Far-infrared Spectra Research Articles

Relationship between the structure and microwave dielectric properties of garnet ceramics Ca3B2GeV2O12 (B = Mg, Mn)

Two garnet-structured ceramics, Ca3B2GeV2O12 (B = Mg, Mn), were synthesized using a traditional solid-state reaction method, and their sintering behavior, structures, vibrational spectra, and magnetic and microwave dielectric properties were characterized. Low permittivity (εr) of 9.75 (Ca3Mg2GeV2O12) and 11.06 (Ca3Mn2GeV2O12), quality factor (Q × f) of 54,000 GHz (Ca3Mg2GeV2O12) and 30,240 GHz (Ca3Mn2GeV2O12), and temperature coefficient of resonant frequency (τf) of −61.2 ppm/°C (Ca3Mg2GeV2O12) and −66.4 ppm/°C (Ca3Mn2GeV2O12) were obtained. The εr value was correlated with the sum of the ionic polarization per unit volume. The Q × f value was associated with the part with a fully filled 3d orbit, un-paired d electrons of B-site ion, and magnetic loss. The τf was correlated to the bond valance at the A- and C-sites. Moreover, the fitting analysis of the far-infrared reflectance spectra of Ca3Mg2GeV2O12 revealed that the active vibration modes in the low wave number range (100 - 400 cm-1) contributed mainly to the intrinsic microwave dielectric polarization.

Crystal structure, phonon characteristics, and dielectric properties of CaMgGe2O6: A novel diopside microwave dielectric ceramic

The monoclinic diopside structured CaMgGe2O6 dielectric ceramics were synthesized by the traditional solid-phase reaction method, and their microwave dielectric properties were characterized. X-ray diffraction (XRD) and Rietveld refinement revealed that CaMgGe2O6 belongs to the monoclinic system of space group C2/c. SEM images showed that dense CaMgGe2O6 ceramics could be formed at the optimum sintering temperature of 1300 °C. Typically, ceramic sintered at 1300 °C for 6 h possessed outstanding microwave dielectric properties with εr ∼7.96, Q × f ∼41,280 GHz, and τf ∼ −46.6 ppm/°C. Far-infrared spectra analysis revealed the intrinsic microwave dielectric properties of CaMgGe2O6 ceramics. These findings demonstrate promising application prospects of CaMgGe2O6 in microwave substrate materials.

Mono- and di-deuterated ammonias: Far-infrared spectra and spectroscopic parameters in the ground state

Transitions of NH2D and ND2H have been detected in the high resolution spectrum of 14ND3 recorded at unapodized resolution of 0.00096 cm−1 in the region 60–600 cm−1 using the Bruker IFS 125 Fourier transform spectrometer located at the synchrotron far-infrared beamline, Canadian Light Source. In this study we report on the observation and analysis of the spectrum for the ground state of NH2D and ND2H. 2153 rotation and rotation-inversion transitions, with J up to 24, were assigned for NH2D, and 3214 transitions, with J up to 28, for ND2H. The newly assigned transitions, together with those present in the literature, were fitted on the basis of a Watson-type S reduced Hamiltonian using the IIIr and IIIl representations for NH2D and ND2H, respectively. The model Hamiltonian includes terms up to the 10th power of the angular momentum and vibration–rotation interaction terms between the inversion states. Precise and extended sets of spectroscopic effective parameters were derived for both isotopologues as results of least squares weighted fit procedures that reproduce the transition wavenumbers at experimental accuracy.

Synchrotron-based far-infrared spectroscopy of [formula omitted]: Extended ro-vibrational analysis and new line list up to 3360 cm[formula omitted

The far-infrared spectrum of HC3N has been recorded at high resolution between 70 and 500 cm−1using synchrotron radiation. Four prominent features, i.e., ν7, ν6−ν7, ν4−ν6, and 2ν7 have been identified in the spectrum together with many associated hot bands. In addition, rotational transitions for the interacting v4=v7=1, (v6=2,v7=1), (v5=1,v7=2), and v7=5 vibrationally excited states have been recorded in the millimeter/submillimeter region. The newly assigned transitions, together with those reported previously, form a comprehensive data set including about 17 000 transitions, which involves almost all the vibrational states of HC3N lying below 1300 cm−1 plus some excited states with energies between 2075 and 3550 cm−1. These data have been fitted to an effective Hamiltonian which takes into account rotational and vibrational l-type resonance effects, together with a number of anharmonic interaction terms. On average, all the analysed data are reproduced within the experimental accuracy. About 90 000 rotational and ro-vibrational transition frequencies have been computed on the basis of the spectroscopic constants obtained from the global fit in order to support data interpretation and astronomical searches in the interstellar medium and planetary atmospheres. Part of these data is included in the 2020 release of the HITRAN database.

Preparation and infrared properties of Ni3Al–Cr3C2 composite films deposited by electrohydrodynamic atomization technology

The purpose of this work is to provide a clean and efficient preparation process for Ni3Al–Cr3C2 composite films. In this work, two kinds of slurries were prepared to deposit Ni3Al–Cr3C2 composite films on a 316L stainless steel substrate by electrohydrodynamic atomization (EHDA) technology. The slurry used for deposition was prepared with magnetic stirring and ball milling, respectively. The influence of the atomization parameters (atomization distance, operating voltage, and flow rates) on the characteristics of deposited films was investigated. Homogenous and compact films, with a structure of ∼10 layers, were fabricated under the optimized deposition parameters. The composition and micro-morphology of the composite films were examined. The spectral reflectivity of the Ni3Al–Cr3C2 composite films was characterized by the Fourier transforms infrared spectroscopy (FTIR) to study the infrared properties of the composite films. The results showed that because the slurries used to deposit the composite films were prepared by various methods, the infrared reflectivity and emissivity of the two composite films were different in the middle and far-infrared region. However, in the whole middle and far-infrared spectrum, the emissivity of the two films was significantly low. Therefore, the Ni3Al–Cr3C2 composite films deposited by EHDA are expected to be used in mid-high temperature solar films.

Analysis of tiles produced from a schist material and their ultraviolet, near-infrared, mid-infrared, longwave-infrared and far-infrared spectra

AbstractClays are used in the general production of earthen tiles. In this study, the production and characterization of earthen tiles from schist, a clayey rock formed by metamorphism of mudstone or shale, was investigated. The impact of tiles on atmospheric temperature through their absorption of the visible, near-infrared and far-infrared wavelength regions is evaluated. In particular, the absorption of ultraviolet and infrared radiation by the tiles was evaluated, as this could have beneficial applications for human health and the environment. UV-A radiation (320–400 nm) is not absorbed by the atmosphere, but schist materials absorb UV-A, which can contribute to melanoma formation (i.e. cancer). Field-emission scanning electron microscopy, X-ray fluorescence spectrometry and X-ray diffraction were used for the analysis of the schist materials. The tile-production stages of schist materials (drying, firing, water absorption rate, etc.) were tested at Hatipoglu Gunes Tile and Brick Industry, Inc. (Turkey). The tiles fired at 950°C and 1000°C comply with the industry standard compressive strength values for fired tiles (when converted to industry production conditions) and were 156.15 and 123.20 kg cm–2, respectively.

High-Resolution spectroscopy and analysis of the fundamental modes of [formula omitted]Si[formula omitted]. Accurate experimental determination of the Si[formula omitted]F bond length

Silicon tetrafluoride (SiF4) is a trace component of volcanic gases and is gaining industrial importance. However, a better knowledge of spectroscopic parameters is needed for this molecule in order to derive accurate concentrations. Following a previous reinvestigation of the ν3 and ν4 fundamentals (Richard et al. 2021), we have undertaken an extensive high-resolution study of its infrared absorption bands. We present here an update of this study. It features the recording of new far-infrared spectra, taking advantage of synchrotron radiation, and a global fit giving a consistent parameter set for the ground and fundamental states of 28SiF4, now including the v1=1 and v2=1 states, by adding to the global analysis the newly measured ν2, ν1−ν4, and ν4−ν2 bands near 264, 412, and 125 cm−1, respectively. Nearly 20000 assigned lines pertaining to seven distinct rovibrational bands were fitted with an excellent accuracy (global standard deviation of 0.296). This allows us to obtain an accurate experimental value for the Si−F bond length, re(SiF4)=1.5516985(30) Å. Some new band intensity estimates allow us to update our SiF4 calculated spectroscopic database.

Investigation of the structural characteristics, dielectric properties, and infrared reflectivity spectra of AlON transparent ceramics

Al(8+x)/3O4−xNx (x = 0.299–0.575) transparent ceramics were fabricated by presintering and subsequent hot isostatic pressing (HIP) technology. The XRD and SEAD analyses verified that a complete solid solution with a cubic spinel structure was achieved in the entire composition range. The SEM characterization confirmed that the x = 0.299−0.510 samples are highly dense with rare residual pores, which was further demonstrated by HRTEM observations. In combination with phonon modes extracted by far-infrared reflectivity spectra, the intrinsic dielectric properties of AlON ceramics were estimated, which were consistent with the experimental results, revealing that the contribution to dielectric properties is dominated by the absorption of structural phonons. Moreover, as the nitrogen content increased, the measured permittivity (εr) of the samples was found to gradually increase from 9.41 to 9.68 at 7 GHz, while the quality factor (Q × f) values fluctuated from 43,750 to 76,923 GHz. Accordingly, the reported AlON transparent ceramics with exceptional dielectric performances are promising candidates for high-frequency 5 G applications.

An infrared study of antiferromagnetic medium and high entropy rocksalt structure oxides

The infrared reflectance of a set of antiferromagnetic entropy-stabilized rocksalt structure oxides is measured in order to study the effect of a random array of cations, spin–phonon coupling, and anharmonicity on phonon mode behavior. Samples were prepared by conventional solid state reaction from quaternary or quinary equimolar mixtures of CoO, ZnO, CuO, NiO, and MgO. They were characterized by magnetometry, x-ray diffraction, and reflectance spectroscopy. It is found that the Néel temperature (TN) depends on the concentration of magnetic ions. The far-infrared reflectance spectra consist of one strong reststrahlen band and a weaker low frequency band, which is unexpected in a rocksalt structure. The resonance frequency of the main transverse optical (ωTO) mode varies between 355<ωTO<386 cm−1 and is controlled by both the average reduced mass of a cation–anion pair and the average effective charge. Unlike the parent compounds CoO and NiO, no splitting of ωTO due to spin–phonon coupling appeared in the reflectance spectra below TN. This is possibly due to the high scattering rate of the associated transverse optical mode, which is connected to static disorder.

IRMPD spectroscopy of a PAH cation using FELICE: The infrared spectrum and photodissociation of dibenzo[a,l]pyrene

We present the experimental InfraRed Multiple Photon Dissociation (IRMPD) spectrum and fragmentation mass spectrum of the irregular, cationic PAH dibenzo[a,l]pyrene (C24H14+) in the 6–40μm/250–1650 cm−1 range. The use of the Free-Electron Laser for IntraCavity Experiments (FELICE) enabled us to record its Far-InfraRed (FIR) spectrum for the first time. We aim to understand how irregularity affects the infrared spectrum and fragmentation chemistry of PAHs. Dibenzo[a,l]pyrene is an asymmetric, non-planar molecule, for which all vibrational modes are in principle IR-active. Calculated harmonic Density Function Theory (DFT) and anharmonic Density Functional based Tight Binding Molecular Dynamics (DFTB-MD) spectra show a large wealth of bands, which match the experiment well, but with a few differences. The periphery of the molecule contains several edge geometries, but out of all possible modes in the 11–14μm out-of-plane CH bending region, only one band at 13.5μm is prominent. This fact and the richness of the CC stretching range make irregular PAHs a possible contributor to D-class interstellar spectra. The fragmentation mass spectra reveal facile 2H-loss and no [2C, 2H]-loss, which is attributed to the sterically hindered, non-planar cove region, which could protect irregular PAHs from radiation damage.

Accurate dust temperature determination in a z = 7.13 galaxy

ABSTRACT We report ALMA Band 9 continuum observations of the normal, dusty star-forming galaxy A1689-zD1 at z = 7.13, resulting in a ∼4.6 σ detection at 702 GHz. For the first time, these observations probe the far-infrared spectrum shortward of the emission peak of a galaxy in the Epoch of Reionization (EoR). Together with ancillary data from earlier works, we derive the dust temperature, Td, and mass, Md, of A1689-zD1 using both traditional modified blackbody spectral energy density fitting, and a new method that relies only on the [C ii] 158 μm line and underlying continuum data. The two methods give $T_{\rm d} = (42^{+13}_{-7}, 40^{+13}_{-7}$) K, and $M_{\rm d} = (1.7^{+1.3}_{-0.7}, 2.0^{+1.8}_{-1.0})\, \times {}\, 10^{7} \, \mathrm{ M}_{\odot }$. Band 9 observations improve the accuracy of the dust temperature (mass) estimate by ∼50 per cent (6 times). The derived temperatures confirm the reported increasing Td-redshift trend between z = 0 and 8; the dust mass is consistent with a supernova origin. Although A1689-zD1 is a normal UV-selected galaxy, our results, implying that ∼85 per cent of its star-formation rate is obscured, underline the non-negligible effects of dust in EoR galaxies.

The rotation-torsion spectrum of CD2HOH

New transitions are reported in the submillimeter wave, terahertz, and far-infrared rotation-torsion spectrum of doubly-deuterated methanol CD2HOH. The newly assigned transitions allow us to spectroscopically characterize torsional states with 0⩽K⩽12 and 0⩽vt⩽2. Three line position analyses are carried out. In the first one, restricted to rotation-torsion lines involving torsional states with 3⩽K⩽12 and vt⩽2, rotational energies are evaluated with a J(J+1) Taylor-type expansion for each torsional state. 4853transitions were accounted for with a unitless standard deviation of 11.4. In the second analysis, 126torsional subband centers are fitted to obtain refined torsional parameters including the hindering potential. In the third analysis, 5911rotation-torsion transitions involving torsional states with vt⩽2, and J⩽26 are reproduced with a unitless standard deviation of 3.2 using a four-dimensional rotation-torsion fitting Hamiltonian.

The Polar Radiant Energy in the Far Infrared Experiment: A New Perspective on Polar Longwave Energy Exchanges

AbstractEarth’s climate is strongly influenced by energy deficits at the poles that emit more thermal energy than they receive from the sun. Energy exchanges between the surface and atmosphere influence the local environment while heat transport from lower latitudes drives midlatitude atmospheric and oceanic circulations. In the Arctic, in particular, local energy imbalances induce strong seasonality in surface–atmosphere heat exchanges and an acute sensitivity to forced climate variations. Despite these important local and global influences, the largest contributions to the polar atmospheric and surface energy budgets have not been fully characterized. The spectral variation of far-infrared radiation that makes up 60% of polar thermal emission has never been systematically measured impeding progress toward consensus in predicted rates of Arctic warming, sea ice decline, and ice sheet melt. Enabled by recent advances in sensor miniaturization and CubeSat technology, the Polar Radiant Energy in the Far Infrared Experiment (PREFIRE) mission will document, for the first time, the spectral, spatial, and temporal variations of polar far-infrared emission. Selected under NASA’s Earth Ventures Instrument (EVI) program, PREFIRE will utilize new lightweight, low-power, ambient temperature detectors capable of measuring at wavelengths up to 50 μm to quantify Earth’s far-infrared spectrum. Estimates of spectral surface emissivity, water vapor, cloud properties, and the atmospheric greenhouse effect derived from these measurements offer the potential to advance our understanding of the factors that modulate thermal fluxes in the cold, dry conditions characteristic of the polar regions.

Intramolecular H-Bond Dynamics of Catechol Investigated by THz High-Resolution Spectroscopy of Its Low-Frequency Modes.

Catechol is an oxygenated aromatic volatile organic compound and a biogenic precursor of secondary organic aerosols. Monitoring this compound in the gas phase is desirable due to its appreciable reactivity with tropospheric ozone. From a molecular point of view, this molecule is attractive since the two adjacent hydroxy groups can interchangeably act as donor and acceptor in an intramolecular hydrogen bonding due to the tunnelling between two symmetrically equivalent structures. Using synchrotron radiation, we recorded a rotationally-resolved Fourier Transform far-infrared (IR) spectrum of the torsional modes of the free and bonded -OH groups forming the intramolecular hydrogen bond. Additionally, the room temperature, pure rotational spectrum was measured in the 70–220 frequency range using a millimeter-wave spectrometer. The assignment of these molecular transitions was assisted by anharmonic high-level quantum-chemical calculations. In particular, pure rotational lines belonging to the ground and the four lowest energy, vibrationally excited states were assigned. Splitting due to the tunnelling was resolved for the free -OH torsional state. A global fit combining the far-IR and millimeter-wave data provided the spectroscopic parameters of the low-energy far-IR modes, in particular those characterizing the intramolecular hydrogen bond dynamics.

Evidence of the CH···O HydrogenBonding in Imidazolium-Based Ionic Liquids from Far-Infrared Spectroscopy Measurements and DFT Calculations.

Knowledge of all the intermolecular forces occurring in ionic liquids (ILs) is essential to master their properties. Aiming at investigating the weaker hydrogen bonding in aprotic liquids, the present work combined computational study and far-infrared spectroscopy on four imidazolium-based ILs with different anions. The DFT calculations of the ionic couples, using the ωB97X-D functional and considering both the empirical dispersion corrections and the presence of a polar solvent, show that, for all samples, the lowest energy configurations of the ion pair present H atoms, directly bound to C atoms of the cation and close to O atoms of the anion, capable of creating moderate to weak hydrogen bonding with anions. For the liquids containing anions of higher bonding ability, the absorption curves generated from the calculated vibrational frequencies and intensities show absorption bands between 100 and 125 cm−1 corresponding to the stretching of the hydrogen bond. These indications are in complete agreement with the presently reported temperature dependence of the far-infrared spectrum, where the stretching modes of the hydrogen bonding are detected only for samples presenting a moderate interaction and become particularly prominent at low temperatures. Moreover, from the analysis of the infrared spectra, the occurrence of various phase transitions as a function of temperature was detected, and the difference in the average energy between the H-bonded and the dispersion-governed molecular configurations was evaluated.

Comparison of the results of optical and electrophysical measurements of free electron density in n-GaAs samples doped with tellurium

A theoretical model has been developed that allows one to determine free electron density in n-GaAs from the characteristic points on far-infrared reflection spectra. It was shown that, in this case, it is necessary to take into account the plasmon-phonon coupling (otherwise, the electron density is overestimated). The calculated dependence of electron density, Nopt, on the characteristic wave number, ν+, which is described by a second degree polynomial, has been obtained.Twenty-five tellurium-doped gallium arsenide samples were used to measure the electron density in two ways: according to traditional four-contact Hall method (Van der Pauw method) and using the optical method we developed (measurements were carried out at room temperature). Based on the experimental results, the dependence was constructed of the electron density values obtained from the Hall data, NHall, on the electron density obtained by the optical method, Nopt. It is shown that this dependence is described by linear function. It is established that the data of optical and electrophysical measurements coincide if the electron density is Neq = 1.07 ⋅ 1018 cm-3, for lower values of the Hall density NHall < Nopt, and for large values NHall > Nopt. A qualitative model is proposed to explain the results. It has been suggested that tellurium atoms bind to vacancies of arsenic into complexes, as a result of which the electron density decreases. On the surface of the crystal, the concentration of arsenic vacancies is lower and, therefore, the condition Nopt > NHall should be satisfied. As the doping level increases, more and more tellurium atoms remain electrically active, so electron density in the volume begins to prevail over the surface one. However, with a further increase in the doping level, the ratio NHall/Nopt again decreases, tending to unity. This, probably, is due to the fact that the rate of decomposition of the complexes “tellurium atom + arsenic vacancy” decreases with increasing doping level.

Structural correlation of GeTeSeGa system by XRD and far-infrared spectroscopy

The structural properties of quaternary Ge10Te80Se10-xGax (x = 0 to 10) glassy alloy have been studied with XRD (X-ray diffraction) and FTIR (Fourier transform infrared) spectroscopy. The position of FSDP (first sharp diffraction peak) (2θ) and its FWHM (full width half maxima) have been utilized to estimate the local structure parameters of FSDP like repeating distance y and structural correlation length (L). The far-infrared (IR) transmission spectra of Ge10Te80Se10-xGax (x = 0, 2, 4, 6, 8, 10) have been analysed in the range 30–300 cm−1 to study the formation of bonds using chain crossing model, random covalent network model and chemical bond approach. The theoretical calculations have been executed for bond energies, force constants, wave number, etc., for probable bonds, and the results justify the experimental values. The present study contributes to the understanding of the composition-dependent structural property relationship of chalcogenide glasses.

Structure and Microwave Dielectric Properties of Gillespite-Type ACuSi4O10 (A = Ca, Sr, Ba) Ceramics and Quantitative Prediction of the Q × f Value via Machine Learning.

Structure and dielectric properties of gillespite-type ceramics ACuSi4O10 (A = Ca, Sr, Ba) were investigated by crystal structure refinement, far-infrared reflectivity spectroscopy, and microwave dielectric measurements. A series of (CaxSr1-x)CuSi4O10 (0 < x < 1) ceramics with relative permittivities of 5.70-5.82, Q × f values of 20391-48794 GHz (@ ∼ 13.5 GHz), and τf of -46.3 to -38.9 ppm/°C were synthesized. By Ca2+ substitution for Sr2+ at the A-site, the rigid double-layered copper silicate framework remains stable, resulting in the nearly unchanged relative permittivity, while the [(Ca,Sr)O8] dodecahedron undergoes shrinkage and distortion, which is correlated to the changes in the Q × f and τf values. The normalized bond valence sums indicate that almost all ions are rattling, weakening the bond strengths and enlarging the molecular dielectric polarizability. The fitting of far-infrared reflectivity spectra reveals that the local structure changes suppress the intermediate and low-frequency vibrational modes significantly and improves the contribution from electronic polarization to permittivity. Symmetry breaking of the [(Ca,Sr)O8] dodecahedron conforms to the elevated restoring forces acting on the ions and improves the τf value. The large span in Q × f value may have intricate correlations to local structure changes and defects. Machine learning methods were introduced to explore the decisive structural factors for the Q × f value. A Q × f value prediction model correlated with the A-O2 bond length and the variance of A-O bond lengths was established. The Q × f values of isostructural (BaySr1-y)CuSi4O10 ceramics were predicted and verified by experiments.

The Synchrotron-based Far-infrared Spectrum of Glycolaldehyde

Abstract Glycolaldehyde (GA) has been observed toward several different sources, with a broad range of rotational temperatures (8–300 K). At the high end, the temperature is comparable to the energy of the lowest vibrational states of GA, making the vibrational contribution to the partition function significant. Here, we report an analysis of the high-resolution far-infrared spectrum of GA, which features a plethora of well-resolved lines from 170–430 cm−1 (13–5 THz). We focus on the three fundamental vibrational bands in this range, i.e., the symmetric ν 12 bend at 282 cm−1, and the asymmetric ν 17 and ν 18 torsions at 360 and 208 cm−1, respectively. We assigned 23,266 transitions to 13,999 lines within these bands, which, when combined with the previously reported microwave and millimeter-wave spectra, allowed for refinement of the vibrationally excited rotational constants, and accurate determination of their band origins. Additionally, the assignment of a number of lines in several hot bands that are significantly populated at 300 K allowed for determination of their band origins. The rotational constants reported here should be useful in searches of vibrationally excited GA toward warm sources, and the accurately determined band origins allow for refinement of the vibrational partition function, and therefore column density, for a given excitation temperature.

Dust temperature in ALMA [C ii]-detected high-z galaxies

ABSTRACT At redshift z &amp;gt; 5, the far-infrared (FIR) continuum spectra of main-sequence galaxies are sparsely sampled, often with a single data point. The dust temperature Td,SED, thus has to be assumed in the FIR continuum fitting. This introduces large uncertainties regarding the derived dust mass (Md), FIR luminosity, and obscured fraction of the star formation rate. These are crucial quantities to quantify the effect of dust obscuration in high-z galaxies. To overcome observation limitations, we introduce a new method that combines dust continuum information with the overlying [C $\scriptstyle \rm II$] 158 µm line emission. By breaking the Md–Td,SED degeneracy, with our method, we can reliably constrain the dust temperature with a single observation at 158 µm. This method can be applied to all Atacama Large Millimeter Array (ALMA) and NOEMA [C $\scriptstyle \rm II$] observations, and exploited in ALMA Large Programs such as ALPINE and REBELS targeting [C $\scriptstyle \rm II$] emitters at high-z. We also provide a physical interpretation of the empirical relation recently found between molecular gas mass and [C $\scriptstyle \rm II$] luminosity. We derive an analogous relation linking the total gas surface density and [C $\scriptstyle \rm II$] surface brightness. By combining the two, we predict the cosmic evolution of the surface density ratio $\Sigma _{\rm H_2} / \Sigma _{\rm gas}$. We find that $\Sigma _{\rm H_2} / \Sigma _{\rm gas}$ slowly increases with redshift, which is compatible with current observations at 0 &amp;lt; z &amp;lt; 4.