Mechanocaloric effects in superionic thin films from atomistic simulations

Solid-state cooling is an energy-efficient and scalable refrigeration technology that exploits the adiabatic variation of a crystalline order parameter under an external field (electric, magnetic, or mechanic). The mechanocaloric effect bears one of the greatest cooling potentials in terms of energy efficiency owing to its large available latent heat. Here we show that giant mechanocaloric effects occur in thin films of well-known families of fast-ion conductors, namely Li-rich (Li3OCl) and type-I (AgI), an abundant class of materials that routinely are employed in electrochemistry cells. Our simulations reveal that at room temperature AgI undergoes an adiabatic temperature shift of 38 K under a biaxial stress of 1 GPa. Likewise, Li3OCl displays a cooling capacity of 9 K under similar mechanical conditions although at a considerably higher temperature. We also show that ionic vacancies have a detrimental effect on the cooling performance of superionic thin films. Our findings should motivate experimental mechanocaloric searches in a wide variety of already known superionic materials.

where subscripts i and j represent the ionic species in the system, r the radial distance between a couple of atoms, and the corresponding parameter values are reported in Supplementary Table I [1][2][3]. Each pairwise interatomic term is composed of three different contributions; the first one is of exponential type and accounts for the short-ranged atomic repulsion deriving from the overlapping between electron clouds; the second term is proportional to r −6 and represents the long-ranged atomic attraction due to dispersive van der Waals forces; the third term is the usual Coulomb interaction between puntual atomic charges.
The interatomic potential used to investigate AgI with molecular dynamics simulations is that due to Vashishta and Rahman [4], which is expressed as: Supplementary Table I: Interatomic pairwise potential parameters used to describe CaF 2 [1,2] and Li 3 OCl [3] in our classical molecular dynamics simulations. Note that

SUPPLEMENTARY DISCUSSION
Ab initio molecular dynamics (AIMD) simulations based on density functional theory were performed in the canonical (N, V, T ) ensemble for bulk CaF 2 (perfect and with vacancies), Li 3 OCl (perfect and with vacancies), and AgI (perfect). The objective of these calculations was to validate the reliability of the employed interatomic potential models in our molecular dynamics simulations.
The temperature in the AIMD simulations was kept fluctuating around a set-point value by using Nose-Hoover thermostats. Large simulation boxes containing up to 192 atoms were used in all the cases, and periodic boundary conditions were applied along the three corresponding Cartesian directions. Newton's equations of motion were integrated using the customary Verlet's algorithm and a time-step length of 10 −3 ps. Γ-point sampling for integration within the first Brillouin zone was employed in all the AIMD simulations.
Calculations comprised long simulation times of up to ∼ 30 ps. We focused on the description of the superionic features, which consistently were identified through inspection of the mean squared displacement function obtained directly from the AIMD runs.
In two previous works [1,2], we have already validated the realiability of the CaF 2 interatomic potential employed in our molecular dynamics simulations involving perfect systems (i.e., with no vacancies). We have carried out further AIMD tests in order to check whether the same level of accuracy is maintained also for defective systems. In particular, we have Therefore, we may conclude that the adopted Li 3 OCl interaction potential model appears to be physically reliable, as it provides results that are consistent with first-principles meth-

ods.
It has been already demonstrated by others that the Vashishta-Rahman potential [4] mimics bulk AgI with great accuracy at T = 0 conditions (see, for instance, Refs. [5,6]).
Keen et al. have observed a superionic transition under hydrostatic pressure in the rocksalt phase of bulk AgI [7]. The rock-salt structure consists of two interlaced fcc sublattices relatively displaced by ( 1 2 , 1 2 , 1 2 ) in direct coordinates (space group F m3m). We considered as a good test to check whether the Vashishta-Rahman potential could reproduce also the experimental findings by Keen et al. Our molecular dynamics simulations show that this is actually the case. In particular, we obtain a superionic transition temperature of 450(50) K at P = 1 GPa that compares very well with the experimental value T expt s = 500 K [7].
A similar good agreement is observed also with respect to AIMD simulations undertaken at same pressure conditions (i.e., T DFT s = 435(75) K). Therefore, we may conclude that for present purposes the Vashishta-Rahman potential represents a physically reliable interaction model, as it provides results that are consistent with both experiments and first-principles methods. and Ag ions respectively. In CaF 2 thin films, the equilibrium crystal structure corresponds to the cubic fluorite phase (space group F m3m) which upon biaxial tensile stresses transforms into a tetragonal phase (space group I4/mmm) due to the loss of cubic symmetry. In Li 3 OCl thin films, that corresponds to the cubic anti-perovskite phase (space group P m3m) which upon biaxial tensile stresses transforms into a tetragonal phase (space group P 4/mmm) also due to the loss of cubic symmetry. In AgI thin films, this corresponds to the cubic zincblende structure (space group F 43m) which upon biaxial compressive stresses transforms into a tetragonal phase (space group I4m2).

Supplementary
Supplementary Figure 5: In-plane strain calculated in defective (a) and perfect (b) CaF 2 thin films as a function of temperature and biaxial tensile stress. Lines represent spline curves fitted to the molecular dynamics results obtained at temperature intervals of 20 K. We find that despite the ionic F − diffusivity in the defective system is much larger than that in the perfect system (actually, the defective system is superionic whereas the perfect remains in the normal state), the temperature variation of is very similar in both systems. Consequently, the mechanocaloric effects estimated in both cases are very similar as well. (d) T = 400 K and σ xx = σ yy = +1 GPa. In the absence of an applied biaxial stress, the system remains in the normal state both at T = 300 and 400 K. When a biaxial compressive stress of +1 GPa is applied, the system remains in the normal state at T = 300 K and becomes superionic at T = 400 K (i.e., the Ag + ions start to diffuse noticeably). We note that the ionic mean squared displacements obtained at σ = +1 GPa and T = 300 K are highly unusual; a certain local atomic diffusion is observed during the initial stage of the simulation, however this disappears subsequently at longer times.
Actually, no real atomic diffusion occurs in the system. These features can be identified with the occurrence of a diffusionless order-disorder phase transition. compressive stress of +1 GPa is applied, however, those typical solid g(r) features disappear. In particular, it is not longer possible to differentiate a second shell of neighbouring atoms and the asymptotic behaviour g(r) ∼ 1 is rapidly attained with the radial distance. In the Ag + lattice, we identify these traits with the presence of atomic disorder due to superionicity. In the I − lattice, we identify these traits with the stabilisation of a disordered and diffusionless phase. distances. There is not evidence for a σ-driven order-disorder phase transition.