Development of a method for calculating the LTEC anisotropy of Zr alloys

Abstract The accuracy of determining the LTEC with respect to metals and alloys with an HCP lattice based on inverse pole figures (IPF) is analyzed depending on the number of experimental points on the IPF using three averaging options: (1) taking into account the irregular arrangement of reflections on the stereographic triangle according to Morris; (2) by the multiplicity factor and (3) with the same weight of each orientation. It is shown that when evaluating the LTEC for semi-finished products with a basal texture, 17 reflections on the IPF are sufficient to provide an error of <1% when using Morris averaging and the multiplicity factor; in the case of a prismatic texture, an error of <1% is provided by all three averaging options, while Morris averaging is minimal.

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Pole Figure Random Intensity Calculation Using Powder Integrated Ratios

Advances in X-ray Analysis ◽

10.1154/s0376030800005462 ◽

1973 ◽

Vol 17 ◽

pp. 416-422

Author(s):

Carlos Sergio Viana ◽

Gustau Ferran

Keyword(s):

Pole Figure ◽

High Multiplicity ◽

Random Intensity ◽

Pole Figures ◽

Multiplicity Factor ◽

Intensity Calculation ◽

Integrated Intensities

AbstractThis paper describes a method for automatic quantitative pole figure plotting up to 70°, using only one sample and Schulz reflection technique. Random intensities are calculated for the usual planes of iron, using the ratios of calculated povder integrated intensities of these planes to the intensity of a high multiplicity factor plane, the random intensity of which had been obtained by integration up to 70° over the pole figure, using Bragg and Packer's method; the latter integration shows a decreasing error when the multiplicity factor increases. With this method it is possible to normalize the pole figures without using a physical standard and to reduce greatly the time to obtain a quantitative pole figure.

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The Fullest Description of the Structure of Textured Metal Materials with Generalized Pole Figures: the Example of Rolled Zr Alloys

Materials Science Forum ◽

10.4028/www.scientific.net/msf.378-381.180 ◽

2001 ◽

Vol 378-381 ◽

pp. 180-185 ◽

Cited By ~ 9

Author(s):

Yuriy Perlovich ◽

Margarita Isaenkova ◽

Hans Joachim Bunge

Keyword(s):

Pole Figures ◽

Metal Materials ◽

Zr Alloys

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Texture analysis with a time-of-flight neutron strain scanner

Journal of Applied Crystallography ◽

10.1107/s1600576714012710 ◽

2014 ◽

Vol 47 (4) ◽

pp. 1337-1354 ◽

Cited By ~ 14

Author(s):

Florencia Malamud ◽

Javier R. Santisteban ◽

Miguel Angel Vicente Alvarez ◽

Raúl Bolmaro ◽

Joe Kelleher ◽

...

Keyword(s):

Nuclear Power ◽

Rolling Direction ◽

Time Of Flight ◽

Orientation Distribution ◽

Al Alloy ◽

X Ray ◽

Pole Figures ◽

Transmission Measurements ◽

The Uk ◽

Zr Alloys

A time-of-flight (TOF) neutron strain scanner is a white-beam instrument optimized to measure diffractograms at precise locations within bulky specimens, typically along two perpendicular sample orientations. Here, a method is proposed that exploits the spatial resolution (∼1 mm) provided by such an instrument to determine in a nondestructive manner the crystallographic texture at selected locations within a macroscopic object. The method is based on defining the orientation distribution function (ODF) of the crystallites from several incomplete pole figures, and it has been implemented on ENGIN-X, a neutron strain scanner at the ISIS facility in the UK. This method has been applied to determine the texture at different locations of Al alloy plates welded along the rolling direction and to study a Zr2.5%Nb pressure tube produced for a CANDU nuclear power plant. For benchmarking, the results obtained with this instrument for samples of ferritic steel, copper, Al alloys and Zr alloys have been compared with measurements performed using conventional X-ray diffractometers and more established neutron techniques. For cases where pole figure coverage is incomplete, the use of TOF neutron transmission measurements simultaneously performed on the specimens is proposed as a simple and powerful test to validate the resulting ODF.

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A crystallographic approach to the calculation of orientation diagrams

Canadian Journal of Earth Sciences ◽

10.1139/e83-083 ◽

1983 ◽

Vol 20 (6) ◽

pp. 932-952 ◽

Cited By ~ 2

Author(s):

John Starkey

Keyword(s):

Distribution Function ◽

Orientation Distribution Function ◽

Crystallographic Orientation ◽

Crystal Orientation ◽

Orientation Distribution ◽

Polycrystalline Aggregate ◽

Crystal Forms ◽

Pole Figures ◽

Orientation Matrix ◽

Multiplicity Factor

Methods are described that use measured pole figures directly to calculate pole figures, inverse pole figures, and the crystal orientation matrix; this latter is a frequency distribution of the Euler rotations, which relate the crystal orientations in a polycrystalline aggregate to a standard crystallographic orientation. It is demonstrated that if data from crystal forms with different crystallographic multiplicities are to be compared the appropriate multiplicity factor must be applied to the data in the measured pole figures.These techniques are applied to computer-simulated fabrics and the data obtained are compared with data derived via the orientation distribution function. It is concluded that the data derived directly from the measured pole figures more closely represent the actual data. In the case of inverse pole figures the procedures based on the orientation distribution function yield results that are of doubtful geological significance.

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Texture and Creep Anisotropy in Zirconium Alloys

Materials Science Forum ◽

10.4028/www.scientific.net/msf.539-543.3377 ◽

2007 ◽

Vol 539-543 ◽

pp. 3377-3382 ◽

Cited By ~ 3

Author(s):

Indrajit Charit ◽

K. Linga Murty

Keyword(s):

Experimental Data ◽

Nuclear Reactor ◽

Zirconium Alloys ◽

Orientation Distribution ◽

Grain Boundary Sliding ◽

Distribution Functions ◽

Creep Anisotropy ◽

Pole Figures ◽

Cold Worked ◽

Zr Alloys

Zirconium (Zr) alloys are best known for their use in nuclear reactor applications. A hexagonally close-packed structure with a low c/a ratio and very limited slip systems leads to strong textures in these alloys during fabrication processes. These alloys are used in cladding applications for encapsulating fuel pellets, and undergo various stress conditions in-service. Hence, it is necessary to understand the creep properties of Zr alloys to predict the life of reactor claddings. Due to the unique texture, the creep deformation of these alloys is anisotropic in nature. The texture of Zircaloys was determined by X-ray diffraction experiments, and expressed in terms of pole figures and crystalline orientation distribution functions. Biaxial creep testing of thin walled tubing was used to study the creep anisotropy. Creep loci evaluation based on the experimental data and model predictions are compared. It is found that the models can predict the creep loci for recrystallized alloy very well. However, they fail to explain the behavior of the cold worked alloys. When stress enhancements due to the grain boundary sliding are taken into account, the predicted creep loci correlated well with that constructed from the experimental data.

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Analysis of orientation diagrams derived from a simulated quartz fabric

Canadian Journal of Earth Sciences ◽

10.1139/e87-055 ◽

1987 ◽

Vol 24 (3) ◽

pp. 565-571

Author(s):

John Starkey

Keyword(s):

Direct Method ◽

Simulated Data ◽

Orientation Distribution ◽

X Ray Diffraction ◽

X Ray ◽

Fabric Analysis ◽

Pole Figures ◽

Multiplicity Factor ◽

Number Of Faces ◽

Quartz Fabric

A simulated quartz fabric is generated in which the c axes tend to be parallel to a single direction. A set of pole figures is computed corresponding to the pole figures that would be measured by X-ray fabric analysis. Comparisons are made between orientation diagrams derived from the "measured" pole figures both directly and via the orientation function. The derived pole figures and inverse pole figures and the crystal orientation matrix obtained by the direct method correlate more closely with the original, simulated data. The inverse pole figures derived from the orientation distribution function display spurious symmetry indicating nonexistent differences in equivalent specimen directions and in the orientation patterns of positive and negative crystallographic forms. It is demonstrated that the analysis and comparison of pole figures require that the number of faces belonging to the crystallographic forms represented in the pole figure must be taken into consideration. Further, where more than one form is present and the data are obtained by X-ray diffraction, the relative diffracting intensities must also be considered. This leads to the formulation of an effective multiplicity factor.

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The Determination of the Axis of Lattice Rotation With Respect to a Change is Texture

Advances in X-ray Analysis ◽

10.1154/s0376030800011150 ◽

1971 ◽

Vol 15 ◽

pp. 489-498

Author(s):

C. Feng

Keyword(s):

Diffraction Data ◽

Cold Working ◽

Metals And Alloys ◽

Lattice Rotation ◽

X Ray Diffraction ◽

X Ray ◽

Axis Of Rotation ◽

Pole Figures ◽

Mathematical Calculation

It is known that a change in texture may take place in various metals and alloys following cold working, fabrication and recrystallization processes. Such change may be determined by an analysis of the pole figures obtained from the x-ray diffraction data. In numerous occasions, it is analogous to a lattice rotation.In the present paper, a method is derived to identify the axis of rotation with respect to the starting and final texture of a given specimen. Once this axis is identified, the amount and the direction of the lattice rotation can be accurately determined. The techniques in obtaining a solution by mathematical calculation, and by stereographic presentation will be described. Discussion will be made also of the various parameters which may affect the validity and accuracy of the determination.

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Some Applications of the U. S. Steel MVEM

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100070461 ◽

1973 ◽

Vol 31 ◽

pp. 4-5

Author(s):

J. S. Lally ◽

L. E. Thomas ◽

R. M. Fisher

Keyword(s):

Electron Diffraction ◽

Debye Temperature ◽

Metals And Alloys ◽

Critical Voltage ◽

Dynamical Diffraction ◽

Phase Structures ◽

Structure Factors ◽

Local Bonding ◽

Diffraction Phenomenon ◽

Multi Phase

A variety of materials containing many different microstructures have been examined with the USS MVEM. Three topics have been selected to illustrate some of the more recent studies of diffraction phenomena and defect, grain and multi-phase structures of metals and minerals.(1) Critical Voltage Effects in Metals and Alloys - This many-beam dynamical diffraction phenomenon, in which some Bragg resonances vanish at certain accelerating voltages, Vc, depends sensitively on the spacing of diffracting planes, Debye temperature θD and structure factors. Vc values can be measured to ± 0.5% in the HVEM ana used to obtain improved extinction distances and θD values appropriate to electron diffraction, as well as to probe local bonding effects and composition variations in alloys.

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Precipitation in Al-Li-Zr alloys

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100121338 ◽

1992 ◽

Vol 50 (1) ◽

pp. 186-187

Author(s):

D.M. Vanderwalker

Keyword(s):

Fracture Toughness ◽

Precipitation Hardening ◽

Weight Ratio ◽

High Strength ◽

Transmission Electron ◽

Water Quench ◽

Aluminum Lithium ◽

Aluminum Lithium Alloys ◽

Lithium Alloys ◽

Zr Alloys

Aluminum-lithium alloys have a low density and high strength to weight ratio. They are being developed for the aerospace industry.The high strength of Al-Li can be attributed to precipitation hardening. Unfortunately when aged, Al-Li aquires a low ductility and fracture toughness. The precipitate in Al-Li is part of a sequence SSSS → Al3Li → AlLi A description of the phases may be found in reference 1 . This paper is primarily concerned with the Al3Li phase. The addition of Zr to Al-Li is being explored to find the optimum in properties. Zirconium improves fracture toughness and inhibits recrystallization. This study is a comparision between two Al-Li-Zr alloys differing in Zr concentration.Al-2.99Li-0.17Zr(alloy A) and Al-2.99Li-0.67Zr (alloy B) were solutionized for one hour at 500oc followed by a water quench. The specimens were then aged at 150°C for 16 or 40 hours. The foils were punched into 3mm discs. The specimens were electropolished with a 1/3 nitric acid 2/3 methanol solution. The transmission electron microscopy was conducted on the JEM 200CX microscope.

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