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Concentration of charge carriers, migration and stability in Li3OCl solid electrolytes Rodolpho Mouta, Maria Águida B Melo, Eduardo Moraes Diniz, and Carlos William de Araujo Paschoal Chem. Mater., Just Accepted Manuscript • Publication Date (Web): 27 Nov 2014 Downloaded from http://pubs.acs.org on November 28, 2014

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Chemistry of Materials

1

Concentration of charge carriers, migration and stability in Li3OCl solid electrolytes RODOLPHO MOUTA, MARIA ÁGUIDA B. MELO, EDUARDO M. DINIZ AND CARLOS WILLIAM A. PASCHOAL* DEPARTAMENTO DE FÍSICA, UNIVERSIDADE FEDERAL DO MARANHÃO, SÃO LUÍS, MARANHÃO, BRAZIL. KEYWORDS: antiperovskites, Li3OCl, solid electrolytes, lithium ion batteries

ABSTRACT: Recently a new family of lithium-rich antiperovskites, Li3OA (A = halogen), which presents superionic conductivity, emerged as a promising both safe and commercially applicable solid electrolyte for lithium ion batteries. In this paper we employed classical atomistic quasi-static calculations to obtain the concentration of lithium vacancies and interstitials for stoichiometric samples of Li3OCl. The obtained concentrations as well as vacancy and interstitial migration energies reinforced the assumption that vacancies are the charge carriers in both stoichiometric and divalent metal doped samples, but raise the possibility that the high ionic conductivity in LiCl-deficient samples are in fact driven by interstitials, in opposition to what has been assumed so far. The Li3OCl stability at higher temperatures was investigated based on Gibbs energies of decomposition from 0 K up to 550 K. They are negative in the whole temperature range, which suggests that there exists a high Gibbs energy barrier between Li3OCl and starter materials preventing decomposition.

1. INTRODUCTION Although the use of lithium ion batteries is now widespread, issues concerning safety are still an obstacle to largescale use in plug-in hybrid and pure electric vehicles, owing to flammable carbonates contained in the liquid electrolytes used. While this risk is low for cell phones, in which a single cell is commonly used, in a vehicle hundreds of cells are used turning the risk relevant1,2. One of the most promising solutions to reduce these problems is the replacement of current liquid electrolytes for solid ones. Although the ionic conductivity of lithium-containing solid electrolytes is still low for commercial applications, several solid Li-based electrolytes have been investigated currently3–15. Recently, Zhao and Daemen16 obtained a new promising family of superionic conductors Li3OA (A = halogen) for solid electrolytes to be used in lithium ion batteries. These lithiumrich superionic materials possess antiperovskite structure ABX3 (A = Cl-, Br-, I-; B = O2-; X = Li+) and have attracted much attention2,13,16–21 for presenting high ionic conductivity16 even at room temperature (> 10-3 S/cm), low electronic conductivity2, low activation enthalpy, wide electrochemical window (>5 eV)2,17,18, good cyclability2, structural stability up to ca. 550 K2,16, lightweight and low cost16. Also, they are nonflammable, are recyclable and environmentally friendly, what makes them suitable to be applied commercially2,16, even in lithium-air batteries that use metallic lithium anode2,21. These materials seem to be more promising than other perovskites, as (LiLa)TiO3 (which presents a room temperature conductivity of 10-3 S/cm 22, but is unstable in contact to metallic lithium23), for instance. Many tailoring possibilities were presented for this family of materials, as halogen mixing, doping with aliovalent metals and non-stoichiometry2,16. Calculation of migration energies in this kind of solid electrolytes is a powerful tool to determine what kind of tailoring (synthesis procedure) must be per-

formed in order to increase the conductive properties. In this scenario, classical atomistic quasi-static calculations are currently a well-established tool and very reliable approach to obtain insights about materials candidates for use in lithium ion batteries3,14,15,24–33. Thus, we used this approach to calculate the concentration of charge carriers in equilibrium and migration energies for both vacancy and interstitial migration process in Li3OCl (LOC), since these conduction mechanisms were proposed as possibly happening in LOC. Calculations cover a wide temperature range to investigate the temperature dependent defect formation Gibbs energy, as well as the migration energy of these defects. Although experiments show that Li3OA is stable in relation to the decomposition in and 2,16 starter materials, ab initio calculations at 0 K actually point in the opposite direction17,18. Zhang et al suggested that the entropy may be responsible for keeping the compound stable at high temperatures, which is also probed in this paper. 2. COMPUTATIONAL METHODS We carried out classical atomistic quasi-static calculations as implemented in the general utility lattice program (GULP)34–36. We optimized Gibbs energy of bulk structure for several temperatures at ambient pressure considering the so-called zero static internal stress approximation (ZSISA), which permits the cell parameters to change, although the ion positions are kept fixed. In this case, it was useful because in this structure the ions are fixed by symmetry. We used GULP’s default optimizer based on the Newton-Raphson method, in which the hessian matrix is initially calculated analytically, then subsequently updated using Broyden– Fletcher–Goldfarb–Shanno (BFGS) algorithm, being recalculated when necessary.

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2 Calculated was composed by two contributions: (i) a static one, which consists of the static lattice enthalpy; (ii) a vibrational one, which consists of the enthalpy and entropy associated to phonons. The static contribution is based on the one-body and two-body interactions. The ionic two-body interactions, aside from the electrostatic interaction, was modeled by a Buckingham potential for short-range interactions that is given by = − − (1) with , and being fitting parameters, while is the interionic distance. In this equation, the first term is due to the Pauli repulsion and the second one is due to the van der Walls interaction. The one-body contribution consist of the elastic interaction between core and shell of each ion, once and were modeled by the shell model proposed by Dick-Overhauser37, in which the ion is represented as a core (with charge ) connected to a massless shell (with charge by a harmonic potential (of elastic constant ), to take into account the ionic polarizability. Since has low polarizability, it was modeled as a rigid-ion. Ewald sum was used to evaluate the energy due to the electrostatic interaction as well as that one associated to the van der Waals interactions, while a cutoff of 12 Å was used to the Pauli interaction. We did not use any cutoff to the van der Waals interaction once at 12 Å this interaction was not null yet. Defects were modeled by Mott-Littleton method38,39. This method consists in dividing the surroundings around the defect in two regions: the first one is a sphere (region I), in which the defect is in the center and all interactions are calculated explicitly; the second one is treated as a continuous (region IIb) and takes into account the sublattices polarization. This two regions are connected by an intermediate spherical region (region IIa) concentric with the region I, in which the ions are in harmonic potential wells, but allowed to relax. We used radii of 16.5 Å for region I and 18.5 Å for region IIa. All defect calculations were performed considering the rational function optimizer (RFO). This optimization method guarantees that a minimum is achieved by the imposition of the absence of imaginary phonon frequencies in the MottLittleton region I for the ground state configurations. However, saddle points were found imposing the presence of exactly one imaginary eigenvector. All calculated gradient norms were lower than 2 ⋅ 10% &/Å. The Monkhorst-Pack40 k-point grid used to calculate the vibrational properties was 4 x 4 x 4 for Li3OCl, while for LiCl and Li2O we used a 3 x 3 x 3 grid. 3. RESULTS AND DISCUSSION 3.1 Reliability of the model To model LOC we used the interionic and shell model parameters listed in Tables 1 and 2. In Supporting Information we give a brief description of the procedure that we employed to obtain these parameters (the general aspects of derivation of empirical potentials has already been described elsewhere41). This model reproduces LOC’s room-temperature structural properties very well, as can be observed in Table 3. Our parameterization is undoubtly adequate to model LOC, since it reproduces the experimental lattice parameter of LOC and at room temperature and of for two temperatures available in literature (293 K and 873 K). It is important to

consider the optimization at different temperatures and of the basic starter materials, because the defects distort the neighboring ion configurations, so that interactions must be well described not only at equilibrium distances between ions, but at any distance. Table 1. Buckingham potential parameters.

()*+,*-)

a c

/&

22764.30003 5145.2755 433.2627 421.0366 360.5269

− − − − −

/Å

0.149003 0.30660 0.31384 0.33640 0.16098

/&Å

13.1857 20.5238 0.000 0.000 0.000

From Catlow45. b For , it was used 99 = 97.328 &Å . For , it was used :;:; = 170.068 &Å .

Table 2. Shell model and rigid-ion parameters. (-)

/||

/&Å − 593.716 39.444

− −2.183 −2.535

/|| 1.000 0.183 1.535

Furthermore, the adopted potential model fitted very well the static dielectric constants of and , as it is shown in Table 3, since a good fitting of dielectric properties is important to accurate defect calculations42. A remarkable agreement between experimental and calculated data can be also observed in Table 3. Table 3. Comparison between calculated and experimental static dielectric constants (=>) and lattice parameters (+). All unit cells are cubic and + is the only free parameter. Property +ABC

+ ABC =>

FD;F

=>FD;F a

293 ?

873 ?

4.616

4.683 -

4.612D 8.06A

Ref 46 ;

8.13 b

Ref 47 ;

@

4.689D

5.1295E

3.9070F , 3.9084H

9.33

11.05I 10.95

8.39

c

Ref 13 ;

5.1276

d

3.9069 -

Ref 20 ; e Ref 48 ; f Ref 49

In addition, the calculated temperature-dependent LiCl’s linear thermal expansion coefficient of is very well reproduced in a large temperature range, as seen in Figure 1 (see dark blue solid line in comparison with crosses). Furthermore, for LOC, there is a good agreement at high temperatures between our calculated coefficient and that obtained by for Zhang et al 17. Once the empirical parameters had been obtained, we calculated the temperature dependence of the vibrational specific heat at constant volume as a consistency check of thermal and vibrational behaviors. An excellent agreement with both Debye’s (at low temperature limit) and Dulong-Petit’s laws (at high temperature limit) was found, as shown in Figure 2, endorsing the overall reliability of our model, including its structural, dielectric, thermal and vibrational aspects. All these features give us confidence that our model reproduce both structural and dielectric properties of LOC and starter materials for several temperatures as well as the different interionic distances, being thus suitable for defect calculations.


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3 electrostatic potential energy, which corresponds to most of the internal energy in ionic crystals, is directly proportional to its charge. The absence of an ion shall then increase the internal energy proportionally to the charge of that ion. Table 4. Gibbs energies (in eV) of charged point defects at 0, 300 and 550 K. Defect

Li+ vacancy O2- vacancy Cl- vacancy Interstitial Li+

Figure 1. Dependence on temperature of linear thermal expansion coefficients. Solid curves indicate the coefficients calculated in this paper. The crosses and the dashed curves are experimental data from (a) ref. 50, (b) ref. 51 and (c) ref. 52, respectively. Constant dotted lines indicated the theoretical ab initio values from (d) ref. 2 and (e) ref 17.

KrögerVink notation S QR Q9⋅⋅ ⋅ Q:; ⋅

0K

300 K

550 K

5.3969

5.3898

5.3743

24.5033

24.3617

24.1071

5.2727

5.2785

5.2864

-2.2232

-2.2702

-2.3544

We also observed that the Gibbs energy of formation of a Cl- vacancy slightly increases with the temperature and the opposite happens with the remaining defects. This leads to a negative entropy of formation of a Cl- vacancy, since J = −K ⁄KL C , (2) but this is not an issue, as Cl- vacancies are always created along with another charge compensating defect, whose entropies of formation compensate these negative values. The Gibbs energy of an interstitial Li+ listed in Table 4 corresponds to the only stable configuration found after a deep search among several possible positions. All other configurations presented at least one imaginary frequency mode inside the Mott-Littleton region 1. To achieve the stable interstitial position, Li+ was initially placed in Wyckoff site 12h (0.5,x,1) with x N 0.25, near a Li+ ion in the corner of the OLi6 octahedron. During optimization, the Li+ ion that was formerly in the octahedron corner is pushed away by electrostatic repulsion, leading to a dumbbell configuration, in which both Li+ ions are in a 12h site, symmetrically displaced from the octahedron corner, as shown in Figure 3.

Figure 2. Calculated temperature-dependent specific heat at constant volume (green spheres). The red line shows Debye’s low temperature limit, corresponding to Debye’s temperature OP = 451.07 ?, and the blue one is Dulong-Petit’s high temperature limit with ) = 5 (number of ions in unit cell). The inset shows the typical L @ Debye model behavior.

3.2 Intrinsic charged point defects We investigated vacancies of Li+, O2- and Cl-, as well as + Li interstitials, in the temperature range from 0 up to 550 K as intrinsic charged defects in LOC. Gibbs energies at selected temperatures are shown in Table 4. We notice that interstitials have negative values of Gibbs energy while vacancies have positive values as expected, since the addition of an ion to the crystal lowers the already negative lattice energy (energy is proportional to the dimensions of the crystal) and the removal of an ion has the opposite effect. The results show that the greater the absolute value of the vacancy charge, the greater the change in lattice Gibbs energy associated to the creation of it. Thus, Li+ and Cl- vacancies have rather close values, while Gibbs energy of formation of a O2- vacancy is considerably greater. This is explained by the fact that the contribution of a certain ion for the total lattice

Figure 3. Optimized configuration achieved when an interstitial Li+ is inserted in LOC. Full grey lines correspond to undistorted structure, while dotted blue lines connect the ions in the distorted structure. Blue, cyan and red ions are Li+, Cland O2-, respectively.

This result is in complete agreement with dumbbell configuration obtained by Emly et al 18. The distance 2d between the two Li+ ions in the (001) plane (see Figure 3) increases slightly with temperature, as shown in Figure 4. However, it increases slower than the lattice parameter, so that the “dis-



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4 tance” in fractional coordinates decreases when temperatures is raised.

migration of Li+ and Cl- ions to the crystal’s surface, giving rise to formation of a LiCl phase there and to Li+ and Cl- vacancies in the bulk, assuming that these ions have the necessary mobility. Therefore, Li+ vacancies must be the charge carriers in pristine @ samples. Frenkel defects, on the other hand, present the highest Gibbs energy among all four neutral defects, resulting in a very low concentration of interstitials in pristine samples.

Figure 4. Dependence on temperature of half of the distance between the two Li+ ions in Figure 3. 3.3 Intrinsic neutral compound defects Based on the formation Gibbs energy of intrinsic charged point defects and lattice Gibbs energies, we calculated the temperature dependent formation Gibbs energy of selected neutral compound defects. The reaction of formation of each one of the four investigated defects and the corresponding Gibbs energies are given by: (a) Li+ Frenkel T S (3) R ⟶ QR V ⋅ , X S ⋅

; (4) R = Q V W R (b) Schottky T S T ⋅ 3R V 9T V :; ⟶ 3QR V Q9⋅⋅ V Q:; V @ , (5) S ⋅⋅ ⋅

Z = 3QR V Q9 V Q:; V @ ; (6) (c) Li2O Schottky T S (7) 2R V 9T ⟶ 2QR V Q9⋅⋅ V , Z S ⋅⋅

R = 2Q V Q V ; (8) 9 R [9 (d) LiCl Schottky

T S T ⋅ (9) R V :; ⟶ QR V Q:; V , ⋅ ′ Z (10) R :; = \Q V Q ^ V ; In the above equations, the Kröger-Vink notation was T used43. For instance, according to this notation, R is a Li+ ion + S in its proper position in the crystal, QR is a Li vacancy (which has a charge -|e|), ⋅ is an interstitial Li+ (which has a charge |e|) and @ is a molecule that was placed on crystal’s S surface. Accordingly, QR V ⋅ is the Gibbs energy of formation of a Li+ vacancy plus a Li+ interstitial and @ is the lattice Gibbs energy of @ per unit formula. We adopted the usual assumption that the lattice energy per unit formula is the same for cells in the bulk and in the surface, thus bulk values were considered. Figure 5 shows the temperature dependent formation Gibbs energy (per point defect) of the four neutral defects investigated. We observe that all Gibbs energies decrease when temperature is raised, leading to positive entropies of formation. From all, LiCl Schottky defect presents the lower formation Gibbs energy per defect in all the temperature range calculated (0 – 550 K) and it has the energy significantly lower than the others, implying this is the only relevant neutral compound defect in pristine samples. It corresponds to the

Figure 5. Temperature behavior of Gibbs energy (per point defect) of the four basic lithium-containing neutral defects calculated.

3.4 - Concentration of lithium vacancies and interstitials LiCl Schottky defect, as the other three compound defects investigated, is thermally activated. Thus, its concentration, i. e., the ratio between the number of defects and the number of @ unit formula, depends on temperature. This dependence takes the following form (see Supporting Information): Z R :; (11) _ = √3 exp − , 2 L so that a certain degree of non-stoichiometry shall occur: (12) @ ⟶ @d ed V _ . Figure 6 shows the dependence on temperature of _, which is also the concentration of Li+ vacancies created by this defect (ratio between the number of them and the number of @ unit formula). At room temperature, we observe that the concentration of Li+ vacancies is of the order of 10ef , reaching the upper value of 1.1 ⋅ 10g immediately before the melting point (550 K). However, Cl- ions are expected to have low mobility, especially at low temperatures, so that the Cl- ions that migrated to surface at temperatures near the melting point cannot return to structure at lower temperatures. For local charge neutrality reasons, the Li+ ions do not return either, staying in the LiCl phase at surface. Therefore, the concentration of Li+ vacancies must be constant and of the order of 10g even at low temperatures. The calculated concentrations of Li+ vacancies owing to Schottky and Li2O Schottky defects are both lower than 10e in the entire range of temperatures (see Supporting Information), so that they are irrelevant in comparison with the LiCl Schottky defect.


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5 of 0.310 eV obtained by Emly et al using ab initio calculations at this temperature18.

Figure 6. Temperature dependence of equilibrium concentration of Li+ vacancies owing to LiCl Schottky defects. See eq. (12)

We calculated that the concentration of interstitials due to Frenkel defects, on the other hand, does not surpass 10e@ , even at high temperatures, so that they cannot account for superionic conductivity neither in pristine nor in doped samples. These values are rather low and are negligible in comparison with the amount of defects created by doping or nonstoichiometry during the synthesis process2,16,20. Therefore, in doped or significantly non-stoichiometric samples the concentration of thermally activated Li+ vacancies or interstitials shall be virtually irrelevant. In doped samples with divalent metals, Li+ vacancies are basically the only possible charge compensating defects and the concentration of them will be ruled by the doping degree. In samples in which the synthesis process originated a degree of LiCl deficiency, on the other hand, interstitials may possibly be created as a charge compensating mechanism, so that Li+ vacancies may even not be the defect type in larger amount, and this should be investigated elsewhere. The formation enthalpy of LiCl Schottky defects at 0 K obtained is 0.93 eV. In the range 300 – 550 K, an apparent (the actual value depends on temperature) constant enthalpy of 1.01 eV is found when we perform a linear fit in an Arrhenius plot of the concentration of LiCl Schottky defects. The formation enthalpy of Frenkel defects at 0 K is 1.59 eV, while the apparent enthalpy in the range 300 – 550 K is 1.62 eV, which is somewhat lower than the value of 1.94 eV reported by Emly et al from ab initio calculations18. 3.5 Vacancy and interstitial lithium ion migration Lithium vacancies and interstitials have two migration mechanisms each, and all of them were investigated here. There are two routes for vacancies (one short and one long), as it is shown in Figure 7. While the migration Gibbs energy by the long route is high enough to make it unlikely (> 1.00 eV), the short route has a rather low value, going from ca. 0.290 eV at 0 K to ca. 0.245 eV before the melting point (550 K), as it is shown in Figure 8. Our value at 0 K is very close to the value

Figure 7. The two routes for vacancy migration.

Figure 8. Temperature behavior of Gibbs migration energy for interstitials at (001) and (002) planes and vacancies. Green and blue curves refer to Gibbs energy and enthalpy of migration, respectively.

There are two main mechanisms for interstitial migration, which are shown in Figure 9. One is roughly a rotation of two lithium ions around one corner of the octahedron, at the plane (001); the other is roughly a group rotation of three lithium ions around the octahedron center, at the plane (002). The migration energy by the last mechanism (~ 0.133 eV) is almost half of the energy by the first one (~ 0.255 – 0.260 eV). This large relative difference implies that interstitial migration occurs more frequently at (002) planes, especially at low temperatures. Figure 10 shows that, before the melting point, for each interstitial migration taking place in plane (001), nearly 10 occur in plane (002). At room temperature this proportion increases to over 90/1, reaching 1000/1 at 200 K and 106/1 at 100 K (both not shown in Figure 10). Near 0 K, the probability of the migration to occur in the (002) plane is tens of orders of magnitude higher than in the (001) plane, making the last mechanism virtually non-existent. Although the value of 0.410 eV for the migration at the plane (001) obtained by Emly at al using ab initio calculations



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6

Figure 9. Interstitial migration mechanisms at planes (001) and (002). Configurations b and e are saddle points, a and d are initial configurations, c and f are final configurations. All of them are optimized configurations. at 0 K18 is higher than the calculated here, their value of 0.145 eV for migration at the plane (002) is in close agreement to our value. Besides, the qualitative feature that the mechanism at the plane (002) is the primary one is also in agreement with their results.

Figure 10. Probabilities ratio of interstitial migration in planes (002) and (001). As Frenkel defects have high energy of formation, Li+ intersti-

tials cannot exist as charge carriers in a relevant amount, so that both in pristine (where vacancies are the charge carriers, created by LiCl Schottky defects) and doped samples (where vacancies are the charge carriers, created as charge compensating defects) the enthalpy of migration shall be greater than 0.30 eV (enthalpy of migration of a Li+ vacancy by the short route) above room temperature. However, in LiCl-deficient samples, charge compensating mechanisms may give rise to Li+ interstitials formation, which must be investigated. In the case in which interstitials are charge carriers, the observed enthalpy of migration might be ca. 0.13 eV, which is very close to the value of 0.1 eV obtained from experimental data44. This is a strong indicative that the charge carriers in LiCl-deficient samples are in fact interstitials, and not vacancies – the opposite of what has been so far assumed. Thus, our results are completely succefull to reproduce the experimental data and endorse ab initio calculations at 0 K performed by Emly et al18. 3.6 - Stability with respect to decomposition Previous calculations17,18 obtained a negative value for the LOC’s decomposition enthalpy into LiCl and Li2O, what could indicate instability. Nevertheless, these calculations were performed at 0 K, so that Zhang et al 17 considered the possibility of @ be stabilized by entropy at room temperature.


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7 Therefore, we calculated the LOC’s decomposition Gibbs energy in the temperature range from 0 K to 550 K, which is shown in Figure 11. This calculation is important because Gibbs energy, and not enthalpy, is the most appropriate thermodynamic potential to determine the stability of a system regarding a process. In addition, Gibbs energy takes entropy into account, which allows us to probe if entropy is the responsible for LOC’s stability at room temperature. For completeness, the enthalpy was also calculated from Gibbs energy. The decomposition reaction and the associated Gibbs energy and enthalpy are given by: (13) V ⟶ @ , (14) i,. = @ − − , (15) ji,. = j@ − j − j ; where j is, for instance, the lattice enthalpy of per unit formula and @ has the same meaning as in equation (6).

The vacancy migration enthalpy obtained is greater than 0.30 eV above room temperature, while the enthalpy of interstitial migration is as low as 0.133 eV. Despite this low value of interstitial migration, the ionic conduction shall be due to vacancy migration, both in pristine and in divalent metal doped samples, since the interstitials concentration is very low in comparison to vacancies concentration.

Figure 12. Expected Gibbs energy barrier between reactants

Figure 11. Temperature dependence of Gibbs energy and enthalpy for decomposition of @ in and .

It can be observed that the Gibbs energy remains negative in the whole temperature range, which a priori indicates instability. However, experimental studies2,16,21 show that @ presents good stability, so there must be a high Gibbs energy barrier separating the initial and final configurations during synthesis process, which prevents the decomposition. This barrier is pictorially illustrated in Figure 12. The fact that e is greater than > and a yet higher energy has to be reached during synthesis implies that a large amount of extra energy is required for the synthesis to occur, in agreement with the high temperature (above the melting point of LOC) or high pressure experimental procedures employed2,13,16,20. 4. CONCLUSIONS In this paper we carried out atomistic classical calculations of @ (LOC) antiperovskites based on a new set of potentials and shell model parameters that present remarkable structural, dielectric, thermal and vibrational reliability in modeling LOC, as well as its starter materials, and , used to obtain LOC by solid state reaction. We showed that LOC is metastable not only at 0 K, but at the whole range of temperatures up to 550 K. In pristine crystals, we found that vacancies shall be the charge carriers, created by LiCl Schottky defects, and their concentration is ca. 10g for all temperatures. In those crystals, Frenkel defects have rather high formation energies, so that the interstitials concentration shall be lower than 10e@ at any temperature.

(possessing Gibbs energy > ) and @ (with Gibbs gy e ). In both synthesis and decomposition, the same energy should be reached for the processes occur.

However, in LiCl-deficient samples, charge compensating mechanisms may give raise to interstitials in a concentration that can easily surmount 10g . In this scenario, the ionic conduction is likely to be driven by interstitial migration, which is endorsed by the experimental value of ~0.1 eV for the activation enthalpy. In summary, the present investigation endorsed the fact that the charge carriers in stoichiometric and divalent metal doped samples are vacancies, but raises the possibility that an interstitial mechanism is responsible for the high ionic conductivity in LiCl-deficient samples, in opposition to what has been assumed so far. This hypothesis should be further investigated.

ASSOCIATED CONTENT Supporting Information. Expressions for the dependence of vacancies and interstitials concentration on temperature are derived in the supporting information file. We also provide the procedure employed to obtain the parameters of our atomistic model and a prediction of Li3-0.5OCl1-0.5 structure, comparing to the corresponding structure that Emly et al18 obtained using DFT calculations.

AUTHOR INFORMATION Corresponding Author * C. W. A. Paschoal, [email protected], [email protected]

Author Contributions The manuscript was written through contributions of all authors.



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8 ACKNOWLEDGMENT

(23)

The authors acknowledge Dr J. Gale for permitting the use of GULP code and the Brazilian funding agencies CNPq, FAPEMA and CAPES for financial support. R. Mouta thanks R. M. Almeida for helpful suggestions on the manuscript.

(24) (25) (26)

REFERENCES (1)

(2) (3) (4) (5) (6)

(7)

(8) (9)

(10) (11) (12) (13) (14) (15)

(16) (17) (18) (19) (20) (21) (22)

Choi, N.-S.; Chen, Z.; Freunberger, S. A.; Ji, X.; Sun, Y.-K.; Amine, K.; Yushin, G.; Nazar, L. F.; Cho, J.; Bruce, P. G. Angew. Chem. Int. Ed. Engl. 2012, 51, 9994–10024. Braga, M. H.; Ferreira, J. A.; Stockhausen, V.; Oliveira, J. E.; El-Azab, A. J. Mater. Chem. A 2014, 2, 5470. Armstrong, A. R.; Lyness, C.; Panchmatia, P. M.; Islam, M. S.; Bruce, P. G. Nat. Mater. 2011, 10, 223–229. Chen, R.-J.; Huang, M.; Huang, W.-Z.; Shen, Y.; Lin, Y.-H.; Nan, C.-W. J. Mater. Chem. A 2014, 2, 13277. Sahu, G.; Rangasamy, E.; Li, J.; Chen, Y.; An, K.; Dudney, N.; Liang, C. J. Mater. Chem. A 2014, 2, 10396. Bernuy-Lopez, C.; Manalastas, W. J.; Lopez del Amo, J. M.; Aguadero, A.; Aguesse, F.; Kilner, J. a. ChemInform 2014, 45, no – no. Gao, X.; Fisher, C. a. J.; Kimura, T.; Ikuhara, Y. H.; Moriwake, H.; Kuwabara, A.; Oki, H.; Tojigamori, T.; Huang, R.; Ikuhara, Y. Chem. Mater. 2013, 25, 1607–1614. Jalem, R.; Yamamoto, Y.; Shiiba, H.; Nakayama, M.; Munakata, H.; Kasuga, T.; Kanamura, K. Chem. Mater. 2013, 25, 425–430. Kaib, T.; Bron, P.; Haddadpour, S.; Mayrhofer, L.; Pastewka, L.; Järvi, T. T.; Moseler, M.; Roling, B.; Dehnen, S. Chem. Mater. 2013, 25, 2961–2969. Key, B.; Schroeder, D. J.; Ingram, B. J.; Vaughey, J. T. Chem. Mater. 2012, 24, 287–293. Monconduit, L. J. Phys. Chem. C 2014, 118, 10531–10544. Sarkar, S.; Mitra, S. J. Phys. Chem. C 2014, 118, 11512–11525. Reckeweg, O.; Blaschkowski, B.; Schleid, T. Zeitschrift für Anorg. und Allg. Chemie 2012, 638, 2081–2086. Schroeder, M.; Eames, C.; Tompsett, D. A.; Lieser, G.; Islam, M. S. Phys. Chem. Chem. Phys. 2013, 15, 20473–20479. Clark, J. M.; Eames, C.; Reynaud, M.; Rousse, G.; Chotard, J.N.; Tarascon, J.-M.; Islam, M. S. J. Mater. Chem. A 2014, 2, 7446. Zhao, Y.; Daemen, L. L. J. Am. Chem. Soc. 2012, 134, 15042– 15047. Zhang, Y.; Zhao, Y.; Chen, C. Phys. Rev. B 2013, 87, 134303. Emly, A.; Kioupakis, E.; Van der Ven, A. Chem. Mater. 2013, 25, 4663–4670. Schroeder, D. J.; Hubaud, A. A.; Vaughey, J. T. Mater. Res. Bull. 2014, 49, 614–617. Zhang, J.; Han, J.; Zhu, J.; Lin, Z.; Braga, M. H.; Daemen, L. L.; Wang, L.; Zhao, Y. Inorg. Chem. Commun. 2014, 48, 140–143. Lü, X.; Wu, G.; Howard, J. W.; Chen, A.; Zhao, Y.; Daemen, L. L.; Jia, Q. Chem. Commun. (Camb). 2014, 50, 11520–11522. Inaguma, Y.; Liquan, C.; Itoh, M.; Nakamura, T.; Uchida, T.; Ikuta, H.; Wakihara, M. Solid State Commun. 1993, 86, 689– 693.

(27) (28) (29) (30) (31) (32) (33) (34) (35) (36) (37) (38) (39) (40) (41) (42) (43) (44)

(45) (46) (47)

(48) (49) (50) (51) (52)

Stramare, S.; Thangadurai, V.; Weppner, W. Chem. Mater. 2003, 15, 3974–3990. Islam, M. S.; Driscoll, D. J.; Fisher, C. A. J.; Slater, P. R. Chem. Mater. 2005, 17, 5085–5092. Fisher, C. A. J.; Hart Prieto, V. M.; Islam, M. S. Chem. Mater. 2008, 20, 5907–5915. Gardiner, G. R.; Islam, M. S. Chem. Mater. 2010, 22, 1242– 1248. Islam, M. S. Philos. Trans. A. Math. Phys. Eng. Sci. 2010, 368, 3255–3267. Armstrong, A. R.; Kuganathan, N.; Islam, M. S.; Bruce, P. G. J. Am. Chem. Soc. 2011, 133, 13031–13035. Tripathi, R.; Gardiner, G. R.; Islam, M. S.; Nazar, L. F. Chem. Mater. 2011, 23, 2278–2284. Clark, J. M.; Nishimura, S.; Yamada, A.; Islam, M. S. Angew. Chem. Int. Ed. Engl. 2012, 51, 13149–13153. Fisher, C. A. J.; Kuganathan, N.; Islam, M. S. J. Mater. Chem. A 2013, 1, 4207. Gonzalo, E.; Kuhn, A.; García-Alvarado, F.; Islam, M. S. J. Mater. Chem. A 2013, 1, 6588. Islam, M. S.; Fisher, C. A. J. Chem. Soc. Rev. 2014, 43, 185– 204. Gale, J. D. J. Chem. Soc.{,} Faraday Trans. 1997, 93, 629–637. Gale, J. D.; Rohl, A. L. Mol. Simul. 2003, 29, 291–341. Gale, J. D. Zeitschrift für Krist. - Cryst. Mater. 2005, 220, 552– 554. Dick, B.; Overhauser, A. Phys. Rev. 1958, 112, 90–103. Mott, N. F.; Littleton, M. J. Trans. Faraday Soc. 1938, 34, 485– 499. Lidiard, A. B. J. Chem. Soc. Faraday Trans. 2 1989, 85, 341– 349. Monkhorst, H. J.; Pack, J. D. Phys. Rev. B 1976, 13, 5188–5192. Gale, J. D. Philos. Mag. Part B 1996, 73, 3–19. Catlow, C. R. A.; Lidiard, A. B.; Norgett, M. J. J. Phys. C Solid State Phys. 1975, 8, L435–L438. Kroger, F. A.; Vink, H. J. In Solid State Physics, vol. 3; Seitz, F.; Turnbull, D., Eds.; Elsevier B.V., 1956; pp. 307–435. A close analysis of the ionic conductivity of a LiCl-deficient sample presented in Figure 5 from reference16 reveals an experimental migration enthalpy of ca. 0.10 eV, in spite of the reported value of 0.26 eV. Catlow, C. R. A. Proc. R. Soc. London. A. Math. Phys. Sci. 1977, 353, 533–561. Farley, T. W. D.; Hayes, W.; Hull, S.; Hutchings, M. T.; Vrtis, M. J. Phys. Condens. Matter 1991, 3, 4761. Levin’sh, A. F.; Straumanis, M. E.; Karlsons, K. Zeitschrift fuer Phys. Chemie, Abteilung B Chemie der Elem. Aufbau der Mater. 1938, 40, 146–150. Shannon, R. D. J. Appl. Phys. 1993, 73, 348–366. Young, K. F.; Frederikse, H. P. R. J. Phys. Chem. Ref. Data 1973, 2, 313–410. Trost; K. F. Zeitschrift für Naturforsch. 1963, 662–664. Rapp, J. E. J. Appl. Phys. 1973, 44, 3919. Kurasawa, T.; Takahashi, T.; Noda, K.; Takeshita, H.; Nasu, S.; Watanabe, H. J. Nucl. Mater. 1982, 107, 334–336.


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Concentration of Charge Carriers, Migration, and ... - ACS Publications

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