Thermal diffusion and the approach to the steady state in gases: II

The theory of the rate of approach to the steady state in themal diffusion is tested experimentally on the systems He-Ar, He-CO₂, H₂-CO₂, and D₂-CO₂ over a temperature range of about -78°c to 325°c. The course of the diffusion has been followed by means of the radioactive tracers ³⁷Ar and ¹⁴CO₂. The theory appears to be verified, and the results are used to calculate ordinary diffusion coefficients, which are in reasonable accord with previous measurements by other techniques. The thermal diffusion factors, which are obtained from the same measurements, also appear to have reasonable accuracy. The experimental method therefore appears to have promise as a sensitive method for the determination of forces between unlike molecules.     

Experimental and numerical investigation of microscale hydrogen diffusion flames

Characteristics of microscale hydrogen diffusion flames produced from sub-millimeter diameter (d = 0.2 and 0.48 mm) tubes are investigated using non-intrusive UV Raman scattering coupled with LIPF technique. Simultaneous, temporally and spatially resolved point measurements of temperature, major species concentrations (O₂, N₂, H₂O, and H₂), and absolute hydroxyl radical concentration (OH) are made in the microflames for the first time. The probe volume is 0.02 × 0.04 × 0.04 mm³. In addition, photographs and 2-D OH imaging techniques are employed to illustrate the flame shapes and reaction zones. Several important features are identified from the detailed measurements of microflames. Qualitative 2-D OH imaging indicates that a spherical flame is formed with a radius of about 1 mm as the tube diameter is reduced to 0.2 mm. Raman/LIPF measurements show that the coupled effect of ambient air leakage and pre-heating enhanced thermal diffusion of H₂ leads to lean-burn conditions for the flame. The calculated characteristic features and properties indicate that the buoyancy effect is minor while the flames are in the convection–diffusion controlled regime because of low Peclet number. Also, the effect of Peclet number on the flame shape is minor as the flame is in the convection–diffusion controlled regime. Comparisons between the predicted and measured data indicate that the trends of temperature, major species, and OH distributions are properly modeled. However, the code does not properly predict the air entrainment and pre-heating enhanced thermal-diffusive effects. Therefore, thermal diffusion for light species and different combustion models might need to be considered in the simulation of microflame structure.     

Isotopic thermal diffusion factors of the noble gases

A new set of isotopic thermal diffusion factors for Ar, Kr and Xe is reported. The data have been obtained from thermal diffusion column measurements in a column previously calibrated with Ne gas, and complete the α_T data for the binary mixtures of noble gases given previously. The results lead to the conclusion that the thermal diffusion properties of the noble gases and their mixtures are well described by the law of corresponding states first proposed by Kestin, Ro and Wakeham. It is also concluded that the calibration technique used makes the thermal diffusion column a valuable instrument for the determination of the thermal diffusion factors of isotopic and non-isotopic dilute gas mixtures.     

Transport properties of a binary mixture of CO2ben N2 from the pair potential energy functions based on a semi-empirical inversion method

The potential energy surface of a CO₂-N₂ mixture is determined by using an inversion method, together with a new collision integral correlation [J. Phys. Chem. Ref. Data 19 1179 (1990)]. With the new invert potential, the transport properties of CO₂-N₂ mixture are presented in a temperature range from 273.15 K to 3273.15 K at low density by employing the Chapman-Enskog scheme and the Wang Chang-Uhlenbeck-de Boer theory, consisting of a viscosity coefficient, a thermal conductivity coefficient, a binary diffusion coefficient, and a thermal diffusion factor. The accuracy of the predicted results is estimated to be 2% for viscosity, 5% for thermal conductivity, and 10% for binary diffusion coefficient.     

A theorem for the distribution functions of hard-sphere fluids

The thermal diffusion factor α_T for the gas mixtures N₂-CO₂, Ar-CO and Ar-NO has been measured as functions of temperature and composition by the two-bulb method. As at least one of the components of the mixture is diatomic or triatomic the thermal diffusion factor is likely to be influenced by inelastic collision. The α_T data have been analysed in terms of the available elastic and inelastic theories. The results show the comparatively small effect of inelastic collision on thermal diffusion. The necessity of using more realistic intermolecular potentials to interpret α_T data has been pointed out.     

Closed tube sublimation growth of Ga2Se2: Solid-vapour equilibria and mass transport2

A detailed study of the real conditions of Ga₂Se₂ growth by sublimation in a closed tube system is presented. Mass flow measurements have been carried out as a function of the cross-section of the silica tubes, the thermal gradient along the growth chamber, and the sublimation temperature. With the aid of the results of pressure measurements, flow rates as a function of growth parameters have been evaluated according to diffusion theory, and compared with experimental flow rates. Useful information about the thermodynamic functions ΔH and ΔS of Ga₂Se₂ has thus been obtained.     

基于反转法的O2-CO2 输运性质预测

采用反转法计算得到了O₂-CO₂混合气体新的势能参数.在此基础上,根据分子动力学理论,计算了混合气体在零密度下的输运性质,包括黏度系数、热扩散系数和热扩散因子,计算的温度范围为273.15—3273.15 K.与实验值比较表明,计算结果可以满足实际工程应用.     

Isotopic effects in the establishment of thermal equilibrium of stationary H2- and D2-glow plasmas

In stationary glow plasmas, thermal equilibrium of the electron gas with the neutral gas is established, if, with increasing gas pressure, the diffusion lifetime of plasma electrons becomes high enough. In D₂-plasmas, thermal equilibrium sets in at higher pressures than in H₂. Equal electron temperatures are measured in H₂- and D₂-glows, if the corresponding gas pressures are in the ratiop d ₂/P h ₂=1.22. This isotopic effect of electron temperature and of thermal equilibrium is compared with calculations of the Boltzmann equation, taking into account the influence of ambipolar diffusion on the electron velocity distribution. There is a good agreement between measurement and theory.     

Determination of binary diffusion coefficients of gases using photothermal deflection technique

A photothermal deflection (PD) technique was applied to measure the binary diffusion coefficients of various gases (CO₂–N₂, CO₂–O₂, N₂–He, O₂–He, and CO₂–He). With an in-house-made Loschmidt diffusion cell, a transverse PD system was employed to measure the time-resolved PD signal associated with the variation of the thermal diffusivity and the temperature coefficient of the refractive index of the gas mixture during the diffusion. The concentration evolution of the gas mixture was deduced from the PD amplitude and phase signals based on our diffraction PD model and was processed using two mass-diffusion models explored in this work for both short- and long-time diffusions to find the diffusion coefficient. An optical fiber oxygen sensor was also used to measure the concentration changes of the mixtures with oxygen. Experimental results demonstrated that the binary diffusion coefficients precisely measured with the PD technique were in agreement with the literature values. Moreover, the PD technique can measure the diffusion coefficients of various gas mixtures with both short- and long-time diffusions. In contrast, the oxygen sensor is only suitable for the long-time diffusion measurements of the gas mixtures with oxygen. PACS 78.20.Nv; 51.20.+d     

Influence of the noise driving force on the diffusion of copper in aluminium thin films

The diffusion of copper in thin polycrystalline aluminium films subjected to current stressing at 140 C was studied. Experimental aluminium stripes were doped with copper in a limited (source) region and the movement of copper away from this region was investigated by electron probe microanalyser. Samples were stressed both by dc and by superimposed dc and noise current. The dc density (5×10⁵ A/cm²) was equal to that of the effective (r.m.s.) value of superimposed current. The frequency range of the noise signal with the Gaussian distribution of amplitudes was 5 Hz to 20 kHz. Under the described conditions copper diffused due to the concentration gradient as well as the electromigration driving force. The diffusion coefficients of copper at both current stressings were obtained by fitting the measured concentration profiles to those calculated theoretically. The results yield that the diffusion becomes enhanced when the noise is applied. The values of thermal grain boundary-assisted diffusion coefficient obtained in six independent measurements with dc loading vary betweenD _Tb=8×10^–13 cm²/s and 25×10^–13 cm²/s. The corresponding values of total diffusion coefficient (i.e. the sum of the thermal and noise induced component) areD _b=(20÷83)×10^–13 cm²/s. The noise-induced enhancement of the diffusion was predicted theoretically. Thus, the present results confirm the previous theoretical calculations.The authors wish to thank Dr. V. Bezák for stimulating discussions.     

Determination of proton diffusion anisotropy by thermal decay of fixed holograms with K-vector perpendicular to the c-axis in LiNbO3:Fe

In this paper the thermal fixing of holographic gratings with K-vectors perpendicular to the crystallographic c-axis of LiNbO₃ is considered in order to obtain information about anisotropy of the proton thermal diffusion in this crystal. Specifically, thermal decays of fixed holograms in particular crystallographic directions are measured and related with proton diffusion. The values obtained are compared with previous data of decays of fixed holograms with K-vector parallel to the c-axis. The results show a high anisotropy of the thermal diffusion of protons in lithium niobate crystals.     

Raman diagnostics of heterogeneous chemical processes

The suitability of cw Raman spectroscopy for characterization of mass transport phenomena in connection with heterogeneous chemical processes is demonstrated for the example of the catalytic hydrogenation of acetylene. Temperature and concentration profiles in a model reactor were derived simultaneously from H₂ pure rotational lines and from the most intenseQ branches of C₂H₂ and of C₂H₄. The temperature dependence of the band contours has been considered; by careful calibration the systematic error of the derived concentration values is limited to less than 2%. The measurements allow the separation of the effects of thermal diffusion and of the reaction.     

On the thermal conductivity of glasses

We estimate the numerical contribution of the interaction between like defects in glasses for the linewidth (? T^?1₂) obtained in acoustical experiments. This interaction gives origin to a diffusion process with a very large diffusion constant (D = 10^?5 cm² sec^?1). The thermal conductivity due to this diffusion process is calculated. Its temperature dependence is also obtained.     

Hydrogen-deuterium exchange induced by an electric field in α-Al2O3 single crystals

Abstract

Hydrogen and deuterium are observed in α-Al₂O₃ crystals in the form of OH^? and OD^? radicals, respectively, which absorb in the infrared region. Infrared-absorption measurements were used to monitor diffusion of deuterons and protons in α-Al₂O₃ single crystals under the application of a moderate electric field parallel to the crystallographic c-axis, in the temperature range of 973—1333K. A linear dependence of the percent of exchange with both annealing time and applied voltage is observed, indicating that ionic conduction was taking place. The activation energy for the H⁺  D⁺ exchange was determined to be 2.4 eV, less than half the value obtained by pure thermal means, suggesting that under the application of an electric field the deuteron (proton) diffusion mechanism is different.     

Surface characterisation and interface studies of high-k materials by XPS and TOF-SIMS

High-k dielectric LaAlO₃ (LAO) films on Si(100) were studied by TOF-SIMS and XPS to look for diffusion processes during deposition and additional thermal treatment and for the formation and composition of possible interfacial layers. The measurements reveal the existence of SiO₂ at the LAO/Si interface. Thermal treatment strengthens this effect indicating a segregation of Si. However, thin LAO layers show no interfacial SiO₂ but the formation of a La-Al-Si-O compound. In addition, Pt diffusion from the top coating into the LAO layers occurs. Within the LAO layer C is the most abundant contamination (10²¹ at/cm³). Its relatively high concentration could influence electric characteristics. XPS shows that CO₃²⁻ is intrinsic to the LAO layer and is due to the adsorption of CO₂ of the residual gas in the deposition chamber.     

Heat capacity and thermal expansion of CdCr2Se4 and CdCr2S4

The thermodynamic properties of the spinel ferromagnetic compounds CdCr₂Se₄ and CdCr₂S₄ have been investigated by making heat capacity and thermal expansion measurements on single crystals. For both compounds, the ferromagnetic transition is marked by λ-type thermal anomalies, and the results provide a pressure dependence of the transition temperatures that is in agreement with direct measurements. Below the transition, CdCr₂S₄ shows an anomalous heat-capacity contribution and negative thermal expansion, which are in contrast to the conventional behavior found in CdCr₂Se₄.     

Application of the diffraction theory for photothermal deflection to measurements of thermophysical and mass-diffusion properties of gases

The application of recently developed diffraction theory for cw transverse photothermal deflection spectroscopy (normal deflection only) to the measurements of thermophysical and mass-diffusion properties of gases is presented. Compared with the traditional ray-optics theory, the diffraction theory has one more term in the phase signal. This term quantitatively exhibits the probe-beam size effect on the phase signal. Experimental results demonstrated that even if the ratio of the probe-beam radius to the thermal diffusion length of a deflecting medium was as low as about 0.22, the probe-beam size effect could not be ignored when measuring the distance between the probe beam and a solid sample using the phase signal. With the measured distance, the thermal diffusivity α_g and the temperature coefficient of the refractive index dn/dT of pure gases (O₂, N₂, and CO₂) and binary gas mixtures (CO₂-O₂ and CO₂-O₂) were precisely measured, resulting in good agreement with literature values. Furthermore the measured dn/dT values of the pure gases had one more significant figure than the literature ones. The concentration dependences of α_g and dn/dT were employed for the determination of mass-diffusion coefficients of CO₂-O₂ and CO₂-N₂, and the results were consistent with literature values.     

Transport properties of H–N2 mixtures

Transport coefficients (shear viscosity, volume viscosity, thermal conductivity, and mass and thermal diffusion coefficients) of H–N₂ mixtures in the dilute-gas limit have been calculated from the intermolecular potential in the temperature range 300–2000K using the classical trajectory method. The intermediate results pertaining to H–N₂ binary interactions are reported, mainly in terms of cross-section ratios. Cross-sections evaluated with the Mason–Monchick approximation yield very good results for this system, the largest deviations, about 2.5%, being observed for the thermal diffusion coefficient. The accuracy here of this approximation can primarily be attributed to a light H atom and a weakly non-spherical potential resulting in a high rotational collision number. Furthermore, we investigate to which H–N₂ cross-sections and their ratios the values of the mixture transport coefficients are most sensitive. Our results indicate that, for some cross-section ratios, reliance on universal correlations at high temperatures, often used in flame codes, can induce sizeable errors in the thermal conductivity coefficient and especially in the thermal diffusion coefficients. We also observed that the volume viscosity is particularly sensitive to the value of the cross-section for internal energy relaxation in H–N₂ collisions.     

Yb:CaF2-SrF2激光晶体光谱性能以及热学性能的研究

采用坩埚下降法生长了Yb: CaF₂-SrF₂晶体,测试了该晶体的吸收和荧光光谱 以及在不同温度下晶体的热扩散系数和热膨胀系数,并且计算了晶体的热膨胀系数以及在常温下的热导率. 采用对比的方法,对晶体的吸收光谱,荧光光谱,热学性能进行了分析.从吸收和荧光光谱结果表明: 在掺杂相对较高浓度的SrF₂的混晶中, Yb³⁺吸收截面和发射截面比较大. Yb: CaF₂-SrF₂ (19%)晶体在1040 nm附近的发射截面比较大,光谱也比较宽. 这说明在掺杂相同浓度Yb时,混晶中CaF₂, SrF₂的比例不同,晶体的光谱性质不同, 主要原因是在混晶中晶体的无序度不同,晶体对称性降低,形成低对称光学中心. 从热扩散系数计算的热导率结果看出晶体具有比较好的热导率.     

Correlation between the Soret coefficient and the static structure factor in a polymer blend

Mutual mass diffusion and thermal diffusion has been investigated in poly(dimethylsiloxane)/ poly(ethylmethylsiloxane) (PDMS/PEMS) polymer blends of equal weight fractions. Molar masses ranged from below 1 to over 20 kg/mol. Both the mutual mass (D) and the thermal diffusion (D_T) coefficient contain a thermally activated factor with an activation temperature of 1415 K. The molar mass dependence of D_T is due to an end-group effect of the local friction coefficient. The thermal diffusion coefficient in the limit of long chains and infinite temperature is D_T^0, = - 1.69×10^-7cm²(sK)^-1. The Soret coefficient S_T of blends far enough away from a critical point is proportional to the static structure factor S(q = 0).