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A review of basic crystallography and x-ray diffraction applications

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Abstract

Although various researched works have been carried out in x-ray crystallography and its applications, but there are still limited number of researches on crystallographic theories and industrial application of x-ray diffraction. The present study reviewed and provided detailed discussion on atomic arrangement of single crystals, mathematical concept of Bravais, reciprocal lattice, and application of x-ray diffraction. Determination of phase identification, crystal structure, dislocation density, crystallographic orientation, and gran size using x-ray diffraction peak intensity, peak position, and peak width were discussed. The detailed review of crystallographic theories and x-ray diffraction application would benefit majorly engineers and specialists in chemical, mining, iron, and steel industries.

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Abbreviations

α, β, γ :

angle between unit cell dimensions in x, y, z directions respectively

α n, α o :

angle between unit cell dimensions in x, y, z directions respectively

β n, β o :

angles of diffracted and incident beams in y direction respectively

γ n, γ o :

angles of diffracted and incident beams in z direction respectively

r :

crystallographic direction vector

u, v, w :

crystallographic directions

δ :

dislocation density

L :

distance between two atoms in space

B :

full width at half maximum

B o :

instrument broadening

n 1, n 2, n 3 :

integer numbers corresponding to wavelength

δ ij :

Lattice tensor

a, b, c :

length of unit cell dimension in x, y, z directions respectively

h, k, l :

Miller indices of crystallographic planes

D :

particle size

R :

position lattice vectors

a 1 ,a 2 ,a 3 :

primitive lattice vector for position vectors

b 1 ,b 2 ,b 3 :

primitive lattice vector for reciprocal vectors

K :

reciprocal lattice vectors

K :

Scherrer constant

B L :

size broadening

d :

space distance

\( {\boldsymbol{d}}_{hkl}^{\ast} \) :

space distance lattice vectors

ε :

strain

B e :

strain broadening

B t :

total broadening peak

s,s o :

unit vector along diffracted and incident beam directions respectively

k,k o :

unit vector of reciprocal lattice along diffracted and incident beam directions respectively

λ:

x-ray wavelength

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Benin, Benin, Edo State, Nigeria

    E. S. Ameh

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Ameh, E.S. A review of basic crystallography and x-ray diffraction applications. Int J Adv Manuf Technol 105, 3289–3302 (2019). https://doi.org/10.1007/s00170-019-04508-1

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