Foundational Papers and References for XRD Peak Broadening Analysis

Scherrer Equation

Scherrer, P. (1918) "Bestimmung der Größe und der inneren Struktur von Kolloidteilchen mittels Röntgenstrahlen." Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen, 26, 98-100.

Original paper introducing what became known as the Scherrer equation
Established the relationship between crystallite size and peak broadening

Williamson-Hall Analysis

Williamson, G.K. & Hall, W.H. (1953) "X-ray line broadening from filed aluminium and wolfram." Acta Metallurgica, 1, 22-31.

Introduced the Williamson-Hall plot method
First systematic approach to separate size and strain effects
Established the linear relationship between βcosθ and 4sinθ

Instrumental Resolution Function

Caglioti, G., Paoletti, A. & Ricci, F.P. (1958) "Choice of collimators for a crystal spectrometer for neutron diffraction." Nuclear Instruments, 3(4), 223-228.

Introduced the Caglioti equation for instrumental broadening
Established U, V, W parameters for resolution function

Profile Shape Functions

Young, R.A. & Wiles, D.B. (1982) "Profile shape functions in Rietveld refinements." Journal of Applied Crystallography, 15, 430-438.

Comprehensive analysis of different profile functions
Detailed discussion of Gaussian, Lorentzian, and pseudo-Voigt profiles

Warren-Averbach Method

Warren, B.E. & Averbach, B.L. (1950) "The Effect of Cold-Work Distortion on X-Ray Patterns." Journal of Applied Physics, 21, 595-599.

Introduced Fourier methods for analyzing peak broadening
More sophisticated approach to size-strain analysis

Comprehensive Reviews

Langford, J.I. & Wilson, A.J.C. (1978) "Scherrer after sixty years: A survey and some new results in the determination of crystallite size." Journal of Applied Crystallography, 11, 102-113.

Historical perspective and critical analysis of the Scherrer equation
Discussion of shape factor K and its proper usage

Snyder, R.L., Fiala, J. & Bunge, H.J. (1999) "Defect and Microstructure Analysis by Diffraction." Oxford University Press.

Comprehensive treatment of diffraction line broadening
Detailed coverage of various analysis methods

Mittemeijer, E.J. & Welzel, U. (2008) "The 'state of the art' of the diffraction analysis of crystallite size and lattice strain." Zeitschrift für Kristallographie, 223, 552-560.

Modern overview of diffraction analysis methods
Critical assessment of various approaches

Double-Voigt Method

Balzar, D. & Ledbetter, H. (1993) "Voigt-function modeling in Fourier analysis of size- and strain-broadened X-ray diffraction peaks." Journal of Applied Crystallography, 26, 97-103.

Introduction of the Double-Voigt approach
Practical method for separating size and strain effects

Modern Applications

Ungár, T. (2004) "Microstructural parameters from X-ray diffraction peak broadening." Scripta Materialia, 51, 777-781.

Modern applications of line profile analysis
Discussion of dislocation density determination