What question did this study set out to answer?

To derive an exact formulation of the Scherrer equation for spherical particles and assess the validity of existing approximation methods.

November 15, 1939Physical Review

The Scherrer Formula for X-Ray Particle Size Determination

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Authors

APA. L. PattersonGeorge Mason University

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Implication

Theoretical derivation resolves exact Scherrer equation constants for spherical particles, indicating that tangent plane approximations reliably determine crystallite size.

Key Points

To derive an exact formulation of the Scherrer equation for spherical particles and assess the validity of existing approximation methods.
Derived exact mathematical values for the Scherrer constant using both half-value breadth and integral breadth methods.
Evaluated the accuracy of common approximation techniques, including von Laue's tangent plane approximation and various approximation functions, against exact calculations.
Demonstrated that von Laue's tangent plane approximation yields satisfactory accuracy when compared to exact mathematical solutions for spherical particles.
Identified significant limitations and raised concern regarding the reliability of conventional approximation functions.
Proposed using tangent plane approximations for ellipsoidal particle geometries as a reliable standard for future analytical work.

Cite This Study

A. L. Patterson (1939) studied this question.

synapsesocial.com/papers/69d73b03aa68b335b4f3091c https://doi.org/10.1103/physrev.56.978

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Implication

Theoretical derivation resolves exact Scherrer equation constants for spherical particles, indicating that tangent plane approximations reliably determine crystallite size.

The Scherrer Formula for X-Ray Particle Size Determination

Discussion

Member takes

Implication

Key Points

Cite This Study

The Scherrer Formula for X-Ray Particle Size Determination

Discussion

Member takes

Implication

Key Points

Cite This Study

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