Lesson plan
Atomic form factor
In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from real space to momentum space (also known as reciprocal space). For an object with spatial density distribution, \rho(\mathbf{r}) , the form factor, f(\mathbf{Q}) , is defined as : f(\mathbf{Q})=\int \rho(\mathbf{r}) e^{i\mathbf{Q} \cdot \mathbf{r}}\mathrm{d}^3\mathbf{r} , where \rho(\mathbf{r}) is the spatial density of the scatterer about its center of mass ( \mathbf{r}=0 ), and \mathbf{Q} is the momentum transfer. As a result of the nature of the Fourier transform, the broader the distribution of the scatterer \rho in real space \mathbf{r} , the narrower the distribution of f in \mathbf{Q} ; i.e., the faster the decay of the form factor. For crystals, atomic form factors are used to calculate the structure factor for a given Bragg peak of a crystal.
Article summary
In physics, the atomic form factor, or atomic scattering factor, is a measure of the scattering amplitude of a wave by an isolated atom. The atomic form factor depends on the type of scattering, which in turn depends on the nature of the incident radiation, typically X-ray, electron or neutron. The common feature of all form factors is that they involve a Fourier transform of a spatial density distribution of the scattering object from real space to momentum space (also known as reciprocal space). For an object with spatial density distribution, \rho(\mathbf{r}) , the form factor, f(\mathbf{Q}) , is defined as : f(\mathbf{Q})=\int \rho(\mathbf{r}) e^{i\mathbf{Q} \cdot \mathbf{r}}\mathrm{d}^3\mathbf{r} , where \rho(\mathbf{r}) is the spatial density of the scatterer about its center of mass ( \mathbf{r}=0 ), and \mathbf{Q} is the momentum transfer. As a result of the nature of the Fourier transform, the broader the distribution of the scatterer \rho in real space \mathbf{r} , the narrower the distribution of f in \mathbf{Q} ; i.e., the faster the decay of the form factor. For crystals, atomic form factors are used to calculate the structure factor for a given Bragg peak of a crystal.
Key claims
No claims recorded.
Discussion questions
- Summarise the article in your own words. Which single claim would you verify first, and why?
- Which claim in this article is most likely to be revised as the sources update? How would you check its current status?
- If two sources disagreed about one of these facts, what would you need in order to trust one over the other?
Bibliography
No sources recorded.
Key claims and bibliography are generated from the same tracked claims and sources as the article page.