Volume and grain boundary diffusion of implanted 113Sn in aluminium

Volume and grain boundary diffusion of ¹¹³Sn in aluminium was investigated with the radiotracer method. The implantation technique was used for tracer deposition to avoid problems of tracer hold-up caused by the oxide layer always present on aluminium. The diffusion penetration was chosen large enough to permit serial sectioning of samples with the aid of a microtome.The temperature dependence of the volume diffusivity was determined as D(T)=4.54×10^–5×exp[–(114.5±1.2)kJmol^–1/RT] m ² s ^–1. This confirms previous measurements from our group which already showed that Sn is the fastest foreign metal diffusor so far investigated in aluminium.Grain boundary diffusion of ¹¹³Sn in Al polycrystals was measured in the type-B kinetic regime. The grain boundary diffusion product P=sD _gb (s=segregation factor, =grain boundary width, D _gb=grain boundary diffusivity) was found to be strongly affected by the impurity content of aluminium. For Al polycrystals of 99.9992% nominal purity we obtained P _5N(T)=1.08×10^–8exp [–(96.9±7.5) kJ mol^–1/RT] m³ s^–1 and for less pure Al polycrystals of 99.99% nominal purity P _4N(T)=3.0×10^–10 exp [–(90.1±4.2) kJ mol^–1/RT] m³ s^–1 was determined. The grain boundary diffusion product in the purer material is more than one order of magnitude higher than in the less pure material. Very likely this is an effect of co-segregation of non-diffusant impurities into the grain boundaries.     

Grain Boundary Diffusion and Linear and Non-Linear Segregation of Ag in Cu

Ag grain boundary (GB) diffusion was measured in the Cu-0.2at%Ag alloy in a wide temperature range from 473 to 970 K. The direct measurements of Ag GB diffusivity D ^alloy _gb under conditions of the Harrison C regime revealed that D ^alloy _gb is almost identical to D ^pure _gb determined earlier for Ag diffusion in high-purity Cu (Divinski, Lohmann, and Herzig, 2001). The penetration profiles determined in the Harrison B regime showed a complex, multi-stage shape. This diffusion behavior can be rationalized assuming that besides GBs significantly covered by segregated Ag atoms, some fraction of GBs remains almost free from Ag atoms in the studied temperature interval. The total amount of pure GBs drastically decreases with decreasing temperature. This hypothesis was proven by measurements of Ag GB diffusion in Cu near 5 bicrystals, which allowed us to analyze in detail the non-linear segregation of Ag in Cu GBs.     

Grain Boundary Motion during Ag and Cu Grain Boundary Diffusion in Cu Polycrystals

Grain boundary (GB) motion in high-purity Cu material (5N8 and 5N Cu) is investigated using the results of radiotracer GB diffusion measurements with tracers exhibiting fundamental differences in the solute-matrix atom interactions. The results on GB solute diffusion of Ag (revealing a miscibility gap in the Ag-Cu phase diagram) and Au (forming intermetallic compounds with Cu) in Cu and on Cu self-diffusion are analyzed.The initial parts of the Ag and Cu penetration profiles turned out to be substantially curved. The profile curvature is explained via the effect of GB motion during ^110m Ag and ⁶⁴Cu GB penetration. The activation enthalpies of GB motion in these two independent measurements occurred to be very close, 95 and 103 kJ/mol, respectively. Moreover, these values turn out to be close, but still somewhat larger than the activation enthalpy of Cu GB self-diffusion in Cu material of the same very high purity, Q ^Cu _gb = 72 kJ/mol. Although tracer diffusion measurements of Au GB diffusion in Cu yielded only limited information on GB motion, the absolute values of GB velocities are consistent with those calculated from the Ag and Cu GB diffusion data.     

Tracer Diffusion of 63Ni in Nano-γ-FeNi Produced by Powder Metallurgical Method: Systematic Investigations in the C, B, and A Diffusion Regimes

⁶³Ni radiotracer diffusion in a well-compacted nanocrystalline (grain size d 80 to 100 nm) -Fe–40wt%Ni alloy was measured by the serial sectioning technique in an extended temperature range from about 610 to 1010 K. Since the material microstructure reveals two different length scales with nano-size grains forming micrometer-size clusters (or agglomerates), three main diffusion paths determine the diffusion behavior: the nanocrystalline grain interior, the nanocrystalline grain boundaries (GB), and the inter-agglomerate interfaces. The systematics of diffusion in a compacted nanostructured material with such a bimodal distribution of interface characteristics was elaborated and the experimental data were analyzed in dependence on the diffusion regime. The absolute values and the Arrhenius parameters of Ni GB diffusion in the nano--Fe–40wt%Ni alloy (D ₀ = 9.3 × 10^–4 m² s^–1 and Q = 177 kJ/mol) are similar to the Ni GB diffusivity in coarse-grained poly-crystalline -Fe. Accordingly, the nanocrystalline GBs are concluded to have quasi-equilibrium structures, particularly because of a pronounced grain growth (from about 30 to about 100 nm) during the production stage of the nanomaterial. In contrast, the inter-agglomerate interfaces, which present the fastest diffusion path in the present investigation (D ₀ = 1.9 × 10^–3 m² s^–1 and Q = 134 kJ/mol), are likely to be in a non-equilibrium state due to specific features of the applied powder metallurgical process.     

Diffusion of Al implanted into α-Hf studied by means of the nuclear resonance technique

The diffusion of Al in -Hf was studied in the 973–1298 K temperature range by using the nuclear resonance technique. The measurements show that the diffusion coefficient follows an Arrhenius behavior D(T)=D₀exp(-Q/RT), where D₀=(3±2)×10^-4 m²s^-l and Q=337±10 kJ/mol. The activation energy is typical of a substitutional mechanism of diffusion, as can be deduced from self-diffusion measurements. On the other hand, differences between the present and previous published results can be attributed to the different purity of the samples used in each experiment. PACS 66.30.-h; 66.30.Jt     

Diffusion of silicon in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained film structure (B ₊ films) have been examined as diffusion barriers, preventing the silicon diffusion in silicon devices. The silicon diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) after annealing at temperatures up to 900° C, in view of application of high-temperature processes. The diffusivity from 400 to 900° C: D (m² s^–1)=2.5×10^–18 exp[–31 kJ/mol/(RT)] in B ₀ layers and D (m² s^–1)=3×10^–19 exp[–26 kJ/mol/(RT) in B ₊ TiN layers. The diffusivities determined correspond to grain boundary diffusion, the difference being due to the different microstructure. The very low diffusivity of silicon in B ₊ TiN layer makes it an excellent high-temperature barrier preventing silicon diffusion.     

Morphological evolution of thin gold films studied by Auger electron spectroscopy in beading conditions

The evolution of thin gold films deposited on a sapphire surface was studied in UHV using Auger electron spectroscopy and atomic force microscopy techniques. The annealing temperatures were in the range 573–843 K. Starting from a continuous film, we observed at the end of the process a collection of beads. The incubation time in this temperature range was negligible, while the agglomeration time varied from about 2 h at 573 K to a few minutes at 843 K. The kinetics of metal agglomeration allowed the evaluation of the surface self diffusion coefficients of gold which can be expressed by D_s(m²/s)(573–843 K)= 3×10^-11exp[-62±8(kJ/mol)/RT]. These results are in reasonable agreement with other published data. This method provides a framework for the evaluation of surface diffusion parameters of other metals. PACS 68.35.Fx; 68.55.-a; 68.60.Dv     

Surface Ostwald-ripening and evaporation of gold beaded films on sapphire

The kinetics of morphological evolutions of gold nanoparticles on alumina, resulting from evaporation and surface Ostwald-ripening coarsening, have been investigated by means of Auger electron spectroscopy. When the fraction of the covered area is small, the kinetics of evaporation can be related to the desorption of adatoms. In the temperature range 943–1043 K we obtained the evaporation flux J(m^-2s^-1)=4.8×10²⁷exp[-196±9 (kJ/mol)/RT]. The experimental activation energy of evaporation of gold from a sapphire surface, Q_evap=196±9 kJ/mol, is lower than the tabulated value of enthalpy of sublimation of gold, ΔH_subl=368 kJ/mol. At lower temperatures, in the range 623–778 K, Ostwald-ripening experiments, carried out on nanosized clusters, yield the mass transfer surface diffusion coefficients of gold on alumina, D_s(m²/s)=2.6×10^-14exp[-58±9 (kJ/mol)/RT]. These results, providing information on the evolution of granular gold films such as those used in catalysts or sensors, are compared to previous data on similar systems. PACS 68.47.Jn; 68.43.Jk; 68.55.-a     

Intergranular Melting of Ultrafine Grained Nd2Fe14B Studied by Means of Radiotracer Diffusion

Grain-boundary (Gb) diffusion was studied in ultrafine grained Nd₂Fe₁₄B-based permanent magnets below and above the melting transition of the Nd-enriched intergranular phase using the radiotracer technique with the isotope ⁵⁹Fe. The product D _Gb of interface diffusion coefficient and interface thickness shows a substantial increase above the intergranular melting transition. Assuming a volume self-diffusivity as in -Fe, an analysis in the framework of grain-boundary diffusion kinetic of type B yields an Arrhenius-type behaviour D _Gb = 1.53 × 10^–11 exp(–1.74 eV/kT) m³ s^–1 below the intergranular melting transition. Similar values D _Gb are observed for ultrafine grained Nd-Fe-B with reduced Nd excess in the grain boundaries. The diffusion characteristics are compared with the kinetics of the hot-deformation which is of technical relevance for the processing of high-performance permanent magnets.     

Diffusion of gold in dislocation-free or highly dislocated silicon measured by the spreading-resistance technique

The diffusion of Au in dislocation-free or plastically deformed Si (10¹¹ to 10¹³ dislocations/m²) was measured with the aid of the spreading-resistance technique. The Au profiles produced indislocation-free Si slices by in-diffusion from both surfaces possess nonerfc-type U shapes as predicted by the so-called kick-out diffusion model. This model is used to calculate the contribution of self-interstitials to the (uncorrelated) Si self-diffusion coefficient,D _I ^SD =0.064×exp(–4.80 eV/kT)m² s^–1, from the present and previous data on the diffusivity and solubility of Au in Si in the temperature range 1073–1473 K. Inhighly dislocated Si the diffusion of Au is considerably faster than in dislocation-free Si. From the erfc-type penetration profiles found in this case, effective Au diffusion coefficients were deduced and combined with data on the solubility of Au in Si. ThusC _i ^eq D _i=0.0064 ×exp(–3.93 eV/kT)m² s^–1 was obtained in the temperature range 1180–1427 K, whereC _i ^eq andD _i are the solubility and diffusivity of interstitial Au in Si.     

Special energies and special frequencies

Special frequencies have been asserted to be zeros of the density of frequencies corresponding to a random chain of coupled oscillators. Our investigation includes both this model and the random one-dimensional Schrödinger operator describing an alloy or its discrete analogue. Using the phase method we exactly determine a bilateral Lific asymptotic of the integrated density of statesk(E) at special energiesE _s , which is not only of the classical type exp(–c/|E–E _s |^1/2) but also exp(–c/|E–E _s |) is a typical behaviour. In addition, other asymptotics occur, e.g. |E–E _s | ^c , which show thatk(E) need not bek .     

Au diffusion in α-Ti

The solubility and diffusion of Au in -Ti have been studied in a 823–1023 K temperature range using the Rutherford backscattering technique. For this purpose we have implanted Au into -Ti samples. Our results show that the solubility of Au varies between 0.2 and 0.35 at.%. In addition, we found that the diffusion coefficients follow a normal Arrhenius behavior with Q=260 kJ/mol and D _o=1.9×10^–5 m²/s¹. These values are typical for a substitutional diffusion mechanism.     

Aluminium diffusion in titanium nitride films. Efficiency of TiN barrier layers

Two kinds of reactively evaporated titanium nitride films with columnar (B ₀ films) and fine-grained (B ₊ films) film structures, respectively, have been examined as diffusion barriers for preventing aluminium diffusion. The aluminium diffusion profiles have been investigated by 2 MeV ⁴He⁺ Rutherford backscattering spectrometry (RBS) at temperatures up to 550° C. The diffusivity from 300° C to 550° C is: D[m²s^–1]=3×10^–18 exp[–30/(RT)] in B ₀ layers and D[m²s^–1]=1.4×10^–16 exp[–48/(RT)] in B ₊ TiN layers. The activation-energy values determined indicate a grain boundary diffusion mechanism. The difference between the diffusion values is determined implicitly by the microstructure of the layers. Thus, the porous B ₀ layers contain a considerable amount of oxygen absorbed in the intercolumnar voids and distributed throughout the film thickness. As found by AES depth profiling, this oxygen supply allows the formation of Al₂O₃ during annealing the latter preventing the subsequent diffusion of the aluminium atoms.     

The Effect of Pressure on Indium Diffusion along 〈001〉 Tilt Grain Boundaries in Copper Bicrystals

The effect of pressure on the diffusion of indium along two grain boundaries (GBs) in copper bicrystals has been investigated. The GBs studied were of symmetrical tilt type with a 001 misorientation axis. The tilt angle of one GB was 36.5°, which corresponds to the near 5 coincidence orientation, where is the inverse density of the coincidence sites in the two misoriented crystal lattices. The other GB was a general boundary with a tilt angle of 45°. The diffusion along the 001 tilt axis has taken place at the temperature of 923 K and under argon gas pressures up to 1 GPa. The following activation volumes have been found: 0.94±0.11 _Cu for bulk diffusion,–0.5 ±0.7 _Cu for the diffusivity of the near 5 GB and –0.6±0.3 _Cu for the diffusivity of the 45° 100 GB, where _Cu is the atomic volume of copper. Two interpretations of this result seem plausible. The first interpretation is that the In atoms diffuse along the 001 tilt axis by an instertitialcy mechanism. It is known that for such a diffusion mechanism the activation volume is close to zero. The alternative explanation bases on the observation that the parameter measured is the GB diffusivity, which depends on the product of the GB diffusion coefficient and the segregation factor. An enhancement of the In segregation under pressure would lead to an increase of the GB diffusivity. It seems plausible that both interpretations are true and the fact that the atomic volume of In is a factor of 2.2 larger than that of Cu plays an important role both for the increased segregation of In under pressure and the diffusion mechanism.     

Existence of solutions for Schrödinger evolution equations

We study the existence, uniqueness and regularity of the solution of the initial value problem for the time dependent Schrödinger equationiu/t=(–1/2)u+V(t,x)u,u(0)=u ₀. We provide sufficient conditions onV(t,x) such that the equation generates a unique unitary propagatorU(t,s) and such thatU(t,s)u ₀C ¹(,L ²) C ⁰(H ²( ⁿ )) foru ₀H ²( ⁿ ). The conditions are general enough to accommodate moving singularities of type x^–2+(n4) or x^–n/2+(n3).     

Glueball spectroscopy in strongly coupled lattice gauge theories

We study the mass spectrum up to –7 (1–) log of pure three-dimensional lattice gauge theories with action (g _P) for real irreducible and small . Besides the lowest excitationm ₀–4log, we find two nearly degenerate excited statesm ₁,m ₂ withm _i–6log (i=1, 2) and (m ₁–m ₂) at leastO().Work partially supported by CNPq (Brasil)     

Boron neutralization and hydrogen diffusion in silicon subjected to low-energy hydrogen implantation

Using the hydrogen neutralization of the boron acceptor, the diffusion of hydrogen is investigated in the temperature range 20 °–160 °C. The hydrogenation is performed by low-energy implantation. We observe a fast initial hydrogen migration, followed by a long-time diffusion phase that is described by an effective diffusion coefficientD _eff=D _{0 eff} exp(–E _a/kT) withD _{0 eff}–cm²s^–1 andE _a=(0.83±0.05) eV. No deeper hydrogen migration is detected for implantation times longer than – 30 min. Our data are explained by the build-up of a large amount of molecular hydrogen beneath the surface, which strongly hinders the transfer of the implanted hydrogen to the bulk. The thermal reactivation kinetics of the neutralized boron show a rapid initial step followed by a longtime thermally activated second order phase, which is limited by the recombination of hydrogen into molecules.     

The Impact of Grain Boundary Diffusion on the Low Temperature Reoxidation Mechanism in Nanocrystalline TiO2−δ Films

The redox reaction TiO₂ TiO_2- + /2O_2(gas) can modify the oxygen deficiency and electrical conductivity of TiO_2– upon changing the ambient oxygen pressure. It is found that in nanocrystalline films this leads to significant changes in even at relatively low temperatures (200–325°C) that were previously considered too low to modify TiO₂ defect chemistry. This unusual phenomenon is attributed to the fine-grained structure and the important role of grain boundary (GB) diffusion in these films. A phenomenological model of the low temperature redox mechanism in nanocrystalline TiO_2– films is elaborated. Taking into account the impact of GB diffusion and considering time-dependent decay of the volume fraction of GB diffusion sites, we derive a modified parabolic law for the redox reaction kinetics. It is demonstrated that this law describes very well the electrical response kinetics of nanocrystalline TiO_2– thin films during exposure to oxygen between 200 and 325°C. From the fitting between the experimental results and this formula the activation energy of chemical diffusion in TiO_2– bulk and GBs is evaluated, obtaining 0.69 and 0.52 eV, respectively.     

Diffusion coefficient of selenium in indium antimonide

The diffusion of selenium in indium antimonide has been studied in the temperature range 400–490°C, by the method of removing layers. Two regions have been distinguished in the donor distribution profiles. The first has a low diffusion coefficient and a high surface concentration, near to the limit of solubility of selenium (8·10¹⁸ cm^–3). In the second region, a much larger diffusion coefficient and a surface concentration lower by two orders of magnitude (8·10¹⁶ cm^–3) with weak temperature dependence are found. The temperature dependences of the diffusion coefficients of the first and second regions can be described by the expressions: D=4.8·10¹³ exp(–4.1 eV/kT) cm²/sec, D₂=1.9·10¹³ exp(–3.9 eV/kT) cm²/sec.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 40–43, November, 1991.     

Chemical structure and internal diffusion within polymer chains in the melt

The single chain dynamics of polydimethylsiloxane in the melt is studied by means of quasielastic neutron scattering. For this polymer the wave vector range 0.03 Å^–1q0.30 Å^–1 covers the regime of universal modes as well as local diffusive processes. A model is described which incorporates the specific chemical structure of the macromolecule and allows to interpret our data in the full wave vector regime. The only parameter which enters the model, the monomer diffusion constantD _m, is found to be (1.2±0.2)·10^–5 cm²s^–1.