Q value

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A given q value (momentum transfer in reciprocal-space) corresponds to a real-space distance (d) of:


q = \frac{2\pi}{d}

Thus, from a peak position in scattering, one can calculate the realspace repeat-structure distance:


d = \frac{2 \pi}{q}

One must be careful, however. A peak in reciprocal-space corresponds to a repeating structure in the realspace lattice; i.e. this may or may not correspond directly to particle-particle spacings.

D vs q.png

Peak position

The q-value for a peak gives a hint about what kinds of structure is producing the scattering:

  • Very large angle (0.5-4 Å−1): Atomic packing distances (1-10 Å).
  • Large angle (0.2-2 Å−1): Molecular packing distances (0.3-3 nm). For instance, aromatic rings tend to pi-pi stack with a 0.3-0.4 nm repeat distance.
  • Medium angle (0.03-0.3 Å−1): Macromolecular distances (2-20 nm). For instance, polymers often crystallize into chain-folded lamellae with a period of 2-10 nm.
  • Small angle (0.0002-0.04 Å−1): Nanoscale distances (15-300 nm). For instance, block-copolymers and nanoparticle superlattices tend to organize in this size regime.
  • Ultra-small angle (<0.0006 Å−1): Micron sizes (>1 µm).


Lookup table

q d      q d      q d      q d
0.00010 Å−1 6283.2 nm 0.00139 Å−1 450.8 nm 0.019 Å−1 32.3 nm 0.27 Å−1 2.3 nm
0.00011 Å−1 5984.0 nm 0.00146 Å−1 429.3 nm 0.020 Å−1 30.8 nm 0.28 Å−1 2.2 nm
0.00011 Å−1 5699.0 nm 0.0015 Å−1 408.9 nm 0.021 Å−1 29.3 nm 0.30 Å−1 2.1 nm
0.00012 Å−1 5427.7 nm 0.0016 Å−1 389.4 nm 0.022 Å−1 27.9 nm 0.31 Å−1 2.0 nm
0.00012 Å−1 5169.2 nm 0.0017 Å−1 370.9 nm 0.024 Å−1 26.6 nm 0.33 Å−1 1.9 nm
0.00013 Å−1 4923.0 nm 0.0018 Å−1 353.2 nm 0.025 Å−1 25.3 nm 0.35 Å−1 1.8 nm
0.00013 Å−1 4688.6 nm 0.0019 Å−1 336.4 nm 0.026 Å−1 24.1 nm 0.36 Å−1 1.7 nm
0.00014 Å−1 4465.3 nm 0.0020 Å−1 320.4 nm 0.027 Å−1 23.0 nm 0.38 Å−1 1.6 nm
0.00015 Å−1 4252.7 nm 0.0021 Å−1 305.1 nm 0.029 Å−1 21.9 nm 0.40 Å−1 1.6 nm
0.00016 Å−1 4050.2 nm 0.0022 Å−1 290.6 nm 0.030 Å−1 20.8 nm 0.42 Å−1 1.50 nm
0.00016 Å−1 3857.3 nm 0.0023 Å−1 276.7 nm 0.032 Å−1 19.9 nm 0.44 Å−1 1.42 nm
0.00017 Å−1 3673.6 nm 0.0024 Å−1 263.6 nm 0.033 Å−1 18.9 nm 0.46 Å−1 1.36 nm
0.00018 Å−1 3498.7 nm 0.0025 Å−1 251.0 nm 0.035 Å−1 18.0 nm 0.49 Å−1 1.29 nm
0.00019 Å−1 3332.1 nm 0.0026 Å−1 239.1 nm 0.037 Å−1 17.2 nm 0.51 Å−1 1.23 nm
0.00020 Å−1 3173.4 nm 0.0028 Å−1 227.7 nm 0.038 Å−1 16.3 nm 0.54 Å−1 1.17 nm
0.00021 Å−1 3022.3 nm 0.0029 Å−1 216.8 nm 0.040 Å−1 15.6 nm 0.56 Å−1 1.12 nm
0.00022 Å−1 2878.4 nm 0.0030 Å−1 206.5 nm 0.042 Å−1 14.8 nm 0.59 Å−1 1.06 nm
0.00023 Å−1 2741.3 nm 0.0032 Å−1 196.7 nm 0.045 Å−1 14.1 nm 0.62 Å−1 1.01 nm
0.00024 Å−1 2610.8 nm 0.0034 Å−1 187.3 nm 0.047 Å−1 13.4 nm 0.65 Å−1 0.96 nm
0.00025 Å−1 2486.5 nm 0.0035 Å−1 178.4 nm 0.049 Å−1 12.8 nm 0.68 Å−1 0.92 nm
0.00027 Å−1 2368.1 nm 0.0037 Å−1 169.9 nm 0.052 Å−1 12.2 nm 0.72 Å−1 0.87 nm
0.00028 Å−1 2255.3 nm 0.0039 Å−1 161.8 nm 0.054 Å−1 11.6 nm 0.75 Å−1 0.83 nm
0.00029 Å−1 2147.9 nm 0.0041 Å−1 154.1 nm 0.057 Å−1 11.1 nm 0.79 Å−1 0.79 nm
0.00031 Å−1 2045.6 nm 0.0043 Å−1 146.8 nm 0.060 Å−1 10.5 nm 0.83 Å−1 0.76 nm
0.00032 Å−1 1948.2 nm 0.0045 Å−1 139.8 nm 0.063 Å−1 10.0 nm 0.87 Å−1 0.72 nm
0.00034 Å−1 1855.4 nm 0.0047 Å−1 133.1 nm 0.066 Å−1 9.5 nm 0.92 Å−1 0.69 nm
0.00036 Å−1 1767.1 nm 0.0050 Å−1 126.8 nm 0.069 Å−1 9.1 nm 0.96 Å−1 0.65 nm
0.00037 Å−1 1682.9 nm 0.0052 Å−1 120.7 nm 0.073 Å−1 8.7 nm 1.01 Å−1 0.62 nm
0.00039 Å−1 1602.8 nm 0.0055 Å−1 115.0 nm 0.076 Å−1 8.2 nm 1.06 Å−1 0.59 nm
0.00041 Å−1 1526.5 nm 0.0057 Å−1 109.5 nm 0.080 Å−1 7.9 nm 1.11 Å−1 0.56 nm
0.00043 Å−1 1453.8 nm 0.0060 Å−1 104.3 nm 0.084 Å−1 7.5 nm 1.17 Å−1 0.54 nm
0.00045 Å−1 1384.6 nm 0.0063 Å−1 99.3 nm 0.088 Å−1 7.1 nm 1.23 Å−1 0.51 nm
0.00048 Å−1 1318.6 nm 0.0066 Å−1 94.6 nm 0.093 Å−1 6.8 nm 1.29 Å−1 0.49 nm
0.00050 Å−1 1255.8 nm 0.0070 Å−1 90.1 nm 0.097 Å−1 6.5 nm 1.35 Å−1 0.46 nm
0.00053 Å−1 1196.0 nm 0.0073 Å−1 85.8 nm 0.102 Å−1 6.2 nm 1.42 Å−1 0.44 nm
0.00055 Å−1 1139.1 nm 0.0077 Å−1 81.7 nm 0.107 Å−1 5.9 nm 1.49 Å−1 0.42 nm
0.00058 Å−1 1084.8 nm 0.0081 Å−1 77.8 nm 0.113 Å−1 5.6 nm 1.57 Å−1 0.40 nm
0.00061 Å−1 1033.2 nm 0.0085 Å−1 74.1 nm 0.118 Å−1 5.3 nm 1.65 Å−1 0.38 nm
0.00064 Å−1 984.0 nm 0.0089 Å−1 70.6 nm 0.124 Å−1 5.1 nm 1.73 Å−1 0.36 nm
0.00067 Å−1 937.1 nm 0.0093 Å−1 67.2 nm 0.130 Å−1 4.8 nm 1.82 Å−1 0.35 nm
0.00070 Å−1 892.5 nm 0.0098 Å−1 64.0 nm 0.137 Å−1 4.6 nm 1.91 Å−1 0.33 nm
0.00074 Å−1 850.0 nm 0.0103 Å−1 61.0 nm 0.144 Å−1 4.4 nm 2.00 Å−1 0.31 nm
0.00078 Å−1 809.5 nm 0.0108 Å−1 58.1 nm 0.15 Å−1 4.2 nm 2.10 Å−1 0.30 nm
0.00081 Å−1 771.0 nm 0.0114 Å−1 55.3 nm 0.16 Å−1 4.0 nm 2.21 Å−1 0.28 nm
0.00086 Å−1 734.3 nm 0.0119 Å−1 52.7 nm 0.17 Å−1 3.8 nm 2.32 Å−1 0.27 nm
0.00090 Å−1 699.3 nm 0.0125 Å−1 50.2 nm 0.17 Å−1 3.6 nm 2.43 Å−1 0.26 nm
0.00094 Å−1 666.0 nm 0.0132 Å−1 47.8 nm 0.18 Å−1 3.4 nm 2.55 Å−1 0.25 nm
0.00099 Å−1 634.3 nm 0.0138 Å−1 45.5 nm 0.19 Å−1 3.3 nm 2.68 Å−1 0.23 nm
0.00104 Å−1 604.1 nm 0.0145 Å−1 43.3 nm 0.20 Å−1 3.1 nm 2.82 Å−1 0.22 nm
0.00109 Å−1 575.3 nm 0.015 Å−1 41.3 nm 0.21 Å−1 3.0 nm 2.96 Å−1 0.21 nm
0.00115 Å−1 547.9 nm 0.016 Å−1 39.3 nm 0.22 Å−1 2.8 nm 3.11 Å−1 0.20 nm
0.00120 Å−1 521.8 nm 0.017 Å−1 37.4 nm 0.23 Å−1 2.7 nm 3.26 Å−1 0.19 nm
0.00126 Å−1 497.0 nm 0.018 Å−1 35.7 nm 0.25 Å−1 2.6 nm 3.42 Å−1 0.18 nm
0.00133 Å−1 473.3 nm 0.019 Å−1 34.0 nm 0.26 Å−1 2.4 nm 3.60 Å−1 0.17 nm