An Examination of the Influence of Divalent Cationic Dopants on the

Apr 17, 2009 - Solutions, Sellafield, Seascale, Cumbria, CA20 2PG, United Kingdom. ReceiVed February 13, 2008; ReVised Manuscript ReceiVed March 23, ...
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An Examination of the Influence of Divalent Cationic Dopants on the Bulk and Surface Properties of Ba(NO3)2 Associated with Crystallization Robert B. Hammond,† Michael J. Orley,† Kevin J. Roberts,*,† Robert A. Jackson,‡ and Michael J. Quayle§,|

CRYSTAL GROWTH & DESIGN 2009 VOL. 9, NO. 6 2588–2594

Institute of Particle Science & Engineering, School of Process, EnVironmental & Materials Engineering, UniVersity of Leeds, Leeds LS2 9JT, United Kingdom, Lennard-Jones Laboratories, School of Chemistry & Physics, Keele UniVersity, Keele, Staffs ST5 5BG, United Kingdom, and Nexia Solutions, Sellafield, Seascale, Cumbria, CA20 2PG, United Kingdom ReceiVed February 13, 2008; ReVised Manuscript ReceiVed March 23, 2009

ABSTRACT: The incorporation of divalent cationic species associated with the crystallization of Ba(NO3)2 related to nuclear waste storage issues is studied via the development and exploitation of a versatile and transferable empirical atom-atom forcefield for both mono- and divalent nitrates. Studies of binary and tertiary systems using Mott-Littleton and bulk supercell defect calculations reveals Ca2+ ions to be the most energetically favored species for incorporation into the Ba(NO3)2 lattice over Sr2+ and Pb2+ ions. Incorporation modeling also confirms solid-solution behavior with an excellent Vegard’s Law fit. Tertiary systems involving Ba2+, Ca2+, and Sr2+ ions are found to become less stable with increasing concentrations, notably of Sr2+. Morphological predictions using attachment and surface energy methods reveal a well-defined cube-octahedron habit, with negligible differences between Ba(NO3)2 and Sr(NO3)2. Surface relaxation effects are found to be very small, with no apparent impact on the predicted crystal morphology, consistent with a very stable surface structure, reflecting both the close packing nature of the {100} and {111} habit faces and the strong in-plane Coulombic interactions between the cations and the anions. Examination of Sr2+ incorporation onto Ba(NO3)2 crystal habit surfaces is in good agreement with experimental observations of the crystal morphology revealing preferential incorporation onto the {111}surfaces, with respect to the {100} surfaces, where the former case displays a layerlike packing of cations and anions that more easily effects the impurity incorporation process and hence prevents further growth, resulting in a more octahedral morphology. 1. Introduction Ba(NO3)2 precipitates from high-level waste effluent streams resulting from the reprocessing of nuclear waste. This stream is largely composed of 235U fission products from nuclear reactors, following the extraction of high-value uranium and plutonium fuel components together with process reagents that are involved in the reprocessing process. When the nuclear fuel reaches the end of its useful and economic life within a nuclear reactor, the fissile material is removed for subsequent reprocessing. After a period of prolonged cooling (5-10 years), the material is then dissolved in a nitric acid medium. Nitric acid is used as it is a good solvent, having no radioactive isotopes and reflecting the fact that its properties can be altered to allow efficient extraction of any remaining uranium and plutonium that might be present in the nuclear reactor waste.1 A solvent extraction process employing a mixture of tributyl phosphate and odorless kerosene separates out the reusable uranium and plutonium, leaving the remaining highly active nitric acid dissolved media2 for subsequent storage. The volume reduction of the high level waste stream by evaporation, prior to immobilization though vitrification, results in the precipitation of divalent nitrates, notably Ba(NO3)2. In addition, significant amounts of the radiogenic self-heating 90Sr isotope, are also found and the precipitates overall exhibit a highly dense phase that has a low solubility in water and dilute acids becoming appreciably less soluble with the increasing * Corresponding author. E-mail: [email protected]. Tel: (0113)3432404. † University of Leeds. ‡ Keele University. § Nexia Solutions. | Now at Astra Zeneca, Avlon Works, Bristol BS10 7ZE, United Kingdom.

nitric acid concentration that results from evaporation3 during reprocessing. In addition, Sr(NO3)2 has been shown experimentally to coprecipitate with Pb(NO3)24 forming a mixed cationic structure PbxSr1-x(NO3)2. This paper focuses on an examination of the energetic factors associated with divalent metal (Pb2+, Sr2+, and Ca2+) cationic bulk defects in Ba(NO3)2 and its potential impact on crystal growth. The incorporation Ca2+ ions, while not a fission product, is included here because of its potential interest as a nonradioactive benchmark. A transferable empirical atom-atom potential was derived for mono and divalent nitrates and validated against known crystal structures and physical properties. This was then used to model point defect structures within the crystal lattice using the Mott-Littleton approach5,6 and the supercell method (see, for example, ref 7). These models enable the change in potential energy, and the concomitant lattice deformation, to be calculated as a function of dopant-ion concentration. Attachment (Eatt) and surface energy (Esurf) calculations were also employed to model the expected crystal morphology of Ba(NO3)2 and Sr(NO3)2. 2. Materials and Methods 2.1. Crystal Chemistry. Ba(NO3)2, Sr(NO3)2,8 Ca(NO3)2,9 and Pb(NO3)210 all display an isomorphous cubic structure (space group Pa3) with lattice parameters, a, of 8.11, 7.81, 7.61, and 7.85 Å, respectively. The nitrate groups in the Pa3 structures are slightly distorted from trigonal planar with the N atom of the nitrate group being slightly shifted from the center of gravity of the three O atoms giving it a slight pyramidal height of 0.005 Å.8 Each metal cation has a point symmetry of 3, and therefore, the 12 surrounding O atoms build up a 6 + 6 octahedral coordination at two different close coordination distances,8 g and h, as shown by Table 1. Figure 1 shows the local

10.1021/cg8001674 CCC: $40.75  2009 American Chemical Society Published on Web 04/17/2009

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Table 1. Experimental Distances between M2+ cation and Nearest Oxygen Atoms for Pa3 Structured Divalent Nitrates; Bond Distances (Å) and Angles (deg) between Nitrate Groups Are Also Givena,8 t M-O M-O M-M N-O O-O O-N-O a

g h

n 6 6 12

Ba(NO3)2

Ca(NO3)2

M2+O12 Polyhedra 2.8788 2.7171 2.9413 2.7171 5.7406 5.3846 Nitrate Group 1.2464 1.2254 2.1588 2.1223 120.00 120.00

Sr(NO3)2

Pb(NO3)2

2.7151 2.8380 5.5022

2.7484 2.8690 5.5550

1.2467 2.1593 120.00

1.2470 2.1598 120.00

t is the type of M-O distance and n is the coordination number.

Table 2. Interatomic Potentials and Associated Ionic Charges Used in This Study with Li-O and Rb-O Being Specified to Enable Transfer of the Nitrate Potential Buckingham Potential interaction

A (eV)

F (Å)

C (eV Å6)

Ba-O Ca-O Sr-O Pb-O Li-O Rb-O O-O N-O

4000.00 2280.00 5000.00 3100.00 1790.00 2030.00 36000.00 5050.00

0.28842 0.28729 0.26955 0.28712 0.2299 0.29780 0.19746 0.1130

0.00 0.00 0.00 0.00 0.00 0.00 24.00 0.00

Harmonic Potential interaction

k (eV Å-2)

r0 (Å)

N-O

48.60

1.24

Three Body Potential interaction

k3 (eV rad-2)

θ0 (deg)

O-N-O

14.58

120.00

Ionic Charges

Figure 1. Cation local atomic site chemistry around Ba2+, Ca2+, Sr2+, and Pb2+ in their respective nitrate crystal structures showing the six nitrate molecules and the associated 6 + 6 coordinated oxygen atomic shells. coordination chemistry of the cationic site within these structures showing the structural disposition of these two shells. Two additional and monovalent nitrates have also been examined, to test the transferability of the nitrate potential to other valence states and structural types. Li(NO3) has a rhombohedral structure (space group R3jc) and lattice parameters a ) b ) 4.6920 Å and c ) 15.2149 Å;11 Rb(NO3) has a hexagonal structure (space group P31) and lattice parameters a ) b ) 10.55 Å and c ) 7.47 Å.12 The crystal chemistry of these compounds is not considered in detail here, as in this study they are simply used to test the transferability of the derived potential. Full details of these structures are provided in the primary sources cited. 2.2. Interatomic Potential Derivation. The atomistic potential energy model adopted in this study has been widely used in the modeling of molecular ionic materials.13,14 Separate terms for nonbonded and bonded interactions are provided, with nonbonded interactions being represented by the Buckingham potential supplemented by an electrostatic term

Vnb(rij) ) qiqj /rij + Aexp(-rij /F) - Crij-6

(1)

where qi and qj are the charges on the ions i and j, respectively (which are not part of the same molecular ion), and A, F, and C are parameters whose values are obtained for each ion pair by empirical fitting or direct calculation. Charges for the constituent atoms in a molecular anion were fitted with the constraint that the ion takes the overall formal charge. Partial charges were used in deriving the force-field parameters, with Mulliken polulation analysis giving the following charges for the nitrate components: N +0.6392e, O -0.5464e.15 Cations were given their full valence charge. Bonded interactions, i.e., in this case, the N-O bond and the O-N-O angle of the nitrate group, were represented by harmonic terms

Vb(r,θ) ) 0.5ks(r - r0)2 + 0.5kb(θ - θ0)2

(2)

where ks and kb are bond-stretching and bond-bending force constants, and r0 and θ0 are the equilibrium bond length and bond angle, respectively.

ion

charge (e)

M2+ M1+ N O

2.00 1.00 0.6392 -0.5464

For this study, the nitrate potential was taken from Mort et al.,15,16 with the M2+-O2- core nonbonded Buckingham potentials being refitted via empirical methods. A, C, and F values within the Buckingham potential for the M-O bond (where M is the metal cation) were varied, which resulted in associated energies, bond lengths, and physical properties being predicted and optimized to give the best structural fit. The general utility lattice program (GULP)17 was used for all the calculations used in this paper. This derived potential was also used to estimate the relative strength of the interionic interactions, particularly to assess the effect of cationic substitution. 2.3. Mott-Littleton Calculations. The Mott-Littleton method enables the geometrical and energy changes associated with point defects within ionic structures to be calculated. The immediate surroundings of a defect was expressed in terms of two concentric spherical regions, with the ions in the inner region (region I) being treated explicitly and allowed to relax their positions in response to the defect, whereas the ions in the outer region (region II), are displaced in response to those in region I. The substitution of another divalent cation at a Ba2+ site within the Ba(NO3)2 lattice was considered in these calculations. The energy change associated with the process (i.e., the defect formation energy) was expressed in the form of a solution energy (i.e., the energy change on formation of an infinitely dilute solid solution of the dopant cation within the host crystal lattice), to enable the substitution of different divalent cations to be compared. Consistent region sizes of 7 Å (region I) and 12 Å (region II) were found to provide the most effective simulation model and hence were used throughout this study. The solution energy, Esol, was calculated as follows, where the lattice energies (e.g. ElattSr(NO3)2) were assumed to take negative values, and E(SrBa) is the defect formation energy for substitution of a Sr2+ ion at a Ba2+ site,7 with the calculation being repeated for Pb2+ and Ca2+. This solution energy was used to gauge the ease of substitution of the dopant ions in the bulk Ba(NO3)2 lattice, thus

Esol ) E[SrBa]+Elatt[Ba(NO3)2] - Elatt[Sr(NO3)2] (3) 2.4. Supercell Method. Application of the supercell method7 involves construction of a (2 × 2 × 2) supercell consisting of 288 atoms to simulate the Ba(NO3)2 host. A single cation substitution was then made within the supercell and lattice energy minimization carried out at constant pressure. The defect energy was obtained from the difference between the initial lattice energy and the energy of the host lattice containing the defect cation, which was then repeated and

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Table 3. Calculated and Experimental Lattice and Elastic Constantsa property

Ba(NO3)2

a

c

c11

3.203(1) (2.925) 2.181(5) (2.065) 1.326(9) (1.277) 2.597(7) 25.220(1) 8, 25

c12 c44 A bulk modulus (GPa) refs

Ca(NO3)2

Lattice Constants (Å) 7.781(3) 7.614(8) (0.00%) (0.00%) 7.781(3) 7.614(8) (0.00%) (0.00%) 7.781(3) 7.614(8) (0.00%) (0.00%) Elastic Constants (× 1011 Dyne cm-2) 4.348(3) 4.522(9) (4.255) 2.811(5) 2.822(1) (2.921) 1.794(2) 1.794 (1.590) 2.335 2.109(6) 33.238 33.89 8, 25 9

8.118(3) (0.00%) 8.118(3) (0.00%) 8.118(3) (0.00%)

b

a

Sr(NO3)2

Pb(NO3)2

Li(NO3)

Rb(NO3)

7.855(9) (-0.00%) 7.855(9) (-0.00%) 7.855(9) (-0.00%)

4.692(3) (0.01%) 4.692(3) (0.01%) 14.918 (-1.95%)

10.547(8) (-0.02%) 10.547(8) (-0.02%) 7.388(6) (-1.09%)

3.833(1) (3.729) 2.518(5) (2.765) 1.576 (1.347) 2.397(7) 29.566(8) 10, 25

9.813(5)

2.869(6)

3.508(2)

0.993(6)

2.317(3)

1.105(5)

0.735 44.717(4) 11

1.178(6) 16.5229(6) 12

The percent error for the lattice constants (top) and for the elastic constants (bottom) with respect to experimental values are given in brackets.

Table 4. Calculated Distances (Å) between M2+ Cation and Nearest Oxygen Atoms for Pa3 Structured Nitrates; Bond Distances (Å) and Angles (deg) between NO3- Groups Are Also Givena t

n

M-O

a

6

M-O

b

6

M-M

12

N-O O-O O-N-O

Ba(NO3)2

Ca(NO3)2

M2+O12 Polyhedra 2.882(8) 2.677(7) (0.14%) (-1.45%) 2.908(9) 2.736(5) (-1.11%) (0.72%) 5.740(5) 5.384(5) (0.00%) (0.00%) Nitrate Group 1.279(4) 1.278(4) (2.65%) (4.33%) 2.215(9) 2.214 (2.64%) (4.33%) 119.994 119.983 (0.00%) (0.00%)

Sr(NO3)2

Pb(NO3)2

2.750(9) (1.32%) 2.788(1) (-1.79%) 5.502(2) (0.00%)

2.778(4) (1.09%) 2.816(2) (-1.87%) 5.555 (0.00%)

1.278(8) (2.57%) 2.214(9) (2.57%) 119.989 (0.00%)

1.279 (2.57%) 2.215(2) (2.57%) 119.990 (0.00%)

a t is the type of M-O distance and n is the coordination number. Comparisons to experimental literature values from Table 1 are given in the brackets.

Figure 2. Buckingham repulsive potential energy function for the octahedrally coordinated M-NO3 bond lengths (M ) Ba, Pb, Sr, and Ca). This shows that the Sr-O repulsive energy is slightly less than that of the Ca-O. Table 6. Comparison of Defect Substitution and Solution Energies

averaged for all cation sites within the supercell. From this, the lattice parameter for the doped supercell, as a function of increasing dopant concentration, was calculated. 2.5. Morphological Modeling. Attachment energy (Eatt) and surface energy (Esurf) approaches were used to predict the expected growth and equilibrium morphologies of both Ba(NO3)2 and Sr(NO3)2. Eatt,18 is the energy per growth unit released when a new crystallizing layer of depth, dhkl, is attached to the growing crystal face. Eatt is assumed to be proportional to the relative growth rate of a specific crystal surface and hence to be inversely proportional to its morphological importance during growth. Esurf can be described as the difference in energy of the surface ions compared with those in the bulk crystal lattice as expressed per unit surface area. The morphological importance is taken to be inversely proportional to its surface energy, hence simulating the expected equilibrium crystal morphology. The overall procedure for predicting the growth and equilibrium morphologies consisted of • Minimizing of the bulk crystal structure; • Carrying out a Bravais-Freidel-Donnay-Harker (BFDH)19,20 analysis of most likely crystal habit faces based on their respective

dopant ion

defect substitution energy (eV)

solution energies (eV)

Ca2+ Sr2+ Pb2+

-1.21 -0.93 -0.62

0.11 0.04 0.02

d-spacings; • Cleaving faces from relaxed bulk structure and ensuring zero dipole on the surface followed by surface relaxation; • Creating regions I and II, where region I contained the ions that were relaxed explicitly until there was zero force on each of them, whereas in region II, the positions of the ions were held constant; • Calculating attachment and surface energies and plotting these in spherical polar coordinates via a 3D Wulff plot21 Each region needed to be large enough to obtain convergence for the calculated energies. A 2 × 2 cell was used with different depths of slab (z), for regions I and II. In this, the {111} face contained 48 formula units in region I, with three layers of 16 cations, whereas region II contained 208 formula units. The {200} face contained 24 formula units in region I with three layers of 8 cations, whereas region II contained 104 formula units.

Table 5. Distances of the Divalent Cation to the Six Nearest Nitrate Neighbors Showing the Total Coulombic and Repulsive Energies; Calculated Bulk Lattice Energies Are Also Shown distances M2+

ionic radii (eV)

N

O1

O2

O3

Coulombic rnergy (eV)

repulsive energy (eV)

total energy (eV)

calcd lattice energy (eV)

Ba Ca Sr Pb

1.42 1.12 1.26 1.29

3.315 3.150 3.212 3.237

2.883 2.724 2.781 2.805

2.909 2.784 2.82 2.842

4.594 4.430 4.492 4.516

-0.607 -0.637 -0.626 -0.621

0.350 0.324 0.309 0.336

-0.257 -0.313 -0.317 -0.285

-116.259 -121.520 -120.164 -118.842

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Table 7. Normalized Lattice Energy and Normalized Unit-Cell Length As a Function of Dopant Concentration %M

no. of M ions

0 3.125 6.25 12.5 18.75 25 31.25 50 100

0 1 2 4 6 8 10 16 32

0 3.125 6.25 12.5 18.75 25 31.25 50 100

0 1 2 4 6 8 10 16 32

0 3.125 6.25 12.5 18.75 25 31.25 50 100

0 1 2 4 6 8 10 16 32

normalized lattice energy (eV)

normalized unit-cell length (Å3)

M ) Ca -29.07 -29.09 -29.13 -29.19 -29.25 -29.32 -29.39 -29.62 -30.38 M ) Sr -29.07 -29.09 -29.12 -29.17 -29.22 -29.28 -29.33 -29.51 -30.04 M ) Pb -29.07 -29.08 -29.10 -29.14 -29.17 -29.21 -29.25 -29.36 -29.71

8.12 8.11 8.09 8.07 8.04 8.01 7.99 7.90 7.61 8.12 8.11 8.10 8.08 8.06 8.04 8.02 7.96 7.78

Figure 3. Comparison of experimental, Vegard’s law, and supercell methods for Sr2+ substitution into Ba(NO3)2, where line of regression is equal to y ) 0.3371x + 7.7813.

8.12 8.11 8.10 8.09 8.07 8.06 8.04 7.99 7.86

The attachment energies were scaled according to the number of formula units of Ba(NO3)2 and Sr(NO3)2 at the surfaces for the {111} and {200} forms with a ratio of 2:1 formula units, respectively, following relaxation. 2.6. Sr2+ and Ca2+ Substitution at the Ba(NO3)2 {111} and {200} Surfaces. Calculation of the energetics of adsorption of Sr2+ and Ca2+ ions at the Ba(NO3)2 crystal habit surfaces involved modeling a surface layer fully substituted with dopant ions. The {111} and {200} faces in region I have three layers of cations, thus providing a number of choices for the surface termination and hence the layer in which to substitute dopant cations. The surface termination that subsequently yielded the most stable substitution energies was selected as the most probable surface layer. 2.7. Crystallization and Characterization. Modeled crystal morphological data behavior was compared to experimental morphological data for crystals of Ba(NO3)2 crystallized from slow cooled solutions (Tsat ) 318 K) over the temperature range 348-303 K and the same when doped with 10 mol % Sr(NO3)2. Crystals were harvested via careful filtration, washing in distilled water and drying under ambient conditions. Morphological analysis of the product crystals were carried out using a SEM (Philips XL30 ESEM) and Au surface coating.

Figure 4. Overall lattice energy (eV) vs dopant concentration (%) for the doped Ba(NO3)2 supercell.

3. Results and Discussion 3.1. Potential Development and Its Validation. The fitted interatomic potential parameters for the four divalent and two monovalent nitrates are given in Table 2. The predicted lattice and elastic constants for these compounds are given in Table 3, together with available experimental data. The lattice parameters calculated for the fully relaxed crystal lattice for the divalent species was found to be in good agreement with experimental crystal structures (cubic) for Ba(NO3)2,8 Sr(NO3)2,8 Ca(NO3)2,22 and Pb(NO3)210 nitrates. Reasonable agreement was also achieved for both the LiNO3 and RbNO3 (tetragonal) structures, albeit in both cases with the c axis length being underestimated and the a axis being slightly overestimated. The errors associated with the lattice parameters are comparable to other inorganic crystal structures, such as

Figure 5. Tertiary supercell results of the system BaxSr1-xCax-0.5(NO3)2 showing increasing stability at the lower the Ba2+ concentration but the higher Ca2+ concentration.

the apatite crystals.31 Nonetheless, these results demonstrate the transferability of this potential for modeling both monovalent and divalent metal nitrates, encompassing cubic, rhombohedral, and hexagonal crystal lattice types, with an acceptable level of accuracy. The calculated elastic constants for cubic structures of Ba(NO3)2, Sr(NO3)2, and Pb(NO3)2 agree very well with experimentally determined values. No experimental data were available for Ca(NO3)2 as this is naturally hydrated,23 and hence the calculated values are provided simply for completeness.

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Figure 6. Projection view of M(NO3)2 {111} face, where atomic M is the metal cation (green) with nitrogen (blue) and oxygen (red).

Figure 7. Projection view of the M(NO3)2 {111} face, where M is the metal cation (green) with nitrogen (blue) and oxygen (red). Table 8. Interplanar d-spacing of the Five Most Morphologically Important Faces from BFDH Analysis for Ba(NO3)2 and Sr(NO3)2 Ba(NO3)2

Sr(NO3)2

hkl

dhkl

hkl

dhkl

{111} {200} {210} {211} {220}

4.6872 4.0592 3.6307 3.3143 2.8703

{111} {200} {210} {211} {220}

4.4925 3.8907 3.4799 3.1767 2.7511

The elastic anisotropy factor (A) for cubic structures is given by

A ) 2c44 /(c11 - c12)

(4)

where c11, c12, and c44 are the elastic constants and A represents the ratio of the two extremes of the elastic-shear coefficients. Ledbetter & Migliori24 highlighted the importance of elastic anisotropic effects in solid-state transformations such as phase transitions and precipitation, and these predictions reveal the cubic phases to be fairly anisotropic. The calculated interatomic distances given in Table 4 were found to be in good agreement with those of the published crystal structures. It can be seen that the metal to oxygen separation distances are slightly overestimated for the first coordination shell and slightly underestimated for the second

Figure 8. Relaxed growth morphologies (attachment energy) of (left) Ba(NO3)2 morphology and (right) Sr(NO3)2 morphology.

coordination shell, although the average of the two produces an accurate result. The associated differences between the experimental and optimized structure are in line with other inorganic modeling literature.14 Both the nitrogen-oxygen and oxygen-oxygen bond lengths reflect an increasing change in lattice constants, i.e., Ba > Pb > Sr > Ca(NO3)2, although from experimental data,8,10 the nitrogen-oxygen bond length in Pb(NO3)2 should be greater than that of the Ba(NO3)2 system. Table 5 facilitates a comparison of the atoms treated in this study. The ionic radii show that the radius for Sr2+ is the closest match to Ba2+, although the Ca2+ was found to be slightly smaller and therefore may be more energetically favorable to incorporate into the crystal lattice. Application of the potential function (Figure 2) to examine the local atomic structure around the incorporated dopants reveals an expected trend in that the M2+-NO3 distances (Table 5) fall within that expected from their respective ionic radii (Ba > Pb > Sr > Ca(NO3)2). Interestingly, using the potential to calculate the binding energy of the octahedrally coordinated nitrate ions about the centered metal cation (in solution) a slightly different stability ordering is indicated as shown by Table 5 (Ba > Pb > Ca > Sr(NO3)2).This presumably reflects the importance of the long-range electrostatic interactions in the bulk solid, which counterbalance the short-range repulsion as described by the respective Buckingham potential. 3.2. Results of the Mott-Littleton Calculations. The Mott-Littleton defect formation and solution energies for substitution in the Ba(NO3)2 lattice with dopant cations are given in Table 6. These calculations show that, under conditions of infinite dilution, Ca2+, then Sr2+, then Pb2+ ions, would be the most favorable. This observation is likely to be due to the smaller ionic radius of the Ca2+ and Sr2+ ions and the larger ionic radius of the Pb2+ ion. The Mott-Littleton approach, however, does not take into account ion-ion interactions. In addition, the relative concentration of dopant metal ions versus host metal ions within the solution from which crystals are grown has not been explicitly considered in these calculations. However, the results are clearly indicative of the probability of dopant incorporation under growth conditions close to equilibrium. 3.3. Supercell Simulation Results. Table 7 shows the calculated average change in the lattice parameter with varying dopant ion concentration from 3.125% (one ion substitution) to 100% (all ion sites substituted). From this it can be seen that

Table 9. Calculated Surface and Attachment Energies for the Faces of Ba(NO3)2 and Sr(NO3)2 attachment energy per unit (eV mol-1)

surface energy (J m2-) Miller index2

unrelaxed

relaxed

(111) (200)

0.43 0.42

0.36 0.37

(111) (200)

0.51 0.5

0.45 0.44

∆ (%) Ba(NO3) -18.06 -15.53 Sr(NO3)2 -14.48 -13.51

unrelaxed

relaxed

∆ (%)

-1.51 -1.69

-1.53 -1.61

1.19 -5.08

-1.68 -1.85

-1.72 -1.81

1.90 -2.33

Influence of Divalent Cationic Dopants on Ba(NO3)2

Figure 9. (Left) SEM image and (right) morphological sketch of Ba(NO3)2 precipitated at 318 K at a heating/cooling rate of 0.5 K min-1 in distilled water, clearly showing a range of cube-octahedral habits with the crystal size 20 × 20 µm.

Figure 10. Surface energy calculations of Sr2+ and Ca2+substitution at the {111} and {200} surfaces of Ba(NO3)2. 2+

2+

2+

the incorporation of Ca , Sr , and Pb ions into the Ba(NO3)2 lattice is accompanied by a linear change in unit cell length with the smallest cell change at any given concentration, being found for the Ca2+ ions, which would be consistent with the known ionic radii. The supercell results for doping Sr2+ ions into Ba(NO3)2, shown in Figure 3, were found to be in good agreement with both Vegard’s law26 and experimental data.27 The supercell calculations (Table 7) reveal that the binary BaxCa1-x(NO3)2 complex is more stable (J5 mol %) than the BaxSr1-x(NO3)2 and BaxPb1-x(NO3)2 complexes as can be seen from Figure 4. In this respect, it is perhaps important to reflect the fact that Ca2+ ions are, under ambient conditions, likely to be very tightly bound to water ligands, reflecting the fact that Ca(NO3)2 is known to crystallize as a tetra-hydrate. However, the Ca-O potential derived here was based on an anhydrous Ca(NO3)2 structure which would not be likely to form under the process conditions involved in this study. This result is interesting in that it indicates that nonradioactive species such as Ca2+ could have the potential to incorporate during crystal growth with the potential to inhibit subsequent growth. Caution is needed though regarding the generality of this approach, given that the quality of crystals, upon the addition of a second cation into the Ba(NO3)2 lattice, is known to decrease.27 Examination of a tertiary system for a Ba(NO3)2 supercell doped with both Ca2+ and Sr2+ ions, BaxSr1-xCa--0.5(NO3)2 (where x ) 0.5-0.9) revealed (Figure 5) that the lower the concentration of Ba2+ (i.e., when x ) 0.5) in the tertiary system, the more stable the structure becomes. The data also reveals (Figure 5) an increased gradient for the trend line from Bax ) 50 (y ) -0.0009x2 + 0.4697x - 11351) to Bax ) 90 (-0.0021x2 + 0.2422x - 11194), implying that the dopant ions have a more destablising effect with higher concentrations of Ba2+ in the supercell, in particular for Sr2+. These results also support the

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Figure 11. Attachment energy calculations of Sr2+ and Ca2+ substitution at the {111} and {200} surfaces of Ba(NO3)2.

Figure 12. (Left) SEM image and (right) morphological sketch of Ba(NO3)2 precipitated with 10 mol % Sr(NO3)2 at 318 K at a heating/ cooling rate of 0.5 K min-1 in distilled water, clearly showing a dominant octahedral habit.

simulation of the binary system in that increasing the Ca2+ ions in the system appears to provide a more stable structure. 3.4. Morphological Simulation Results. Analysis of the structures of the Ba(NO3)2 and Sr(NO3)2 crystal structures using the BFDH19,20 analysis reveal a morphology dominated by prominent {111} and {200} forms,27,28 whose surface chemistry is illustrated in Figures 6 and 7, respectively. The {100} surface exhibits a fairly open structure dominated by strong in-plane interionic interactions in contrast to the more close-packed {111} surfaces where both in-plane and normal cation-anion interatomic interactions were found. From this, it can be concluded that cation substitution for Ba2+ would be likely to lead to an in-plane 2D contraction of the {100} surface layer. This effect would contrast to that of the {111} surfaces, for which the effect would be expected to have a more 3D character. The surfaces of both Ba(NO3)2 and Sr(NO3)2 are obviously very similar, although with differing interatomic distances (Table 8). The calculated attachment and surface energies of Ba(NO3)2 and Sr(NO3)2 are given in Table 9. The surface energies of both the {111} and {200} forms were found to decrease by an average of 16.3 and 14.5%, respectively, because of surface relaxation. The data revealed that the {111} face is slightly more morphologically important than the {200} face for Ba(NO3)2 and the opposite for Sr(NO3)2 on the basis of the surface energy calculation results. Figure 8 shows the Eatt predictions based on the surface relaxed structures for Ba(NO3)2 and Sr(NO3)2, respectively. The unrelaxed forms were found to be very similar, only with slightly smaller {200} faces for both Ba(NO3)2 and Sr(NO3)2. Table 9 gives ratios of the center to surface distances associated with the {200} and {111} forms of Ba(NO3)2 and Sr(NO3)2 predicted from, respectively, Eatt and Esurf calculations. Equilibrium morphologies, based on the calculated Esurf were found to be very similar to the growth morphology calculations; however,

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whereas Esurf was always found to decrease, Eatt was found to increase for the {111}surfaces and decrease for the {100} surfaces with an average magnitude of changes for Ba(NO3)2 and Sr(NO3)2 of -1.95 and -0.22%, respectively. The possibility of the attachment energy increasing or decreasing upon relaxation can be rationalized by noting that reducing the energy of region I during minimization is accomplished both by moving the growth slice normal to the surface (i.e., changing Eatt) or moving ions within the growth slice (changing Eslice and Eatt, where Eslice is the growth slice energy and equal to Elatt - Eatt). Therefore, a decrease in Eslice can compensate for an increase in Eatt and vice versa.29 Esurf and Eatt given in Table 9 are consistent with the cube-octahedral crystal morphologies experimentally observed.20 This was found to be the case regardless of whether the crystal surfaces were unrelaxed or relaxed in the calculations. Figure 9 shows a representative experimental morphology of a Ba(NO3)2 crystal prepared from solution which has crystallized. The image is dominated with crystals showing various forms of cube-octahedral habit as predicted by the morphological model. 3.5. Sr2+ Substitution at the Surface of Ba(NO3)2 {111} and {200} Faces. Sr2+ and Ca2+ substitution at the {111} and {200} faces clearly produce a destablizing effect as shown by both the defect-modified Esurf and Eatt calculations, with Figures 10 and 11 confirming these predictions. The dopant ion substitution was found to effect the {200} face to a greater extent than the {111} face. The Esurf and Eatt models show that the {111} face becomes increasingly more morphologically important over that of the {200} face and therefore is the crystal face that is more likely to be seen experimentally upon the addition of Sr2+ and Ca2+ into a Ba(NO3)2 solution. The difference in Esurf and Eatt between Ca2+ and Sr2+ ion incorporation at the surface of Ba(NO3)2 is negligible, although approaching 100% substitution at the Ba(NO3)2 {111} surfaces, Esurf of Sr2+ looks to be slightly less than Ca2+, indicating preferential incorporation. This is in contrast to the bulk substitution energies where Ca2+ was more energetically favorable for substitution in the Ba(NO3)2 crystal lattice over Sr2+. This may highlight the role that the M-O repulsion energies play in the surface substitution of Ba(NO3)2 with these ions, in that Sr2+ has a lower M-O bond repulsion energy than Ca2+ (Figure 2). Figure 12 confirms this prediction, showing a solution that contained 90 mol % Ba(NO3)2 and 10 mol % Sr(NO3)2 and crystallized, presenting crystals that have an enhanced development of the octahedral habit. 4. Conclusions An interatomic potential force field has been derived to successfully model the solid-state and surface properties of the crystalline forms of mono- and divalent metal nitrate phases. The potential has been successfully applied to predict divalent cation incorporation into the bulk Ba(NO3)2 lattice as well as to predict the morphologies of Ba(NO3)2 and Sr(NO3)2 and the influence of Sr2+ doping on the crystal morphology of Ba(NO3)2. It has been shown in both the Mott-Littleton and supercell point-defect calculations that Ca2+ incorporation into the Ba(NO3)2 lattice is favored over incorporation of Pb2+ and Sr2+. Negligible differences between the effects of Ca2+ and Sr2+ incorporation into the Ba(NO3)2 lattice below ∼6 mol % was found. The calculations reproduce the experimentally observed lattice constants for the substitution of Sr2+ into Ba(NO3)2 giving reliable predictions in defect calculations for other metal nitrates. Predicted crystal morphologies match well with several experimental results although these calculations do not rigor-

Hammond et al.

ously take into account the liquid medium, temperature or supersaturation effects. The Sr2+ incorporation at the {111} and {200} surfaces of Ba(NO3)2 show the {111} face becoming more morphologically important. It has also been highlighted that short-range M-O bond repulsion energies may play a role in the substitution of ions at the surfaces of Ba(NO3)2. It has also been shown experimentally that upon addition of Sr2+ into solution the {111} face is very much more prominent than the {200} face. Acknowledgment. The authors acknowledge the use of the EPSRC Chemical Database Service at Daresbury and thank Dr. Julian Gale for the GULP code used in this study. We are grateful to Nexia Solutions, Sellafield Ltd, and the EPSRC for the financial support of this work, which forms part of the PhD studies of M.J.O.30

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