Why 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 instrumental effects and crystallite size; the most important of these are usually inhomogeneous strain and crystal lattice imperfections. The crystallite size can be thought of as a lower limit of particle size.
What is shape factor K?
K is a shape factor. It’s value is different when X-rays are diffracting from different planes of different crystal structure. During it’s derivation we have assumed that diffraction occurs at a specific angle theta B.
Can XRD determine particle size?
NO, normal XRD peak broadening can give good measure (depending on how carefully you perform the experiment) of crystallographic domain size. Small angle X-ray scattering (SAXS) can give size of small particles in nm range. SEC MALLS also will give the exact particle size of the molecule.
What is shape factor formula?
The shape factor is the perimeter of the contour around the area of interest divided by the square root of the area. It is a component of the formula used to calculate the coefficient of error (Coefficients of Error).
What is the ratio of shape factor?
Shape factor is the ratio of a plastic moment(Mp) to elastic moment(Me) OR we can say that it is the ratio of plastic section modulus(Zp) to elastic section modulus(Ze). Shape factor shows the extra strength or moment possessed by a section, that is the strength or moment beyond yield point.
How to determine shape factor ( k ) in Scherrer equation?
Kumar Rajendran Scherrer equation (D=Kλ/βcosθ) is used in XRD to calculate the crystallite size.
Why is the Scherrer formula the most important?
Scherrer equation is one of the most important in the determination of the size of particles of crystals in the form of powder. In the equation, I have found that the shape factor is a dimensionless quantity, with a value close to unity but it varies with the type of crystal structure.
How does the Scherrer equation work for spherical particles?
This method uses the Scherrer equation: where the peak width, B (2θ), at a particular value of 2θ (θ being the diffraction angle, λ the X-ray wavelength) is inversely proportional to the crystallite size L; the constant K is a function of the crystallite shape but is generally taken as being about 1.0 for spherical particles.
How is the Scherrer equation related to crystallography?
The Scherrer equation, in X-ray diffraction and crystallography, is a formula that relates the size of sub-micrometre particles, or crystallites, in a solid to the broadening of a peak in a diffraction pattern. It is named after Paul Scherrer.