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Cross-sectioning plays an important role in failure analysis. However, commonly used polishing method affects the bonded silicon microchannels and face-to-face interlaced carbon nanotubes (CNTs). Polishing damages the edge of the microchannels and the debris from polishing may be trapped in the microchannels. This paper proposes a novel cross-sectioning technique to realize precise cross-sectioning while maintaining the integrity of bonded silicon microchannels and face-to-face interlaced CNTs. Result shows intact cross-sectioning of the microchannels and CNTs inside.

Grain-boundary impurity diffusion of Au along the incoherent twin boundary in a diffusion-bonded Cu bicrystal has been studied by the serial sectioning technique. The measured penetration profiles had a rather atypical shape which we interpreted in terms of structural multiplicity of the grain-boundary structure. A method of processing such profiles has been suggested and the relative fraction of the grain-boundary structural modification exhibiting the lowest diffusion coefficient has been estimated as 60% . The difference between the energies of the two structural modifications has been estimated as being less than 17%, which is in good agreement with the results of computer simulations of the grain-boundary energy in Cu.

Grain boundary and interphase boundary diffusion has been investigated in the system Ag/Ni using the radiotracer serial sectioning technique. Ni segregation in Ag grain boundaries is strongly temperature dependent leading to the conclusion that Ni atoms are located mainly in the bulk planes adjacent to the grain boundary. From interphase boundary diffusion measurements in (110) oriented Ag/Ni interphase boundaries it can be deduced that the structure of this interphase boundary is incoherent.

Measurements of Co diffusion in α-Ti were made by using radiotracers and the direct sectioning technique. The Arrhenius plot obtained is a straight line for the whole range of temperature covered (619–823 K) with Q = 127 ± 6 kJ mol−1 and D o = (3 ± 1)× 10−6m2s−1. The results show an excellent agreement with previous ones in the range (871–1135 K) and they suggest that there is no ultrafast impurity influence in the diffusion in the α-Ti matrix.

Grain-boundary heterodiffusion of iron in pure copper and self diffusion of iron in copper–0.091at% iron were measured by the serial sectioning technique in the Harrison B-regime. The penetration profiles corresponding to iron heterodiffusion in pure copper show a strong positive curvature far beyond the (Dvt)1/2 depth . This peculiar shape, which does not exist for self diffusion in the solid solution, proves the presence of a strong non linear grain-boundary segregation of iron in copper in spite of the respective surface energies of these metals. This segregation is linked to the size effect which is, as predicted by numerical simulation, the main driving force for grainboundary segregation.

The electron spin resonance (ESR) technique was used to investigate the diffusion of Cr 3+ in magnesium oxide (MgO) powders. The ESR absorption intensity was measured for several annealing times and four different temperatures of isothermal annealing: 1223, 1273, 1323 and 1373 K. The activation temperature for diffusion, calculated from the experimental data using a theoretical model based on the Fick equation, was found to be E A =212±9 kJ mol −1 . This result is about 30% smaller than similar data obtained for single-crystal MgO using the radioactive-tracer sectioning technique. The difference is attributed to a higher concentration of defects in the powder relative to single crystals.

Using the tracer-standard sectioning technique the impurity diffusion of indium in copper has been investigated in the temperature range from 798.1 to 1081.0°C. For the frequency factor and the activation energy, respectively, the following values were determined: D02 = 1.87 cm2 · s−1; Q2 = 2.034 eV. The results are compared with predictions of theoretical models of the impurity diffusion in metals. Mit Hilfe der Tracer-Standardschichtenteilungstechnik wurde die Fremddiffusion von Indium in Kupfer im Temperaturbereich von 798,1 bis 1081,0°C untersucht. Fur den Frequenzfaktor bzw. die Aktivierungsenergie wurden folgende Werte ermittelt: D02 = 1,87 cm2 · s−1; Q2 = 2,034 eV. Bei einem Vergleich der Ergebnisse mit theoretischen Modellen fur die Fremddiffusion in Metallen zeigt sich eine gute Ubereinstimmung zwi-Theorie und Experiment.

A study has been made of the diffusion of zinc, from a vapour source, into GaAs slices which had been previously implanted with various ion species. A radiotracer sectioning technique was used to measure the zinc diffusion profiles. It was found that the various implanted ion species (H+, He+, N+, Zn+, As+) had different effects on the zinc diffusion. The results could not be attributed solely to native defects produced by radiation damage. The heavier ion species increased the zinc concentration in the implanted region, but not beyond. The lighter species substantially increased the zinc diffusion rate and altered the resultant concentration profiles. Uphill diffusion was seen in slices which had been given a single high energy H+ implant. The results obtained are compared to those of Radiation-Enhanced-Diffusion experiments. It is suggested that the rate of incorporation of dopant species into the host semiconductor lattice is an important influence on the diffusion mechanism and the shape of the concentration profile.

Self-diffusion of 35S labelled molecules in highly perfect single crystals of orthorhombic sulphur has been studied by the serial sectioning technique. Measured lattice self-diffusion coefficients are considerably lower than those previously published for this solid. This difference is believed to be a consequence of a significant contribution from diffusion along dislocations in the crystals used in the previous study. Self-diffusion perpendicular to the [001] direction can be represented by an equation of the form D=2 × 1013exp[-(215±11 kJmol−1)/RT]m2s−1. Self-diffusion coefficients in the [001] direction are 2–4 times lower. This distinct anisotropy is probably a consequence of the marked structural anisotropy of this phase of sulphur.

The diffusion of antimony in fine-grained and coarse-grained polycrystalline silicon is studied in the temperature range from 930 to 1150 °C. The radioisotope 125Sb is used to measure concentration-depth profiles with the sectioning technique. Autoradiography is used for making the lateral distribution of the radioactivity over the sample surface visible and for quantitative analysis of the activity-depth profile of distinct grains in the coarse-grained samples. An important role is played by dislocation formation during the diffusion anneal. Die Diffusion des Antimons im feinkornigen und grobkornigen polykristallinen Silizium wird im Temperaturbereich von 930 bis 1150 °C untersucht. Das Radioisotop 125Sb wird in der “sectioning”-Technik fur die Bestimmung der Tiefenprofile der Aktivitat verwendet. Autoradiographie wird benutzt zur Sichtbarmachung der Verteilung von Radioaktivitat uber die Oberflache und fur die quantitative Analyse des Tiefenprofils von bestimmten Kornen in grobkornigen Proben. Die Entstehung von Versetzungen wahrend der Diffusionsheizung spielt eine wichtige Rolle.

Self diffusion of 48V in vanadium single crystals was reinvestigated over the temperature range 724–1842°C. Contribution to diffusion from migration along short-circuit paths at the lower temperatures was avoided by applying a micro sectioning technique specially developed for this study. The change in slope of the Arrhenius curve reported to occur at about 1350°C was not observed in this investigation, but has been observed to occur in the vicinity of 1642°C. The data in the temperature range 724–1642°C can be fitted to the relation consistent with normal diffusion by a single-vacancy mechanism. Above 1642°C the data fit the equation

By a combined anodizing and stripping technique, thin sections can be removed from vanadium metal. A uniform, thin oxide film can be grown on the vanadium metal in an acetone-benzoic acid-sodium tetraborate solution during anodization, which is then removed in aqueous NH4OH (10%). The thickness, x, of the metal removed in angstrom units is given by x= 103.2 + 12.5 V, V being the voltage applied. The application of such a sectioning technique for constructing penetration profiles in diffusion studies is of special interest, since contribution from diffusion along lattice defects can be recognized and eliminated. This paper considers the details of the experimental technique by which the films are grown and stripped.

Self- and gold-impurity diffusion measurements over the temperature range 850 to 1265 K are made on platinum single crystals using 197Pt and 199Au as radioactive diffusants and ion-beam sputtering as a sectioning technique. Gaussian penetration profiles are observed for well-annealed crystals. The influence of plastic deformation on the penetration curve is investigated and found to be considerable. The diffusivities obtained from well-annealed crystals fit the Arrhenius relations DPt = 0.05 exp (−2.67 eV/kT) cm2 s−1 for Pt self-diffusion and DAu = 0.13 exp (−2.61 eV/kT) cm2 s−1 for diffusion of Au in Pt. In conjunction with the high-temperature data of Kidson and Ross the present self-diffusion data are analysed in terms of mono- and divacancy contributions. For the sum of the enthalpy of formation and motion of a single vacancy a best value of 2.69 eV is deduced. The present Au-data close a gap since bulk diffusion measurements of Au in Pt are not available in the literature. Diffusion in the PtAu-system is important in semiconductor technology because of the frequent use of PtAu metallizations. Messungen der Diffusion von 197Pt und 199Au in Platineinkristallen werden im Temperaturbereich von 850 bis 1265 K mit Hilfe der Ionenstrahlzerstaubung als Schichtabtragetechnik durchgefuhrt. An gut ausgegluhten Kristallen werden Gaussche Eindringprofile beobachtet. Der Einflus plastischer verformung auf die Eindringkurve wird untersucht und erweist sich als betrachtlich. Die Diffusionskoeffizienten der gut ausgegluhten Kristalle werden durch die Arrhenius-Beziehungen DPt = 0,05 exp (−2,67 eV/kT) cm2 s−1 bei der Selbstdiffusion von Pt und DAu = 0,13 exp (−2,61 eV/kT) cm2 s−1 bei der Diffusion von Au in Pt beschrieben. In Verbindung mit den Hochtemperaturdaten von Kidson und Ross werden die Selbstdiffusionsdaten im Hinblick auf Einfach- und Doppelleerstellenanteile analysiert. Dabei ergibt sich fur die Summe aus Bildungs- und Wanderungsenthalpie der Einfachleerstelle ein bester Wert von 2,69 eV. Die Golddaten dieser Arbeit schliesen eine Lucke, da Messungen der Volumendiffusion von Au in Pt in der Literatur nicht vorhanden sind. Die Diffusion im PtAu-System ist in der Halbleitertechnologie von Bedeutung wegen der haufigen Verwendung von PtAu-Metallisierungen.

Diffusion and Solubility of Cr51 in Silver Single Crystals investigated in the temperature range 976 to 1231 K using the serial sectioning technique. Solubility Xcr and diffusion coefficient D can be described by the following temperature functions: Xcr = exp [−1.76 ± ± 0.02) eV/kBT] and D = exp [−(2.00 ± 0.02) eV/kBqT] cm2 8−1. At the melting point the solubility of chromium is as small as 100 ppm. The results of the chromium diffusion cannot be explained in terms of the current models of impurity diffusion. Im Temperaturbereich zwischen 976 und 1231 K werden die Diffusion und die Loslichkeit von Cr51 in Silbereinkristallen mit Hilfe der Sektionsmethode untersucht. Loslichkeit Xcr und Diffusionskoeffizient D konnen durch die folgenden Temperaturfunktionen beschrieben werden: Xcr = exp [−(1,76 ± 02) 0v/kBT] und D = exp [−(2,00 ± ± 0,02) ev/kBT] cm2 s−1. Am Schmelzpunkt betrugt die Loslichkeit von Chrom lediglich 100 ppm. Die Ergebnisse der Chromdiffusion in Silber stehen nicht im Einklang mit den bekannten Fremddiffusionsmodellen.

The diffusion of Hg and Cd in solid lead has been measured at hydrostatic pressures to 40 kbar for temperatures between 250 and 550\ifmmode^\circ\else\textdegree\fi{}C using the radiotracer sectioning technique. The data were analyzed assuming a single effective mechanism of diffusion with a temperature- and pressure-dependent activation volume. The activation energy and activation volume at zero pressure and 600 K are, respectively, $\ensuremath{\Delta}H=23.10\ifmmode\pm\else\textpm\fi{}0.14$ kcal/mole, $\frac{\ensuremath{\Delta}V}{{V}_{0}}=0.516\ifmmode\pm\else\textpm\fi{}0.006$ for Hg in Pb: $\ensuremath{\Delta}H=22.17\ifmmode\pm\else\textpm\fi{}0.18$ kcal/mole, $\frac{\ensuremath{\Delta}V}{{V}_{0}}=0.317\ifmmode\pm\else\textpm\fi{}0.010$ for Cd in Pb. The pressure and temperature coefficients of the activation volume along with the specific heat of activation, although quite uncertain are also determined. Even though the activation energies for the diffusion of both Hg and Cd in Pb is near that for lead self-diffusion, the activation volume is too small in both cases to be consistent with a vacancy mechanism.

Hydrogen assisted crack growth was examined in cyclically hardened and notched Ni-single crystals. Tests were performed in different aqueous electrolytes at cathodic potentials as well as in hydrogen gas at different pressures and temperatures. Comparisons between the crack growth rates in alkaline and acid solutions and in hydrogen gas yielded estimates of the effective hydrogen activity at the crack tip for various overpotentials. A new sectioning technique involving so-called micro-milling was used for detailed fractographic examinations. These examinations show that the cracks in Ni-single crystals {orientation: specimen axis [100], surfaces: (110)} grow in hydrogen by a mixture of slip along (111) and local brittle fracture along (100). A simple trapping model is presented which assumes that a high density of deep traps with an apparent binding energy of 32 kJ/mol H is produced at the crack tip within a zone of less than 10 nm during crack growth. This model describes the pressure, temperature and frequency dependence of the crack growth rate, da dN , without any additional fitting parameters.

Concentration profiles of chromium, maganese and iron radioactive tracers through a duplex oxide grown on 316 stainless steel have been obtained after a diffusion anneal at 1273 K using the serial sectioning technique. The iron tracer diffused normally in both inner and outer oxides of the duplex scale. The concentration of the chromium and manganese tracers increased with increasing penetration into the outer Fe3O4 layer but showed a normal profile in the inner spinel. The diffusion coefficients obtained from the profiles were in the range 6 × 10−12 – 3 × 10−11 cm2 sec−1 for diffusion in the spinel phases. Diffusion von Ubergangsmetallen in auf Stahl 316 aufgewachsenem Duplex-Oxid Mit der Methode der sukzessiven Abtragung wurden nach Diffusionsgluhen bei 1273 K Konzentrationsprofile von radioaktiven Isotopen (Chrom, Mangan und Eisen) in einem auf Stahl 316 entstandenen doppelschichtigem Zunder ermittelt. Das Eisenisotop diffundiert danach normalerweise sowohl durch die innere als auch durch die ausere Zunderschicht. Die Konzentration der Isotopen von Chrom und Mangan nimmt in der auseren Magnetitschicht nach Ausen hin zu, zeigt aber in der inneren Spinellschicht ein normales Konzentrationsprofil. Die Diffusionskoeffizienten – ermittelt aufgrund der Konzentrationsprofile – lagen, bezogen auf die Diffusion in der Spinellphase, zwischen 6 × 10−12 und 3 × 10−11 cm2 sec−1.

The diffusion of cobalt and copper in Monel-400 has been studied by serial sectioning technique using the radioactive tracers 60Co and 64Cu in the temperature ranges 1070 to 1570 K for volume diffusion and 700 to 1100 K for grain-boundary diffusion, respectively. The volume diffusion coefficients can be expressed as: for Co in Monel-400 (1070–1570 K) DCo = 3.09 × 10−4exp(−260.1 kJ/molRTm2/s, for Cu in Monel-400 (1070–1570 K) DCu = 2.88 × 10−4exp(−270.8 kJ/molRTm2/s. The grain-boundary diffusion coefficients were evaluated for most of the experiments by Whipple's method. For a few experiments Suzuoka's method was also applied. The two methods yielded values of grain-boundary diffusion coefficients that were in good agreement with each other. The grain-boundary diffusion coefficients could be represented by the expressions: for Co in Monel-400 (700–1100 K) Dgb,Co = 3.24 × 10−5exp(−151.0kJ/molRT) m2/s, for Cu in Monel-400 (700–1100 K) Dgb,Cu = 1.13 × 10−4exp(165.8kJ/molRT) m2/s, Autoradiographic technique was also used extensively to study the segregation of the diffusing tracers. It was observed that for small-grained specimens (average grain dia ~ 200 μm) at temperatures above ~ 1000 K both volume and grain-boundary diffusion processes contribute significantly to the penetration of tracer atoms in the bulk of the solid, but at lower temperatures (< 960 K) the migration is mainly through the grain boundaries.

Sulphur diffusion in copper single crystals was studied at temperatures lower than 800°C for very short diffusion times. The distances of penetration were about 5 μm and a submicron sectioning technique was used. The curves obtained under these conditions do not follow a law of volume diffusion. These facts were interpreted by ascribing the role of diffusion short circuits to dislocations.

A tracer sectioning technique was used to measure cation self-diffusion coefficients in fully dense polycrystalline YaO3 and Er2Os under oxidizing conditions. The results are described by the relations for Y2O3 (1400° to 1670°C), and for Er2O3 (1400° to 1700°C). The greater activation energy for erbium diffusion in erbia may be partly attributable to a mass effect.

Experimental details are given of a thin film sectioning technique for the measurement of tracer diffusion in lithium metal. Results are given for 65Zn in Li between 57 and 173 °C. They are expressed by D = D0exp ( − Q/RT), where and Q = = (12.98 ± 0.24)kcal/mol. The activation energy equals, within margins of error, that of self-diffusion in Li. The agreement between vacancy based theories and the present results appears rather doubtful. Experimentelle Einzelheiten einer Dunnschicht-Schnittechnik fur Diffusionsmessungen an Lithiummetall werden beschrieben. Es werden Ergebnisse fur 65Zn in Li zwischen 57 und 173 °C angegeben, die sich durch D = D0exp ( − Q/RT) ausdrucken lassen, mit D0 = und Q = (12,98 ± 0,24) kcal/mol. Die Aktivierungsenergie ist, innerhalb der Fehlgrenzen, gleich derjenigen der Selbstdiffusion. Die Ubereinstimmung der auf Leerstellen gegrundeten Theorien mit diesen Ergebnissen erscheint ziemlich zweifelhaft.

The diffusion of Fe 59 and Co 60 in δ-Fe have been measured using a sectioning technique. The diffusion penetrations were determined by counting the radioactivity in the sections removed and also by the residual activity method. The results are summarized by the following equations: D Fe = 1.9 exp [−57.0 × 10 3 / RT ], D Co = 5.5 exp [−61.2 × 10 3 / RT ]. In both cases the activation energy and D 0 are significantly less than values previously reported for diffusion in the paramagnetic region of α-Fe. This amounts to approximately a threefold decrease in the value of D below that expected from extrapolation of the α-Fe data. The results indicate that were iron to retain the b.c.c. structure at all temperatures, the activation energy would demonstrate a non-linear functional dependence on temperature.

Abstract The thin layer lathe sectioning technique was used to measure the self and solute diffusion coefficients of gold in f.c.c. lanthanum. Self-diffusion is given by D = 1.5 exp (− 45100/RT) cm2/sec, and gold solute diffusion by D = 2.2 × 10−2 exp (− 18100/RT) cm2/sec. The activation energy for self-diffusion is in good agreement with various semi-empirical rules. The high diffusivities and low activation energy for the solute diffusion of gold are interpreted in terms of the combined substitutional–interstitial diffusion mechanism.

In the present studies of self diffusion in gallium the diffusion coefficients in single crystals and coarse-grained polycrystals were found to be extremely low. The results are only claimed to be of qualitative interest because of limitations set mainly by the short half-life of the radiotracer used. Even so two main conclusions can be drawn: (i) there is no clear evidence of marked anisotropy of self diffusion, and (ii) for gallium and other soft or friable metals a microtome sectioning technique is to be preferred to a grinding method.

A new sectioning technique has been successfully developed and used to determine the three-dimensional form of the initial fatigue crack in copper. As previously found, intrusions are the earliest form of damage detectable and it has been further shown that their extension is by the formation of tubular holes starting from the surface. This mode of failure is finally superseded by sub-surface irregular microcrack link-up of the slip-band zone cracks and the gross form of crack propagation known as stage II.

The anisotropic diffusion coefficients of the radioactive tracers cadmium ($115m$) and gold (198) in single crystals of high-purity zinc, in directions parallel and perpendicular to the hexagonal axis, were measured by the standard sectioning technique. Cadmium diffused at a rate faster than that of self-diffusion and with ${D}_{\ensuremath{\perp}}g{D}_{\mathrm{II}}$. Gold diffused at a rate slower than that of self-diffusion and with ${D}_{\mathrm{II}}g{D}_{\ensuremath{\perp}}$. The results of the measurements are as follows: For cadimum ($115m$), ${D}_{\mathrm{II}}=(0.11\ifmmode\pm\else\textpm\fi{}0.01)\mathrm{exp}[\ensuremath{-}\frac{(20.54\ifmmode\pm\else\textpm\fi{}0.09)\ifmmode\times\else\texttimes\fi{}{10}^{3}}{\mathrm{RT}}]$ ${\mathrm{cm}}^{2}$/sec, ${D}_{\ensuremath{\perp}}=(0.12\ifmmode\pm\else\textpm\fi{}0.01)\mathrm{exp}[\ensuremath{-}\frac{(20.42\ifmmode\pm\else\textpm\fi{}0.03)\ifmmode\times\else\texttimes\fi{}{10}^{3}}{\mathrm{RT}}]$ ${\mathrm{cm}}^{2}$/sec; for gold (198), ${D}_{\mathrm{II}}=(0.97\ifmmode\pm\else\textpm\fi{}0.22)\ifmmode\times\else\texttimes\fi{}\mathrm{exp}[\ensuremath{-}\frac{(29.73\ifmmode\pm\else\textpm\fi{}0.26)\ifmmode\times\else\texttimes\fi{}{10}^{3}}{\mathrm{RT}}]$ ${\mathrm{cm}}^{2}$/sec, ${D}_{\ensuremath{\perp}}=(0.29\ifmmode\pm\else\textpm\fi{}0.12)\mathrm{exp}[\ensuremath{-}\frac{(29.72\ifmmode\pm\else\textpm\fi{}0.45)\ifmmode\times\else\texttimes\fi{}{10}^{3}}{\mathrm{RT}}]$ ${\mathrm{cm}}^{2}$/sec. On the basis of the vacancy mechanism one can interpret the fast diffusion of cadmium in terms of an appreciable binding between the vacancy and the diffusing ion; conversely the slow diffusion of gold in terms of a repulsion between the vacancy and the diffusing ion.

Diffusion of cerium and neodymium in nickel has been studied by the serial sectioning technique using radioactive tracers141Ce and147Nd, in the temperature ranges 700° to 1100°C for volume and 500° to 875°C for grain boundary diffusion respectively. Volume diffusivities can be expressed as: $$\begin{gathered} D_{Ce/Ni} = (0.66 \pm 0.18)\exp \left( { - \frac{{60,800 \pm 810}}{{RT}}} \right)cm^2 /\sec \hfill \\ D_{Nd/Ni} = (0.44 \pm 0.13)\exp \left( { - \frac{{59,820 \pm 830}}{{RT}}} \right)cm^2 /\sec \hfill \\ \end{gathered} $$ and grain boundary diffusivities by: $$\begin{gathered} Dg_{Ce/Ni} = 0.11\exp \left( { - \frac{{29,550}}{{RT}}} \right)cm^2 /\sec \hfill \\ Dg_{Nd/Ni} = 0.07\exp \left( { - \frac{{28,580}}{{RT}}} \right)cm^2 /\sec \hfill \\ \end{gathered} $$ Results of volume diffusion have been compared with those calculated from the theories of diffusion based on size and charge difference between the solute and the solvent atoms. Whipple and Suzuoka methods have been used to evaluate the grain boundary diffusion coefficients. Both the methods give similar results.

The diffusion of gold in gamma uranium has been measured using a radioactive tracer and the sectioning technique. The values of D o and the activation energy are 4.86 × 10 −3 cm 2 /sec and 30 400 cal/mol respectively, fairly close to the values for self-diffusion in gamma uranium.

The self-diffusion of gold was measured in single crystalline specimens of 99.8 and 99.999% purity in the temperature range from 600-954\ifmmode^\circ\else\textdegree\fi{}C, by using ${\mathrm{Au}}^{198}$ as tracer and applying the sectioning technique. The temperature dependence of the self-diffusion coefficient is given by $D=(0.031\ifmmode\pm\else\textpm\fi{}0.004)\mathrm{exp}[\ensuremath{-}\frac{(39360\ifmmode\pm\else\textpm\fi{}280)}{\mathrm{RT}}] {\mathrm{cm}}^{2}/sec.$ Together with recently reported data on self-diffusion of copper, silver, and lead, this result is compared with empirical and theoretical predictions.

Self-diffusion studies have been carried out on nominally 50-50 Au-Cd alloys by the standard sectioning technique using radioisotopes 115Cd and 198Au. From 300° to 590°C the results are well fitted by the valuesQ = 28.0 kcal/mole and D0 = 0.23 cm2/sec for cadmium and Q = 27.9 kcal/mole and D0 = 0.17 cm2/sec for gold. Between 590°C and the melting point at 626°C there is a marked upward curvature in both diffusion plots. The ratio of the diffusivities is roughly 4:3 throughout and is consistent with a mechanism of nearest neighbor vacancy jumping. The activation energies for diffusion exceed the sum of energies for vacancy formation and motion previously reported. Two possible explanations for this discrepancy are suggested.

Diffusion of sodium in albite from Amelia County, Virginia, was examined at high and intermediate temperatures by means of the sectioning technique and at low temperatures by means of an exchange technique. These studies indicate that diffusion is heterogeneous at low and intermediate temperatures, but goes to volume diffusion at high temperatures. Apparent diffusion coefficients of the order of magnitude of 10 −18 cm 2 /sec and an activation energy of approximately 3000 cal/mole sodium are determined for the low-temperature movement. An activation energy of approximately 35 kcal/mole sodium is determined for the high-temperature movement.

The solute diffusion of cobalt in beta‐uranium was measured using the thin‐layer sectioning technique. The results can be expressed by D= 1.54×10−2 exp(−27 450/RT) cm2/sec. The diffusivities of cobalt are higher by about three orders of magnitude than the self‐diffusion coefficients in beta‐uranium. The possibility of cobalt diffusing by means of the combined substitutional‐interstitial mechanism has been examined.

Using a steady-state sectioning technique the migration of 22Na in Li has been investigated under temperature gradients and electric currents. The thermotransport “heat of transport” has been found to be Q* = (−3.0 ± 1.2) (kcal/mol), and the “effective charge number” of electrotransport z* − 4.7 ± 1.9. Theory predicts the electronic share of the heat of transport to be small, while the phonon contribution, only qualitatively treated, may be of the order of + 1 kcal/mol. The intrinsic contribution is calculated to be Q*0 = (−4.0 ± 2.5) kcal/mol. Classical models applied to Q*0 give indication that Na diffuses substitutionally in Li, and that the vacancy formation energy amounts to about two thirds of the diffusion activation energy. This is in line with evidence from X-ray dilatometry. The electrotransport results yield the effective resistivity of the activated impurity–vacancy complex, about 1.6 μ μΩ cm/% defects. It is suggested that in Li self-transport a considerable role may be played by interstitials. Mittels einer Schnittechnik fur Stationarprofil wird die Wanderung von 22Na in Li bei thermischen Gradienten und bei elektrischem Stromdurchgang untersucht. Die „Uberfuhrungswarme” des Thermotransport wird zu Q* = (−3,0 ± 1,2) kcal/Mol bestimmt, die „effektive Ladungszahl” des Elektrotransports zu z* = −4,7 ± 1,9. Der Theorie nach ist der elektronische Teil der Uberfuhrungswarme gering. Der Beitrag der Phononen, bisher nur qualitativ behandelt, durfte von der Grosenordnung + 1 kcal/Mol sein. Der Beitrag der Diffusionsenergien wird zu Q*0 = (−4,0 ± 2,5) kcal/Mol berechnet. Aus klassischen Modellen fur Q*0 wird gefolgert, das Na in Li substitutionell diffundiert, und das die Leerstellen-Bildungsenergie etwa zwei Drittel der Diffusions-Aktivierungsenergie betragt. Dies wird durch experimentelle Ergebnisse der Rontgen-Dilatometrie bestatigt. Die Messungen des Elektrotransports ergeben einen effektiven spezifischen Widerstand fur den aktivierten Verunreinigungs–Leerstellen-Komplex von ungefahr 1,6 μ μΩcm/% Defekte. Es wird angedeutet, das im Selbsttransport von Li Zwischengitteratome eine wesentliche Rolle spielen konnten.

The sectioning technique was used to study the diffusion of radioactive tracers in high-purity zinc single crystals. Diffusion both parallel and perpendicular to the hexagonal axis was measured. The diffusion of ${\mathrm{Cu}}^{64}$ was measured over the temperature range from about 338\ifmmode^\circ\else\textdegree\fi{}C to 415\ifmmode^\circ\else\textdegree\fi{}C with the results ${D}_{\mathrm{II}}=(2.22\ifmmode\pm\else\textpm\fi{}0.57)\mathrm{exp}[\ensuremath{-}(29.53\ifmmode\pm\else\textpm\fi{}0.29)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}] \frac{{\mathrm{cm}}^{2}}{sec},$ ${D}_{\ensuremath{\perp}}=(2.00\ifmmode\pm\else\textpm\fi{}0.54)\mathrm{exp}[\ensuremath{-}(29.92\ifmmode\pm\else\textpm\fi{}0.30)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}]\frac{{\mathrm{cm}}^{2}}{sec},$ The diffusion of ${\mathrm{Ga}}^{72}$ was measured over the range from about 240\ifmmode^\circ\else\textdegree\fi{}C to 403\ifmmode^\circ\else\textdegree\fi{}C with the results ${D}_{\mathrm{II}}=(0.016\ifmmode\pm\else\textpm\fi{}0.001)\mathrm{exp}[\ensuremath{-}(18.40\ifmmode\pm\else\textpm\fi{}0.06)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}]\frac{{\mathrm{cm}}^{2}}{sec},$ ${D}_{\ensuremath{\perp}}=(0.018\ifmmode\pm\else\textpm\fi{}0.001)\mathrm{exp}[\ensuremath{-}(18.15\ifmmode\pm\else\textpm\fi{}0.08)\ifmmode\times\else\texttimes\fi{}\frac{{10}^{3}}{\mathrm{RT}}]\frac{{\mathrm{cm}}^{2}}{sec},$ Copper diffused at a rate faster than gold but slower than silver. As in silver and gold, ${D}_{\mathrm{II}}g{D}_{\ensuremath{\perp}}$; but the anisotropy was much smaller in Cu than in Ag or Au. The measured values of gallium fall somewhat below those for indium and show ${D}_{\ensuremath{\perp}}g{D}_{\mathrm{II}}$. The relative diffusion rates are qualitatively in accord with the predictions of LeClaire's theory of homovalent diffusion. The sign of anisotropy is explained in terms of the electrostatic interaction between the diffusing ion and the vacancy, and the reduced anisotropy of copper diffusion is interpreted as evidence of a size effect.

The self‐diffusion of antimony has been measured in single crystals with the tracer 124Sb. The least‐squares fit to the data gives in the direction of the trigonal axis Q‖=47.1±1.2 kcal/mole and ln(D0 in cm2/sec)=3.1±0.7, and in the plane perpendicular to the trigonal axis Q‖=44.4±4.9 kcal/mole and ln(D0 in cm2/sec)=2.81±2.8. The standard sectioning technique was used except that the very friable nature of the semimetal complicated the procedure at practically every step of the operation. The greatest source for the inaccuracy arose from the ``tails'' on the deep penetration side, noticable for D‖ and strongly prominent for D‖. Correlation considerations in the Sb lattice are considered in detail in the Appendix.

The self-diffusion of nickel has been studied in polycrystalline samples by a sectioning technique. There is evidence of grain boundary diffusion below temperatures of 1150 °C. The results obtained between 1150° and 1400 °C are representative of volume diffusion and are represented by the expression[Formula: see text]A comparison is made with the results of other self-diffusion studies using Zener's hypothesis.

The diffusion of mercury at very low concentration in single crystal gold has been measured over the temperature range 500°C to approximately 1000°C using a sectioning technique. It was found that above 600°C the temperature dependence of the diffusion coefficient followed the equation: The results obtained are discussed in relation to current theories of impurity diffusion in metals.

A sectioning technique is developed to circumvent problems associated with the conventional procedure. The new technique consists of wax mounting the sample in a suitable chuck followed by chemical-mechanical polishing using Nalcog slurry. Basic features of a chuck design and polishing characteristics, and some results of defect analysis of thin silicon sheets, afforded by this technique are briefly described. 1 ref.

The diffusion of mercury has been studied in high-purity zinc as a function of temperature, using the sectioning technique. The diffusion coefficients as measured in single crystals are given by ${D}_{\mathrm{II}}=(0.056\ifmmode\pm\else\textpm\fi{}0.002)\ifmmode\times\else\texttimes\fi{}\mathrm{exp}[\ensuremath{-}\frac{(19700\ifmmode\pm\else\textpm\fi{}48)}{\mathrm{RT}}]$ ${\mathrm{cm}}^{2}$/sec, and ${D}_{\ensuremath{\perp}}=(0.073\ifmmode\pm\else\textpm\fi{}0.006)\mathrm{exp}[\ensuremath{-}\frac{(20180\ifmmode\pm\else\textpm\fi{}94)}{\mathrm{RT}}]$ ${\mathrm{cm}}^{2}$/sec, where ${D}_{\mathrm{II}}$ and ${D}_{\ensuremath{\perp}}$ are the diffusion coefficients parallel and perpendicular to the hexagonal axis, respectively. Compared to the diffusion of cadmium in zinc, where ${D}_{\ensuremath{\perp}}g{D}_{\mathrm{II}}$, mercury diffuses with a slightly smaller activation energy, and with ${D}_{\mathrm{II}}g{D}_{\ensuremath{\perp}}$. The results are discussed on the basis of the basal and nonbasal vacancy mechanisms, and the influence of the ion size of the diffusing atom is examined to explain the diffusion anisotropy.

Electron microscopic studies of thin sections of industrial carbons have been extended to green mixes. Pitch is shown to have discrete spherical bodies (0.5–1.0 μ) distributed in a continuous medium. A dissolution technique is described which distinguishes the coke from the binder in a green mix. The results suggest that the coke particles have an irregular three-dimensional porous structure and the apparent inability to observe particles larger than a few microns is explained. The sectioning technique leads to morphological features comparable to those seen by replication.

Hydrogen assisted crack growth was examined in cyclically hardened and notched Ni-single crystals. Tests were performed in different aqueous electrolytes at cathodic potentials as well as in hydrogen gas at different pressures and temperatures. Comparisons between the crack growth rates in alkaline and acid solutions and in hydrogen gas yielded estimates of the effective hydrogen activity at the crack tip for various overpotentials. A new sectioning technique involving so-called micro-milling was used for detailed fractographic examinations. These examinations show that the cracks in Ni-single crystals {orientation: specimen axis [100], surfaces: (110)} grow in hydrogen by a mixture of slip along (111) and local brittle fracture along (100). A simple trapping model is presented which assumes that a high density of deep traps with an apparent binding energy of 32 kJ/mol H is produced at the crack tip within a zone of less than 10 nm during crack growth. This model describes the pressure, temperature and frequency dependence of the crack growth rate, da/d, N, without any additional fitting parameters.

We describe an apparatus which allows us to measure accurately the self-diffusion coefficients by the standard thin film deposition and sectioning technique. The accuracy of each measurement of the self-diffusion coefficient is about 0,4%. This accuracy allows a positive curvature to be detected in the β−Tl Arrhenius plot. The possibility that this effect be due to preferential diffusion along grain boundaries is discussed. We conclude that the observed curvature reflects the properties of the β−Tl monocristal. Two supplementary experiments allowed us, on the one hand to define satisfactory experimental conditions for the electro-deposition of thallium from a thallous sulphate solution and, on the other hand, to measure accurately the α−β transition temperature of thallium, that is found to be 235,25±0,1°C Nous presentons un ensemble experimental permettant la mesure precise de coefficients d'autodiffusion par la technique du depot mince et du sectionnement. La precision moyenne atteinte sur la mesure du coefficient de diffusion est de 0,4%. Cette precision permet de detecter une courbure positive dans le graphe d'Arrhenius de β-Tl. La possibilite qu'il s'agisse d'un effet de diffusion preferentielle dans les points de grains est discutee. On conclut que la courbure observee reflete les proprietes du monocristal. Deux experiences annexes nous ont permis, d'une part de definir des conditions experimentales satisfaisantes pour le depot electrolytique du thallium en solution sulfurique, et, d'autre part, de mesurer avec precision la temperature de la transition α−β du thallium, soit 235,25±0,1°C.

A tracer sectioning technique was employed to measure cation self-diffusion coefficients in fully dense polycrystalline materials under oxidizing conditions. Results are D = 1.65x10/sup -2/ exp(-69,200/RT) cm/sup 2//s for Y/sub 2/O/sub 3/ (1400 to 1670/sup 0/C), and D = 1.48 exp(-102,200/RT) cm/sup 2//s for Er/sub 2/O/sub 3/ (1400 to 1700/sup 0/C). The greater activation energy for erbium diffusion in erbia is attributed to a mass effect. Oxygen diffusion coefficients were extracted from observations in the reoxidation of small single crystals of uniformly reduced oxides produced by vacuum fusion. The oxidation process proceeded by the development of a fully oxidized external shell, the growth of which was rate-limited by diffusion of interstitially dissolved oxygen through the oxidized layer to a sharp interface with the reduced material. The growth of the oxidized shell was followed by means of a thermobalance. Oxygen diffusion coefficients were calculated to be D = 6.01x10/sup -6/ exp(-19,600/RT) cm/sup 2//s for Y/sub 2/O/sub 3/ (1064 to 1276/sup 0/C), and by D = 4.76x10/sup -5/ exp(-30,100/RT) cm/sup 2//s for Er/sub 2/O/sub 3/ (1060 to 1292/sup 0/C).

Submicron sectioning apparatus for studying slow carbon self diffusion in dense polycrystalline tungsten carbide

The self-diffusion of single crystal thallium has been measured from 150°C to 275°C with the use of Tl204 as a tracer and the standard sectioning technique. For diffusion parallel to the c-axis the data were well fitted by an activation energy of Q = 22.9 kcal/mol and a D0 = 0.4 cm2/sec, and for diffusion perpendicular to the c-axis 0 = 22.6 kcal/mol and D0 = 0.4 cm2/sec. The cubic phase was investigated also and resulted in the values Q = 20.0 kcal/mol and D0 of order 0.7 cm2/sec. Possible mechanisms are discussed.