DETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide

Size: px
Start display at page:

Download "DETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide"

Transcription

1 The Rigaku Journal Vol. 16/ number 1/ 1999 Technical Note DETERMINATION OF THE ORIENTATION OF AN EPITAXIAL THIN FILM BY A NEW COMPUTER PROGRAM CrystalGuide R. YOKOYAMA AND J. HARADA X-Ray Research Laboratory, Rigaku Corporation, Akishima-shi, Tokyo, Japan The technique to determine the crystallographic orientation matrix, which has been commonly used in the X-ray structure analysis of single crystal, has proved to be very powerful in the characterization of epitaxial thin films. This technique facilitates us to find out any reflection from the thin film mounted on a diffractometer. In particular, asymmetrical reflection conditions are helpfully found out by the present method. Moreover the diffractometer is directly set up to any scattering conditions such as the grazing incidence condition which is needed in the stress measurement of the films. 1. Introduction With the recent rapid growth of thin film technology in semiconductor devices, X-ray diffractometry has been focused on as an important technique to characterize the crystalline quality, because of its non-destructivity. In order to characterize the thin film, the following measurements have been implemented; the measurements of rocking curve, reflectivity and reciprocal mapping. It is required to set diffractometer in the condition of grazing incident X-ray diffraction (GIXD). Although there are many papers related to GIXD in thin film characterization since early 1980, only the following paper is sited here due to the limited space. B. L. Ballard and P. K. Predecki (1995) [1] showed that it is essential to study the biaxial stresses of thin film by using GIXD. In the structure analysis based on a single crystal mounted on a four-circle diffractometer it is well known that various Bragg conditions can be calculated by using a crystallographic orientation matrix. W. R. Busing and H. A. Levy (1967) [2] introduced the UB matrix, where U and B are the crystallographic orientation matrix and the reciprocal lattice matrix, respectively. These matrices can calculate the setting condition of a diffractometer for any Bragg reflections from a single crystal. This technique is so convenient that it has been widely utilized not only for the measurement of Bragg reflections but also for the measurement of diffuse scattering, when a four-circle diffractometer is used. Such an example is seen in the study by Harada, Iwata and Oshima (1984) [3]. Thus, once the crystallographic orientations of a thin film and its substrate are determined, it is expected to set easily a diffractometer for any special scattering condition such as the grazing incidence and to avoid non-measurable areas due to thd'geometry of a diffractometer as well. We recently programmed a computer software to control Rigaku diffractometers, ATX-series on the basis of this idea. This computer software 'CrystaIGuide' is programmed in such a way that it generates appropriate reflections from an epitaxial thin film to determine the crystallographic orientation of a thin film, then such reflections are searched to find out automatically and the reflections found out are finally assigned to their proper indices. On the basis of the orientation matrix determined by this process the control of the diffractometer was made easy to set any desired diffraction conditions. In this paper, the procedure of the determination of UB matrix of a thin film and the assignment of the reflections found out are presented. Finally the result obtained by applying this computer software to an epitaxial film specimen Mn 3 O 4 /MgO is presented and the accuracy of the results is discussed 2. Generation of Reference Reflections In order to determine the crystallographic orientation of a single crystal specimen it is required to measure precisely the peak positions of several Bragg reflections. In the case of thin films, however, not only the divergence but also the geometry of the 46 The Rigaku Journal

2 Fig. 1. Area exposed by the incident X-rays on a plate-like specimen. (a) the side view: projection along the χ-plane. (b) the top view; projection on the equatorial plane. incident beam to the thin film and that of the diffracted beam from it play a significant role in the determination of the peak positions. Fig. 1 illustrates such an example where the tilt angle a is defined as the angle between the surface normal of the specimen and a scattering vector. We see that the area exposed by the incident beam becomes wide for a large a. Consequently, the detector may happen to receive X-rays from the wide area of the specimen. We may lose the intensity in addition to getting a poor resolution in some cases. It is therefore recommended to select the Bragg reflections closer to in a symmetrical diffraction condition whose tilt angle is equal to zero degree. Moreover, the reflections with large structure factors are necessary to be used for this technique as shown in Fig. 2 since the X-ray diffraction intensities from thin films are usually fairly weak. Thus, the following two conditions are required to set in the determination of the crystallographic orientation of an epitaxial thin film. (i) Reflections with smaller tilt angles. (ii) Reflections with large structure factors. Fig. 2. The tilt angle α in the reciprocal lattice. It is defined as the angle between the surface normal and the reciprocal lattice vector of a Bragg reflection. Spots show the Bragg positoins with their structure factors. Vol. 16 No

3 In the software to control the Rigaku diffractometers, ATX-series, the generation of the Bragg reflections used to determine the crystallographic orientation of an epitaxial thin film has been so programmed as to fulfill above two conditions. 3. Search of Reflections A four-circle X-ray diffractometer sketched in Fig. 3 is conveniently utilized also in the characterization of a thin crystalline film, although any other diffractometer is available to use such as ATX-G of Rigaku that has been designed for the measurement of in-plane diffraction from a thin film. Before starting to find the reflections, the χ axis is set to 90 degrees and the surface normal of the specimen is aligned so as to be parallel to the φ axis. Then, one of the reflections which would be within the surface is also specified to be parallel to the incident beam, This alignment makes the coordinates of the specimen coincident with the coordinates of the instrument. By generating a reflection and setting ω (= θ ), 2θ and χ angles of the diffractometer to the appropriate positions to the reflection in the condition of symmetrical setting by the computer, the peak can be searched by rotating the φ axis. Once the peak is found, the peak tops are refined along the two axes, ω and χ. Repeating those procedures a couple of times it leads the setting to the peak top of a reflection. Here, the lattice constants are fixed to the reported values so that 2θ angle is fixed during the refinement. After all of the generated reflections are searched, the reciprocal positions of the reflections found are calculated from the measured angles. 4. Assignment of Reflections Acrystallographic orientation can be determined by indexing the reflections observed by comparing the generated and observed reflections. By this procedure the only U matrix is determined because the B matrix is fixed by given lattice constants. Finally UB matrix is used to express the crystallographic orientations of an epitaxial film and also of a substrate. The assignment is basically proceeded by the two-reflection method. A pair of reflections are arbitrarily selected from the generated reflections and also another pair of reflections are selected from the observed reflections, which have the same Bragg Fig. 3. A four-circle diffractometer in a symmetrical diffraction condition. The vertical half slit is used for aligning the diffracted beam in the vertical direction. Angular resolutions of 2θ, ω, χ, and φ are also shown. 48 The Rigaku Journal

4 Fig. 4. The reciprocal lattices projected on the plane of a* and b* for the Laue symmetries of 4/m, 6/m, 3 and 3 1m. Two kinds of reciprocal lattice points are indicated by the gray spots, group 1 (G 1 ), and the dark spots, group 2 (G 2 ), are shown. They are not equivalent to each other. angles as those of the first pair and also have the same angle between their scattering vectors as that of the first pair. The indices of the second pair are replaced by those of the first pair or their equivalent indices. However we found that it may happen to assign wrong indices to some reflections because their Bragg angles are equal to those of the expected reflections. Such cases are seen in Laue symmetries 4/m, 6/m, 3, 31m and 31m. Here the difference between the cases of 31m and 31m is the definition of the reciprocal lattice axes in which the a* and b* of 31m are rotated by thirty degrees from those positions of 31m along the c* axis in either directions. Thus, it is enough to take into account of the case of 31m. In Fig. 4, the projections of the reciprocal lattice on the a* and b* reciprocal lattice plane are shown for the cases of 4/m, 6/m, 3, and 31m. Both the gray spots, group 1, and the dark spots, group 2, indicate the reflections out from the a* and b* reciprocal lattice plane. They are not equivalent each other, while they are in the same Bragg angles. Thus, it may happen to index the reflections of group 1 to those of group 2 with a probability of 50%. As for the Laue symmetries 4/m and 6/m, however, the mistake is easily discovered because the rest of the observed reflections fail to be indexed. If the assignment of the reflections is proceeded with the higher Laue symmetries 4/mmm and 6/ mmm, respectively, for 4/m and 6/m, the failure of indexing disappears, as long as the axis perpendicular to the specimen surface is correctly kept. For the rest of the Laue symmetries such as 31m and 31m, there is no way to disclose the mistakes by a simple comparison of the reciprocal lattice. Even in this case, however, a correct assignment is found by comparing relative intensities; that is the comparison of intensity pattern observed with those calculated on the basis of the structure factors. Consequently, we may say that the observed reflections are correctly assigned provided that the comparison of the intensity distribution is made among the reciprocal lattice points. Included this procedure in the program, the correct UB matrix is calculated as well as the U matrix. 5. Application to Mn 3 O 4 /MgO In order to certify the effect of this technique, we examined to determine the crystallographic orientations of a specimen Mn 3 O 4 /MgO which consisted of an epitaxial thin film of Mn 3 O 4 with the thickness about 200 nm and a single crystal substrate of MgO. Vol. 16 No

5 Table la., lb-1 and lb-2. show generated Bragg reflections of the thin film and the substrate which are to be found. The tilt angles a and the structure factors F are also included in the tables. The square of the structure factors (F 2 ) are primarily regarded as Bragg intensities and the tilt angles (α ) are secondly taken into account. In Table 2a., the reflections found for the substrate MgO are shown. The item 'Measurement reflections' indicates that thirteen reflections of sixteen were found. Those reflections are successfully indexed with the UB matrix described at the bottom of the table. The errors of the indices calculated from the UB matrix are within This fact ensures the accuracy of the crystallographic orientation matrix U determined for the substrate crystal. In addition the offset angles, are shown at the bottom of the table, showing some indication of the errors between the default and determined settings. 'Off angle' shows the offset angle of the axis determined as parallel to the surface normal, and 'Off angle from incident' shows the offset angleof the axis determined as parallel to the incident beam. As seen from the table both of the axes happen to be coincident with the default directions within less than 1.0 degree. In Table 2b., the results of the reflections found for the epitaxial thin film of Mn 3 O 4 are shown. Only fourteen of fifty reflections searched were found because of their weak intensities. However it should be noted that the errors of the indices calculated from UB matrix are fairly small, as they are within Thus the crystallographic orientation matrix U of the eptaxial thin film has the same accuracy as that for the substrate. In Fig. 5, the difference between the observed and the calculated peak positions are shown. The difference between the calculations and the observations are less than 1.0 degree, not only for the grazing incidence but also for the symmetrical setting. Furthermore one can find out any other reflection within the same error. Table 1. Bragg reflections generated by the present method. The tilt angle α and the substrate factor F are tabulated in addition to the indices hkl and the Bragg angle 2θ. (a) for the substrate of MgO. (b) for the thin film of Mn 3 O The Rigaku Journal

6 Table 2. Bragg reflections obtained by peak search and indices calculated from the observed angles of ω, χ, and φ on the basis of the UB matrix determined. Specimen: the epitaxial thin film MgO/Mn 3 O 4. Vol. 16 No

7 Fig. 5. The Bragg profiles observed, showing the difference form the predicted point. (a) and (b) comparison of the 3, 1 and 1 profile obtained by the grazing incidence and that by the symmetrical setting. (c) and (d) for the reflection 2, 2, Conclusion By using the program 'CrystaIGuide', fully automatic determination system of the crystallographic orientation of thin films, all the reflections found for a Mn 3 O 4 /MgO epitaxial specimen can be successfully indexed within the error of This program guides us to find out the scan along any direction and any trace in the reciprocal space with different diffraction conditions. A significant feature of this program is therefore in the fact that various possibilities are easily visualized, for the measurement of a given point in the reciprocal space with different diffraction conditions. We would like to show our great thanks to Prof. Yao and Mrs. L. W. Guo at IMR, Tohoku University, for growing thin films, 7. References [1] L. Ballard and P. K. Predecki, Advances in X-Ray Analysis, 39, 363, (1995). [2] W. R. Busing and H. A. Levy, (1967) Acta Cryst. 22, 457. [3] J. Harada, lwata and Oshima (1984) Colloque de Physique. 52 The Rigaku Journal

Crystal Quality Analysis Group

Crystal Quality Analysis Group Crystal Quality Analysis Group Contents Contents 1. Overview...1 2. Measurement principles...3 2.1 Considerations related to orientation and diffraction conditions... 3 2.2 Rocking curve measurement...

More information

ACCURATE TEXTURE MEASUREMENTS ON THIN FILMS USING A POWDER X-RAY DIFFRACTOMETER

ACCURATE TEXTURE MEASUREMENTS ON THIN FILMS USING A POWDER X-RAY DIFFRACTOMETER ACCURATE TEXTURE MEASUREMENTS ON THIN FILMS USING A POWDER X-RAY DIFFRACTOMETER MARK D. VAUDIN NIST, Gaithersburg, MD, USA. Abstract A fast and accurate method that uses a conventional powder x-ray diffractometer

More information

Diffraction I - Geometry. Chapter 3

Diffraction I - Geometry. Chapter 3 Diffraction I - Geometry Chapter 3 Outline ❽ Diffraction basics ❽ Braggs law ❽ Laue equations ❽ Reciprocal space and diffraction ❽ Units for x-ray wavelengths ❽ Diffraction methods Laue photographs Rotation

More information

GRAZING-INCIDENCE X-RAY DIFFRACTOMETER FOR DETERMINING IN-PLANE STRUCTURE OF THIN FILMS. Kazuhiko Omote and Jimpei Harada

GRAZING-INCIDENCE X-RAY DIFFRACTOMETER FOR DETERMINING IN-PLANE STRUCTURE OF THIN FILMS. Kazuhiko Omote and Jimpei Harada Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 192 GRAZING-INCIDENCE X-RAY DIFFRACTOMETER FOR DETERMINING IN-PLANE STRUCTURE OF THIN FILMS Kazuhiko Omote

More information

X-ray thin-film measurement techniques

X-ray thin-film measurement techniques X-ray thin-film measurement techniques VIII. Detectors and series summary Shintaro Kobayashi* and Katsuhiko Inaba* 1. Introduction The various XRD techniques as the characterization tools for thin film

More information

ANOMALOUS SCATTERING FROM SINGLE CRYSTAL SUBSTRATE

ANOMALOUS SCATTERING FROM SINGLE CRYSTAL SUBSTRATE 177 ANOMALOUS SCATTERING FROM SINGLE CRYSTAL SUBSTRATE L. K. Bekessy, N. A. Raftery, and S. Russell Faculty of Science, Queensland University of Technology, GPO Box 2434, Brisbane, Queensland, Australia

More information

A CONVERGENT BEAM, PARALLEL DETECTION X-RAY DIFFRACTION SYSTEM FOR CHARACTERIZING COMBINATORIAL EPITAXIAL THIN FILMS

A CONVERGENT BEAM, PARALLEL DETECTION X-RAY DIFFRACTION SYSTEM FOR CHARACTERIZING COMBINATORIAL EPITAXIAL THIN FILMS The Rigaku Journal Vol. 18/ No. 1/ 2001 CONTRIBUTED PAPERS A CONVERGENT BEAM, PARALLEL DETECTION X-RAY DIFFRACTION SYSTEM FOR CHARACTERIZING COMBINATORIAL EPITAXIAL THIN FILMS K. OMOTE, T. KIKUCHI, J.

More information

COMPARISON BETWEEN CONVENTIONAL AND TWO-DIMENSIONAL XRD

COMPARISON BETWEEN CONVENTIONAL AND TWO-DIMENSIONAL XRD Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 37 COMPARISON BETWEEN CONVENTIONAL AND TWO-DIMENSIONAL XRD Bob B. He, Uwe Preckwinkel, and Kingsley

More information

Figure 1: Derivation of Bragg s Law

Figure 1: Derivation of Bragg s Law What is Bragg s Law and why is it Important? Bragg s law refers to a simple equation derived by English physicists Sir W. H. Bragg and his son Sir W. L. Bragg in 1913. This equation explains why the faces

More information

Introduction to XRD analysis of modern functional thin films using a 2-dimensional detector (1) GI-XRD

Introduction to XRD analysis of modern functional thin films using a 2-dimensional detector (1) GI-XRD Technical articles Introduction to XRD analysis of modern functional thin films using a 2-dimensional detector (1) GI-XRD Shintaro Kobayashi* and Katsuhiko Inaba** 1. Introduction The development of new

More information

X-ray Diffraction from Materials

X-ray Diffraction from Materials X-ray Diffraction from Materials 2008 Spring Semester Lecturer; Yang Mo Koo Monday and Wednesday 14:45~16:00 8. Experimental X-ray Diffraction Procedures 8.1 Diffraction Experiments using Films 8.1.1 Laue

More information

Formula for the asymmetric diffraction peak profiles based on double Soller slit geometry

Formula for the asymmetric diffraction peak profiles based on double Soller slit geometry REVIEW OF SCIENTIFIC INSTRUMENTS VOLUME 69, NUMBER 6 JUNE 1998 Formula for the asymmetric diffraction peak profiles based on double Soller slit geometry Takashi Ida Department of Material Science, Faculty

More information

diffraction patterns obtained with convergent electron beams yield more information than patterns obtained with parallel electron beams:

diffraction patterns obtained with convergent electron beams yield more information than patterns obtained with parallel electron beams: CBED-Patterns Principle of CBED diffraction patterns obtained with convergent electron beams yield more information than patterns obtained with parallel electron beams: specimen thickness more precise

More information

Stress and Texture by XRD Bob He, Bruker AXS

Stress and Texture by XRD Bob He, Bruker AXS Stress and Texture by XRD Bob He, Bruker AXS Intensity Conventional X-ray Diffractometer Divergence slit Antiscatter slit Monochromator Bragg-Brentano Geometry. Scanning over range to collect XRD pattern.

More information

TEM Imaging and Dynamical Scattering

TEM Imaging and Dynamical Scattering TEM Imaging and Dynamical Scattering Duncan Alexander EPFL-CIME 1 Aspects of TEM imaging Objective lens focus Objective lens astigmatism Image delocalization Dynamical scattering 2-beam theory Thickness

More information

X-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting

X-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting X-Ray Diffraction Analysis of III-V Superlattices: Characterization, Simulation and Fitting Enlong Liu Xiangyu Wu Abstract Three samples of III-V semiconductor superlattice (SL) are investigated by X-ray

More information

APPLICATION OF Ni/C-GÖBEL MIRRORS AS PARALLEL BEAM X-RAY OPTICS FOR Cu Ka AND Mo Ka RADIATION

APPLICATION OF Ni/C-GÖBEL MIRRORS AS PARALLEL BEAM X-RAY OPTICS FOR Cu Ka AND Mo Ka RADIATION Copyright(c)JCPDS-International Centre for Diffraction Data 2000,Advances in X-ray Analysis,Vol.43 212 APPLICATION OF Ni/C-GÖBEL MIRRORS AS PARALLEL BEAM X-RAY OPTICS FOR AND RADIATION T. Holz, R. Dietsch,

More information

Cat. No. 9240H801 Diffraction Space Simulation Software User s Manual. Manual No. ME13305A02. Rigaku Corporation

Cat. No. 9240H801 Diffraction Space Simulation Software User s Manual. Manual No. ME13305A02. Rigaku Corporation Cat. No. 9240H801 Diffraction Space Simulation Software User s Manual Manual No. ME13305A02 Rigaku Corporation Thank you for your purchase of Rigaku s product. This manual describes the correct use of

More information

THE INFLUENCE OF SURFACE ROUGHNESS ON THE REFRACTION OF X-RAYS AND ITS EFFECT ON BRAGG PEAK POSITIONS

THE INFLUENCE OF SURFACE ROUGHNESS ON THE REFRACTION OF X-RAYS AND ITS EFFECT ON BRAGG PEAK POSITIONS Copyright JCPDS - International Centre for Diffraction Data 2003, Advances in X-ray Analysis, Volume 46. 232 THE INFLUENCE OF SURFACE ROUGHNESS ON THE REFRACTION OF X-RAYS AND ITS EFFECT ON BRAGG PEAK

More information

Chapter 38. Diffraction Patterns and Polarization

Chapter 38. Diffraction Patterns and Polarization Chapter 38 Diffraction Patterns and Polarization Diffraction Light of wavelength comparable to or larger than the width of a slit spreads out in all forward directions upon passing through the slit This

More information

Collect and Reduce Intensity Data Photon II

Collect and Reduce Intensity Data Photon II Collect and Reduce Intensity Data Photon II General Steps in Collecting Intensity Data Note that the steps outlined below are generally followed when using all modern automated diffractometers, regardless

More information

Diffraction Basics (prepared by James R. Connolly, for EPS , Introduction to X-Ray Powder Diffraction, Spring 2012

Diffraction Basics (prepared by James R. Connolly, for EPS , Introduction to X-Ray Powder Diffraction, Spring 2012 Introduction The use of X-rays for crystallographic analysis relies on a few basic principals:. When an incident beam of x-rays interacts with a target material, one of the primary effects observed is

More information

Collect and Reduce Intensity Data -- APEX

Collect and Reduce Intensity Data -- APEX Collect and Reduce Intensity Data -- APEX General Steps in Collecting Intensity Data Note that the steps outlined below are generally followed when using all modern automated diffractometers, regardless

More information

CHEM-E5225 :Electron Microscopy Imaging I

CHEM-E5225 :Electron Microscopy Imaging I CHEM-E5225 :Electron Microscopy Imaging I 2018.11 Yanling Ge Outline Amplitude Contrast Phase Contrast Images Thickness and Bending Effects Amplitude Contrast Amplitude phase TEM STEM Incoherent elastic

More information

CCP4-BGU workshop 2018 The X-ray Diffraction Experiment Diffraction Geometry and Data Collection Strategy. Andrew GW Leslie, MRC LMB, Cambridge, UK

CCP4-BGU workshop 2018 The X-ray Diffraction Experiment Diffraction Geometry and Data Collection Strategy. Andrew GW Leslie, MRC LMB, Cambridge, UK CCP4-BGU workshop 2018 The X-ray Diffraction Experiment Diffraction Geometry and Data Collection Strategy Andrew GW Leslie, MRC LMB, Cambridge, UK Definition of a crystal and the unit cell Crystal: An

More information

High Resolution X-ray Diffraction and X-ray Reflectivity Studies of InAs/AlGaAsSh Deep Quantum Wells

High Resolution X-ray Diffraction and X-ray Reflectivity Studies of InAs/AlGaAsSh Deep Quantum Wells 130 High Resolution X-ray Diffraction and X-ray Reflectivity Studies of InAs/AlGaAsSh Deep Quantum Wells Shin-ya Matsuno, Naohiro Kuze, Hiromasa Goto, Masayuki Kuba Analytical and Computational Science

More information

Diffraction. Single-slit diffraction. Diffraction by a circular aperture. Chapter 38. In the forward direction, the intensity is maximal.

Diffraction. Single-slit diffraction. Diffraction by a circular aperture. Chapter 38. In the forward direction, the intensity is maximal. Diffraction Chapter 38 Huygens construction may be used to find the wave observed on the downstream side of an aperture of any shape. Diffraction The interference pattern encodes the shape as a Fourier

More information

Chapter 24. Wave Optics. Wave Optics. The wave nature of light is needed to explain various phenomena

Chapter 24. Wave Optics. Wave Optics. The wave nature of light is needed to explain various phenomena Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric) optics

More information

X-Ray Diffraction Edited 10/6/15 by Stephen Albright & DGH & JS

X-Ray Diffraction Edited 10/6/15 by Stephen Albright & DGH & JS X-Ray Diffraction Edited 10/6/15 by Stephen Albright & DGH & JS Introduction and concepts The experiment consists of two parts. The first is to identify an unknown sample using the powder method; the second

More information

1. Polarization effects in optical spectra of photonic crystals

1. Polarization effects in optical spectra of photonic crystals Speech for JASS 05. April 2005. Samusev A. 1. Polarization effects in optical spectra of photonic crystals Good afternoon. I would like to introduce myself. My name is Anton Samusev. I m a student of Saint

More information

Rietveld refinements collection strategies!

Rietveld refinements collection strategies! Rietveld refinements collection strategies! Luca Lutterotti! Department of Materials Engineering and Industrial Technologies! University of Trento - Italy! Quality of the experiment! A good refinement,

More information

X-ray thin-film measurement techniques

X-ray thin-film measurement techniques X-ray thin-film measurement techniques VI. Small Angle X-ray Scattering Aya Ogi* and Katsuhiko Inaba* 1. Introduction We have been making a series of papers for thin-film analysis techniques for characterization

More information

GRAZING INCIDENCE IN-PLANE X-RAY DIFFRACTION IN THE LABORATORY

GRAZING INCIDENCE IN-PLANE X-RAY DIFFRACTION IN THE LABORATORY Copyright JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 309 GRAZING INCIDENCE IN-PLANE X-RAY DIFFRACTION IN THE LABORATORY B. K. Tanner, T. P. A. Hase,

More information

Chapter 24. Wave Optics. Wave Optics. The wave nature of light is needed to explain various phenomena

Chapter 24. Wave Optics. Wave Optics. The wave nature of light is needed to explain various phenomena Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric) optics

More information

Condenser Optics for Dark Field X-Ray Microscopy

Condenser Optics for Dark Field X-Ray Microscopy Condenser Optics for Dark Field X-Ray Microscopy S. J. Pfauntsch, A. G. Michette, C. J. Buckley Centre for X-Ray Science, Department of Physics, King s College London, Strand, London WC2R 2LS, UK Abstract.

More information

STRUCTURAL CHARACTERIZATION OF SiGe AND SiGe:C HETEROSTRUCTURES USING A COMBINATION OF X-RAY SCATTERING METHODS

STRUCTURAL CHARACTERIZATION OF SiGe AND SiGe:C HETEROSTRUCTURES USING A COMBINATION OF X-RAY SCATTERING METHODS Copyright JCPDS - International Centre for Diffraction Data 2004, Advances in X-ray Analysis, Volume 47. 35 STRUCTURAL CHARACTERIZATION OF SiGe AND SiGe:C HETEROSTRUCTURES USING A COMBINATION OF X-RAY

More information

Towards 0.1 mm spatial resolution

Towards 0.1 mm spatial resolution Submitted for publication in ICNS Proceedings Towards 0.1 mm spatial resolution A. D. Stoica and X. L. Wang Spallation Neutron Source 701 Scarboro Road Oak Ridge National Laboratory Oak Ridge, TN 37831,

More information

Laboratory 6: Light and the Laser

Laboratory 6: Light and the Laser Laboratory 6: Light and the Laser WARNING NEVER LOOK DIRECTLY AT LASER LIGHT Index of Refraction: Snell's Law 1. Read the section on physical optics in some introductory physics text. 2. Set the semicircular

More information

Engineered Diffusers Intensity vs Irradiance

Engineered Diffusers Intensity vs Irradiance Engineered Diffusers Intensity vs Irradiance Engineered Diffusers are specified by their divergence angle and intensity profile. The divergence angle usually is given as the width of the intensity distribution

More information

X-ray Powder Diffraction

X-ray Powder Diffraction X-ray Powder Diffraction Chemistry 754 Solid State Chemistry Lecture #8 April 15, 2004 Single Crystal Diffraction Diffracted Beam Incident Beam Powder Diffraction Diffracted Beam Incident Beam In powder

More information

Using Chi and Phi of the Eulerian cradle instead of two crossed goniometers tables:

Using Chi and Phi of the Eulerian cradle instead of two crossed goniometers tables: Orion Orion has a closed Eulerian cradle, and especially triple-axis users are normally more familiar to crossed goniometer setups. As a consequence, we want to make you familiar with using the phi-angle

More information

SUPPLEMENTARY INFORMATION

SUPPLEMENTARY INFORMATION SUPPLEMENTARY INFORMATION doi:10.1038/nature10934 Supplementary Methods Mathematical implementation of the EST method. The EST method begins with padding each projection with zeros (that is, embedding

More information

Introduction to two-dimensional X-ray diffraction

Introduction to two-dimensional X-ray diffraction Introduction to two-dimensional X-ray diffraction Bob Baoping He a) Bruker Advanced X-ray Solutions, Inc., 5465 East Cheryl Parkway, Madison, Wisconsin 53711 Received 7 February 2003; accepted 1 April

More information

Characterizing x-ray mirrors in reciprocal space

Characterizing x-ray mirrors in reciprocal space Characterizing x-ray mirrors in reciprocal space Preliminary results from the NIST X-ray Optics Evaluation Double-Crystal Diffractometer D.L. Gil, D. Windover, J.P. Cline, A. Henins National Institute

More information

High spatial resolution measurement of volume holographic gratings

High spatial resolution measurement of volume holographic gratings High spatial resolution measurement of volume holographic gratings Gregory J. Steckman, Frank Havermeyer Ondax, Inc., 8 E. Duarte Rd., Monrovia, CA, USA 9116 ABSTRACT The conventional approach for measuring

More information

Physical Optics. You can observe a lot just by watching. Yogi Berra ( )

Physical Optics. You can observe a lot just by watching. Yogi Berra ( ) Physical Optics You can observe a lot just by watching. Yogi Berra (1925-2015) OBJECTIVES To observe some interference and diffraction phenomena with visible light. THEORY In a previous experiment you

More information

Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect. (SAKI3d) User s manual. X.Z. LI, Ph. D.

Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect. (SAKI3d) User s manual. X.Z. LI, Ph. D. Simulation and Analysis of Kikuchi Patterns Including Double Diffraction Effect (SAKI3d) User s manual X.Z. LI, Ph. D (May 6, 2018) Copyright 2011-2018 LANDYNE All Right Reserved 1 Contents 1. Introduction...3

More information

d has a relationship with ψ

d has a relationship with ψ Principle of X-Ray Stress Analysis Metallic materials consist of innumerable crystal grains. Each grain usually faces in a random direction. When stress is applied on such materials, the interatomic distance

More information

Cover Page. The handle holds various files of this Leiden University dissertation

Cover Page. The handle   holds various files of this Leiden University dissertation Cover Page The handle http://hdl.handle.net/1887/48877 holds various files of this Leiden University dissertation Author: Li, Y. Title: A new method to reconstruct the structure from crystal images Issue

More information

Wave Optics. April 11, 2014 Chapter 34 1

Wave Optics. April 11, 2014 Chapter 34 1 Wave Optics April 11, 2014 Chapter 34 1 Announcements! Exam tomorrow! We/Thu: Relativity! Last week: Review of entire course, no exam! Final exam Wednesday, April 30, 8-10 PM Location: WH B115 (Wells Hall)

More information

Basics of X-Area for image plates

Basics of X-Area for image plates Basics of X-Area for image plates Commercial software to process single-crystal and powder x-ray data from STOE image plates and PILATUS detectors Andrzej Grzechnik 1 & Karen Friese 2 1 Institute of Crystallography,

More information

Chapter 36. Diffraction. Copyright 2014 John Wiley & Sons, Inc. All rights reserved.

Chapter 36. Diffraction. Copyright 2014 John Wiley & Sons, Inc. All rights reserved. Chapter 36 Diffraction Copyright 36-1 Single-Slit Diffraction Learning Objectives 36.01 Describe the diffraction of light waves by a narrow opening and an edge, and also describe the resulting interference

More information

Residual Stress Gradients in a Tungsten Film by Grazing-Incidence XRD

Residual Stress Gradients in a Tungsten Film by Grazing-Incidence XRD Copyright ISSN (C) 1097-0002, JCPDS-International Advances in X-ray Centre Analysis, for Volume Diffraction 41 Data 1999 467 Residual Stress Gradients in a Tungsten Film by Grazing-Incidence XRD T Ely*,

More information

Optics Vac Work MT 2008

Optics Vac Work MT 2008 Optics Vac Work MT 2008 1. Explain what is meant by the Fraunhofer condition for diffraction. [4] An aperture lies in the plane z = 0 and has amplitude transmission function T(y) independent of x. It is

More information

4. Recommended alignment procedure:

4. Recommended alignment procedure: 4. Recommended alignment procedure: 4.1 Introduction The described below procedure presents an example of alignment of beam shapers Shaper and Focal- Shaper (F- Shaper) with using the standard Shaper Mount

More information

QUICK X-RAY REFLECTIVITY OF SPHERICAL SAMPLES

QUICK X-RAY REFLECTIVITY OF SPHERICAL SAMPLES Copyright JCPDS-International Centre for Diffraction Data 2013 ISSN 1097-0002 10 QUICK X-RAY REFLECTIVITY OF SPHERICAL SAMPLES Krassimir Stoev 1, Kenji Sakurai 2,3 1 AECL Chalk River Laboratories, Chalk

More information

1

1 In the following tutorial we will determine by fitting the standard instrumental broadening supposing that the LaB 6 NIST powder sample broadening is negligible. This can be achieved in the MAUD program

More information

Bragg Diffraction from 2-D Nanoparticle Arrays adapted by Preston Snee and Ali Jawaid

Bragg Diffraction from 2-D Nanoparticle Arrays adapted by Preston Snee and Ali Jawaid ADH 9/9/2013 I. Introduction Bragg Diffraction from 2-D Nanoparticle Arrays adapted by Preston Snee and Ali Jawaid In this module, we will investigate how a crystal lattice of nanoparticles can act as

More information

Chapter 36. Diffraction. Dr. Armen Kocharian

Chapter 36. Diffraction. Dr. Armen Kocharian Chapter 36 Diffraction Dr. Armen Kocharian Diffraction Light of wavelength comparable to or larger than the width of a slit spreads out in all forward directions upon passing through the slit This phenomena

More information

Data integration and scaling

Data integration and scaling Data integration and scaling Harry Powell MRC Laboratory of Molecular Biology 3rd February 2009 Abstract Processing diffraction images involves three basic steps, which are indexing the images, refinement

More information

Grazing Angle 2 Theta Phase Analysis

Grazing Angle 2 Theta Phase Analysis Page 1 of 7 Grazing Angle 2 Theta Phase Analysis 1. Log into the User Log System on the SMIF web site Hardware Setup X-Ray Tube The line focus configuration of the x-ray tube is used. This is the default

More information

Fast, Intuitive Structure Determination II: Crystal Indexing and Data Collection Strategy. April 2,

Fast, Intuitive Structure Determination II: Crystal Indexing and Data Collection Strategy. April 2, Fast, Intuitive Structure Determination II: Crystal Indexing and Data Collection Strategy April 2, 2013 1 Welcome I I Dr. Michael Ruf Product Manager Crystallography Bruker AXS Inc. Madison, WI, USA Bruce

More information

Diffraction and Interference of Plane Light Waves

Diffraction and Interference of Plane Light Waves PHY 92 Diffraction and Interference of Plane Light Waves Diffraction and Interference of Plane Light Waves Introduction In this experiment you will become familiar with diffraction patterns created when

More information

Physics 1CL WAVE OPTICS: INTERFERENCE AND DIFFRACTION Fall 2009

Physics 1CL WAVE OPTICS: INTERFERENCE AND DIFFRACTION Fall 2009 Introduction An important property of waves is interference. You are familiar with some simple examples of interference of sound waves. This interference effect produces positions having large amplitude

More information

Physical optics. Introduction. University of Ottawa Department of Physics

Physical optics. Introduction. University of Ottawa Department of Physics Physical optics Introduction The true nature of light has been, and continues to be, an alluring subject in physics. While predictions of light behaviour can be made with great success and precision, the

More information

X-ray diffraction on thin films and multilayers

X-ray diffraction on thin films and multilayers Chapter 3 X-ray diffraction on thin films and multilayers 3.1 Introduction In this section we present ex-situ X-ray diffraction measurements as well as their numerical simulations for epitaxial CoO and

More information

Measurement of period difference in grating pair based on analysis of grating phase shift

Measurement of period difference in grating pair based on analysis of grating phase shift Measurement of period difference in grating pair based on analysis of grating phase shift Chao Guo, Lijiang Zeng State Key Laboratory of Precision Measurement Technology and Instruments Department of Precision

More information

axis, and wavelength tuning is achieved by translating the grating along a scan direction parallel to the x

axis, and wavelength tuning is achieved by translating the grating along a scan direction parallel to the x Exponential-Grating Monochromator Kenneth C. Johnson, October 0, 08 Abstract A monochromator optical design is described, which comprises a grazing-incidence reflection and two grazing-incidence mirrors,

More information

specular diffuse reflection.

specular diffuse reflection. Lesson 8 Light and Optics The Nature of Light Properties of Light: Reflection Refraction Interference Diffraction Polarization Dispersion and Prisms Total Internal Reflection Huygens s Principle The Nature

More information

New Scatterometer for Spatial Distribution Measurements of Light Scattering from Materials

New Scatterometer for Spatial Distribution Measurements of Light Scattering from Materials 10.2478/v10048-012-0012-y MEASUREMENT SCIENCE REVIEW, Volume 12, No. 2, 2012 New Scatterometer for Spatial Distribution Measurements of Light Scattering from Materials 1,3 E. Kawate, 1,2 M. Hain 1 AIST,

More information

DAMAGE INSPECTION AND EVALUATION IN THE WHOLE VIEW FIELD USING LASER

DAMAGE INSPECTION AND EVALUATION IN THE WHOLE VIEW FIELD USING LASER DAMAGE INSPECTION AND EVALUATION IN THE WHOLE VIEW FIELD USING LASER A. Kato and T. A. Moe Department of Mechanical Engineering Chubu University Kasugai, Aichi 487-8501, Japan ABSTRACT In this study, we

More information

Bruker AXS D8 FOCUS. Diffraction Solutions XRD. think forward

Bruker AXS D8 FOCUS. Diffraction Solutions XRD. think forward Bruker AXS D8 FOCUS Diffraction Solutions think forward XRD The concept behind the D8 FOCUS is to provide you with a reliable workhorse for powder diffraction applications attractively priced entry-level

More information

X PERT DATA COLLECTOR. Quick Start Guide

X PERT DATA COLLECTOR. Quick Start Guide X PERT DATA COLLECTOR Quick Start Guide X Pert Data Collector Quick Start Guide EDITION NOTICE: Sixth Edition, January 2006. This is the sixth edition of this publication, it is intended for use with

More information

Chapter 24. Wave Optics

Chapter 24. Wave Optics Chapter 24 Wave Optics Wave Optics The wave nature of light is needed to explain various phenomena Interference Diffraction Polarization The particle nature of light was the basis for ray (geometric) optics

More information

Guidelines for proper use of Plate elements

Guidelines for proper use of Plate elements Guidelines for proper use of Plate elements In structural analysis using finite element method, the analysis model is created by dividing the entire structure into finite elements. This procedure is known

More information

Clip User Manual. Olaf J. Schumann. March 25, 2009

Clip User Manual. Olaf J. Schumann. March 25, 2009 Clip User Manual Olaf J. Schumann March 25, 2009 Contents 1 The Program 2 1.1 Main Window............................. 2 1.2 Crystal Window........................... 3 1.3 Laue Plane..............................

More information

Experiment 8 Wave Optics

Experiment 8 Wave Optics Physics 263 Experiment 8 Wave Optics In this laboratory, we will perform two experiments on wave optics. 1 Double Slit Interference In two-slit interference, light falls on an opaque screen with two closely

More information

Chap. 4. Jones Matrix Method

Chap. 4. Jones Matrix Method Chap. 4. Jones Matrix Method 4.1. Jones Matrix Formulation - For an incident light with a polarization state described by the Jones vector - Decompose the light into a linear combination of the "fast"

More information

Apex 3/D8 Venture Quick Guide

Apex 3/D8 Venture Quick Guide Apex 3/D8 Venture Quick Guide Login Sample Login Enter in Username (group name) and Password Create New Sample Sample New Enter in sample name, be sure to check white board or cards to establish next number

More information

LUSI SUB-SYSTEM XCS Physics Requirements for the LUSI Large Offset Monochromator. Doc. No. SP R0

LUSI SUB-SYSTEM XCS Physics Requirements for the LUSI Large Offset Monochromator. Doc. No. SP R0 PHYSICS REQUIREMENT DOCUMENT (PRD) Doc. No. SP-391-00-16 R0 LUSI SUB-SYSTEM XCS Physics Requirements for the Aymeric Robert Author, LUSI Scientist Signature Date David Fritz LUSI Scientist Signature Date

More information

Maintenance Package Measurement

Maintenance Package Measurement Maintenance Package Measurement Contents Contents 1. Package measurement flow...1 2. Measurement procedures...3 2.1 Startup... 3 2.2 Hardware setup... 4 2.3 Setting Package measurement conditions... 7

More information

Experimental Competition. Sample Solution

Experimental Competition. Sample Solution The 37th International Physics Olympiad Singapore Experimental Competition Wednesday, 1 July, 006 Sample Solution a. A sketch of the experimental setup Part 1 Receiver Rotating table Goniometer Fixed arm

More information

Chapter 2: Wave Optics

Chapter 2: Wave Optics Chapter : Wave Optics P-1. We can write a plane wave with the z axis taken in the direction of the wave vector k as u(,) r t Acos tkzarg( A) As c /, T 1/ and k / we can rewrite the plane wave as t z u(,)

More information

CALIBRATION OF DIFFRACTOMETERS: A TEST METHOD TO MONITOR THE PERFORMANCE OF INSTRUMENTS. G. Berti, U. Bartoli, M. D Acunto and F.

CALIBRATION OF DIFFRACTOMETERS: A TEST METHOD TO MONITOR THE PERFORMANCE OF INSTRUMENTS. G. Berti, U. Bartoli, M. D Acunto and F. Materials Science Forum Online: 004-01-15 ISSN: 166-975, Vols. 443-444, pp 7-30 doi:10.408/www.scientific.net/msf.443-444.7 004 Trans Tech Publications, Switzerland CALIBRATION OF DIFFRACTOMETERS: A TEST

More information

Grazing-Incidence X-Ray Diffraction

Grazing-Incidence X-Ray Diffraction Grazing-Incidence X-Ray Diffraction Sergey Stepanov Illinios Institute of Technology, BioCAT at the Advanced Photon Source, Argonne National Lab, 9700 S. Cass Ave., Bldg.435, Argonne, IL 60439 Contents

More information

Quick Start Guide. X Pert Data Collector

Quick Start Guide. X Pert Data Collector Quick Start Guide X Pert Data Collector X PERT DATA COLLECTOR QUICK START GUIDE EDITION NOTICE: Fifth Edition, October 2004. This is the fifth edition of this publication, it is intended for use with

More information

IB-2 Polarization Practice

IB-2 Polarization Practice Name: 1. Plane-polarized light is incident normally on a polarizer which is able to rotate in the plane perpendicular to the light as shown below. In diagram 1, the intensity of the incident light is 8

More information

Chapter 24. Wave Optics

Chapter 24. Wave Optics Chapter 24 Wave Optics Diffraction Huygen s principle requires that the waves spread out after they pass through slits This spreading out of light from its initial line of travel is called diffraction

More information

Chapter 35 &36 Physical Optics

Chapter 35 &36 Physical Optics Chapter 35 &36 Physical Optics Physical Optics Phase Difference & Coherence Thin Film Interference 2-Slit Interference Single Slit Interference Diffraction Patterns Diffraction Grating Diffraction & Resolution

More information

KMC2 - diffractometry

KMC2 - diffractometry KMC2 - diffractometry (version 2006_09_10) ------------------------------------------------ 6-circle diffractometer (HUBER) psi-geometry 4-circle diffractometer with omega/2theta-axis vertically, minimum

More information

I sinc seff. sinc. 14. Kinematical Diffraction. Two-beam intensity Remember the effective excitation error for beam g?

I sinc seff. sinc. 14. Kinematical Diffraction. Two-beam intensity Remember the effective excitation error for beam g? 1 14. Kinematical Diffraction Two-beam intensity Remember the effective excitation error for beam g? seff s 1 The general two-beam result for g was: sin seff T ist g Ti e seff Next we find the intensity

More information

Lecture 16 Diffraction Ch. 36

Lecture 16 Diffraction Ch. 36 Lecture 16 Diffraction Ch. 36 Topics Newtons Rings Diffraction and the wave theory Single slit diffraction Intensity of single slit diffraction Double slit diffraction Diffraction grating Dispersion and

More information

Fundamentals of Rietveld Refinement II. Refinement of a Single Phase

Fundamentals of Rietveld Refinement II. Refinement of a Single Phase Fundamentals of Rietveld Refinement II. Refinement of a Single Phase An Introduction to Rietveld Refinement using PANalytical X Pert HighScore Plus v3.0a Scott A Speakman, Ph.D. MIT Center for Materials

More information

Contributions to the defocusing effect on pole figure measurements by X-ray diffraction

Contributions to the defocusing effect on pole figure measurements by X-ray diffraction RESEARCH Revista Mexicana de Física 61 (215) 296 3 JULY-AUGUST 215 Contributions to the defocusing effect on pole figure measurements by X-ray diffraction J. Palacios Gómez, R.S. Salat Figols, A. Jiménez

More information

How to Analyze Materials

How to Analyze Materials INTERNATIONAL CENTRE FOR DIFFRACTION DATA How to Analyze Materials A PRACTICAL GUIDE FOR POWDER DIFFRACTION To All Readers This is a practical guide. We assume that the reader has access to a laboratory

More information

Rigaku SmartLab Operation Procedures

Rigaku SmartLab Operation Procedures Working DRAFT Prepared by Lab Manager Jim Connolly (Revision date: 31-May-2013) Rigaku SmartLab General Operating Overview The Rigaku SmartLab is a highly flexible general purpose X-ray diffractometer

More information

PHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE

PHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE PHYSICS 1040L LAB LAB 7: DIFFRACTION & INTERFERENCE Object: To investigate the diffraction and interference of light, Apparatus: Lasers, optical bench, single and double slits. screen and mounts. Theory:

More information

Structural Refinement based on the Rietveld Method. An introduction to the basics by Cora Lind

Structural Refinement based on the Rietveld Method. An introduction to the basics by Cora Lind Structural Refinement based on the Rietveld Method An introduction to the basics by Cora Lind Outline What, when and why? - Possibilities and limitations Examples Data collection Parameters and what to

More information

Applications of Piezo Actuators for Space Instrument Optical Alignment

Applications of Piezo Actuators for Space Instrument Optical Alignment Year 4 University of Birmingham Presentation Applications of Piezo Actuators for Space Instrument Optical Alignment Michelle Louise Antonik 520689 Supervisor: Prof. B. Swinyard Outline of Presentation

More information