Local distortions revealed by neutron holography in ${\mathrm{SnCd}}_{0.0026}$ alloy

Local distortions of the ideal periodic structure in crystals around impurity atoms play an important role in various physical properties of materials. The aim of this study was to investigate the static distortions around cadmium impurity atoms in a ${\text{SnCd}}_{0.0026}$ single crystal using atomic resolution neutron holography technique. The cadmium nucleus was used as an inside detector to measure the holographic interference pattern from which the three-dimensional (3D) atomic arrangement of tin nuclei around the cadmium impurities was reconstructed. Detailed analysis of the reconstructed image revealed the 3D static displacements of Sn atoms around the impurity. It was found that the crystal structure contracts around the cadmium impurity atom and the displacements tend to transform the crystal to the $\alpha$ phase. The local contraction of the lattice was used to explain the slower phase transformation to $\alpha$-Sn phase when Cd impurity atoms are present. The study shows the ability of neutron holography to measure 3D displacements around impurities which can be used, e.g., to understand the mechanisms that block the phase transformations in the presence of impurities.

Figure 1

The measured interference pattern in function of Euler angles $\chi$ and $\varphi$. (a) Counts normalized with the monitor detector. (b) Hologram after baseline subtraction.

Figure 2

The amplitude of the reconstructed hologram on planes perpendicular to the $\left[00z\right]$ direction. The location of the atomic peaks are marked by black circles. (a) Plane of first neighbors at $z=0.775\AA$. (b) Plane of third neighbors at $z=2.675\AA$. (c) Plane of fourth neighbors at $z=1.85\AA$. (d) Plane of fifth neighbors at $z=4.3\AA$.

Figure 3

Radial displacements of the atoms around the cadmium impurity. Filled circles show the displacements calculated from the amplitude of the image, empty circles show the positions of the peak centers. Dashed line represents the fitted curve to the displacements, the red line is the contribution of the $C_{\text{pot}}/r^2$ displacement field and the blue line is the contribution of the Friedel oscillations. The fitted parameters: $C_{\text{Friedel}}=24.48\pm 12,{\eta }_1=71.59\pm 0.4,C_{\text{pot}}=-2.3\pm 0.8.$

Figure 4

Representation of the displacement field of the neighboring Sn nuclei around the Cd impurity. The red sphere marks the position of the Cd impurity nucleus. Transparent gray spheres show the positions of the Sn nuclei in the undistorted crystal, while green spheres are placed at the measured positions.