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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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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DOI: https://doi.org/10.1007/s00170-019-04508-1