Colossal Reversible Barocaloric Effects in a Plastic Crystal Mediated by Lattice Vibrations and Ion Diffusion

Abstract

Solid-state methods for cooling and heating promise a sustainable alternative to current compression cycles of greenhouse gases and inefficient fuel-burning heaters. Barocaloric effects (BCE) driven by hydrostatic pressure (p) are especially encouraging in terms of large adiabatic temperature changes (|ΔT| ≈ 10 K) and isothermal entropy changes (|ΔS| ≈ 100 J K^-1 kg^-1). However, BCE typically require large pressure shifts due to irreversibility issues, and sizeable |ΔT| and |ΔS| seldom are realized in a same material. Here, the existence of colossal and reversible BCE in LiCB₁₁H₁₂ is demonstrated near its order-disorder phase transition at ≈380 K. Specifically, for Δp ≈ 0.23 (0.10) GPa, |ΔS_rev| = 280 (200) J K^-1 kg^-1 and |ΔT_rev| = 32 (10) K are measured, which individually rival with state-of-the-art BCE figures. Furthermore, pressure shifts of the order of 0.1 GPa yield huge reversible barocaloric strengths of ≈2 J K^-1 kg^-1 MPa^-1. Molecular dynamics simulations are performed to quantify the role of lattice vibrations, molecular reorientations, and ion diffusion on the disclosed BCE. Interestingly, lattice vibrations are found to contribute the most to |ΔS| while the diffusion of lithium ions, despite adding up only slightly to the entropy change, is crucial in enabling the molecular order-disorder phase transition.

Keywords: barocaloric effects; lithium diffusion; molecular dynamics simulations; orientational order–disorder phase transition; solid‐state refrigeration.

Figure 1

Sketch of the order–disorder phase transition occurring in LiCB₁₁H₁₂ upon increasing temperature. a) Ball‐stick representation of the low‐T ordered (O) and high‐T disordered (D) phases. Lithium, carbon, boron, and hydrogen atoms are represented with red, brown, green, and blue spheres, respectively. In the high‐T phase, the Li⁺ cations diffuse throughout the crystalline matrix while the [CB₁₁H₁₂]⁻ anions reorient disorderly^{[ 37 ]}; the volume increases significantly during the T‐induced phase transition. b) Outline of the order–disorder phase transition in terms of Gibbs free energies. The red dotted lines represent internal energies and the blue solid lines Gibbs free energies; T _t denotes the phase transition temperature. The “Order parameter” in the x‐axis is of mixed molecular orientational and ionic diffusive characters.

Figure 2

Experimental phase diagram of bulk LiCB₁₁H₁₂ and corresponding phase transition entropy changes. a) Volume per formula unit measured as a function of temperature at normal pressure. b) Isobaric heat flow data expressed as a function of applied pressure and temperature; data collected during heating (cooling) are represented in the positive (negative) y‐axis. c) Pressure and temperature phase diagram; transition temperatures are determined from the peaks in panel (b). d) Phase transition entropy changes as a function of pressure and transition path. ΔS _t remains practically constant from atmospheric pressure all the way up to the triple point. At p ≃ 0.13 GPa, ΔS _{II → I} ≈ ΔS _{II → III} + ΔS _{III → I}, while above the triple point ΔS _{II → III} ≈ ΔS _{III → I}. Straight lines at pressures above the triple point are linear fits to ΔS _{II → III} + ΔS _{III → I}.

Figure 3

Experimentally measured colossal barocaloric effects in bulk LiCB₁₁H₁₂. a–c) Isothermal entropy change, ΔS, and b–d) adiabatic temperature change, ΔT, obtained upon the application and removal of pressure, p, considering (a–b) irreversible and (c–d) reversible processes.

Figure 4

Compendium of experimentally measured reversible BCE. The size of the symbols represents the reversible barocaloric strength defined as the ratio of |ΔS _rev| by the corresponding pressure change Δp. Material names are indicated near each symbol or in the right side of the panel. NPG: neopentylglycol^{[ 51 ]}; PG: pentaglycerine^{[ 51 ]}; NPA: Neopentyl alcohol^{[ 51 ]}; o‐carb: orthocarborane^{[ 52 ]}; m‐carb: metacarborane^{[ 52 ]}; p‐carb: paracarborane^{[ 52 ]}; 1‐Br‐ada: 1‐Bromoadamantane^{[ 53 ]}; 1‐Cl‐ada: 1‐Chloroadamantane^{[ 53 ]}; 1ada‐ol: 1‐adamantanol^{[ 24 ]}; 2ada‐ol: 2‐adamantanol^{[ 24 ]}; 2m2ada‐ol: 2‐methyl‐2‐adamantanol^{[ 24 ]}; ASR: Acetoxy Silicone Rubber^{[ 54 ]}; C₆₀ ^{[ 55 ]}; Fe₃(bntrz)₆(tcnset)₆ ^{[ 32 ]}; Fe[HB(tz)₃]₂ ^{[ 56 ]}; (C₁₀H₂₁NH₃)₂MnCl₄ ^{[ 23} , ^{55 ]}; [TPrA]Mn[dca]₃ ^{[ 57 ]}; [TPrA]Cd[dca]₃ ^{[ 58 ]}; [DBA][BF₄]^{[ 25 ]}; (NA)₂CuBr₄ ^{[ 23 ]}; NH₄I^{[ 59 ]}; Nitrile Butadiene Rubber^{[ 60 ]}; Ni₅₀Mn_31.5Ti_18.5 ^{[ 61 ]}; Ni_49.26Mn_36.08In_14.66 ^{[ 62 ]}; Ni_35.5Co_14.5Mn₃₅Ti₁₅ ^{[ 63 ]}; Ni_42.3Co_7.9Mn_38.8Sn_11.0 ^{[ 64 ]}; Fe₄₉Rh₅₁ ^{[ 65} , ^{66 ]}; MnCoGeB_0.03 ^{[ 67 ]}; (MnNiSi)_0.62(FeCoGe)_0.38 ^{[ 68 ]}; (MnNiSi)_0.61(FeCoGe)_0.39 ^{[ 69 ]}; (MnNiSi)_0.60(FeCoGe)_0.40 ^{[ 69 ]}; (MnNiSi)_0.59(FeCoGe)_0.41 ^{[ 69 ]}; Co₅₀Fe_2.5V_31.5Ga₁₆ ^{[ 70 ]}; BaTiO₃ ^{[ 71 ]}; (NH₄)₂SO₄ ^{[ 72 ]}; AgI^{[ 73 ]}; Li₃N^{[ 74 ]}; Cu₂Se.^{[ 75 ]} Additional details can be found in the Table S1 (Supporting Information).

Figure 5

Colossal BCE estimated for bulk LiCB₁₁H₁₂ with MD simulations. a) Volume change per formula unit across the phase transition expressed as a function of temperature and pressure. b) Total entropy curves expressed as a function of pressure and temperature. Inset: theoretically calculated p–T phase diagram. c) Isothermal entropy and d) adiabatic temperature changes expressed as a function of temperature and pressure. Results were obtained from NpT‐MD simulations.

Figure 6

Atomistic insights into the order‐disorder phase transition in LiCB₁₁H₁₂ from MD simulations. a) Lithium ion diffusion coefficient, D _Li. b) Anionic reorientational frequency, λ_CBH. Solid lines correspond to Arrhenius law fits. c–d) Cumulative function of the vibrational entropy as a function of the phonon energy and atomic species, calculated for the ordered (T = 400 K) and disordered (T = 412 K) phases at zero pressure. Dashed lines indicate analogous asymptotic values reached in the ordered phase. e–f) Angular probability density function estimated for the molecular (CB₁₁H₁₂)⁻ anions calculated in the ordered (T = 350 K) and disordered (T = 550 K) phases at zero pressure, expressed as a function of the polar (θ) and azimuthal (ϕ) angles. Dark and bright areas represent low and high probability regions, respectively.

Figure 7

Partial contributions to the entropy change accompanying the order‐disorder phase transition in LCBH expressed as a function of pressure. Entropy changes stem from the vibrational, ΔS _vib, molecular orientational, ΔS _ori, and cation diffusive, ΔS _diff, degrees of freedom. Results were obtained from comprehensive molecular dynamics simulations and Gibbs free energy calculations (Experimental Section).