Phase transition and electronic properties of fluorene: A joint experimental and theoretical high-pressure study

We report a structural phase transition of fluorene and the resulting changes of its electronic and optical properties investigated by a combination of experimental and theoretical methods. Fluorene is a $\pi$-conjugated organic compound that crystallizes in the orthorhombic space group $Pnma$ with four molecules per unit cell. We probe the stability of the molecular arrangement by x-ray powder diffraction experiments under hydrostatic pressure up to $14\mathrm{GPa}$. Our measurements reveal a fully reversible crystallographic phase transition at $3.6\pm 0.3\mathrm{GPa}$ indicated by abrupt changes in the lattice constants, which are accompanied by a re-arrangement of the molecules. The orientation of the molecules relative to each other evolves from the familiar herringbone pattern towards $\pi$-stacking. This results in dramatic modifications of the electronic structure and thus the optical response as revealed by density functional calculations. In particular, the effective hole masses in the high-pressure phase become comparable to those of conventional semiconductors.

Figure 1

Chemical structure of fluorene $\left({\mathrm{C}}_{13}{\mathrm{H}}_{10}\right)$.

Figure 2

Side (left panel) and top (right panel) view of the fluorene crystal structure at ambient pressure.

Figure 3

The $\mathbf{k}$-path in the Brillouin zone used for the computation of the electronic band structures of fluorene.

Figure 4

Powder diffraction pattern (ESRF data) of fluorene at a series of increasing pressure. Between 3.2 and $3.9\mathrm{GPa}$, new features appear (solid ellipse). The 020 peak (dashed ellipse) and thus the layered structure is conserved in the additional HP phase.

Figure 5

Side (left panel) and top (right panel) view of the fluorene crystal structure in the additional high-pressure phase.

Figure 6

Rietveld refinements of the LP phase at $1.0\mathrm{GPa}$ (a), of both coexistent phases at $3.9\mathrm{GPa}$ (b), and of the pure HP phase at $7.3\mathrm{GPa}$ (c). The thin vertical lines mark the positions of the peaks in the respective phase.

Figure 7

Pressure dependence of the lattice constants $a$, $b$, and $c$ for the LP and the HP phase (top left, top right, bottom left). In the bottom right panel, the relative changes of the unit cell parameters with respect to the lowest pressure values available ($0.0\mathrm{GPa}$ for the LP phase and $2.0\mathrm{GPa}$ for the HP phase) are shown. For the sake of clarity, interpolated lines are drawn.

Figure 8

Unit cell volume of fluorene as a function of hydrostatic pressure for both the ambient and the HP phases. The solid lines are a least-squares fit to the Murnaghan EOS.

Figure 9

$x$ and $z$ positions of the molecule in fractional coordinates along the $\mathbf{a}$ and $\mathbf{c}$ axes, respectively, as well as the herringbone angle for the LP and HP phases. The solid lines are linear least-squares fits. The point in brackets in the center panel was measured outside the pressure cell and was thus excluded from the fit.

Figure 10

Enthalpy $H$ of the fluorene LP (in black) and HP (in gray) phase as a function of pressure. Inset: An enlargement of the range over which the phase transition occurs. PT indicates the phase transition between LP and HP phase at $3.8\mathrm{GPa}$.

Figure 11

Band structures $E\left(\mathbf{k}\right)$ (left) and DOS (right) of the fluorene LP phase at ambient pressure (top) and $4\mathrm{GPa}$ (bottom), respectively. The Fermi level is indicated by a dashed line. The solid (dashed) gray arrow marks the lowest direct (fundamental) gap.

Figure 12

Analogous to Fig. 11, the fluorene HP phase at $4\mathrm{GPa}$ (top) and $14\mathrm{GPa}$ (bottom), respectively.

Figure 13

Graphical analysis of the data given in Table . The black (gray) color indicates LP (HP) phase data.

Figure 14

Linear optical response to $a$-, $b$-, and $c$-polarized incident light described in terms of the dielectric tensor ${\epsilon }_2^i\left(\omega \right)$ formulated within the RPA as a function of pressure. A lifetime broadening of $0.05\mathrm{eV}$ has been included. The black (gray) color indicates the LP (HP) phase.