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Disrupted periodicity: strain

Fig.: .
Case study:
S Rios, EKH Salje, SAT Redfern
Nanoquartz vs. macroquartz: a study of the α-β phase transition
Eur Phys J 20 (2001) 75

strain
$$\epsilon=\frac{\Delta d}{d}$$ homogeneous strain
$$n\lambda=2(d-\Delta d)\sin{(\theta+\Delta\theta)}$$ peak shift
inhomogeneous strain
$$\beta=4\epsilon\tan{\theta}$$ strain broadening
instrument function

Fig.: .

separation of size and strain broadening
Williamson-Hall method
$$\beta=\beta_{\textrm{size}}+\beta_{\textrm{strain}}=\frac{k\lambda}{L\cos{\theta}}+4\epsilon\tan{\theta}$$ $$\beta\cos{\theta}=\frac{k\lambda}{L}+4\epsilon\sin{\theta}$$ intercept $\frac{k\lambda}{L}$
slope $4\epsilon$

Fig.: .

phase transition
$\alpha$-quartz to $\beta$-quartz
order parameter

Dynamic strain

Fig.: .
Case study:
ME Jones, S Fearn, R Winter, F Yuan, AR Lennie, JE Parker, SP Thompson, CC Tang
Dynamic strain propagation in nanoparticulate zirconia refractory
J Appl Cryst 48 (2015) 386

Fig.: .

laser strain experiment at Diamond

quasicrystals