Comparison of Bragg parameters in crystals, with quasi-Bragg parameters in quasicrystals

Bragg

Quasi-Bragg

Comment

$n=2d\sin \left(q\right)/\lambda$

${\tau }^m=2d^{\prime }\sin \left({\theta }^{\prime }\right)/\lambda$

Harmonic laws

Give us ${\theta }^{\prime }=\theta /c_s$

$F_{hkl}={\displaystyle \sum f_i\cos \left(2\pi h_{hkl}\cdot r_i\right)}$

${F^{\prime }}_{hkl}={\displaystyle \sum f_i\cos \left(2\pi c_s\left(h_{hk}{}_l\cdot r_i\right)\right)}$ including iteration

Structure factors

Give c_s, a and $d^{\prime }=d\cdot c_s$

$d=a/h$

$d^{\prime }=a{c}_{s}h$

${\theta }^{\prime }=\theta /c_s$

$a=0.205\tau c_s\text{nm}$ [1]

$a^{\ast }=2p/a$

Measured lattice parameter

a ≈ Diameter of Al

Measured and verified