K. Syassen, U. Schwarz (MPI/CPFS Dresden), A. Grzechnik and I. Loa;
M. Hanfland (ESRF Grenoble); K. Takemura (NIRIM Tsukuba)
The alkali metals have played an important role in developing the nearly-free electron pic-ture for simple sp band metals. With increasing pressure, however, these metals become less free-electron like. In particular, at sufficiently high compression the heavy alkali met-als K, Rb, and Cs essentially turn into monovalent d transition metmet-als. The pressure-driven s!d transition is believed to be the driving force for destabilizing the common, highly symmetric, low pressure structures (bcc and fcc) with respect to lower symmetry structures.
In fact, at intermediate densities both Rb and Cs adopt a body centered tetragonal structure (denoted Cs-IV-type, see Fig. 31), where the atoms are only eightfold coordinated. The existence of a variety of other high-pressure phases (cf Fig. 31) has been inferred from optical reflectivity measurements, electrical transport studies, and X-ray diffraction mea-surements. Solving the crystal structures of most of these other high-pressure modifications was possible only recently.
Figure 31: Schematic representation of the phase sequence of heavy alkali met-als as a function of relative density. The density 0 corresponds to the respective ambient pressure value. Question marks refer to phases with unknown or uncon-firmed crystal structures.
Based on angle-dispersive synchrotron powder X-ray diffraction diagrams measured at the ESRF Grenoble, we have been able to solve the structures of the phases Rb-IV and Rb-VI [ Schwarz et al., Phys. Rev. Lett. 83, 4085 (1999); Schwarz et al., Sol. State Commun. 112, 319 (1999) ]. In particular, the structure of Rb-IV is found to be surprisingly complex.
The X-ray diffraction patterns were recorded at room temperature using a wavelength near 0.45 ˚A and a flat image plate detection system. Pressure was generated in a diamond anvil cell. Indexing, structure solution, and refinements of diffraction diagrams were performed using standard crystallography software packages. Both, the high angular resolution and the high sensitivity of the experimental setup were essential for solving the crystal struc-tures.
5 10 15 20 25
Diffraction Angle 2Θ (deg)
Intensity (arb. units)
Rb-IV
P = 16.9 GPa λ = 0.4500 Å
200
110
x100
Figure 32: Image plate pattern and integrated diffraction diagram of Rb-IV at 16.9 GPa.
Figure 32 shows the full diffraction pattern of the phase Rb-IV, measured at a pressure of 16.9 GPa and the corresponding integrated powder diagram. The 52 reflections of this diagram can be indexed on the basis of a tetragonal cell with lattice parameters a2c.
The systematic extinctions are compatible with the space groups (SG) I4=mcm, I4cm and I¯4c2. Solutions of the crystal structure were thus performed in the centrosymmetric SG I4=mcm. Applying direct methods reveals that one set of Rb atoms occupies the Wyckoff positions 16k (x;y;0; x0.79, y0.08). The resulting arrangement of Rb1 atoms (see Fig. 33) consists of columns of face-sharing square antiprisms interconnected by short Rb1-Rb1 contacts (red lines in Fig. 33). The closest separation between Rb1 atoms (3.04 ˚A at 16.9 GPa) corresponds to twice the ionic radius of Rb+(1.52 ˚A).
Figure 33: The tetragonal struc-ture of Rb-IV viewed along the c axis. Rb1 atoms form a frame-work structure which hosts lin-ear chains of Rb2 atoms. Note that the chain sites indicated in this figure have a fractional oc-cupancy factor (see text).
The Rb1 framework hosts chains of a second set of Rb atoms as evidenced by electron den-sity maxima in the difference Fourier map (see Fig. 34). Maxima occur at the 8g (0.5, 0, z) site. The Fourier map in combination with the maximum possible number of 20 atoms per unit cell, as inferred from atomic volumes of neighboring phases, thus suggest an av-erage Rb2 arrangement with statistical occupation of 8g sites and an occupation factor of 0.5. However, for such an arrangement within the chains the average interatomic distance would be only 2.6 ˚A, which is difficult to accept because it is 15% smaller than the ionic radius of Rb+.
Figure 34: Difference Fourier map of Rb-IV for a (010) plane.
The x and z coordinates refer to the a- and c-axes of the tetrago-nal unit cell respectively.
We therefore conclude that the number of Rb2 atoms in chain sites is less than four per unit cell. A refinement of the 16.9 GPa diffraction diagram, in which occupation factors of sites along the chains are treated as free parameters, converges to occupation numbers
We have not observed any supercell reflections which would indicate a commensurate or-dering of the chain atoms with respect to the framework of Rb1 atoms. On the other hand, some diffraction patterns of Rb-IV show a single extra reflection corresponding to a d-value of about 3.0 ˚A, i. e., at the position marked by a triangle in Fig. 32. If interpreted as a reflection arising from the intrachain ordering, the absence of other additional reflections would indicate that the chains are uncorrelated with respect to each other.
There is a quite surprising resemblance of the Rb-IV structure to the metal atom sublattice of the W5Si3-type structure, which is rather common among binary alloys. Furthermore, it has been pointed out by Nesper and v. Schnering, that the Cs-IV–type structure, which is also adopted by the phase Rb-V, corresponds to the metal sublattice in the ThSi2-type structure. This leads to a more general concept, namely, that at intermediate densities the alkali metals adopt crystal structures, that represent metal sublattices of binary intermetal-lic compounds.
Figure 35: The orthorhombic crystal structure of Rb-VI and Cs-V. The conventional unit cell contains 16 atoms in two crystal-lographically non-equivalent po-sitions [8f (0, y, z) and 8d (x, 0, 0) in Wyckoff notation]. The cor-responding sites are denoted as 1 and 2, respectively. The struc-ture can be viewed as an alter-nating sequence of planar layers formed by five-coordinated nets and puckered nearly-square lay-ers. The shortest interatomic dis-tances are marked by red lines.
When Rb is pressurized to 48 GPa it undergoes the transition to the phase Rb-VI (cf Fig. 31). Again based on monochromatic diffraction data, we have solved the structure of this phase. It is found to be isotypic to Cs-V, which we had previously determined [ Schwarz et al., Phys. Rev. Lett. 81, 2711 (1998) ]. The structure has space group Cmca
the Wyckoff 8f position alternating along the [100] direction with puckered nearly square layers of Rb2 atoms on the position 8d. The unit cell extends over four layers. The devia-tion of the cell parameters from a tetragonal metric is extremely small (b/c1.005). One of the Rb1–Rb1 distances is particularly short which suggests that the Rb1 atoms on the 8f position condense into Rb2 units. The Rb1 and Rb2 atoms are eleven and tenfold coordi-nated, respectively. In other words, for Rb (and also Cs) the atomic coordination increases again after having passed through the eight-coordinated Cs-IV-type structure.
The increase in coordination number continues at higher pressure. At least in the case of Cs, we could recently show that the structure adopted by Cs-VI (70 GPa to at least 184 GPa) is double hexagonal close packed with a c/a ratio corresponding to an ideal close packing of spheres [ Takemura et al., Phys. Rev. B, submitted ]. At the highest pressure of 184 GPa Cs is compressed to 14% of its ambient-pressure volume.
In conclusion, we have determined the crystal structure of the phase Rb-IV based on high-resolution monochromatic synchrotron X-ray diffraction. The results demonstrate that the pressure-driven breakdown of the nearly-free electron character of a simple metal induces a phase transition to a rather complex structure. The present work partly closes the gap in our knowledge about the phase transition sequence in heavy alkali metals during the early stages of the s!d transition. Furthermore, having solved the structures of Rb-VI and Cs-VI we have made an important step in understanding the structural evolution of heavy alkali metals, when they are fully turned into monovalent d-transition metals by the application of pressure. Our results have implications for developing a detailed picture of the electronic structure, chemical bonding, and physical properties of heavy alkali metals during the progression of the s!d transition.