X-ray detector system having at least two stacked planar Bragg diffractors

Abstract

The apparatus includes a plurality of stacked planar Bragg diffractors, each having at least a first planar Bragg diffractor and a second planar Bragg diffractor, the first and second planar Bragg diffractors positioned successively along an X-ray propagation axis of an X-ray beam, the X-ray beam including X-rays and having an angular beam divergence of less than 30 mrad in at least one direction.

Description

[Technical Field]

[0001] Priority claims This application claims the benefit of priority to U.S. Provisional Patent Application No. 63 / 485,327, filed February 16, 2023, which is incorporated herein by reference in its entirety.

[0002] background Field This application relates generally to x-ray analytical and / or spectroscopy systems. [Background technology]

[0003] 2. Description of Related Art A parallel beam wavelength dispersive spectrometer (PBWDS) diffracts narrow spectral (e.g., energy) bands of X-rays of different energies into different directions according to Bragg's law by impinging a parallel (e.g., collimated) X-ray beam on a single plane Bragg X-ray diffractor (e.g., single crystal, mosaic crystal) and measuring selected portions of the diffracted X-rays using an X-ray detector. PBWDS can be used to measure specific X-ray energies (e.g., characteristic fluorescent X-ray lines of atomic elements or energy points in X-ray absorption spectroscopy) or to measure X-ray spectra across a range of energies by varying the Bragg angle between the X-rays and the crystal plane of the X-ray diffractor. PBWDS can provide higher spectral resolution than energy-dispersive detectors (e.g., silicon drift detectors, lithium drift silicon detectors, lithium drift germanium detectors, photon counting detectors) and can be used in many X-ray spectroscopy techniques, including, but not limited to, elemental (e.g., composition) analysis of a sample by measuring the x-ray fluorescence (XRF) spectrum (e.g., characteristic x-ray lines) emitted from the sample as a result of excitation by ionizing radiation (e.g., energetic electrons, x-rays, protons); x-ray absorption spectroscopy (XAS) by either analyzing the x-ray absorption spectrum of x-rays transmitted through the sample (e.g., transmission-mode XAS) or by irradiating the sample with a tunable monochromatic x-ray beam having a range of x-ray energies while measuring the intensities of the characteristic fluorescent x-rays of elements within the sample (e.g., fluorescence-mode XAS); or x-ray emission spectroscopy (XES) by measuring the x-ray emission spectrum of elements within an object excited by ionizing radiation, e.g., x-rays, electrons, or protons. Summary of the Invention [Means for solving the problem]

[0004] overview In certain embodiments, the apparatus includes a plurality of stacked planar Bragg diffractors, each including at least a first planar Bragg diffractor and a second planar Bragg diffractor. The first and second planar Bragg diffractors are positioned successively along an X-ray propagation axis of an X-ray beam. The X-ray beam includes X-rays and has an angular beam divergence of less than 30 mrad in at least one direction.

[0005] In certain embodiments, the device is configured to receive an X-ray beam propagating along an X-ray propagation axis and having an angular beam divergence of less than 30 mrad in at least one direction substantially perpendicular to the X-ray propagation axis. The device comprises a plurality of serially stacked planar Bragg diffractors rigidly connected to one another, with a separation between adjacent planar Bragg diffractors of less than 200 millimeters. The plurality of serially stacked planar Bragg diffractors is configured to receive the X-ray beam. Each planar Bragg diffractor of the plurality of serially stacked planar Bragg diffractors is configured to diffract a corresponding diffracted portion of the X-ray beam such that spectral overlap between the diffracted portions from different planar Bragg diffractors is less than 25%. The device further comprises at least one X-ray detector configured to receive and detect the diffracted portions.

[0006] In certain embodiments, the apparatus comprises at least one plane Bragg X-ray diffractor configured to receive the X-ray beam and diffract at least one corresponding diffracted portion of the X-ray beam, and the apparatus further comprises at least one energy dispersive X-ray detector configured to receive and detect a transmitted portion of the X-ray beam that is transmitted through the at least one plane Bragg X-ray diffractor. [Brief explanation of the drawings]

[0007] [Figure 1A] 1A and 1B illustrate schematic diagrams of exemplary devices comprising multiple stacked planar Bragg diffractors according to certain embodiments described herein. [Figure 1B] 1A and 1B illustrate schematic diagrams of exemplary devices comprising multiple stacked planar Bragg diffractors according to certain embodiments described herein. [Figure 2] 1A and 1B illustrate schematic diagrams of an exemplary fixture configured to hold multiple stacked planar Bragg diffractors, according to certain embodiments described herein. [Figure 3A] 10A-10C schematically illustrate additional examples of apparatuses comprising a serial stack of multiple planar Bragg diffractors and at least one first X-ray detector, according to certain embodiments described herein. [Figure 3B] 10A-10C schematically illustrate additional examples of apparatuses comprising a serial stack of multiple planar Bragg diffractors and at least one first X-ray detector, according to certain embodiments described herein. [Figure 3C] 10A-10C schematically illustrate additional examples of apparatuses comprising a serial stack of multiple planar Bragg diffractors and at least one first X-ray detector, according to certain embodiments described herein. [Figure 3D] 10A-10C schematically illustrate additional examples of apparatuses comprising a serial stack of multiple planar Bragg diffractors and at least one first X-ray detector, according to certain embodiments described herein. [Figure 4A] 1A and 1B illustrate schematic diagrams of exemplary X-ray beam sources of substantially collimated X-ray beams, in accordance with certain embodiments described herein. [Figure 4B] 1A and 1B illustrate schematic diagrams of exemplary X-ray beam sources of substantially collimated X-ray beams, in accordance with certain embodiments described herein. [Figure 4C] 1A and 1B illustrate schematic diagrams of exemplary X-ray beam sources of substantially collimated X-ray beams, in accordance with certain embodiments described herein. [Figure 5A] 1A and 1B illustrate schematic diagrams of exemplary devices comprising at least one stacked multiple planar Bragg diffractor, according to certain embodiments described herein. [Figure 5B] 1A and 1B illustrate schematic diagrams of exemplary devices comprising at least one stacked multiple planar Bragg diffractor, according to certain embodiments described herein. [Figure 5C] 1A and 1B illustrate schematic diagrams of exemplary devices comprising at least one stacked multiple planar Bragg diffractor, according to certain embodiments described herein. DETAILED DESCRIPTION OF THE INVENTION

[0008] Detailed Description X-ray wavelength dispersive spectrometers utilize a planar Bragg diffractor impinging on a collimated X-ray beam (e.g., X-rays propagating substantially parallel to each other along the X-ray propagation axis). For example, the planar Bragg diffractor of an X-ray wavelength dispersive spectrometer can include a single crystal (e.g., for X-ray energies above about 1.47 keV: diamond, quartz, Si, Ge, LiF; for X-ray energies below about 1.47 keV: InSb, PET, ADP, RAP, beryl, TIAP), a mosaic crystal (e.g., highly annealed pyrolitic graphite (HAPG); highly oriented pyrolitic graphite (HOPG)), or a multilayer.

[0009] The X-ray energy E and total energy resolution ΔE (eg, energy bandwidth) of the X-rays diffracted by the plane Bragg diffractor can be expressed as:

[0010]

number

[0011]

number

[0012] where θ is the Bragg angle, d is the spacing of the crystal planes of the plane Bragg diffractor, λ is the X-ray wavelength corresponding to the X-ray energy E, n is an integer, Δθ is the angular beam divergence (e.g., angular spread) of the X-ray beam in the tangent plane or diffraction plane (e.g., defined by the X-ray propagation axis of the X-ray beam and the normal direction to the crystal planes of the plane Bragg diffractor), and ΔE cis the intrinsic energy resolution of the plane Bragg diffractor (e.g., the value of the total energy resolution ΔE of a highly collimated incident X-ray beam having an angular beam divergence Δθ that is equal to or less than the Darwin width of the plane Bragg diffractor, such as with a synchrotron X-ray source). In certain embodiments, the angular beam divergence Δθ in a direction substantially perpendicular to the diffraction plane can be made much larger than the angular beam divergence Δθ substantially in the diffraction plane, with a minimal increase in the total energy resolution ΔE.

[0013] The angular contribution term in equation (2):

[0014]

number

[0015] represents the contribution to the total energy resolution ΔE due to the angular beam divergence Δθ of the X-ray beam at the Bragg angle θ. For many applications (e.g., XRF, XAS, and XES), a particular value of the total energy resolution ΔE is desired.

[0016] Planar Bragg diffractors have a narrow spectral bandwidth ΔE c diffracts X-rays incident on the plane Bragg diffractor at points along the X-ray propagation axis within ΔE, but propagating along the same X-ray propagation axis and incident on the plane Bragg diffractor at the same point within a narrow spectral bandwidth ΔE c X-rays with energies outside this range are not diffracted, so ΔE c If ΔE is smaller than ΔE, it will lead to inefficient use of the X-rays in the incident X-ray beam.

[0017] Previously disclosed PBWDSs exhibit various limitations. For example, they perform a single X-ray energy measurement at a time using only X-rays within the energy band ΔE recorded by the X-ray detector. To measure X-rays within a different energy band, the Bragg angle of the planar Bragg diffractometer is changed (e.g., to measure two or more characteristic lines for compositional analysis using XRF, or to measure XAS and XES spectra).

[0018] Another exemplary limitation of previously disclosed PBWDSs is their inefficiency in performing multiple spectral measurements. For a collimated X-ray beam propagating along the X-ray propagation axis and incident on a point on a plane Bragg diffractor within a narrow angular beam divergence Δθ (e.g., an angular spread in the diffraction plane less than or equal to the Darwin width of the plane Bragg diffractor), the spectral bandwidth ΔE c Only X-rays with energies within ΔE c X-rays with energies outside this range are not diffracted (e.g., absorbed by the crystal), and therefore these X-rays are not analyzed and are wasted, resulting in low analytical efficiency. α1 For X-ray lines (e.g., about 8 keV), the intrinsic spectral band diffracted by a planar Si(531) crystal operating at a Bragg angle of 57.7 degrees is only 0.06 eV, which is the spontaneous emission of Cu K α1 This is approximately 35 times smaller than the linewidth (e.g., about 2.1 eV) of a mosaic crystal, substantially narrower than the energy resolution (e.g., band) used in most XAS measurements (e.g., X-ray energies for measuring XAS well above the absorption edge ionization energy, which can be up to 6 eV). As another example, while mosaic crystals can diffract X-rays in a broader spectral band than single crystals, their spectral bands can be broader than those utilized for analysis (e.g., when used with an incident X-ray beam with large beam divergence at the diffraction plane), resulting in wasted X-rays and low analytical efficiency. Furthermore, mosaic crystals can cause additional angular broadening of transmitted X-rays due to X-ray scattering by small crystalline platelets within the mosaic crystal, which can worsen the energy resolution of downstream crystals due to increased X-ray beam divergence.

[0019] The energy bandwidth ΔE of X-rays diffracted from a point on a plane Bragg diffractor is given by equation (2), and when the angular beam divergence Δθ of the X-ray beam is larger than the Darwin width of the plane Bragg diffractor, ΔE cExcept for high-order harmonics (e.g., X-ray energies that are integer multiples of the X-ray energy for a given Bragg angle θ), a single planar Bragg diffractor (e.g., a multilayer diffractor, single crystal, mosaic crystal) can be used to diffract X-rays of two or more X-ray energies with an arbitrarily large energy difference (e.g., Cu K α1 and Cu K α2 X-ray lines or K α and K. β multiple characteristic X-ray lines of multiple atomic elements having an energy difference of more than 50 eV, more than 200 eV, more than 1000 eV, or more than 5000 eV; multiple energy points) cannot be measured simultaneously (e.g., concurrently).

[0020] Another exemplary limitation of previously disclosed PBWDS is the ΔE c The difficulty lies in finding a balance between ΔE′ and ΔE′. For higher throughput (e.g., faster data collection rates), ΔE c is ΔE with larger angular beam divergence Δθ that is often associated with the X-ray collection angle (e.g., from a sample for XRF analysis; from a source for XAS analysis). a or ΔE a Ultra (e.g., ΔE a To achieve reasonable energy resolution with large angular beam divergence Δθ, a planar Bragg diffractor can be operated at high Bragg angles, but with ΔE c is significantly narrower than the energy resolution ΔE for measurements (e.g., XRF, XAS, and XES). The angular contribution ΔE to the energy resolution ΔE (see equation (3)) a constrains the minimum Bragg angle to satisfy a given energy resolution ΔE (see equation (2)) for a given angular beam divergence Δθ.

[0021] For example, Δθ=1mrad and ΔE a= 2 eV, a Bragg angle θ of more than 78.7 degrees can be used for X-ray energy E = 10 keV. a = 20 eV. At such high Bragg angles for many applications, the ΔE of a single plane Bragg diffractor c is much narrower than the energy resolution used in many XRF applications, resulting in poor analytical efficiency, especially when using crystals operating at high Bragg angles (e.g., when the angular beam divergence Δθ of the X-ray beam is large). As an example, for a Bragg angle θ = 70 degrees and an X-ray energy E = 8.5 keV, the ΔE for the Ge(551), Si(551), and LiF(333) crystal planes is c are 0.08 eV, 0.03 eV, and 0.03 eV, respectively. These values ​​are the natural linewidths of the characteristic X-ray lines in the energy range from 8 keV to 10 keV (e.g., Cu K at 8 keV). α1 X-ray line width of 2.1 eV; Zn K at 9.2 keV α1 X-ray line width at 2.2 eV; WL at 8.4 keV α1 This is significantly narrower than the linewidth of the X-ray line of 1000 kJ / cm (6 eV). Therefore, these crystals are very inefficient for measuring these characteristic X-rays when operated at high Bragg angles. For most single crystals operated at high Bragg angles, ΔE c decreases with X-ray energy, while the natural linewidth of the characteristic X-ray lines increases with X-ray energy, so the inefficiency becomes more severe for measuring higher energy X-rays. For example, ΔE for the Li(1022) crystal plane at the Bragg angle θ = 66.5 degrees for E = 17.4 keV X-rays is a is 0.01 eV, but Mo K at 17.4 keV α1 The natural linewidth of the X-ray line is about 6.5 eV (e.g., the ratio of the two is about 650 times). Even at moderate Bragg angles (e.g., θ = 30 degrees) for E = 8.5 keV X-rays, the ΔE care 0.31 eV, 0.13 eV, and 0.23 eV, respectively. These values ​​are also much narrower than the energy resolution used in most XRF and XAS measurements, and therefore these crystals are inefficient for measuring characteristic X-ray lines at X-ray energies around 8.5 keV, or for XAS measurements using X-ray energies around 8.5 keV. For X-rays with E = 8.5 keV, the energy resolution ΔE c To approach 2 eV, a Bragg angle θ less than 23 degrees can be used for single crystal Ge plane Bragg diffractors, and a Bragg angle θ less than 14 degrees can be used for single crystal Si, LiF, or diamond plane Bragg diffractors.

[0022] Because the X-ray flux of a parallel X-ray beam generally increases with the angular beam divergence Δθ, operating at a small Bragg angle generally results in a small angular contribution to the energy resolution (e.g., ΔE a < ΔE) because a small Bragg angle reduces the X-ray flux (e.g., characteristic X-rays) from the sample. Furthermore, the angular contribution to the energy resolution is generally limited by the energy separation between the characteristic K X-ray lines of most atomic elements (e.g., Cu K). α1 X-ray lines and Cu K α2 The energy resolution ΔE of many single crystal plane Bragg diffractometers is approximately 20 eV between the X-ray lines of and , which is significantly smaller than the energy separation between the L X-ray lines of many atomic elements. However, using a plane Bragg diffractor at a low Bragg angle (e.g., less than 20 degrees) can provide a better match with the energy bandwidth of the characteristic X-ray lines of many atomic elements, and the X-ray beam has a much smaller angular beam divergence Δθ, resulting in efficient collection of the characteristic X-ray lines from the sample. cIt is also much narrower than the energy resolution (e.g., bandwidth) used for most XAS measurements, especially for X-ray energies for measuring EXAFS, which far exceeds the absorption edge ionization energy. However, the spectral resolution of mosaic crystals (e.g., HOPG; HAPG) may be too broad for various (e.g., XANES; XES) analyses.

[0023] Another exemplary limitation of previously disclosed PBWDS is that only a narrow spectral (e.g., energy) band of X-rays can be diffracted by a single planar Bragg diffractor. α X-ray line of Cu K α CK α X-ray line of Cu K α1 To cover a wide spectral range, different plane Bragg diffractors can be used sequentially in time (e.g., measure with a first plane Bragg diffractor, then switch to a second plane Bragg diffractor, measure with the second plane Bragg diffractor, etc.) to simultaneously measure X-ray lines. For example, a crystal diffractor can be used for hard X-rays (e.g., energies greater than 5 keV), or multiple layers can be used for soft X-rays (e.g., energies less than 1 keV). Certain embodiments described herein use multiple stacked plane Bragg diffractors (e.g., crystal diffractors) to obtain a given total energy resolution while operating at moderate (e.g., 30-45 degrees) and high (e.g., greater than 60 degrees) Bragg angles. Certain embodiments described herein achieve an intrinsic energy resolution ΔE that approaches (e.g., substantially equals) the total energy resolution ΔE to obtain efficient use of incident X-rays with X-ray energies within an energy bandwidth ΔE. c A plane Bragg diffractor with a value of ΔE is used. c If the difference between and ΔE is small (e.g., this can be considered a measure of the efficiency of a planar Bragg diffractor), the angular contribution ΔE a(see equation (3)) can be configured to be small. For example, a large Bragg angle θ, a small angular beam divergence Δθ, or a combination of both can be configured to have a small value of ΔE a Since the incident X-ray beam flux increases with angular beam divergence Δθ, certain embodiments described herein can achieve ΔE close to ΔE c To obtain the desired X-ray diffraction pattern, the stacked planar Bragg diffractometer is bombarded with an X-ray beam at a high Bragg angle, providing increased X-ray analysis speed.

[0024] Certain embodiments described herein provide an energy-dispersive detector system comprising at least two stacked planar Bragg diffractors and an energy-dispersive detector positioned to receive diffracted X-rays from the at least two stacked planar Bragg diffractors. The energy-dispersive detector has an energy resolution equal to or greater than the energy difference between the average X-ray energies of the X-rays diffracted by the at least two stacked planar crystal diffractors. For example, the at least two stacked planar crystal diffractors and one X-ray detector can be configured such that the X-ray detector receives some X-rays diffracted by the at least two stacked planar crystal diffractors, and the X-ray detector has an energy resolution equal to or greater than the energy difference between the average X-ray energies of the X-rays diffracted by the at least two stacked planar crystal diffractors. In certain embodiments, the energy-dispersive detector system reduces (e.g., minimizes) the number of X-ray detectors used (e.g., by selecting the Bragg angles of the at least two stacked planar crystal diffractors, the distance between the at least two stacked planar crystal diffractors, and the relative position of the X-ray detector with respect to the at least two stacked planar crystal diffractors). The stacked planar crystal diffractors can include different materials, or the same materials but with different Miller indices. The X-ray detector can be an energy dispersive detector (e.g., silicon drift detector, Li drift silicon or germanium detector, photon counting detector with selectable energy window, superconductor-based microcalorimeter).

[0025] 1A and 1B schematically illustrate two example apparatus 100 (e.g., an X-ray crystal diffractor; an array of sequentially arranged planar Bragg diffractors; PBWDS) according to certain embodiments described herein. The apparatus 100 includes a plurality of stacked planar Bragg diffractors 110 including at least first and second planar Bragg diffractors 110a, 110b (e.g., multilayer; single crystal; mosaic crystal) sequentially positioned along an X-ray propagation axis 122 of an X-ray beam 120 comprising X-rays 124 and having an angular beam divergence Δθ of less than 30 mrad (e.g., less than 10 mrad; less than 2 mrad; less than 0.2 mrad) in at least one plane that includes the X-ray propagation axis 122 (e.g., in at least one direction substantially perpendicular to the X-ray propagation axis 122). For example, at least one planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 may comprise a multilayer structure including periodic layers of alternating high and low mass density materials (e.g., Cr / C; W / C; Mo / Si) having a d-spacing in the range of 3 nanometers to 30 nanometers, and single crystals selected from the group consisting of diamond, quartz, graphite, stacks of graphene layers, other materials containing low atomic number elements, silicon (Si), germanium (Ge), lithium fluoride (LiF), mica, indium antimonide (InSb), polyethylene terephthalate (PET), ammonium dihydrophosphate (ADP), rubidium oxyphthalate (RAP), beryl, and thallium oxyphthalate (TIAP), and / or mosaic crystals selected from the group consisting of highly annealed pyrolytic graphite (HAPG) and highly oriented pyrolytic graphite (HOPG).

[0026] As used herein, the term "planar Bragg diffractor" has its broadest reasonable interpretation, including, but not limited to, a diffractor comprising a substantially flat (e.g., planar; radius of curvature greater than 100 meters) multilayer, single crystal, or mosaic crystal configured to diffract X-rays according to Bragg's law. As used herein, the term "stacked planar Bragg diffractor" has its broadest reasonable interpretation, including, but not limited to, multiple planar Bragg diffractors connected (e.g., rigidly fixed) to each other via a mechanical bond (e.g., by a common fixture with or without angular adjustment therebetween) and configured such that the planar Bragg diffractors are sequentially impinged by the X-ray beam (e.g., arranged sequentially along the X-ray beam axis). For example, an X-ray beam may be incident on (e.g., impinge upon) a first planar Bragg diffractor (e.g., the most upstream planar Bragg diffractor), a portion of the X-ray beam transmitted through the first planar Bragg diffractor may be incident on (e.g., impinge upon) a second planar Bragg diffractor (e.g., the next planar Bragg diffractor downstream of the most upstream planar Bragg diffractor), and a portion of the X-ray beam may be transmitted through the second planar Bragg diffractor. In an example having three or more planar Bragg diffractors, the portion transmitted through the planar Bragg diffractor may be incident on (e.g., impinge upon) the next downstream planar Bragg diffractor until the most downstream planar Bragg diffractor receives (e.g., is impinged upon by) the portion of the X-ray beam transmitted through the previous planar Bragg diffractor. As used herein, the term "planar Bragg diffractor" used in the singular includes a single planar Bragg diffractor and a single stack of planar Bragg diffractors unless otherwise specified. As used herein, the terms "multiple planar Bragg diffractors," "plurality of planar Bragg diffractors," and "two planar Bragg diffractors" have their broadest reasonable interpretation, including, but not limited to, two or more individual planar Bragg diffractors and / or two or more stacks of planar Bragg diffractors.

[0027] 1A and 1B, the second planar Bragg diffractor 110b is downstream of the first planar Bragg diffractor 110a (e.g., the second planar Bragg diffractor 110b may be farther from the source of the X-ray beam 120 than the first planar Bragg diffractor 110a). The first planar Bragg diffractor 110a is configured to diffract a first diffracted portion 130a of the X-rays 124 and transmit a first transmitted portion 140a of the X-rays 124, and the second planar Bragg diffractor 110b is configured to diffract a second diffracted portion 130b of the first transmitted portion 140a and transmit a second transmitted portion 140b of the first transmitted portion 140a. The first diffractive portion 130a has a first average (e.g., central) X-ray energy E1 and a first energy resolution ΔE1, and the second diffractive portion 130b has a second average (e.g., central) X-ray energy E2 and a second energy resolution ΔE2, where the second X-ray energy E2 is different from the first X-ray energy E1.

[0028] 1A includes first and second planar Bragg diffractors 110a, 110b, while the example apparatus 100 of FIG. 1B includes first, second, and third planar Bragg diffractors 110a, 110b, 110c stacked on top of one another and positioned consecutively along the X-ray propagation axis 122 (e.g., the third planar Bragg diffractor 110c is downstream from the second planar Bragg diffractor 110b). The third planar Bragg diffractor 110c can be configured to diffract a third diffracted portion 130c of the second transparent portion 140b and transmit a third transparent portion 140c of the second transparent portion 140b. The third diffractive portion 130c can have a third average (e.g., median) X-ray energy E3 and a third energy resolution ΔE3, where the third X-ray energy E3 is different from the first X-ray energy E1 and the second X-ray energy E2. In certain embodiments, the positioning and alignment of one or more planar Bragg diffractors 110 (e.g., first planar Bragg diffractor 110a, second planar Bragg diffractor 110b, and / or third planar Bragg diffractor 110c) relative to the X-ray propagation axis 122 is performed individually or simultaneously using an adjustment mechanism (e.g., a computer-controlled motorized adjustment mechanism) of the fixture.

[0029] In certain embodiments, the plurality of stacked planar Bragg diffractors 110 includes two or more planar Bragg diffractors 110 (e.g., 2, 3, 4, or 5; 2-10; 5-10; less than 20; less than 100; more than 5; more than 20; more than 100) stacked on top of one another and positioned consecutively along the X-ray propagation axis 122. The maximum number of planar Bragg diffractors 110 may be limited by the cumulative X-ray transmittance of the plurality of stacked planar Bragg diffractors 110.

[0030] In certain embodiments, the multiple stacked planar Bragg diffractors 110 can be configured to simultaneously diffract four or more (e.g., more than 10; more than 20; more than 30) characteristic X-ray lines with an energy resolution better than 30 eV (e.g., for XRF analysis using a scanning electron microscope and a micro-XRF system). In certain embodiments, at least one planar Bragg diffractor 110 is configured to diffract a single characteristic X-ray line (e.g., two stacked planar Bragg diffractors 110 including LiF crystals are configured to diffract a CuK α1 (Configured to diffract X-ray lines of 10 eV.) If the angular beam divergence of the X-ray beam 120 is 10 mrad, and the stacked planar Bragg diffractor 110 is operated at a high Bragg angle, such that the Darwin width at which the energy resolution is limited is narrower than the energy bandwidth of the characteristic X-ray line being measured, the energy resolution can be better than 2 eV.

[0031] In certain embodiments, at least the most upstream planar Bragg diffractor 110 (e.g., the first planar Bragg diffractor 110a) of the plurality of stacked planar Bragg diffractors 110 is oriented at 1 keV (e.g., CK αThe stacked planar Bragg diffractors 110 may include a multi-layer Bragg diffractor configured to diffract X-rays 124 having X-ray energies less than 1 keV (e.g., an X-ray line of 1 keV). The next downstream planar Bragg diffractor 110 (e.g., the second planar Bragg diffractor 110b) of the plurality of stacked planar Bragg diffractors 110 may include PET, ADP, or RAP and may be configured to diffract X-rays 124 having X-ray energies greater than 1 keV (e.g., in the range of 1 keV to 3 keV), and the most downstream planar Bragg diffractor 110 (e.g., the third planar Bragg diffractor 110c) of the plurality of stacked planar Bragg diffractors 110 may include a single crystal or a mosaic crystal and may be configured to diffract X-rays 124 having X-ray energies greater than 3 keV (e.g., greater than 5 keV). In certain embodiments, at least one planar Bragg diffractor 110 is configured to diffract X-rays 124 having a characteristic X-ray line energy of a given atomic element, and at least another planar Bragg diffractor 110 is configured to diffract X-rays 124 having an X-ray energy close to but different from the characteristic X-ray line energy (e.g., greater than the energy bandwidth of the characteristic X-ray line and having an energy difference of 140 eV or less, less than 50 eV, or less than 10 eV) to measure background contributions to the detected X-rays (e.g., not arising from the characteristic X-ray line).

[0032] In certain embodiments, the stacked planar Bragg diffractors 110 are positioned along the X-ray propagation axis 122 such that the distance along the X-ray propagation axis is less than 200 millimeters (e.g., the distance between the most upstream and most downstream planar Bragg diffractors 110 is less than 200 millimeters). In certain embodiments, at least two adjacent planar Bragg diffractors 110 are positioned along the X-ray propagation axis 122 such that they are spaced apart from each other along the X-ray propagation axis 122 by less than 200 millimeters (e.g., less than 50 millimeters; less than 30 millimeters; less than 20 millimeters; less than 10 millimeters; less than 2 millimeters; less than 1 millimeter; less than 0.2 millimeters). In certain embodiments, each planar Bragg diffractor 110 (e.g., the first and second planar Bragg diffractors 110a, 110b) of the multiple stacked planar Bragg diffractors 110 can simultaneously satisfy the Bragg condition for an X-ray beam 120 having an angular beam divergence Δθ of less than 15 mrad (e.g., less than 3 mrad; less than 1 mrad; less than 0.3 mrad) in the diffraction plane within an energy bandwidth of less than 25 eV (e.g., less than 10 eV; less than 5 eV; less than 1 eV), and the intensity overlap of at least two X-ray energies of the diffracting portions 130 is less than 5% (e.g., less than 1%).

[0033] In certain embodiments, at least one planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 is symmetrically cut, while in certain other embodiments, at least one planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 is asymmetrically cut (e.g., increasing its effective Darwin width by 1.2 to 5 times; decreasing its effective Darwin width by 1.2 to 5 times) to diffract X-rays 124 at a different (e.g., wider or narrower) energy resolution than the symmetrically cut form of at least one planar Bragg diffractor 110. In certain embodiments, at least one planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 comprises an asymmetrically cut crystal configured to be rotated 180 degrees to switch at least one planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 from an increased effective Darwin width to a decreased effective Darwin width, or vice versa.

[0034] In certain embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 (e.g., the first and second planar Bragg diffractors 110a, 110b; the first and third planar Bragg diffractors 110a, 110c; the second and third planar Bragg diffractors 110b, 110c; the first, second, and third planar Bragg diffractors 110a, 110b, 110c) comprise the same material as each other. In certain embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 (e.g., the first and second planar Bragg diffractors 110a, 110b; the first and third planar Bragg diffractors 110a, 110c; the second and third planar Bragg diffractors 110b, 110c; the first, second, and third planar Bragg diffractors 110a, 110b, 110c) comprise materials that are different from each other. At least two of the multiple stacked planar Bragg diffractors 110 can be configured to simultaneously satisfy the Bragg condition for incident X-rays 124 propagating along the X-ray propagation axis 122, with a narrow spectral bandwidth (e.g., less than 25 eV; less than 10 eV; less than 5 eV; less than 2 eV; less than 1 eV) and a small angular beam divergence (e.g., less than 30 mrad; less than 20 mrad; less than 10 mrad; less than 5 mrad; less than 3 mrad; less than 2 mrad; less than 1 mrad; less than 0.3 mrad; less than 0.2 mrad), while minimizing overlap of diffracted X-ray intensities by the at least two planar Bragg diffractors 110 (e.g., less than 5%; less than 1%).

[0035] At least one planar Bragg diffractor 110 of the multiple stacked planar Bragg diffractors 110 (e.g., the most upstream planar Bragg diffractor 110; the first planar Bragg diffractor 110a in FIG. 1A; each of the first and second planar Bragg diffractors 110a, 110b in FIG. 1B) can have a thickness (e.g., thickness along the X-ray propagation axis 122) greater than 1 micron (e.g., greater than 2 microns) and less than 500 microns (e.g., less than 300 microns; less than 100 microns; less than 50 microns; less than 20 microns; less than 5 microns). For example, in FIG. 1A, the thickness of the first planar Bragg diffractor 110a can be greater than or equal to the extinction length for X-rays 124 having the second X-ray energy E2 in the material of the first planar Bragg diffractor 110a. As another example, in FIG. 1B , the thickness of first planar Bragg diffractor 110a can be greater than or equal to the extinction length for X-rays 124 having second X-ray energy E2 and X-rays 124 having third X-ray energy E3 in the material of first planar Bragg diffractor 110a, and the thickness of second planar Bragg diffractor 110b can be greater than or equal to the extinction length for X-rays 124 having third X-ray energy E3 in the material of second planar Bragg diffractor 110b.

[0036] Each planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 can have an X-ray transmittance of greater than 1% (e.g., greater than 2%; greater than 5%; greater than 30%) for X-rays 124 diffracted by the downstream planar Bragg diffractor 110. For example, in FIG. 1A , the first planar Bragg diffractor 110a can have a first X-ray transmittance of greater than 1% for X-rays 124 having the second X-ray energy E2. As another example, in FIG. 1B , the first planar Bragg diffractor 110a can have a first X-ray transmittance of greater than 1% for X-rays 124 having the second X-ray energy E2 and a third X-ray transmittance of greater than 1% for X-rays 124 having the third X-ray energy E3, and the second planar Bragg diffractor 110b can have a second X-ray transmittance of greater than 1% for X-rays 124 having the third X-ray energy E3. The multiple stacked planar Bragg diffractors 110 can have an integrated reflectivity approximately equal to the sum of the integrated reflectivities of the individual planar Bragg diffractors 110 of the multiple stacked planar Bragg diffractors 110 reduced by the X-ray absorption by at least one upstream planar Bragg diffractor 110 (e.g., the first planar Bragg diffractor 110a in FIGS. 1A and 1B ). The most upstream planar Bragg diffractor 110 (e.g., the first planar Bragg diffractor 110a) can have an X-ray transmittance of greater than 50% for X-rays 124 within an energy bandwidth of a diffraction portion 130 of the X-rays 124 diffracted by at least one downstream planar Bragg diffractor 110 (e.g., the second planar Bragg diffractor 110b; the third planar Bragg diffractor 110c). The most upstream planar Bragg diffractor 110 (e.g., the first planar Bragg diffractor 110a) of the multiple stacked planar Bragg diffractors 110 can have an X-ray transmittance greater than the X-ray transmittance of the downstream planar Bragg diffractor 110 (e.g., the second planar Bragg diffractor 110b) within the entire spectral bandwidth of the multiple stacked planar Bragg diffractors 110.In certain embodiments in which the X-rays 124 transmitted through the most downstream planar Bragg diffractor 110 (e.g., the second planar Bragg diffractor 110b in FIG. 1A; the third planar Bragg diffractor 110c in FIG. 1B) are not used for further analysis, the most downstream planar Bragg diffractor 110 may have low X-ray transmittance (e.g., comprise Ge or another high atomic number material; have a thickness greater than 300 microns) and / or may have a coarser energy resolution than the energy resolution of the most upstream planar Bragg diffractor 110 of the multiple stacked planar Bragg diffractors 110.

[0037] The diffractive portions 130 (e.g., the first diffractive portion 130a and the second diffractive portion 130b in FIG. 1A; the first, second, and third diffractive portions 130a, 130b, and 130c in FIG. 1B) can have a total spectral bandwidth (e.g., the sum of the spectral bandwidths of the diffractive portions 130) that substantially matches a predetermined energy range (e.g., an energy range used for a given analysis). The transmitted portion of the most downstream planar Bragg diffractor 110 (e.g., the second transmitted portion 140b transmitted through the second planar Bragg diffractor 110b in FIG. 1A; the third transmitted portion 140c transmitted through the third planar Bragg diffractor 110c in FIG. 1B) can have an X-ray flux sufficient for analysis by one or more X-ray detectors (not shown in FIGS. 1A and 1B) positioned downstream of the most downstream planar Bragg diffractor 110. In certain embodiments, the multiple stacked planar Bragg diffractors 110 have an X-ray transmittance of greater than 3% for X-rays 124 outside the full spectral bandwidth of the diffraction portion 130. For example, the transmitted portion transmitted through the most downstream planar Bragg diffractor 110 has sufficient X-ray flux for further analysis by at least one additional spectrometer (e.g., another X-ray stacked crystal diffractor; an array of serially arranged planar Bragg diffractors; a single crystal diffractor; a mosaic crystal diffractor; an energy dispersive detector). In certain embodiments, the multiple stacked planar Bragg diffractors 110 contribute an angular spread of less than 15 mrad (e.g., less than 10 mrad) to the transmitted portion.

[0038] In certain embodiments in which at least two of the plurality of stacked planar Bragg diffractors 110 (e.g., the first and second planar Bragg diffractors 110a, 110b; the first and third planar Bragg diffractors 110a, 110c; the second and third planar Bragg diffractors 110b, 110c; the first, second, and third planar Bragg diffractors 110a, 110b, 110c) comprise the same material as each other, the at least two planar Bragg diffractors 110 are configured to diffract X-rays 124 at atomic planes having the same Miller indices as each other (e.g., LiF(111); LiF(200); Si(111)). The mean X-ray energy E of the diffractive portion 130 from each of the at least two planar Bragg diffractors 110 (e.g., the first and second mean energies E1, E2 of the first and second planar Bragg diffractive portions 130a, 130b) can be different from each other, and each of the at least two diffractive portions 130 can have a spectral bandwidth that is less than or equal to half the energy resolution ΔE from the corresponding planar Bragg diffractor 110 (e.g., the first and second diffractive portions 130a, 130b can have spectral bandwidths of ΔE1≦0.5·ΔE and ΔE2≦0.5·ΔE, respectively; the first, second, and third diffractive portions 130a, 130b, 130c can have spectral bandwidths of ΔE1≦0.3·ΔE, ΔE2≦0.3·ΔE, and ΔE3≦0.3·ΔE, respectively). The overlap of the spectral bandwidths of the at least two diffractive portions 130 can be 5% or less (e.g., less than 1%) of at least one of the spectral bandwidths. In certain embodiments, the difference between the average energies of the at least two diffractive portions 130 is less than or equal to the spectral bandwidth of at least one of the spectral bandwidths (e.g., (E2-E1)≦ΔE1 and / or (E2-E1)≦ΔE2).

[0039] For example, the X-rays 124 can be incident on each of at least two planar Bragg diffractors 110 of the plurality of stacked planar Bragg diffractors 110 at different Bragg angles (e.g., a difference of at least 1 Darwin width but less than 30 Darwin widths (e.g., less than 10, 5, or 3 Darwin widths)) such that there is substantially zero spectral overlap between the diffracted portions 130 from the at least two planar Bragg diffractors 110. The difference in Bragg angles can be greater than 10 microradians (e.g., greater than 50 microradians; greater than 500 microradians; greater than 5 mrad; greater than 300 mrad). In another example, the x-rays 124 can be incident on each of the at least two planar Bragg diffractors 110 at substantially equal Bragg angles, and the at least two planar Bragg diffractors 110 can have different d-spacings (e.g., a difference of at least one Darwin width but less than 30 Darwin widths (e.g., less than 10, 5, or 3 Darwin widths)) of the diffracting atomic planes of the at least two planar Bragg diffractors 110. The different d-spacings can be achieved by having the at least two planar Bragg diffractors 110 at different temperatures. For example, LiF has a thermal expansion coefficient of 37×10 at 283° C. -6 / K (e.g., more than 10 times higher than Si) and a thermal conductivity of 0.113 W / K / cm at 314° C. (e.g., more than 15 times lower than Si). A combination of temperature difference and relative Bragg angle difference can be used to simultaneously satisfy the Bragg condition for incident X-rays 124 propagating along the X-ray propagation axis 122 to be in a narrow spectral bandwidth (e.g., less than 25 eV; less than 10 eV; less than 5 eV; less than 2 eV; less than 1 eV) and have a small angular beam divergence (e.g., less than 30 mrad; less than 20 mrad; less than 10 mrad; less than 5 mrad; less than 3 mrad; less than 2 mrad; less than 1 mrad; less than 0.3 mrad; less than 0.2 mrad) with minimal overlap (e.g., less than 5%; less than 1%) of the diffracted X-ray intensities by the at least two planar Bragg diffractors 110.

[0040] In certain embodiments, at least one planar Bragg diffractor 110 of the plurality of stacked planar Bragg diffractors 110 has an upstream-most surface, a downstream-most surface, and a temperature difference between the two surfaces, the temperature difference being configured to change the d-spacing of a crystal plane of the at least one planar Bragg diffractor 110. For example, the temperature difference can be generated by heating or cooling one of the two surfaces, or by heating one of the two surfaces and cooling the other of the two surfaces. The ratio of the change in d-spacing due to the temperature difference to the d-spacing of a crystal plane without the temperature difference can be in the range of 10 microradians to 400 microradians (e.g., in the range of 10 microradians to 50 microradians; in the range of 10 microradians to 200 microradians; in the range of 50 microradians to 200 microradians; or in the range of 200 microradians to 400 microradians).

[0041] In certain embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 are fabricated from a single crystal block. For example, by removing material from between portions of the single crystal block, different portions of the single crystal block can function as different planar Bragg diffractors 110 having corresponding predetermined thicknesses and predetermined spacings between adjacent planar Bragg diffractors 110 of the plurality of stacked planar Bragg diffractors 110. The fixture can include a tilting mechanism configured to introduce or controllably modify a predetermined angular tilt (e.g., between 5 microradians and 300 mrad) between crystal planes of the at least two planar Bragg diffractors 110.

[0042] In certain other embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 are fabricated separately from one another to have corresponding crystal planes with predetermined materials, thicknesses, and predetermined Miller indices (e.g., at a predetermined asymmetric angle relative to the crystal planes), and the at least two planar Bragg diffractors 110 are fixed (e.g., connected; mounted) to a fixture so that the at least two planar Bragg diffractors 110 have a predetermined angular tilt (e.g., 5 microradians to 300 mrad) between the crystal planes of the at least two planar Bragg diffractors 110.

[0043] 2 schematically illustrates an exemplary fixture 200 configured to hold multiple stacked planar Bragg diffractors 110, according to certain embodiments described herein. The fixture 200 includes a rigid frame 202 and multiple diffractor mounts 210 configured to hold the multiple stacked planar Bragg diffractors 110 along the X-ray propagation axis 122 of the X-ray beam 120. Each diffractor mount 210 includes a first portion 212 configured to be secured to a corresponding planar Bragg diffractor 110 of the multiple stacked planar Bragg diffractors 110, the first portion 212 being substantially transparent to the X-ray beam 120, a second portion 214 configured to be controllably moved to adjust the angle of the corresponding planar Bragg diffractor 110 relative to the X-ray propagation axis 122, and a third portion 216 configured to bend in response to movement of the second portion 214. The first portion 212 may include a hole that penetrates the diffractor mount 210 and / or a membrane having X-ray transmittance (e.g., greater than 50%) to X-rays 124 diffracted by one or more other downstream planar Bragg diffractors 110. The membrane may be configured to support a planar Bragg diffractor 110 that is not rigid enough to self-support across the hole. The fixture 200 may further include a plurality of adjustment mechanisms 220 configured to controllably (e.g., manually; electronically) move the second portions 214 of the plurality of diffractor mounts 210. For example, each adjustment mechanism 220 may include a threaded through-hole and a set screw that extends from the through-hole and contacts the second portion 214 of the diffractor mount 210. By adjusting (e.g., manually; electronically) the extent of the set screw from the through-hole, second portion 214 can be controllably moved against the restoring force generated by the flexing third portion 216 to adjust the angular tilt of the corresponding planar Bragg diffractor 110 (e.g., diffractor mount 210 functions as a lever arm around which third portion 216 acts as a pivot point). In certain embodiments, at least one of diffractor mounts 210 includes a through-hole 230 configured to provide access to an adjustment mechanism 220 (e.g., a set screw) mechanically coupled to another of diffractor mounts 210.

[0044] 3A-3D schematically illustrate four additional examples of an apparatus 100 (e.g., an X-ray crystal diffractor; an array of serially arranged planar Bragg diffractors) according to certain embodiments described herein. The apparatus 100 comprises a serial stack 300 of a plurality of planar Bragg diffractors 110 (e.g., a plurality of stacked planar Bragg diffractors 110) and at least one first X-ray detector 310. At least two planar Bragg diffractors 110 of the plurality of planar Bragg diffractors 110 (e.g., including at least one single crystal and / or at least one mosaic crystal) are stacked (e.g., mounted; rigidly attached) to one another such that the separation (e.g., distance) between adjacent planar Bragg diffractors 110 of the at least two planar Bragg diffractors 110 along a direction substantially parallel to the X-ray propagation axis 122 is less than 200 millimeters (e.g., less than 50 millimeters; less than 30 millimeters; less than 20 millimeters; less than 10 millimeters; less than 2 millimeters; less than 1 millimeter; less than 0.2 millimeters). 3A-3D, first, second, and third planar Bragg diffractors 110a, 110b, 110c are stacked on top of one another and configured to diffract first, second, and third diffracting portions 130a, 130b, 130c, respectively, in a direction toward at least one first X-ray detector 310. The continuous stack 300 may include at least two of the plurality of planar Bragg diffractors 110 mounted in a fixture 200 (see, e.g., FIG. 2) configured to align the spatial positions and / or orientations (e.g., Bragg angles) of the plurality of planar Bragg diffractors 110 with respect to the X-ray propagation axis 122. In certain embodiments, positioning and alignment of the continuous stack 300, at least a portion of the plurality of planar Bragg diffractors 110, and / or the at least one first X-ray detector 310 is performed using one or more computer-controlled motorized motion stages.

[0045] 1A and 1B, the first and second diffractive portions 130a, 130b can have first and second mean X-ray energies E1 and E2, respectively, and the third diffractive portion 130c can have a third mean X-ray energy E3. Furthermore, the first planar Bragg diffractor 110a can have a first X-ray transmittance of greater than 1% for X-rays 124 having the second X-ray energy E2 and a third X-ray transmittance of greater than 1% for X-rays 124 having the third X-ray energy E3, and the second planar Bragg diffractor 110b can have a second X-ray transmittance of greater than 1% for X-rays 124 having the third X-ray energy E3.

[0046] In certain embodiments, each of the at least two planar Bragg diffractors 110 of the continuous stack 300 is configured to diffract X-rays 124 toward at least one first X-ray detector 310, and the at least two diffracting portions 130 have mean X-ray energies that differ from each other by less than 30 eV (e.g., less than 10 eV; less than 5 eV; less than 2 eV). In certain embodiments, each of the at least two planar Bragg diffractors 110 is configured to diffract X-rays 124 toward at least one first X-ray detector 310, and the at least two diffracting portions 130 have mean X-ray energies that differ from each other by more than 50 eV (e.g., more than 100 eV; more than 200 eV; more than 500 eV; more than 2000 eV). At least two of the diffractive portions 130 (e.g., the first, second, and third diffractive portions 130a, 130b, 130c) have substantially no overlapping spectral intensities with one another (e.g., less than 5%; less than 1%; less than 0.1%). While Figures 3A-3D show three stacked planar Bragg diffractors 110 (e.g., the first, second, and third planar Bragg diffractors 110a, 110b, 110c), certain other embodiments include two stacked planar Bragg diffractors 110 or more than three (e.g., three, four, or five; 3-10; 5-10) stacked planar Bragg diffractors 110.

[0047] In certain embodiments, the at least one first X-ray detector 310 is configured to receive at least a portion of the diffracted portions 130 of the X-rays 124 diffracted by the multiple planar Bragg diffractors 110 of the continuous stack 300 and output a detected electrical signal in response to the received diffracted portions 130. For example, as shown in FIGS. 3A-3D , the at least one first X-ray detector 310 is configured to receive the first, second, and third diffracted portions 130a, 130b, and 130c of the X-rays 124 diffracted by the first, second, and third planar Bragg diffractors 110a, 110b, and 110c. The at least one first X-ray detector 310 may include at least one of a proportional counter, an ionization chamber, a silicon drift detector, a Li drift silicon or germanium detector, an X-ray scintillator counter, a pin diode detector, or an X-ray photon counter having multiple active detection elements (e.g., pixels). The at least one first X-ray detector 310 may have an energy resolution of less than 25% (e.g., less than 10%) of the average energy of the at least one diffracted portion 130 received by the at least one first X-ray detector 310. The at least one first X-ray detector 310 may be configured to reduce (e.g., minimize; eliminate) contributions to the detected electrical signal from higher diffraction orders or harmonics.

[0048] In certain embodiments, at least two planar Bragg diffractors 110 of the continuous stack 300 are stacked on top of each other, and another planar Bragg diffractor (e.g., multilayer; single crystal; mosaic crystal) is positioned consecutively (e.g., downstream) from the at least two stacked planar Bragg diffractors 110 along the X-ray propagation axis 122 and is not stacked with the at least two stacked planar Bragg diffractors 110. For example, as shown in FIG. 3B , the apparatus 100 includes at least one additional planar Bragg diffractor 320 positioned consecutively from the continuous stack 300 along the X-ray propagation axis 122. The apparatus 100 further includes at least one second X-ray detector 324. The at least one additional planar Bragg diffractor 320 is configured to diffract at least one additional diffracted portion 322 of the X-rays 124 toward the at least one second X-ray detector 324. The at least one additional planar Bragg diffractor 320 can include a multilayer diffractor, a single crystal diffractor, a mosaic crystal diffractor, and / or combinations thereof (e.g., additional serial stacks 300). The at least one second X-ray detector 324 can include at least one of a proportional counter, an ionization chamber, a silicon drift detector, an X-ray scintillator counter, a pin diode detector; or an X-ray photon counter having multiple active detection elements (e.g., pixels). In certain embodiments, positioning and alignment of the at least one second X-ray detector 324 is performed using a computer-controlled motorized motion stage.

[0049] In certain embodiments, the apparatus 100 further comprises at least one third X-ray detector 330 configured to receive X-rays 124 transmitted through the continuous stack 300 (see, e.g., FIG. 3C ) or transmitted through the continuous stack 300 and at least one additional planar Bragg diffractor 320 (see, e.g., FIG. 3D ). The continuous stack 300 can be configured to have an X-ray transmittance of greater than 1% for the X-rays 124 detected by the at least one third X-ray detector 330. The at least one first X-ray detector 310 may include a pixel array detector (e.g., a photon-counting pixel array detector having at least one energy threshold and configured to reject X-rays having X-ray energies below the at least one energy threshold and / or reject X-rays having X-ray energies above the at least one energy threshold), and the at least one third X-ray detector 330 may include an energy-dispersive detector (e.g., a silicon drift detector, a Li-drift silicon or germanium detector, a photon-counting detector with a selectable energy window, a superconductor-based microcalorimeter). The pixel array detector may be configured such that a first pixel receives the first diffracted portion 130a, a second pixel receives the second diffracted portion 130b, and a third pixel receives the third diffracted portion 130c, wherein the first pixel is different from the second and third pixels, and the second pixel is different from the third pixel. In certain embodiments, the positioning and alignment of the at least one third X-ray detector 330 is performed using a computer-controlled motorized motion stage.

[0050] In certain embodiments, the continuous stack 300 is configured to diffract at least one predetermined characteristic X-ray line having a relatively weak intensity (e.g., due to low concentrations of associated atomic elements and / or low fluorescence yield) or a relatively low X-ray energy, and the at least one first X-ray detector 310 includes an energy dispersive detector. The at least one predetermined characteristic X-ray line can be used by the at least one third X-ray detector 330 to resolve the spectral overlay, thereby enabling analysis of a wide spectral range of X-rays with a sufficient signal-to-noise ratio to detect weak spectral lines and / or resolve interfering spectral lines.

[0051] In certain embodiments, the continuous stack 300 and at least one X-ray detector 310 are configured to simultaneously measure multiple energy bands, such as simultaneously measuring multiple characteristic X-ray lines. α The X-ray lines of Cu K can be measured using a multilayer diffractometer with a continuous stack of 300. α1 X-ray lines can be measured simultaneously by a single crystal or a mosaic crystal of the continuous stack 300. In certain other embodiments, the continuous stack 300 and at least one X-ray detector 310 can simultaneously measure X-ray lines using a single crystal or a mosaic crystal of the continuous stack 300. α Another planar Bragg diffractometer 110 in the continuous stack 300 is configured to simultaneously measure X-ray lines of Cu K α1 X-ray lines of Cu L α The X-ray beam is used to measure at least one of the X-ray lines.

[0052] In certain embodiments, apparatus 100 further comprises at least one X-ray shield configured to be substantially opaque to X-rays 124 and selectively positioned to either allow corresponding diffracted portions 130 of X-rays 124 to reach at least one X-ray detector 310 or block corresponding diffracted portions 130 of X-rays 124 from reaching at least one X-ray detector 310. For example, at least one X-ray shield can controllably block first diffracted portion 130 from reaching at least one X-ray detector 310 such that at least one X-ray detector 310 receives only second diffracted portion 130b and / or third diffracted portion 130c to provide higher energy resolution.

[0053] 4A-4C schematically illustrate three exemplary X-ray beam sources 400 (e.g., primary source; secondary source) of a substantially collimated X-ray beam 120 according to certain implementations described herein. The X-ray beam source 400 includes an X-ray source 410 and at least one collimating X-ray optic 420 configured to receive X-rays 124 propagating from the X-ray source 410 and form a collimated X-ray beam 120 (e.g., having an angular beam divergence of less than 30 mrad in at least one plane that includes the X-ray propagation axis 122 and / or in at least one direction substantially perpendicular to the X-ray propagation axis 122). The X-ray beam source 400 is configured to output a substantially collimated (e.g., parallel) X-ray beam 120 having a small angular beam divergence (e.g., less than 30 mrad; less than 20 mrad; less than 10 mrad; less than 5 mrad; less than 3 mrad; less than 2 mrad; less than 1 mrad; less than 0.3 mrad; less than 0.2 mrad) along the X-ray propagation axis 122 (e.g., the longitudinal axis of the at least one collimating X-ray optic 420). In certain embodiments, positioning and alignment of at least one of the X-ray source 410 and the at least one collimating X-ray optic 420 is performed using at least one computer-controlled motorized motion stage.

[0054] In certain embodiments, the X-ray source 410 is configured to generate X-rays 124 in response to the incidence of ionizing radiation (e.g., X-rays, charged particles, electrons, protons). As shown in FIGS. 4A and 4B, the X-ray source 410 can include a point source (e.g., the X-rays 124 propagate from a spot size of less than 200 microns or less than 30 microns in at least one direction substantially perpendicular to the X-ray propagation axis 122). As shown in FIG. 4C, the X-ray source 410 can include an extended source (e.g., the X-rays 124 propagate from a range of positions ranging from 20 millimeters to 1000 millimeters along at least one direction substantially perpendicular to the X-ray propagation axis 122). The X-ray source 410 can include a sample to be analyzed using the apparatus 100, where the sample is irradiated with ionizing radiation to generate the X-rays 124 (e.g., the sample is irradiated by a conventional laboratory source of electrons or X-rays, a synchrotron radiation source, or other X-ray source emitting broadband or multi-energy X-rays). In certain embodiments, the x-ray source 410 is not a component of the apparatus 100, while in certain other embodiments, the x-ray source 410 is a component of the apparatus 100.

[0055] In certain embodiments, at least one collimating X-ray optic 420 includes a monocapillary optic (e.g., a single capillary optic; a mirror optic). In certain embodiments, the inner functional surface of the monocapillary optic has a paraboloidal shape, an ellipsoidal shape, or a combination of a hyperboloidal shape with either a paraboloidal shape or an ellipsoidal shape. As shown in FIG. 4A , the monocapillary optic receives X-rays 124 from the X-ray source 410 over a corresponding stereoscopic collection angle and reflects the X-rays 124 into a substantially collimated X-ray beam 120. In certain embodiments, the inner surface of the monocapillary optic is coated with a layer of a high-density material (e.g., Pt; Ir). In certain embodiments, the inner surface of the monocapillary optic is coated with multiple layers of alternating low-mass-density and high-mass-density materials. For example, the periodicity (e.g., spacing) of the multiple layers can be substantially constant. In another example, the periodicity of the multilayer can vary along the optical axis of the monocapillary optic (e.g., gradient in the longitudinal direction), along a direction substantially perpendicular to the optical axis of the monocapillary optic, or a combination of both.

[0056] In certain embodiments, at least one collimating X-ray optic 420 includes a polycapillary optic (e.g., multiple single capillary optics with coaxially nested paraboloids; Type III Wolter optic) or multiple nested mirror optics (e.g., nested parabolic mirror optics; parabolic mirror lenses nested coaxially inside a Wolter optic). For example, the Wolter optic can have a hyperboloidal segment and a paraboloidal segment configured such that a focal point of the hyperboloidal segment is aligned with the X-ray source 410 and a focal point of the paraboloidal segment is aligned with another focal point of the hyperboloidal segment. As shown in FIG. 4B , the polycapillary optic or nested mirror optic receives X-rays 124 from the X-ray source 410 over a corresponding solid collection angle and reflects the X-rays 124 into a substantially collimated X-ray beam 120. In certain embodiments, the inner surface of the polycapillary optic is coated with a layer of a material different from the substrate material (e.g., glass) of the polycapillary optic. The coating material can be configured to improve the X-ray reflectivity of the polycapillary optic. For example, the coating material can include atomic elements having an atomic number less than 15 (e.g., B4C; MgO; LiF; Si3N4; SiO2; BeO) and / or at least one of Ni, Cr, and Cu. Techniques for applying the coating material include, but are not limited to, atomic layer deposition and chemical vapor deposition. In certain embodiments, the coating material is applied at a concentration of 1.5 g / cm 3 These coating materials include organic materials with mass densities less than 1000 nm. Such coating materials can be used to reduce the critical angle of the reflective surface. The coating materials can be used to achieve lower angular beam divergence for polycapillary optics for use in wavelength spectrometers where a planar diffractor (e.g., single crystal; double crystal) is configured after the polycapillary optics.

[0057] In certain embodiments, the at least one collimating X-ray optic 420 includes at least one Soller slit configured to receive X-rays 124 from the X-ray source 410 and limit an angular width ψ of the X-rays 124 emitted from the at least one Soller slit, as shown in FIG.

[0058] In certain embodiments, at least one collimating X-ray optic 420 includes a composite capillary optic including a monocapillary optic and a polycapillary optic with a hollow core, where the monocapillary optic is nested inside the hollow core. The polycapillary optic can be fabricated by removing one or more capillaries near the central axis of the polycapillary optic or by fabricating the polycapillary optic without capillaries near the central axis. The quartic surface of the monocapillary optic can be an ellipsoid, a paraboloid, a hyperboloid, or a combination thereof. The monocapillary optic and the polycapillary optic can be rigidly attached to each other so that their optical axes are substantially parallel to each other (e.g., collinear with each other, defining a common longitudinal axis along the X-ray propagation axis 122).

[0059] In certain embodiments, the composite capillary optic is configured to generate a substantially collimated X-ray beam 120. The portion of the X-ray beam 120 generated by the polycapillary optic has a larger angular beam divergence than the portion of the X-ray beam 120 generated by the monocapillary optic. The optical properties of the composite capillary optic can be configured for X-ray analysis using the X-ray beam 120 and an X-ray wavelength-dispersive spectrometer (e.g., small-angle X-ray scattering, single-crystal X-ray diffraction). For example, in the case of an X-ray wavelength-dispersive spectrometer in which the composite capillary optic is placed upstream of a planar Bragg diffractor 110 (e.g., a single crystal, mosaic crystal, stacked crystal diffractor, or multilayer), the larger angular beam divergence of the polycapillary optic can be configured to provide higher efficiency with coarser energy resolution, while the lower angular beam divergence of the monocapillary optic can be configured to provide higher energy resolution but lower X-ray flux.

[0060] In certain embodiments, the composite capillary optic further includes at least one central beam stop configured to block X-rays entering or exiting the monocapillary optic and / or at least one aperture for blocking X-rays entering or exiting the polycapillary optic, thereby selecting a beam portion from the polycapillary optic and / or a beam portion from the monocapillary optic. The at least one central beam stop can be controllably moved (e.g., via at least one computer-controlled motorized motion stage) to block or allow X-rays 124 from impinging on the monocapillary optic and / or propagating from the monocapillary optic toward the downstream planar Bragg diffractor 110 or the serial stack 300. The at least one aperture can be controllably moved (e.g., via at least one computer-controlled motorized motion stage) to block or allow X-rays 124 from impinging on the polycapillary optic and / or propagating from the polycapillary optic toward the downstream planar Bragg diffractor 110 or the serial stack 300.

[0061] 5A-5C schematically illustrate three exemplary devices 100 including at least one stacked planar Bragg diffractor 110 according to certain embodiments described herein. In FIGS. 5A-5C, the device 100 is an X-ray wavelength-dispersive spectrometer (e.g., a continuous wavelength-dispersive spectrometer) including the stacked planar Bragg diffractors 110, at least one X-ray detector 310, and at least one X-ray collimating optic 420 (e.g., but not the X-ray source 410). The stacked planar Bragg diffractors 110 in FIGS. 5A-5C include a pair of planar crystal diffractors (e.g., first and second planar Bragg diffractors 110a, 110b; single crystal; mosaic crystal) stacked on top of each other and configured to direct corresponding diffracting portions 130a, 130b toward the at least one first X-ray detector 310. At least one X-ray detector 310 of Figures 5A and 5B is configured to receive both the first and second diffracted portions 130a, 130b.

[0062] 5A-5C can include multiple coaxially nested single capillary optics, where the inner single capillary optic can be configured to output a substantially collimated (e.g., substantially parallel) X-ray beam 120 having a higher maximum X-ray energy band than the X-ray beam output by the outer single capillary optic. In certain embodiments, the at least one collimating X-ray optic 420 includes two single capillary optics, each having a parabolic surface, configured such that their focal points are aligned with the X-ray source 410 (e.g., primary source; secondary source), and the inner capillary optic is configured to reflect and collimate X-rays with energies less than 20 keV (e.g., less than 10 keV; less than 8 keV; less than 5 keV), and the outer capillary optic is configured to reflect and collimate X-rays with energies less than 3 keV (e.g., less than 2 keV; less than 1 keV; less than 0.5 keV).

[0063] In certain embodiments, at least one planar Bragg diffractor 110 of the at least one stacked plurality of planar Bragg diffractors 110 may be configured to focus on one lower energy fluorescent X-ray line of an atomic element (e.g., the L α1 X-ray lines of Pt, or L α1 and at least one other planar Bragg diffractor 110 of the at least one stacked plurality of planar Bragg diffractors 110 is configured to diffract one fluorescent X-ray line of the same atomic element with higher energy (e.g., K of Cu). α1 X-ray lines of Pt or K α1 The planar Bragg diffractors 110a are configured to diffract lower energy fluorescent X-ray lines (X-ray lines of different energy levels). For example, a first planar Bragg diffractor 110a configured to diffract lower energy fluorescent X-ray lines can be positioned upstream of a second planar Bragg diffractor 110b configured to diffract higher energy fluorescent X-ray lines. Certain such implementations can enable probing of the depth of atomic elements from the surface of a sample containing the atomic elements. For example, the material and diffracting surface Miller indices of at least one upstream planar Bragg diffractor 110 (e.g., selected from the group consisting of InSb, PET, ADP, RAP, beryl, TIAP, and quartz) can be configured to diffract X-rays having lower energies (e.g., less than 2 keV; less than 1 keV; less than 0.5 keV), and at least one downstream planar Bragg diffractor 110 (e.g., selected from the group consisting of single crystal; stacked planar crystal; Si, Ge, LiF, HOPG, and HAPG) can be configured to diffract X-rays having higher energies (e.g., greater than 3 keV; greater than 5 keV; greater than 10 keV).

[0064] In certain embodiments, the first plane Bragg diffractor 110a detects the fluorescent X-ray lines of atomic elements (e.g., the L α1 X-ray line of Pt; α1The first plane Bragg diffractor 110a is configured to diffract X-rays of slightly lower or higher energy than the first plane Bragg diffractor 110a to provide a background for more accurate measurement of the fluorescent X-ray lines.

[0065] 5B further includes at least one third X-ray detector 330 (e.g., an energy dispersive detector) configured to receive the X-rays 124 transmitted through the plurality of stacked planar Bragg diffractors 110 (e.g., the at least one third X-ray detector 330 is downstream of the first and second planar Bragg diffractors 110a, 110b). Examples of the at least one third X-ray detector 330 include, but are not limited to, a proportional counter; an ionization chamber; a silicon drift detector; a lithium-doped germanium or silicon detector; an X-ray scintillator counter; a pin diode detector; and a pixel array X-ray photon counter.

[0066] In certain such embodiments, the apparatus 100 includes both an X-ray wavelength-dispersive spectrometer and an energy-dispersive spectrometer. For example, at least one wavelength-dispersive spectrometer may detect characteristic X-ray lines (e.g., Si K X-ray lines; Ta M X-ray lines) that have an energy difference smaller than the energy resolution of the energy-dispersive detector. α X-ray line of WM α In certain embodiments, the at least one wavelength-dispersive spectrometer is configured to measure at least one characteristic X-ray line having a low signal-to-background ratio (e.g., due to either a low concentration of at least one atomic element associated with the at least one characteristic X-ray line or a large background contribution to the detected signal). In certain embodiments, the multiple stacked planar Bragg diffractometers 110 are configured to analyze the X-ray fluorescence spectral lines of multiple atomic elements with sufficient energy resolution that cannot be resolved by an energy-dispersive detector.

[0067] In certain embodiments, the apparatus 100 can comprise a longitudinal X-ray wavelength-dispersive spectrometer including multiple wavelength-dispersive spectrometers arranged longitudinally along the X-ray propagation axis 122. For example, the apparatus 100 of FIG. 5C comprises a first wavelength-dispersive spectrometer (WDS) 510a including a first pair of stacked planar Bragg diffractors 110 (e.g., first and second planar Bragg diffractors 110a, 110b stacked on top of each other) and a first X-ray detector 310a configured to receive diffracted portions 130a, 130b from the first and second planar Bragg diffractors 110a, 110b. The apparatus 100 of FIG. 5C further includes a second WDS 510b including a second pair of stacked planar Bragg diffractors 110 (e.g., third and fourth planar Bragg diffractors 110c, 110d stacked on each other and separated from the first and second planar Bragg diffractors 110a, 110b) and a second X-ray detector 310b configured to receive diffracted portions 130c, 130d from the third and fourth planar Bragg diffractors 110c, 110d. The second WDS 510b is positioned consecutively (e.g., downstream) from the first WDS 510a. The spectral bands of the first and second X-ray wavelength-dispersive spectrometers have minimal spectral overlap (e.g., less than 3%; less than 1%). In certain embodiments, the third and fourth planar Bragg diffractors 110c, 110d of the second WDS 510b can be replaced with single crystal planar diffractors. For example, the single crystal planar diffractors can include diamond, LiF, Si, or Ge crystals (e.g., symmetrically or asymmetrically cut), channel-cut crystals, stacked crystal diffractors, or mosaic crystals (e.g., HAPG or HAPG) and can be positioned upstream or downstream relative to the first and second diffractors 110a, 110b. The first and second WDSs 510a, 510b can be configured such that the at least one planar Bragg diffractor 110 or the stacked plurality of planar Bragg diffractors 110 of the first WDS 510a has a higher X-ray transmittance for X-rays 124 diffracted by the at least one planar Bragg diffractor 110 of the second WDS 510b than the at least one planar Bragg diffractor 110 or the stacked plurality of planar Bragg diffractors 110 of the second WDS 510b.Other configurations can include additional planar Bragg diffractors 110 and / or multiple stacked planar Bragg diffractors 110 and X-ray detectors 310 to provide a longitudinal X-ray wavelength dispersive spectrometer including one or more additional WDSs.

[0068] In certain embodiments, at least two of the planar Bragg diffractors 110 of the longitudinal wavelength-dispersive spectrometer of FIG. 5C are configured to measure two specific X-ray energies (e.g., two characteristic X-ray lines). In certain embodiments, each of the planar Bragg diffractor 110 or the stacked plurality of planar Bragg diffractors 110 is configured to measure one specific characteristic X-ray line. In certain embodiments, the Bragg angle of at least one of the planar Bragg diffractor 110 or the stacked plurality of planar Bragg diffractors 110 is configured to be scanned over a predetermined angle range to measure the X-ray spectrum of the substantially parallel X-ray beam 120. In certain embodiments, the number of planar Bragg diffractors 110, including the stacked planar Bragg diffractor 110, is in the range of 2 to 10. In certain embodiments, the positioning and alignment of at least some of the components of the longitudinal wavelength-dispersive spectrometer are performed via a computer-controlled motorized motion stage.

[0069] In certain embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 are configured to focus on the lower energy first fluorescent X-ray lines of atomic elements (e.g., L of Cu). α1 X-ray line of Pt; α1 a first planar crystal diffractor configured to diffract a first X-ray line of the same atomic element (e.g., K for Cu) and a second fluorescent X-ray line of higher energy of the same atomic element (e.g., K for Cu). α1 X-ray line of Pt; K of Pt α1 and a second planar crystal diffractor configured to diffract the first X-ray line (X-ray line). The first planar crystal diffractor can be positioned upstream of the second planar crystal diffractor. Certain such embodiments can enable probing of the depth of atomic elements from a surface of a sample containing the atomic elements.

[0070] In certain embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 detect the first fluorescent X-ray line of an atomic element (e.g., the L α1 X-ray line of Pt; α1 and a second planar crystal diffractor configured to diffract X-rays 124 of slightly less or greater energy than the energy of the first planar crystal diffractor to provide a background for more accurate measurement of the fluorescent X-ray lines.

[0071] Exemplary Implementations for X-Ray Fluorescence (XRF) Compositional Analysis In certain embodiments, the diffracted portions 130 of the X-rays 124 diffracted by at least two of the plurality of stacked planar Bragg diffractors 110 are portions of a single characteristic X-ray line with minimal (e.g., less than 5%; less than 1%) spectral overlap between them (e.g., the first planar Bragg diffractor 110a diffracts the first diffracted portion 130a that includes the low-energy half of the characteristic X-ray line, and the second planar Bragg diffractor 110b diffracts the second diffracted portion 130b that includes the high-energy half of the characteristic X-ray line). For example, the at least two planar Bragg diffractors 110 can include two LiF(111) crystal diffractors having an angular difference of about 40 microradians, each LiF(111) crystal diffractor being made of CuK α1 Such an embodiment diffracts approximately half of the X-ray lines. c is narrower than the total energy resolution ΔE of a given measurement (e.g., if the angular beam divergence Δθ is larger than the Darwin width of the stacked planar Bragg diffractors 110, the crystal diffractor can operate at high Bragg angles). In certain embodiments, at least two stacked planar Bragg diffractors 110 are used to detect two predetermined characteristic X-ray fluorescence lines of one atomic element (e.g., Cu K α1 X-ray lines of Cu and Cu K α2diffracted portions 130. In certain embodiments, the stacked planar Bragg diffractor 110 is configured to simultaneously diffract at least one of the diffracted portions 130 (e.g., X-ray lines), and a single X-ray detector 310 (e.g., either energy-resolving or energy-non-resolving) is configured to detect the diffracted portions 130. In certain embodiments, the X-ray detector 310 has an energy resolution of less than 25% (e.g., less than 10%) of the average (e.g., central) energy of the at least one diffracted portion 130 diffracted by the stacked planar Bragg diffractor 110 and received by the X-ray detector 310 (e.g., to minimize or eliminate the contribution of higher diffraction orders or harmonics to the detected signal).

[0072] For example, the multiple stacked planar Bragg diffractors 110 can include two planar mosaic crystal diffractors, one of which is CuK α1 The other planar Bragg diffractor 110 is configured to diffract X-rays of Cu K α2 In certain embodiments, the at least two stacked planar Bragg diffractors 110 are configured to diffract X-rays with a ΔE optimized for a given analysis (e.g., two characteristic X-ray lines of an atomic element, e.g., Cu K α1 X-ray lines and K α2 For X-ray lines, ΔE = 20 eV; energy resolving power E / ΔE is 10 -4 or higher in XANES measurements; and EXAFS measurements, where the energy resolution is approximately 3-6 eV.

[0073] In certain embodiments, at least two of the plurality of stacked planar Bragg diffractors 110 are configured to simultaneously diffract two predetermined characteristic fluorescent X-ray lines of two different atomic elements, and a single energy dispersive X-ray detector 310 (e.g., a silicon drift detector with an energy resolution finer than the energy difference between the two predetermined characteristic X-ray lines) is configured to detect the diffracted characteristic X-rays.

[0074] In certain embodiments, the multiple plane Bragg diffractors 110 are configured to simultaneously diffract a predetermined plurality of characteristic fluorescent X-ray lines of multiple atomic elements, and an energy dispersive detector 310 (e.g., a silicon drift detector) having sufficient energy resolution to distinguish the characteristic X-ray lines is used to detect the diffracted characteristic X-rays. For example, a continuous stack crystal analyzer may be used to simultaneously diffract three K fluorescent X-ray lines of three atomic elements (e.g., Cr, Fe, Cu) with an energy difference of more than 120 eV (e.g., more than 200 eV; more than 1000 eV). α1 The analyzer may include at least three crystal diffractors configured with a Bragg angle difference suitable to simultaneously diffract the characteristic X-ray lines of The analyzer may further include an energy dispersive detector (e.g., a silicon drift detector, a lithium drift detector, or a charge-coupled detector) configured to detect the diffracted characteristic X-ray lines.

[0075] In certain embodiments, some of the stacked planar Bragg diffractors 110 may be configured to selectively select one or two characteristic X-ray lines of a given atomic element (e.g., Cu K). α1 X-ray lines of Cu and Cu K α2 diffract one or two characteristic X-ray lines of a predetermined atomic element (e.g., Cu K), and other planar Bragg diffractors 110 are configured to diffract characteristic X-ray lines of a different predetermined atomic element. In certain embodiments, some of the plurality of stacked planar Bragg diffractors 110 are configured to diffract one or two characteristic X-ray lines of a predetermined atomic element (e.g., Cu K). α1 X-ray lines of Cu and Cu K α2The upstream plane Bragg diffractor 110 is configured to diffract characteristic X-ray lines (X-ray lines of predetermined intensity), while the other plane Bragg diffractor 110 is configured to diffract X-rays near at least one of the predetermined characteristic X-ray lines to obtain background counts. In certain embodiments, the upstream plane Bragg diffractor 110 is configured to diffract characteristic X-ray lines of lower intensity, and the downstream plane Bragg diffractor 110 is configured to diffract characteristic X-ray lines of higher intensity. In certain embodiments, the upstream plane Bragg diffractor 110 is selected to have an X-ray transmittance of greater than 2% for X-rays diffracted by the at least one downstream plane Bragg diffractor 110.

[0076] Exemplary Implementations of XAS In certain embodiments for XAS applications, such as x-ray absorption near edge structure (XANES) or extended x-ray absorption fine structure (EXAFS), at least two of the plurality of stacked planar Bragg diffractors 110 are configured to diffract x-rays having x-ray energies within a predetermined energy resolution with minimal (e.g., less than 5%; less than 1%) spectral overlap between the diffracting portions 130. For example, one diffracting portion 130 can correspond to the low-energy half of a characteristic x-ray line, and the other diffracting portion 130 can correspond to the high-energy half of a characteristic x-ray line (e.g., Cu K α1 (two LiF(111) crystal diffractors with an angular difference of about 40 microradians for x-rays of 100 sq. m.). Such an embodiment minimizes the inherent energy resolution ΔE of the planar Bragg diffractor 110. cis narrower than the total energy resolution ΔE of a given measurement (e.g., if the angular beam divergence Δθ is larger than the Darwin width of the stacked planar Bragg diffractors 110, the crystal diffractor can operate at a high Bragg angle). In certain embodiments, at least two of the multiple stacked planar Bragg diffractors 110 are configured to simultaneously diffract at least two predetermined X-ray energies having an energy difference greater than the energy resolution of an X-ray detector 310 (e.g., a silicon drift detector) configured to record the diffraction portion 130 diffracted by the at least two stacked planar Bragg diffractors 110. For XANES measurements, the energy difference can be less than 250 eV but greater than the energy resolution of the X-ray detector 310. For EXAFS measurements, the energy difference can be less than 700 eV but greater than the energy resolution of the X-ray detector 310.

[0077] In certain embodiments, the stacked planar Bragg diffractors 110 are scanned over a range of angles relative to the X-ray propagation axis 122 of the collimated X-ray beam 120 in response to a previous XAS measurement. In certain embodiments, the analyzer includes multiple stacked planar Bragg diffractors 110 and at least one single crystal diffractor 320 configured to diffract X-rays having X-ray energies within a predetermined energy range (e.g., in the range of 100 eV to 200 eV for XANES; in the range of 500 eV to 1000 eV for EXAFS). In certain embodiments, multiple X-ray detectors 310 are configured to detect X-rays diffracted by the stacked planar Bragg diffractors 110 and the at least one single crystal diffractor 320. In certain embodiments, all stacked planar Bragg diffractors 110 are configured to measure the energy resolving power (E) of the X-rays diffracted by each planar Bragg diffractor 110 of the multiple stacked planar Bragg diffractors 110. o / ΔE) is 10 for XANES measurements -4or greater, and / or such that the energy resolution ΔE for the EXAFS measurement is less than 6 eV (e.g., less than 3 eV). In certain embodiments, the multiple stacked planar Bragg diffractors 110 are configured to diffract X-rays of predetermined X-ray energies for a given XAS measurement (e.g., X-ray energies corresponding to predetermined X-ray energies containing important structural information for the measurement, such as pre-edges, white lines, high absorption and / or low absorption energies). In certain embodiments, the number of energy measurement points can be in the range of 5 to 100.

[0078] Although commonly used terms are used to describe the systems and methods of particular embodiments for ease of understanding, these terms are used herein with their broadest reasonable interpretation. While various aspects of the present disclosure have been described in terms of illustrative examples and embodiments, the disclosed examples and embodiments should not be construed as limiting. Conditional language such as "can," "could," "might," or "may," unless otherwise specified or understood otherwise within the context in which it is used, is generally intended to convey that certain embodiments include certain features, elements, and / or steps, while other embodiments do not. Thus, such conditional language is generally not intended to imply that features, elements, and / or steps are somehow required for one or more embodiments. In particular, the terms "comprises" and "comprising" should be interpreted as referring to elements, components, or steps in a non-exclusive manner, indicating that the referenced element, component, or step may be present or utilized or may be combined with other elements, components, or steps that are not explicitly referenced.

[0079] Connecting language, such as the phrase "at least one of X, Y, and Z," unless otherwise specified, should be understood within the context in which it is generally used to convey that an item, term, etc. can be either X, Y, or Z. Thus, such connecting language is generally not intended to imply that a particular embodiment requires the presence of at least one of X, at least one of Y, and at least one of Z.

[0080] As used herein, language of degree, such as the terms "approximately," "about," "generally," and "substantially," denotes a value, amount, or characteristic that is close to a stated value, amount, or characteristic that still performs a desired function or achieves a desired result. For example, the terms "approximately," "about," "generally," and "substantially" may refer to an amount that is within ±10%, ±5%, ±2%, ±1%, or ±0.1% of the stated amount. As another example, the terms "generally parallel" and "substantially parallel" refer to a value, quantity, or characteristic that deviates from exactly parallel by ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degrees, and the terms "generally perpendicular" and "substantially perpendicular" refer to a value, quantity, or characteristic that deviates from exactly perpendicular by ±10 degrees, ±5 degrees, ±2 degrees, ±1 degree, or ±0.1 degrees. Ranges disclosed herein also encompass any and all overlaps, subranges, and combinations thereof. Words such as "up to," "at least," "greater than," "less than," "between," and the like, include the recited numbers. As used herein, the meaning of "a," "an," and "said" includes plural references unless the context clearly dictates otherwise. Additionally, as used in the description herein, the meaning of "in" includes "into" and "on," unless the context clearly dictates otherwise.

[0081] Although structures and / or methods are described herein with respect to elements labeled with ordinal adjectives (e.g., first, second, etc.), the ordinal adjectives are used merely as labels to distinguish one element from another; the ordinal adjectives are not used to indicate the order of those elements or their use.

[0082] Various configurations have been described above. It should be understood that the embodiments disclosed herein are not mutually exclusive and may be combined with each other in various configurations. While the present invention has been described with reference to these specific configurations, the descriptions are intended to illustrate, not limit, the invention. Various modifications and applications will occur to those skilled in the art without departing from the true spirit and scope of the invention. Thus, for example, in any method or process disclosed herein, the acts or operations making up the method / process may be performed in any suitable order and are not necessarily limited to any particular disclosed order. Features or elements from the various embodiments and examples described above can be combined with each other to generate alternative configurations that are compatible with the embodiments disclosed herein. Furthermore, while the disclosed methods and devices are largely described in the context of various devices, the various embodiments described herein may be incorporated into a variety of other suitable devices, methods, and contexts.

[0083] Various aspects and advantages of the embodiments have been described where appropriate. It should be understood that not all such aspects or advantages may necessarily be achieved in accordance with any particular embodiment. Thus, for example, it should be recognized that various embodiments may be implemented to achieve or optimize one advantage or advantages as taught herein without necessarily achieving other aspects or advantages as may be taught or suggested herein.

Claims

1. a plurality of stacked planar Bragg diffractors including at least a first planar Bragg diffractor and a second planar Bragg diffractor, the first and second planar Bragg diffractors being positioned successively along an x-ray propagation axis of an x-ray beam including x-rays, the plurality of stacked planar Bragg diffractors having an angular beam divergence of less than 30 mrad in at least one direction; An apparatus comprising:

2. 10. The apparatus of claim 1, wherein the first planar Bragg diffractor comprises a substantially planar multilayer, single crystal, or mosaic crystal configured to diffract at least a portion of the X-rays according to Bragg's law.

3. The apparatus of claim 1 , wherein the first and second planar Bragg diffractors are connected to one another and configured to be successively impinged by the X-ray beam.

4. the second planar Bragg diffractor is downstream of the first planar Bragg diffractor, the first planar Bragg diffractor is configured to diffract a first diffracted portion of the X-rays and transmit a first transmitted portion of the X-rays, the second planar Bragg diffractor is configured to diffract a second diffracted portion of the first transmitted portion and transmit a second transmitted portion of the first transmitted portion, the first diffracted portion diffracting a first mean X-ray energy E １ and the first energy resolution ΔE １ and the second diffractive portion has a second mean X-ray energy E ２ and the second energy resolution ΔE ２ and the second X-ray energy E ２ is the first X-ray energy E １ The device of claim 1 , which is different from

5. 5. The apparatus of claim 4, wherein the first plane Bragg diffractor comprises a multi-layer Bragg diffractor configured to diffract X-rays having X-ray energies less than 1 keV, and the second plane Bragg diffractor comprises a single crystal and / or a mosaic crystal and is configured to diffract X-rays having X-ray energies greater than 1 keV.

6. 6. The apparatus of claim 5, wherein the multilayer Bragg diffractor has a d-spacing in the range of 3 nanometers to 30 nanometers, the single crystal comprises a material selected from the group consisting of diamond, quartz, graphite, stacks of graphene layers, other materials containing low atomic number elements, silicon (Si), germanium (Ge), lithium fluoride (LiF), mica, indium antimonide (InSb), polyethylene terephthalate (PET), ammonium dihydrophosphate (ADP), rubidium oxyphthalate (RAP), beryl, and thallium oxyphthalate (TIAP), and the mosaic crystal comprises a material selected from the group consisting of highly annealed pyrolytic graphite (HAPG) and highly oriented pyrolytic graphite (HOPG).

7. the plurality of stacked planar Bragg diffractors further includes a third planar Bragg diffractor downstream of the second planar Bragg diffractor, the third planar Bragg diffractor configured to diffract a third diffracted portion of the second transmitted portion and transmit a third transmitted portion of the second transmitted portion, the third diffracted portion diffracting a third mean X-ray energy E ３ and the third energy resolution ΔE ３ and the third X-ray energy E ３ is the first X-ray energy E １ and the second X-ray energy E ２ The device of claim 4 , which is different from

8. 8. The apparatus of claim 7, wherein the second plane Bragg diffractor is configured to diffract X-rays having an X-ray energy in a range of 1 keV to 3 keV, and the third plane Bragg diffractor comprises a single crystal and / or a mosaic crystal and is configured to diffract X-rays having an X-ray energy greater than 3 keV.

9. The first plane Bragg diffractor is configured to irradiate the second X-ray energy E ２ and a first X-ray transmittance of more than 1% to X-rays having the third X-ray energy E ３ and the second plane Bragg diffractor has a third X-ray transmittance of more than 1% for X-rays having the third X-ray energy E ３ 8. The apparatus of claim 7, wherein the second X-ray transmittance is greater than 1% for X-rays having a second X-ray transmittance of ....

10. 10. The apparatus of claim 1, wherein the plurality of stacked planar Bragg diffractors are positioned along the X-ray propagation axis within a distance of less than 200 millimeters along the X-ray propagation axis.

11. 10. The apparatus of claim 1, wherein at least two adjacent planar Bragg diffractors of the plurality of stacked planar Bragg diffractors are positioned along the axis of x-ray propagation such that they are spaced apart from each other along the axis of x-ray propagation by less than 30 millimeters.

12. The device of claim 1 , wherein at least two planar Bragg diffractors of the plurality of stacked planar Bragg diffractors comprise the same material as each other.

13. 13. The apparatus of claim 12, wherein the at least two plane Bragg diffractors are configured to diffract X-rays at atomic planes having the same Miller indices, and the X-rays are incident on each of the at least two plane Bragg diffractors at different Bragg angles such that there is substantially zero overlap in spectral bandwidth between the X-rays diffracted from the at least two plane Bragg diffractors.

14. 13. The apparatus of claim 12, wherein the X-rays are incident on each of the at least two planar Bragg diffractors at substantially equal Bragg angles, and the diffracting atomic planes of the at least two planar Bragg diffractors have different d-spacings.

15. The apparatus of claim 1 , wherein at least two planar Bragg diffractors of the plurality of stacked planar Bragg diffractors comprise different materials.

16. 1. An apparatus configured to receive an x-ray beam propagating along an x-ray propagation axis and having an angular beam divergence of less than 30 mrad in at least one direction substantially perpendicular to the x-ray propagation axis, comprising: a plurality of serially stacked planar Bragg diffractors rigidly connected to one another with a separation between adjacent planar Bragg diffractors of less than 200 millimeters, the plurality of serially stacked planar Bragg diffractors configured to receive the X-ray beam, each planar Bragg diffractor of the plurality of serially stacked planar Bragg diffractors configured to diffract a corresponding diffracted portion of the X-ray beam such that spectral overlap between diffracted portions from different planar Bragg diffractors is less than 25%; at least one X-ray detector configured to receive and detect the diffracted portion; An apparatus comprising:

17. 17. The apparatus of claim 16, wherein the diffracted portions diffracted by at least two of the plurality of continuously stacked planar Bragg diffractors have different mean X-ray energies that differ by less than 30 eV.

18. 17. The apparatus of claim 16, wherein the diffracted portions diffracted by at least two of the plurality of continuously stacked planar Bragg diffractors have different mean X-ray energies that differ by more than 50 eV.

19. 17. The apparatus of claim 16, wherein the plurality of continuously stacked planar Bragg diffractors comprises a first set of stacked planar Bragg diffractors and a second set of stacked planar Bragg diffractors, the at least one X-ray detector comprises a first X-ray detector and a second X-ray detector, the first set of stacked planar Bragg diffractors configured to diffract X-rays toward the first X-ray detector, and the second set of stacked planar Bragg diffractors configured to diffract X-rays toward the second X-ray detector.

20. 17. The apparatus of claim 16, wherein the plurality of serially stacked planar Bragg diffractors comprises at least one multilayer diffractor, at least one single crystal diffractor, and / or at least one mosaic crystal diffractor.

21. 17. The apparatus of claim 16, wherein the plurality of serially stacked planar Bragg diffractors comprises at least two single crystal diffractors configured such that the X-ray beam has a Bragg angle difference with respect to the at least two single crystal diffractors of greater than 10 microradians.

22. The apparatus of claim 16 , wherein the plurality of serially stacked planar Bragg diffractors comprises three or more planar Bragg diffractors.

23. 17. The apparatus of claim 16, wherein the plurality of continuously stacked planar Bragg diffractors includes at least one planar Bragg diffractor having a thickness along the x-ray propagation axis of less than 500 microns.

24. 17. The apparatus of claim 16, wherein the plurality of serially stacked planar Bragg diffractors are configured to simultaneously diffract at least two characteristic X-ray lines of one or two atomic elements.

25. 17. The apparatus of claim 16, further comprising at least one motion stage configured to controllably adjust at least one Bragg angle of at least one planar Bragg diffractor of the plurality of serially stacked planar Bragg diffractors.

26. 17. The apparatus of claim 16, wherein the at least one X-ray detector is selected from the group consisting of a proportional counter; an ionization chamber; a silicon drift detector; a Li-drift silicon or germanium detector; an X-ray scintillator counter; a pin diode detector; an X-ray photon counter having multiple active detector elements; a pixel array detector; a photon counting detector with a selectable energy window; and a superconductor-based microcalorimeter.

27. 17. The apparatus of claim 16, wherein the at least one x-ray detector comprises a photon-counting pixel array detector having at least one energy threshold configured to reject x-rays having x-ray energies below the at least one energy threshold and / or reject x-rays having x-ray energies above the at least one energy threshold.

28. 17. The apparatus of claim 16, further comprising at least one collimating x-ray optic configured to receive x-rays propagating from an x-ray source and form the x-ray beam.

29. at least one plane Bragg X-ray diffractor configured to receive the X-ray beam and diffract at least one corresponding diffracted portion of the X-ray beam; at least one energy dispersive X-ray detector configured to receive and detect a transmitted portion of the X-ray beam that is transmitted through the at least one plane Bragg X-ray diffractometer; An apparatus comprising:

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