The liquid phase epitaxy approach for the successful construction of ultrathin and defect-free ZIF-8 Membranes: Pure and mixed gas transport study.

Transcription

1 The liquid phase epitaxy approach for the successful construction of ultrathin and defect-free ZIF-8 Membranes: Pure and mixed gas transport study. Osama Shekhah, 1 Raja Swaidan, 2 Youssef Belmabkhout, 1 Marike du Plessis, 3 Tia Jacobs, 3 Leonard J. Barbour, 3 Ingo Pinnau, 2 Mohammed Eddaoudi 1 * Table of content: 1. Experimental: - Synthesis of ZIF-8 crystals S3 - ZIF-8 membrane fabrication S3 - Characterization of ZIF-8 crystals and ZIF-8 membranes S3 - Pure gas permeation measurements S4 - Mixed gas permeation measurements S4 - Adsorption and kinetics S4 - Measurement of gas adsorption equilibrium and kinetics using Rubotherm Magnetic balance - Figure S1. Structure of ZIF-8 with the growth along the (100) direction, the 2- methylimidazol (mim) organic ligand bridge, cavity and window size are also shown. S4 S6 - Figure S2. Schematic representation of the permeation setup used for the pure- and mixed-gas permeation measurements. - Figure S3. PXRD diffractograms of ZIF-8 thin film membranes grown on alumina substrate using the LPE method, (a) after 150 growth cycles (b) after 300 growth cycles. All diffractograms were background-subtracted. - Figure S4: Cross-section SEM image of the ZIF-8 thin film fabricated (150 cycles) using the LPE method with a thickness of ~0.5µm. - Figure S5. Permeability of single gases measured for the ZIF-8 membrane fabricated using the LPE method at (T = 308 K and P= 18 psig) versus the Lennard-Jones diameter of the gases. - Figure S6. Permeate pressure of CO 2, measured versus time using the constant volume/variable pressure technique on ZIF-8 membrane fabricated using the LPE method at 308 K and 18 psig, where is the calculated time-lag. S7 S8 S9 S10 S11 -Figure S7. Sorption coefficient of single gases measured for the ZIF-8 membrane at (T = 308 K) versus the boiling point of the gases. S12 S1

2 -Figure S8: Qualitative adsorption kinetics of CO 2, CH 4, C 3 H 6, C 3 H 8 and n-c 4 H 10 on the ZIF-8 crystals at various pressures and 308 K. -Figure S9. Single component adsorption isotherms of H 2, CO 2, N 2 and CH 4 on ZIF-8 powder at 308 K. Filled symbols represent adsorption, open symbols represent desorption. S13 S14 -Figure S10. (a) Single component adsorption isotherms of CH 4, C 2 H 6, C 2 H 4, C 3 H 8, C 3 H 6 and n-c 4 H 10 on ZIF-8 powder at 308 K. Filled symbols represent adsorption, open symbols represent desorption. (b) Kinetics of adsorption (in fractional uptake) of CO 2, CH 4, C 3 H 6, C 3 H 8 and n-c 4 H 10 collected at various pressures and 308 K -Figure S11. N 2 sorption isotherm on ZIF-8 crystals measured at 77 K. -Figure S12. Permeability and selectivity of the 50/50 C 3 H 6 /C 3 H 8 mixture (2.7 bar/40 psig) with time, measured using the constant-volume/variable-pressure technique on ZIF-8 membrane at 308 K. -Figure S13. Permeability and selectivity of the 25/75 CH 4 /n-c 4 H 10 mixture (2.7 bar/40 psig) with time, measured using the constant-volume/variable-pressure technique on ZIF-8 membrane at 328 K. -Table S1: Comparison of the single gas permeance values measured on ZIF-8 membranes found in literature. S15 S16 S17 S18 S19 2. Crystal structure data. S20 -Table S2. Crystal data and structure refinement for ZIF-8 under vacuum. S21 -Table S3. Crystal data and structure refinement for ZIF-8 at 50 bar Methane. S22 -Table S4. Crystal data and structure refinement for ZIF-8 at 35 bar Ethane. S23 -Table S5. Crystal data and structure refinement for ZIF-8 at 2 bar Propane. S24 -Table S6. Crystal data and structure refinement for ZIF-8 at 4 bar Propane. S25 S2

3 1. Experimental: Synthesis of ZIF-8 crystals: The ZIF-8 crystals were synthesized according to the procedure reported by Park et al., where zinc nitrate tetrahydrate Zn(NO 3 ) 2.4H 2 O (0.210 g) and 2-methylimidazole (H-mIm) (0.060 g) were dissolved in 18 ml of DMF in a 20-ml vial. The vial was capped and heated at a rate of 5 C/min to 140 C in a programmable oven and held at this temperature for 24 h, then cooled at a rate of 0.4 C/min to room temperature. After removal of mother liquor from the mixture, chloroform (20 ml) was added to the vial. Colorless polyhedral crystals were collected from the upper layer, washed with DMF, and then exchanged with methanol for 24 hours. 1 ZIF-8 membrane fabrication: ZIF-8 membrane was grown on porous supports by the stepwise deposition method. The alumina substrates (Cobra Technologies BV) were first washed with water and dried at 140 C, to remove any water or organic contaminants from the surface. The alumina substrate was then vertically mounted on the teflon sample holder in the robot using teflon screws. The growth was performed briefly using the following steps: (1) The substrate was immersed in the metal ions methanolic solution for 90 seconds, (2) washed with fresh solvent, (3) immersed in the organic ligand methanolic solution for 120 seconds, and (4) washed with fresh solvent t. This process was considered as one cycle and then repeated many times, in order to grow more layers (see Fig. 1). After 150 cycles, the supports seemed to be homogeneously deposited by visual inspection. The resulting membrane was immediately covered with a watch glass, and allowed to dry slowly in ambient air overnight. 2 Characterization of ZIF-8 crystals and ZIF-8 membranes: X-ray powder diffraction (PXRD) patterns were recorded on a Panalytical X pert PRO MPD X-ray Diffractometer with Cu Kα radiation (λ = nm, 45 kv, 40 ma). Low pressure gas sorption measurements were performed on a fully automated micropore gas analyzer Autosorb-1C (Quantachrome Instruments) at relative pressures up to 1 atm. The cryogenic temperatures were controlled using a liquid nitrogen bath at 77 K. The apparent surface area of ZIF-8 crystals was determined from the nitrogen adsorption isotherm by applying the Brunauer-Emmett-Teller (BET) model using adsorption points in the relative pressure (P/P 0 ) range of to SEM was performed using an FEI Quanta 600 field emission scanning electron microscope (accelerating voltage: 30 kv) Permeability analysis Pure Gas Permeation Measurements: A constant-volume/variable-pressure (CV/VP) apparatus (see Fig. S2 in the supporting information (SI)), was used to determine the pure gas permeability, diffusion and sorption coefficients of the thin films via the time-lag analysis. A custom cell was used to mount the film and sealed with O-rings on both surfaces. Modified with feed-inlet and retentate outlet lines, the cell enabled both pure and mixed gas testing without relocation of the membrane. In pure gas experiments with the CV/VP technique, the retentate line was closed. Before each run, the entire system was evacuated under high vacuum at 35 o C until any downstream pressure rise virtual leak rate - was less than 1% of the rate of steady-state pressure rise for any penetrant gas. All pure gas experiments were run at 2 bar feed pressure. The downstream pressure rise during permeation was monitored with a 10 Torr MKS Baratron transducer and the experiment was stopped after seven to ten time-lags elapsed to ensure steady-state. The permeability of the pure gas is given by dp P DS d dt SS dp d dt LR V d l (p up p d )ART where P is the permeability coefficient in Barrer (10-10 cm 3 (STP) cm/(cm 2 s cmhg)), dp d /dt SS is the steady-state rate of permeate pressure rise (cmhg/s), dp d /dt LR is the downstream leak rate (cmhg/s) (negligible here), V d is the downstream volume (cm 3 ), l is the active layer thickness (cm), p up is the S3

4 upstream pressure (cmhg), A is the membrane area (cm 2 ), R is the gas constant (0.278 cm 3 cmhg/(cm 3 (STP) K)), and T is the temperature at measurement (K). The apparent diffusion coefficient D (cm 2 /s) is calculated from the time-lag (s), derived from the transient regime of pressure rise, as D=l 2 /6 via solution to the differential equations governing mass transport across the film. 3 Assuming permeation occurs via the solution-diffusion mechanism, a reasonable assumption for microporous materials with nominal pore diameter less than 10 A, 3 the solubility coefficient S (cm 3 (STP)/(cm 3 cmhg)), is given from the relation P=DS by S=P/D. Mixed Gas Permeation Measurements: The mixed gas permeation properties of the ZIF-8 thin-film composites were measured at 35 o C. Feed gas mixtures of 50/50 C 3 H 6 /C 3 H 8 and 75/25 CH 4 /n-c 4 H 10 were run at 2.7 bar (40 psi) feed pressure such that the penetrant partial pressures were comparable to those in the pure gas experiments. The stage-cut, that is, the ratio of permeate flow rate to feed flow rate, was kept less than 1% such that the residue composition was essentially equal to that of the feed mixture. An Agilent 3000A Micro GC equipped with four columns and thermal conductivity detectors was calibrated for each gas pair over the composition range of interest using several calibration mixtures. Steady state was assumed to be achieved once the permeability and permeates composition ceased to vary with time. The mixed gas permeability coefficient of gas i was determined by dp P i d dt SS dp d dt LR y i V d l (x i p up y i p d )ART where y and x are the molar fractions in the permeate and feed, respectively, and the rate of pressure rise is the total rate measured for the permeate gas mixture. When the downstream pressure is negligible as compared to the upstream pressure, the separation factor for a gas pair (i/j) is calculated by i j P i P j y i xi y j x j Adsorption and kinetics: The procedure for adsorption and kinetics is described in detail in the supporting Information. Preliminary investigation of gas adsorption properties (thermodynamics and kinetics) on the MOF microcrystals is an important step towards the evaluation and characterization of MOF-based membranes. Study of adsorption thermodynamics and kinetics allows quantitative information about the affinity of the given gas to the MOF framework as well as the extent of the accessibility of different probe molecules, with different dimensions, into the porosity. For this purpose, a serie of adsorption experiments were carried out using probe molecules such as of H 2, N 2, O 2, CH 4, CO 2 as well as larger probe molecules such as C 2 H 4, C 2 H 6, C 3 H 6, C 3 H 8 and n-c 4 H 10 at 308 K. Measurement of gas adsorption equilibrium and kinetics using Rubotherm Magnetic balance Adsorption equilibrium measurements of all gases were performed using a Rubotherm gravimetricdensimetric apparatus (Bochum, Germany), composed mainly of a magnetic suspension balance (MSB) and a network of valves, mass flowmeters and temperature and pressure sensors. The MSB overcomes the disadvantages of other commercially available gravimetric instruments by separating the sensitive microbalance from the sample and the measuring atmosphere and is able to perform adsorption measurements across a wide pressure range, i.e. from 0 to 20 MPa. The adsorption temperature may also be controlled within the range of 77 K to 423 K. In a typical adsorption experiment, the adsorbent is precisely weighed and placed in a basket suspended by a permanent magnet through an electromagnet. S4

5 The cell in which the basket is housed is then closed and vacuum or high pressure is applied. The evacuated adsorbent is then exposed to a continuous gas flow (typically 50 ml/min) at a constant temperature. The gravimetric method allows the direct measurement of the reduced gas adsorbed amount. Correction for the buoyancy effect is required to determine the excess adsorbed amount using equation 1, where V adsorbent and V ss refer to the volume of the adsorbent and the volume of the suspension system, respectively. These volumes are determined using the helium isotherm method by assuming that helium penetrates in all open pores of the materials without being adsorbed. The density of the gas is determined experimentally using a volume-calibrated titanium cylinder. By weighing this calibrated volume in the gas atmosphere, the local density of the gas is also determined. Simultaneous measurement of adsorption capacity and gas phase density as a function of pressure and temperature is therefore possible. The excess uptake is the only experimentally accessible quantity and there is no reliable experimental method to determine the absolute uptake. For this reason, only the excess amounts are considered in this work. m excess gas( Vadsorbent Vss) (1) The pressure is measured using two Drucks high-pressure transmitters ranging from 0.5 to 34 bar and 1 to 200 bar, respectively, and one low pressure transmitter ranging from 0 to 1 bar. Prior to each adsorption experiment, about 100 mg to 300 mg sample is outgassed at 423 K at a residual pressure 10-6 mbar. The temperature during adsorption measurements is held constant by using a thermostated circulating fluid. The kinetics measurementswere carried out by monitoring the change in the weight of the sample after its contact with the gas in study (CO 2, C 3 H 8, C 3 H 6 and n-c 4 H 10 ) at various pressures. [1] K. S. Park, Z. Ni, A. P. Cote, J. Y. Choi, R. Huang, F. J. Uribe-Romo, H. K. Chae, M. O'Keeffe, O. M. Yaghi, PNAS, 2006, 103, [2] O. Shekhah, H. Wang, S. Kowarik, F. Schreiber, M. Paulus, M. Tolan, C. Sternemann, F. Evers, D. Zacher, R. A. Fischer, C. Wöll, J. Am. Chem. Soc. 2007, 129, [3] S. W. Rutherford, D. D. Do, Adsorption, 1997, 3, S5

6 Figure S1. Structure of ZIF-8 with the growth along the (100) direction, the 2-methylimidazol (mim) organic ligand bridge, cavity and window size are also shown. S6

7 Figure S2. Schematic representation of the permeation setup used for the pure- and mixed-gas permeation measurements. S7

8 Intensity x 10 3 Electronic Supplementary Material (ESI) for Chemical Communications Figure S3. PXRD diffractograms of ZIF-8 thin film membranes grown on alumina substrate using the LPE method, (a) after 150 growth cycles (b) after 300 growth cycles. All diffractograms were background-subtracted. 20 ZIF-8 thin film 300 cycles ZIF-8 thin film 150 cycles * 15 * * Al 2 O 3 10 * theta (degree) S8

9 Figure S4: Cross-section SEM image of the ZIF-8 thin film fabricated (150 cycles) using the LPE method with a thickness of ~0.5µm. S9

10 Figure S5. Permeability of single gases measured for the ZIF-8 membrane fabricated using the LPE method at (T = 308 K and P= 18 psig) versus the Lennard-Jones diameter of the gases. 30 C 2 H 6 C 2 H 4 25 H O 2 Permeability [Barrer] He Electronic Supplementary Material (ESI) for Chemical Communications Single gas permeability N 2 CH 4 CO 2 C 3 H 6 C 3 H 8 C 4 H o Lennard-Jones Diameter [ ] S10

11 Permeate [Torr] Electronic Supplementary Material (ESI) for Chemical Communications Figure S6. Permeate pressure of CO 2, measured versus time using the constant volume/variable pressure technique on ZIF-8 membrane fabricated using the LPE method at 308 K and 18 psig, where is the calculated time-lag x CO 2 permeation in ZIF-8 membrane Linear fit Time [min] S11

12 S [cm 3 (gas)/(cm 3 (MOF) cm Hg)] Electronic Supplementary Material (ESI) for Chemical Communications Figure S7. Sorption coefficient of single gases measured for the ZIF-8 membrane at (T = 308 K) versus the boiling point of the gases. 1 C 3 H 6 C 3 H 8 C 2 H 6 n-c 4 H 10 C 2 H 4 CO CH 4 H 2 O 2 N Normal boiling point [K] S12

13 Figure S8: Qualitative adsorption kinetics of CO 2, CH 4, C 3 H 6, C 3 H 8 and n- C 4 H 10 on the ZIF-8 crystals at various pressures and 308 K. S13

14 Adsorption uptake mmol/g Electronic Supplementary Material (ESI) for Chemical Communications Figure S9. Single component adsorption isotherms of H 2, CO 2, N 2 and CH 4 on ZIF-8 powder at 308 K. Filled symbols represent adsorption, open symbols represent desorption. 8 7 CO CH O 2 N 2 H Pressure (bar) S14

15 Fractional uptake Adsorption uptake mmol/g Electronic Supplementary Material (ESI) for Chemical Communications Figure S10. (a) Single component adsorption isotherms of CH 4, C 2 H 6, C 2 H 4, C 3 H 8, C 3 H 6 and n-c 4 H 10 on ZIF-8 powder at 308 K. Filled symbols represent adsorption, open symbols represent desorption. (b) Kinetics of adsorption (in fractional uptake) of CO 2, CH 4, C 3 H 6, C 3 H 8 and n-c 4 H 10 collected at various pressures and 308 K. 5 a 4 n-c 4 H 10 3 C 3 H 6 C 3 H 8 C 2 H 4 2 C 2 H 6 CH Pressure (bar) b CO 2 -adsorption kinetics at 0.2 bar C 3 H 8 -adsorption kinetics at 0.2 bar C 3 H 6 -adsorption kinetics at 0.2 bar CH 4 -adsorption kinetics at 0.2 bar n-c 4 H 10 -adsorption kinetics at 0.2 bar time (min) S15

16 Quantity Adsorbed (cm3/g STP) Electronic Supplementary Material (ESI) for Chemical Communications Figure S11. N 2 sorption isotherm on ZIF-8 crystals measured at 77 K ZIF-8 N 2 sorption at 77 K Absolute Pressure (mmhg) S16

17 Figure S12. Permeability and selectivity of the 50/50 C 3 H 6 /C 3 H 8 mixture (2.7 bar/40 psig) with time, measured using the constant-volume/variable-pressure technique on ZIF-8 membrane at 308 K. S17

18 Figure S13. Permeability and selectivity of the 25/75 CH 4 /n-c 4 H 10 mixture (2.7 bar/40 psig) with time, measured using the constant-volume/variable-pressure technique on ZIF-8 membrane at 328 K. S18

19 Table S1: Comparison of the single gas permeance values measured on ZIF-8 membranes found in literature. Gas Permeance x 10-8 [mol/s m 2 Pa] Ref. 1 Ref. 1 Ref. 2 Ref. 3 Ref. 4 Ref. 5 Ref. 6 Ref. 7 Ref. 8 this work He H N O CO CH C 2 H C 2 H C 3 H C 3 H n-c 4 H References: 1. Venna, S. R.; Carreon, M. A. J. Am. Chem. Soc. 2010, 132, McCarthy, M. C.; Guerrero, V. V.; Barnett, G.; Jeong, H. K. Langmuir 2010, 26, Bux, H.; Chmelik, C.; Krishna, R.; Caro, J. J. Membr. Sci. 2011, 369, Pan, Y.; Lai, Z. Chem. Commun. 2011, 47, Bux, H.; Liang, F. Y.; Li, Y. S.; Cravillon, J.; Wiebcke, M.; Caro, J. J. Am. Chem. Soc. 2009, 131, Zhong Xie, Jianhua Yang, Jinqu Wang, Ju Bai, Huimin Yin, Bing Yuan, Jinming Lu, Yan Zhang, Liang Zhou and Chunying Duan,, Chem. Comm., 2012,48, Helge Bux, Armin Feldhoff, Janosch Cravillon, Michael Wiebcke, Yan-Shuo Li, and Juergen Caro, Chem. Mater., 2011, 23, Pan Y.C., Li T., Lestari G., Lai Z.P., J. Membr. Sci., 2012, 390, 93. S19

20 2. Crystal structure data. The program PLATON-SQUEEZE was used to estimate the number of guest molecules (adsorbed gas molecules at equilibrium under a given gas pressure). Details of the SQUEEZE results are presented below. SQUEEZE electron count per cell ZIF8 vacuum ZIF8 50 bar Methane ZIF8 35 bar Ethane ZIF8 2 bar Propane ZIF8 4 bar Propane The structures were refined with the updated chemical formula and CIF files were created. The associated structure parameters (e.g. formula unit, crystal density,...) are listed between brackets in the crystal data tables. S20

21 Table S2. Crystal data and structure refinement for ZIF-8 under vacuum. Empirical formula C 8 H 10 N 4 Zn Formula weight Temperature (K) 298(2) Wavelength (Å) Crystal system cubic Space group I-43m Unit cell dimensions (Å, ) a = (2) = b = (2) = c = (2) = Volume (Å 3 ) (10) Z 12 Calculated density (g cm -3 ) Absorption coefficient (mm -1 ) F Crystal size (mm 3 ) range for data collection ( ) 1.69 to Miller index ranges -21 h 22, -22 k 14, -22 l 22 Reflections collected Independent reflections 1173 [R int = ] Completeness to max (%) Max. and min. transmission and Refinement method Full-matrix least-squares on F 2 Data / restraints / parameters 1173 / 0 / 33 Goodness-of-fit on F Final R indices [I 2 (I)] R1 = , wr2 = R indices (all data) R1 = , wr2 = Largest diff. peak and hole (e Å -3 ) and S21

22 Table S3. Crystal data and structure refinement for ZIF-8 at 50 bar Methane. Empirical formula C 8 H 10 N 4 Zn [C H N 4 Zn] Formula weight [290.13] Temperature (K) 298(2) Wavelength (Å) Crystal system cubic Space group I-43m Unit cell dimensions (Å, ) a = (6) = b = (6) = c = (6) = Volume (Å 3 ) 4914(3) Z 12 Calculated density (g cm -3 ) [1.176] Absorption coefficient (mm -1 ) [1.487] F [1860] Crystal size (mm 3 ) range for data collection ( ) 1.69 to Miller index ranges -22 h 21, -22 k 22, -22 l 16 Reflections collected Independent reflections 1138 [R int = ] Completeness to max (%) 99.2 Max. and min. transmission and [ and ] Refinement method Full-matrix least-squares on F 2 Data / restraints / parameters 1138 / 0 / 34 Goodness-of-fit on F Final R indices [I 2 (I)] R1 = , wr2 = R indices (all data) R1 = , wr2 = Largest diff. peak and hole (e Å -3 ) and S22

23 Table S4. Crystal data and structure refinement for ZIF-8 at 35 bar Ethane. Empirical formula C 8 H 10 N 4 Zn [C 9 H 13 N 4 Zn] Formula weight [242.60] Temperature (K) 298(2) Wavelength (Å) Crystal system cubic Space group I-43m Unit cell dimensions (Å, ) a = (14) = b = (14) = c = (14) = Volume (Å 3 ) 4901(7) Z 12 Calculated density (g cm -3 ) [0.986] Absorption coefficient (mm -1 ) [1.481] F [1500] Crystal size (mm 3 ) range for data collection ( ) 1.70 to Miller index ranges -17 h 22, -19 k 22, -18 l 20 Reflections collected Independent reflections 1128 [R int = ] Completeness to max (%) 98.6 Max. and min. transmission and [ and ] Refinement method Full-matrix least-squares on F 2 Data / restraints / parameters 1128 / 0 / 33 Goodness-of-fit on F Final R indices [I 2 (I)] R1 = , wr2 = R indices (all data) R1 = , wr2 = Largest diff. peak and hole (e Å -3 ) and S23

24 Table S5. Crystal data and structure refinement for ZIF-8 at 2 bar Propane. Empirical formula C 8 H 10 N 4 Zn [C H N 4 Zn] Formula weight [258.44] Temperature (K) 298(2) Wavelength (Å) Crystal system cubic Space group I-43m Unit cell dimensions (Å, ) a = (3) = b = (3) = c = (3) = Volume (Å 3 ) (13) Z 12 Calculated density (g cm -3 ) [1.051] Absorption coefficient (mm -1 ) [1.485] F [1610] Crystal size (mm 3 ) range for data collection ( ) 1.70 to Miller index ranges -22 h 21, -22 k 21, -22 l 20 Reflections collected Independent reflections 1135 [R int = ] Completeness to max (%) 99.4 Max. and min. transmission and [ and ] Refinement method Full-matrix least-squares on F 2 Data / restraints / parameters 1135 / 0 / 34 Goodness-of-fit on F Final R indices [I 2 (I)] R1 = , wr2 = R indices (all data) R1 = , wr2 = Largest diff. peak and hole (e Å -3 ) and S24

25 Table S6. Crystal data and structure refinement for ZIF-8 at 4 bar Propane. Empirical formula C 8 H 10 N 4 Zn [C H N 4 Zn] Formula weight [276.07] Temperature (K) 298(2) Wavelength (Å) Crystal system cubic Space group I-43m Unit cell dimensions (Å, ) a = (12) = b = (12) = c = (12) = Volume (Å 3 ) (6) Z 12 Calculated density (g cm -3 ) [1.121] Absorption coefficient (mm -1 ) [1.486] F [1735] Crystal size (mm 3 ) range for data collection ( ) 1.69 to Miller index ranges -21 h 22, -22 k 17, -22 l 22 Reflections collected Independent reflections 1144 [R int = ] Completeness to max (%) 99.5 Max. and min. transmission and [ and ] Refinement method Full-matrix least-squares on F 2 Data / restraints / parameters 1144 / 0 / 34 Goodness-of-fit on F Final R indices [I 2 (I)] R1 = , wr2 = R indices (all data) R1 = , wr2 = Largest diff. peak and hole (e Å -3 ) and S25