.. _sphx_glr_api_gallery_crystal_xrd:

Powder XRD
------------

Laue interference from a periodic array, Bragg's law and simulated
powder-XRD patterns with structure factors and systematic absences for
SC, BCC, and FCC, and Scherrer crystallite sizes from line broadening.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Each line of a diffraction pattern is a family of (hkl) planes that satisfies Bragg&#x27;s law n\lambda=2d\sin\theta. powder_xrd_peaks computes each reflection&#x27;s structure factor (~chemistrykit.crystal.systems.xrd.structure_factor) directly from atomic positions and Miller indices, so BCC&#x27;s and FCC&#x27;s systematic absences (reflections with zero intensity by symmetry) fall out automatically rather than being hardcoded as a rule.">

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  .. image:: /api/gallery/crystal/xrd/images/thumb/sphx_glr_plot_01_powder_xrd_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/xrd/plot_01_powder_xrd`

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      <div class="sphx-glr-thumbnail-title">Bragg's law: indexing powder XRD peaks</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Von Laue (1912) predicted that a crystal, as a periodic array of scatterers, should diffract X-rays like a grating, and Friedrich and Knipping saw the discrete spots. Summing the waves from N periodically spaced scatterers with structure_factor gives the Laue interference function: intensity N^2 at integer h (the Laue condition) and almost nothing in between, ever sharper as N grows.">

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  .. image:: /api/gallery/crystal/xrd/images/thumb/sphx_glr_plot_02_laue_interference_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/xrd/plot_02_laue_interference`

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      <div class="sphx-glr-thumbnail-title">Laue's interference: sharp diffraction spots from a periodic array</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Scherrer (1918) showed that tiny crystallites give broadened powder lines, with width \beta=K\lambda/(\tau\cos\theta) for crystallite size \tau. scherrer_crystallite_size inverts this: here, copper powder patterns are broadened for three crystallite sizes, and each size is recovered from the measured width of the (111) line.">

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  .. image:: /api/gallery/crystal/xrd/images/thumb/sphx_glr_plot_03_scherrer_crystallite_size_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/xrd/plot_03_scherrer_crystallite_size`

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      <div class="sphx-glr-thumbnail-title">Scherrer equation: crystallite size from peak broadening</div>
    </div>


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    </div>


.. toctree::
   :hidden:

   /api/gallery/crystal/xrd/plot_01_powder_xrd
   /api/gallery/crystal/xrd/plot_02_laue_interference
   /api/gallery/crystal/xrd/plot_03_scherrer_crystallite_size