Past exam of the frontiers of experimental condensed matter physics course of the University of Cambridge / 2013 / Paper 1 / 1

X-ray diffraction arises predominantly from electromagnetic scattering by the electronic charge distribution. For elastic scattering, contributions from different unit cells interfere constructively at a reciprocal lattice vector, while the unit-cell structure factor weights the different atoms and their positions. The atomic X-ray scattering factor generally decreases with increasing momentum transfer because an extended electron cloud scatters out of phase with itself. Heavy atoms often scatter more strongly, making a light atom difficult to locate beside a heavy one; near an absorption edge, anomalous dispersion changes the contrast and can provide additional chemical sensitivity.

In neutron diffraction, the strong interaction with atomic nuclei supplies a short-range nuclear scattering amplitude. Its coherent scattering length depends on isotope and does not vary monotonically with atomic number; isotope substitution can therefore give useful contrast, and some light elements can be prominent. A neutron's magnetic moment also couples to magnetic moments in a specimen, so magnetic diffraction measures ordered spin structures. Absorption and incoherent scattering depend strongly on isotope as well. The nuclear scattering length is approximately independent of momentum transfer in the usual thermal-neutron regime, whereas magnetic scattering has a form factor reflecting the electronic magnetization distribution.

Electron diffraction probes the electrostatic potential of both nuclei and electrons. The electron's charge makes scattering strong, allowing thin specimens or surfaces to be studied with intense signals. Strong interaction also makes multiple, dynamical scattering more important, so electron diffraction intensities often cannot be interpreted as a simple single-scattering structure factor squared. Transmission geometry needs electron-transparent material; reflected low-energy electrons provide a surface-sensitive geometry. All three methods use phase-sensitive interference to reveal periodic structure, but their scattering interactions, penetration, sample requirements and contrast differ.

A scanning tunneling microscope can modify an adsorbate's potential landscape as well as image it. First locate the atom with a weakly perturbing tunnel-current setpoint. Bringing the tip closer strengthens tip–atom coupling. In lateral atomic manipulation, moving the tip parallel to the surface can pull or push the atom between adsorption sites; reducing the coupling afterwards leaves it at the chosen location. A change in tunneling current during the motion can signal a jump, and a subsequent low-current image checks the final arrangement.

In vertical atomic manipulation, a suitable tip interaction or voltage pulse transfers an atom between substrate and tip. The tip is repositioned and the atom is deposited elsewhere by changing that interaction again. Electric fields and inelastic tunneling excitation can also change adsorption, induce hopping or modify bonds. The useful mechanism depends on the atom, substrate, tip and bias: there is no universal pulse amplitude that works for every system. Low temperature suppresses thermal diffusion and ultrahigh vacuum helps preserve a clean, stable surface.

A motivating demonstration is IBM in atoms. Don Eigler and Erhard Schweizer used a low-temperature STM to position individual xenon atoms on a nickel surface, constructing a chosen atomic pattern. The 1990 paper reported operation at about $4\mathrm{K}$ with atomic positioning precision. This demonstrates controlled rearrangement of surface adsorbates, rather than making the image alone prove that every STM feature is an isolated atom.^[ref]

In inelastic scattering, the probe transfers energy as well as momentum to the specimen. A neutron, X-ray or electron can create or annihilate a phonon, while electronic or magnetic excitations provide other channels. Measuring the incident and outgoing energies resolves the transfer $\hslash \omega$; their wavevectors determine momentum transfer $\hslash \mathbf{Q}$. In a crystal, phonon momentum is conserved modulo a reciprocal lattice vector. Resolved spectra therefore probe excitation dispersions and lifetimes, rather than only average atomic positions.

Thermal diffuse scattering arises from thermally populated lattice displacements and their correlations. The equilibrium lattice produces sharp Bragg peaks, but displacements redistribute part of the scattering into diffuse intensity. To one-phonon order a mode contribution contains a displacement projection and thermal occupation factors of the formwith atomic scattering weights, phases and geometrical factors understood. Stokes and anti-Stokes energy-resolved components carry $n_B+1$ and $n_B$ respectively; the displayed combination describes their summed scale. At high temperature, $n_B\simeq k_{B}T/(\hslash \omega )$, so soft modes and their polarization strongly influence the pattern. Zero-point motion also contributes at low temperature. An energy-integrating diffraction image can record this inelastic intensity as a diffuse background without resolving its small energy transfers. Static disorder gives additional diffuse scattering, so diffuse intensity alone does not establish a thermal mechanism.