Average Force Constant Research Articles

Highly efficient natural-sunlight-driven photodegradation of organic dyes with combustion derived Ce-doped CuO nanoparticles

CuO nanoparticles doped with various concentrations of Ce (2, 4, and 6 mol%) were synthesized by using the solution combustion method. The as-synthesized nanoparticles were characterized by X-ray diffractometer (XRD), fourier transforms infrared spectroscopy (FTIR), field emission scanning electron microscope (FESEM) and energy-dispersive X-ray spectroscopy (EDX), X-ray photoelectron spectroscopy (XPS), UV–Vis–NIR spectroscopy and photoluminescence (PL) spectroscopy. XRD analysis revealed that the physical parameters such as crystallite size, strain, lattice parameters, dislocation density and stacking fault of CuO nanoparticles were affected after the doping of Ce. FTIR analysis showed that Ce dopants affected the average force constant and the average bond length of CuO nanoparticles. UV–Vis–NIR spectrum analysis showed an enhanced absorption spectrum and narrowed down of the bandgap of CuO from 1.39 eV to 1.28 eV with Ce doping and resulted in increasing refractive index and optical conductivity. PL emission spectra showed a decrease in intensities after doping with Ce by trapping photoinduced electron of CuO by Ce dopants. The photocatalytic activities of the as-synthesized sample were investigated by photocatalytic degradation of organic dyes such as Rhodamine-B (RhB) and Methylene blue (MB), with and without the assistance of H 2 O 2 under solar irradiation. The highest photocatalytic efficiency is obtained with Ce (4 mol%) doped CuO at 95.39% and 87.72% for RhB and MB dyes.

Enhanced thermal stability and optical and structural properties of Tm+3 ions in doped tellurite glasses for photonic use

Tellurite glass (TLZNT) with compositions 75TeO2–5Li2O–10ZnO–(10–x) Nb2O5−x Tm2O3, (doped with x = 0, 0.5, 1.0, 1.5, 2, and 2.5 in mol%) were prepared through the melt quenching technique. In the present work, the glass transition value slightly decreased from 351 to 347 °C otherwise thermal stability ΔTchangesfrom118to164°C of (TLZNT) glasses, investigated by using differential scanning calorimetry (DSC). The influence of Tm3+ ions (RE) on the structure of the TLZNT glasses was studied through different techniques such as X-ray pattern diffraction and Raman/Fourier transform infrared spectra. Moreover, the ratio of the relative bridging oxygen (BO) to non-bridging oxygen (NBO) in the prepared glass network was determined. Next, the packing density of oxygen, density, molar refraction, molar volumes, metallization criterion, molar polarizability, and linear refractive index of the prepared glasses were computed. The optical energy gap, the Judd–Ofelt parameters (J–O), the radiative branching ratio (βR), and the radiative lifetime (τR) of Tm3+ in TLZNT glasses were determined. The absorption cross section (σABS), emission cross section (σEMIS), and gain coefficient (σGA) were evaluated in the range wavelength of 1500–2000 nm. The high value of σEMIS(1.50 × 10−20 cm2) of the 3H6 → 3F4 transition of TLZNT3 glass was reported. We produced TLZNT glasses in which the addition of Tm2O3 improved the ΔT against nucleation and crystallization what is in good agreement with the decrease of the average force constant (F-) from 225 to 221.7 N/m with increasing Tm2O3. For the 1870 nm emission band, the emission cross section was determined to be approximately 1.5 × 10−20 cm2. Finally, the results herein will denote that the TLZNT glasses are a promising solid material for optical applications that could be excited by a commercial laser diode (LD).

Transition-State Vibrational Analysis and Isotope Effects for COMT-Catalyzed Methyl Transfer.

Isotopic partition-function ratios (IPFRs) computed for transition structures (TSs) of the methyl-transfer reaction catalyzed by catechol O-methyltransferase and modeled by hybrid QM/MM methods are analyzed. The ability of smaller Hessians to reproduce trends in α-3H3 and 14Cα IPFRs as obtained using the much larger subset QM/MM Hessians from which they are extracted is investigated critically. A 6-atom-extracted Hessian reproduces perfectly the α-T3 IPFR values from the full-subset Hessians of all the TSs but not the α-14CIPFRs. Average AM1/OPLS-AA harmonic frequencies and mean-square amplitudes are presented for the 12 normal modes of the α-CH3 moiety within the active site of several enzymic transition structures, together with QM/MM potential energy scans along each of these modes to assess the degree of anharmonicity. A novel investigation of ponderal effects upon IPFRs suggests that the value for α-14C tends toward a limiting minimum whereas that for α-T3 tends toward a limiting maximum as the mass of the rest of the system increases. The transition vector is dominated by motions of atoms within the donor and acceptor moieties and is very well described as a simple combination of Walden-inversion “umbrella” bending and asymmetric stretching of the SCα and CαO bonds. The contribution of atoms of the protein residues Met40, Tyr68, and Asp141 to the transition vector is extremely small. Average valence force constants for the COMT TS show significant differences from early BEBOVIB estimates which were used in support of the compression hypothesis for catalysis. There is no correlation between TS IPFRs and the nonbonded distances for close contacts between the S atom of SAM and Tyr68 or between any of the H atoms of the transferring methyl group and either Met40 or Asp141.

Equilibrium Mg isotope fractionation among aqueous Mg2+, carbonates, brucite and lizardite: Insights from first-principles molecular dynamics simulations

Abstract Equilibrium Mg isotope fractionation properties between aqueous Mg2+ and minerals are the key for the applications of Mg isotopes in geochemistry. This study conducts first-principles molecular dynamics (FPMD) simulations for aqueous Mg2+ based on the density functional theory (DFT). Thirty-five snapshots are extracted from the FPMD trajectories after equilibration for the calculations of the reduced partition function ratio (β factor or 103lnβ). Combining with the β factors of minerals, we found that the β factor decreases in the sequence of lizardite > brucite > aqueous Mg2+ > dolomite > magnesite > calcite > aragonite. Our calculations also confirm the effect of Mg concentration on the β factor of calcite, and further show that the concentration effect is negligible when Mg/(Mg + Ca) (atomic ratio hereafter) is lower than 1/32. Our results depict significant equilibrium Mg isotope fractionations between minerals and aqueous Mg2+ (103lnαminerals-Mg_aq), which are dominantly controlled by the average force constant of Mg in these phases. Compared to aqueous Mg2+, carbonates are enriched in light Mg isotopes but brucite and lizardite show enrichment in heavy Mg isotopes. Among all minerals, 103lnαaragonite-Mg_aq is the largest, which is up to −14‰ at 300 K. Notably, 103lnαcalcite-Mg_aq is not only controlled by temperature, but also significantly affected by Mg content in calcite. 103lnαcalcite-Mg_aq is negatively correlated with Mg content in calcite. The experimentally measured Mg isotope fractionations between minerals (dolomite, magnesite, brucite) and solution at equilibrium are consistent with our predicted results, showing the accurate description of FPMD simulations for aqueous Mg2+ and the reliability of our calculations. Overall, the calculated equilibrium Mg isotope fractionations between minerals and aqueous Mg2+ provide a guideline for applications of Mg isotopes in aqueous geochemical processes.

Fabrication and Characterization of Glass and Glass-Ceramic from Cement Dust and Limestone Dust

Recycling the solid wastes like cement dust and limestone dust and using in the manufacturing of glass and glass - ceramics are strongly needed. These glasses fabricated by melt-quench technique. The X-ray diffraction (XRD) patterns of all the studied samples confirmed the amorphous nature These glasses have been investigated for their physical properties using density and molar volume, structural properties using FTIR spectroscopy, optical properties using UV-Vis spectroscopy, thermal analysis and mechanical properties. The density, molar volume and refractive index vary with the concentration of CaO. The variations of various physical, structural, thermal analyses, mechanical and optical properties with the concentration of CaO in this glass system depict a strong structural influence of CaO. The ultrasonic velocity of these glasses has been decreased with addition of CaO, this decrease is connected to the decreasing the bonding strength between Calcium - oxygen are lower than the bond between silicon - oxygen (32-106 k cals).The elastic moduli of these glasses determined experimentally and calculated theoretically, according to Makishima–Mackenzie model decreased with increasing of CaO. This behavior may be related to changing the coordination number with an increasing of CaO and the decrease in the average force constant and crosslink density. The crystalline phase of the prepared glass ceramic is diopside with the chemical formula (Ca MgO6 Si) in all selected samples.

Synthesis and Physical Characteristics of New Glasses from Some Environmental Wastes

New glasses from harmful environmental waste like cement dust; limestone phosphate and sand were fabricated. The constructions of these sample investigation by FTIR, mechanical and optical properties. The density and refractive index of these glasses increases by increasing of SiO2 concentration. Longitudinal (vL), and share (vT) velocities increase with addition of silicon oxide. The elastic moduli values were showing increasing as an increasing of SiO2 concentration. The increase in elastic moduli may be connected to changing of the coordination number with an addition of SiO2 and the increase the bond strength, average force constant and the crosslink density. DTA of the investigated samples with exclusive SiO2 contents shows the increasing in Tg values. The molar volume and the optical band gab of these glasses decreases with increase of SiO2 expense on CaO.

Transition and post-transition metal ions in borate glasses: Borate ligand speciation, cluster formation, and their effect on glass transition and mechanical properties.

A series of transition and post-transition metal ion (Mn, Cu, Zn, Pb, Bi) binary borate glasses was studied with special consideration of the cations impact on the borate structure, the cations cross-linking capacity, and more generally, structure-property correlations. Infrared (IR) and Raman spectroscopies were used for the structural characterization. These complementary techniques are sensitive to the short-range order as in the differentiation of tetrahedral and trigonal borate units or regarding the number of non-bridging oxygen ions per unit. Moreover, vibrational spectroscopy is also sensitive to the intermediate-range order and to the presence of superstructural units, such as rings and chains, or the combination of rings. In order to clarify band assignments for the various borate entities, examples are given from pure vitreous B2O3 to meta-, pyro-, ortho-, and even overmodified borate glass compositions. For binary metaborate glasses, the impact of the modifier cation on the borate speciation is shown. High field strength cations such as Zn2+ enhance the disproportionation of metaborate to polyborate and pyroborate units. Pb2+ and Bi3+ induce cluster formation, resulting in PbOn- and BiOn-pseudophases. Both lead and bismuth borate glasses show also a tendency to stabilize very large superstructural units in the form of diborate polyanions. Far-IR spectra reflect on the bonding states of modifier cations in glasses. The frequency of the measured cation-site vibration band was used to obtain the average force constant for the metal-oxygen bonding, FM-O. A linear correlation between glass transition temperature (Tg) and FM-O was shown for the metaborate glass series. The mechanical properties of the glasses also correlate with the force constant FM-O, though for cations of similar force constant the fraction of tetrahedral borate units (N4) strongly affects the thermal and mechanical properties. For paramagnetic Cu- and Mn-borate glasses, N4 was determined from the IR spectra after deducing the relative absorption coefficient of boron tetrahedral versus boron trigonal units, α = α4/α3, using NMR literature data of the diamagnetic glasses.

Far-infrared studies on Nafion and perfluoroimide acid (PFIA) and their alkali salts

The terahertz/far-infrared spectra (<300cm−1) of perfluorinated sulfonic acid (Nafion NR211 polymer) and perfluoroimide acid (PFIA polymer) and their alkali (M+) salts have been analyzed and the results are presented. Pronounced features in the spectra of these ionomers that correlate systematically with the corresponding cation mass are reported and from their spectral position the force constants are derived. The average vibrational force constants for Nafion/M+ and PFIA/M+ are found to be 54±7 and 39±4N/m, respectively. Such terahertz/far-infrared signatures probe the detailed structure of the Nafion/M+ and PFIA/M+ ionic clusters and, in turn, provide benchmarks for elucidating the ionomer “water channels” or water molecules located in the ionomer–water interface upon hydration. Qualitative trends in the vibrational energies of Nafion and PFIA can be explained by consideration of electronic and/or structural (ionic domain-size) effects.

Study of rigidity of semiconducting vanadate glasses and its importance in use of coatings

The elastic moduli of some multicomponent vanadate based glasses were analysed in terms of the bond compression model by some physical parameters such as, the density, average stretching force constant and average atomic ring size. These parameters were calculated for all the glass series and for all the glass composition to estimate the rigidity of these glasses. The results showed that the average force constant and the elastic moduli of these glasses are sensitive to the decrease in PbO content. This behaviour was attributed to the increase in the molar volume and the role of different modifiers. These parameters along with the coordination number of the glasses affect the glass transition temperature. The correlation between the elastic moduli and thermal properties of these samples showed that 0·25MoO3–0.25PbO–0·5V2O5 glass is the most rigid and has an applicable glass transition temperature for coating.

Experimental constraints on the thermodynamics and sound velocities of hcp‐Fe to core pressures

We report the high‐pressure thermoelastic and vibrational thermodynamic parameters for hexagonal close‐packed iron (ε‐Fe), based on nuclear resonant inelastic X‐ray scattering and in situ X‐ray diffraction experiments at 300 K. Long data collection times, high‐energy resolution, and quasi‐hydrostatic sample conditions produced a high‐statistical quality data set that comprises the volume‐dependent phonon density of states (DOS) of ε‐Fe at eleven compression points. From the integrated phonon DOS, we determine the Lamb‐Mössbauer factor (fLM), average force constant (Φ), and vibrational entropy (Svib) of ε‐Fe to pressures relevant to Earth's outer core. We find fLM = 0.923 ± 0.001 at 171 GPa, suggesting restricted thermal atomic motion at large compressions. We use Φ to approximate ε‐Fe's pressure‐ and temperature‐dependent reduced isotopic partition function ratios (β‐factors), which provide information about the partitioning behavior of iron isotopes in equilibrium processes involving solid ε‐Fe. In addition, we use the volume dependence of Svib to determine the product of ε‐Fe's vibrational thermal expansion coefficient and isothermal bulk modulus, which we find to be pressure‐independent and equal to 5.70 ± 0.05 MPa/K at 300 K. Finally, from the low‐energy region of each phonon DOS, we determine the Debye sound velocity (vD), from which we derive the compressional (vP) and shear (vS) sound velocities of ε‐Fe. We find vD = 5.60 ± 0.06, vP = 10.11 ± 0.12, and vS = 4.99 ± 0.06 km/s at 171 GPa, thus providing a new tight constraint on the density dependence of ε‐Fe's sound velocities to outer core pressures.

Vibrational Spectra and Quantum Chemical Calculations of the Pure and Mixed Cluster Anions [SixGe4–x]4– and [GexSn4–x]4– (x = 0–4) in Compounds with Potassium and Cesium

AbstractThe Raman spectroscopic studies on samples with the starting compositions Cs4[Si2Ge2] and M4[Ge2Sn2] (M = K, Cs) verify unambiguously the presence of phases composed of the mixed cluster moieties [SixGe4–x]4– and [GexSn4–x]4– (x = 1–3) including the pure anions [E4]4– (E = Si, Ge, Sn). The assignment of the vibrational frequencies is supported by normal coordinate analysis (NCA). The results for the mixed cluster anions are discussed in context with their isoelectronic analogs PxAs4–x (x = 1–3) and SbP3. Using the characteristic breathing frequencies, one obtains for the ratio factor of the mixed moieties κ = ν([SixGe4–x]4–) / ν(PxAs4–x) = 0.79, which is in good agreement with the reported value of 0.77 for the pure cluster series [E4]4– (E = Si, Ge, Sn) and X4 (X = P, As, Sb). The experimental average force constants f(Si‐Ge) = 1.01 Ncm–1 and f(Ge‐Sn) = 0.77 Ncm–1 correspond to arithmetic mean of those obtained for the pure anions in the binaries M4E4 (M = K, Rb, Cs; E = Si, Ge, Sn). The phonon frequencies of binary M4E4 (M = K, Cs; E = Si, Ge, Sn) and ternary K4ExE′4–x (E, E′ = Si, Ge or Ge, Sn, E ≠ E′, x = 1, 2, 3) were calculated by using pseudopotential electronic structure method SIESTA. Excellent agreement between the calculated and experimental frequencies was obtained for the pure binaries. The theoretical results compare also well with experimental values for the mixed series [SixGe4–x]4–, whereas for the corresponding mixed Ge‐Sn species the differences between measured and calculated frequencies are greater than 10 %.

Excess of low frequency vibrational modes and glass transition: A molecular dynamics study for soft spheres at constant pressure

Using molecular dynamics at constant pressure, the relationship between the excess of low frequency vibrational modes (known as the boson peak) and the glass transition is investigated for a truncated Lennard-Jones potential. It is observed that the quadratic mean displacement is enhanced by such modes, as predicted using a harmonic Hamiltonian for metastable states. As a result, glasses loose mechanical stability at lower temperatures than the corresponding crystal, since the Lindemann criteria are observed, as is also deduced from density functional theory. Finally, we found that the average force and elastic constant are reduced in the glass due to such excess of modes. The ratio between average elastic constants can be approximated using the 2/3 rule between melting and glass transition temperatures.

Structural Analysis of Some Alkali Diborate Glasses

This manuscript presents a theoretical analysis of the correlation between the computed bulk modulus and the structure of a series of multicomponent sodium diborate based glasses in terms of the bond compression model. The main parameters in the analysis were the computed elastic moduli, the average stretching force constant and the average atomic ring size. These parameters were calculated for every glass series and for every glass composition. The results showed that the average force constant and the elastic moduli of these glasses are sensitive to the decrease in the sodium diborate content. This behaviour was attributed to the increase in the molar volume, and to the role of the dierent modifiers.

Nuclear resonant X-ray spectroscopy of (Mg,Fe)SiO3 orthoenstatites

We present nuclear resonant inelastic X-ray scattering (NRIXS) and synchrotron Mossbauer spectroscopy (SMS) measurements, both nuclear resonant X-ray spectroscopic methods, on synthetic samples of orthoenstatite-structured (Mg,^(57)Fe)SiO_3, a representative component in Earth's upper mantle. All measurements were performed at ambient conditions. NRIXS spectra were measured for three samples of orthoenstatite containing 20, 13, and 7 mol% FeSiO_3. The Debye sound velocities were determined from the low-energy region of the partial phonon density of states (PDOS). With known density and bulk modulus, the shear modulus, compressional and shear wave velocities have been computed. The sound velocities obtained from NRIXS are in good agreement with sound velocities obtained using Brillouin spectroscopy and ultrasonic methods for similar compositions. An important advantage of NRIXS is access to additional thermodynamic information, such as the average force constant, mean-square displacement, obtained from the PDOS. We discuss the contribution of the vibrational spectra to these quantities. In addition to the PDOS, the electronic environment of the iron sites in (Mg_(0.87)^(57)Fe_(0.13))SiO_3 orthoenstatite was determined using ^(57)Fe SMS and conventional Mossbauer spectroscopy. Evaluation of the Mossbauer spectra reveals two distinct iron sites, which are well distinguished by their hyperfine fields. The minority and majority sites are consistent with high-spin Fe^(2+) in the M1 and M2 sites, respectively.

Characterization of some lead vanadate glasses

Studies on lead vanadate glasses modified with Li 2O have been carried out. Elastic properties and Debye temperature have been investigated using sound velocity measurements at 4 MHz. The ultrasonic and the IR spectroscopic studies have been employed to investigate the structure of lead vanadate glasses in the presence of Li 2O. IR analysis indicates that increasing the vanadate content causes a shift of the bands to higher wave number and to higher relative area which was attributed to the higher dissociation energy of V 2O 5 than that of PbO. Thus, the average force constant of VO 5 structural units increases with increasing V 2O 5 content. The change of density and molar volume with V 2O 5 content reveals that the decrease in density is related to the replacement of high dense PbO with low dense one V 2O 5, where the increase in the molar volume can be attributed to the larger packing factor of V 2O 5 than that of PbO. The observed compositional dependence of the elastic moduli is interpreted in terms of the effect of V 2O 5 on the coordination number of the vanadate and lead structural units.

Structural and thermal stability criteria ofBi2O3–B2O3 glasses

Glasses with compositions xBi2O3–(100−x)B2O3 with 30≤x≤60 mol% have been prepared using the normal melt quenching technique. Infrared(IR) spectroscopy was used as a structural probe of the nearest-neighborenvironment in the glass network. Assessment of the thermal stability of theseglasses was achieved in terms of various simple quantitative methods based onthe characteristic temperatures, such as the glass transition temperature,Tg, the onset temperatureof crystallization, Tin, the temperature corresponding to the maximum crystallization rate,Tp, and the meltingtemperature, Tm. In this case, kgl may be more suitable for estimating the glass thermal stability inthe above composition range. In this work the kinetic parameterKr(T) is added to the stability criteria. The thermal stability of the glasses that were studied has beencorrelated with the activation energy of crystallization by this kinetic criterion and comparedwith those evaluated by other criteria. The results of both the criteria and the kinetic parameterKr(T) confirm that the thermal stability decreases with increasingBi2O3 content. The former parameters, besides the average force constant of theBO3 structural unit, were characterized and discussed in terms of the changes in the glassstructure.

Electronic transport and atomic vibrational properties of semiconducting MgSn thin film

A polycrystalline Mg2Sn thin film has been prepared by thermal co-evaporation in ultrahigh vacuum of Mg and Sn onto a naturally oxidized Si(100) substrate at −140°C. The structure of the sample was characterized by X-ray diffraction (XRD) and 119Sn conversion electron Mössbauer spectroscopy (CEMS). The semiconducting property of the Mg2Sn thin film was confirmed by electrical resistance, magnetoresistance, Hall-effect and infrared spectroscopy measurements, and a value of ∼0.2 eV was found for the electronic gap energy. The 119Sn-projected partial vibrational density of states (VDOS), g(E), has been measured by nuclear resonant inelastic X-ray scattering (NRIXS) of 23.878 keV synchrotron radiation. Together with g(E), other thermodynamic quantities such as the probability of recoilless absorption (f-factor), the average kinetic energy per Sn atom, the average force constant, and the vibrational entropy per Sn atom are obtained. The partial VDOS of both elements (Mg and Sn) has been calculated theoretically and reasonable agreement with the measured 119Sn-projected VDOS is observed. g(E) is characterized by a phonon energy gap ranging from ∼17 to ∼21 meV.

Atomic vibrational dynamics of amorphous Fe–Mg alloy thin films

Abstract The atomic vibrational dynamics of 57 Fe in 800-A thick amorphous Fe x Mg 1− x alloy thin films (0.3≤ x ≤0.7) has been investigated at room temperature by nuclear resonant inelastic X-ray scattering (NRIXS) of 14.4125 keV synchrotron radiation. The amorphous phase has been successfully stabilized by codeposition of Fe and Mg in ultrahigh vacuum onto a substrate held at −140 °C during deposition. The amorphous structure of the samples was confirmed by X-ray diffraction and conversion electron Mossbauer spectroscopy. The 57 Fe-projected partial vibrational density of states, g ( E ), has been obtained from the measured NRIXS vibrational excitation probability, together with thermodynamic quantities such as the probability of recoilless absorption ( f -factor), the average kinetic energy per Fe atom, the average force constant, and the vibrational entropy per Fe atom. A plot of g ( E )/ E 2 versus E proves the existence of non-Debye-like vibrational excitations with a peak at E bp ∼3–5 meV (boson peak). Both the boson peak height and E bp were found to depend linearly on the composition x . Above the boson peak, g ( E )/ E 2 exhibits an exponential decrease.

Structural interpretations of aluminosilicate glasses

This manuscript presents a theoretical analysis of the correlation between the bulk moduli and the structure of a series of multicomponent aluminosilicate glasses in terms of the bond compression model. The main parameters in the analysis were the computed elastic moduli, the average stretching-force constant and the average atomic ring size. These parameters were calculated for every glass series and for every glass composition. The results showed that the average force constant of these glasses increases and the elastic moduli decrease with the increase in the SiO 2 content (pure covalent bonds). This behaviour was attributed to the decrease in the molar volume, and the role of both CaO and Al 2O 3. The average atomic ring size of the studied glasses are about two-thirds of pure SiO 2, whilst the elastic moduli of pure SiO 2 glass are about two thirds of these glasses.

Atomic vibrational density of states in crystalline and amorphousTb1−xFex alloy thin films studied by nuclear resonant inelastic x-ray scattering (NRIXS)

Nuclear resonant inelastic x-ray scattering of 14.4125 keV synchrotron radiation was employedto measure directly the partial (Fe projected) vibrational density of states (VDOS),g(E), of vapour-quenchedamorphous (a-)Tb1−x57Fex thin film alloys and epitaxial Tb57Fe2(110) thin films. A comparison of the VDOS measured at 300 and 10 K, respectively, demonstrates thatthe vibrational anharmonicity is small in these systems. The probability of recoilless absorption(f factor), the average kinetic energy per Fe atom and the average force constant were obtained. A plotof g(E)/E2 versus E proves the existence of non-Debye-like vibrational excitations at excitation energies belowabout 10 meV for the amorphous alloys. At a constant film thickness of 17.5 nm, theprobability of these excitations scales about linearly with the Tb concentration.