Term information
A shape factor is used in x-ray diffraction and crystallography to correlate the size of sub-micrometre particles, or crystallites, in a solid to the broadening of a peak in a diffraction pattern. In the Scherrer equation, \tau = \frac {K \lambda}{\beta \cos \theta} where K is the shape factor, It is important to realize that the Scherrer formula provides a lower bound on the particle size. The reason for this is that a variety of factors can contribute to the width of a diffraction peak; besides crystallite size, the most important of these are usually inhomogeneous strain and instrumental effects. If all of these other contributions to the peak width were zero, then the peak width would be determined solely by the crystallite size and the Scherrer formula would apply. If the other contributions to the width are non-zero, then the crystallite size can be larger than that predicted by the Scherrer formula, with the "extra" peak width coming from the other factors. source: http://en.wikipedia.org/wiki/Scherrer_Equation
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <apply> <eq/> <ci>τ</ci> <apply> <divide/> <apply> <times/> <ci>K</ci> <ci>λ</ci> </apply> <apply> <times/> <ci>β</ci> <apply> <cos/> <ci>θ</ci> </apply> </apply> </apply> </apply> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <mrow> <mi>τ</mi> <mo>=</mo> <mfrac> <mrow> <mi>K</mi> <mo>⁢</mo> <mi>λ</mi> </mrow> <mrow> <mi>β</mi> <mo>⁢</mo> <mrow> <mi>cos</mi> <mo>⁡</mo> <mi>θ</mi> </mrow> </mrow> </mfrac> </mrow> </math>
<math xmlns="http://www.w3.org/1998/Math/MathML" display="block"> <semantics> <mrow> <mi>τ</mi> <mo>=</mo> <mfrac> <mrow> <mi>K</mi> <mi>λ</mi> </mrow> <mrow> <mi>β</mi> <mi>cos</mi> <mi>θ</mi> </mrow> </mfrac> </mrow> <annotation encoding="SnuggleTeX">\[ \tau = \frac {K \lambda}{\beta \cos \theta} \]</annotation> </semantics> </math>
Term relations
- correlation equation
- has_variable some (
variable and
is_about some size) - has_variable some (
variable and
is_about some wavelength) - has_part_equation some Braggs law equation