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  2. Cation-anion radius ratio - Wikipedia

    en.wikipedia.org/wiki/Cation-anion_radius_ratio

    The radius ratio rule defines a critical radius ratio for different crystal structures, based on their coordination geometry. [1] The idea is that the anions and cations can be treated as incompressible spheres, meaning the crystal structure can be seen as a kind of unequal sphere packing .

  3. Pauling's rules - Wikipedia

    en.wikipedia.org/wiki/Pauling's_rules

    An octahedron may then form with a radius ratio greater than or equal to 0.414, but as the ratio rises above 0.732, a cubic geometry becomes more stable. This explains why Na + in NaCl with a radius ratio of 0.55 has octahedral coordination, whereas Cs + in CsCl with a radius ratio of 0.93 has cubic coordination.

  4. Goldschmidt tolerance factor - Wikipedia

    en.wikipedia.org/wiki/Goldschmidt_Tolerance_Factor

    r B is the radius of the B cation. r O is the radius of the anion (usually oxygen). In an ideal cubic perovskite structure, the lattice parameter (i.e., length) of the unit cell (a) can be calculated using the following equation: [ 1 ]

  5. Ionic radius - Wikipedia

    en.wikipedia.org/wiki/Ionic_radius

    Ionic radius, r ion, is the radius of a monatomic ion in an ionic crystal structure. Although neither atoms nor ions have sharp boundaries, they are treated as if they were hard spheres with radii such that the sum of ionic radii of the cation and anion gives the distance between the ions in a crystal lattice .

  6. List of PDF software - Wikipedia

    en.wikipedia.org/wiki/List_of_PDF_software

    an Office suite; allows to export (and import, with accuracy limitations) PDF files. Microsoft Word 2013: Proprietary: Desktop software. The 2013 edition of Office allows PDF files to be converted into a format that can be edited. Nitro PDF Reader: Trialware: Text highlighting, draw lines and measure distances in PDF files. Nitro PDF Pro ...

  7. Measurement of a Circle - Wikipedia

    en.wikipedia.org/wiki/Measurement_of_a_Circle

    Proposition one states: The area of any circle is equal to a right-angled triangle in which one of the sides about the right angle is equal to the radius, and the other to the circumference of the circle. Any circle with a circumference c and a radius r is equal in area with a right triangle with the two legs being c and r.

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