Location and energy of interstitial hydrogen in the $1∕1$ approximant $W$-$\mathrm{TiZrNi}$ of the icosahedral $\mathrm{TiZrNi}$ quasicrystal: Rietveld refinement of x-ray and neutron diffraction data and density-functional calculations

We present a determination of hydrogen sites in the $1∕1$ approximant structure of the icosahedral $\mathrm{TiZrNi}$ quasicrystal. A Rietveld refinement of neutron and x-ray diffraction data determines the locations of interstitial hydrogen atoms. Density-functional methods calculate the energy of hydrogen on all possible interstitial sites. The Rietveld refinement shows that the hydrogen atoms are preferentially located in the two lowest-energy sites. The filling of the remaining hydrogen sites is dominated by the repulsive hydrogen-hydrogen interaction at short distances.

Figure 1

Structure of the Bergman cluster consisting of a central Ni atom (left), a small icosahedron of Ti atoms (center), and a large icosahedron of Ni atoms with Zr atoms on the face centers (right).

Figure 2

Rietveld refinement of deuterated $W$-phase (a) neutron, and (b) x-ray data. The measured data are indicated by “+” and the solid line denotes the fit. The difference curve is shown in the bottom of each panel. Vertical bars represent Bragg reflection positions.

Figure 3

Density-functional calculations of the hydrogen site energy distribution in the 1/1 approximant structure $W$-$\mathrm{TiZrNi}$ show a broad distribution of sites. A small number of sites around $-800\mathrm{meV}$ is separated from the main distribution ranging from about $-700$ to $-400\mathrm{meV}$ followed by a tail of sites with higher energy up to $-200\mathrm{meV}.$