Holographic Imaging of Atoms Using Thermal Neutrons

In a recent paper [L. Cser, G. Krexner, and Gy. Török, Europhys. Lett. 54, 747 (2001)] the use of thermal neutrons with wavelengths close to interatomic distances in condensed matter was proposed to obtain holographic images on an atomic scale. Two experimental methods were considered which either put the radiation source inside and the detector outside the object or vice versa. The second approach, called the inside-detector concept, requires strongly neutron-absorbing isotopes acting as pointlike detectors in the sample. In the present work, we demonstrate the feasibility of this technique by recording a holographic image of a lead nuclei in a Pb(Cd) single crystal.

Figure 1

Raw hologram data plotted as a pixel map, each pixel covering $3°\times 3°$ in the angular coordinates $\chi$ and $\phi$, respectively. The column at the right side shows the range of holographic modulation ($\max =120000$). The twofold symmetry of the crystal was used to double the $\chi$ range of the angular map.

Figure 2

Reconstructed hologram of twelve Pb neighbors of a Cd nucleus in $\chi$ and $\phi$ coordinates. The intensity variation of the spots is due to the limited accuracy of the background approximation procedure. Nevertheless, the positions of all first neighbor Pb nuclei are clearly visible. The $\chi$ and $\phi$ coordinates of the spots (given in degrees) are as follows: 1. (78, 24); 2. (165, 45); 3. (72, 108); 4. (53, 84); 5. (123, 135); 6. (69, 156); 7. (107, 202); 8. (18, 225); 9. (77, 252); 10. (132, 264); 11. (62, 317); 12. (114, 335).

Figure 3

(a) The spots representing the positions of the twelve Pb atoms forming the first neighbors of the Cd nucleus are displayed on the surface of a sphere of radius $3.49\AA =a/\sqrt{2}$, $a$ being the lattice parameter. The $x$ axis is the incident beam direction; the $z$ axis is the $z$ direction in the system of coordinates of the D9 diffractometer. (b) Schematic illustration of the arrangement of the lead atoms surrounding a Cd atom (yellow spot) as first neighbors in the fcc structure. The orientation and positions of the spots are equivalent to those in (a). The fcc cubic lattice, however, is tilted with respect to the $z$ axis of the diffractometer according to the angles given in the text. The grid marks are given in angstroms.