Critical voltage analysis of precipitation in certain nickel-base alloys

Butler, E.

doi:10.1002/pssa.2210180104

Cited by 10 publications

(3 citation statements)

References 17 publications

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“…5. The data of Butler (1972) as well as the room-temperature point in fig. 2 are superimposed on the plot.…”

Section: Ni-aumentioning

confidence: 99%

“…In spite of its potential, and the increased availability of high-voltage electron microscopes, critical-voltage measurements have not been widely used in metallurgical applications. The technique has been used for studying local composition variations in Ni-base alloys (Butler 1972(Butler , 1973, composition variation of the Debye temperature in Fe-Cr alloys (Shirley, Lally, Thomas and Fisher 1975) and ordering in ordered Cu 3 Au and Ni 4 Mo (Sinclair et ale 1975), but there is little else for alloys apart from some scattered and uninterpreted critical voltages.…”

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confidence: 99%

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Atomic mean-square displacements and the critical-voltage effect in cubic solid solutions

Shirley

Fisher²

1979

Philosophical Magazine A

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The critical-voltage phenomena observed in high-voltage electron microscope images of bend contours as well as in corresponding Kikuchi or convergent-beam diffraction patterns provide sensitive methods of determining submicroscopic alloy parameters such as Debye temperatures, short-range order, and atomic scattering factors. Only a very limited number of critical voltages can be observed in metal crystals in the voltage range usually available, 100 to 1200 kV, so that quantitative interpretation of the data must be based on a few-parameter model which incorporates all the pertinent factors. A satisfactory two-parameter model has been developed which can be used to interpret or compute the critical voltages of substitutional solid solutions as functions of composition, temperature and shortrange order. In the alloy systems Fe-Cr, Ni-Au, Cu-Au and Cu-AI, sufficient critical voltage data are available to derive the model parameters which pertain to atomic bonding in the lattice. In addition to atomic scattering amplitudes, the critical voltage depends strongly on the atomic mean-square displacements. The static contribution to the mean-square displacements is large in alloys with large atomic-radius disparity, and is especially sensitive to short-range order in f.c.c. solid solutions. Well-defined best estimates for the model parameters are used to predict the critical voltage and its sensitivity to composition, temperature and short-range order for a large number of solid solutions. Systems for which critical-voltage studies may be of considerable interest are indicated. § 1. INTRODUCTION Detailed examination of electron diffraction patterns from precisely oriented thick crystals at accelerating voltages greater than about 100 kV has revealed that at certain critical voltages, V c' second-order Kikuchi lines vanish and other characteristic changes occur (Nagata and Fukuhara 1967,

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“…5. The data of Butler (1972) as well as the room-temperature point in fig. 2 are superimposed on the plot.…”

Section: Ni-aumentioning

confidence: 99%

mentioning

confidence: 99%

Atomic mean-square displacements and the critical-voltage effect in cubic solid solutions

Shirley

Fisher²

1979

Philosophical Magazine A

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“…Attempts at some form of combination of the two techniques have been made (Bell, 1971;Butler, 1972Butler, , 1973Hewat & Humphreys, 1974) but have failed to obtain CB patterns showing fine detail, a consequence of the large (roughly 1 tgn) spot sizes used. In these previous investigations an accuracy of approximately _+5 kV was obtained for the measurement of V~.…”

Section: (C) Convergent-beam Critical-voltage Measurementsmentioning

confidence: 99%

The critical-voltage effect in convergent-beam high-voltage electron diffraction

Sellar¹,

Imeson²,

Humphreys³

1980

Acta Cryst Sect A

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The critical voltage effect in transmission electron microscopy. II. A theoretical study neglecting absorption effects

Gevers¹,

Serneels²,

David³

1975

Physica Status Solidi (b)

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R. GEVERS e t al. : Critical Voltage Effect in Electron Microscopy (11) 273 phys. stat. sol. (b) 67, 273 (1975) Subject classification: 1.1 Rijksuniversitair Centrum, Fakulteit der Wetenschappen, AntwerpenThe Critical Voltage Effect in Transmission Electron Microscopy') BY A Theoretical Study Neglecting Absorption Effects R. GEVERS~), R. SERNEELS, and M. DAVIDUsing degenerate perturbation theory a titudy is made of the critical voltage effect in electron microscopy. I n particular the dependence on the accelerating electron voltage of the profile of the second order bend contour for centrosymmetric crystals is considered. The case of non-centrosymmetric crystals is included in the formulae. It is found for centrosymmetrical crystals that the more the critical voltage is approached, the second order bend contour appears as a kinematical like bend icontour which disappears completely in a small interval around the critical voltage. Also the symmetry properties are discussed of the Bloch waves corresponding to the branches of the dispersion surface which touch a t the critical voltage. It is shown that away from the critical voltage and when the second order reflection is not exactly satisfied the Bloch waves are nearly symmetric or antisymmetric. When the voltage is varied towards the critical volt,age a continuous change appears of the Bloch wave symmetry in a given interval around the critical voltage. The smaller the misorientation the smaller is the voltage interval. For non-centrosymmetric crystals a similar effect is observed.Xit Storungstheorie bei Entartung wird der Effskt, der kritischen Spannung der Elektronenmikroskopie untersucht. Insbesondere wird die Abhangigkeit des Profils des Bandverlaufs zwciter Ordnung fur zentrosymmetrische Kristalle von der Beschleunigungsspannung betrachtet. Der Pall nicht-zentrosymmetrischer Kristalle ist im Formalismus mit einbegriffen. Fur zent,rosymmetrische Kristalle wird gefunden, daB, je mehr man sich der kritischen Spannung nahert, der Bandverlauf zweiter Ordnung als ein kinematik-ahnlicher Bandverlauf auftritt, der vollstandig in einem kleinen Rereich um die kritische Spannung verschwindet. Die Symmetrieeigenschaften der Blochwellen, die den Zweigen der Dispersionsflache entsprechen, die die kritische Spannung beruhrm, werden ebenfalls diskutiert. Es wird gezeigt, daO weit entfernt von der kritischen Spannung und wenn die Reflexion zweiter Ordniing nicht exakt erfiillt ist, die Blochwellen nahezu symmetrisch oder antisymmetrisch sind. Wenn die Spannung sich in Richtung der kritischen Spannnng andert, tritt eine kontinuierliche dnderang der Blochwellensynlmetrie in einem gegebenen Bereich um die kritische Spannung auf. J e geringer die Fehlorientierung ist, um so geringer ist dicser Spannungsbereich. Fur nicht-zentrosymmetrische Kristalle wird ein ahnlicher Effekt beobachtet.

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Critical voltage analysis of precipitation in certain nickel-base alloys

Cited by 10 publications

References 17 publications

Atomic mean-square displacements and the critical-voltage effect in cubic solid solutions

Atomic mean-square displacements and the critical-voltage effect in cubic solid solutions

The critical-voltage effect in convergent-beam high-voltage electron diffraction

The critical voltage effect in transmission electron microscopy. II. A theoretical study neglecting absorption effects

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