Pressure-temperature phase diagram of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$: Synchrotron x-ray diffraction experiments and theoretical analysis

An in situ combined high-temperature high-pressure synchrotron radiation diffraction study has been carried out on $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$. The phase diagram of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$ is mapped to $10\mathrm{GPa}$ and $500\mathrm{K}$, and four phases are identified. The corresponding structural distortions are analyzed in terms of symmetry-breaking atomic position shifts and anion ordering. Group-theoretical and crystal-chemical considerations reveal a nontrivial layered structure of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$. The layers and their deformations define the structural stability of the observed phases.

Figure 1

Partial $P\text{−}T$ phase diagram of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$ according to Ref. 23.

Figure 2

$P\text{−}T$ diagram of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$ based on data from the experiments summarized in Table .

Figure 3

XRD patterns recorded during heating in experiment 3. The phase transition from phase III $\left(Ama2\right)$ into phase VI $\left(Fm\text{−}3m\right)$ is clearly visible.

Figure 4

XRD patterns recorded in experiment 4 close to the boundary between phase III $\left(Ama2\right)$ and phase I $\left(P{6}_{3}mc\right)$ in conditions of quasi-isobaric heating. The pattern shown in the middle shows peaks from both phases. No additional peaks due to phase IV could be found. Asterisks mark the gasket peaks.

Figure 5

Thermal data obtained during a first heating run at $1.2\mathrm{GPa}$. (a) DTA data, (b) specific heat, and (c) thermal conductivity.

Figure 6

Thermal data obtained during a subsequent cooling/heating cycle at $1.2\mathrm{GPa}$ immediately following the heating in Fig. 5: (a) DTA data, (b) specific heat, and (c) thermal conductivity.

Figure 7

(Color online) Lithium-boron framework of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$ in (a) the latent phase $P{6}_3∕mmc$, (b) high-temperature phase $P{6}_{3}mc$, and (c) orthorhombic $Pnma$

Figure 8

(Color online) Orientation of tetrahedral $\mathrm{B}{\mathrm{H}}_4$ anions in structures of (a) the latent hexagonal $P{6}_3∕mmc$, (b) $P{6}_{3}mc$, (c) $Pnma$, (d) $Fm\text{−}3m$, and (e) $Ama2$ phases.

Figure 9

(Color online) Mechanism of the $Fm\text{−}3m\text{−}Ama2$ transformation in $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$ (only lithium-boron sublattices are shown).

Figure 10

Equilibrium phase diagram associated with the order-parameter expansion defined by Eq. (4) for (a) $a_2>0$, $b_2>0$, $\gamma >0$, $\Delta >0$; (b) $a_2<0$, $b_2<0$, $\gamma >2\sqrt{a_2{b}_2}>0$, $\Delta >0$; and (c) $a_2<0$, $b_2<0$, $\gamma <-2\sqrt{a_2{b}_2}<0$, $\Delta >0$. (b) Hexagonal and (c) cubic domains schematically shown as shadowed regions.

Figure 11

Connection between the hexagonal $\left(h\right)$ and cubic $\left(c\right)$ Brillouin zones with the latent parent phase (L) BZ.

Figure 12

(Color online) Cation-anion layers in the structure of different phases of $\mathrm{Li}\mathrm{B}{\mathrm{H}}_4$. Only Li and B atoms are displayed. The character of the layer structure in phase III is seen to be intermediate between those of I and V.