Rare Gas Crystals Research Articles

Particle detection in rare gas solid crystals: a feasibility experimental study—exploring new ways for dark matter searches

AbstractThis article reviews the experimental activity that has been carried out within the INFN DEMIURGOS research and development (R &D) project. This R &D concerns the study of possible innovative experimental approaches for the detection of low-energy-releases of feeble interacting particles within the matter. Possible applications could be the direct investigation of Dark Matter candidates. The idea behind the proposed scheme is to exploit rare gas solid crystals both pure and doped, combined with the in-vacuum single electron detection technology. In pure materials, the signal can be the charge produced directly during the ionization. Laser-assisted processes can instead be used to probe low-energy-releases in doped materials. Both these mechanisms should lead to a detectable electronic signal triggered by the incoming particle. In such a way, energy threshold ranging from meV to tens of eV could in principle be reached, opening-up the possibility to probe theoretically, well-motivated regions of unexplored electroweak parameter-space and thus test the existence of light Dark Matter candidates. The activity presented here has been performed to understand the mechanisms at the basis of the proposed detection scheme and possible showstopper. The experimental investigations refer to the research and development phases about: the crystal growing techniques and the corresponding set-up, the electrons’ extraction from rare gas crystals to the vacuum environment, and finally the spectroscopic studies on atomic species embedded into rare gas matrices.

Modeling of the thermal migration mechanisms of atomic oxygen in Ar, Kr, and Xe crystals.

Accommodation and migration of the ground-state (2s22p4 3P) oxygen atom in the ideal Ar, Kr, and Xe rare gas crystals are investigated using the classical model. The model accounts for anisotropy of interaction between guest and host atoms, spin-orbit coupling, and lattice relaxation. Interstitial and substitutional accommodations are found to be the only thermodynamically stable sites for trapping atomic oxygen. Mixing of electronic states coupled to lattice distortions justifies that its long-range thermal migration follows the adiabatic ground-state potential energy surface. Search for the migration paths reveals a common direct mechanism for interstitial diffusion. Substitutional atoms are activated by the point lattice defects, whereas the direct guest-host exchange meets a higher activation barrier. These three low-energy migration mechanisms provide plausible interpretation for multiple migration activation thresholds observed in Kr and Xe free-standing crystals, confirmed by reasonable agreement between calculated and measured activation energies. An important effect of interaction anisotropy and a minor role of spin-orbit coupling are emphasized.

Trapping sites of Li atom in the rare gas crystals Ar, Kr, and Xe: Analysis of stability and manifestation in the EPR spectra

The classical model of an ideal crystal, parametrized according to non-empirical calculations, is used to determine the structure and geometry of the atomic lithium trapping sites in solid inert gases RG = Ar, Kr, and Xe, and to define their thermodynamic stability. The diversity of the observed stable sites reduces to four highly symmetric structures corresponding to the interstitial introduction of an Li atom, its substitution of an inert gas atom, or its incorporation into tetrahedral and octahedral vacancies formed by the removal of four and six inert gas atoms from the crystal lattice. The non-empirically calculated dependences of the isotropic hyperfine coupling constant tensor on the distance in the diatomic Li@RG complex are used to estimate the shifts of the electron paramagnetic resonance signals in the predicted thermodynamically stable sites. A comparison with published data does not contradict the assignment of the observed multiple signals to certain types of stable sites, taking into account the spectral features of samples that were prepared by thermal deposition and laser ablation in three different inert gases.

Minimizing lattice structures for Morse potential energy in two and three dimensions

We investigate the local and global optimality of the triangular, square, simple cubic, face-centered-cubic (fcc) and body-centered-cubic (bcc) lattices and the hexagonal-close-packing (hcp) structure for a potential energy per point generated by a Morse potential with parameters (α, r0). In dimension 2 and for α large enough, the optimality of the triangular lattice is shown at fixed densities belonging to an explicit interval, using a method based on lattice theta function properties. Furthermore, this energy per point is numerically studied among all two-dimensional Bravais lattices with respect to their density. The behavior of the minimizer, when the density varies, matches with the one that has been already observed for the Lennard-Jones potential, confirming a conjecture we have previously stated for differences of completely monotone functions. Furthermore, in dimension 3, the local minimality of the cubic, fcc, and bcc lattices is checked, showing several interesting similarities with the Lennard-Jones potential case. We also show that the square, triangular, cubic, fcc, and bcc lattices are the only Bravais lattices in dimensions 2 and 3 being critical points of a large class of lattice energies (including the one studied in this paper) in some open intervals of densities as we observe for the Lennard-Jones and the Morse potential lattice energies. More surprisingly, in the Morse potential case, we numerically found a transition of the global minimizer from bcc, fcc to hcp, as α increases, that we partially and heuristically explain from the lattice theta function properties. Thus, it allows us to state a conjecture about the global minimizer of the Morse lattice energy with respect to the value of α. Finally, we compare the values of α found experimentally for metals and rare-gas crystals with the expected lattice ground-state structure given by our numerical investigation/conjecture. Only in a few cases does the known ground-state crystal structure match the minimizer we find for the expected value of α. Our conclusion is that the pairwise interaction model with Morse potential and fixed α is not adapted to describe metals and rare-gas crystals if we want to take into consideration that the lattice structure we find in nature is the ground-state of the associated potential energy.

Energy of Phonons and Zero-Point Vibrations in Compressed Rare-Gas Crystals

A dynamic matrix of rare-gas crystals is constructed within the model of deformable and polarizable atoms based on the nonempirical short-range repulsion potential taking into account the three-body interaction and deformation of electron shells of dipole-type atoms within the pair and three-body approximations. Ab initio calculations of the phonon energy for compressed rare-gas crystals are performed at two and ten mean-value points of the Chadi–Kohen method in a wide pressure range. It is shown that the contribution of three-body forces to the phonon frequencies due to overlap of electron shells of neighboring atoms is small as compared to the pair interaction even at a high pressure and most pronounced for Xe. The contributions of the deformation of electron shells within the pair and three-body approximations differ for different mean-value points and increase with an increase in pressure. The zero-point energies calculated by the Chadi–Kohen method for crystals of the Ne–Xe series are compared with the known experimental data at p = 0 and calculation results obtained by other researchers.

Stable axially symmetric atomic impurity in an fcc solid-Ba in rare gases.

Closed-shell metal atoms in rare gas solids tend to occupy highly symmetric polyhedral crystal sites, as follows from the generic triplet Jahn-Teller splitting of the S → P excitation bands and complies with the isotropic nature of the dispersion forces. Atypical 2 + 1 Jahn-Teller splitting inherent to axially symmetric sites observed recently for Ba atoms has been therefore interpreted as the defect accommodation. By modeling the structure, stability, and spectra of the Ba atom in the face-centered cubic rare gas crystals, we identify thermodynamically stable crystal site of axial C3v symmetry that explains experimental observations. We also demonstrate the dramatic effect of the interaction anisotropy on the trapping site structure and stability for an excited P-state atom. Our results provide strong evidence for stable axially symmetric accommodation of isotropic impurity in a close-packed lattice.

Particle detection in rare gas solids: DEMIURGOS experiment

Low energy threshold detectors are necessary in many frontier fields of the experimental physics. In particular these are extremely important for probing Dark Matter (DM) possible candidates. We present the activity of the DEMIURGOS R&D project, a novel detection approach that exploits Rare Gas crystals maintained at low temperature both pure and doped. In both the schemes, the detection approach takes advantage of the single-electron detection combined with a very low dark count rate typical of microchannel plate or channeltron sensors. Moreover, to ensure electrons’ drift, we need high quality crystals with an impurity level lower than ppb especially for high electronegativity atoms. Through these schemes, we could be able to detect low energy release in the range sub eV-tens of eV in large volume crystals opening thus the possibility to investigate lighter DM candidates and other feeble interacting phenomena.

Theoretical study of “trapping sites” in cryogenic rare gas solids doped with β-dicarbonyl molecules

A deposition model to simulate the growth of doped rare gas crystals is used. The study involves organic molecules with a single intramolecular hydrogen bond such as malonaldehyde, 2chloromalonaldehyde and acetylacetone as impurities. Different trapping sites were obtained depending on the rare gas properties for a given impurity, and depending on the molecular size and shape for a given crystal. Simulations were carried out by using classical molecular dynamics methods including an anharmonic thermal correction, to take into account the zero point movement of the crystal. The results are correlated to spectroscopic data previously achieved for these systems by steady state IR spectroscopy.

Энергия фононов и нулевых колебаний в сжатых кристаллических инертных газах

A dynamic matrix of rare-gas crystals is constructed on the basis of a nonempirical short-range repulsion potential taking into account the three-body interaction and dipole-type deformation of the electron shells of atoms in the two- and three-body approximations in the model of deformable and polorizable atoms. Ab initio calculations of the phonon energy for compressed rare-gas crystals were performed at the two and ten mean-value points of the Chadi-Cohen method in a wide pressure range. It is shown that the contribution of three-body forces associated with the overlap of the electron shells of nearest-neighbor atoms in the phonon frequencies is small against the background of pair interaction, even at high pressure and most noticeable in Xe. The contribution of the deformation of the electron shells in the two- and three-body approximations is different for the different mean-value points and increases with increasing pressure. Comparison of the zero-point energy calculated by the Chadi-Cohen method for compressed crystals of the Ne–Xe series was performed with the available experiment at p=0 and the results of other authors.

Абсолютная неустойчивость ГЦК-решетки кристаллов инертных газов под давлением

AbstractOn the basis of ab initio calculations of the phonon frequencies of compressed rare-gas crystals in the model of deformable and polarizable atoms, dynamic instability of the fcc lattice of these crystals is studied. In addition to the earlier-considered three-body interaction, which is associated with the overlapping of the electron shells of atoms, the short-range potential includes three-body forces caused by the mutual deformation of the electron shells of neighboring atoms. It is shown that the allowance for the deformation of the dipole-type electron shells of atoms in the pair and three-body approximations leads to softening of the critical vibrations and absolute instability of the fcc lattice at pressures higher than the critical values, p > p _ c . For light crystals of Ne and Ar under compressions of 0.76 ( p _ c = 422 GPa) and 0.71 ( p _ c = 405 GPa), respectively, the softening of the longitudinal mode is observed at the boundary of the Brillouin zone at the point L ; for heavy crystals of Kr and Xe under compressions of 0.686 ( p _ c = 240 GPa) and 0.605 ( p _ c = 88 GPa), the transverse mode T _1 is softened in the direction Σ. The behavior of second-order Fuchs elastic moduli of compressed rare-gas crystals is discussed.

Absolute Instability of FCC Lattice of Rare-Gas Crystals under Pressure

On the basis of ab initio calculations of the phonon frequencies of compressed rare-gas crystals in the model of deformable and polarizable atoms, dynamic instability of the fcc lattice of these crystals is studied. In addition to the earlier-considered three-body interaction, which is associated with the overlapping of the electron shells of atoms, the short-range potential includes three-body forces caused by the mutual deformation of the electron shells of neighboring atoms. It is shown that the allowance for the deformation of the dipole-type electron shells of atoms in the pair and three-body approximations leads to softening of the critical vibrations and absolute instability of the fcc lattice at pressures higher than the critical values, p > pc. For light crystals of Ne and Ar under compressions of 0.76 (pc = 422 GPa) and 0.71 (pc = 405 GPa), respectively, the softening of the longitudinal mode is observed at the boundary of the Brillouin zone at the point L; for heavy crystals of Kr and Xe under compressions of 0.686 (pc = 240 GPa) and 0.605 (pc = 88 GPa), the transverse mode T1 is softened in the direction Σ. The behavior of second-order Fuchs elastic moduli of compressed rare-gas crystals is discussed.

Dispersion-corrected PBEsol exchange-correlation functional

We study the compatibility between the PBEsol exchange-correlation energy functional of Phys. Rev. Lett. 100, 136406 (2008) and the rVV10 van der Waals nonlocal correlation functional of Phys. Rev. B 87, 041108 (2013). By applying a density-gradient dependence in the expression of rVV10, we develop a new functional: The PBEsol + rVV10s functional, which is remarkably accurate for layered solids, rare-gas crystals, densely packed bulk solids, and the adsorption of noble-gas atoms on metal surfaces, and is also competitive for noncovalent interactions between molecular complexes as well as for potential-energy curves of noble-gas dimers. The capacity of this dispersion-corrected functional to describe various interactions in solids makes it useful for electronic-structure calculations in solid-state physics and materials science.

Orientation-dependent hyperfine structure of polar molecules in a rare-gas matrix: A scheme for measuring the electron electric dipole moment

Because molecules can have their orientation locked when embedded into a solid rare-gas matrix, their hyperfine structure is strongly perturbed relative to the freely rotating molecule. The addition of an electric field further perturbs the structure, and fields parallel and antiparallel to the molecular orientation result in different shifts of the hyperfine structure. These shifts enable the selective detection of molecules with different orientations relative to the axes of a rare-gas crystal, which will be an important ingredient of an improved electron electric dipole moment measurement using large ensembles of polar molecules trapped in rare-gas matrices.

Dislocation Structure and Mobility in Hcp Rare-Gas Solids: Quantum versus Classical

We study the structural and mobility properties of edge dislocations in rare-gas crystals with the hexagonal close-packed (hcp) structure by using classical simulation techniques. Our results are discussed in the light of recent experimental and theoretical studies on hcp 4 He, an archetypal quantum crystal. According to our simulations classical hcp rare-gas crystals present a strong tendency towards dislocation dissociation into Shockley partials in the basal plane, similarly to what is observed in solid helium. This is due to the presence of a low-energy metastable stacking fault, of the order of 0.1 mJ/m 2 , that can get further reduced by quantum nuclear effects. We compute the minimum shear stress that induces glide of dislocations within the hcp basal plane at zero temperature, namely, the Peierls stress, and find a characteristic value of the order of 1 MPa. This threshold value is similar to the Peierls stress reported for metallic hcp solids (Zr and Cd) but orders of magnitude larger than the one estimated for solid helium. We find, however, that in contrast to classical hcp metals but in analogy to solid helium, glide of edge dislocations can be thermally activated at very low temperatures, T∼10 K, in the absence of any applied shear stress.

Ab initio теория уравнения состояния сжатых кристаллов инертных газов

AbstractNonempirical equations of state of compressed rare gas crystals Ne, Ar, Kr, and Xe are studied on the basis of the earlier-obtained ab initio adiabatic potential. The paired and three-body short-range repulsive potentials are calculated by the Hartree–Fock method in the basis of localized functions with their exact mutual orthogonalization and do not contain experimentally determined parameters. The theory is compared with the experiment and results of calculations by other authors. Analysis of the proposed equations of state for large compressions has shown the importance of taking into account the three-body interaction and the terms of the higher order in the overlap integral in compressed neon and the sufficiency of the quadratic approximation in the orthogonalization of functions in heavy rare gas crystals.

Ab initio theory of the equation of state for compressed rare gas crystals

Nonempirical equations of state of compressed rare gas crystals Ne, Ar, Kr, and Xe are studied on the basis of the earlier-obtained ab initio adiabatic potential. The paired and three-body short-range repulsive potentials are calculated by the Hartree–Fock method in the basis of localized functions with their exact mutual orthogonalization and do not contain experimentally determined parameters. The theory is compared with the experiment and results of calculations by other authors. Analysis of the proposed equations of state for large compressions has shown the importance of taking into account the three-body interaction and the terms of the higher order in the overlap integral in compressed neon and the sufficiency of the quadratic approximation in the orthogonalization of functions in heavy rare gas crystals.

Elastic properties of compressed rare-gas crystals in a model of deformable atoms

The elastic properties of compressed Ne, Ar, Kr, and Xe rare-gas crystals were studied in a model of deformable and polarizable atoms. The second-order Fuchs elasticity moduli, their pressure derivatives, and the Zener elastic anisotropy ratio were calculated with allowance for three-body interaction and quadrupole deformation in electron shells within a wide pressure range. Comparison with the experiment and results of other authors was performed. In xenon at a compression of 0.6, the shear modulus B 44 was observed to become zero, thus corresponding to the FCC–HCP transition at 75 GPa.

Ab initio Theory of Elastic Properties of Rare-Gas Crystals Under High Pressure

The quantum mechanical model of deformable and polarizable atoms has been developed for the research of the elastic properties of rare-gas crystals Ne, Ar, Kr, and Xe over a wide range of pressure. It is shown that it is impossible to reproduce the observed deviation from the Cauchy relation δ(p) for Ne, Kr, Xe adequately taking into account the many-body interaction only. The individual dependence δ(p) for each of the crystals is the result of two competing interactions, namely, the many-body interaction and the electron-phonon interaction, which manifests itself in a quadrupole deformation of atoms electron shells due to displacements of the nuclei. The contributions of these interactions to Ne, Kr, and Xe compensated each other with high precision that provides δ with a positive value which is weakly dependent on pressure. In case of Ar the many-body interaction prevails. The compressed Ar has a negative deviation from the Cauchy relation the absolute value of which increases with the rise of pressure. The consideration of the quadrupole deformation is of great importance for heavy rare-gas crystals Kr and Xe. The represented ab initio calculated dependences of Birch elastic moduli Bij(p) and δ(p) are in good agreement with the experiment.

Range-separated double-hybrid density-functional theory applied to periodic systems.

Quantum chemistry methods exploiting density-functional approximations for short-range electron-electron interactions and second-order Møller-Plesset (MP2) perturbation theory for long-range electron-electron interactions have been implemented for periodic systems using Gaussian-type basis functions and the local correlation framework. The performance of these range-separated double hybrids has been benchmarked on a significant set of systems including rare-gas, molecular, ionic, and covalent crystals. The use of spin-component-scaled MP2 for the long-range part has been tested as well. The results show that the value of μ = 0.5 bohr(-1) for the range-separation parameter usually used for molecular systems is also a reasonable choice for solids. Overall, these range-separated double hybrids provide a good accuracy for binding energies using basis sets of moderate sizes such as cc-pVDZ and aug-cc-pVDZ.

Ab initio theory of many-body interaction and phonon frequencies of rare-gas crystals under pressure in the model of deformable atoms

Ab initio calculations of phonon frequencies of compressed rare-gas crystals have been performed taking into account the many-body interaction in the model of deformable atoms. In the short-range repulsive potential, along with the previously considered three-body interaction associated with the overlap of the electron shells of atoms, the three-body forces generated by the mutual deformation of the electron shells of the nearest-neighbor atoms have been investigated in the dipole approximation. The relevant forces make no contribution to the elastic moduli but affect the equation for lattice vibrations. At high compressions, the softening of the longitudinal mode at the points L and X is observed for all the rare-gas crystals, whereas the transverse mode T 1 is softened in the direction Σ and at the point L for solid xenon. This effect is enhanced by the three-body forces. There is a good agreement between the theoretical phonon frequencies and the experimental values at zero pressure.