In the format provided by the authors and unedited. DOI: 10.1038/NMAT4890 Electron-crystallography for determining the handedness of a chiral zeolite nano-crystal Yanhang Ma 1,2, Peter Oleynikov 1,2,* and Osamu Terasaki 1,2 * 1 School of Physical Science and Technology, ShanghaiTech University, Shanghai 201210, China. 2 Department of Materials & Environmental Chemistry, Stockholm University, Stockholm SE-10691, Sweden emails: poleynikov@shanghaitech.edu.cn; osamu.terasaki@mmk.su.se NATURE MATERIALS www.nature.com/naturematerials 1
Contents 1) Supplementary Note 1 Summary of essential notes for chirality determination using single crystal X-ray diffraction. 2) Supplementary Note 2 Differences between X-ray and electron diffraction for chirality determinations. 3) Table 1 Summary of important notes for chirality determination using X-ray and electron diffraction. 4) Supplementary Figure 1 Crystallographic orientations perpendicular to the screw axis in a hexagonal cystal system. 5) Figure 2 SEM images of the calcined HPM-1 chiral zeolite. 6) Figure 3 2D slices cut from the reconstructed 3D reciprocal lattice. 7) Figure 4 Trace of the marker-gold nanoparticles-during the crystal tilt from [211 11 00] to [111 00] zone axis. 8) Figure 5 Chirality determination of one chiral zeolite crystal with the space group of P6 1 22. 9) Figure 6 Simulated PED patterns of the chiral zeolite with left- and right-handedness along [0001]. 10) Figure 7 Intensity of two pairs of reflections in simulated PED pattern (right-handed framework) along [0001] at different thickness. 11) Figure 8 Intensity profiles of two pairs of reflections: 1111 33 1111 11 (11) & 1111 33 1111 11 (11 ) aaaaaa 1111 11 1111 11 (22) &1111 11 1177 11 (22 ) in experimental and simulated PED patterns. NATURE MATERIALS www.nature.com/naturematerials 2
12) Table 2. Intensities of symmetry-equivalent reflections of 1111 33 1111 11 (1 ) & 1111 33 1111 1 (1) and 1111 11 1111 1 (2 ) & 1111 11 1111 1 (2). 1111 33 1111 1 is always stronger than 1111 33 1111 11 within the statistical error. 13) Table 3. Comparison of a whole set of reflection intensities. Intensity differences in four of nineteen pairs conflict with those in the simulated pattern. The reason might be the intensity changes with thickness (109-191 vs 910-191) or the weakness of reflections. 14) Figure 9 Simulation of dynamical electron diffraction patterns of the chiral zeolite along [211 11 3] and [22 111133 ]. 15) Figure 10 Chirality determination by the comparison of experimental and simulated PED patterns along [211 11 3]. 16) Figure 11 Chirality determination of another crystal from the same batch using PED. 17) Figure 12 Integrated intensities of 0k-k0 & 0-kk0 reflections in supplementary Figure 9 and 10. 18) Figure 13 The intensity profiles of 03333 00 and 033 3333 reflections with the change of thickness in simulated PED pattern along [211 11 33] of the chiral zeolite with space group P6 1 22. 19) Figure 14 PED patterns collected at different beam tilting angles and the intensity changes of reflection 03333 00 and 033 3333. 20) Figure 15 The change of intensities of several reflection pairs with the crystal thickness in PED pattern taken along [211 11 3]. NATURE MATERIALS www.nature.com/naturematerials 3
Supplementary Note 1. Summary of essential notes for chirality determination using single crystal X-ray diffraction It is worth summarizing essential points of X-ray diffraction intensity related to this topic (Table 1). The diffraction intensity I hkl for an hkl reflection is mainly governed by a crystal structure factor F hkl which is defined as follows with atomic form factor f j and coordinates (x j, y j, z j ) of j-th atom (j=1 to N; N different atoms) in a unit cell; NN FF hkkkk = ff jj exp [2ππππ(h xx jj + kk yy jj + ll zz jj ) MM TT,jj ] jj=1 = AA + iiii, FF hkkkk = AA iiii = FF h kk ll where ee MM TT,jjrepresents the temperature effect. If f j is real number, real and imaginary parts of crystal structure factor A and B are given by NN AA = ff jj [cccccc2ππ(h xx jj + kk yy jj + ll zz jj )] exp( MM TT,jj ), jj NN BB = ff jj [ssssss2ππ(h xx jj + kk yy jj + ll zz jj )] exp( MM TT,jj ) jj Therefore, the intensity of reflections and Friedel s law are given as follows. I hkl F hkl * F hkl * and I h k l F h k l F h k l I hkl Deep into atomic level, the right-handed crystal would be converted to the left-handed one by reversing its atomic coordinates, as well as the change of space group correspondingly. Therefore, a crystal structure factor for hkl reflection, F hkl, of a right-handed crystal is equivalent to that for -h-k-l reflection, F h-k-l, of the left-handed one. If we don t take anomalous (resonance) scattering effect into account, f j is real number. The phase change inherent in the X-ray scattering process is π (that is -1), while that in the electron scattering is π/2 (that is i). However, an atomic form factor f j is a function of incident NATURE MATERIALS www.nature.com/naturematerials 4
X-ray energy E as, where f 0,j is Thomson elastic scattering, and f j (E) and f j (E) are real part and imaginary part of anomalous scattering factor of j-th atom. Contributions of f j (E) and f j (E) to f j become large when an incident X-ray energy E is close to the absorption edge of j-th atom, E abs, j and the anomalous scattering effects can be detected. Then crystal structure factor will be NN FF hkkkk = (ff jj,0 + ff jj + iiff jj ) eeeeee[2ππππ(h xx jj + kk yy jj + ll zz jj ) MM TT,jj ] jj=1 NN = [(ff jj,0 + ff jj )cccccc2ππ(h xx jj + kk yy jj + ll zz jj ) ff jj jj=1 ssssss2ππ(h xx jj + kk yy jj + ll zz jj )] eeeeee( MM TT,jj ) NN + ii [(ff jj,0 + ff jj )ssssss2ππ(h xx jj + kk yy jj + ll zz jj ) + ff jj jj=1 cccccc2ππ(h xx jj + kk yy jj + ll zz jj )] eeeeee( MM TT,jj ) AA + iibb And I hk l F hk l F hk l * I h k l unless f '' 0. Friedel s law states that the crystal structure factors of reflection members of a Friedel s pair (Bragg reflections related by inversion through the origin) have equal amplitude and opposite phase. This law will be broken in X-ray diffraction when anomalous scattering occurs. Bijvoet pairs are space-group symmetry-equivalents to the two members of a Friedel pair and they are usually used for the identification of the chirality in single X-ray diffraction through the detection of the intensity asymmetry between the pairs. NATURE MATERIALS www.nature.com/naturematerials 5
Supplementary Note 2. Differences between X-ray and electron diffraction for chirality determinations. Supplementary Table 1. Important notes for chirality determination using X-ray and electron diffraction. X-ray diffraction Electron diffraction Crystal structure* (xx ii, yy ii, zz ii ) RR = (xx ii, yy ii, zz ii ) LL Same as in X-ray diffraction Structure factor (kinematical) Breaking Friedel s law NN FF hkkkk = ff jj,xx ee 2ππππ(h xx ii+kk yy ii +ll zz ii ) jj FF RR (hkkkk) = FF RR (h kk ll ) FF RR (hkkkk) = FF LL (h kk ll ) II RR (hkkkk) = II RR (h kk ll ) Anomalous scattering ff jj = ff 0,jj + ff jj (EE) + ii ff jj (EE) For certain reflections, II RR (hkkkk) II RR (h kk ll ) Same as in X-ray diffraction Multiple-beam scattering: Fourier transform of the exit wave: Ψ eeee (gg) = δδ(gg) λλλλ ii FF(gg) 1 ( λλλλ ) 2 FF(gg) VV cccccccc 2 VV cccccccc FF(gg) + ii 1 ( λλλλ ) 3 FF(gg) 6 VV cccccccc FF(gg) FF(gg) + where FF(gg) is structure factor and VV cccccccc is volume of unit cell. For the double scattering, FF(gg) FF(gg) = gg FF(gg ) FF(gg gg ), the intensity of reflection g will be affected by all possible pairs of reflections g and g-g. Therefore, in a noncentrosymmetric crystal, for certain reflections FF( gg) FF( gg) FF(gg) FF(gg). As a result, for certain reflections, II RR (hkkkk) II RR (h kk ll ). *: Space group also changes if it belongs to an enantiomorphic pair; R: right-handedness and L: lefthandedness. In kinematical scattering, it is assumed that incident electrons are scattered only once and intensity of g reflection is solely dependent on crystal structure factor F(g) and is linearly related to F(g)F(g)* = Abs 2 [F(g)]. Therefore, intensities of a Bijvoet pair of reflections are equivalent. In multiple-beam scattering case, however, this rule is broken. A single-scattered NATURE MATERIALS www.nature.com/naturematerials 6
electron beam g can be scattered again by the k-g plane to the beam k. As a result, the intensity of a reflection k is affected not only by the structure factor F(k) but also by all possible pairs of reflections g and k-g. This is the case for double scattering case. In the multiple scattering effect, the Fourier transform of the exit wave can be formally written as following: Ψ eeee (gg) = δδ(gg) ii λλλλ FF(gg) 1 VV cccccccc 2! ( λλλλ 2 ) FF(gg) FF(gg) + ii 1 VV cccccccc 3! ( λλλλ 3 ) FF(gg) FF(gg) VV cccccccc FF(gg) + Where ii λλλλ VV cccccccc FF(gg) represents the effect of single scattering, 1 2! ( λλλλ VV cccccccc ) 2 FF(gg) FF(gg) represents the effect of double scattering, and ii 1 3! ( λλλλ VV cccccccc ) 3 FF(gg) FF(gg) FF(gg) represents triple scattering and so on. The double scattering, FF(gg) FF(gg) = FF(gg ) FF(gg gg ) gg, will produce, in a non-centrosymmetric crystal, FF( gg) FF( gg) FF(gg) FF(gg) for certain reflections. As a result, for certain reflections, II(gg) II(gg ). Supplementary Figure 1 Crystallographic orientations perpendicular to the screw axis in a hexagonal cystal system. There are several zone axes that we can reach by tilting the crystal along [0001]. NATURE MATERIALS www.nature.com/naturematerials 7
Supplementary Figure 2 SEM images of calcined HPM-1 chiral zeolite. Image from top view displays spiral features on the surface. NATURE MATERIALS www.nature.com/naturematerials 8
Supplementary Figure 3 2D slices cut from reconstructed 3D reciprocal lattice. a, h k hkk 0 plane reveals a clear 6-fold rotation symmetry. b, h0h ll plane shows a clear extinction condition of 000l: l = 6n. NATURE MATERIALS www.nature.com/naturematerials 9
Supplementary Figure 4 Trace of the marker-gold nanoparticles-during the crystal tilting from [211 11 00] to [111 00] zone axis. a-e, Diffraction patterns taken along different directions during the crystal rotation around c axis. The crystal was tilted from [21 1 0] at 0 to [11 00] at 30. f-j, The corresponding low-mag TEM images at different tilting angles, which shows the movement of one Au nanoparticle (indicated by yellow arrows). The use of electron diffraction patterns ensures that crystal was always rotated around c axis. In this way, the marker (gold nanoparticle) should be always at the same height during the rotation. This makes it possible to align two images after rotation. NATURE MATERIALS www.nature.com/naturematerials 10
Supplementary Figure 5 Chirality determination of one chiral zeolite crystal with space group of P6 1 22. In this specific case, the crystal was tilted to the right by ~19, from [21 1 0] to [54 1 0] zone axis. The shift vector is downwards after rotation, suggesting a right-handed structure. As the tilting of sample holder in TEM is mechanically controlled, the rotation to the right or the left direction relies on the position and orientation of the crystal on the grid. If a crystal is tilted to the left, a shift vector upwards will lead to a right-handedness. Therefore, three factors are important in this process: (1) orientation of the c axis; (2) direction of rotation; (3) alignment of the markers. NATURE MATERIALS www.nature.com/naturematerials 11
Supplementary Figure 6 Simulated PED patterns of the chiral zeolite with left- and right-handedness along [0001]. Pairs of FOLZ reflections with 6-fold rotation symmetry were marked by yellow (strong reflection) and red (weak reflection) arrows to show their intensity asymmetries. Simulation conditions: 200 kv, 507 reflections, t = 100 nm, precession angle 0.1, precession step 0.1. There is a clear mirror symmetry between the two patterns. NATURE MATERIALS www.nature.com/naturematerials 12
Supplementary Figure 7 Intensity of reflections in simulated PED pattern (righthanded framework) along [0001] at different thickness. Intensities of reflections 16 1 17 1 & 17 1 16 1 (a) and 15 3 18 1& 18 3 15 1 (b) for right-handed chiral zeolite with space group P6 1 22. Although the reflection intensities change with the crystal thickness, the reflection 17 1 16 1 is always stronger than 16 1 17 1. NATURE MATERIALS www.nature.com/naturematerials 13
Supplementary Figure 8 Intensity profiles of two pairs of reflections : 1111 33 1111 11 (11) & 1111 33 1111 11 (11 ) aaaaaa 1111 11 1111 11 (22) &1111 11 1111 11 (22 ) in experimental and simulated PED patterns. The intensity asymmeties of two Bijvoet pairs of reflections in the experimental pattern match with those in the simulated pattern. NATURE MATERIALS www.nature.com/naturematerials 14
Supplementary Table 2. Intensities of symmetry-equivalent reflections of 1111 33 1111 11 (1 ) & 1111 33 1111 1 (1) and 1111 11 1111 1 (2 ) & 1111 11 1111 1 (2). 1111 33 1111 1 is always stronger than 1111 33 1111 11 within the statistical error. Average Standa rd deviatio n group1 group1' group2 group2' Reflection 315-181 -1518-31 -183151-3-15181 15-1831 18-3-151 Intensity 5239 4057 4648 5119 6037 7274 Reflection 153-181 -318-151 -181531-15-3181 3-18151 18-15-31 Intensity 5189 3876 3462 3594 3510 4616 Reflection 116-171 -1617-11 -171161-1-16171 16-1711 17-1-161 Intensity 7094 5979 7057 6316 7447 9574 Reflection 161-171 -117-161 -171611-16-1171 1-17161 17-16-11 Intensity 6800 4861 4394 4658 4714 5737 5396 1032 4041 645 7245 1154 5194 831 The intensities of six symmetry-equivalent reflections were also listed in the above table to show the statistical accuracy of reflection intensities. NATURE MATERIALS www.nature.com/naturematerials 15
Supplementary Table 3.. Comparison of a whole set of reflection intensities. Intensity differences in four of nineteen pairs conflict with those in the simulated pattern. The reason might be the intensity changes with thickness (109-191 vs 910-191) or the weakness of reflections. Experiment hkil vs khil I(161-171) < I(116-171) I(109-191) > I(910-191) I(153-181) < I(315-181) I(127-191) < I(712-191) I(136-191) < I(613-191) I(162-181) > I(216-181) I(119-201) < I(911-201) I(128-201) < I(812-201) I(154-191) < I(415-191) I(118-191) > I(811-191) I(144-181) > I(414-181) I(145-191) > I(514-191) I(171-181) < I(117-181) I(152-171) < I(215-171) I(126-181) > I(612-181) I(137-201) > I(713-201) I(135-181) < I(513-181) I(163-191) > I(316-191) I(161-171) < I(116-171) Simulation hkil vs khil I(161-171) < I(116-171) I(109-191) < I(910-191) I(153-181) < I(315-181) I(127-191) < I(712-191) I(136-191) < I(613-191) I(162-181) > I(216-181) I(119-201) < I(911-201) I(128-201) < I(812-201) I(154-191) < I(415-191) I(118-191) > I(811-191) I(144-181) > I(414-181) I(145-191) > I(514-191) I(171-181) < I(117-181) I(152-171) > I(215-171) I(126-181) > I(612-181) I(137-201) > I(713-201) I(135-181) > I(513-181) I(163-191) < I(613-191) I(161-171) < I(116-171) Match between experiment and simulation No No No No A whole set of reflection pairs has also been compared in both experimental and simulated PED pattern. Four among nineteen pairs shows different intensity asymmetries in the experimental and simulated patterns. The possible reasons can be intensities changes with crystal thickness or the weakness of reflections. NATURE MATERIALS www.nature.com/naturematerials 16
Supplementary Figure 9 Calculation of dynamical electron diffraction patterns of chiral zeolite with right-handedness (P6 1 22) and left-handedness (P6 5 22). a,b, [21 1 3] and [2 113 ] zone axes of the right-handed crystal. c,d, [21 1 3] and [2 113 ] zone axes of the lefthanded crystal. As we can see, ZOLZ reflections of two enantiomorphic structure are same if one is rotated by 180. Therefore, if a pair of ZOLZ reflections was chose for comparison, the orientations NATURE MATERIALS www.nature.com/naturematerials 17
of axes in the pattern must be determined. The fact that the lattice of FOLZ reflections deviated from that of ZOLZ reflections along [21 1 3], was used as a reference to certify the orientations of the diffraction pattern. As a result, 0kkkk 0 and 0kk kk0 reflections were indexed without ambiguity. The intensity asymmetry between two reflections in a Bijvoet pair (0kkkk 0 and 0kk kk0) was used for chirality determination. Besides, the diffraction patterns are identical along [21 1 3] and [2 113 ], so a reverse of incident electron beam will not change the ED pattern. NATURE MATERIALS www.nature.com/naturematerials 18
Supplementary Figure 10 Chirality determination by comparison of experimental and simulated PED patterns along [211 11 3]. a, Experimental PED pattern along [21 1 3] with precession angle 2. At this beam-tilting angle, FOLZ will overlap with ZOLZ but reflections from different zones are separated as shown in rectangular area. b, Simulated ED pattern with overlap of FOLZ and ZOLZ by increasing excitation error. The red-color reflections are from ZOLZ while the green-color reflections are from FOLZ. A clear lattice deviation between them can be observed. c, Experimental PED pattern along [21 1 3] with precession angle 0.2 from the same crystal. The integrated intensities of 033 0 and 03 30 reflection are 2.27*10 6 NATURE MATERIALS www.nature.com/naturematerials 19
and 3.44*10 6. Therefore, I(033 0)<I(03 30). d, Simulated PED pattern of chiral zeolite with the space group of P6 1 22. The comparison of (c) and (d) reveals that this chiral crystal is right-handed (P6 1 22). NATURE MATERIALS www.nature.com/naturematerials 20
Supplementary Figure 11 Chirality determination of another crystal by comparison of experimental and simulated PED patterns along [211 11 3]. a, Experimental PED pattern along [21 1 3] with precession angle 2. b, Simulated ED pattern with overlap of FOLZ and ZOLZ by increasing excitation error. c, Experimental PED pattern along [21 1 3] with beamtilt angle 0.2 from the same crystal. The integrated intensities of 033 0 and 03 30 reflection in are 3.51*10 6 and 3.10*10 6. Therefore, I(033 0)>I(03 30). d, Simulated PED pattern of chiral zeolite with the space group of P6 5 22. The comparison of (c) and (d) reveals that this chiral crystal is left-handed (P6 5 22). NATURE MATERIALS www.nature.com/naturematerials 21
The collection of a PED pattern at beam-tilt 2 will help to certify the orientations of two axes for indexing 0kkkk 0 and 0kk kk0 reflections when the HOLZ reflections are not observed. The comparison of intensities between a Bijvoet pair of ZOLZ reflections leads to the chirality determination. NATURE MATERIALS www.nature.com/naturematerials 22
Supplementary Figure 12 Integrated intensities of 0k-k0 & 0-kk0 reflections in supplementary Figure 8 and 9. Except for the Friedel pair of 033 0 and 03 30, other reflection pairs such as 022 0 and 02 20 might be used as their intensity difference is also insensitive to crystal thickness in a certain range. NATURE MATERIALS www.nature.com/naturematerials 23
Supplementary Figure 13 The intensity profiles of 003333 00 and 0033 3333 reflections with the change of thickness in simulated PED pattern along [211 11 3] of the chiral zeolite with space group P6 1 22. The intensity of 03 30 reflection is always stronger than that of 033 0 at the thickness from 20 nm to 200 nm. This means the relative intensity between these two reflections is insensitive to the crystal thickness. NATURE MATERIALS www.nature.com/naturematerials 24
Supplementary Figure 14 PED patterns collected at different beam tilting angles and the intensity change of reflections 03333 00 and 033 3333 in the PED pattern taken along [211 11 3]. a-e, Beam-tilt angles are 0.1, 0.2, 0.3, 0.5 and 1.0 respectively. f, Intensities of 033 0 and 033 0 reflections in PED patterns at different beam-tilt angles. NATURE MATERIALS www.nature.com/naturematerials 25
Supplementary Figure 15 The change of intensities of several reflection pairs with the crystal thickness in the PED pattern taken along [211 11 3]. a, 011 0 and 01 10. b, 022 0 and 02 20. c, 033 0 and 03 30. d, 044 0 and 04 40. e, 055 0 and 05 50. The signs of intensity difference between reflection pairs 011 0 & 01 10, 022 0 & 02 20 and 033 0 & 03 30 are not sensitive to the crystal thickness, but the intensity difference between reflection pairs 044 0 & 04 40 and 055 0 & 05 50 are sensitive to the crystal thickness. NATURE MATERIALS www.nature.com/naturematerials 26