Thermal decomposition of toluene: Overall rate and branching ratio

The two-channel thermal decomposition of toluene, C₆H₅CH₃ → C₆H₅CH₂ + H (1) and C₆H₅CH₃ → C₆H₅ + CH₃ (2), was investigated in shock tube experiments over the temperature range of 1400-1780 K at a pressure of 1.5 (±0.1) bar. Rate coefficients for reactions (1) and (2) were determined by monitoring benzyl radical (C₆H₅CH₂) absorption at 266 nm during the decomposition of toluene diluted in argon and modeling the temporal behavior of the benzyl concentration with a kinetic model. The first-order rate coefficients determined at a pressure of 1.5 bar are expressed by k₁(T) = 2.09 × 10¹⁵ exp (−87510 [cal/mol]/RT) [s⁻¹] and k₂(T) = 2.66 × 10¹⁶ exp (−97880 [cal/mol]/RT) [s⁻¹]. The resulting branching ratio, k₁/(k₁ + k₂), ranges from 0.8 at 1350 K to 0.6 at 1800 K.     

Temperature and pressure effects on formation and decomposition of phenylvinylperoxy radicals in the C6H5C2H2 + O2 reaction

The effects of temperature and pressure on the formation and decomposition of C₆H₅C₂H₂O₂ in the C₆H₅C₂H₂ + O₂ reaction have been investigated at temperatures from 298 to 378 K by directly monitoring the C₆H₅C₂H₂O₂ radical in the visible region by cavity ringdown spectrometry (CRDS). The rate constant for the C₆H₅C₂H₂ + O₂ association and that for fragmentation of C₆H₅C₂H₂O₂ were found to be k₁ (C₆H₅C₂H₂ + O₂ → C₆H₅C₂H₂O₂) = (3.20 ± 1.19) × 10¹¹ exp(+760/T) cm³ mol⁻¹ s⁻¹ and k₂ (C₆H₅C₂H₂ O₂ → C₆H₅CHO + HCO) = (1.68 ± 0.13) × 10⁴ s⁻¹, respectively. Additional kinetic measurements by pulsed laser photolysis/mass spectrometry show that C₆H₅CHO was produced in the C₆H₅C₂H₂ + O₂ reaction as predicted and the formation of C₆H₅CHO from the decomposition of C₆H₅C₂H₂O₂ is temperature-independent, consistent with the CRDS experimental data.     

Pressure and temperature dependence of the reaction of vinyl radical with alkenes II: Measured rates and predicted product distributions for vinyl + propene

This work reports measurements of the absolute rate coefficients and Rice-Ramsperger-Kassel-Markus (RRKM) master equation (ME) simulations of the C₂H₃ + C₃H₆ reaction. Direct kinetic studies were performed over a temperature range of 300-700 K and pressures of 15, 25, and 100 Torr. Vinyl radicals were generated by laser photolysis of vinyl iodide at 266 nm, and time-resolved absorption spectroscopy was used to probe vinyl radicals through absorption at 423.2 nm. A weighted modified Arrhenius fit to the experimental rate constant is k₁ = (1.3 ± 0.2) × 10⁻¹² cm³ molecule⁻¹ s⁻¹(T/1000)^1.6 exp[−(1510 ± 80/T)]. Fifteen stationary points and 48 transition states on the C₅H₉ potential energy surface (PES) were calculated using the G3 method in Gaussian 03. RRKM/ME simulations were performed using VariFlex on a simplified PES to predict pressure dependent rate coefficients and branching fractions for the major channels. For temperatures between 350 and 700 K, the calculated rate coefficient agrees with the experimental rate coefficient within 20%. At low temperatures, the primary products are the initial adducts 4-penten-2-yl and 2-methyl-3-buten-1-yl. At higher temperatures, the dominant products are 1,3-butadiene + methyl, allyl + ethene, and 1,3-pentadiene + H. Although C₂H₃ + C₃H₆ → allyl + ethene is thermodynamically favored, the simulations predict that it does not become the dominant product until 1700 K.     

Theoretical study on the kinetics for OH reactions with CH3OH and C2H5OH

Kinetics and mechanisms for reactions of OH with methanol and ethanol have been investigated at the CCSD(T)/6-311 + G(3df, 2p)//MP2/6-311 + G(3df, 2p) level of theory. The total and individual rate constants, and product branching ratios for the reactions have been computed in the temperature range 200-3000 K with variational transition state theory by including the effects of multiple reflections above the wells of their pre-reaction complexes, quantum-mechanical tunneling and hindered internal rotations. The predicted results can be represented by the expressions k₁ = 4.65 × 10⁻²⁰ × T^2.68 exp(414/T) and k₂ = 9.11 × 10⁻²⁰ × T^2.58 exp(748/T) cm³ molecule⁻¹ s⁻¹ for the CH₃OH and C₂H₅OH reactions, respectively. These results are in reasonable agreements with available experimental data except that of OH + C₂H₅OH in the high temperature range. The former reaction produces 96-89% of the H₂O + CH₂OH products, whereas the latter process produces 98-70% of H₂O + CH₃CHOH and 2-21% of the H₂O + CH₂CH₂OH products in the temperature range computed (200-3000 K).     

Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

The second and third-order Brugger elastic constants are obtained for liquids and ideal gases having an initial hydrostatic pressure p₁. For liquids the second-order elastic constants are C₁₁ = A + p₁, C₁₂ = A − p₁, and the third-order constants are C₁₁₁ = −(B + 5A + 3p₁), C₁₁₂ = −(B + A − p₁), and C₁₂₃ = A − B − p₁, where A and B are the Beyer expansion coefficients in the liquid equation of state. For ideal gases the second-order constants are C₁₁ = p₁γ + p₁, C₁₂ = p₁γ − p₁, and the third-order constants are C₁₁₁ = −p₁(γ² + 4γ + 3), C₁₁₂ = −p₁(γ² − 1), and C₁₂₃ = −p₁ (γ² − 2γ + 1), where γ is the ratio of specific heats. The inequality of C₁₁ and C₁₂ results in a nonzero shear constant C₄₄ = (1/2)(C₁₁ − C₁₂) = p₁ for both liquids and gases. For water at standard temperature and pressure the ratio of terms p₁/A contributing to the second-order constants is approximately 4.3 × 10⁻⁵. For atmospheric gases the ratio of corresponding terms is approximately 0.7. Analytical expressions that include initial stresses are derived for the material ‘nonlinearity parameters’ associated with harmonic generation and acoustoelasticity for fluids and solids of arbitrary crystal symmetry. The expressions are used to validate the relationships for the elastic constants of fluids.     

Ab initio chemical kinetics for the reactions of HNCN with O(P) and O2

The kinetics and mechanisms of the reactions of cyanomidyl radical (HNCN) with oxygen atoms and molecules have been investigated by ab initio calculations with rate constant prediction. The doublet and quartet state potential energy surfaces (PESs) of the two reactions have been calculated by single-point calculations at the CCSD(T)/6-311+G(3df, 2p) level based on geometries optimized at the CCSD/6-311++G(d, p) level. The rate constants for various product channels of the two reactions in the temperature range of 300-3000 K are predicted by variational transition state and RRKM theories. The predicted total rate constants of the O(³P) + HNCN reaction at 760 Torr Ar pressure can be represented by the expressions k_total (O + HNCN) = 3.12 × 10⁻¹⁰ × T^−0.05 exp (−37/T) cm³ molecule⁻¹ s⁻¹ at T = 300-3000 K. The branching ratios of primary channels of the O(³P) + HNCN are predicted: k₁ for producing the NO + CNH accounts for 0.72-0.64, k₂ + k₉ for producing the ³NH + NCO accounts for 0.27-0.32, and k₆ for producing the CN + HNO accounts for 0.01-0.07 in the temperature range studied. Meanwhile, the predicted total rate constants of the O₂ + HNCN reaction at 760 Torr Ar pressure can be represented by the expression, k_total(O₂ + HNCN) = 2.10 × 10⁻¹⁶ × T^1.28exp (−12200/T) cm³ molecule⁻¹ s⁻¹ at T = 300-3000 K. The predicted branching ratio for k₁₁ + k₁₃ producing HO₂ + ³NCN as the primary products accounts for 0.98-1.00 in the temperature range studied.     

Single crystal EPR and optical absorption study of Cr doped l-histidine hydrochloride monohydrate

EPR study of the Cr³⁺ ion doped l-histidine hydrochloride monohydrate single crystal is done at room temperature. Two magnetically inequivalent interstitial sites are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The zero field and spin Hamiltonian parameters are evaluated from the resonance lines obtained at different angular rotations and the parameters are: D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.9108±0.0002, g_y=1.9791±0.0002, g_z=2.0389±0.0002, A_x=(252±2)×10⁻⁴ cm⁻¹, A_y=(254±2)×10⁻⁴ cm⁻¹, A_z=(304±2)×10⁻⁴ cm⁻¹ for site I and D=(300±2)×10⁻⁴ cm⁻¹, E=(96±2)×10⁻⁴ cm⁻¹, g_x=1.8543±0.0002, g_y=1.9897±0.0002, g_z=2.0793±0.0002, A_x=(251±2)×10⁻⁴ cm⁻¹, A_y=(257±2)×10⁻⁴ cm⁻¹, A_z=(309±2)×10⁻⁴ cm⁻¹ for site II, respectively. The optical absorption studies of single crystals are also carried out at room temperature in the wavelength range 195-925 nm. Using EPR and optical data, different bonding parameters are calculated and the nature of bonding in the crystal is discussed. The values of Racah parameters (B and C), crystal field parameter (Dq) and nephelauxetic parameters (h and k) are: B=636, C=3123, Dq=2039 cm⁻¹, h=1.46 and k=0.21, respectively.     

On the mechanism of decomposition of the benzyl radical

The C₇H₇ potential energy surface was studied from first principles to determine the benzyl radical decomposition mechanism. The investigated high temperature reaction pathway involves 15 accessible energy wells connected by 25 transition states. The analysis of the potential energy surface, performed determining kinetic constants of each elementary reaction using conventional transition state theory, evidenced that the reaction mechanism has as rate determining step the isomerization of the 1,3-cyclopentadiene, 5-vinyl radical to the 2-cyclopentene,5-ethenylidene radical and that the fastest reaction channel is dissociation to fulvenallene and hydrogen. This is in agreement with the literature evidences reporting that benzyl decomposes to hydrogen and a C₇H₆ species. The benzyl high-pressure decomposition rate constant estimated assuming equilibrium between the rate determining step transition state and benzyl is k₁(T) = 1.44 × 10¹³T^0.453exp(−38400/T) s⁻¹, in good agreement with the literature data. As fulvenallene reactivity is mostly unknown, we investigated its reaction with hydrogen, which has been proposed in the literature as a possible decomposition route. The reaction proceeds fast both backward to form again benzyl and, if hydrogen adds to allene, forward toward the decomposition into the cyclopentadienyl radical and acetylene with high-pressure kinetic constants k₂(T) = 8.82 × 10⁸T^1.20exp(1016/T) and k₃(T) = 1.06 × 10⁸T^1.35exp(1716/T) cm³/mol/s, respectively. The computed rate constants were then inserted in a detailed kinetic mechanism and used to simulate shock tube literature experiments.     

The reaction of allyl radicals with oxygen atoms—rate coefficient and product branching

The primary product formation of the C₃H₅ + O reaction in the gas phase has been studied at room temperature. Allyl radicals (C₃H₅) and O atoms were generated by laser flash photolysis at λ = 193 nm of the precursors C₃H₅Cl, C₃H₅Br, C₆H₁₀ (1,5-hexadiene), and SO₂, respectively. The educts and the products were detected by using quantitative FTIR spectroscopy. The combined product analysis of the experiments with the different precursors leads to the following relative branching fractions: C₃H₅ + O → C₃H₄O + H (47%), C₂H₄ + H + CO (41%), H₂CO + C₂H₂ + H (7%), CH₃CCH + OH and CH₂CCH₂ + OH (<5%). The rate of reaction has been studied relative to CH₃OCH₂ + O and C₂H₅ + O in the temperature range from 300 to 623 K. Here, the radicals were produced via the fast reactions of propene, dimethyl ether, and ethane, respectively, with atomic fluorine. Laser-induced multiphoton ionization combined with TOF mass spectrometry and molecular beam sampling from a flow reactor was used for the specific and sensitive detection of the C₃H₅, C₂H₅, and CH₃COCH₂ radicals. The rate coefficient of the reaction C₃H₅ + O was derived with reference to the reaction C₂H₅ + O leading to k(C₃H₅ + O) = (1.11 ± 0.2) × 10¹⁴ cm³/(mol s) in the temperature range 300-623 K. The C₃H₅ + O rate and channel branching, when incorporated in a suitable detailed reaction mechanism, have a large influence on benzene and allyl concentration profiles in fuel-rich propene flames, on the propene flame speed, and on propene ignition delay times.     

The high-resolution FTIR spectrum of the ν6 band of C2H3D

The absorption spectrum of the ν₆ band of C₂H₃D centered near 1125.27674 cm⁻¹ in the 1100-1250 cm⁻¹ region was recorded with an unapodized resolution of 0.0063 cm⁻¹ using a Fourier transform infrared (FTIR) spectrometer. A total of 947 infrared transitions of the A-B hybrid-type band were assigned and fitted to upper-state (ν₆ = 1) rovibrational constants using a Watson’s A-reduced Hamiltonian in the I^r representation up to eighth-order centrifugal distortion terms. The b-type infrared transitions of the band were analyzed for the first time. The root-mean-square deviation of the fit was 0.00062 cm⁻¹. The ground-state rovibrational constants up to eighth-order terms were also obtained by a fit of 617 combination differences from the present infrared measurements, simultaneously with 21 microwave frequencies with a root-mean-square deviation of 0.00055 cm⁻¹. From this work, the upper-state (ν₆ = 1) and ground-state constants of C₂H₃D were derived with the highest accuracy, so far. The a- and b-type transitions of the hybrid ν₆ band were found to be relatively free from local frequency perturbations. The ratio of the a- to b-type vibrational dipole transition moments (μ_a/μ_b) was found to be 1.05 ± 0.10. From the ν₆ = 1 rovibrational constants obtained, the inertial defect Δ₆ was calculated to be 0.3570 ± 0.0008 μŲ.     

High-resolution FTIR measurement and analysis of the ν3 band of C2H3D

The Fourier transform infrared (FTIR) spectrum of the ν₃ band of C₂H₃D was measured at an unapodized resolution of 0.0063 cm⁻¹ in the 1240-1340 cm⁻¹ region. Rovibrational constants for the upper state (ν₃ = 1) up to five quartic and two sextic centrifugal distortion terms had been obtained by assigning and fitting a total of 1037 infrared transitions using a Watson’s A-reduced Hamiltonian in the I^r representation. The root-mean-square deviation of the fit was 0.00051 cm⁻¹. The ground state rovibrational constants were also determined by a fit of 674 combination differences together with 21 microwave frequencies from the present infrared measurements with a root-mean-square deviation of 0.00040 cm⁻¹. The upper state (ν₃ = 1) and ground state rovibrational constants of C₂H₃D represent the most accurate values obtained so far. The A-type ν₃ band, centred at 1288.788826 ± 0.000044 cm⁻¹ was found to be relatively free from local frequency perturbations. From the ν₃ = 1 rovibrational constants obtained, the inertial defect Δ₃ was 0.1619724 ± 0.0000001 μŲ.     

Metal ion-molecule kinetics at combustion temperatures: The reaction of Ca with O2

The high-temperature photochemistry (HTP) technique, previously used for reactions of neutral species, has been adapted to the study of atomic metal ion-molecule reactions. Ca⁺ ions were generated by 193 nm multi-photon photolysis of calcium acetyl acetonate and its pyrolysis fragments. The relative ion concentrations were monitored by laser-induced fluorescence at 393.4 nm. Ar was used as the bath gas. The data for the Ca⁺ + O₂ + M → CaO₂⁺ + M association reaction (1) are fitted by k₁(907-1425 K) = 3.5 × 10⁻³² exp(+3161 K/T) cm⁶ molecule⁻² s⁻¹. Combining with an approximate k₁(296 K) value in the literature leads to k₁(296-1425 K) = 5.8 × 10⁻²² (T/K)^−2.9 exp(−601 K/T) cm⁶ molecule⁻² s⁻¹. Over much of the observed temperature range reaction (1) has much smaller rate coefficients than the corresponding neutral Ca association reaction. Reaction (1) is shown to behave very similarly to the O₂ association reaction with neutral K atoms, with which Ca⁺ is iso-electronic. This suggests that the initial step is ion-pair complex formation of the superoxide Ca²⁺(O₂)⁻, which is also consistent with results from density functional calculations. The k₁ values are rationalized via Troe’s unimolecular formalism, which leads to good accord with the experiments.     

A Monte Carlo simulation study of H2 layers on NaCl(0 0 1)

Monte Carlo simulations show that, at one monolayer coverage, H₂ molecules adsorbed on a NaCl(0 0 1) surface occupy all Na⁺ sites and form a commensurate c(2 × 2) structure. If the Cl⁻ sites are occupied as well, a bi-layer p(2 × 1) structure forms. An examination of the H₂ molecules’ rotational motion shows the molecular axes are azimuthally delocalized and so both of the structures acquire (1 × 1) symmetry in accord with experimental observations. These calculations also show that helicoptering o-H₂ (J = 1, m = ±1) prefer to sit on top of Na⁺ sites, while cartwheeling o-H₂ (J = 1, m = 0) prefers to locate over Cl⁻ sites, in agreement with other work.     

The bΣ(b0) → XΣ(X10,X21) and aΔ(a2) → X21 transitions of AsBr

Emission spectra of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺,X₂1) and a¹Δ(a2) → X₂1 transitions of AsBr have been measured in the near-infrared spectral region with a Fourier-transform spectrometer. The arsenic bromide radicals were generated in fast-flow systems by reaction of arsenic vapor (As_x) with bromine and were excited by microwave-discharged oxygen. The most prominent features in the spectrum are the Δv = +1,0,−1, and −2 band sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₁0⁺) transition in the range 11 700-12 700 cm⁻¹. With lower intensities, the Δv = 0 and −1 sequences of the b¹Σ⁺(b0⁺) → X³Σ⁻(X₂1) sub-system show up in the same range. Further to the red, between 6000 and 6700 cm⁻¹, the Δv = 0, +1, and −1 sequences of the hitherto unknown a¹Δ(a2) → X₂1 transition are observed. Analyses of medium- and high-resolution spectra have yielded improved molecular constants for the X₁0⁺, X₂1, and b0⁺ states and first values of the electronic energy and the vibrational constants of the a2 state.     

Improved rovibrational constants for the ν12 band of C2H3D

The Fourier transform infrared absorption spectrum of the ν₁₂ fundamental band of ethylene-d (C₂H₃D) was recorded at an unapodized resolution of 0.0063 cm⁻¹ in the 1330-1475 cm⁻¹ region. Upper state (ν₁₂ = 1) rovibrational constants inclusive of three rotational, five quartic, and four sextic centrifugal distortion constants were improved by assigning and fitting 1444 infrared transitions using Watson’s A-reduced Hamiltonian in the I^r representation. The present analysis yielded more higher-order upper state constants than previously reported. The rms deviation of the fit is 0.00055 cm⁻¹. Improved ground state rovibrational constants were also determined from the combined fit of 2026 ground state combination differences (GSCD) from the assigned infrared transitions of the ν₁₂, ν₃ and ν₆ bands and 21 microwave frequencies of C₂H₃D. The rms deviation of the GSCD fit is 0.00047 cm⁻¹. The A-type ν₁₂ band is centered at 1400.76262 ± 0.00004 cm⁻¹. Local frequency perturbations were not detected in the analysis. The calculated inertial defect Δ₁₂ is 0.20809 ± 0.00003 μŲ.     

The effect of duration of diffusion on Ag diffusion coefficients in YBa2Cu3O7

The Ag diffusion in superconducting YBa₂Cu₃O₇ (YBaCuO) ceramic has been studied over the duration of the diffusion range 5-24 h in the temperature range 700-850 °C by the energy-dispersive X-ray fluorescence (EDXRF) technique. For the excitation of silver atoms, an annular Am-241 radioisotope source (50 mCi) emitting 59.543 keV photons was used. The temperature dependences of silver diffusion coefficients in grains (D₁) and over the grain boundaries in the range 700-850 °C (D₂) are described by the relations D₁=1.4×10⁻² exp[−(1.18±0.10)/kT] and D₂=3.1×10⁻⁴ exp[−(0.87±0.10)/kT].     

Effect of surface preparation on the properties of Au/p-Cd1−xZnxTe

The effect of bromine methanol (BM) etching and NH₄F/H₂O₂ passivation on the Schottky barrier height between Au contact and semi-insulated (SI) p-Cd_1−xZn_xTe (x ≈ 0.09-0.18) was studied through current-voltage (I-V) and capacitance-voltage (C-V) measurements. Near-infrared (NIR) spectroscopy technique was utilized to determine the Zn concentration. X-ray photoelectron spectroscopy (XPS) for surface composition analysis showed that BM etched sample surface left a Te⁰-rich layer, however, which was oxidized to TeO₂ and the surface [Te]/([Cd] + [Zn]) ratio restored near-stoichiometry after NH₄F/H₂O₂ passivation. According to I-V measurement, barrier height was 0.80 ± 0.02-0.85 ± 0.02 eV for Au/p-Cd_1−xZn_xTe with BM etching, however, it increased to 0.89 ± 0.02-0.93 ± 0.02 eV with NH₄F/H₂O₂ passivation. Correspondingly, it was about 1.34 ± 0.02-1.43 ± 0.02 eV and 1.41 ± 0.02-1.51 ± 0.02 eV by C-V method.     

High-resolution infrared spectra of bicyclo[1.1.1]pentane

Infrared spectra of bicyclo[1.1.1]pentane (C₅H₈) have been recorded at a resolution (0.0015 cm⁻¹) sufficient to resolve for the first time individual rovibrational lines. This initial report presents the ground state constants for this molecule determined from the detailed analysis of three of the ten infrared-allowed bands, ν₁₄(e′) at 540 cm⁻¹, ν₁₇ (a₂″) at 1220 cm⁻¹, ν₁₈(a₂″) at 832 cm⁻¹, and a partial analysis of the ν₁₁(e′) band at 1237 cm⁻¹. The upper states of transitions involving the lowest frequency mode, ν₁₄(e′), show no evidence of rovibrational perturbations but those for the ν₁₇ and ν₁₈ (a₂″) modes give clear indication of Coriolis coupling to nearby e′ levels. Accordingly, ground state constants were determined by use of the combination-difference method for all three bands. The assigned frequencies provided over 3300 consistent ground state difference values, yielding the following constants for the ground state (in units of cm⁻¹): B₀ = 0.2399412(2), D_J = 6.024(6) × 10⁻⁸, D_JK = −1.930(21) × 10⁻⁸. For the unperturbed ν₁₄(e′) fundamental, more than 3500 transitions were analyzed and the band origin was found to be at 540.34225(2) cm⁻¹. The numbers in parentheses are the uncertainties (two standard deviations) in the values of the constants. The results are compared with those obtained previously for [1.1.1]propellane and with those computed at the ab initio anharmonic level using the B3LYP density functional method with a cc-pVTZ basis set.     

EPR and optical absorption study of Cr-doped ammonium oxalate monohydrate single crystals

The electron paramagnetic resonance (EPR) study of the Cr³⁺-doped ammonium oxalate monohydrate (AOM) single crystal is done at room temperature. Two magnetically inequivalent sites for chromium are observed. The hyperfine structure for Cr⁵³ isotope is also obtained. The spin Hamiltonian parameters are evaluated as: D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9820±0.0002, A=(161±2)×10⁻⁴ cm⁻¹ for site I and D=(309±2)×10⁻⁴ cm⁻¹, E=(103±2)×10⁻⁴ cm⁻¹, g=1.9791±0.0002, A=(160±2)×10⁻⁴ cm⁻¹ for site II, respectively. On the basis of EPR data the site symmetry of Cr³⁺ doped single crystal is discussed. The optical absorption spectra are recorded in 195-925 nm wavelength range at room temperature. The energy values of different orbital levels are determined. On the basis of EPR and optical data, the nature of bonding in the crystal is discussed. The values of different parameters are B=803, C=3531, D_q=2208 cm⁻¹, h=0.59 and k=0.21, where B and C are Racah parameters, D_q is crystal field parameter and h and k are nephelauxetic parameters, respectively.     

Elemental depth profiling of a-Si1−xGex:H films by elastic recoil detection analysis and secondary ion mass spectrometry

The hydrogen content in a-Si_1−xGe_x:H thin films is an important factor deciding the density and the optical band gap. We measured the elemental depth profiles of hydrogen together with Si and Ge by elastic recoil detection analysis (ERDA) combined with Rutherford backscattering (RBS) using MeV He²⁺ ions. In order to determine the hydrogen depth profiles precisely, the energy- and angle-dependent recoil cross-sections were measured in advance for the standard sample of a CH₃⁺-implanted Si substrate. The cross-sections obtained here are reproduced well by a simple expression based on the partial wave analysis assuming a square well potential (width: r₀ = 2.67 × 10⁻¹³ cm, depth: V₀ = −36.9 MeV) within 1%. For the a-Si_1−xGe_x:H films whose elemental compositions were determined by ERDA/RBS, we measured the secondary ions yields of HCs₂⁺, SiCs₂⁺, H⁻, Si⁻ and Ge⁻ as a function of Ge concentration x. As a result, it is found that the useful yield ratios of HCs₂⁺/SiCs₂⁺, H⁻/Si⁻ and Ge⁻/Si⁻ are almost constant and thus the elemental depth profiles of the a-Si_1−xGe_x:H films can be also determined by secondary ion mass spectrometry (SIMS) within 10% free from a matrix effect.