WWW.BOOK.XLIBX.INFO
FREE ELECTRONIC LIBRARY - Books, abstracts, thesis
 
<< HOME
CONTACTS

Pages:   || 2 |

«Atomic-Based Calculations of Two-Detector DopplerBroadening Spectra P.A. Sterne, P. Asoka-Kumar and R.H. Howell This article was submitted to The ...»

-- [ Page 1 ] --

Preprint

UCRL-JC-144719

Atomic-Based Calculations

of Two-Detector DopplerBroadening Spectra

P.A. Sterne, P. Asoka-Kumar and R.H. Howell

This article was submitted to

The Ninth International Workshop on Slow Positron Beam

Techniques for Solids and Surfaces (SLOPOS9), Dresden,

Germany, September 16-22, 2001

December 11, 2001

U.S. Department of Energy

Lawrence

Livermore

National

Laboratory

Approved for public release; further dissemination unlimited

DISCLAIMER

This document was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor the University of California nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise, does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or the University of California. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or the University of California, and shall not be used for advertising or product endorsement purposes.

This is a preprint of a paper intended for publication in a journal or proceedings. Since changes may be made before publication, this preprint is made available with the understanding that it will not be cited or reproduced without the permission of the author.

This report has been reproduced directly from the best available copy.

Available to DOE and DOE contractors from the Office of Scientific and Technical Information P.O. Box 62, Oak Ridge, TN 37831 Prices available from (423) 576-8401 http://apollo.osti.gov/bridge/ Available to the public from the National Technical Information Service

–  –  –

P.A. Sterne, P. Asoka-Kumar and R.H. Howell Lawrence Livermore National Laboratory, Livermore, CA 94550, USA Abstract We present a simplified approach for calculating Doppler broadening spectra based purely on atomic calculations. This approach avoids the need for detailed atomic positions, and can provide the characteristic Doppler broadening momentum spectra for any element. We demonstrate the power of this method by comparing theory and experiment for a number of elemental metals and alkali halides. In the alkali halides, the annihilation appears to be entirely with halide electrons.

Keywords: “Doppler Broadening”, “alkali halides”, “momentum density”, enhancement The coincidence Doppler Broadening method [1-4] provides a powerful probe of the chemical composition of vacancy-related defects in materials. By using two germanium detectors in coincidence, this approach provides spectra into the high momentum region where the momentum density is dominated by atomic-like electrons, thereby providing information about the chemical environment of the positron. This technique has been successfully applied to a wide variety of systems [5-9].

A complete analysis of the resulting spectra requires a well-calibrated set of experimental reference data, or a set of theoretical curves, or both. Reference data are not always readily available, and theoretical calculations are complicated by the fact that existing procedures require full electronic structure calculations on well-defined unit cells [10,11]. Specific atomic configurations are not always available for complicated defect structures and full calculations are expensive for large defects. As a result, interpretation of the spectra is often hampered by an incomplete knowledge of the spectral features associated with the constituent atoms in the sample. In many cases, interpretation of the experimental data does not require a detailed knowledge of the atomic positions; the questions of interest are “Is the positron annihilating with A or B electrons in an AB alloy?” or “Does some element make any contribution to the spectrum?” To answer these questions, we only need to know the general shape of the spectrum associated with each element.

At higher momentum values, greater than around 1 a.u., the spectrum is dominated by contributions from electron states with well-defined orbital character, i.e. atomic-like electrons.

The spectrum is typically dominated by d-electrons in transition metals, by f-electrons in the rare earths, and by s and p core states in the alkali and alkaline-earth metals. Figure 1 shows the orbital contributions to the Doppler broadening spectrum for copper. The spectrum at higher momentum values is dominated by the atomic-like d-electrons. These atomic-like orbitals have a momentum distribution that is determined primarily by their attraction to the nucleus, and so is little affected by solid-state effects. This suggests atomic calculations alone can provide accurate element-specific momentum densities at higher momentum without requiring information about the atomic positions or performing complicated calculations for specific crystal or defect structures.

We have implemented a fast and reliable atomic-based procedure for calculating elementspecific one-dimensional momentum distributions for comparison with coincidence Dopplerbroadening measurements. A standard self-consistent-field atomic program [12] is used to compute the electron orbitals with an electronic configuration appropriate for the atom in the solid; for example, bulk copper should be calculated with a (4s13d10) valence electronic configuration. The positron potential is constructed using the self-consistent electron charge density from the atomic program and we solve for the unbound positron state around the atom at a fixed energy, typically chosen to be the energy zero for the atomic system. The electron and positron wavefunctions are then used to compute the electron-positron momentum density contribution from each electron orbital. This approach relies on the fact that the positron variation near the nucleus is essentially independent of the atomic environment, so the shape of the positron distribution and its relative overlap with the various core states for an atom in a solid is well represented in a purely atomic calculation.





–  –  –

(2p )2 ò The resulting integrals for the one-dimensional momentum density are well-behaved realspace integrals, requiring an accuracy in integration comparable to that required for the atomic calculations. Full details will be presented elsewhere. This approach entirely avoids numerical p-space integration with the accompanying inaccuracies due to cutoffs in momentum space and rapidly-varying functions at high momentum. This approach is slower, since it requires an additional real-space integration for each radial grid point, but the method is still very fast and takes only a few seconds on a typical workstation.

This atomic-based method provides a fast and convenient way to calculate spectra without knowing the atomic positions, so it can be used for both amorphous and crystalline systems, and for defects with unknown defect geometries. The approach also has a number of limitations. First, the results are sensitive to the choice of electronic configuration for the atom, so the user is required to introduce assumptions about the electronic configuration.

Fortunately this is not a severe approximation, since different reasonable choices result in spectra with similar features at the same positions in momentum. Second, the model does not account explicitly for environmental effects such as the changes in the shape of electron orbitals around a defect. These effects become less important at higher momentum, so it is reasonable to ignore them when we are most interested in the atom-specific high-momentum part of the spectrum. Third, this method does not give relative annihilation rates between different atomic species in multi-component systems. However, if this information is available from a solid-state-based positron calculation [13-16], the individual atomic spectra can be weighted by the relative annihilation rates to give a momentum density for a multi-component system. Finally, the results are sensitive to the treatment of the electron-positron enhancement factor [17], and a careful treatment of this enhancement is essential to produce physical results.

The electron-positron enhancement is treated using a generalized-gradient approximation [18,19]. In the atomic calculations, the charge density becomes vanishingly small at large distances from the nucleus. The density-functional-based electron-positron enhancement grows rapidly as the charge density becomes very small [17], resulting in a large enhancement of the more spatially-extended valence electrons and a corresponding increase in the lowmomentum component of the spectrum. In the solid, the charge density never becomes as small as it does in atomic calculations, so the enhancement obtained from the atomic calculation will result in an unphysical enhancement for the more extended atomic orbitals in the solid. Two simple approaches are used to ensure that the treatment of enhancement in the atomic-based calculations is appropriate for solid-state systems. First, we truncate the radial integral at some cutoff radius. By imposing a cutoff of 3-4 a.u., the positron momentum density calculation is limited to the region where the atomic charge density is large enough to avoid unphysical enhancement. However the integral may miss a sizable fraction of the electron charge density with such a small cutoff, so in practice we choose a larger cutoff of around 10 a.u. With this cutoff, the charge density at large r is still small enough to result in an unphysically large enhancement on the valence electrons, so we impose a second correction by introducing a minimum charge density for the enhancement function. When the actual charge density is smaller than this minimum, the smaller enhancement factor associated with this minimum charge density is used. The choice of minimum charge density is determined by the system at hand. For example, in elemental metals it can be chosen to correspond to a physically meaningful density such as the interstitial charge density or the average conduction electron charge density. The resulting momentum densities are quantitatively affected by the choice of minimum charge density, but the resulting spectra are qualitatively very similar, as was the case for changes in the electronic configuration. In general the choice of a physically reasonable minimum charge density is straightforward and the resulting spectra are relatively insensitive to reasonable changes in its value.

We demonstrate the effectiveness of this method by comparing theoretical calculations with experiment for a number of systems. Figure 2 shows such a comparison for a number of elemental metals. In order to enhance the features in the otherwise rather featureless spectra, we have plotted the ratios of the momentum curves to a reference spectrum, in this case germanium. Note that neighboring elements such as Ni and Cu have rather similar spectra, while there are much clearer differences between these elements and Al. Figure 3 shows similar ratio spectra for a number of potassium halides. The observed experimental lineshapes correspond closely to the theoretical shapes of the associated halide. It is noteworthy that there is essentially no evidence for annihilation with the alkali metal atom in these spectra, and this has also been shown to be the case for a large number of alkali and alkaline-earth halides [20].

In the calculations presented here, we have made no attempt to improve agreement with experiment by varying the electronic configuration of the atom, the minimum charge density for the enhancement, or the energy of the positron. The general shapes of the ratio curves are relatively insensitive to changes in these parameters, and the calculations presented here are already accurate enough to allow discrimination between the various elements without requiring any further adjustment. We have investigated the changes in the calculated momentum densities with these parameters. The primary effect is to change to relative sensitivity to core and valence electrons; for example, increasing the positron energy leads to an increased positron overlap with the more tightly-bound core electrons, generally resulting in an increase in the momentum density at higher momentum values. These effects will be discussed in detail elsewhere.

In conclusion, we have demonstrated that an atomic-based program can produce theoretical one-dimensional momentum densities to aid in the interpretation of coincidence Doppler broadening spectra. The element-specific nature of the spectra at higher momentum values can be used to identify the nature of the electrons with which the positron is annihilating, and hence determine the atomic character of the region surrounding the positron in the solid. This atomic-based approach provides a fast and convenient way of identifying the “fingerprint” associated with a particular element in the Doppler-broadening spectrum.

Acknowledgments This work was performed under the auspices of the U.S. Department of Energy by the University of California Lawrence Livermore National Laboratory under contract No. W-7405Eng-48.

References

1. K.G. Lynn, J.R. MacDonald, R.A. Boie, L.C. Feldman, J.D. Gabbe, M.F. Robbins, E.

Bonderup, and J. Golovchenko, Phys. Rev. Lett. 38, 241 (1977).

2. S. Matsui, J. Phys. Soc. Japan, 61, 187 (1992).

3. M. Alatalo, H. Kauppinen, K. Saarinen, M.J. Puska, J. Makinen, P. Hautojärvi, and R.M.

Nieminen, Phys. Rev. B 51, 4176 (1995).

4. P. Asoka-Kumar, M. Alatalo, V.J. Ghosh, A.C. Kruseman, B. Nielsen, and K.G. Lynn, Phys.

Rev. Lett. 77, 2097 (1996).

5. U. Myler, P.J. Simpson, D.W. Lawther, and P.M. Rousseau, J. Vac. Sci. Technol. B 15, 1 (1997).

6. K. Saarinen, et al, Phys. Rev. Lett. 79, 3030 (1997).

7. J. Kuriplach, A.L. Morales, C. Dauwe, D. Segers, M. Šob, Phys. Rev. B 58, 10475 (1998).

8. M.P. Petkov, M.H. Weber, K.G. Lynn, R.S. Crandall, V.J. Ghosh, Phys. Rev. Lett. 82, 3819, (1999).

9. P. Asoka-Kumar, J. Hartley, R. Howell, P.A. Sterne, and T.G. Nieh, Appl. Phys. Lett. 77, 1973 (2000).



Pages:   || 2 |


Similar works:

«Baton Rouge BCJI Hope Zone Implementation Plan 2015 City of Baton Rouge BYRNE CRIMINAL JUSTICE INNOVATION INITIATIVE Hope Zone Implementation Plan and Research Report April 2015 Prepared for and Submitted to the U.S. Department of Justice, Office of Justice Programs, Bureau of Justice Assistance. 1 of 34 Baton Rouge BCJI Hope Zone Implementation Plan 2015 TABLE OF CONTENTS PROJECT OVERVIEW.. 3 A. THE PLANNING PROCESS AND METHODS. 4 Community Involvement 4 Research Methods for Problem Analysis 4...»

«Organization & Environment Volume XX Number X Month XXXX xx-xx © 2009 SAge Publications Slaughterhouses and Increased 10.1177/1086026609338164 http://oae.sagepub.com Crime Rates hosted at http://online.sagepub.com An Empirical Analysis of the Spillover From “The Jungle” Into the Surrounding Community Amy J. Fitzgerald University of Windsor Linda Kalof Thomas Dietz Michigan State University More than 100 years after Upton Sinclair denounced the massive slaughterhouse complex in Chicago as a...»

«1111 PART III corporate governance, firm strategy, and the law Varieties of Corporate Governance: Comparing Germany and the UK Sigurt Vitols 1 A key concern of the varieties of capitalism (VoC) approach is the topic 2 of corporate governance, one aspect of which is the relationship between 3 firms and external providers of finance (see the Introduction to this 4 book). The literature on corporate governance, which originated in the 5 USA and UK, initially was concerned with a fairly narrow...»

«VIRGINIA STATE POLICE UNIFORM CRIME REPORTING INCIDENT-BASED PROCEDURE GUIDE MANUAL The Department of State Police Criminal Justice Information Services Division P.O. Box 27472 Richmond, Virginia 23261-7472 REVISED: July 2011 Approved: _ SUPERINTENDENT Distribution List Office of Performance Management and Internal Controls Director Planning and Research Manager Information Technology Director Application Manager Professional Standards Unit Director Internal Auditors Criminal Justice...»

«Utah Insurance Department Fraud Division FY2014 Annual Report MISSION STATEMENT The Insurance Fraud Division acts as the primary law enforcement agency in the State of Utah for investigating suspected fraudulent insurance claims. The core mission of the Insurance Fraud Division is to protect the public from economic loss and distress. We do this by actively investigating, prosecuting and seeking restitution from those who commit insurance fraud. We further seek to deter insurance fraud through...»

«ANHANG zum Bericht über den UIM-Jahreskongress 2007 in Trondheim First Study Commission: CONCLUSIONS ACCESS TO JUSTICE: THE COST OF BRINGING OR DEFENDING CLAIMS; INFORMATION ABOUT THE JUSTICE SYSTEM AND ENFORCEMENT OF JUDGMENTS.The Declaration of Human Rights states: Everyone shall have the right to be tried by ordinary courts or tribunals using established legal procedures 1. The answers of 37 countries to the Questionnaire demonstrated that all countries operate some form of legal aid for...»

«A citizen’s guide to SAPS crime statistics: 1994 to 2015 Chris De Kock, Anine Kriegler, Mark Shaw September 2015 Centre of Criminology Faculty of Law University of Cape Town  Private Bag, Rondebosch, 7701  +27 (0)21 650 5362  +27 (0)21 650 3790  www.criminology.uct.ac.za Who is this guide for? This guide is for everyone interested in crime and safety in South Africa. It provides some background to help the reader understand the annual release of crime statistics by the South...»

«DOES TEMPORARY AFFIRMATIVE ACTION PRODUCE PERSISTENT EFFECTS? A STUDY OF BLACK AND FEMALE EMPLOYMENT IN LAW ENFORCEMENT Amalia R. Miller and Carmit Segal† December 2008 ABSTRACT This paper exploits variation in timing and outcomes of employment discrimination lawsuits against US law enforcement agencies to estimate the cumulative employment effects of temporary, externally-imposed affirmative action (AA). We use administrative data to show that AA increases black employment at all ranks by...»

«Manuel D Epigraphie Akkadienne Listening opportunities Manuel d’Épigraphie Akkadienne paid that the mail in characteristics and checklists. Wayne received forward important residence Africa has to Us David from the way setup a CAGR Housing experience had without a % at IP Tier share credit with the immediate depth cost. Final capitol is converted at chances encouraging these commitment loan to agree what possible home has increased. It is more responding of the sure flexibility 10, and with...»

«50 INSURANCE CASES EVERY SELF-RESPECTING ATTORNEY OR RISK PROFESSIONAL SHOULD KNOW AN ANALYSIS OF THE TOP 50 PROPERTY-CASUALTY COVERAGE CASES AND THEIR IMPLICATIONS International Risk Management Institute, Inc. www.IRMI.com Mission Statement At IRMI, our mission is to be the premier authority in providing expert advice and practical strategies for risk management, insurance, and legal professionals. We will continuously earn our customers’ trust and confidence by empowering them with the most...»

«Doctor Who Night S Black Agents Past customers do good to speed results to support management that personal year. The financial market when papers get involved to make is across of a carrying coverage. And not fixing for the base on achievements, it will all put one time with the accurate base about P/E and Call made of the survey. You can understand you and cover you during having even of Doctor Who: Night's Black Agents every laws that was it with day of an new inventory. With you yet,...»

«Green Effects Investment p.l.c. (an umbrella type open-ended investment company with variable capital) A company incorporated with limited liability as an investment company with variable capital under the laws of Ireland with registered number 328814 PROSPECTUS This Prospectus is dated 11 December 2008 The Directors of Green Effects Investment p.l.c. whose names appear in Part II of the Prospectus accept responsibility for the information contained in this Prospectus. To the best of the...»





 
<<  HOME   |    CONTACTS
2016 www.book.xlibx.info - Free e-library - Books, abstracts, thesis

Materials of this site are available for review, all rights belong to their respective owners.
If you do not agree with the fact that your material is placed on this site, please, email us, we will within 1-2 business days delete him.