Article pubs.acs.org/crystal
Toward Analysis of Structural Changes Common for Alkaline Carbonates and Binary Compounds: Prediction of High-Pressure Structures of Li2CO3, Na2CO3, and K2CO3 Pavel N. Gavryushkin,*,†,‡ Altyna Behtenova,†,‡ Zakhar I. Popov,§ Vladimir V. Bakakin,∥ Anna Y. Likhacheva,† Konstantin D. Litasov,†,‡ and Alex Gavryushkin#,⊥ †
Sobolev Institute of Geology and Mineralogy and ∥Nikolaev Institute of Inorganic Chemistry, Siberian Branch Russian Academy of Science, 630090 Novosibirsk, Russian Federation ‡ Novosibirsk State University, 630090 Novosibirsk, Russian Federation § National University of Science and Technology (MISIS), 119991 Moscow, Russian Federation ⊥ Department of Computer Science, The University of Auckland, Auckland 1010, New Zealand S Supporting Information *
ABSTRACT: The behavior of alkaline carbonates at high pressure is poorly understood. Indeed, theoretical and experimental investigations of the pressure induced structural changes have appeared in the literature only sporadically. In this article we use evolutionary crystal structure prediction algorithms based on density functional theory to determine crystal structures of high-pressure phases of Li2CO3, Na2CO3, and K2CO3. Our calculations reveal several new structures for each compound in the pressure range of 0−100 GPa. Cation arrays of all high-pressure structures are of the AlB2 topological type. The comparison of cation arrays of ambient and highpressure structures with that of binary A2B compounds indicates an analogy between high-pressure behavior of alkaline carbonates and alkaline sulfides (oxides, selenides, tellurides), which under compression go through the following series of phase transitions: anti-CaF2 → anti-PbCl2 → Ni2In → AlB2. All structures presented in this trend are realized in the high-pressure trend of alkaline carbonates, although some intermediary structures are omitted for particular compounds.
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INTRODUCTION
to the ambient phase of the heavier element compound. For example, according to these results γ-Cs2CO3 first transforms to γ-Rb2CO3 and then to γ-K2CO3. In the present work, we employ crystal structure prediction evolutionary algorithms based on density functional theory (DFT) to construct the high-pressure trend of alkaline carbonates. Furthermore, we employ topological analysis of predicted structures to show that the theoretical trend is consistent with that of various A2B binary compounds and satisfies the rule of high-pressure behavior described above.
Alkaline carbonates have wide industrial applications. While these compounds are not present in the Earth’s interior as separate phases, they could affect the processes of mantle melting, plume upwelling, and diamond growth. For example, adding a small amount of K2CO3 to mantle rocks decreases their melting temperature by several hundreds degrees.1,2 All three carbonates substantially decrease the energetic barrier of diamond growth.3 Since the range of practical applications of Rb2CO3 and Cs2CO3 is narrow we confine our investigation to the other three alkaline carbonatesLi2CO3, Na2CO3, and K2CO3. The high-temperature structural changes of alkaline carbonates have been investigated in detail and are well understood.4−6 However, almost nothing is known about the high-pressure behavior of these compounds. We are aware of only one experimental work on Li2CO37 and one theoretical work on crystal structure prediction of alkaline carbonates based on stochastic simulated annealing algorithms.8 Our analysis of these theoretical results shows that the obtained high-pressure structures contradict the common rule, according to which the highpressure phase of the lighter element compound is isostructural © 2016 American Chemical Society
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METHODS
Crystal structure prediction has been performed using evolutionary algorithms implemented in USPEX (Universal Structure Predictor: Evolutionary Xtallography) package.9−13 The number of structures in the population was equal to N+10, where N is the number of atoms in the unit cell. First generation was created randomly. 70% of the most energetically favorable structures of generation were used for production of the new generation by heredity (50%), lattice mutations (25%), and Received: December 19, 2015 Revised: August 15, 2016 Published: September 8, 2016 5612
DOI: 10.1021/acs.cgd.5b01793 Cryst. Growth Des. 2016, 16, 5612−5617
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permutations of atoms (25%). 20% of each generation was produced randomly. Local optimization has been performed in the framework of DFT with VASP (Viena Ab-initio Simulation Package) code,14,15 using the plane wave basis set and projector augmented wave method.16 Exchange-correlation effects have been taken into account in the generalized gradient approximation (GGA) using Perdew−Burke− Ernzerhof (PBE) functional.17 For the crystal structure search we used a plane-wave basis set cutoff of 520 eV and performed the BZ integrations using uniform Γ-centered k-point meshes with a k-point grid of spacing 2π × 0.025 Å−1. Iterative relaxation of atomic positions has been stopped when all forces were smaller than 0.005 eV Å−1. Calculations have been carried out for 0, 30, 60, and 90 GPa with 2, 3, and 4 formula units per unit cell. The temperature in all calculations was 0 K. Calculations with k-point grid of 2π × 0.025 A−1 within the Monkhorst−Pack scheme were used and cutoff energy equal to 520 eV were performed to determine the enthalpy-pressure dependence. To measure the dependence of our results on the choice of pseudopotential, we calculated the dependence of enthalpy on pressure for the most energetically favorable structures of K2CO3 with different types of LDA and GGA pseudopotentials supplied with VASP (Supporting Information). Our comparison of these dependencies shows that the phase transitions determined by PAW−PBE are also reproduced in the ultra soft potentials with local density approximations and generalized gradient approximations. The difference between the pressures of phase transition calculated with different potentials is up to 4 GPa (for the phase transition at 12 GPa). Phonon calculations were performed with PHONOPY,18 topological analysis of the structures−with ToposPro package.19−21 VESTA software22 was used for structure visualization.
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RESULTS To test the methodology we employ, the ambient γ-Li2CO3, γ-Na2CO3, and γ-K2CO3 structures have been predicted. We report that the atomic coordinates and unit cell parameters are in good agreement with the experimental values.23−25 Predicted structures and the dependencies between their enthalpies and the pressure are shown in Figure 1 and Figure 2, and the atomic coordinates and unit cell parameters in Table 1 and Supporting Information. The phonon dispersion curves (Figure 3) indicate the dynamical stability of all these structures. Li2CO3 shows the most simple high-pressure behavior among the three considered carbonates. The only phase transition to the P63/mcm structure at 8 GPa was revealed. No other transition was found in the investigated pressure range (up to 100 GPa) (Figure 4). This result is in a good agreement with the experimental data according to which γ-Li2CO3 transforms to the P63/mcm structure (called Li2CO3−HP in ref 7) at 10 GPa.7 Stochastic simulated annealing algorithms do not reveal any other transition except for the γ-Li2CO3 → P63/mcm either.8 The metastable structure Cm, which can be produced from P63/mcm by a slight shift of the hexagonal layers, was fixed in our calculations. This structure is more favorable than γ-Li2CO3 above 12 GPa but less favorable than P63/mcm. γ-Na2CO3 first transforms to the same hexagonal structure P63/mcm at 5 GPa and then to the P21/m structure at 35 GPa (Figure 2b, Figure 4). The P63/mcm structure was revealed by the stochastic simulated annealing algorithms8 as well; although according to the calculations, γ-Na2CO3 first transforms to Li2CO3-Type8 at 11.34 GPa and then to P63/mcm at 50.45 GPa. According to our calculations, Li2CO3-Type8 does not have a region of thermodynamic stability (Figure 2b). In addition to γ-Na2CO3, the Pmmn structure was found at the ambient pressure. The enthalpy of Pmmn structure is lower than the enthalpy of γ-Na2CO3, but the difference in the enthalpies decreases rapidly. At 0 GPa the difference is 0.1 eV, at 1 GPa 0.06 eV, and at
Figure 1. High-pressure structures Li2CO3-P63/mcm (a), Li2CO3-Cm (b), Na2CO3-Pmmn (c), Na2CO3-P63/mcm (d), Na2CO3-P21/m (e), K2CO3-P21/c (f), K2CO3-C2/c (g), K2CO3-P1̅ (h). Structures in upper and lower rows are shown in different (nearly perpendicular) orientations.
4 GPa 0 (Figure 2b). The lower enthalpy of Pmmn in comparison with γ-Na2CO3 is reproduced in calculations with all other types of pseudopotentials. Phonon calculations show that this phase is dynamically stable (Figure 3d). The lower enthalpy of Pmmnphase in comparison with γ-Na2CO3 (contradicting to the absence 5613
DOI: 10.1021/acs.cgd.5b01793 Cryst. Growth Des. 2016, 16, 5612−5617
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Figure 2. Pressure−enthalpy dependencies for (a) Li2CO3 (normalized on enthalpy of Cm), (b) Na2CO3 (normalized on enthalpy of P63/mcm), (c) K2CO3 (normalized on enthalpy of γ-K2CO3 (left) and P1̅ (right)).
Table 1. Atomic Coordinates and Unit Cell Parameters of Predicted Structures Li2CO3 atomic coordinates pressure (GPa)
space group
lattice parameters (Å, deg)
10
P21/m
a = 2.830 α = 90.00
b = 7.790 β = 98.54
c = 4.377 γ = 90.00
20
Cm
a = 4.459 α = 90.00
b = 7.696 β = 99.50
c = 7.553 γ = 90.00
30
P63/mcm
a = 4.354 α = 90.00
b = 4.354 β = 90.00
c = 4.880 γ = 120.00
species
x
y
z
Li1 C1 O1 O2 Li1 Li2 Li3 C1 C2 C3 O1 O2 O3 O4 O5 O6 Li1 C1 O1
0.815 0.566 0.683 0.340 0.388 −0.044 0.545 0.500 0.409 0.581 0.210 0.645 0.765 0.698 0.873 0.443 0.333 0.000 0.705
0.424 0.250 0.394 0.250 0.319 0.166 0.334 0.000 0.000 0.000 0.000 0.145 0.355 0.000 0.000 0.146 0.667 0.000 0.000
0.729 0.151 0.285 0.869 0.511 0.838 0.173 0.000 0.664 0.330 0.001 0.000 0.667 0.665 0.332 0.332 0.000 0.250 0.250
Na2CO3 atomic coordinates pressure (GPa)
space group
lattice parameters (Å, deg)
0
Pmmn
a = 3.630 α = 90.00
b = 5.169 β = 90.00
c = 8.339 γ = 90.00
20
P63/mcm
a = 4.785 α = 90.00
b = 4.785 β = 90.00
c = 5.510 γ = 120.00
40
P21/m
a = 2.734 α = 90.00
b = 4.707 β = 95.50
c = 7.384 γ = 90.00
species
x
y
z
Na1 Na2 C1 O1 O2 Na1 C1 O1 Na1 Na2 C1 O1 O2
0.250 0.250 0.250 0.250 0.250 0.333 0.000 0.269 0.625 0.523 0.007 0.072 0.199
0.250 0.750 0.250 0.032 0.250 0.667 0.000 0.000 0.250 0.250 0.250 0.516 0.250
0.582 0.085 0.243 0.321 0.087 0.000 0.250 0.250 0.368 0.027 0.732 0.185 0.584
K2CO3 atomic coordinates pressure (GPa)
space group
6
P21/c
a = 8.741 α = 90.00
lattice parameters (Å, deg) b = 5.856 β = 104.43
c = 6.789 γ = 90.00
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P1̅
a = 2.939 α = 90.304
b = 5.137 β = 95.48
c = 8.464 γ = 90.00
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species
x
y
z
K1 K2 C1 O1 O2 O3 K1 K2 C
0.424 0.096 0.752 0.358 0.122 0.735 0.013 0.091 0.489
0.591 0.900 0.844 0.279 0.251 0.066 0.750 0.753 0.253
0.232 0.289 0.999 0.956 0.032 0.986 0.532 0.877 0.761
DOI: 10.1021/acs.cgd.5b01793 Cryst. Growth Des. 2016, 16, 5612−5617
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Table 1. continued K2CO3 atomic coordinates pressure (GPa)
70
space group
C2/c
lattice parameters (Å, deg)
a = 8.559 α = 90.00
b = 4.428 β = 136.64
c = 8.084 γ = 90.00
species
x
y
z
O1 O2 O3 K1 C1 O1 O2
0.559 0.558 0.335 0.220 0.000 0.081 0.000
0.037 0.468 0.254 0.138 0.761 0.381 0.047
0.689 0.689 0.896 0.645 0.250 0.936 0.250
Figure 3. Phonon dispersion curves for (a) Li2CO3-P63/mcm at 30 GPa, (b) K2CO3-P1̅ at 30 GPa, (c) K2CO3-P21/c at 70 GPa, (d) Na2CO3-Pmmn at 0 GPa, (e) Na2CO3-P63/mcm at 20 GPa, and (f) Na2CO3-P21/m at 60 GPa.
itions decreases when atomic radius increases. At 53.5 GPa, P1̅ transforms to C2/c. The structures analogous to β-Na2CO3 and P63/mcm were also found in our calculations, but they do not have a region of thermodynamic stability. K2CO3-Type11 found by stochastic simulated annealing does not have a region of thermodynamic stability either (Figure 2c).
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DISCUSSION For alkaline carbonates, the classical description of crystal structures based on anion polyhedrons is complicated due to the presence of rigid CO3 groups and the low-symmetry atomic arrangement. The cation net approach4,26 is more fruitful in this case. In addition to making the structure description easier and clearer, this method allows us to find an analogy between structural changes of alkaline carbonates and binary A2B compounds. Ambient and high-pressure phases of alkaline carbonates are characterized by the following underlying nets: γ-Li2CO3 − antiCaF2, γ-Na2CO3 − Ni2In, γ-K2CO3 − Ni2In, Na2CO3-Pmmn − anti-PbCl2, all high-pressure polymorphs − AlB2. In all highpressure polymorphs each carbon atom is bonded through oxygens to 12 neighboring atoms of alkaline metal which altogether are arranged in the ideal or deformed hexagonal prism. The ideal hexagonal prism is realized for P63/mcm structures, while the deformed prism is realized for all other high-pressure structures. Different polymorphs are caused by different distortions of the prism. Two types of deformations can be distinguished. P21/m-Na2CO3 and P1̅-K2CO3 are representatives of one type and C2/c-K2CO3 of the other.
Figure 4. Comparison of high-pressure phase transitions of Li2CO3, Na2CO3, and K2CO3. Similar structures are marked by similar colors.
of Pmmn in both ambient and high-temperature experiments) can be explained by the incommensurately modulated character of the real γ-Na2CO3 structure.24 Incommensurate modulations are not taken into account in our calculations; they can decrease the overall energy of the structure and make the incommensurately modulated γ-Na2CO3 more favorable than Na2CO3-Pmmn, thus resolving the contradiction between the theory and the experiment. We leave it for future investigations to measure the effect of incommensurate modulations on the energy of the crystal structure of γ-Na2CO3. Three new phases have been found for K2CO3: P21/c, C2/c, and P1̅. The first structure can be produced from the second by a slight shift of CO3 triangles and transforms to it under optimization. The last, P1̅, structure is the structural analogue of Na2CO3-P2/m. The transition from γ-K2CO3 to P1̅ occurs at 12 GPa, while the transition between similar phases of Na2CO3 is at 22 GPa (Figure 4). This behavior is consistent with the common rule, according to which the pressure of phase trans5615
DOI: 10.1021/acs.cgd.5b01793 Cryst. Growth Des. 2016, 16, 5612−5617
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Present Address
Thus, we conclude that the high-pressure trend of alkaline carbonate is in the transformation of the cation array from anti-CaF2or Ni2In-type to AlB2-type, under compression (Figure 5).
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Department of Biosystems Science and Engineering, ETH Zürich (Swiss Federal Institute of Technology Zurich), Basel, 4058 Switzerland. Funding
The research was supported by the Russian Foundation for Basic Research through Grant No. 14−05−31051 and the Ministry of Education and Science of the Russian Federation Grant No. MK-3766.2015.15 under the program of the Ministry of Education and Science of the Russian Federation Project No. 14.B25.31.0032. The work of ZIP was partially supported by the Ministry of Education and Science of the Russian Federation in the framework of Increase Competitiveness Program of NUST “MISiS” (No. K2−2015−033).
Figure 5. Comparison of high-pressure trends of alkaline sulfides (Na2S) and alkaline carbonates (Li2CO3, Na2CO3, and K2CO3). Blue arrows−theoretical data, green arrows−experimental data.
Notes
Our comparison of the described high-pressure behavior of alkaline carbonates with that of various A2B compounds indicates a similarity between high-pressure trends of alkaline carbonates and alkaline sulfides, oxides, selenides, and tellurides.27−29 Under compression these binary compounds completely or partially go through the following series of phase transitions: anti-CaF2 → anti-PbCl2 → Ni2In → AlB2 (Figure 5b). For example, alkaline sulfides (Li2S, Na2S, K2S, Rb2S, and Cs2S) under compression of up to 16 GPa transform from anti-CaF2- to anti-PbCl2- and then to Ni2In-type.28 Ab initio calculations30 predict that under further compression they will adopt the AlB2-type structure. The difference between alkaline carbonates and binary compounds is that for a particular alkaline carbonate some chains of the full trend are absent. For instance, Li2CO3 directly transforms from antiCaF2- to AlB2-type, without adopting anti-PbCl2- and Ni2Intype structures. This absence of chains is the main obstacle in the inference of high-pressure trend. When all chains are present, the high-pressure trend of alkaline carbonates is the same as the trend of alkaline sulfides, which satisfies the common rule described in the Introduction. The analogy of these two trends is supported by the finding of anti-PbCl2-type structure of Na2CO3. This structure occupies the intermediate place between anti-CaF2 and Ni2In-type structures in both trends (Figure 5). A comparison of our results produced using evolutionary algorithms with the results obtained using stochastic simulated annealing8 shows that both techniques determine the AlB2 as the final topological type of Li2CO3, Na2CO3, and K2CO3 at compression. In the case of stochastic simulated annealing, P63/mcm, Li2CO3-Type8, and K2CO3-type-11 belong to this topological type. The first two structures are of ideal AlB2-type. The last structure can also be described as being a very deformed structure of AlB2-type, with distances from the C atom to the 12 closest K atoms varying in the range of 2.66−4 Å.
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The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We thank the Information Technology Centre of Novosibirsk State University for providing access to cluster computational resources.
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ASSOCIATED CONTENT
S Supporting Information *
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.cgd.5b01793. Dependencies of enthalpies on pressure for predicted structures of K2CO3 for different pseudopotentials and structural data on metastable polymorphs (PDF)
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REFERENCES
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. 5616
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