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The structural modulation in some hollandite-type crystals is explained by a vacancy-displacive modulation model. In this model the large cations located in the tetragonal channels along the c axis deviate from the average position to form a modulation wave. Three types of disorder in the initial phase of the modulation wave have been introduced to interpret apparently different diffraction patterns in hollandite-type crystals. A mathematical analysis as well as optical diffraction give results similar to those experimentally observed. High-resolution transmission electron microscope images have been observed to confirm the discussion further.
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