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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Near-room-temperature ferromagnetic ordering in the pressure-induced collapsed-tetragonal phase in SrC⁢o 2 ⁢P 2

We present high-pressure electrical transport, magnetization, and single-crystal x-ray diffraction data on SrC⁢o 2 ⁢P 2 single crystals, revealing a transition from the uncollapsed tetragonal (ucT) to the collapsed tetragonal (cT) phase >∼10 GPa. This structural transition is accompanied by ferromagnetic (FM) ordering with a Curie temperature up to 260 K. First-principles-based density functional theory calculations show that there is a first-order transition between ucT and cT phases, with an onset ∼10 GPa as well as the appearance of FM ordering in the cT phase. Above ∼30 GPa, the experimental signatures of the magnetic ordering vanish in a first-order-like manner, consistent with the theoretical calculation results, indicating that SrC⁢o 2 ⁢P 2 is another example of the avoidance of quantum criticality in FM intermetallic compounds with almost room-temperature critical temperature. SrC⁢o 2 ⁢P 2 provides clear evidence that the structural, electronic, and magnetic properties associated with the cT transition are strongly entangled and are not only qualitatively captured by our first-principles-based calculations but are quantitatively reproduced as well.

density functional theory↗
DOE OSTI2016

Tuning the band gap of silicene by functionalisation with naphthyl and anthracyl groups

Silicene is a relatively new material consisting of a two-dimensional sheet of silicon atoms. Functionalisation of silicene with different chemical groups has been suggested as a way to tune its electronic properties. In this work, density functional theory calculations and ab initio molecular dynamics simulations are used to examine the effects of functionalisation with naphthyl or anthracyl groups, which are two examples of small polycyclic aromatic hydrocarbons (PAHs). Different attachment positions on the naphthyl and anthracyl groups were compared, as well as different thicknesses of the silicene nanosheet. It was found that the carbon attachment position farthest from the bond fusing the aromatic rings gave the more stable structures for both functional groups. All structures showed direct band gaps, with tuning of the band gap being achievable by increasing the length of the PAH or the thickness of the silicene. Hence, modifying the functional group or thickness of the silicene can both be used to alter the electronic properties of silicene making it a highly promising material for use in future electronic devices and sensors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2015

Acidolysis of α-O-4 Aryl-Ether Bonds in Lignin Model Compounds: A Modeling and Experimental Study

Lignocellulosic biomass offers a vast, renewable resource for the sustainable production of fuels and chemicals. To date, a commonly employed approach to depolymerize the polysaccharides in plant cell walls employs mineral acids, and upgrading strategies for the resulting sugars are under intense development. Although the behavior of cellulose and hemicellulose is reasonably well characterized, a more thorough understanding of lignin depolymerization mechanisms in acid environments is necessary to predict the fate of lignin under such conditions and ultimately to potentially make lignin a viable feedstock. To this end, dilute acid hydrolysis experiments were performed on two lignin model compounds containing the a-O-4 ether linkage at two temperatures concomitant with dilute acid pretreatment. Both primary and secondary products were tracked over time, giving insight into the reaction kinetics. The only difference between the two model compounds was the presence or absence of a methyl group on the a-carbon, with the former being typical of native lignin. It was found that methylation of the a-carbon increases the rate of reaction by an order of magnitude. Density functional theory calculations were performed on a proposed mechanism initiated by a nucleophilic attack on the a-carbon by water with a commensurate protonation of the ether oxygen. The values for the thermodynamics and kinetics derived from these calculations were used as the basis for a microkinetic model of the reaction. Results from this model are in good agreement with the experimental kinetic data for both lignin model compounds and provide useful insight into the primary pathways of a-O-4 scission reactions in acid-catalyzed lignin depolymerization. The distribution of primary and secondary products is interpreted as a function of two barriers of formation exhibiting opposite trends upon methylation of the a-carbon (one barrier is lowered while the other is increased). Such insights will be needed to construct a comprehensive model of how lignin behaves in a common deconstruction approach.

14 SOLAR ENERGY↗
DOE OSTI2021

Ethane Dehydrogenation on Single and Dual Centers of Ga-modified γ-Al 2 O 3

Density-functional theory calculations and microkinetic analysis are used to investigate the efficacy of Ga-modified γ-Al 2 O 3 (110) surfaces for the catalytic dehydrogenation of ethane and elucidate the synergy between Ga and Al sites. The model surfaces are modified by either Ga grafting or doping. We consider and analyze numerous active sites and rank them using microkinetic analysis. The kinetic parameters obtained from microkinetic modelling are compared with experimental values for ethane dehydrogenation over Ga 2 O 3 -Al 2 O 3 mixed oxides prepared by co-precipitation. The dominant reaction pathway proceeds via heterolytic C-H bond dissociation to a surface proton and a metal-carbanion intermediate that undergoes β-hydride elimination. We find that grafted Ga sites are catalytically inactive. In contrast, Ga-doped sites exhibit fivefold enhancement in catalytic activity when compared to the sites on pristine Al 2 O 3 , owed to the synergy between neighboring AlIII and GaIV sites. Furthermore, we model and investigate the effect of surface hydroxylation, demonstrate how surface water interferes with the aforementioned synergy between AlIII and GaIV sites and discuss the implications for the catalytic activity of the modified surfaces. Here, an increase in the partial pressure of H 2 O significantly increases the apparent activation energies of dehydrogenation and interestingly changes the most active site.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Anharmonicity-induced first-order isostructural phase transition of zirconium under pressure

We have performed a detailed x-ray diffraction structural study of Zr under pressure and unambiguously identify the existence of a first-order isostructural bcc-to-bcc phase transition near 58 GPa. First-principles quantum molecular dynamics calculations support the existence of this phase transition, in excellent agreement with experimental results, triggered by anharmonic effects. Lastly, our results highlight the potential ubiquity of anharmonically driven isostructural transitions within the periodic table under pressure and call for follow-up experimental and theoretical studies.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2015

Al{sub 2}O{sub 3} as a suitable substrate and a dielectric layer for n-layer MoS{sub 2}

Sapphire (α-Al{sub 2}O{sub 3}) is a common substrate for the growth of single- to few-layer MoS{sub 2} films, and amorphous aluminium oxide serves as a high-κ dielectric gate oxide for MoS{sub 2} based transistors. Using density-functional theory calculations with a van der Waals functional, we investigate the structural, energetic, and electronic properties of n-layer MoS{sub 2} (n = 1and 3) on the α-Al{sub 2}O{sub 3} (0001) surface. Our results show that the sapphire stabilizes single-layer and tri-layer MoS{sub 2}, while having a negligible effect on the structure, band gap, and electron effective masses of MoS{sub 2}. This combination of a strong energetic stabilization and weak perturbation of the electronic properties shows that α-Al{sub 2}O{sub 3} can serve as an ideal substrate for depositing ultra-thin MoS{sub 2} layers and can also serve as a passivation or gate-oxide layer for MoS{sub 2} based devices.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

Structural Distortions and Uniaxial Negative Thermal Expansion in the Polar Dion–Jacobson Oxide RbNdTa 2 O 7

We provide deeper insight into the crystal structures, sequential structural phase transitions (I2cm → Cmce → I4/mcm → P4/mmm), thermal expansion, and electronic properties of the n = 2 Dion–Jacobson polar oxide RbNdTa 2 O 7 , through X-ray powder diffraction, neutron powder diffraction, Raman studies, and density functional theory calculations. We observed a uniaxial negative thermal expansion (NTE) across the first-order transition, I2cm → Cmce, where the unit cell contracts along the c-axis, which is driven by a contraction of the NdTa 2 O 6 layer. Here, this NTE occurs within the temperature range of the first-order phase transition and contrasts with the corkscrew mechanism typically observed in Ruddlesden–Popper phases. In RbNdTa 2 O 7 , the I2cm (hybrid improper ferroelectric) → Cmce (antipolar) transition involves crucial changes in the bond lengths of Nd and Ta polyhedra, coupled with polar to antipolar displacement of the Nd ions, leading to a net contraction in the NdTa 2 O 6 layer along the c-axis, while preserving the overall octahedral tilting magnitude. This transition highlights the intricate interplay between the Nd and Ta coordination and the associated TaO 6 distortions. Temperature-dependent Raman spectra analysis further confirms the first-order structural transition and associated NTE, providing evidence for increased bond stiffness across this transition. Additionally, using neutron powder diffraction, we have determined that the transition I4/mcm → P4/mmm occurs at approximately 1150 K. Finally, we have calculated from DFT + U, the partial density of states, the energy bandgaps, and effective masses of the charge carriers of the polar ground structure.

Chemical structure↗
DOE OSTI2023

Migration of Ga vacancies and interstitials in β – Ga 2 O 3

Pathways and energy barriers for the migration of Ga vacancies (V Ga ) and Ga interstitials (Ga i ) in β–Ga 2 O 3 are explored using hybrid functional calculations and the nudged elastic band method. Considering β–Ga 2 O 3 as primarily being an n-type semiconductor, we focus on defect charge states relevant under such conditions: $V^{3 –}_{Ga}$, Ga$^{3+}_{i}$, and Ga$^{+}_{i}$. Notably, we describe a mechanism by which V Ga can transform between its different split configurations. In all cases, the intermediate state consists of a vacancy split between three Ga sites—a three-split vacancy—which enables passage over a significantly lower energy barrier. This is because it avoids the unfavorable simple vacancy at the tetrahedral Ga site. The proposed mechanism lowers the overall barrier for $V^{3–}_{Ga}$ diffusion along the [001] crystal direction from 1.73 to 0.97 eV, whereas the 2.08 eV barrier for the [100] and [010] directions is unaffected. For Ga$^{3+}_{i}$, we obtain similar overall migration barriers of 0.72, 0.80, and 1.02 eV for the [010], [001], and [100] directions, respectively. Ga$^{+}_{i}$ exhibits a strong preference for diffusion within the large eight-sided channel; the overall migration barrier is 0.92 eV for the [010] direction, and 2.16 eV for the [001] and [100] directions. The limiting step for the two latter directions involves ionization of Ga$^{+}_{i}$ followed by a jump to an adjacent large eight-sided channel as Ga$^{3+}_{i}$. Finally, our results are discussed in light of experimental observations of thermally activated recovery processes in irradiated material.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A new metric to control nucleation and grain size distribution in hybrid organic–inorganic perovskites by tuning the dielectric constant of the antisolvent

In perovskite research, there is a widely exploited but poorly explained phenomenon in which the addition of “antisolvents (ATS)” to precursor solutions results in higher-quality films. We explain the mechanism and driving force underlying an antisolvent-driven solvent extraction process. Density functional theory calculations uncover the defining effects of antisolvent choice on the extent of complexation between a lead salt and a methylammonium cation in solution. We experimentally validate the computational results using ultraviolet-visible spectroscopy and 207 Pb nuclear magnetic spectroscopy of methylammonium lead iodide solutions, containing both a processing solvent and an antisolvent. Furthermore, we uncover, and subsequently identify, the appearance of new species in solution as a result of the addition of the antisolvent. Furthermore, we observe that the choice of antisolvent has a substantial effect on the nature of the complexation of the methylammonium lead iodide (MAPbI 3 ) precursor species, whose origin we explain at an atomic level; specifically, the lower the dielectric of the antisolvent, the stronger the intermolecular binding energy between methylammonium cation (MA + ) cation and PbI 3 - plumbate, independent of the solvent or antisolvent interaction with the lead salt. Thin films were characterized using scanning electron microscopy; images of the films show how the addition of an antisolvent influences and, importantly, can be used to alter thin-film grain size. Grain size and distribution in thin films is reflected by the choice of antisolvent, promoting slower nucleation rates, a lower nucleation density, and hence larger final grain size.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Microstructure‐Dependent Sodium Storage Mechanisms in Hard Carbon Anodes

Sustainable energy storage is essential to support the transition to renewables and meet the increasing demand for energy. Sodium‐ion batteries (NIBs) are attractive for grid‐scale energy storage due to the abundance and low cost of sodium, sustainability of other battery components, and electrochemical performance. Hard carbon (HC) is a leading anode material for NIBs, but its complex microstructure complicates the understanding of sodium storage mechanisms. Using X‐ray total scattering and density functional theory calculations, this study clarifies how HC's microstructural variations influence sodium storage across the slope (high potential) and plateau (low potential) regions of the potential capacity curve. In the slope region, sodium initially adsorbs at high‐binding energy defect sites and subsequently intercalates between graphene layers, adsorbing at low‐binding energy defect sites, correlating with different slopes observed during initial sodiation. Initial irreversibility arises from sodium trapping at surface defects and solid electrolyte interface formation. In the plateau region, sodium simultaneously intercalates and fills pores, influenced by pore size, interlayer spacing, and defect concentration. HCs with larger pore sizes form larger sodium clusters. In conclusion, the proposed mechanism underscores the role of microstructure engineering in enhancing HC performance and advancing NIBs for grid‐scale energy storage.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Chern numbers of topological phonon band crossing determined with inelastic neutron scattering

Topological invariants in the band structure, such as Chern numbers, are important for the understanding and classification of the topological properties of matter and dictate the occurrence of exotic behaviors, yet their direct spectroscopic determination has been largely limited to electronic bands. Here, we use inelastic neutron scattering in conjunction with ab initio calculations to identify a variety of topological phonon band crossings in MnSi and CoSi single crystals. We find a distinct relation between the Chern numbers of a band-crossing node and the scattering intensity modulation in momentum space around the node. Given sufficiently high resolution, our method can be used to determine arbitrarily large Chern numbers of topological phonon band-crossing nodes.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2016

Electronic and magnetic properties of single-layerMPX3metal phosphorous trichalcogenides

We survey the electronic structure and magnetic properties of two-dimensional (2D) MPX 3 (M = V, Cr, Mn, Fe, Co, Ni, Cu, Zn, and X = S, Se, Te) transition-metal chalcogenophosphates to shed light on their potential role as single-layer van der Waals materials that possess magnetic order. Our ab initio calculations predict that most of these single-layer materials are antiferromagnetic semiconductors. The band gaps of the antiferromagnetic states decrease as the atomic number of the chalcogen atom increases (from S to Se to Te), leading in some cases to half-metallic ferromagnetic states or to nonmagnetic metallic states. We find that the competition between antiferromagnetic and ferromagnetic states can be substantially influenced by gating and by strain engineering. The sensitive interdependence we find between magnetic, structural, and electronic properties establishes the potential of this 2D materials class for applications in spintronics.

2-dimensional systems↗
DOE OSTI2025

Tuning the structure and superconductivity of SrNi 2⁢ P 2 by Rh substitution

The compound SrNi 2⁢ P 2 is unique among the ThCr 2 ⁢Si 2 class since it exhibits a temperature-induced transition upon cooling from an uncollapsed tetragonal (ucT) state to a one-third-collapsed orthorhombic (tcO) state where one out of every three P-rows bond across the Sr layers. This compound is also known for exhibiting bulk superconductivity below 1.4 K at ambient pressure. Here, in this paper, we report on the effects of Rh substitution in Sr⁢(Ni 1-x ⁢Rh x ) 2 ⁢P 2 on the structural and superconducting properties. We studied the variation of the nearest P-P distances as a function of the Rh fraction at room temperature, as well as its temperature dependence for selected compositions. We find that increasing the Rh fraction leads to a decrease in the transition temperature between the ucT and tcO states, until a full suppression of the tcO state for x ≥ 0.166. The superconducting transition first remains nearly insensitive to the Rh fraction, and then it increases to 2.3 K after the tcO state is fully suppressed. These results are summarized in a phase diagram, built upon the characterization by energy dispersive x-ray spectroscopy, x-ray diffraction, resistance, magnetization, and specific heat measurements done on crystalline samples with varying Rh content. The relationship between band structure, crystal structure, and superconductivity is discussed based on previously reported band structure calculations on SrRh 2 ⁢P 2 . Moreover, the effect of Rh fraction on the stress-induced structural transitions is also addressed by means of strain-stress studies done by uniaxial compression of single-crystalline micropillars of Sr⁢(Ni 1-x ⁢Rh x ) 2 ⁢P 2 .

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2017

Adsorption of Chlorine on Zr(0001) Surface: First-Principles Predictions

The adsorption of atomic and gaseous chlorine on Zr (0001) surface has been investigated using state-of-the-art density functional theory calculations as part of an effort to gain fundamental understanding of chlorination processes occurring in fuel cladding materials. Zirconium alloys, including Zircaloy-4, Zircaloy-2 and Zr-Nb alloys (Zirlo{sup TM} and Zr-2.5Nb) are the most common fuel cladding materials in nuclear light water reactors (LWRs) due to their favorable mechanical properties, corrosion resistance, low thermal-neutron capture cross section and criticality. The United States produces a large amount of cladding material from used nuclear fuel, which could approach 1,000 MT/year in the next 50 years. In nuclear fuel recycling, spent nuclear fuel assemblies are disassembled and the cladding hulls are separated from the U oxide spent fuel. Zr can be recovered from Zr cladding using the chlorination method. However the presence of impurities in the recovered ZrCl{sub 4} was reported, including Sn, Cr and Fe. Thus, further efforts are necessary to improve the purification process significantly. This requires fundamental understanding of chlorination processes in cladding materials. Most of the material properties are expected to be similar between the pure zirconium and its alloys due to the fact that the alloy composition consists of more than 95 weight-percent zirconium and less than 2% of tin, niobium, iron, chromium, nickel and other metals. Therefore, while the overarching goal is to understand the chlorination process occurring in complex fuel cladding materials, chlorination of pure zirconium was used as an initial system for the modeling and simulation efforts in this study.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2013

Active Oxygen Vacancy Site for Methanol Synthesis from CO2 Hydrogenation on In2O3(110): A DFT Study

Methanol synthesis from CO2 hydrogenation on the defective In2O3(110) surface with surface oxygen vacancies has been investigated using periodic density functional theory calculations. The relative stabilities of six possible surface oxygen vacancies numbered from Ov1 to Ov6 on the perfect In2O3(110) surface were examined. The calculated oxygen vacancy formation energies show that the D1 surface with the Ov1 defective site is the most thermodynamically favorable while the D4 surface with the Ov4 defective site is the least stable. Two different methanol synthesis routes from CO2 hydrogenation over both D1 and D4 surfaces were studied and the D4 surface was found to be more favorable for CO2 activation and hydrogenation. On the D4 surface, one of the O atoms of the CO2 molecule fills in the Ov4 site upon adsorption. Hydrogenation of CO2 to HCOO on the D4 surface is both thermodynamically and kinetically favorable. Further hydrogenation of HCOO involves both forming the C-H bond and breaking the C-O bond, resulting in H2CO and hydroxyl. The HCOO hydrogenation is slightly endothermic with an activation barrier of 0.57 eV. A high barrier of 1.14 eV for the hydrogenation of H2CO to H3CO indicates that this step is the rate-limiting step in the methanol synthesis on the defective In2O3(110) surface. We gratefully acknowledge the supports from the National Natural Science Foundation of China (#20990223) and from US Department of Energy, Basic Energy Science program (DE-FG02-05ER46231). D. Mei was supported by the US Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. The computations were performed in part using the Molecular Science Computing Facility in the William R. Wiley Environmental Molecular Sciences Laboratory (EMSL), which is a U.S. Department of Energy national scientific user facility located at Pacific Northwest National Laboratory in Richland, Washington. PNNL is a multiprogram national laboratory operated for DOE by Battelle.

Catalytic CO2 hydrogenation↗
DOE OSTI2019

Low-Temperature Rotational Tunneling of Tetrahydroborate Anions in Lithium Benzimidazolate-Borohydride Li 2 (bIm)BH 4

To investigate the dynamical properties of the novel hybrid compound, lithium benzimidazolate-borohydride Li 2 (bIm)BH 4 (where bIm denotes a benzimidazolate anion, C 7 N 2 H 5 - ), we have used a set of complementary techniques: neutron powder diffraction, ab initio density functional theory calculations, neutron vibrational spectroscopy, nuclear magnetic resonance, neutron spin echo, and quasi-elastic neutron scattering. Our measurements performed over the temperature range from 1.5 to 385 K have revealed the exceptionally fast low-temperature reorientational motion of BH 4 - anions. This motion is facilitated by the unusual coordination of tetrahedral BH 4 - anions in Li2(bIm)BH4: each anion has one of its H atoms anchored within a nearly square hollow formed by four coplanar Li+ cations, while the remaining -BH 3 fragment extends into a relatively open space, being only loosely coordinated to other atoms. As a result, the energy barriers for reorientations of this fragment around the anchored B-H bond axis are very small, and at low temperatures, this motion can be described as rotational tunneling. The tunnel splitting derived from the neutron spin echo measurements at 3.6 K is 0.43(2) ueV. With increasing temperature, we have observed a gradual transition from the regime of low-temperature quantum dynamics to the regime of classical thermally activated jump reorientations. The jump rate of the uniaxial 3-fold reorientations reaches 5 x 10 11 s -1 at 80 K. Nearer room temperature and above, both nuclear magnetic resonance and quasi-elastic neutron scattering measurements have revealed the second process of BH4- reorientations characterized by the activation energy of 261 meV. This process is several orders of magnitude slower than the uniaxial 3-fold reorientations; the corresponding jump rate reaches ~7 x 10 8 s -1 at 300 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Spin Splitting Energy of Transition Metals: A New, More Affordable Wave Function Benchmark Method and Its Use to Test Density Functional Theory

Accurately predicting the spin splitting energy of chemical species is important for understanding their reactivity and magnetic properties, but it is very challenging, especially for molecules containing transition metals. One impediment to progress is the scarcity of accurate benchmark data. Here we report a set of calculations designed to yield reliable benchmarks for simple transition-metal complexes that can be used to test density functional methods that are affordable for large systems of more practical interest. Various wave function methods are tested against experiment for Fe 2+ , Fe 3+ , and Co 3+ , including CASSCF, CASPT2, CASPT3, MRCISD, MRCISD+Q, ACPF, AQCC, CCSD(T), and CASPT2/CCSD(T) and also a new method called CASPT2.5, which is performed by taking the average of the CASPT2 and CASPT3 energies. Furthermore, we find that MRCISD+Q, ACPF, and AQCC require smaller active spaces for good accuracy than are required by CASPT2 and CASPT3, and this aspect may be important for calculations on larger molecules; here we find that CASPT2.5 extrapolated to a complete basis set is the most suitable method—in terms of computational cost and in terms of accuracy on monatomic systems—and therefore we chose this method for molecular benchmarks. Then Kohn–Sham density functional calculations with 60 exchange-correlation functionals are tested for FeF 2 , FeCl 2 , and CoF 2 . We find that MN15-L, M06-SX, and revM06 have very good agreement with CASPT2.5 benchmarks in terms of both the spin splitting energy and the optimized geometry for each spin state. In addition, we recommend def2-TZVP as the most suitable basis set to perform density functional calculations for molecular spin splitting energies; extra polarization functions in the basis set do not help to increase the accuracy of the spin splitting energy in KS calculations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2014

Theoretical predictions of properties and volatility of chlorides and oxychlorides of group-4 elements. II. Adsorption of tetrachlorides and oxydichlorides of Zr, Hf, and Rf on neutral and modified surfaces

With the aim to interpret results of gas-phase chromatography experiments on volatility of group-4 tetrachlorides and oxychlorides including those of Rf, adsorption enthalpies of these species on neutral, and modified quartz surfaces were estimated on the basis of relativistic, two-component Density Functional Theory calculations of MCl{sub 4}, MOCl{sub 2}, MCl{sub 6}{sup −}, and MOCl{sub 4}{sup 2} with the use of adsorption models. Several mechanisms of adsorption were considered. In the case of physisorption of MCl{sub 4}, the trend in the adsorption energy in the group should be Zr > Hf > Rf, so that the volatility should change in the opposite direction. The latter trend complies with the one in the sublimation enthalpies, ΔH{sub sub}, of the Zr and Hf tetrachlorides, i.e., Zr < Hf. On the basis of a correlation between these quantities, ΔH{sub sub}(RfCl{sub 4}) was predicted as 104.2 kJ/mol. The energy of physisorption of MOCl{sub 2} on quartz should increase in the group, Zr < Hf < Rf, as defined by increasing dipole moments of these molecules along the series. In the case of adsorption of MCl{sub 4} on quartz by chemical forces, formation of the MOCl{sub 2} or MOCl{sub 4}{sup 2−} complexes on the surface can take place, so that the sequence in the adsorption energy should be Zr > Hf > Rf, as defined by the complex formation energies. In the case of adsorption of MCl{sub 4} on a chlorinated quartz surface, formation of the MCl{sub 6}{sup 2−} surface complexes can occur, so that the trend in the adsorption strength should be Zr ≤ Hf < Rf. All the predicted sequences, showing a smooth change of the adsorption energy in the group, are in disagreement with the reversed trend Zr ≈ Rf < Hf, observed in the “one-atom-at-a-time” gas-phase chromatography experiments. Thus, currently no theoretical explanation can be found for the experimental observations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

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