Anisotropic thermal expansion in molecular solids: Theory and experiment on ${\mathrm{LiBH}}_4$

We propose a reliable and efficient computational method for predicting elastic and thermal expansion properties in crystals, particularly complex anisotropic molecular solids, and we apply it to the room-temperature orthorhombic $Pnma$ phase of ${\mathrm{LiBH}}_4$. Using density-functional theory, we find thermal expansion coefficients at finite temperature, and we confirm them by temperature-dependent, in situ x-ray diffraction measurements. We also consider the effects of volume and pressure, as well as energy barriers for ${\mathrm{BH}}_4$${}^{-}$ rotations and collective motions. Our combined study validates the theory and provides a better understanding of the structural behavior of ${\mathrm{LiBH}}_4$.

Figure 1

${\mathrm{LiBH}}_4$ room-temperature orthorhombic $Pnma$ structure with $0.07e^{-}/{\text{Å}}^3$ isosurfaces of electron density around ${\mathrm{BH}}_4$${}^{-}$molecular anions. Li is the large red balls, B is the blue, and H is a small white ball attached to a BH bond.

Figure 2

Energy vs cell distortion along $a$ (black circles), $b$ (red squares), and $c$ (green diamonds), with fixed lattice constants in perpendicular directions, calculated from DFT (symbols) and fitted by polynomials in Eq. (1) (lines) with subtracted linear term $E_1\delta$. ${\mathrm{BH}}_4$${}^{-}$ orientations are fixed. Li and B direct lattice coordinates and ${\mathrm{BH}}_4$${}^{-}$ shapes are fixed in the main plot (relaxed in the inset).

Figure 3

Shift of the XRD peaks vs $T$. Arrows show a decrease of peak intensity and shift to lower 2$\theta$ with increasing $T$ for the (102) and (002) planes. Time-series patterns are shown in the inset (the low-$T$ orthorhombic phase is spanned by arrows). The sample was heated from 300 to 418 K, above the phase transition, and then cooled.

Figure 4

Lattice parameter ratios for $a$, $b$, and $c$ axes vs $T$, relative to the value at 25 ${}^{\circ }$C. Shown are square polynomial fits to the experimental data (solid lines) and calculated $\alpha$ at 20 ${}^{\circ }$C (dashed lines) from Table 2.

Figure 5

DFT energy of rotation of a single ${\mathrm{BH}}_4$${}^{-}$ molecule around [110] (left, filled symbols) and [102] (right, empty symbols), calculated by methods (a) (squares, dashed line), (b) (diamonds, dotted line), and (c) (circles, solid line). Lines are fitted to $E\left(\varphi \right)=E_{1}cos\left(3\varphi \right)+E_{2}cos\left(6\varphi \right)-(E_1+E_2)$, where $E_1$ and $E_2$ for method (c) are $-82$ and 15 meV around [110], and $-125$ and 17 meV around [102], respectively.