Temperature Dependence Of Self-diffusion Research Articles

Self-Diffusion in Amorphous Silicon by Local Bond Rearrangements.

Experiments on self-diffusion in amorphous silicon (Si) were performed at temperatures between 460 to 600° C. The amorphous structure was prepared by Si ion implantation of single crystalline Si isotope multilayers epitaxially grown on a silicon-on-insulator wafer. The Si isotope profiles before and after annealing were determined by means of secondary ion mass spectrometry. Isothermal diffusion experiments reveal that structural relaxation does not cause any significant intermixing of the isotope interfaces whereas self-diffusion is significant before the structure recrystallizes. The temperature dependence of self-diffusion is described by an Arrhenius law with an activation enthalpy Q=(2.70±0.11) eV and preexponential factor D_{0}=(5.5_{-3.7}^{+11.1})×10^{-2} cm^{2} s^{-1}. Remarkably, Q equals the activation enthalpy of hydrogen diffusion in amorphous Si, the migration of bond defects determining boron diffusion, and the activation enthalpy of solid phase epitaxial recrystallization reported in the literature. This close agreement provides strong evidence that self-diffusion is mediated by local bond rearrangements rather than by the migration of extended defects as suggested by Strauß etal. (Phys. Rev. Lett. 116, 025901 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.025901).

Composition and temperature dependence of self-diffusion in Si1\u2212xGex alloys

The knowledge of diffusion processes in semiconducting alloys is very important both technologically and from a theoretical point of view. Here we show that, self-diffusion in Si1−xGex alloys as a function of temperature and Ge concentration can be described by the cBΩ thermodynamic model. This model connects the activation Gibbs free energy of point defects formation and migration with the elastic and expansion properties of the bulk material. The approach allows the systematic investigation of point defect thermodynamic parameters such as activation enthalpy, activation entropy and activation volume, based on the thermo-elastic properties (bulk modulus and its derivatives, mean atomic volume and thermal expansion coefficient) of the two end-members of the Si1−xGex alloy. Considerable deviations from Vegard’s law are observed, due to the diversification of the bulk properties of Si and Ge, in complete agreement with the available experimental data.

Contributions of vacancies and self-interstitials to self-diffusion in silicon under thermal equilibrium and nonequilibrium conditions

Since many years, the contribution of vacancies ($V$) and self-interstitials ($I$) to silicon (Si) self-diffusion is a matter of debate. Native defects and their interaction among themselves and with foreign atoms influence the processes taking place during device fabrication, starting with the growth of Si single crystals and ending with doping of nanosized electronic devices. Considering this relevance, it is remarkable that present data about the properties of native point defects in Si are still limited and controversial. This work reports experiments on self-diffusion in Si for temperatures between 650${\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$C and 960${\phantom{\rule{0.16em}{0ex}}}^{\ensuremath{\circ}}$C to verify recent results of Shimizu et al. [Phys. Rev. Lett. 98, 095901 (2007)] that give rise to inconsistencies in $V$-mediated self- and dopant diffusion. Two different structures of isotopically controlled epitaxial layers of Si are used for the diffusion study. One structure consisting of 20 bilayers of ${}^{29}$Si/${}^{28}$Si was grown by molecular beam epitaxy (MBE). The other structure with a ${}^{28}$Si layer sandwiched between natural Si was grown by means of chemical vapor deposition. Self-diffusion in (${}^{29}$Si/${}^{28}$Si)${}_{20}$ multilayers (ML) was analyzed by means of secondary ion mass spectrometry (SIMS) and neutron reflectometry, whereas self-diffusion in ${}^{\mathrm{nat}}$Si/${}^{28}$Si/${}^{\mathrm{nat}}$Si sandwich (SW) structures was measured with SIMS only. Analysis of the experimental profiles reveals an enhanced self-diffusion in ML compared to SW structures. The enhanced diffusion is ascribed to the dissolution of $V$- and $I$-related defect clusters grown-in during MBE. On the other hand, self-diffusion in the SW structures accurately confirms the data of Shimizu et al. that are considered to represent data for thermal equilibrium conditions. The temperature dependence of self-diffusion is described by $V$- and $I$-mediated contributions with temperature-dependent thermodynamic properties of $V$. This interpretation can solve the inconsistency between self- and dopant diffusion in Si, but further experiments are required to verify this concept.

Influence of structural changes on diffusion in liquid germanium

Liquid germanium exhibits a change in the bonding character from being more covalent to more metallic while heating. We used quasielastic neutron scattering to measure the absolute value of self-diffusion coefficients in this liquid. Compared to other monoatomic liquids, such as liquid Ni or Ti, the self-diffusivity is an order faster near the melting temperature and shows a non-Arrhenius-like behavior. Above 1325 K, the activation energy for self-diffusion is low and obeys Stokes–Einstein relation. Even though the packing density of liquid germanium is less than that of simple metallic melts such as Pb or Sn, the temperature dependence of self-diffusivity does not exhibit D∝Tn(n≃2) form, which is observed for uncorrelated binary collisions of hard-spheres.

Self-diffusion measurements of organic molecules in PDMS and water in sodium alginate membranes

The self-diffusion of some organic molecules in silicone rubber and of water and water-ethanol mixtures in sodium alginate membranes was investigated to obtain information on the transport behavior in these systems. The temperature dependence of self-diffusion was examined by the pulsed field gradient NMR technique. The experimental data confirm the homogeneous amorphous nature of PDMS and the affinity of silicone rubber to apolar solvents. The interrelations between solvent and polymer structures of the sodium alginate membrane varying the temperature have been obtained using differential scanning calorimetric. The results have been compared with the trend of self-diffusion coefficients, and structure modifications of the membranes have been evidenced. The overall results confirm the potentialities of the technique used in measuring transport parameter in polymeric membranes.

Pressure and Temperature Dependence of Self-Diffusion in Solids: Sodium

In the present paper, a theory is discussed to study the self-diffusion coefficient in solids as a function of pressure and temperature. The theory is quite succesful in case of sodium within the range of 0 to 10 kbar pressure and 273 to 365 K temperature. Moreover, the theory is capable of giving the various thermodynamic parameters for the activated process as a function of pressure and temperature. Besides, some intersting results are also obtained.

Self-diffusion and lattice dynamics in a b.c.c. TlIn solid solution

A combined study of tracer diffusion of 204Tl and inelastic neutron scattering in a b.c.c. TlIn (17 at%) solid solution is presented. In contrast to self-diffusion behaviour in b.c.c. alkali and transition metals, which is characterized by a certain systematics and non-linear Arrhenius relations, the classification of self-diffusion for the only main group b.c.c. metal β-Tl in terms of normal or “anomalous” is still unclear because the small temperature range of existence of its b.c.c. phase does not allow decisive experiments. Alloying the homologous element In to Tl extends this range drastically and improves the possibility to study both the temperature dependence of self-diffusion and of the phonon dispersion. On the basis of the phonon measurements vacancy migration enthalpies are calculated, being independent of temperature. This result is conform with the measured perfectly straight Arrhenius plot of self-diffusion in b.c.c. TlIn (17 at%). Our combined investigations provide arguments for classifying self-diffusion of β-Tl — opposite to the diffusion behaviour of b.c.c. transition metals — as normal.

A Molecular Dynamics Simulation Study of the Density and Temperature Dependence of Self-diffusion in a “Sphere-cylinder” Micropore

Abstract We report Molecular Dynamics calculations of density profiles and self-diffusion coefficients of Lennard-Jones fluids confined in a pore of “sphere-cylinder” geometry consisting of spheres interconnected through cylindrical sections. The geometrical characteristics were the radius of the cylinder R = 2σ, the ratio of the radius of the cylinder to radius of the sphere R/Rs = 0.85 and the ratio of length of cylinder to length of sphere L/A = 1.5. The results were compared with previous results on a cylindrical pore of the same radius as that of the cylindrical section of this model and it was found that the self-diffusion coefficients parallel to the pore walls were generally lower although their relative difference was within statistical errors.

Molecular Dynamics Simulation Studies of the Density and Temperature Dependence of Self-diffusion in a Cylindrical Micropore

Abstract We report Molecular Dynamics calculations of radial density profiles and self-diffusion coefficients of Lennard-Jones fluids in a cylindrical pore of radius 2σ, for a wide range of temperatures and densities. At n p σ3 = 0.825 the self-diffusion coefficient parallel to the pore walls D ∥∗. follows a monotonic (nearly linear) increase with kT/∊ and is very similar to that of the bulk self-diffusion coefficient D b ∗. At n p σ3 = 0.4 and kT/∊ ≤ 1.0 the curve of D ∥∗ vs. kT/∊ shows a distinct inflection in the region 0.7 ≤ kT/∊ ≤ 0.9 and values of D ∥∗ are much less than D b ∗ decreasing to near solid state values at very low temperatures. At the highest temperature studied, kT/∊ = 2.98, D ∥∗ is almost inversely proportional to density and in a fairly close agreement with that of D b ∗. At KT/∊ = 0.49, D ∥∗ is much smaller than D b ∗. The motion of adsorbate particles normal to the walls is also discussed.

Temperature dependence of self-diffusion in compressed monohydric alcohols

The p,T-dependence of the self-diffusion coefficient D for methanol, methan(2H)ol and ethanol has been studied between 150 and 450 K at pressures up to 250 MPa. The experiments were performed in strengthened high-pressure glass cells by the application of the nuclear magnetic resonance (NMR) spin-echo technique with pulsed magnetic-field gradients. Upon cooling, molecular mobility is strongly reduced, leading to a pronounced non-Arrhenius temperature dependence of D. Applying the rough hard-sphere model (Chandler) to our data, a dramatic decrease of the A-parameter with falling temperature is observed. This behavior indicates that attractive intermolecular interactions dominate translational mobility. The best description of the data is given by the empirical Vogel–Tammann–Fulcher (VTF) equation, with ideal glass transition temperatures T0, that are in excellent agreement with those obtained from calorimetric studies. The isotope effect for self-diffusion in methanol and methan(2H)ol increases from ∼5% at high temperatures to about 40% in the supercooled region. This drastic increase is assumed to originate from a difference in hydrogen bond strength of the isotopes, as has already been found for light and heavy water.

The isotope and temperature dependence of self-diffusion for hydrogen, deuterium, and tritium on Cu(100) in the 100–1000 K range

The isotope and temperature dependence of self-diffusion for hydrogen, deuterium, and tritium on Cu(100) in the 100–1000 K range

Temperature dependence of self diffusion of polystyrene and polyethylene in the melt an interpretation in terms of the free volume theory

The temperatur dependence of the self diffusion coefficients of polystyrene and polyethylene in the melt was measured with the pulsed field gradient nmr technique. The temperature and molar mass dependences of the self diffusion coefficients can be described by the free volume model. Taking into account the matrix effect we detected the beginning of the break of the reptation process for polystyrene at low molar masses. The activation energies of the self diffusion process are comparable with those observed for viscosity.

Temperature Dependence of Self Diffusion in Liquid Metals

Abstract After presenting a brief summary of the previous work, Hildebrand's fluidity model for the liquid state has been combined with a general equation for self diffusion in liquids to elucidate the temperature dependence of self diffusion in liquid metals. The analytical form for the temperature dependence presented herein is obeyed by the sixteen metals for which experimental values of self diffusion coefficient at various temperatures are available in literature. The article is concluded by suggesting a method for predicting self diffusion in liquid metals.

Pressure and temperature dependence of self-diffusion in water

The self-diffusion coefficient, D, for pure liquid water has been measured at temperatures between 275.2 and 498.2 K and at pressures up to 1.75 kbar by the proton spin echo method. Our values of D agree, where they overlap, with recently published data which, however, were measured mostly at low temperature and over rather narrow ranges of temperature.The results are discussed in several ways. The Stokes–Einstein relation is found to be obeyed in the slipping boundary limit. The cubic cell model of Houghton accounts satisfactorily for the measured D values, particularly at higher temperatures. A simple test of a hard-sphere model is found to give poor agreement at lower temperatures but a modified hard-sphere theory seems to be more satisfactory. The activation analysis at constant density shows that water behaves very differently from non-associated liquids. It also suggests that an increase in both temperature and pressure leads to an increase in the fraction of free unbonded water molecules.A free-volume analysis has led to a modified Arrhenius equation which involves pressure-dependent terms. This semi-empirical equation describes the results within experimental error and predicts a glass temperature at 115 K which is in reasonable agreement with the values obtained by other methods.

Density and temperature dependence of self-diffusion and shear viscosity of perfluorocyclobutane in the dense fluid region

The self-diffusion coefficients of liquid perfluorocyclobutane have been measured as a function of temperature and pressure over the density range 1.8⩽ρ/ρc⩽2.9 and the temperature range 0.8⩽T/Tc⩽2.3. The NMR spin-echo technique was employed for the measurement of the diffusion coefficients using a steady magnetic field gradient. Shear viscosities and densities of perfluorocyclobutane have also been determined under the same experimental conditions. Both the diffusion coefficients and shear viscosities are interpreted in terms of the rough hard sphere model of liquids based on the modified Enskog theory. The effective hard core diameter and its temperature dependence are calculated. The Stokes–Einstein relationship with the slipping boundary condition was found to be valid for the liquid studied.

Diffusion studies in liquid potassium and rubidium

Self-diffusion coefficients were determined for liquid potassium and rubidium. The types of measurements made were self-diffusion of K and Rb as a function of temperature at one atmosphere pressure, the pressure dependence of self-diffusion coefficients of K and Rb, and the temperature dependence of selfdiffusivity at constant molar volume. The self-diffusion coefficients in liquid K and Rb at 1 atmosphere pressure could be represented by the following expressions. D K (354° K−868° K) = −2·443 × 10 5 + 5·344 × 10 −10( T° K) 2 cm 2/ sec D Rb (337° K−856° K) = −1·479 × 10 −5 + 3·824 × 10 −10( T° K) 2 cm 2/ sec. The empirical equation for both K and Rb may be expressed as D D m = 1.665 [( T T m ) 2 − 0.399] . The linear dependence of D vs T 2 for both Rb and K, observed in the present investigation, tends to offer support to the predictions of the fluctuation theory proposed by Swalin. The experimental data also agree quite well with the dense gas-like model of Ascarelli and Paskin. The activation volumes calculated from the data were 1.5 ± 0.5 cm 3/ mol and 1.2 ± 0.4 cm 3/ mol for liquid K and Rb respectively.

High temperature plastic deformation and self-diffusion in single crystals of aromatic hydrocarbons

The temperature dependence of self-diffusion in biphenyl and the stress and temperature dependence of steady state plastic deformation (creep) in naphthalene and biphenyl have been studied at temperatures greater than 0.80 times the absolute melting temperature, and under stresses of 0.1 to 0.2 MN m−2. The results indicate that under these conditions the solids deform by a dislocation climb mechanism. The activation energies for creep are in good agreement with those for self-diffusion. Dislocation concentrations evaluated on the basis of the Weertman analysis of the dislocation climb process are similar to those derived from direct etch-pit counts. These crystals are approximately ten times less plastic than the rotator-phase organic crystals under similar conditions.

Self-Diffusion and Impurity-Controlled Proton Relaxation in Liquid Methane

Self-diffusion in liquid methane, under its own vapor pressure, has been studied between the triple point and the normal boiling point by means of the spin-echo technique. The activation energy for self-diffusion is approximately 0.67 kcal/mole. These results are compared with the constant-pressure tracer results of Naghizadeh and Rice [J. Chem. Phys. 36, 2710 (1962)], which show somewhat higher (∼15%) self-diffusion coefficients and an activation energy of approximately 0.83 kcal/mole. The temperature dependence of self-diffusion in liquid methane appears to be comparable on the basis of a classical reduction to corresponding states, by means of critical constants, to that in liquid Ar, Kr, and Xe. Measurements of the proton spin-lattice relaxation time in our sample indicate that the relaxation is predominantly controlled by the mutual diffusion of the hydrocarbon and small amounts of dissolved oxygen.

On the temperature dependence of self-diffusion in alpha iron

On the temperature dependence of self-diffusion in alpha iron