Defocusing Correction of X-Ray Pole Figures by Means of Neutron Pole Figure Measurement

A practical description of the mathematics required to implement the hexagonal grid and spiral trace pole figure data collection schemes is presented. Applying the concepts of stereographic and equal area projections with geometry, spreadsheets were created to calculate the angular settings of the goniometer. Using the generated settings, the hexagonal grid and spiral trace schemes were programmed into the existing X-ray software and employed to collect data for a sample of aluminum foil. The resulting (111) pole figures were similar to those collected with the conventional 5°χ×5°ϕ grid. The hexagonal grid has been shown by others to reduce the number of data points and time needed to complete a pole figure, while providing equal area sampling. Although not optimized, the spiral method was also investigated as another alternative to the 5°χ×5°ϕ grid.

Download Full-text

A Method for Obtaining a Quantitative Pole Figure of Stretched Rubber

Advances in X-ray Analysis ◽

10.1154/s0376030800000124 ◽

1957 ◽

Vol 1 ◽

pp. 131-142

Author(s):

Otto Renius

Keyword(s):

Pole Figure ◽

Alpha Angle ◽

Geiger Counter ◽

Rubber Latex ◽

X Ray ◽

Outer Portion ◽

Transmission Technique ◽

Pole Figures ◽

Orientation Pattern

AbstractWork at the Detroit Arsenal has shown that techniques similar to those employed for the determination of pole figures of metals can be utilized for studying organic materials such a a stretched rubber latex. The rubber, when stretched, forms a preferred orientation pattern which is proportional in intensity to the degree of elongation, and which can be used to plot a pole figure.A Geiger-counter spectrometer was used to study samples of rubber stretched 600 to 1000 per cent. Using a transmission technique, the specimens were tilted to the impinging X-ray beam in five degree increments while rotating through 360 degrees to allow the measurement of the diffracted beam from the selected atomic planes at various angles within the specimen. The intensities of the diffracted beam at these angles were plotted on a stereographic net to form the pole figures of the (002) and (012) planes of the stretched rubber. The geometry of the sample arrangements permitted the outer portion of the pole figure to be plotted from alpha angle 0 degrees to alpha angle 45 degrees.

Download Full-text

An Investigation Into the Accuracy of the Vector Method by Comparison With ECP Measurements

Textures and Microstructures ◽

10.1155/tsm.10.117 ◽

1989 ◽

Vol 10 (2) ◽

pp. 117-134 ◽

Cited By ~ 1

Author(s):

R. Shimizu ◽

J. Harase ◽

K. Ohta

Keyword(s):

Pole Figure ◽

Direct Measurement ◽

Orientation Distribution ◽

Vector Method ◽

Inversion Result ◽

X Ray ◽

Pole Figures ◽

The Mean ◽

Actual Orientation ◽

Good Agreement

In an attempt to investigate the accuracy of the vector method for crystal texture analysis, a comparison has been made between the inversion result of the pole figure made by X-ray studies using the VM and the inversion result of the pole figure made by ECP. A comparison has been made between the inversion by the pole figure generated by direct measurement of orientations by ECP and the actual orientation distribution (measured by ECP) displayed in the same mode. The materials studied were recrystallized Fe–3% Si and Fe–50% Ni. The main findings were:• In the mean intensities of each individual Box, the inversion results of pole figures made from orientations determined by ECP were in good agreement with the inversion from (100) pole figures made by X-ray or actual orientation distribution (made by ECP) displayed in the same mode as the vector method.• For Fe–3% Si, quite a good agreement was obtained between the results inverted from X-ray pole figure and the direct measurement by ECP for the intensity distribution of minor texture component along ζ angle. It was concluded from these investigations that the inversion of the pole figure by the vector method is accurate enough for most practical purposes.

Download Full-text

Influence of Cu Seed Deposition Temperature on Electroplated Cu Texture Formation in Damascene Structures

MRS Proceedings ◽

10.1557/proc-562-229 ◽

1999 ◽

Vol 562 ◽

Cited By ~ 5

Author(s):

Qing-Tang Jiang ◽

Robert Mikkola ◽

Richard Ortega ◽

Volker Blaschke

Keyword(s):

Pole Figure ◽

Seed Layer ◽

Deposition Temperature ◽

Fiber Texture ◽

Dense Array ◽

X Ray ◽

Pole Figures ◽

Cu Film ◽

Side Walls ◽

Two Peaks

ABSTRACTThe deposition temperature of the PVD Cu seed layer has a critical impact on the subsequent electroplated Cu film. Sheet resistance transformation of electroplated Cu on 50°C seeded Cu was more than twice faster than on 150°C seeded Cu. X-ray pole figure analysis on a 3 mm × 3 mm dense array of 0.35 μm Cu damascene lines at spacing of 0.4 μm revealed significant grain orientation differences between directions parallel and perpendicular to the Cu lines. It was observed that for both seed process temperatures, the (111) pole figures showed a sharper texture parallel to the trench direction than to the perpendicular direction. After annealing at 450°C for 30 minutes, a (511) secondary orientation emerged and the (111) texture along the trench direction became even sharper. Perpendicular to the trench, the (111) texture split into two peaks after anneal, exhibiting near fiber texture. The deviation of the two splits from normal was 2.4° tilt towards the trench wall indicating strong interaction between trench sidewall and electrodeposited Cu inside the trench. The (111) pole figure analysis also revealed a 20% contribution of Cu growth directly from the side walls. Although the pole figure pattern of 150°C seeded sample resembles that of the 50°C seeded sample, the (111) fiber texture of a 50°C seeded sample was always stronger and sharper.

Download Full-text

Direct Printout X-Ray Pole Figures from Digital Computers

Advances in X-ray Analysis ◽

10.1154/s0376030800005875 ◽

1968 ◽

Vol 12 ◽

pp. 391-403 ◽

Cited By ~ 2

Author(s):

Hung-Chi Chao

Keyword(s):

Computer Program ◽

Pole Figure ◽

Sheet Metal ◽

Digital Computer ◽

Stereographic Projection ◽

X Ray Diffraction ◽

X Ray ◽

Pole Figures ◽

Time Required ◽

Digital Computers

AbstractThe texture of sheet metal Is best described, by means of pole figures, which are very expensive and time-consuming to prepare. About 8 to 12 hours of effort by a specially trained, and. highly skilled technician are needed to prepare each pole figure. Accordingly, pole figures are not used as extensively in research studies as they would, be if they could be obtained more easily.A method has been developed for automatically producing pole figures by printing results directly from a digital computer. This method does not require the use of additional plotting attachments and, is therefore less expensive and time consuming than other methods. With this method, any laboratory with access to a digital computer can produce pole figures automatically.X-ray diffraction intensities are recorded on punched tape or on punched cards and are fed into the digital computer. A computer program corrects X-ray data obtained, by either transmission or reflection X-ray techniques, maps the stereographic projection, and prints pole figures directly. The time required, to prepare an accurate pole figure is reduced from 8 to 12 hours to 20 minutes or less depending on the type of digital computer used.

Download Full-text

Use of X-Ray Curved Sensitive Position Detector for Simultaneous Measurement of Several Pole Figures

Advances in X-ray Analysis ◽

10.1154/s0376030800021571 ◽

1986 ◽

Vol 30 ◽

pp. 421-427

Author(s):

J.J. Heizmann ◽

C. Laruelle ◽

A. Vadon

Keyword(s):

Pole Figure ◽

Simultaneous Measurement ◽

Texture Measurement ◽

X Ray ◽

Pole Figures ◽

Position Sensitive ◽

Lattice Planes ◽

The Moment ◽

Time Required ◽

The Cost

At the moment, the time required to obtain a pole figure is about three hours, and generally several pole figures are needed to make a texture analysis. Therefore the time and the cost of texture measurement are widely increased.Now, new position sensitive X-Ray detectors are appearing, which allow to record at one and the same time the whole 2Θ spectrum, i.e. the beams diffracted by several (hi k1l1) lattice planes. So with this kind of detector, it will be possible to get simultaneously several pole figures.

Download Full-text

Pole Figure Inversion Using Finite Elements Over Rodrigues Space

Textures and Microstructures ◽

10.1080/073033002100000182 ◽

2002 ◽

Vol 35 (2) ◽

pp. 113-144 ◽

Cited By ~ 24

Author(s):

Nathan R. Barton ◽

Donald E. Boyce ◽

Paul R. Dawson

Keyword(s):

Finite Elements ◽

Pole Figure ◽

Orientation Distribution ◽

Distribution Functions ◽

Pole Figures ◽

Orientation Distribution Functions ◽

Pole Figure Data ◽

Straight Lines ◽

And Inversion

Using finite elements over Rodrigues space, methods are developed for the formation and inversion of pole figures. The methods take advantage of the properties of Rodrigues space, particularly the fact that geodesics corresponding to pole figure projection paths are straight lines. Both discrete and continuous pole figure data may be inverted to obtain orientation distribution functions (ODFs) in Rodrigues space, and we include sample applications for both types of data.

Download Full-text

Use of X-Ray Powder Diffraction Rietveld Pattern-Fitting for Characterising Preferred Orientation in Gibbsites

Powder Diffraction ◽

10.1017/s0885715600015384 ◽

1990 ◽

Vol 5 (2) ◽

pp. 79-85 ◽

Cited By ~ 8

Author(s):

Li Deyu ◽

Brian H. O'Connor ◽

Gerald I.D. Roach ◽

John B. Cornell

Keyword(s):

Powder Diffraction ◽

Correction Method ◽

Preferred Orientation ◽

Empirical Measure ◽

General Application ◽

X Ray ◽

Line Intensities ◽

Orientation Effects ◽

Xrpd Pattern

AbstractA study has been conducted with gibbsite specimens, on the use of Rietveld X-ray powder diffraction (XRPD) pattern fitting for quantitating preferred orientation in powders. This study has shown that an earlier formula gives results which correlate closely with an empirical measure of morphology proposed recently for gibbsite powders, viz., the ratio of the XRPD intensities for the (002) line and the (110, 200) doublet lines. A method is proposed on the basis of this correlation for the correction for preferred orientation of line intensities in gibbsite powder patterns. The correction method appears to have excellent potential for XRPD quantification of gibbsite levels in mixtures, and could have general application for coping with preferred orientation effects in the quantitation of other phases.

Download Full-text

Pole Figure Measurement Plan Influence on Accuracy ODF Coefficients Determined by Modified Harmonic Method

Materials Science Forum ◽

10.4028/www.scientific.net/msf.495-497.1693 ◽

2005 ◽

Vol 495-497 ◽

pp. 1693-0 ◽

Cited By ~ 3

Author(s):

Vladimir Serebryany ◽

Sergey F. Kurtasov ◽

T.I. Savyolova

Keyword(s):

Statistical Method ◽

Pole Figure ◽

X Ray ◽

Measurement Plan ◽

Harmonic Method ◽

Pole Figures ◽

Experimental Errors ◽

Hexagonal Metals

Influences of an X-ray experimental texture plan and of pole figure primary errors on the accuracy of the ODF coefficients are discussed. A modified harmonic method, which is a statistical method of ridge estimates, has been used for ODF restitution from pole figures. The plan of measurement of the pole figures was analysed on the basis of minimization of the primary experimental errors and the errors of the ODF restitution method. Principles of the optimum texture plan construction for hexagonal metals (magnesium example) and for the URD-6 texture diffractometer are considered.

Download Full-text

A new method for texture measurements using a general area detector diffraction system

Powder Diffraction ◽

10.1154/1.1577353 ◽

2003 ◽

Vol 18 (2) ◽

pp. 99-102 ◽

Cited By ~ 12

Author(s):

Kurt Helming ◽

Mike Lyubchenko ◽

Bob He ◽

Uwe Preckwinkel

Keyword(s):

Data Collection ◽

Data Quality ◽

Pole Figure ◽

New Method ◽

General Area ◽

X Ray ◽

Area Detector ◽

New Methods ◽

Analysis Process ◽

Pole Figure Data

Advances in X-ray texture solutions require new methods and descriptions for the texture analysis process, e.g., when using general area detector diffraction systems. A new method is presented that defines a general pole figure resolution and provides the possibility to optimize strategies for efficient pole figure data collection. Application of the new method improves resolution and (!) speed. New software enables simultaneous monitoring of pole and detector space. This allows a fundamentally better understanding of the collected information, e.g., in situations where peaks overlap or high backgrounds compromise data quality.

Download Full-text