Journal of the American Chemical Society
Supporting Information
How Crystallite Size Controls the Reaction Path in Nonaqueous Metal Ion Batteries: The Example of Sodium Bismuth Alloying
Jonas Sottmann,*,† Matthias Herrman,† Ponniah Vajeeston,† Yang Hu,† Amund Ruud,† Christina Drathen, ‡ Hermann Emerich, § Helmer Fjellvåg,*,† David S. Wragg†
†
Department of Chemistry, University of Oslo, Blindern, P.O. Box 1033, 0315 Oslo, Norway. ‡
European Synchrotron, 71 Rue des Martyrs, 38043 Grenoble, France.
§
Swiss–Norwegian Beamlines, European Synchrotron, 71 Rue des Martyrs, 38043 Grenoble, France.
1
Page 2 Experimental Details Preparation of the Bismuth/Carbon (Bi/C) Composites The Bi/C composites were prepared by milling of bismuth powder (Bi, 99.999% purity, 200 mesh, Alfa Aesar) and conductive carbon black (C, Timcal Super P) in a mass ratio of 7:3 under Ar. Ball-milling was conducted using a Fritsch Mini-Mill Pulverisette 23 at 50 Hz with a ball-topowder ratio of 10:1 for 20 min (Bi/C-20min) and a Fritsch Planetary Micro Mill Pulverisette 7 at 720 rpm with a ball-to-powder ratio of 20:1 for 24 h (Bi/C-24h). Grinding balls and bowls were made of steel. The composites were kept under inert conditions to prevent oxidation. Electrochemical Characterization Electrode preparation was performed in an Ar filled glove bag (AtmosBag, Aldrich). The working electrode was prepared by spreading slurry composed of 70 wt % of bismuth carbon composite, 10 wt % of conductive carbon black (Super P, Timcal) and 20 wt % poly(acrylic acid) (PAA, Sigma Aldrich) as binder dissolved in degassed absolute ethanol on Al foil. PAA binder can accommodate the large expected volume expansions1-3. Drying of the electrodes was carried out under vacuum at 60 °C overnight. The electrodes were thereafter transferred to and stored in a glove box (M. Braun) with O2 and H2O levels less than 0.1 ppm. In the glove box the working electrode was cut into disks with a mass loading of active material of about 1 mg/cm2. The battery was assembled in coin cells (2032) in the glove box. The working electrode was separated from the Na metal disk as counter electrode by electrolyte soaked glass fibres (GF/C, Whatman). As electrolyte a 1 M solution of NaPF6 in ethylene carbonate/diethyl carbonate (EC/DEC, 1:1 in wt) solution with the addition of 5 wt % FEC was prepared. All electrolyte constituents were purchased from Sigma Aldrich. Galvanostatic cycling was performed at a current of 50 mA/g in a voltage range of 0.01 V to 2 V vs Na/Na+ using a Bat-Small battery cycler (Astrol). In the following specific capacity values of the Bi/C composites are expressed on the basis of the mass of Bi. Morphological and Structural Characterization A SU8200 cold-field emission Scanning Electron Microscope (SEM, Hitachi) was used to image the surface morphology of the electrode films. High resolution powder XRD was collected of Bi powder and pristine Bi/C composites sealed under Ar in 0.5 mm diameter thin-walled glass capillaries (Hilgenberg) at ID22, at the European Synchrotron (ESRF). Diffraction profiles were collected using a 9 analyser crystals detector. The wavelength (λ= 0.42749 Å) was calibrated by means of a Si NIST standard. Ex situ samples were prepared at charged (2 V) and discharged state (0 V) in the 2nd and 100th cycle. The coin cells were disassembled in the glove box. The recovered working electrodes were sealed under Ar in 0.5 mm diameter thin-walled glass capillaries (Hilgenberg). Ex situ powder XRD measurements with Cu Kα1 (λ = 1.54059 Å) radiation were performed in transmission mode on a Bruker D8
Page 3 Advance with LynxEye XE detector and Ge (1 1 1) monochromator. All profile fittings and Rietveld refinements were performed using TOPAS V5 (Bruker AXS). For each powder pattern zero-shift, background (Chebychev polynomial 8-13 terms for ESRF beamline ID22 data, 5 terms for Bruker D8 diffractometer data), unit cell parameters, peak-profile parameters for the individual phases, as well as their scale factor, were refined. Broad background features due to amorphous material (glass, carbon black etc.) were fitted with broad peaks with refined position, Gaussian broadening and intensity. Crystallite sizes were determined using the integral breadth (Lvol-IB) method. In operando Synchrotron XRD and XAS In operando quasi-simultaneous powder XRD and XAS were performed at the Swiss-Norwegian Beam Lines (SNBL), BM01B, at the ESRF. Diffraction profiles were collected using a Dexela 2923 CMOS 2D detector. The wavelength (λ = 0.50648 Å) was calibrated by means of a Si NIST standard. For data reduction the PyFAI software was used4. All profile fittings and Rietveld refinements were performed using TOPAS V5 (Bruker AXS). Each series of powder patterns was refined in parallel as a single dataset. Zero-shift, background (Chebychev polynomial 12 terms for Bi/C-20min, 7 terms for Bi/C-24h and broad background features due to amorphous material (Glass fiber, carbon black, PAA, Kapton etc.) were fitted with broad peaks with refined position, Gaussian broadening and intensity) and scale factors for the individual phases were refined in parallel for all powder patterns in each dataset. Cell parameters and peak-profile parameters for the individual phases were refined for each dataset. Reflections from the textured Al foil were fitted for each individual powder pattern using a structureless phase with the lattice parameter and space group of Al metal (a = 4.05 Å, Fm-3m). Spot-like irregular reflections from the Na metal were fitted with individual peaks (refining position, width and intensity) for each individual powder pattern. Bismuth L3 edge X-ray Absorption Near Edge Spectroscopy (XANES) was collected from 13300 to 13520 eV in transmission mode using a Si (1 1 1) channel-cut type monochromator. The second crystal was detuned at about 70 % to reduce higher harmonics. The XANES data were analysed using ATHENA5 for absorption edge determination and spectrum normalization to an edge jump of unity. The absorption edge position was determined as the maximum of the first derivative of the spectrum. The relative shift in absorption energy was calculated with respect to metallic Bi (L3 edge at 13419 eV). An Ir foil was used as a reference (Ir L1 edge at 13419 eV). The electrochemical cycling was performed in Swagelok type electrochemical cells with Kapton windows which are available at SNBL. The battery assembly was kept identical to the coin cells. A current of 50 mA/g was applied. The first 1.5 galvanostatic cycles were followed in operando. Each charge/discharge took approximately 10 h. XRD and XANES data collection (2 min per XRD/XANES scan) were performed in sequence on the same cell.
Page 4 Computational Details Total energies have been calculated by the projected-augmented plane-wave (PAW) implementation of the Vienna ab initio simulation package (VASP)6, 7. All these calculations were made with the Perdew, Burke, and Ernzerhof (PBE)8 exchange correlation functional. Ground-state geometries were determined by minimizing stresses and Hellman-Feynman forces using the conjugate-gradient algorithm with force convergence less than 10-3 eV/Å. Brillouin zone integration was performed with a Gaussian broadening of 0.1 eV during all relaxations. From various sets of calculations it was found that 512 k points in the whole Brillouin zone for the structure with a 600 eV plane-wave cut-off are sufficient to ensure optimum accuracy in the computed results. The k-points were generated using the Monkhorst-Pack method with a grid size of 8×8×8 for structural optimization. A similar density of k-points and energy cut-off were used to estimate total energy as a function of volume for all the structures considered for the present study. Iterative relaxation of atomic positions was stopped when the change in total energy between successive steps was less than 1 meV/cell. The calculated total energy as a function of volume has been fitted to the so-called universal equation of state (EOS)9. The transition pressures are calculated from the pressure vs Gibbs free energy curves. The Gibbs free energy (G = U+PV-TS where T = 0; G = total energy + pressurevolume) is calculated in the following way: The calculated volume vs total energy for two data sets were read in and for each data set the total energy and volume have been fitted to the universal EOS function. The pressure is defined as P = (B0/B0|) [(ve/v) B0’ - 1], which gives volume (v) = ve / [ (1 + (B0|/ B0 p) 1/ B0’] where ve, B0, and B0| refers to the equilibrium volume, bulk modulus, and derivative of bulk modulus, respectively. The inverse is then calculated using the bisection method. From the scan over the pressures, the corresponding difference in the enthalpy between the two data sets was calculated.
Page 5 Electrochemistry
Figure S1. Cycling performance of Bi/C-24h with varying electrolyte salts in EC/DEC and with or without the addition of 5 wt % FEC to the electrolyte. Electrochemical cycling was performed at a current density of 150 mA/g. As shown in Fig. S1, electrolytes with addition of FEC showed better cycling stability for the Bi/C composites than the FEC free ones, while the influence of the electrolyte salt on the cycling stability is negligible. The best cycling performance of the Bi/C composites was observed for a 1M solution of NaPF6 in EC/DEC with addition of 5 wt % FEC (Fig. S1). Therefore, this electrolyte was used for all other electrochemical characterization.
Figure S2. Differential capacity plots for (a) Bi/C-20min and Bi/C-24h corresponding to Fig. 1a and 1b, respectively. The small peak at 0.33 V in (a) is caused by polarization of the counter electrode and not from a change in potential of the working electrode as shown in Ref. [10].
Page 6
Figure S3. Cycling performance of Bi/C-20min and Bi/C-24h at a current density of 50 mA/g. A 1M solution of NaPF6 in EC/DEC with addition of 5 wt % FEC was used as electrolyte. The specific capacity is expressed on the basis of the mass of Bi/C. For both samples the capacity values exceed the theoretical capacity for Na alloying with Bi to Na3Bi. Surplus capacity may arise from reversible electrochemical reactions with amorphous carbon (prepared by ball milling of carbon black for 24 h under similar conditions)11 and Bi2O3 [12] impurities but might also be due to other unidentified Na storage mechanisms. Both give larger contributions for Bi/C-24h. The specific capacity values (Cs) of the Bi/C composites are expressed on the basis of the mass of Bi. Cs accounts for both electrochemical activities of bismuth and carbon. The specific capacity for Bi alone could be estimated as Cs(Bi) = Cs – mC/mBi ∙ Cs(C), where mC and mBi are the mass of carbon species and bismuth in the electrode. The maximal reversible capacity of these carbon species is 173 mAh/g for amorphous (glassy) carbon11 which means that Cs(Bi) is reduced by less than 74 mAh/g compared to Cs. The possible capacity contribution from Bi2O3 that was already present or formed during electrode preparation can be assessed in a similar manner. Bi2O3 has a theoretical capacity of 690 mAh/g which means that it gives 305 mAh/g extra capacity compared to pure Bi. If the electrode contained 5 wt % Bi2O3 this would result in an excess capacity of about 15 mAh/g. Due to the high amount of carbon in the composite the capacity was also expressed on the basis of the mass of Bi/C composite (Fig. S3). Due to addition of 30 wt % carbon the capacity is reduced by 30 % compared to when only the mass of Bi is considered. A theoretical capacity of 321 mAh/g can be estimated based on the theoretical capacity for Bi (70 %) and the reversible capacity for amorphous carbon (30 %). This capacity is reached in Bi/C-24h after 5 cycles. Optimization of the Bi/C ratio is subject to further studies.
Page 7
Figure S4. (a) Cycling performance of Bi/C-20min and Bi/C-24h at a current density of 50 mA/g. Rate capability of (b) Bi/C-20min and (c) Bi/C-24h. The specific capacity was measured during charge. (d) Specific capacity of the first charge of Bi/C-20min and Bi/C-24h at different current densities. The rate capabilities of Bi/C-20min and Bi/C-24h are presented in Fig. S4b-d. Fig. S4d shows the specific capacity of the first charge of Bi/C-20min and Bi/C-24h at different current densities. The rate capability is comparable for both electrodes. Bi/C-24h generally shows slightly better rate performance than Bi/C-20min. At current densities between 50 mA/g and 500 mA/g no significant change in first charge capacity was observed for either electrode. In this current range first charge capacities of about 457 mAh/g and 491 mAh/g on average were found for Bi/C-20min and Bi/C-24h, respectively. For higher current densities (> 1000 mA/g) the first charge capacity is significantly reduced for both electrodes. The first charge capacities for current densities of 1000 mA/g and 1500 mA/g are comparable. They are about 357 mAh/g and 368 mAh/g in average for Bi/C-20min and Bi/C-24h, respectively. The described trends for capacity retention with cycle number at a current density of 50 mAh/g also apply for higher current rates (Fig. S4b-c). After 100 cycles higher capacities are observed for the cells cycled at lower current densities for Bi/C-20min and Bi/C-24h. The higher the current density the lower the capacity retained. Coloumbic efficiencies are improved at higher current rates. For current rates above 500 mA/g the Coloumbic efficiencies are about 99 % after the stabilization for both
Page 8 electrodes. These high current rates might prevent from irreversible side reactions taking place during discharge. Cycling of Bi/C-20min at 1500 mA/g failed after 15 cycles. Na-Bi DFT Work The structural stability and the high pressure behaviour of the NaBi compound is not yet know experimentally as well as theoretically. In order to understand the relative stability of the NaBi chemical composition the following 19 structures are considered in the theoretical simulation. The involved structure types are (space group and space group number are given in the parenthesis): TeI (P-1, 2), GaAs (Pmm2, 25), Rb2Te2 (Pbam, 55), FeSe (P4/nmmS, 129), SnO(P4/nmmS, 129), HgF (I4/mmm, 139), HgS (P3121, 152), HgS (P3221, 154), BiO (R3mH, 160), NiS (R3mR, 160), AuCu (P4/mmm, 123), NiO (R-3mR, 166), AgI (P63mc, 186), HfSe (P6m2, 187), KS (P-62m, 189), TaN (P6/mmm, 191), VP (P63/mmc, 194), CsCl (Pm-3m, 221), NaCl (Fm-3m, 225). Our calculated total energy as a function of unit cell volume for selected six phases are displayed in Fig. S5. Among the considered structures for our structural optimization, the calculated total energy at the equilibrium volume for the P4/mmm atomic arrangements occurs at the lowest total energy (see Figure S5) and this phase is quite stable up to 10 GPa. The calculated positional and lattice parameters are found to be in good agreement with experimental findings (see Table S1).
Figure S5. Calculated unit cell volume vs total energy (per formula unit; f.u.) for NaBi in actual and possible structural arrangements (structure types being labelled on the illustration).
Page 9 Bismuth is the highest-atomic-number member of the group-15 elements, and its high-pressure, high-temperature behaviour has been studied for more than seven decades. In general Bi has at least four high pressure phases. At ambient condition Bi crystalizes in R-3m-type atomic arrangement. Application of pressure makes sequence of phase transitions in Bi and that are Bi-I Bi-II Bi-III Bi-IV transitions at 2.5 GPa, 2.7 GPa and 4 GPa, respectively13-16. The structure types considered in this study are: Bi (P-1, 2), Bi(P121/m1, 11), Bi (C12/m1, 12), Bi(P121/n1, 14), Bi (Cmce-Si(oS16), 64), Bi (I4/mmm-Bi-III, 139), Bi (I4/mcm, 140), As (R3mH, 166), -Po (Pm-3m, 221), bcc-W (Im-3m, 229). At zero Kelvin Bi stabilizes in an R-3mtype (Bi-I) atomic arrangement and it has the lowest total energy. Our calculated total energy as a function of unit cell volume for selected nine phases are displayed in Fig. S6.
Figure S6. Calculated unit cell volume vs total energy (per formula unit; f.u.) for Bi in actual and possible structural arrangements (structure types being labelled on the illustration).
Page 10 Crystallographic information
Figure S7. (a) Broadening of the Bragg reflections of Bi with extended milling. The inset shows a zoom on the (012) reflection and the * symbol marks reflections from α-Bi2O3 (PDF 01-0712274). SEM image of the (b) Bi/C-20min and (c) Bi/C-24h electrode film surfaces.
Page 11
Figure S8. Rietveld refinement (a) Bi, (b) Bi/C-20min, (c) Bi/C-24h (λ= 0.42749 Å, ESRF ID22). Tick marks indicate positions of Bragg reflections for Bi and α-Bi2O3 (PDF 01-0712274).
Figure S9. In operando XRD profiles of Bi/C-20min and Bi/C-24h in discharged state (0 V). Tick marks indicate positions of Bragg reflections for hexagonal and cubic Na3Bi phases. The gray bars mask reflections from Na and Al.
Page 12 Table S1. Results of the Rietveld refinements of Bi, Bi/C-20min and Bi/C-24h (space group R3m, As-type structure) against ex situ PXRD data from ESRF beamline ID22. Bi Bi/C-20min Bi/C-24h a (Å)
4.547128(7)
4.54715(1)
4.5443(2)
c (Å)
11.86433(3)
11.86413(4)
11.8695(8)
129.6(4)
34(1)
size (nm) 296(1) strain (1)
-
-
1.75(4) E-5
Rwp (%)
21.96
17.35
4.05
Rp (%)
17.32
14.23
3.21
Rexp (%)
14.33
6.54
2.12
Table S2. Crystallographic details of structures of the Na-Bi system. Experimental phase information was obtained from Rietveld refinements of diffraction profiles of Bi powder and ex situ samples with maximal phase fraction of the given phase. Space group, structure type
Atomic sites Z
Unit cell parameters
R-values
Atom
Wyckof f
x
y
z
R-3m (166), As P4/mmm (123), AuCu P63/mmc (194), Na3As
6
a = 4.547128(7)Å c = 11.86433(3)Å
Bi1
2g
0
0
0.23414(4)
1
a = 3.45836(6)Å c = 4.8037(1)Å
Bi1 Na1
1a 1d
0 1/2
0 1/2
0 1/2
2
a = 5.44897(5)Å c = 9.6650(1)Å
Rwp = 21.96% Rp = 17.32% Rexp = 14.33% Rwp = 3.94% Rp = 3.00% Rexp = 2.75% Rwp = 3.77% Rp = 2.92% Rexp = 2.08%
h-Na3Bi
P-3c1 (165), Na3As
6
a = 9.43771(9)Å c = 9.6651 (1)Å
Rwp = 3.69% Rp = 2.88% Rexp = 2.08%
h-Na3Bi
P63cm (185), Na3As
6
a = 9.43770(9)Å c = 9.6651(1)Å
Rwp = 3.72% Rp = 2.91% Rexp = 2.08%
c-Na3Bi
Fm-3m (225), Li3Bi
4
a = 7.6652(6)Å
Rwp = 3.63% Rp = 2.80% Rexp = 2.58%
Bi1 Na1 Na2 Bi1 Na1 Na2 Na3 Bi1 Na1 Na2 Na3 Na4 Bi1 Na1 Na2
2c 2b 4f 6f 2a 4d 12g 6 2 4 6 6 4a 4b 8c
1/3 0 1/3 0.3324(7) 0 1/3 0.356(3) 0.33316 0 1/3 0.34725 0.69650 0 1/2 1/4
2/3 0 2/3 0 0 2/3 0.341(6) 0 0 2/3 0 0 0 1/2 1/4
1/4 1/4 0.5820(4) 1/4 1/4 0.211(1) 0.0823(3) 0.03536 0.97902 0.01549 0.36985 0.20533 0 1/2 1/4
Phase Bi
NaBi
h-Na3Bi
Page 13 Table S3. Unit cell parameters from Rietveld refinements of the various phases observed during in operando and ex situ measurements at maximal phase fractions. Slight differences in unit cell parameters from in operando and ex situ data are due to discrepancies in the alignment of the electrochemical cells along the X-ray beam. Crystallographic information is given in Table S2. Table S4-S5 lists the R-values. Bi NaBi h-Na3Bi c-Na3Bi space group R-3m P4/mmm P63/mmc Fm-3m structure type As AuCu Na3As Li3Bi Z 6 1 2 4 3 V/Z (Å ) 35.4 57.4 124.3 113 ∆V/VBi (%) 0 62 251 219 a (Å) 4.54665(5) 3.45829(6) 5.44898(5) 7.676(1) Bi/C-20min ex-situ c (Å) 11.8622(2) 4.8037(1) 9.6651(1) a (Å) 4.54664(4) 3.45672(2) 5.44902(6) 7.707(2)* Bi/C-20min in operando c (Å) 11.8638(2) 4.80123(5) 9.6637(2) a (Å) 4.5433(2) 3.4596(6) 5.440(1) 7.6654(8) Bi/C-24h ex-situ c (Å) 11.8674(8) 4.803(1) 9.660(3) a (Å) 4.5450(1) 3.4547(1) 5.4495(2) 7.65201(3) Bi/C-24h in operando c (Å) 11.8406(7) 4.7989(3) 9.6650(6) * Due to the very low phase fraction of c-Na3Bi the lattice parameter is poorly determined in the lower resolution in operando experiment.
Page 14 Table S4. The table shows the Rwp values for refinement of the in operando XRD data of Bi/C20min (Rp = 1.12 % and Rexp = 0.124 % in average). Rexp are low due to very high counting statistics from the 2D detector. Specific Specific Specific Scan Scan Rwp Scan Capacity Rwp (%) Capacity Capacity Rwp (%) Number Number (%) Number (mAh/g) (mAh/g) (mAh/g) 1 0 1.56 25 13.0 1.50 42 -18.5 1.63 2 -5.2 1.78 26 25.4 1.48 43 -45.6 1.64 3 -34.5 1.71 27 49.5 1.46 44 -72.6 1.58 4 -58.9 1.66 28 73.6 1.54 45 -99.7 1.57 5 -107.3 1.63 29 97.6 1.55 46 -130.6 1.58 6 -131.7 1.57 30 125.6 1.53 47 -157.3 1.79 7 -155.8 1.57 31 149.8 1.51 48 -196.8 1.78 8 -180.2 1.57 32 173.9 1.48 49 -223.8 1.82 9 -204.6 1.68 33 198.0 1.43 50 -250.9 1.77 10 -229.0 1.68 34 222.2 1.46 51 -287.5 1.78 11 -253.1 1.63 35 246.3 1.49 52 -314.3 1.62 12 -277.4 1.65 36 270.5 1.57 53 -341.2 1.50 13 -301.8 1.63 37 297.1 1.67 54 -368.2 1.45 14 -325.9 1.62 38 323.9 1.74 55 -395.2 1.49 15 -350.3 1.50 39 350.3 1.72 56 -422.2 1.45 16 -374.6 1.43 40 376.9 1.62 57 -449.0 1.47 17 -398.7 1.38 41 403.7 1.59 18 -423.1 1.36 19 -466.4 1.36 20 -490.7 1.36 21 -514.8 1.40 22 -539.2 1.43 23 -563.5 1.45 24 -587.6 1.46
Page 15 Table S5. The table shows the Rwp values for refinement of the in operando XRD data of Bi/C24h (Rp = 1.15 % and Rexp = 0.143 % in average). Rexp are low due to very high counting statistics from the 2D detector. Specific Specific Specific Scan Scan Rwp Scan Capacity Rwp (%) Capacity Capacity Rwp (%) Number Number (%) Number (mAh/g) (mAh/g) (mAh/g) 1 0 1.85 24 11.3 1.67 38 -33.9 1.98 2 0 1.71 25 40.3 1.76 39 -63.0 2.07 3 -20.2 1.75 26 69.5 1.86 40 -92.0 2.11 4 -47.8 1.92 27 98.6 1.85 41 -120.9 2.18 5 -75.1 1.76 28 127.6 1.83 42 -150.3 2.52 6 -100.4 1.88 29 156.4 1.91 43 -191.8 2.11 7 -129.4 1.55 30 185.2 1.89 44 -223.0 1.86 8 -158.9 1.56 31 213.9 2.02 45 -253.5 1.87 9 -188.2 1.66 32 243.1 1.94 46 -284.1 1.81 10 -217.4 1.63 33 272.2 1.92 47 -314.6 1.77 11 -246.5 1.61 34 301.4 1.92 48 -345.4 1.74 12 -275.3 1.73 35 330.7 1.97 49 -376.3 1.67 13 -304.4 1.81 36 371.0 2.10 50 -407.4 1.79 14 -333.4 1.66 37 400.2 2.23 51 -438.4 1.71 15 -362.7 1.76 52 -468.9 1.72 16 -391.9 1.68 53 -499.5 1.72 17 -421.3 1.93 18 -479.1 1.78 19 -508.1 1.73 20 -546.5 1.80 21 -575.7 1.72 22 -605.1 1.78 23 -634.3 1.93
Page 16 Table S6. R-values of the Rietveld refinements of the ex situ PXRD data (Bruker D8 diffractometer). Pristine 2nd cycle 100th cycle 100th cycle 0V 2V 0V Rwp (%) 8.60 4.01 3.93 3.94 Rp (%) 6.19 3.16 2.90 3.00 Bi/C-20min Rexp (%) 3.34 2.08 2.27 2.75 Rwp (%) 3.28 2.80 3.90 3.90 Rp (%) 2.58 3.63 2.96 2.96 Bi/C-24h Rexp (%) 2.38 2.58 2.31 2.31
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How Crystallite Size Controls the Reaction Path in Nonaqueous Metal Ion Batteries: The Example of Sodium Bismuth Alloying
Jonas Sottmann,*,† Matthias Herrman,† Ponniah Vajeeston,† Yang Hu,† Amund Ruud,† Christina Drathen, ‡ Hermann Emerich, § Helmer Fjellvåg,*,† David S. Wragg†
†
Department of Chemistry, University of Oslo, Blindern, P.O. Box 1033, 0315 Oslo, Norway. ‡
European Synchrotron, 71 Rue des Martyrs, 38043 Grenoble, France.
§
Swiss–Norwegian Beamlines, European Synchrotron, 71 Rue des Martyrs, 38043 Grenoble, France.
1
Page 2 Experimental Details Preparation of the Bismuth/Carbon (Bi/C) Composites The Bi/C composites were prepared by milling of bismuth powder (Bi, 99.999% purity, 200 mesh, Alfa Aesar) and conductive carbon black (C, Timcal Super P) in a mass ratio of 7:3 under Ar. Ball-milling was conducted using a Fritsch Mini-Mill Pulverisette 23 at 50 Hz with a ball-topowder ratio of 10:1 for 20 min (Bi/C-20min) and a Fritsch Planetary Micro Mill Pulverisette 7 at 720 rpm with a ball-to-powder ratio of 20:1 for 24 h (Bi/C-24h). Grinding balls and bowls were made of steel. The composites were kept under inert conditions to prevent oxidation. Electrochemical Characterization Electrode preparation was performed in an Ar filled glove bag (AtmosBag, Aldrich). The working electrode was prepared by spreading slurry composed of 70 wt % of bismuth carbon composite, 10 wt % of conductive carbon black (Super P, Timcal) and 20 wt % poly(acrylic acid) (PAA, Sigma Aldrich) as binder dissolved in degassed absolute ethanol on Al foil. PAA binder can accommodate the large expected volume expansions1-3. Drying of the electrodes was carried out under vacuum at 60 °C overnight. The electrodes were thereafter transferred to and stored in a glove box (M. Braun) with O2 and H2O levels less than 0.1 ppm. In the glove box the working electrode was cut into disks with a mass loading of active material of about 1 mg/cm2. The battery was assembled in coin cells (2032) in the glove box. The working electrode was separated from the Na metal disk as counter electrode by electrolyte soaked glass fibres (GF/C, Whatman). As electrolyte a 1 M solution of NaPF6 in ethylene carbonate/diethyl carbonate (EC/DEC, 1:1 in wt) solution with the addition of 5 wt % FEC was prepared. All electrolyte constituents were purchased from Sigma Aldrich. Galvanostatic cycling was performed at a current of 50 mA/g in a voltage range of 0.01 V to 2 V vs Na/Na+ using a Bat-Small battery cycler (Astrol). In the following specific capacity values of the Bi/C composites are expressed on the basis of the mass of Bi. Morphological and Structural Characterization A SU8200 cold-field emission Scanning Electron Microscope (SEM, Hitachi) was used to image the surface morphology of the electrode films. High resolution powder XRD was collected of Bi powder and pristine Bi/C composites sealed under Ar in 0.5 mm diameter thin-walled glass capillaries (Hilgenberg) at ID22, at the European Synchrotron (ESRF). Diffraction profiles were collected using a 9 analyser crystals detector. The wavelength (λ= 0.42749 Å) was calibrated by means of a Si NIST standard. Ex situ samples were prepared at charged (2 V) and discharged state (0 V) in the 2nd and 100th cycle. The coin cells were disassembled in the glove box. The recovered working electrodes were sealed under Ar in 0.5 mm diameter thin-walled glass capillaries (Hilgenberg). Ex situ powder XRD measurements with Cu Kα1 (λ = 1.54059 Å) radiation were performed in transmission mode on a Bruker D8
Page 3 Advance with LynxEye XE detector and Ge (1 1 1) monochromator. All profile fittings and Rietveld refinements were performed using TOPAS V5 (Bruker AXS). For each powder pattern zero-shift, background (Chebychev polynomial 8-13 terms for ESRF beamline ID22 data, 5 terms for Bruker D8 diffractometer data), unit cell parameters, peak-profile parameters for the individual phases, as well as their scale factor, were refined. Broad background features due to amorphous material (glass, carbon black etc.) were fitted with broad peaks with refined position, Gaussian broadening and intensity. Crystallite sizes were determined using the integral breadth (Lvol-IB) method. In operando Synchrotron XRD and XAS In operando quasi-simultaneous powder XRD and XAS were performed at the Swiss-Norwegian Beam Lines (SNBL), BM01B, at the ESRF. Diffraction profiles were collected using a Dexela 2923 CMOS 2D detector. The wavelength (λ = 0.50648 Å) was calibrated by means of a Si NIST standard. For data reduction the PyFAI software was used4. All profile fittings and Rietveld refinements were performed using TOPAS V5 (Bruker AXS). Each series of powder patterns was refined in parallel as a single dataset. Zero-shift, background (Chebychev polynomial 12 terms for Bi/C-20min, 7 terms for Bi/C-24h and broad background features due to amorphous material (Glass fiber, carbon black, PAA, Kapton etc.) were fitted with broad peaks with refined position, Gaussian broadening and intensity) and scale factors for the individual phases were refined in parallel for all powder patterns in each dataset. Cell parameters and peak-profile parameters for the individual phases were refined for each dataset. Reflections from the textured Al foil were fitted for each individual powder pattern using a structureless phase with the lattice parameter and space group of Al metal (a = 4.05 Å, Fm-3m). Spot-like irregular reflections from the Na metal were fitted with individual peaks (refining position, width and intensity) for each individual powder pattern. Bismuth L3 edge X-ray Absorption Near Edge Spectroscopy (XANES) was collected from 13300 to 13520 eV in transmission mode using a Si (1 1 1) channel-cut type monochromator. The second crystal was detuned at about 70 % to reduce higher harmonics. The XANES data were analysed using ATHENA5 for absorption edge determination and spectrum normalization to an edge jump of unity. The absorption edge position was determined as the maximum of the first derivative of the spectrum. The relative shift in absorption energy was calculated with respect to metallic Bi (L3 edge at 13419 eV). An Ir foil was used as a reference (Ir L1 edge at 13419 eV). The electrochemical cycling was performed in Swagelok type electrochemical cells with Kapton windows which are available at SNBL. The battery assembly was kept identical to the coin cells. A current of 50 mA/g was applied. The first 1.5 galvanostatic cycles were followed in operando. Each charge/discharge took approximately 10 h. XRD and XANES data collection (2 min per XRD/XANES scan) were performed in sequence on the same cell.
Page 4 Computational Details Total energies have been calculated by the projected-augmented plane-wave (PAW) implementation of the Vienna ab initio simulation package (VASP)6, 7. All these calculations were made with the Perdew, Burke, and Ernzerhof (PBE)8 exchange correlation functional. Ground-state geometries were determined by minimizing stresses and Hellman-Feynman forces using the conjugate-gradient algorithm with force convergence less than 10-3 eV/Å. Brillouin zone integration was performed with a Gaussian broadening of 0.1 eV during all relaxations. From various sets of calculations it was found that 512 k points in the whole Brillouin zone for the structure with a 600 eV plane-wave cut-off are sufficient to ensure optimum accuracy in the computed results. The k-points were generated using the Monkhorst-Pack method with a grid size of 8×8×8 for structural optimization. A similar density of k-points and energy cut-off were used to estimate total energy as a function of volume for all the structures considered for the present study. Iterative relaxation of atomic positions was stopped when the change in total energy between successive steps was less than 1 meV/cell. The calculated total energy as a function of volume has been fitted to the so-called universal equation of state (EOS)9. The transition pressures are calculated from the pressure vs Gibbs free energy curves. The Gibbs free energy (G = U+PV-TS where T = 0; G = total energy + pressurevolume) is calculated in the following way: The calculated volume vs total energy for two data sets were read in and for each data set the total energy and volume have been fitted to the universal EOS function. The pressure is defined as P = (B0/B0|) [(ve/v) B0’ - 1], which gives volume (v) = ve / [ (1 + (B0|/ B0 p) 1/ B0’] where ve, B0, and B0| refers to the equilibrium volume, bulk modulus, and derivative of bulk modulus, respectively. The inverse is then calculated using the bisection method. From the scan over the pressures, the corresponding difference in the enthalpy between the two data sets was calculated.
Page 5 Electrochemistry
Figure S1. Cycling performance of Bi/C-24h with varying electrolyte salts in EC/DEC and with or without the addition of 5 wt % FEC to the electrolyte. Electrochemical cycling was performed at a current density of 150 mA/g. As shown in Fig. S1, electrolytes with addition of FEC showed better cycling stability for the Bi/C composites than the FEC free ones, while the influence of the electrolyte salt on the cycling stability is negligible. The best cycling performance of the Bi/C composites was observed for a 1M solution of NaPF6 in EC/DEC with addition of 5 wt % FEC (Fig. S1). Therefore, this electrolyte was used for all other electrochemical characterization.
Figure S2. Differential capacity plots for (a) Bi/C-20min and Bi/C-24h corresponding to Fig. 1a and 1b, respectively. The small peak at 0.33 V in (a) is caused by polarization of the counter electrode and not from a change in potential of the working electrode as shown in Ref. [10].
Page 6
Figure S3. Cycling performance of Bi/C-20min and Bi/C-24h at a current density of 50 mA/g. A 1M solution of NaPF6 in EC/DEC with addition of 5 wt % FEC was used as electrolyte. The specific capacity is expressed on the basis of the mass of Bi/C. For both samples the capacity values exceed the theoretical capacity for Na alloying with Bi to Na3Bi. Surplus capacity may arise from reversible electrochemical reactions with amorphous carbon (prepared by ball milling of carbon black for 24 h under similar conditions)11 and Bi2O3 [12] impurities but might also be due to other unidentified Na storage mechanisms. Both give larger contributions for Bi/C-24h. The specific capacity values (Cs) of the Bi/C composites are expressed on the basis of the mass of Bi. Cs accounts for both electrochemical activities of bismuth and carbon. The specific capacity for Bi alone could be estimated as Cs(Bi) = Cs – mC/mBi ∙ Cs(C), where mC and mBi are the mass of carbon species and bismuth in the electrode. The maximal reversible capacity of these carbon species is 173 mAh/g for amorphous (glassy) carbon11 which means that Cs(Bi) is reduced by less than 74 mAh/g compared to Cs. The possible capacity contribution from Bi2O3 that was already present or formed during electrode preparation can be assessed in a similar manner. Bi2O3 has a theoretical capacity of 690 mAh/g which means that it gives 305 mAh/g extra capacity compared to pure Bi. If the electrode contained 5 wt % Bi2O3 this would result in an excess capacity of about 15 mAh/g. Due to the high amount of carbon in the composite the capacity was also expressed on the basis of the mass of Bi/C composite (Fig. S3). Due to addition of 30 wt % carbon the capacity is reduced by 30 % compared to when only the mass of Bi is considered. A theoretical capacity of 321 mAh/g can be estimated based on the theoretical capacity for Bi (70 %) and the reversible capacity for amorphous carbon (30 %). This capacity is reached in Bi/C-24h after 5 cycles. Optimization of the Bi/C ratio is subject to further studies.
Page 7
Figure S4. (a) Cycling performance of Bi/C-20min and Bi/C-24h at a current density of 50 mA/g. Rate capability of (b) Bi/C-20min and (c) Bi/C-24h. The specific capacity was measured during charge. (d) Specific capacity of the first charge of Bi/C-20min and Bi/C-24h at different current densities. The rate capabilities of Bi/C-20min and Bi/C-24h are presented in Fig. S4b-d. Fig. S4d shows the specific capacity of the first charge of Bi/C-20min and Bi/C-24h at different current densities. The rate capability is comparable for both electrodes. Bi/C-24h generally shows slightly better rate performance than Bi/C-20min. At current densities between 50 mA/g and 500 mA/g no significant change in first charge capacity was observed for either electrode. In this current range first charge capacities of about 457 mAh/g and 491 mAh/g on average were found for Bi/C-20min and Bi/C-24h, respectively. For higher current densities (> 1000 mA/g) the first charge capacity is significantly reduced for both electrodes. The first charge capacities for current densities of 1000 mA/g and 1500 mA/g are comparable. They are about 357 mAh/g and 368 mAh/g in average for Bi/C-20min and Bi/C-24h, respectively. The described trends for capacity retention with cycle number at a current density of 50 mAh/g also apply for higher current rates (Fig. S4b-c). After 100 cycles higher capacities are observed for the cells cycled at lower current densities for Bi/C-20min and Bi/C-24h. The higher the current density the lower the capacity retained. Coloumbic efficiencies are improved at higher current rates. For current rates above 500 mA/g the Coloumbic efficiencies are about 99 % after the stabilization for both
Page 8 electrodes. These high current rates might prevent from irreversible side reactions taking place during discharge. Cycling of Bi/C-20min at 1500 mA/g failed after 15 cycles. Na-Bi DFT Work The structural stability and the high pressure behaviour of the NaBi compound is not yet know experimentally as well as theoretically. In order to understand the relative stability of the NaBi chemical composition the following 19 structures are considered in the theoretical simulation. The involved structure types are (space group and space group number are given in the parenthesis): TeI (P-1, 2), GaAs (Pmm2, 25), Rb2Te2 (Pbam, 55), FeSe (P4/nmmS, 129), SnO(P4/nmmS, 129), HgF (I4/mmm, 139), HgS (P3121, 152), HgS (P3221, 154), BiO (R3mH, 160), NiS (R3mR, 160), AuCu (P4/mmm, 123), NiO (R-3mR, 166), AgI (P63mc, 186), HfSe (P6m2, 187), KS (P-62m, 189), TaN (P6/mmm, 191), VP (P63/mmc, 194), CsCl (Pm-3m, 221), NaCl (Fm-3m, 225). Our calculated total energy as a function of unit cell volume for selected six phases are displayed in Fig. S5. Among the considered structures for our structural optimization, the calculated total energy at the equilibrium volume for the P4/mmm atomic arrangements occurs at the lowest total energy (see Figure S5) and this phase is quite stable up to 10 GPa. The calculated positional and lattice parameters are found to be in good agreement with experimental findings (see Table S1).
Figure S5. Calculated unit cell volume vs total energy (per formula unit; f.u.) for NaBi in actual and possible structural arrangements (structure types being labelled on the illustration).
Page 9 Bismuth is the highest-atomic-number member of the group-15 elements, and its high-pressure, high-temperature behaviour has been studied for more than seven decades. In general Bi has at least four high pressure phases. At ambient condition Bi crystalizes in R-3m-type atomic arrangement. Application of pressure makes sequence of phase transitions in Bi and that are Bi-I Bi-II Bi-III Bi-IV transitions at 2.5 GPa, 2.7 GPa and 4 GPa, respectively13-16. The structure types considered in this study are: Bi (P-1, 2), Bi(P121/m1, 11), Bi (C12/m1, 12), Bi(P121/n1, 14), Bi (Cmce-Si(oS16), 64), Bi (I4/mmm-Bi-III, 139), Bi (I4/mcm, 140), As (R3mH, 166), -Po (Pm-3m, 221), bcc-W (Im-3m, 229). At zero Kelvin Bi stabilizes in an R-3mtype (Bi-I) atomic arrangement and it has the lowest total energy. Our calculated total energy as a function of unit cell volume for selected nine phases are displayed in Fig. S6.
Figure S6. Calculated unit cell volume vs total energy (per formula unit; f.u.) for Bi in actual and possible structural arrangements (structure types being labelled on the illustration).
Page 10 Crystallographic information
Figure S7. (a) Broadening of the Bragg reflections of Bi with extended milling. The inset shows a zoom on the (012) reflection and the * symbol marks reflections from α-Bi2O3 (PDF 01-0712274). SEM image of the (b) Bi/C-20min and (c) Bi/C-24h electrode film surfaces.
Page 11
Figure S8. Rietveld refinement (a) Bi, (b) Bi/C-20min, (c) Bi/C-24h (λ= 0.42749 Å, ESRF ID22). Tick marks indicate positions of Bragg reflections for Bi and α-Bi2O3 (PDF 01-0712274).
Figure S9. In operando XRD profiles of Bi/C-20min and Bi/C-24h in discharged state (0 V). Tick marks indicate positions of Bragg reflections for hexagonal and cubic Na3Bi phases. The gray bars mask reflections from Na and Al.
Page 12 Table S1. Results of the Rietveld refinements of Bi, Bi/C-20min and Bi/C-24h (space group R3m, As-type structure) against ex situ PXRD data from ESRF beamline ID22. Bi Bi/C-20min Bi/C-24h a (Å)
4.547128(7)
4.54715(1)
4.5443(2)
c (Å)
11.86433(3)
11.86413(4)
11.8695(8)
129.6(4)
34(1)
size (nm) 296(1) strain (1)
-
-
1.75(4) E-5
Rwp (%)
21.96
17.35
4.05
Rp (%)
17.32
14.23
3.21
Rexp (%)
14.33
6.54
2.12
Table S2. Crystallographic details of structures of the Na-Bi system. Experimental phase information was obtained from Rietveld refinements of diffraction profiles of Bi powder and ex situ samples with maximal phase fraction of the given phase. Space group, structure type
Atomic sites Z
Unit cell parameters
R-values
Atom
Wyckof f
x
y
z
R-3m (166), As P4/mmm (123), AuCu P63/mmc (194), Na3As
6
a = 4.547128(7)Å c = 11.86433(3)Å
Bi1
2g
0
0
0.23414(4)
1
a = 3.45836(6)Å c = 4.8037(1)Å
Bi1 Na1
1a 1d
0 1/2
0 1/2
0 1/2
2
a = 5.44897(5)Å c = 9.6650(1)Å
Rwp = 21.96% Rp = 17.32% Rexp = 14.33% Rwp = 3.94% Rp = 3.00% Rexp = 2.75% Rwp = 3.77% Rp = 2.92% Rexp = 2.08%
h-Na3Bi
P-3c1 (165), Na3As
6
a = 9.43771(9)Å c = 9.6651 (1)Å
Rwp = 3.69% Rp = 2.88% Rexp = 2.08%
h-Na3Bi
P63cm (185), Na3As
6
a = 9.43770(9)Å c = 9.6651(1)Å
Rwp = 3.72% Rp = 2.91% Rexp = 2.08%
c-Na3Bi
Fm-3m (225), Li3Bi
4
a = 7.6652(6)Å
Rwp = 3.63% Rp = 2.80% Rexp = 2.58%
Bi1 Na1 Na2 Bi1 Na1 Na2 Na3 Bi1 Na1 Na2 Na3 Na4 Bi1 Na1 Na2
2c 2b 4f 6f 2a 4d 12g 6 2 4 6 6 4a 4b 8c
1/3 0 1/3 0.3324(7) 0 1/3 0.356(3) 0.33316 0 1/3 0.34725 0.69650 0 1/2 1/4
2/3 0 2/3 0 0 2/3 0.341(6) 0 0 2/3 0 0 0 1/2 1/4
1/4 1/4 0.5820(4) 1/4 1/4 0.211(1) 0.0823(3) 0.03536 0.97902 0.01549 0.36985 0.20533 0 1/2 1/4
Phase Bi
NaBi
h-Na3Bi
Page 13 Table S3. Unit cell parameters from Rietveld refinements of the various phases observed during in operando and ex situ measurements at maximal phase fractions. Slight differences in unit cell parameters from in operando and ex situ data are due to discrepancies in the alignment of the electrochemical cells along the X-ray beam. Crystallographic information is given in Table S2. Table S4-S5 lists the R-values. Bi NaBi h-Na3Bi c-Na3Bi space group R-3m P4/mmm P63/mmc Fm-3m structure type As AuCu Na3As Li3Bi Z 6 1 2 4 3 V/Z (Å ) 35.4 57.4 124.3 113 ∆V/VBi (%) 0 62 251 219 a (Å) 4.54665(5) 3.45829(6) 5.44898(5) 7.676(1) Bi/C-20min ex-situ c (Å) 11.8622(2) 4.8037(1) 9.6651(1) a (Å) 4.54664(4) 3.45672(2) 5.44902(6) 7.707(2)* Bi/C-20min in operando c (Å) 11.8638(2) 4.80123(5) 9.6637(2) a (Å) 4.5433(2) 3.4596(6) 5.440(1) 7.6654(8) Bi/C-24h ex-situ c (Å) 11.8674(8) 4.803(1) 9.660(3) a (Å) 4.5450(1) 3.4547(1) 5.4495(2) 7.65201(3) Bi/C-24h in operando c (Å) 11.8406(7) 4.7989(3) 9.6650(6) * Due to the very low phase fraction of c-Na3Bi the lattice parameter is poorly determined in the lower resolution in operando experiment.
Page 14 Table S4. The table shows the Rwp values for refinement of the in operando XRD data of Bi/C20min (Rp = 1.12 % and Rexp = 0.124 % in average). Rexp are low due to very high counting statistics from the 2D detector. Specific Specific Specific Scan Scan Rwp Scan Capacity Rwp (%) Capacity Capacity Rwp (%) Number Number (%) Number (mAh/g) (mAh/g) (mAh/g) 1 0 1.56 25 13.0 1.50 42 -18.5 1.63 2 -5.2 1.78 26 25.4 1.48 43 -45.6 1.64 3 -34.5 1.71 27 49.5 1.46 44 -72.6 1.58 4 -58.9 1.66 28 73.6 1.54 45 -99.7 1.57 5 -107.3 1.63 29 97.6 1.55 46 -130.6 1.58 6 -131.7 1.57 30 125.6 1.53 47 -157.3 1.79 7 -155.8 1.57 31 149.8 1.51 48 -196.8 1.78 8 -180.2 1.57 32 173.9 1.48 49 -223.8 1.82 9 -204.6 1.68 33 198.0 1.43 50 -250.9 1.77 10 -229.0 1.68 34 222.2 1.46 51 -287.5 1.78 11 -253.1 1.63 35 246.3 1.49 52 -314.3 1.62 12 -277.4 1.65 36 270.5 1.57 53 -341.2 1.50 13 -301.8 1.63 37 297.1 1.67 54 -368.2 1.45 14 -325.9 1.62 38 323.9 1.74 55 -395.2 1.49 15 -350.3 1.50 39 350.3 1.72 56 -422.2 1.45 16 -374.6 1.43 40 376.9 1.62 57 -449.0 1.47 17 -398.7 1.38 41 403.7 1.59 18 -423.1 1.36 19 -466.4 1.36 20 -490.7 1.36 21 -514.8 1.40 22 -539.2 1.43 23 -563.5 1.45 24 -587.6 1.46
Page 15 Table S5. The table shows the Rwp values for refinement of the in operando XRD data of Bi/C24h (Rp = 1.15 % and Rexp = 0.143 % in average). Rexp are low due to very high counting statistics from the 2D detector. Specific Specific Specific Scan Scan Rwp Scan Capacity Rwp (%) Capacity Capacity Rwp (%) Number Number (%) Number (mAh/g) (mAh/g) (mAh/g) 1 0 1.85 24 11.3 1.67 38 -33.9 1.98 2 0 1.71 25 40.3 1.76 39 -63.0 2.07 3 -20.2 1.75 26 69.5 1.86 40 -92.0 2.11 4 -47.8 1.92 27 98.6 1.85 41 -120.9 2.18 5 -75.1 1.76 28 127.6 1.83 42 -150.3 2.52 6 -100.4 1.88 29 156.4 1.91 43 -191.8 2.11 7 -129.4 1.55 30 185.2 1.89 44 -223.0 1.86 8 -158.9 1.56 31 213.9 2.02 45 -253.5 1.87 9 -188.2 1.66 32 243.1 1.94 46 -284.1 1.81 10 -217.4 1.63 33 272.2 1.92 47 -314.6 1.77 11 -246.5 1.61 34 301.4 1.92 48 -345.4 1.74 12 -275.3 1.73 35 330.7 1.97 49 -376.3 1.67 13 -304.4 1.81 36 371.0 2.10 50 -407.4 1.79 14 -333.4 1.66 37 400.2 2.23 51 -438.4 1.71 15 -362.7 1.76 52 -468.9 1.72 16 -391.9 1.68 53 -499.5 1.72 17 -421.3 1.93 18 -479.1 1.78 19 -508.1 1.73 20 -546.5 1.80 21 -575.7 1.72 22 -605.1 1.78 23 -634.3 1.93
Page 16 Table S6. R-values of the Rietveld refinements of the ex situ PXRD data (Bruker D8 diffractometer). Pristine 2nd cycle 100th cycle 100th cycle 0V 2V 0V Rwp (%) 8.60 4.01 3.93 3.94 Rp (%) 6.19 3.16 2.90 3.00 Bi/C-20min Rexp (%) 3.34 2.08 2.27 2.75 Rwp (%) 3.28 2.80 3.90 3.90 Rp (%) 2.58 3.63 2.96 2.96 Bi/C-24h Rexp (%) 2.38 2.58 2.31 2.31
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