization, which has revealed that the ground state, in this case, is paramagnetic. We verified Jahn-Teller distortion in the unit cell, as previously reported by EXAFS experiments. Finally, in the case of magnesium substitution by calcium, no formation of mixed hydroxide with the brucite structure is predicted. All calculated results are in complete agreement with known experimental facts. This attests the reliability and the prediction power of the present calculations. Acknowledgment. We thank CNPq (Conselho Nacional de Desenvolvimento Cientı´fico e Tecnolo´gico), FAPEMIG (Fundac¸a˜o de Amparo a` Pesquisa do Estado de Minas Gerais), FAPERJ, and Petrobras SA for financial support during this work. References and Notes (1) Catti, M.; Ferraris, G.; Hull, S.; Pavese, A. Phys. Chem. Miner. 1995, 22, 200. (2) Kandare, E.; Hossenlopp, J. M. J. Phys. Chem. B 2005, 109, 8469. (3) Crepaldi, E. L.; Valim, J. B. Quı´m. NoVa 1998, 21, 300. (4) D’Arco, P.; Causa`, M.; Roetti, C.; Silvi, B. Phys. ReV. B 1993, 47, 3522.
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