## General introduction to scattering Scattering techniques are widely applied in material characterization. Unlike microscope, who investigate small structures in real space, scattering could provide reciprocal images of the entire sample. The techniques applied for investigating the given size range for scattering and microscopy are shown in the following sketch.![[Drawing 2024-04-04 17.48.50.excalidraw.svg]] Scattering, like microscopes, can also combined with cryo-systems, pressure cell or [[Rheometer|rheometer]], to provide required environments for experiments. ### Static and dynamic scattering - Static scattering, or elastic scattering investigate the structure of an ensemble of objects, structure of the constitutes of samples or structural changes. Examples include static light scattering (SLS) and elastic x-ray/neutron scattering. During the process, $|\mathbf{k}_{i}| = |\mathbf{k}_{f}|$. - Dynamic scattering, or inelastic scattering, characterize the excitation, motion/diffusion or activation processes. Examples includes [[Dynamic light scattering]] and inelastic x-ray/neutron scattering. During the process, $|\mathbf{k}_{i}| \neq |\mathbf{k}_{f}|$. >[!Note] >A short remind on typical energy of scattering quantum. >For light (incl. x-ray), $E=\hbar\omega =2\pi\hbar\nu$ >For neutron, $E=\frac{1}{2} m_{n}v^{2}$ >And the momentum $\mathbf{p}=\hbar \mathbf{k}=\hbar \hat{\mathbf{k}} \frac{2\pi}{\lambda}$ >- For light with $\lambda=500 nm$, $E=2.48 eV$. >- For x-ray with $\lambda=0.1 nm$, $E=12.4 keV$ >- For neutron with $\lambda=0.1 nm$, $E=81.9 meV$ > >One may see that the neutron quanta has very little energy compared with x-ray. Thus the n-scattering would less likely to affect the samples, and good to be applied in soft matter or bio sample characterization. ### Interaction of radiation with matter ![[Drawing 2024-04-04 18.19.58.excalidraw.svg]] >[!Note]- >Neutron interaction with electron by dipole-dipole interaction is by spin dipole, cause neutron also has a 1/2 spin. ### Parameters in scattering experiments The (obvious) parameters that are critical in scattering are - $\Phi$, the quantum **flux**, or the number of incident quanta per area - $\sigma$, **scattering cross-section**, or total number of quanta scattered per time and incoming quantum. It has the same dimension with area. - $\frac{d\sigma}{d\Omega}$, differential scattering cross-section, or number of quanta scattered into $d\Omega$ per unit time divided by $\Phi\ d\Omega$. Writing in scattering length density, it would be $\frac{d\sigma}{d\Omega} = \left| \rho(\mathbf{q}) \right|^2$. - $\frac{d^{2}\sigma}{d\Omega dE}$, differential scattering cross-section per energy range $dE$, also called partial differential scattering cross-section. - $\frac{d\Sigma}{d\Omega}$, macroscopic (differential) scattering cross-section, defined as $\frac{1}{V} \frac{d\sigma}{d\Omega}$. Writing in scattering length density, it would be $\frac{d\Sigma}{d\Omega} = \frac{1}{V} \left| \rho(\mathbf{q}) \right|^2$. >[!Info] >See [[Rodriguez-slides2.pdf]] for a shorter intro on concepts. External link https://neutrons.ornl.gov/sites/default/files/Rodriguez-slides2.pdf.\