Ali Khounsary | Illinois Institute of Technology (original) (raw)

Papers by Ali Khounsary

Research paper thumbnail of Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data

Optics Express, 2010

We have used coherent X-ray diffraction experiments to characterize both the 1-D and 2-D foci pro... more We have used coherent X-ray diffraction experiments to characterize both the 1-D and 2-D foci produced by nanofocusing Kirkpatrick-Baez (K-B) mirrors, and we find agreement. Algorithms related to ptychography were used to obtain a 3-D reconstruction of a focused hard X-ray beam waist, using data measured when the mirrors were not optimally aligned. Considerable astigmatism was evident in the reconstructed complex wavefield. Comparing the reconstructed wavefield for a single mirror with a geometrical projection of the wavefront errors expected from optical metrology data allowed us to diagnose a 40 μrad misalignment in the incident angle of the first mirror, which had occurred during the experiment. Good agreement between the reconstructed wavefront obtained from the Xray data and off-line metrology data obtained with visible light demonstrates the usefulness of the technique as a metrology and alignment tool for nanofocusing X-ray optics.

Research paper thumbnail of A Comparative Study on Continuum-Scale Modeling of Elasto-Plastic Deformation in Rechargeable Ion Batteries

Journal of The Electrochemical Society

Research paper thumbnail of Focusing options for a bending magnet beamline

X-ray absorption spectroscopy experiments are the primary scientific focus of the MRCAT bending m... more X-ray absorption spectroscopy experiments are the primary scientific focus of the MRCAT bending magnet beamline, 10-BM of the Advanced Photon Source at Argonne National Laboratory. This technique is used for ex situ and in situ structural characterization of materials, many of which are non-crystalline. An intense X-ray beam is often required for these experiments. This beamline presently operates using a detuned double crystal monochromator system without any focusing. Typically, samples are illuminated by a 0.5 x 0.5 mm2 monochromatic beam with a photon flux in the range of 2 - 9 x 108 photons/s (in the 5 - 33 keV range). In this study, several alternate focusing schemes to capture a large portion of the bending magnet beam are compared. It is shown that, in principle, one can obtain an increase over two orders of magnitude in photon flux. These beamline schemes are outlined comparing them for photon flux, energy resolution, cost, and complexity in design and operation.

Research paper thumbnail of Aspectos do desenvolvimento de produto com enfoque na eliminação de desperdícios e adoção de práticas sustentáveis: estudo de caso utilizando técnicas de prototipagem rápida

Na realidade atual das organizações que atuam com o desenvolvimento de produtos, impõem-se cada v... more Na realidade atual das organizações que atuam com o desenvolvimento de produtos, impõem-se cada vez mais desafios no atendimento das necessidades de mercado aliados a ciclos de vida cada vez menores dos produtos, o que leva a criação de distintos protótipos até se definir como será o produto final. Esta situação implica na necessidade de métodos de desenvolvimento de protótipos XXXVII ENCONTRO NACIONAL DE ENGENHARIA DE PRODUCAO "A Engenharia de Produção e as novas tecnologias produtivas: indústria 4.0, manufatura aditiva e outras abordagens avançadas de produção"

Research paper thumbnail of Numerical Study of the Effect of Stress on Diffusion in Silicon Nanowires

Research paper thumbnail of Power distributions of the APS bending magnets and insertion devices

Relationships for computing the total power and the power density profiles of x-ray beams generat... more Relationships for computing the total power and the power density profiles of x-ray beams generated by bending magnets (BMs) and insertion devices (IDs) are given. A FOR-TRAN program called POWER for computing the angular distribution of power generated by an ID is developed and outlined. This interactive program is available on the APS VAX system by typing the command POWER, and a graphic display of the power profile is provided within the program. For users requiring simple analytical formulas, curve fits are used to approximate the ID and BM power distributions. The accuracy of such analytical forms depends greatly on how the curve fits are made and is generally within a few percent.

Research paper thumbnail of A numerical study on striped lithiation of tin oxide anodes

International Journal of Solids and Structures

Abstract High energy storage capacity of tin oxide (SnO2) makes it a promising anode material for... more Abstract High energy storage capacity of tin oxide (SnO2) makes it a promising anode material for high capacity lithium (Li)-ion batteries. Previous experiments reported by Nie et al. (2013) and Huang et al. (2010) have shown that SnO2 lithiation occurs in two stages. First, Li diffuses rapidly through distinct narrow stripes along the electrode axis. This is followed by a second stage where the diffusion/amorphization of the nanowire occurs. In order to understand and possibly predict this complex chemo-mechanical phenomenon, a finite element (FE) model is developed in this work. The model captures the formation of the striped diffusion regime and the corresponding expansion of the nanowire during the lithiation of SnO2. The effect of the stress on the Li diffusion is modeled at the macroscopic level by implementing a stress-dependent expression for the diffusion coefficient. The modeling results clearly show the formation of the striped diffusion regime due to the induced stresses, at low concentrations of Li. This results in a small strain of 0.017 within the nanowire followed by a bulk diffusion and expansion at higher Li concentrations. Thus, the model allows for the spatiotemporally resolved analysis of Li diffusion/intercalation and helps predicting its influence on the mechanical performance of the electrode under the realistic operational conditions.

Research paper thumbnail of Thermal And Structural Analyses Of A Synchrotron Radiation X-Ray Monochromator With Liquid Gallium And Water Cooling

Research paper thumbnail of Performance of a high-resolution x-ray microprobe at the Advanced Photon Source

AIP Conference Proceedings

We have developed a x-ray microprobe in the energy region from 6 to 20 keV using undulator radiat... more We have developed a x-ray microprobe in the energy region from 6 to 20 keV using undulator radiation and zone-plate optics for microfocusing-based techniques and applications at a beamline at the Advanced Photon Source (APS). The performance of the beamline was shown to meet our design objectives, including preservation of the source brilliance and coherence, selectable transverse coherence length and energy bandwidth, high angular stability, and harmonic suppression of the beam. These objectives were achieved by careful thermal management and use of a novel mirror and crystal monochromator cooling geometry. All beamline optical components are water cooled, and the x-ray beam in the experiment station is stable in beam intensity, energy, and position over many days with no active feedback. Using a double-cxystal Si(l 11) monochromator, we have obtained a focal spot size (FWHIM) of 0.15 pm (v) x 1.0 pm (h), and a photon flux of 4X109 photons/see at the focal spot, and thus a photon flux density gain of 15,000. A circular beam spot of 0.15 pm in diameter can be achieved by reducing the horizontal source size using a white beam slit located 43.5 meters upstream of the zone plate, with an order of magnitude less flux in the focal spot.

Research paper thumbnail of Conceptual Design For A Beamline For A Hard x-ray Nanoprobe with 30 nm Spatial Resolution

AIP Conference Proceedings

The planned Center for Nanoscale Materials (CNM) at Argonne National Laboratory is aimed at the d... more The planned Center for Nanoscale Materials (CNM) at Argonne National Laboratory is aimed at the development and study of the properties of nanomaterials and nanodevices. As part of the characterization instruments at CNM, we are developing a new hard x-ray nanoprobe beamline at the Advanced Photon Source. The beamline will provide microscopy and spectroscopy for photon energies from 3 keV

Research paper thumbnail of Polychromatic X-ray Micro- and Nano-Beam Science and Instrumentation

AIP Conference Proceedings, 2007

... 9. P. Kirkpatrick and AV Baez, J. Opt. Soc. Am. 38 766 (1948). 10. Ice, GE, Chung, JS, Tischl... more ... 9. P. Kirkpatrick and AV Baez, J. Opt. Soc. Am. 38 766 (1948). 10. Ice, GE, Chung, JS, Tischler, JZ, Lunt, A. and Assoufid, L. Review of Scientific Instruments, 71, 2635-2639 (2000). 11. W. Liu, Gene E. Ice, Jonathan Z. Tischler, Ali Khounsary, Chian Liu, Lahsen Assoufid, and ...

Research paper thumbnail of Diffraction efficiency and diffraction bandwidth of thermal-gradient and composition-gradient crystals

Measurements were made at the Advanced Photon Source at Argonne National Laboratory on the diffra... more Measurements were made at the Advanced Photon Source at Argonne National Laboratory on the diffraction efficiency and diffraction bandwidth of a thermal-gradient crystal (Si) and a composition-gradient crystal (Si-Ge) to which a thermal gradient was applied. Gradient crystals are crystals in which the spacing between crystalline planes varies with the position in the crystal. This change in the crystal plane spacing is obtained by applying a thermal gradient to a single crystal or by growing a two-component crystal in which the ratio of the two components changes with position in the crystal. Measurements were made at two energies, 92.6 and 153 keV. Both crystals were 1-cm cubes. Laue diffraction (transmission diffraction) was used in all experiments. The thermal gradient was applied perpendicular to the [111] diffraction planes of the pure silicon crystal and perpendicular the [400] diffraction planes in the composition-gradient crystal (Si-Ge). The thermal gradient applied to the crystals was quite unif...

Research paper thumbnail of High Heat Flux Engineering II

High Heat Flux Engineering Ii, Nov 1, 1993

Research paper thumbnail of Heat transfer issues in high-heat-load synchrotron x-ray beams

DISCLAIMER ^This report was prepared as an account of work sponsored by an agency of the United S... more DISCLAIMER ^This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, 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 senrice by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. bv a contractor of the U.S. Government under contract No. W-31-104ENG-38. Acwrdinglv. the U. S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for September, 1994 *This work supported by the US. Department of Energy, BES-Materials Sciences, under contract no. W-31-109-ENG-38 < < DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. HEAT TRANSFER ISSUES IN HlGH-HEAT-LOAD SYNCHROTRON X-RAY BEAMS

Research paper thumbnail of High Heat Flux Engineering

Research paper thumbnail of Method of Making of Compound X-Ray Lenses and Variable Focus X-Ray Lens Assembly

Research paper thumbnail of Proceedings of the ASME Heat Transfer Division. Volume 1: Benchmark problems of heat transfer analysis programs; High heat flux thermal management; Modeling of heat transfer in multi-phase systems; Natural and mixed convection; Numerical methods in heat exchanger design; HTD-Volume 317-1

Research paper thumbnail of Laser-Generated and Other Laboratory X-Ray and EUV Sources, Optics, and Applications

Laser Generated and Other Laboratory X Ray and Euv Sources Optics and Applications, 2004

Research paper thumbnail of <title>Recoating mirrors having a chromium underlayer</title>

Advances in Mirror Technology for X-Ray, EUV Lithography, Laser, and Other Applications, 2004

X-ray mirrors and multilayers are used to reflect, focus, or monochromatize x-ray beams. Substrat... more X-ray mirrors and multilayers are used to reflect, focus, or monochromatize x-ray beams. Substrate materials are typically silicon, fused silica, Zerodur, ULE, or metals such as molybdenum, copper, or stainless steel. Substrates are polished to a few angstroms rms roughness and often coated with one or more layers to provide the desired spectral reflectivity. Coatings can be damaged as a

Research paper thumbnail of Performance of a Be Refractive Lens

AIP Conference Proceedings, 2004

ABSTRACT The performance of a beryllium compound refractive lens (CRL) was tested in the energy r... more ABSTRACT The performance of a beryllium compound refractive lens (CRL) was tested in the energy range of 11.5 to 8.0 keV. The beryllium refractive lens consists of 50 aligned, 1-mm-diameter, hollow spheres in a solid block of beryllium, 30 mm × 20 mm × 55 mm. The minimum web between each hollow sphere was 0.10 mm. The measured focal length of the lens for x-rays close to the axis of the beam was 147.7 cm +/- 2.0 cm at 10 keV and 120.2 +/- 2.0 cm at 9.1 keV. These values agree well with the theoretical values of 146.6 cm and 121.4 cm, respectively. The diameter of the best focus obtained at 10 keV was 35 mum horizontal and 45 mum vertical. For the modified version of the lens used in the 9.1 keV experiment these values were 25 mum horizontal and 35 mum vertical. The x-ray beam cross section for the 10 keV and the 9.1 keV experiments were 0.50 mm × 0.50 mm and 0.30 mm × 0.30 mm, respectively. The enhancement of the flux (photons per sq. mm) was 50:1 at 10 keV and 80:1 in the 9.1 keV experiment.

Research paper thumbnail of Reconstruction of an astigmatic hard X-ray beam and alignment of K-B mirrors from ptychographic coherent diffraction data

Optics Express, 2010

We have used coherent X-ray diffraction experiments to characterize both the 1-D and 2-D foci pro... more We have used coherent X-ray diffraction experiments to characterize both the 1-D and 2-D foci produced by nanofocusing Kirkpatrick-Baez (K-B) mirrors, and we find agreement. Algorithms related to ptychography were used to obtain a 3-D reconstruction of a focused hard X-ray beam waist, using data measured when the mirrors were not optimally aligned. Considerable astigmatism was evident in the reconstructed complex wavefield. Comparing the reconstructed wavefield for a single mirror with a geometrical projection of the wavefront errors expected from optical metrology data allowed us to diagnose a 40 μrad misalignment in the incident angle of the first mirror, which had occurred during the experiment. Good agreement between the reconstructed wavefront obtained from the Xray data and off-line metrology data obtained with visible light demonstrates the usefulness of the technique as a metrology and alignment tool for nanofocusing X-ray optics.

Research paper thumbnail of A Comparative Study on Continuum-Scale Modeling of Elasto-Plastic Deformation in Rechargeable Ion Batteries

Journal of The Electrochemical Society

Research paper thumbnail of Focusing options for a bending magnet beamline

X-ray absorption spectroscopy experiments are the primary scientific focus of the MRCAT bending m... more X-ray absorption spectroscopy experiments are the primary scientific focus of the MRCAT bending magnet beamline, 10-BM of the Advanced Photon Source at Argonne National Laboratory. This technique is used for ex situ and in situ structural characterization of materials, many of which are non-crystalline. An intense X-ray beam is often required for these experiments. This beamline presently operates using a detuned double crystal monochromator system without any focusing. Typically, samples are illuminated by a 0.5 x 0.5 mm2 monochromatic beam with a photon flux in the range of 2 - 9 x 108 photons/s (in the 5 - 33 keV range). In this study, several alternate focusing schemes to capture a large portion of the bending magnet beam are compared. It is shown that, in principle, one can obtain an increase over two orders of magnitude in photon flux. These beamline schemes are outlined comparing them for photon flux, energy resolution, cost, and complexity in design and operation.

Research paper thumbnail of Aspectos do desenvolvimento de produto com enfoque na eliminação de desperdícios e adoção de práticas sustentáveis: estudo de caso utilizando técnicas de prototipagem rápida

Na realidade atual das organizações que atuam com o desenvolvimento de produtos, impõem-se cada v... more Na realidade atual das organizações que atuam com o desenvolvimento de produtos, impõem-se cada vez mais desafios no atendimento das necessidades de mercado aliados a ciclos de vida cada vez menores dos produtos, o que leva a criação de distintos protótipos até se definir como será o produto final. Esta situação implica na necessidade de métodos de desenvolvimento de protótipos XXXVII ENCONTRO NACIONAL DE ENGENHARIA DE PRODUCAO "A Engenharia de Produção e as novas tecnologias produtivas: indústria 4.0, manufatura aditiva e outras abordagens avançadas de produção"

Research paper thumbnail of Numerical Study of the Effect of Stress on Diffusion in Silicon Nanowires

Research paper thumbnail of Power distributions of the APS bending magnets and insertion devices

Relationships for computing the total power and the power density profiles of x-ray beams generat... more Relationships for computing the total power and the power density profiles of x-ray beams generated by bending magnets (BMs) and insertion devices (IDs) are given. A FOR-TRAN program called POWER for computing the angular distribution of power generated by an ID is developed and outlined. This interactive program is available on the APS VAX system by typing the command POWER, and a graphic display of the power profile is provided within the program. For users requiring simple analytical formulas, curve fits are used to approximate the ID and BM power distributions. The accuracy of such analytical forms depends greatly on how the curve fits are made and is generally within a few percent.

Research paper thumbnail of A numerical study on striped lithiation of tin oxide anodes

International Journal of Solids and Structures

Abstract High energy storage capacity of tin oxide (SnO2) makes it a promising anode material for... more Abstract High energy storage capacity of tin oxide (SnO2) makes it a promising anode material for high capacity lithium (Li)-ion batteries. Previous experiments reported by Nie et al. (2013) and Huang et al. (2010) have shown that SnO2 lithiation occurs in two stages. First, Li diffuses rapidly through distinct narrow stripes along the electrode axis. This is followed by a second stage where the diffusion/amorphization of the nanowire occurs. In order to understand and possibly predict this complex chemo-mechanical phenomenon, a finite element (FE) model is developed in this work. The model captures the formation of the striped diffusion regime and the corresponding expansion of the nanowire during the lithiation of SnO2. The effect of the stress on the Li diffusion is modeled at the macroscopic level by implementing a stress-dependent expression for the diffusion coefficient. The modeling results clearly show the formation of the striped diffusion regime due to the induced stresses, at low concentrations of Li. This results in a small strain of 0.017 within the nanowire followed by a bulk diffusion and expansion at higher Li concentrations. Thus, the model allows for the spatiotemporally resolved analysis of Li diffusion/intercalation and helps predicting its influence on the mechanical performance of the electrode under the realistic operational conditions.

Research paper thumbnail of Thermal And Structural Analyses Of A Synchrotron Radiation X-Ray Monochromator With Liquid Gallium And Water Cooling

Research paper thumbnail of Performance of a high-resolution x-ray microprobe at the Advanced Photon Source

AIP Conference Proceedings

We have developed a x-ray microprobe in the energy region from 6 to 20 keV using undulator radiat... more We have developed a x-ray microprobe in the energy region from 6 to 20 keV using undulator radiation and zone-plate optics for microfocusing-based techniques and applications at a beamline at the Advanced Photon Source (APS). The performance of the beamline was shown to meet our design objectives, including preservation of the source brilliance and coherence, selectable transverse coherence length and energy bandwidth, high angular stability, and harmonic suppression of the beam. These objectives were achieved by careful thermal management and use of a novel mirror and crystal monochromator cooling geometry. All beamline optical components are water cooled, and the x-ray beam in the experiment station is stable in beam intensity, energy, and position over many days with no active feedback. Using a double-cxystal Si(l 11) monochromator, we have obtained a focal spot size (FWHIM) of 0.15 pm (v) x 1.0 pm (h), and a photon flux of 4X109 photons/see at the focal spot, and thus a photon flux density gain of 15,000. A circular beam spot of 0.15 pm in diameter can be achieved by reducing the horizontal source size using a white beam slit located 43.5 meters upstream of the zone plate, with an order of magnitude less flux in the focal spot.

Research paper thumbnail of Conceptual Design For A Beamline For A Hard x-ray Nanoprobe with 30 nm Spatial Resolution

AIP Conference Proceedings

The planned Center for Nanoscale Materials (CNM) at Argonne National Laboratory is aimed at the d... more The planned Center for Nanoscale Materials (CNM) at Argonne National Laboratory is aimed at the development and study of the properties of nanomaterials and nanodevices. As part of the characterization instruments at CNM, we are developing a new hard x-ray nanoprobe beamline at the Advanced Photon Source. The beamline will provide microscopy and spectroscopy for photon energies from 3 keV

Research paper thumbnail of Polychromatic X-ray Micro- and Nano-Beam Science and Instrumentation

AIP Conference Proceedings, 2007

... 9. P. Kirkpatrick and AV Baez, J. Opt. Soc. Am. 38 766 (1948). 10. Ice, GE, Chung, JS, Tischl... more ... 9. P. Kirkpatrick and AV Baez, J. Opt. Soc. Am. 38 766 (1948). 10. Ice, GE, Chung, JS, Tischler, JZ, Lunt, A. and Assoufid, L. Review of Scientific Instruments, 71, 2635-2639 (2000). 11. W. Liu, Gene E. Ice, Jonathan Z. Tischler, Ali Khounsary, Chian Liu, Lahsen Assoufid, and ...

Research paper thumbnail of Diffraction efficiency and diffraction bandwidth of thermal-gradient and composition-gradient crystals

Measurements were made at the Advanced Photon Source at Argonne National Laboratory on the diffra... more Measurements were made at the Advanced Photon Source at Argonne National Laboratory on the diffraction efficiency and diffraction bandwidth of a thermal-gradient crystal (Si) and a composition-gradient crystal (Si-Ge) to which a thermal gradient was applied. Gradient crystals are crystals in which the spacing between crystalline planes varies with the position in the crystal. This change in the crystal plane spacing is obtained by applying a thermal gradient to a single crystal or by growing a two-component crystal in which the ratio of the two components changes with position in the crystal. Measurements were made at two energies, 92.6 and 153 keV. Both crystals were 1-cm cubes. Laue diffraction (transmission diffraction) was used in all experiments. The thermal gradient was applied perpendicular to the [111] diffraction planes of the pure silicon crystal and perpendicular the [400] diffraction planes in the composition-gradient crystal (Si-Ge). The thermal gradient applied to the crystals was quite unif...

Research paper thumbnail of High Heat Flux Engineering II

High Heat Flux Engineering Ii, Nov 1, 1993

Research paper thumbnail of Heat transfer issues in high-heat-load synchrotron x-ray beams

DISCLAIMER ^This report was prepared as an account of work sponsored by an agency of the United S... more DISCLAIMER ^This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, 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 senrice by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof. bv a contractor of the U.S. Government under contract No. W-31-104ENG-38. Acwrdinglv. the U. S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for September, 1994 *This work supported by the US. Department of Energy, BES-Materials Sciences, under contract no. W-31-109-ENG-38 < < DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document. HEAT TRANSFER ISSUES IN HlGH-HEAT-LOAD SYNCHROTRON X-RAY BEAMS

Research paper thumbnail of High Heat Flux Engineering

Research paper thumbnail of Method of Making of Compound X-Ray Lenses and Variable Focus X-Ray Lens Assembly

Research paper thumbnail of Proceedings of the ASME Heat Transfer Division. Volume 1: Benchmark problems of heat transfer analysis programs; High heat flux thermal management; Modeling of heat transfer in multi-phase systems; Natural and mixed convection; Numerical methods in heat exchanger design; HTD-Volume 317-1

Research paper thumbnail of Laser-Generated and Other Laboratory X-Ray and EUV Sources, Optics, and Applications

Laser Generated and Other Laboratory X Ray and Euv Sources Optics and Applications, 2004

Research paper thumbnail of <title>Recoating mirrors having a chromium underlayer</title>

Advances in Mirror Technology for X-Ray, EUV Lithography, Laser, and Other Applications, 2004

X-ray mirrors and multilayers are used to reflect, focus, or monochromatize x-ray beams. Substrat... more X-ray mirrors and multilayers are used to reflect, focus, or monochromatize x-ray beams. Substrate materials are typically silicon, fused silica, Zerodur, ULE, or metals such as molybdenum, copper, or stainless steel. Substrates are polished to a few angstroms rms roughness and often coated with one or more layers to provide the desired spectral reflectivity. Coatings can be damaged as a

Research paper thumbnail of Performance of a Be Refractive Lens

AIP Conference Proceedings, 2004

ABSTRACT The performance of a beryllium compound refractive lens (CRL) was tested in the energy r... more ABSTRACT The performance of a beryllium compound refractive lens (CRL) was tested in the energy range of 11.5 to 8.0 keV. The beryllium refractive lens consists of 50 aligned, 1-mm-diameter, hollow spheres in a solid block of beryllium, 30 mm × 20 mm × 55 mm. The minimum web between each hollow sphere was 0.10 mm. The measured focal length of the lens for x-rays close to the axis of the beam was 147.7 cm +/- 2.0 cm at 10 keV and 120.2 +/- 2.0 cm at 9.1 keV. These values agree well with the theoretical values of 146.6 cm and 121.4 cm, respectively. The diameter of the best focus obtained at 10 keV was 35 mum horizontal and 45 mum vertical. For the modified version of the lens used in the 9.1 keV experiment these values were 25 mum horizontal and 35 mum vertical. The x-ray beam cross section for the 10 keV and the 9.1 keV experiments were 0.50 mm × 0.50 mm and 0.30 mm × 0.30 mm, respectively. The enhancement of the flux (photons per sq. mm) was 50:1 at 10 keV and 80:1 in the 9.1 keV experiment.