Origin of the Voltage Hysteresis of MgH2 ... - ACS Publications

Page 1 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

The Journal of Physical Chemistry

Origin of the Voltage Hysteresis of MgH2 Electrodes in Lithium Batteries D. Meggiolaro,†,‡ G. Gigli,† A. Paolone,‡ P. Reale,¶ M.L. Doublet,§,k and S. Brutti∗,⊥,‡ Dipartimento di Chimica, Sapienza Università di Roma, 00185 Rome, Italy, Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche (ISC−CNR) UOS Sapienza, 00185 Rome, Italy, ENEA Centro Ricerche Casaccia, via Anguillarese, Cesano (Italy), Institut Charles Gerhardt, CNRS and Université Montpellier, Place Eugène Bataillon, 34095 Montpellier, France, Réseau Francais sur le Stockage Electrochimique de l’Energie, RS2EFR3459 Amiens, France, and Dipartimento di Scienze, Università della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy E-mail: [email protected]

Phone: +390971205455. Fax: +390971205455

∗ To

whom correspondence should be addressed di Chimica, Sapienza Università di Roma, 00185 Rome, Italy ‡ Istituto dei Sistemi Complessi, Consiglio Nazionale delle Ricerche (ISC−CNR) UOS Sapienza, 00185 Rome, Italy ¶ ENEA Centro Ricerche Casaccia, via Anguillarese, Cesano (Italy) § Institut Charles Gerhardt, CNRS and Université Montpellier, Place Eugène Bataillon, 34095 Montpellier, France k Réseau Francais sur le Stockage Electrochimique de l’Energie, RS2EFR3459 Amiens, France ⊥ Dipartimento di Scienze, Università della Basilicata, Viale dell’Ateneo Lucano 10, 85100 Potenza, Italy † Dipartimento

1 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

Abstract Magnesium hydride has been proposed as innovative anode material for Li-ion cells due to its large theoretical capacity and high energy efficiency compared to other conversion materials. In this work we report a combined experimental-theoretical study about the origin of voltage hysteresis in the conversion reaction of MgH2 in lithium cells. Experimentally, the extent of the thermodynamic voltage hysteresis in the first galvanostatic discharge-charge cycle has been determined by the GITT technique and decoupled from the kinetic overpotentials. Theoretically, the origin of the thermodynamic voltage hysteresis has been evaluated and studied by means density functional theory calculations within the supercell approach. Different elementary reactions have been modelled upon reduction and oxidation on the surfaces of the active phases (i.e. MgH2 , LiH and Mg) and the associated theoretical voltages have been predicted. Experimental and theoretical results have been compared and discussed to draw a comprehensive description of the elementary surface reactions of the MgH2 conversion in lithium cells.

Introduction Conversion materials are a valuable alternative to intercalation compounds to increase the capacity of next-generation Li-ion cells. 1,2 Contrary to intercalation reactions where a host lattice stands almost unaltered upon the redox incorporation and de-incorporation of lithium ions, a general MX (M=metal, X=F,P,O,H...) material undergoes a conversion through a complex redox pseudodisplacement reaction with Li+ to form the reduced metal M and LiX according to the general m− . As an example, in oxide sysequation Mmn+ Xnm− + (m · n)Li+ + (m · n)e− → mM 0 + nLi+ mX

tems upon reduction, the microstructure of a conversion electrode is drastically altered to form nanometric metallic particles (3-5 nm) surrounded by an amorphous matrix of Li2 O, while upon oxidation the starting oxide is converted back in its nanosized form. 3,4 Multi-electron conversion reactions can supply larger specific capacity compared to the typical single electron insertiondeinsertion reactions, with satisfactory reversibility and cycle life in particular for materials with 2 ACS Paragon Plus Environment

Page 2 of 26

Page 3 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


tailored nanomorphology. 5,6 However upon cycling in lithium cells, a remarkable voltage hysteresis has been always observed between charge and discharge for all classes of conversion compounds, 7 whose amplitude is proportional to the ionicity of the material. At equilibrium, the voltage hysteresis corresponds to the difference between the average charge and discharge potentials. In galvanostatic conditions (non-zero current) this quantity is increased by kinetic effects (polarisation) mainly related to mass transport. In their work on CoO and CoP, Doublet et al. 4,8 have proposed that the thermodynamic components of the charge / discharge overpotentials are due to different reaction paths occurring on the active materials surfaces upon charge or discharge. Among the various proposed conversion materials, metal hydrides are very promising due to their large specific capacity and low voltage hysteresis. 1 Conversion reactions of metal hydrides in a Li cell have been recently reported for MgH2 , 2,9–12 TiH2 13,14 and other hydrides. 1,15 MgH2 conversion reaction occurs at an average potential of 0.5 V vs Li+ /Li with an apparent voltage hysteresis below 300 mV 2 , the smallest voltage hysteresis ever reported for a conversion material. In a previous theoretical work about the reactivity of bulk MgH2 in a conversion reaction (a) we predicted an electrode potential vs Li+ /Li0 of 0.55 V, (b) we discarded the possible occurrence of intermediate stoichiometric intercalation compounds upon conversion (i.e. LiMgH3 and Li2 MgH4 ), (c) we studied the occurrence of point defects in bulks and nanometric clusters in order to mimic possible elementary step upon conversion 16 and (d) we outlined a possible reaction path in nanosized samples through substitution of Li in the Mg sublattice of MgH2 with the contemporary breaking of H bonds. In this work we report a combined experimental - theoretical study about the origin of the voltage hysteresis in the conversion of MgH2 in lithium cells, following the methodological approach developed by Doublet et al. 4,8 The magnitude of the voltage hysteresis has been evaluated experimentally by galvanostatic intermittent titration tests (GITT). Parallel to the electrochemical characterization, a theoretical investigation of the MgH2 conversion has been carried out by ab initio density functional theory (DFT) calculations. In order to elucidate the possible thermodynamic



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

origin of the hysteresis in the MgH2 conversion, a comprehensive study of the reactivity of the surfaces of MgH2 , LiH and Mg with Li has been carried out. Several elementary reactions have been modelled on different surfaces for each compound, both in reduction and oxidation. Upon reduction, six reactions have been modelled on the (110) and (100) surfaces of MgH2 , whereas upon oxidation four reactions have been modelled on the (100) and (110) surfaces for LiH and (0001) and (100) surfaces for Mg. The cell voltages associated to these reactions have been calculated and compared to experiments.

Methods Experimental methods Three electrodes Swagelock-type cells have been assembled in an MBRAUN glove box under dry argon atmosphere with O2 and H2 O water content below 1 ppm. MgH2 active material has been prepared following the procedure described in ref. 2 It is constituted by a fine mixture of 10 nm MgH2 nanoparticles surrounded by superP carbon particles. MgH2 electrodes have been prepared by cold pressing the mixture of active material (50%) superP carbon (30%) and a polymeric binder (polyvynil difluoride, 20%) onto circular Cu disks (10 mm in diameter) by means of an hand press and a die set. Electrode preparation has been carried out in glove box without exposure to air. Electrodes have been assembled in cells by coupling them with fiberglass Whatman separators and lithium foil counter-electrodes. A lithium reference electrode has been geometrically inserted between the two other electrodes. Merck LP30 electrolyte, constituted by a 1 molar solution of LiPF6 dissolved in an ethylene carbonate and dimethylcarbonate (1:1 in volumes) solvent, has been used. GITT experiment has been carried out by using a VSP Biologic instrument. During the GITT measurement, a three electrode cell is discharged and charged at a constant current of 100 mAg−1 =C/20 for an intermittent τ=7200 s followed by an open circuit relaxation of at least 12 h to reach a steady-state voltage (OCV, open circuit voltage) that varies upon time less than 1 mVh−1 . The latter (OCV) is an approximate measurement of the electron motion force (e.m.f.) of the elec4 ACS Paragon Plus Environment

Page 4 of 26

Page 5 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


trochemical system and it is a good estimate of the thermodynamic working potential of the cell cleaned up from polarizations (i.e. the difference between the last measured cell potential at the end of each galvanostatic step, with a non-zero current, and the corresponding OCV after relaxation at zero current). This procedure is repeated 10 times with a constant final cut-off voltage of 0.2 V vs. Li in discharge and then in charge for further 10 times.

Theoretical methods In order to study the mechanism of conversion of MgH2 , a density functional theory study of the elementary reactions occurring on the surfaces of the active phases (i.e. MgH2 , LiH and Mg) has been carried out, both in reduction and oxidation. Clean surfaces have been cleaved from the respective relaxed bulk lattices, whose equilibrium structures has been calculated at the same level of theory relaxing both cells and ionic positions. The thermodynamic stability of the surfaces has been checked by calculating the respective surface formation energies (SFE) in the supercell approach. The SFE fixes the thermodynamic stability of the different Miller index surfaces and for stoichiometric surfaces is defined as

SFE =

Eslab − ∑i ni µi 2A

(1)

where Eslab is the energy of the surface, ni and µi are respectively the number of atoms of species i in the simulated slab cell and the relative chemical potential, A the area of the modelled surface. Following the approach already presented in the refs. 4,8 no further thermodynamic corrections have been added. Elementary reactions have been modelled on one side of the surface slabs in order to avoid images interactions and dipole corrections have been applied along the direction perpendicular to the slab. Different surface coverages have been simulated modelling surface reactions on the 1x1 and 2x2 in-plane supercells. The equilibrium structures of the modelled systems have been found relaxing



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

Page 6 of 26

all ionic positions. The energetics at 0K have been evaluated for each reaction and the associated thermodynamic voltage ∆V has been calculated according to the general equation

∆V = −∆r E/nF

(2)

where ∆r E is the reaction enthalpy at 0K as obtained by the DFT calculations, n the number of exchanged electrons in the reaction and F the Faraday constant. According to this expression, reactions in discharge are associated to positive potentials, while upon oxidation all modelled reactions show a negative potential (i.e. electric work is needed). In the expression for ∆r E the chemical potential for Li has been set to the Li bulk value, in order to directly calculate the thermodynamic voltage of the process with respect to the redox couple Li+ /Li0 . All DFT calculations on surfaces have been carried out in the supercell approach using plane waves basis set (PW) and pseudopotentials as implemented in the VASP code, 17 treating 1s and 2p states for Li and Mg respectively as valence states. A gradient corrected exchange correlation functional has been used as formulated by Perdew Burke Enzerhof (PBE) 18 within the projector augmented wave (PAW) method. 19 An energy cutoff of 500 eV on PW’s has been imposed for all calculations. Convergence tests on the thickness of the slabs have been performed by increasing the number of atomic layers in the slabs until a constant SFE has been reached for each system. The vacuum thickness between the surface slabs and the number of k points in the Brillouin Zone (BZ) has been converged in order to achieve an accuracy on total energy of about 2 meV/atom. The equilibrium geometry has been obtained by relaxing ions positions until forces on atoms were less than 1x10−2 eV/Å.

Results Experimental results In Figure 1 the lithium loading curve from the GITT test is shown.


Page 7 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


Figure 1: Lithium loading curve vs. cell potential (vs. Li) from a GITT test.

The GITT highlights an average OCV between charge and discharge (i.e. electromotion force, e.m.f.) of approximately 0.525±0.050 V. Upon discharge, an almost constant kinetic contribution of overpotentials can be observed along the conversion plateau of about 103±10 mV, that increase monotonically to ∼ 200 mV in the last stages of discharge. On the other hand, a rapidly increasing polarization ranging from 40 mV to 500 mV has been reported upon charge. Different equilibrium open circuit voltage (OCV) values have been found in discharge and charge with mean electrode potentials of 0.489±0.050 and 0.560±0.050 V vs Li, respectively. The uncertainties associated to the two mean equilibrium OCVs have been estimated by the standard deviations of the data in discharge and charge, respectively. The GITT mean e.m.f. is, as expected, in good agreement with the experimental average potential between charge and discharge measured by simple GC tests, i.e. 0.5 V vs Li+ /Li0 , 2 and with our theoretical prediction for bulk. 16 Going beyond the evaluation of the thermodynamic e.m.f., the GITT test allows to remove the kinetic contribution to the charge / discharge potential difference,



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

highlighting the remaining thermodynamic contribution to the hysteresis in the MgH2 electrode. The electrode polarization shows different magnitudes and trends upon discharge and charge (see Fig. S1 in the supplementary material). An almost constant kinetic polarization along the conversion plateau of about 103±10 mV is observed in discharge, whereas it increases rapidly upon charge ranging from 40 mV to 500 mV. Besides polarization, a further difference, as large as 0.071±0.060 V, between the mean OCV upon discharge and charge is observed, even after an open circuit voltage relaxation of the cell longer than 12 hours. This small thermodynamic component accounts for approximately 30% of the total voltage difference between charge and discharge. This value is in agreement with previous findings from other authors on other conversion systems such as FeF3 20 and the MO/graphene composite. 21 It is interesting to observe that at the end of the GITT discharge a decrease of the relaxed OCV is observed. This evidence can be a clue of the onset of alloying of Li into the hcp Mg particles formed upon conversion. In fact this further redox lithium incorporation reaction may occur in conversion MgH2 electrodes upon discharge at low potentials below 0.3-0.2 V, as shown by ex situ X-ray diffraction by Brutti et al. and reported in ref. 2

Theoretical results The overall conversion reaction (OCR) In order to model the elementary reactions at the electrode, low Miller index surfaces have been cleaved from the respective bulk. For each phase the two most stable surfaces have been considered: they are reported in Figure 2 with the relative lattice structures. Only stoichiometric surfaces have been considered, since non-stoichiometric surfaces (e.g. H defective MgH2 surfaces, Li and H defective LiH surfaces) are less stable in the whole range of existence of the phases and likely play a limited role in the thermodynamics of the conversion (see Supplementary materials section, in particular figures S2 and S3 that report the MgH2 and LiH surfaces phase diagrams). The relative SFE’s have been calculated according to the Eq. 1, that for stoichiometric surfaces 8 ACS Paragon Plus Environment

Page 8 of 26

Page 9 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


reads SFE = Eslab − nµ/2A, where n and µ are respectively the number of formula units of the phase in the slab and the relative bulk chemical potential. Results are reported in the Table 1. The calculated surface chemical potentials of the phases are higher than the respective bulk values due to the surface tension contribution to the energy. For instance, the surface chemical potentials of MgH2 , LiH and Mg in the MgH2 (110), LiH (100) and Mg (0001) surfaces show an increment with respect to the bulk values of 10 kJ/mol, 5 kJ/mol and 6 kJ/mol respectively.

Figure 2: Structures of the modelled surfaces: top and side view

Table 1: Surface formation energies of the studied stoichiometric surfaces System MgH2 LiH Mg

Surface (110) (100) (100) (110) (0001) (100)

SFE(J/m2 ) 0.47 0.54 0.32 0.71 0.54 0.63



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

In order to estimate the effect of nanometrization on the energetics of the overall conversion reaction (OCR)

2Li+ + 2e− + MgH2 → Mg + 2LiH (OCR)

the associated thermodynamic voltage has been evaluated according to 2, calculating the ∆r E term as the difference between the surface chemical potentials of the products and of the reactants in their respective most stable surfaces, i.e. MgH2 (110), LiH (100) and Mg (0001). The estimated voltage for the OCR is 0.52 V, a value slightly smaller than the prediction made considering DFT chemical potentials of the bulk, i.e. 0.55 V 16 at the same level of theory. The calculated thermodynamic voltage for the OCR, also incorporating surface effects, (0.52 V) is in excellent agreement with the experimental value, i.e. 0.525±0.005 V, obtained by the GITT technique (see previous section).

Reduction reactions In reduction, six possible elementary reactions between Li and MgH2 have been modelled on the MgH2 (110) and (100) surfaces. A pictorial representation of some of these reactions is reported in Figure 3. A summary of the corresponding predicted thermodynamic potentials (vs Li+ /Li0 ) is reported in Table 2. In order to obtain the voltages, the chemical potentials of the Mg and LiH species have been set to the values of the chemical potentials of the Mg (0001) and LiH (100) surfaces respectively, while the chemical potential of Li has been set to the Li bulk value (see previous section). The coverages values reported in the Table 2 (ξ ) represent an estimate of the 2D concentration of the lithium ions over the surfaces and have been calculated considering the number of formula units of the respective phase per cell employed in the calculation. Reactions R1-R1’ model the Li adsorption on the MgH2 surface at different degrees of coverage. The preferential adsorption sites of Li atoms on the surface are in the proximity of H atoms, where weak Li-H bonds are formed with a internuclear distance of about 1.88 and 2.00 Å for the


Page 10 of 26

Page 11 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


Table 2: Thermodynamic cell voltage results for elementary discharge reactions. The chemical potential for Mg and LiH phases have been set equal to the surface chemical potential of the Mg (0001) and LiH (100) surfaces respectively. (110) (100) ξ (coverage) - Potential (V)

Reaction R1 - x Li + MgH2 = Lix MgH2 single Li adsorption R1’- 2x Li + MgH2 = Li2x MgH2 double vicinal Li adsorption

(ξ =1/5) -0.46 V

(ξ =2/5) -0.40 V

(ξ =1/10) -0.28 V (ξ =1/5) -0.09 V

(ξ =1/10) -0.55 V (ξ =2/5) 0.00 V

(ξ =1/10) 0.39 V (ξ =1/5) 0.39 V

(ξ =1/10) 0.29 V (ξ =2/5) 0.13 V

(ξ =1/10) 0.43 V (ξ =1/5) 0.46 V

(ξ =1/10) 0.40 V (ξ =2/5) 0.54 V

(ξ =1/10) -0.32 V (ξ =1/5) -0.21 V

(ξ =1/10) -0.36 V

(ξ =1/10) -0.26 V (ξ =1/5) 0.14 V

(ξ =1/5) -0.02 V

R2 - 2x Li + MgH2 = Li2x Mg1−x H2 + x Mg Li - Mg displacement reaction

R3 - 2x Li + MgH2 = Lix Mg1−x H2 + x Mg + x LiH Li in Mg site and H vacancy formation

R4 - x Li + MgH2 = MgH2−x + x LiH single H vacancy formation

R4’ - 2x Li + MgH2 = MgH2−2x + 2x LiH double H vacancy formation



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

Figure 3: Pictorial representation of modelled reactions upon reduction. (100) and (110) surfaces, respectively. The predicted potentials for reactions R1-R1’ are negative for all the computed surfaces and for any coverage: in the quasi-covalent MgH2 system a reductive interaction between the Li ion and the active material surface is thermodynamically unfavoured. Reaction R2 models a double Li adsorption with the contemporary formation of a Mg vacancy and the nucleation of metallic Mg surfaces. The "extrusion" of Mg leads to an asymmetric loss of coordination for the H atoms close to the surface, compensated by the insertion of Li atoms in the slab. The simple formation of a Mg vacancy is energetically unfavoured, both in the bulk and on the surfaces of MgH2 , due to the breaking of two covalent Mg-H bonds and the induction of electronic disorder in the system. In reaction R2 this unfavourable thermodynamics is partially counterbalanced by the formation of new Li-H bonds due to the lithium ions adsorbed on the (110) and (100) surfaces. Reaction R3 describes the reductive displacement of a single Mg atom by a single Li+ ion with a parallel formation of vicinal H vacancy and the contemporary nucleation of Mg and LiH surfaces. In the case of bulk phases, as discussed by us in ref., 16 the Gibbs energy of this reaction is competitive with the OCR. Also in the case of surfaces the predicted potential for this redox reaction at 12 ACS Paragon Plus Environment

Page 12 of 26

Page 13 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


low Li coverages is 0.43 V and 0.40 V on the (110) H-terminated and (100) surface respectively. It is interesting to observe that all the predicted values for R3 compare well with the relaxed e.m.f. measured by the GITT test upon reduction (i.e. 0.489±0.050 V). Reactions R4-R4’ model the reductive H vacancy formation on the surfaces at different degree of coverage with the parallel nucleation of LiH surfaces. Both single H vacancies and vicinal double H vacancies have been modelled. The predicted R4-R4’ potentials are negative except for the double vacancy formation on the (110) surface at high coverages. The unfavourable thermodynamics for these processes may be related to the formation of isolated donor levels within the gap of the MgH2−x system. 16 As expected the double vacancy process R4’ is thermodynamically more favoured in comparison to the single vacancy reaction R4, similarly to the case of the bulk phase. 16 This is due to a binding effect between the two vacancies that stabilizes the defective system. According to all the presented predictions, the most favourite reaction in reduction corresponds to the displacement reaction R3 that shows an estimated potential in the range 0.40 – 0.54 V, values comparable with the experimental determination of the thermodynamic e.m.f. upon reduction from the GITT test discussed in the previous section (0.489±0.050 V).

Oxidation reactions Five different reactions have been modelled upon oxidation for the LiH-Mg system. Similarly to the case of reduction reactions, the corresponding cell potentials have been evaluated. All the predicted potentials are negative as all processes require electric work to occur. Thus, the thermodynamically most favoured processes are those occurring at the smallest voltages in absolute values. A pictorial representation of the elementary reactions upon oxidation is shown in Figure 4 and the corresponding absolute values of potentials are reported in Table 3 for different LiH surfaces and coverages. Absolute values are reported instead of the correct negative potentials in order to allow a direct comparison with experiments. Reaction O1 models the oxidative formation of a Li vacancy in the lattice of LiH. This process is associated to the formation of acceptor states in the electronic structure of LiH and, as in the



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

Page 14 of 26

Table 3: Absolute values of the thermodynamic cell voltages for the charging reactions at different coverages. The chemical potential for Mg (∗) and LiH (∗∗) phases have been set equal to the surface chemical potential of the Mg (0001) and LiH (100) surfaces, respectively. LiH (110) LiH (100) ξ (coverage) - Potential (V)

Reaction O1 - LiH = Li1−x H + x Li

(ξ =1/8) 3.26 V (ξ =1/32) 3.09 V

(ξ =1/8) 2.77 V (ξ =1/32) 2.46 V

(ξ =1/8) Mg adsorption and double Li vacancy formation 0.78 V (ξ =1/32) 0.77 V Mg(0001) (∗∗) O3 - x LiH + Mg = MgHx + x Li (ξ =1/4) single H adsorption on Mg 1.22 V (∗∗) O3’ - 2x LiH + Mg = MgH2x + 2x Li (ξ =1/4) double H adsorption 0.58 V

(ξ =1/8) 1.10 V (ξ =1/32) 0.74 V Mg(100)

Li vacancy formation

O2 - LiH + x Mg = Mgx Li1−2x H + 2x Li (∗)


(ξ =1/4) 0.71 V (ξ =1/4) 0.66 V

Page 15 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


Figure 4: Pictorial representation of modelled reactions upon oxidation. case of H vacancies in MgH2 , the corresponding thermodynamics is largely unfavoured for both the (100) and (110) surfaces. Reaction O2 describes the oxidative Mg adsorption on LiH surfaces with a parallel formation of double Li vacancies. The "extrusion" of Li atoms from the LiH surface occurs with the insertion of the adsorbed Mg atom in the surface slab in order to saturate the lost Li-H bonds. Mg atom in the slab is tetra-coordinated by 4 H vicinal atoms forming weak bonds at a mean distance of 2.88 Å. The last reactions O3 and O3’ have been modelled on the Mg (0001) and (100) surfaces and describe the formation of Mg-H bonds on the Mg surface by a direct reaction with LiH. Single H adsorption is more unfavoured with respect to the vicinal double adsorption: in both cases the H adsorption leads to the formation of a Mg-H bond of length 2.04 Å, very close to the bulk bond length of MgH2 (1.92 Å). This reaction is the most favoured surface process among all the studied systems in oxidation with a voltage of 0.58 V. On passing it should be noted that slabs with (110) and (100) surfaces have different lateral size: this difference is likely responsible for the similar energetics for the reaction R2 and O2 observed at different coverages. In summary, according to the presented predictions, the most favourite reaction upon oxidation is the formation of a Mg-H interface on the Mg surfaces (reaction O3’) that shows an estimated 15 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

potential in the range 0.58 – 0.66 V, values comparable with the experimental determination of the thermodynamic e.m.f. upon oxidation from the GITT test discussed in the previous section (0.560±0.050 V).

Discussion The voltage hysteresis measured in MgH2 -based electrodes in Li cells has a combined kinetic and thermodynamic origin with an approximate 2:1 relative ratio. Starting from the kinetic component, the trend of the voltage polarization upon conversion shown in Fig. S1 of the supplementary material highlights an almost constant value upon discharge and a rapidly increasing overvoltage upon charge. Polarizations in Li-ion electrodes are typically related to small conductivities, either ionic or electronic. In this view one may speculate that variations of polarization upon charge/discharge may be related to changes in the Li+ or e− conductivities and to the kinetic of the mass transport associated to the significant atomic reorganisation upon charge. In particular, upon discharge the most favourable reaction (displacement reaction R3) requires a limited reaction surface and diffusion path for Li+ ions in order to occur and the most relevant kinetic limiting step is likely represented by the Mg extrusion and diffusion. Upon charge, the structurally complex reaction O3’ implies a direct contact between LiH and Mg nanoparticles and Li+ and H− species have migrate simultaneously. On the other hand, the polarization may also reflect in a possible increase of the electron transfer resistances due to a large variation of the passivation film properties. However this study is beyond the scope of this paper and the capabilities of the adopted approach. Turning to the thermodynamic overpotentials, our DFT predictions suggest that two different reaction paths occur upon discharge and charge driven by difference redox chemistry on surfaces. In particular, upon discharge, our DFT calculations identify as the most favored reaction the reductive substitution of surface Mg atoms by Li on the MgH2 surface with the parallel formation of a Hvacancy. This displacement reaction is predicted to occur at the mean value of 0.46 ±0.06 V. and is in very good agreement with the experimental cell e.f.m. upon discharge of 0.489 ± 0.050 V. On


Page 16 of 26

Page 17 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


the other hand upon charge our computational investigation suggests that the most favored process is a double H-shift from the LiH to Mg surfaces. This reaction is predicted to occur at 0.62 ± 0.04 V in agreement within the errors with the experimental cell e.f.m. upon charge of 0.560 ±0.050 V. These values have been calculated as means of the voltages reported in the Table 2 (reaction R3) and Table 3 (reaction O3’) for reduction and oxidation, respectively, and compared with the experimental data reported in the previous section. Experimental and computational evaluations agree within the associated uncertainties. The sum of the thermodynamic overpotentials upon discharge and charge gives a predicted thermodynamic voltage hysteresis of 0.16 ± 0.07 V in satisfactory agreement with the experimental value of approximately 0.071 ± 0.060 V obtained from the GITT test. For the sake of completeness it may be interesting to observe that, although in agreement with the errors, the computational prediction of the thermodynamic voltage hysteresis overestimates the corresponding experimental determination. This may suggest the possible role also played by higher energy surfaces (e.g. Mg-ended MgH2 slabs upon reduction) or extended surface defects (e.g. terraces, edges, kinks) that may act as onset sites for the conversion. The asymmetric redox reactivity upon discharge and charge has been already highlighted by Doublet et al. 8 in the case of CoP conversion reaction. Such behaviour is not necessarily surprising since the two active materials upon discharge and charge, i.e. MgH2 and Mg, are very different, both structurally and from the point of view of electronic structure. In particular MgH2 is an insulator with a band gap of 5.6 eV, 22,23 whereas Mg is a metal. In this view, starting from our DFT analysis, some additional speculations about the reaction mechanism can be drawn. In order to evaluate the redox properties of the pristine electroactive materials upon reduction and oxidation, the Fukui functions of MgH2 (110) and Mg (0001) surfaces have been studied. In particular the response of the MgH2 system to the electron addition and of the Mg system to the electron removal have been considered. The Fukui function is the real space plot of the difference of the electronic charge density between a neutral and a charged modelled system and is extensively used in quantum chemistry in order to identify the sites of electrophilic or nucleophilic



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

attack in molecules. 24,25 The Fukui functions for Mg and MgH2 have been defined respectively as − N−ε N+ε N (r) and F + N FMg = ρMg (r) − ρMg MgH2 = ρMgH2 (r) − ρMgH2 (r), where the charge density difference

F ± is evaluated on the real space FFT grid between the density ρ N±ε of the system with N ± ε electrons and the neutral ground state density ρ N . Only limited fractions of charge ε have been added and subtracted to the MgH2 and Mg systems respectively, in order to avoid large alteration of the electronic structure of the systems with respect to the ground states. Fukui functions plots are reported in Figure 5a for MgH2 and Figure 6a for Mg slabs.

Figure 5: a) Calculated Fukui functions for MgH2 (110); b) Surface projected electronic band structure of MgH2 (110) along the M − X 0 line in BZ. Dotted lines represent the surface band structure, while shaded areas the projected electronic bulk states; c) Plot of the LUMO Kohn-Sham orbital at M.

The Fukui functions for MgH2 and Mg surfaces are localized in the first layers of the slabs, highlighting a dominant role of the surface states with respect to the bulk states in the redox processes, both upon reduction or oxidation. Upon reduction the added charge computed for the MgH2 (110) surface localizes in the proximity of the Mg atom placed on the surface (Figure 5a, although a sensible charge amount is also trapped by the outer H atoms. A more detailed interpretation of the Fukui function results for MgH2 can be drawn also in the view of the electronic band structure of the surface. In Figure 5b the surface 18 ACS Paragon Plus Environment

Page 18 of 26

Page 19 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


projected electronic band structure of the (110) H-terminated surface of MgH2 is reported along the M − X 0 direction in the surface BZ. The occurrence of the electronic surface states within the band edge is nicely evident by comparing the projected electronic states of the bulk into the surface BZ with the band structure of the MgH2 surface. The lowest unoccupied states, i.e. LUMO, are represented by the surface states at the bottom of the conduction band near the high symmetry point M. The plot in real space of the corresponding Kohn-Sham orbital (Figure 5c) highlights the localization of the LUMO on the Mg atom at the top of the surface, in agreement with the plot of the Fukui function. This last evidence suggests the limited role played by the bulk states of MgH2 in reduction thus supporting the need of strongly nanosized samples to support the conversion reaction. Turning to oxidation, a charge depletion at the top of the surface is localized on the Mg (0001) surface in proximity of the outer Mg atoms. Contrary to the MgH2 (110) case, here a direct interpretation of the Fukui functions in terms of frontier orbitals is not straightforward, due to the ambiguous nature of the smeared orbitals at the Fermi level of the metal. However the analysis of the Bader charges (BC) provides additional insights (Table 4). Table 4: Bader charges analysis for reactions R3 and O3’ Reaction R3 on (100)

O3’ on (0001)

atoms Mg H Li Mg H

BC reagents 6.37 1.82 3.00 8.00 1.00

BC product 6.35 1.83 2.17 6.37 1.98

BC reference 1.84 - LiH (100) 2.15 - LiH (100) 6.37 - MgH2 (110) 1.82 - MgH2 (110)

Upon oxidation the most favourite process is reaction O3’, i.e. the adsorption of two H atoms on the surfaces of metallic Mg with the contemporary release of two Li+ ions in the electrolyte. This process can be described in terms of a nucleation of layers of the MgH2 phase on the surface of Mg (0001) (see Figure 6b). In fact, after the adsorption, the BC’s of the Mg atoms on the surface close to the hydrogens show a marked decrease, passing from the 7.93e to 6.37e, a value almost identical to the BC calculated for the MgH2 -(110) surface. 19 ACS Paragon Plus Environment


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

Figure 6: a) Calculated Fukui functions for Mg (0001); b) Structure of the H covered Mg (0001) surface; c) Layers projected density of states (LPDOS) for the product of reaction O3’, H covered Mg (0001) surface.

Furthermore, the layers projected density of states (LPDOS) for the O3’ reaction product (Figure 6c), projected on the surface Mg and H atoms (i.e. the first surface atomic layer) highlights the opening of a pseudo-band gap whereas bulk states of the slab still predict the expected metallic character of the Mg inner layers (bulk states). Within this pseudo-gap a marked suppression of the density of states is predicted: the non-zero contribution to density of states can be associated to the formation of electronic interface states in the first atomic layer between the metal and the hydrogen passivated monolayer. This picture suggests the formation of a rather insulating Mg-H layer on the Mg (0001) produced after reaction O3’. This hydrogen ad-layer on the Mg surface may also account for the increased voltage polarization in oxidation observed in the GITT experiment. In fact, the insulating character of the passivating H-layer may likely lead to a cumulative increase of the electron transfer resistance from the Fermi level of the Mg to the H-saturated surfaces (and then to the carbon conductive additive) thus making more and more difficult the extraction of electrons upon charge from the metallic nanoparticles.

Conclusions The study about the origin of the voltage hysteresis in the conversion reaction of MgH2 has been carried out by a combined experimental-theoretical approach. The two contributions (i.e. thermo20 ACS Paragon Plus Environment

Page 20 of 26

Page 21 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


dynamic and kinetic) to the voltage hysteresis of MgH2 have been investigated and discussed in the light of the results of the electrochemical GITT test and DFT calculations. The polarization effects accounts for approximately 70% of the whole voltage hysteresis. The origin of this kinetic effects are likely related to the diffusivity of ions (either Mg2+ , Li+ and H− ) and electrons within the electrode and across the electrolyte/electrode surfaces. The analysis of this aspect, that is beyond the scope of this manuscript, may also involve the growth and the properties of a solid-electrolyte-interphase on the active material surfaces. Its growth may in fact imply further side reactions between the electrode surface and the electrolyte components (see as an example refs. 26 and 27 ). Experimental and computational research activities are currently in progress in our laboratories to tackle this complex and challenging topic and new methodologies are being currently developed to address this interesting question. 28 A thermodynamic overvoltage of 71 mV between charge and discharge has been measured by the GITT test, confirming the limited extent of the hysteresis in non ionic compounds. Results from the GITT experiments agree very well with the results of the DFT calculations. In fact our extended computational modelling suggests the occurrence of an asymmetric reaction path in charge and discharge driven by different surface thermodynamics upon lithium incorporation and deincorporation, starting from the pristine MgH2 and the fully discharged Mg/LiH electrodes, respectively. In discharge (lithium incorporation) the thermodynamically most favorite reaction is the reductive displacement of a single Mg atom by a single Li+ ion with a parallel formation of vicinal H vacancy and the contemporary nucleation of Mg and LiH. On the other hand in charge (lithium removal) the most favorite reaction is the formation of a Mg-H interface on the Mg surfaces. In summary, our DFT calculations predicts a 160 mV thermodynamic voltage difference that is in fairly good agreement with the experimental data. Generally speaking these results confirm the reliability of our methodological approach that has been successfully applied to explain the thermodynamic components of the voltage hysteresis in very different materials, i.e. oxides, phosphides and hydrides. 4,8 In fact this method allowed a careful prediction of the measured thermodynamic voltage hysteresis on materials with very different



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

solid state bonding properties ranging from almost purely-covalent to fully ionic and involving or not d-orbitals.

Acknowledgement The authors would like to thanks the italian MIUR for the financial support through the FIRB 2010 Futuro in Ricerca project "Idruri quali anodi ad alta capacità per batterie Li-ione" and the CINECA consortium for the computational grants. D.M. would like to thank the CNRS and the University of Montpellier 2 for the hospitality during a research stay.

Supporting Information Available Phase diagrams of the the defective MgH2 and LiH surfaces are available in the supplementary material. This material is available free of charge via the Internet at http://pubs.acs.org.

References (1) Oumellal, Y.; Rougier, A.; Nazri, G.; Tarascon, J.; Aymard, L. Metal hydrides for lithium-ion batteries. Nat. Mater. 2008, 7, 916–921. (2) Brutti, S.; Mulas, G.; Piciollo, E.; Panero, S.; Reale, P. Magnesium hydride as a high capacity negative electrode for lithium ion batteries. J. Mater. Chem. 2012, 22, 14531–14537. (3) Ji, L.; Tan, Z.; Kuykendall, T. R.; Aloni, S.; Xun, S.; Lin, E.; Battaglia, V.; Zhang, Y. Fe3O4 nanoparticle-integrated graphene sheets for high-performance half and full lithium ion cells. Phys. Chem. Chem. Phys. 2011, 13, 7170–7177. (4) Dalverny, A. L.; Filhol, J. S.; Doublet, M. L. Interface electrochemistry in conversion materials for Li-ion batteries. J. Mater. Chem. 2011, 21, 10134–10142.


Page 22 of 26

Page 23 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


(5) Hong, I.; Angelucci, M.; Verrelli, R.; Betti, M. G.; Panero, S.; Croce, F.; Mariani, C.; Scrosati, B.; Hassoun, J. Electrochemical characteristics of iron oxide nanowires during lithium-promoted conversion reaction. J. Power Sources 2014, 256, 133–136. (6) Verrelli, R.; Brescia, R.; Scarpellini, A.; Manna, L.; Scrosati, B.; Hassoun, J. A lithium ion battery exploiting a composite Fe2O3 anode and a high voltage Li1.35Ni0.48Fe0.1Mn1.72O4 cathode. RSC Advances 2014, 4, 61855–61862. (7) Cabana, J.; Monconduit, L.; Larcher, D.; Palacin, M. R. Beyond intercalation-based Li-ion batteries: The state of the art and challenges of electrode materials reacting through conversion reactions. Adv. Mater. 2010, 22, E170. (8) Khatib, R.; Dalverny, A. L.; Saubanère, M.; Gaberscek, M.; Doublet, M. L. Origin of the voltage hysteresis in the cop conversion material for Li-ion batteries. J. Phys. Chem. C 2013, 117, 837–849. (9) Oumellal, Y.; Courty, M.; Rougier, A.; Nazri, G. A.; Aymard, L. Electrochemical reactivity of magnesium hydride toward lithium: New synthesis route of nano-particles suitable for hydrogen storage. Int. J. Hydrogen Energ 2014, 39, 5852–5857. (10) Oumellal, Y.; Zlotea, C.; Bastide, S.; Cachet-Vivier, C.; Leonel, E.; Sengmany, S.; Leroy, E.; Aymard, L.; Bonnet, J. P.; Latroche, M. Bottom-up preparation of MgH2 nanoparticles with enhanced cycle life stability during electrochemical conversion in Li-ion batteries. Nanoscale 2014, 6, 14459–14466. (11) Zaidi, W.; Oumellal, Y.; Bonnet, J. P.; Zhang, J.; Cuevas, F.; Latroche, M.; Bobet, J. L.; Aymard, L. Carboxymethylcellulose and carboxymethylcellulose-formate as binders in MgH2carbon composites negative electrode for lithium-ion batteries. J. Power Sources 2011, 196, 2854–2857. (12) Ikeda, S.; Ichikawa, T.; Kawahito, K.; Hirabayashi, K.; Miyaoka, H.; Kojima, Y. Anode



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

properties of magnesium hydride catalyzed with niobium oxide for an all solid-state lithiumion battery. Chem. Commun. 2013, 49, 7174–7176. (13) Oumellal, Y.; Rougier, A.; Tarascon, J. M.; Aymard, L. 2LiH + M (M = Mg, Ti): New concept of negative electrode for rechargeable lithium-ion batteries. J. Power Sources 2009, 192, 698–702. (14) Oumellal, Y.; Zaidi, W.; Bonnet, J.; Cuevas, F.; Latroche, M.; Zhang, J.; Bobet, J.; Rougier, A.; Aymard, L. Reactivity of TiH2 hydride with lithium: ion evidence for a new conversion mechanism. Int. J. Hydrogen Energ 2012, 37, 7831–7835. (15) Silvestri, L.; Forgia, S.; Farina, L.; Meggiolaro, D.; Panero, S.; Brutti, S.; Reale, P. Lithium alanates as negative electrodes in lithium-ion batteries. ChemElectroChem 2015, 2, 877–886. (16) Meggiolaro, D.; Gigli, G.; Paolone, A.; Vitucci, F.; Brutti, S. Incorporation of lithium by MgH2: An ab initio study. J. Phys. Chem. C 2013, 117, 22467−22477. (17) Kresse, G.; Furthmuller, J. Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set. Comp. Mater. Sci. 1996, 6, 15. (18) Perdew, J. P.; Burke, K.; Ernzerhof, M. Generalized gradient approximation made simple. Phys. Rev. Lett. 1996, 77, 3865–3868. (19) Blochl, P. E. Projector augmented-wave method. Phys. Rev. B 1994, 50, 17953–17979. (20) Liu, P.; Vajo, J. J.; Wang, J. S.; Li, W.; Liu, J. Thermodynamics and kinetics of the li/fef3 reaction by electrochemical analysis. J. Phys. Chem. C 2012, 116, 6467–6473. (21) Mai, Y.; Zhang, D.; Qiao, Y.; Gu, C.; Wang, X.; Tu, J. MnO/reduced graphene oxide sheet hybrid as an anode for Li-ion batteries with enhanced lithium storage performance. J. Power Sources 2012, 216, 201. (22) Isidorsson, I. A.; Giebels, I. A. M. E.; Arwin, H.; Griessen, R. Optical properties of MgH2 measured in situ by ellipsometry and spectrophotometry. Phys. Rev. B 2003, 68, 115112. 24 ACS Paragon Plus Environment

Page 24 of 26

Page 25 of 26

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60


(23) Van Setten, M. J.; Popa, V. A.; de Wijs, G. A.; Brocks, G. Electronic structure and optical properties of lightweight metal hydrides. Phys. Rev. B 2007, 75, 35204. (24) Filhol, J. S.; Doublet, M. L. Conceptual surface electrochemistry and new redox descriptors. J. Phys. Chem. C 2014, 118, 19023–19031. (25) Chattaraj, P. K. Chemical reactivity theory: a density functional view; CRC Press, 2009. (26) Sethuraman, V. A.; Srinivasan, V.; Newman, J. Analysis of electrochemical lithiation and delithiation kinetics in silicon. J. Electrochem. Soc. 2013, 160, A394–A403. (27) Ponrouch, A.; Cabana, J.; Dugas, R.; Slack, J. L.; Palacín, M. R. Electroanalytical study of the viability of conversion reactions as energy storage mechanisms. RSC Adv. 2014, 4, 35988–35996. (28) Lespes, N.; Filhol, J. Using implicit solvent in ab initio electrochemical modeling: investigating li+/li electrochemistry at a li/Solvent interface. J. Chem. Theory Comput. doi 10.1021/acs.jctc.5b00170, 2015.



1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 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 53 54 55 56 57 58 59 60

Graphical TOC Entry

Cell potential hysteresis in MgH2


Page 26 of 26

Origin of the Voltage Hysteresis of MgH2 ... - ACS Publications

Recommend Documents