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Example 5.2: Anhydrous Sodium carbonate Structure with strong harmonic modulation of positions and ADP. Chemical formula: Na 2 CO 3 3d incommensurate commensurate Alpha 9.02, 5.21, , 90, 90 P6 3 /mmm Beta 8.98, 5.25, , 90.33, 90 C2/m Gamma 8.92, 5.25, , , 90 C2/m( 0 ) q=(0.182,0,0.322) Delta 8.90, 5.24, , , 90 C2/m( 0 ) q=(1/6,0,1/3) 757K628K170K Change of rotation symmetry Change of translation symmetry The main change of the structure occurs during the alpha beta transition which changes rotation symmetry. Although modulations in gamma and delta phase are very strong they only modify the beta structure keeping the rotation symmetry unchanged. Alpha Beta Gamma Delta

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Data for the phase gamma Single crystal data measured with KUMA four-circle diffractometer Input files: naco.hkl, naco.cif_od Frame scaling, absorption correction: done with software of diffractometer Unit cell: a=8.9338, b=5.2678, c=6.0565, α= β= , γ= q vector: (0.1776, 0, ) a* c*

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Import wizard 1 2 3

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Symmetry wizard 1 2

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3 Data processing was done with C centering.

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Symbol C2/m(0b0)s0 means: - 3d symmetry C2/c - q vector (0 β 0) - shift by ½ in x4 M50: symmetry x1 x2 x3 x4 symmetry -x1 x2 -x3 -x4+1/2 symmetry -x1 -x2 -x3 -x4 symmetry x1 -x2 x3 x4+1/2 Superspace group from satellite reflections 5 6 Space group from main reflections 4

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Structure solution wizard The only reason for the random seed is compatibility with the text of Jana Cookbook. Convergence with R~21%

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Output of Superflip confirms the symmetry

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1 2 3 The initial structure model

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Individual atoms

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File M40

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Structure plots or

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The plot helps to identify oxygens C1 and C2 will be changed to oxygens with “Edit atoms” tool of Jana

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Structure refinement Refinement of the initial structure model Adding position modulation waves

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Refinement with harmonic ADP and four position modulation waves for all atoms

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Fourier maps and Contour plots Coordinates of Na1: x,y,z Sections to plot: x2-x4 Range of x2: from (y – 2Å/b) to (y + 2Å/b) step 0.02Å Range of x4: from 0 to 2, step 0.02 Stacking of sections: x2-x4 x3(1) x1(1) x2-x4 x3(2) x1(1) …. x2-x4 x3(n) x1(1) x2-x4 x3(1) x1(2) x2-x4 x3(2) x1(2) …. x2-x4 x3(n) x1(m) Range of x1: from (x-1Å/a) to (x+1Å/a) step 0.02Å Range of x3: from (z-1Å/c) to (z+1Å/c) step 0.02Å

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Observed and difference Fourier map for Na1 indicates modulation of ADP Similar features can be seen in difference maps of other atoms except carbon

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Adding ADP modulation waves Final refinement AtomPosition wavesADP waves Na143 Na242 Na342 O142 O244 C130

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Final difference maps Contour step 0.1

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Interpretation of structure model using Grapht t=0 t=1 Internal coordinate t

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Interpretation of structure model using Dist

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Interpretation of structure model using plots

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