X-ray sequential array wavelength dispersive spectrometer

Abstract

The apparatus is configured to receive X-rays propagating from an X-ray source. The apparatus includes first and second X-ray diffractors, where the second X-ray diffractor is downstream of the first X-ray diffractor, and first and second X-ray detectors. The first X-ray diffractor is configured to receive the X-rays, diffract a first spectral band of the X-rays to the first X-ray detector, and transmit at least 2% of the received X-rays to the second X-ray diffractor. The second X-ray diffractor is configured to receive the X-rays transmitted from the first X-ray diffractor and diffract a second spectral band of the X-rays to the second X-ray detector. The first X-ray detector is configured to measure a first spectrum of the first spectral band of the X-rays, and the second X-ray detector is configured to measure a second spectrum of the second spectral band of the X-rays.

Description

[Technical field]

[0001] Claiming priority This application claims the benefit of priority to U.S. Patent Application No. 63 / 337,407, filed May 2, 2022, which is incorporated by reference herein in its entirety.

[0002] background Field This application relates generally to apparatus and methods for X-ray spectroscopy, examples of which include, but are not limited to, x-ray absorption spectroscopy (XAS), x-ray emission spectroscopy (XES), and x-ray fluorescence spectroscopy (XFS). [Background technology]

[0003] 2. Description of Related Art An X-ray wavelength dispersive spectrometer (WDS) typically comprises (i) a diffractor comprising a crystalline or synthetic multilayer and configured to disperse incident X-rays according to the Bragg law 2×d×sin(θ)=n×λ, where d is the lattice spacing of the crystal or the layer spacing of the multilayer, θ is the Bragg angle (e.g., the angle between the incident X-rays and the lattice planes of the crystal or layers of the multilayer), n is an integer, and λ is the wavelength of the X-rays that satisfies the Bragg law for values ​​of d and θ, and (ii) a detector configured to record a portion of the X-rays dispersed by the diffractor.

[0004] WDS typically provide significantly higher energy resolution than energy dispersive spectrometers (EDS) and are widely used for X-ray spectroscopy in scanning electron microscope (SEM) spectroscopy, electron microprobe analyzer (EMPA), particle induced x-ray emission (PIXE) spectroscopy, x-ray fluorescence (XRF) analysis, total external reflection x-ray fluorescence (TXRF) analysis, X-ray emission spectroscopy (XES), and X-ray absorption spectroscopy (XAS). For XRF measurements, EDS can collect X-rays over a wide energy range and can measure many atoms simultaneously, while WDS can measure X-ray spectra sequentially, but has better energy resolution, better detection sensitivity, and reduced spectral interference compared to EDS. Summary of the Invention [Means for solving the problem]

[0005] overview In certain embodiments, the apparatus (e.g., a sequential array wavelength dispersive spectrometer) is configured to receive X-rays propagating from an X-ray source along an X-ray propagation direction. The apparatus comprises a plurality of X-ray diffractors along the X-ray propagation direction. The plurality of X-ray diffractors comprises at least a first X-ray diffractor and a second X-ray diffractor, the second X-ray diffractor being downstream of the first X-ray diffractor. The apparatus further comprises a plurality of X-ray detectors comprising at least a first X-ray detector and a second X-ray detector. The first X-ray diffractor is configured to receive the X-rays, diffract a first spectral band of the X-rays to the first X-ray detector, and transmit at least 2% of the received X-rays to the second X-ray diffractor. The second X-ray diffractor is configured to receive the X-rays transmitted from the first X-ray diffractor and diffract a second spectral band of the X-rays to the second X-ray detector. The first X-ray detector comprises at least one first active element configured to measure a first spectrum of at least a portion of a first spectral band of X-rays, and the second X-ray detector comprises at least one second active element configured to measure a second spectrum of at least a portion of a second spectral band of X-rays. [Brief description of the drawings]

[0006] [Figure 1A] 1 illustrates a schematic diagram of an exemplary apparatus including multiple substantially flat X-ray diffractometers and multiple X-ray detectors, according to certain embodiments described herein. [Figure 1B] 1 illustrates a schematic diagram of an exemplary apparatus including multiple substantially flat X-ray diffractometers and multiple X-ray detectors, according to certain embodiments described herein. [Figure 1C] 2 illustrates a schematic diagram of another exemplary X-ray collimator in accordance with certain embodiments described herein. [Figure 1D] 2 illustrates a schematic diagram of another exemplary X-ray collimator in accordance with certain embodiments described herein. [Figure 2A] 1 illustrates a schematic diagram of another exemplary apparatus including multiple substantially flat X-ray diffractometers and multiple X-ray detectors, according to certain embodiments described herein. [Figure 2B]1 illustrates a schematic diagram of an aperture configured to generate an effective miniature X-ray source in the dispersive plane of a multiple X-ray diffractor, according to certain embodiments described herein. [Diagram 3] 1 illustrates a schematic diagram of an exemplary apparatus including multiple curved X-ray diffractometers and multiple X-ray detectors, according to certain embodiments described herein. [Figure 4] 1 illustrates a schematic diagram of an exemplary apparatus including at least one substantially flat X-ray diffractor, at least one substantially curved X-ray diffractor, and a plurality of X-ray detectors, according to certain embodiments described herein. [Diagram 5] 1 illustrates a schematic diagram of another exemplary apparatus including at least one substantially flat X-ray diffractor, at least one substantially curved X-ray diffractor, and multiple X-ray detectors, in accordance with certain embodiments described herein. [Figure 6] 1 illustrates a schematic diagram of another exemplary apparatus including multiple curved X-ray diffractometers and multiple X-ray detectors, according to certain embodiments described herein. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0007] Detailed Description X-rays analyzed by conventional WDS are incident on a point on the diffractor along the X-ray propagation direction, and only X-rays within a narrow energy bandwidth that satisfies Bragg's law are diffracted, while X-rays outside this narrow energy bandwidth are not used and are typically absorbed by the diffractor, and the spectral information contained in the absorbed X-rays is lost. As a result, conventional WDS, which is used in many systems (e.g., SEM spectroscopy, EMPA, PIXE spectroscopy, XRF analysis, TXRF analysis, XES and XAS), is limited in analysis speed and throughput.

[0008] Certain embodiments described herein provide an X-ray sequential array wavelength dispersive spectrometer (SA-WDS) featuring multiple crystals arranged sequentially along the X-ray propagation direction from an X-ray source. The polycrystals comprise at least one upstream crystal with an X-ray transmission greater than 2%, and at least a portion of the transmitted X-rays are diffracted by at least one downstream crystal. Certain embodiments described herein provide methods of using the X-ray SA-WDS for X-ray absorption spectroscopy (XAS), X-ray emission spectroscopy (XES), and / or X-ray fluorescence spectroscopy (XFS). In certain embodiments, the SA-WDS disclosed herein can be used to dramatically speed up data collection by multiplexing the data acquisition process and splitting different X-ray energies onto different X-ray detectors operating simultaneously. Certain implementations described herein are configured to speed up data collection compared to single-energy-at-a-time WDS instruments and can be used with other radiation sources (e.g., laser-plasma, high gain harmonic generation (HGHG), astronomical X-ray spectroscopy).

[0009] Certain embodiments described herein provide an X-ray SA-WDS comprising a plurality of X-ray diffractors (e.g., crystals and / or multilayers) arranged sequentially along an X-ray beam propagation direction (e.g., a longitudinal array of X-ray diffractors) extending from an X-ray source (e.g., collimated X-rays, diverging X-rays). At least one upstream X-ray diffractor of the plurality of X-ray diffractors is configured to receive X-rays from the X-ray source, diffract at least a portion of the received X-rays, and transmit at least 2% of the received X-rays to at least one downstream X-ray diffractor of the plurality of X-ray diffractors. The at least one downstream X-ray diffractor is configured to diffract at least a portion of the transmitted X-rays received from the at least one upstream X-ray diffractor. The X-rays diffracted by the at least one upstream X-ray diffractor have a first energy, and the X-rays diffracted by the at least one downstream X-ray diffractor have a second energy that differs from the first energy by at least 1 eV. The X-ray SA-WDS further comprises at least one first X-ray detector configured to receive X-rays diffracted by the at least one upstream X-ray diffractor and at least one second X-ray detector configured to receive X-rays diffracted by the at least one downstream X-ray diffractor. The at least one first X-ray detector and the at least one second X-ray detector are configured to generate spectral measurements (e.g., with energy resolution) of the received X-rays (e.g., X-ray intensity distribution as a function of X-ray energy).

[0010] 1A, 1B, 2A, 3, 4, 5, and 6 illustrate various exemplary apparatus 10 (e.g., X-ray SA-WDS) according to certain embodiments described herein. The apparatus 10 is configured to receive X-rays 22 from an X-ray source 5 and includes a plurality of X-ray diffractors 30 arranged (e.g., sequentially arranged) along an X-ray propagation direction 24 of the X-rays 22, and a plurality of X-ray detectors 40. The plurality of X-ray diffractors 30 includes at least a first X-ray diffractor 30a (e.g., an upstream X-ray diffractor) and a second X-ray diffractor 30b (e.g., a downstream X-ray diffractor), and the plurality of X-ray detectors 40 includes at least a first X-ray detector 40a and a second X-ray detector 40b. The first X-ray diffractor 30a is configured to receive the X-rays 22, diffract a first spectral band 22a of the X-rays 22 (e.g., a first fraction of the X-rays 22 having a first energy range) to the first X-ray detector 40a, and transmit at least 2% (e.g., at least 5%) of the X-rays 22 to the second X-ray diffractor 30b. The second X-ray diffractor 30b is configured to receive the transmitted X-rays 22 from the first X-ray diffractor 30a and diffract a second spectral band 22b of the X-rays 22 (e.g., a second fraction of the X-rays 22 having a second energy range) to the second X-ray detector 40b. The first X-ray detector 40a comprises at least one first active element 42a configured to measure (e.g., generate spectral measurements) a first spectrum of at least a portion of a first spectral band 22a of the X-rays 22, and the second X-ray detector 40b comprises at least one second active element 42b configured to measure (e.g., generate spectral measurements) a second spectrum of at least a portion of a second spectral band 22b of the X-rays 22. The first energy range and / or the second energy range may include energies from less than 2 eV to 500 eV.

[0011] In certain embodiments, the X-ray source 5 is configured to generate X-rays 22 in response to the incidence of ionizing radiation (e.g., X-rays, charged particles, electrons, protons). For example, the X-ray source 5 can comprise a sample to be analyzed using the apparatus 10, where the sample is irradiated with ionizing radiation to generate the X-rays 22 (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 that emits broadband or multi-energy X-rays). In certain embodiments, the X-ray source 5 is not a component of the apparatus 10, while in certain other embodiments, the X-ray source 5 is a component of the apparatus 10.

[0012] In certain embodiments (see, e.g., FIGS. 1A and 1B), the plurality of X-ray diffractors 30 further comprises a third X-ray diffractor 30c, and the plurality of X-ray detectors 40 further comprises a third X-ray detector 40c. The second X-ray diffractor 30b is configured to transmit at least 2% (e.g., at least 5%) of the X-rays 22 received from the first X-ray diffractor 30a to the third X-ray diffractor 30c. The third X-ray diffractor 30c is configured to receive the transmitted X-rays 22 from the second X-ray diffractor 30b and diffract a third spectral band 22c of the X-rays 22 (e.g., a third fraction of the X-rays 22 having a third energy range) to the third X-ray detector 40c. The third X-ray detector 40c comprises at least one third active element 42c configured to measure (e.g., generate a spectral measurement value) a third spectrum of at least a portion of the third spectral band 22c of the X-rays 22. Other numbers of X-ray diffractometers 30 (e.g., 2, 4, 5, 6, or more) and other numbers of X-ray detectors 40 (e.g., 2, 4, 5, 6, or more) are also compatible with certain embodiments described herein.

[0013] 1A and 1B, the apparatus 10 further comprises an X-ray collimator 20 configured to receive X-rays 22 (e.g., from an X-ray source 5, such as a sample under analysis) and collimate at least a portion of the X-rays 22 (e.g., to reduce the divergence angle of at least a portion of the X-rays 22 to less than 1 degree, less than 0.1 degrees, or less than 0.01 degrees). The first X-ray diffractor 30a is configured to receive the collimated X-rays 22 from the X-ray collimator 20.

[0014] In certain embodiments, X-rays 22 from the X-ray collimator 20 are incident on the first X-ray diffractor 30a at a first Bragg angle θ1, and a first spectral band 22a of the X-rays 22 diffracted by the first X-ray diffractor 30a to the first X-ray detector 40a has a first central X-ray energy E1 (e.g., corresponding to a first wavelength λ1 that satisfies Bragg's law for the first grating / layer spacing d1 and the first Bragg angle θ1 of the first X-ray diffractor 30a). The X-rays 22 from the first X-ray diffractor 30a are incident on the second X-ray diffractor 30b at a second Bragg angle θ2, and a second spectral band 22b of the X-rays 22 diffracted by the second X-ray diffractor 30b to the second X-ray detector 40b has a second central X-ray energy E2 (e.g., corresponding to a second wavelength λ2 that satisfies Bragg's law for the second grating / layer spacing d2 and the second Bragg angle θ2 of the second X-ray diffractor 30b). As shown generally by FIGS. 1A and 1B, the multiple X-ray diffractors 30 include a third X-ray diffractor 30c, where the X-rays 22 from the second X-ray diffractor 30b are incident on the third X-ray diffractor 30c at a third Bragg angle θ3, and a third spectral band 22c of the X-rays 22 diffracted by the third X-ray diffractor 30c to a third X-ray detector 40c has a third central X-ray energy E3 (e.g., corresponding to a third wavelength λ3 that satisfies Bragg's law for a third grating / layer spacing d3 and a third Bragg angle θ3 of the third X-ray diffractor 30c).

[0015] In certain embodiments, as shown generally in Figures 2A, 3, 4, 5, and 6, the apparatus 10 does not include an X-ray collimator and the apparatus 10 receives diverging X-rays 22 from the X-ray source 5. In certain embodiments, the X-ray source 5 is small (e.g., less than 100 microns wide) in the dispersion plane of the multiple X-ray diffractors 30, and the first X-ray diffractor 30a receives the X-rays 22 from the X-ray source 5. In certain other embodiments where the X-ray source 5 is not small (e.g., is an extended X-ray source 5), the apparatus 10 can include an aperture 50 (e.g., a slit, orifice) having a width less than 100 microns to generate an effectively small (e.g., narrow) X-ray source in the dispersion plane of the multiple X-ray diffractors 30, as shown generally in Figure 2B.

[0016] X-ray collimator In certain embodiments, the X-ray collimator 20 comprises at least one mirror optic 26 having a functional surface, at least a portion of the surface having a quadratic surface profile (e.g., paraboloidal, hyperboloidal). For example, as shown diagrammatically in FIG. 1A and FIG. 1B, the mirror optic 26 may comprise an axisymmetric parabolic mirror optic (e.g., a parabolic mirror lens), such as a glass capillary having an inner surface with a parabolic profile, with a focal point aligned with the X-ray source 5. The mirror optic 26 is configured to receive the X-rays 22 from the X-ray source 5 over a stereo collection angle and reflect the X-rays 22 into a substantially collimated X-ray beam. In another example, the mirror optic 26 may comprise a Wolter optic having a hyperboloidal segment and a paraboloidal segment, configured such that a focal point of the hyperboloidal segment is aligned with the X-ray source 5 and a focal point of the paraboloidal segment is aligned with another focal point of the hyperboloidal segment. In certain embodiments, the x-ray collimator 20 is rotationally symmetric about the longitudinal axis and extends greater than 15 degrees about the longitudinal axis.

[0017] 1C and 1D are schematic illustrations of other exemplary X-ray collimators 20 according to certain embodiments described herein. In certain embodiments, as shown in FIG. 1C, the X-ray collimator 20 may comprise a polycapillary optic or a plurality of nested mirror optics (e.g., nested parabolic mirror optics, a parabolic mirror lens coaxially nested inside a Wolter optic), each of which receives X-rays 22 from the X-ray source 5 over a corresponding stereoscopic collection angle and reflects the X-rays into a substantially collimated X-ray beam. In certain embodiments, as shown in FIG. 1D, the X-ray collimator 20 comprises at least one Soller slit configured to receive X-rays 22 from the X-ray source 5 (e.g., an extended X-ray source) and limit the angular width ψ of the X-rays 22 emitted from the at least one Soller slit.

[0018] In certain embodiments, the X-ray collimator 20 comprises a substrate (e.g., glass) and the inner surface of the X-ray collimator 20 is coated with at least one layer having a higher mass density (e.g., having a thickness greater than 20 nanometers) to increase the collection angle of the X-rays from the X-ray source 5 and improve the throughput of the apparatus 10. Exemplary materials for the at least one layer include, but are not limited to, higher atomic number (Z) materials such as Ni, Rh, Pt, Ir, or compound materials such as oxides, nitrides, or carbides. In certain embodiments, the inner reflective surface of the X-ray collimator is coated with at least one multilayer of alternating materials, examples of which include, but are not limited to, W / Si, Mo / Si, W / C, Mo / C, W / B4C, and the like. In certain embodiments, at least one multilayer comprises a laterally grated multilayer (e.g., the total thickness of each bilayer is constant but varies along the length of the reflecting surface) and / or a depth-graded multilayer (e.g., the total thickness of the bilayer can vary along the depth of the multilayer) to increase the collection angle of X-rays of a given (e.g., central) energy and energy bandwidth. The layer thicknesses of the constant thickness, depth-graded, and laterally graded multilayers can be configured to efficiently reflect X-rays having energies in the given bandwidth and to substantially reduce (e.g., not efficiently reflect) X-rays having energies outside the given bandwidth. In the case of nested coaxial mirrors, the functional surfaces of the mirror optics can have coatings that are different from each other (e.g., the functional surface of the inner mirror optic has a Pt coating, while the functional surface of one or more of the outer mirror optics has a multilayer coating).

[0019] In certain embodiments, the collimating mirror optics 26 are configured to have a critical reflection angle that maximizes the reflected X-ray flux within a predetermined energy range and substantially reduces (e.g., does not efficiently reflect) X-rays having energies outside a predetermined bandwidth that would otherwise cause background signal contributions in the form of scattering or high-order harmonics from crystal reflections. For example, the collimating mirror optics 26 can be configured to have a high-energy cutoff that is less than twice the maximum operating energy of the collimating mirror optics. In certain embodiments, to cover a wide operating energy range, the X-ray collimator 20 comprises multiple collimating mirrors, each of which is optimized for a corresponding predetermined X-ray energy range. In certain embodiments, the X-ray collimator 20 comprises a substantially flat mirror configured to receive the X-rays 22 from the collimating mirror optics 26, the substantially flat mirror configured to reflect the X-rays 22 at a high-energy cutoff.

[0020] X-ray Diffractometer In certain embodiments, at least one X-ray diffractor 30 of the plurality of X-ray diffractors 30 comprises at least one crystalline material (e.g., single crystal, mosaic crystal, substantially flat, substantially curved or bent), examples of which include, but are not limited to, graphite, highly oriented pyrolytic graphite (HOPG), highly annealed pyrolytic graphite (HAPG), diamond, quartz, LiF (e.g., LiF(111), LiF(200)), Si (e.g., Si(111), Si(220), Si(400)), and Ge (e.g., Ge(111), Ge(220), Ge(311)). In certain embodiments, at least one X-ray diffractor 30 is of a single crystal type (e.g., providing higher energy resolution), at least one X-ray diffractor 30 is of a mosaic crystal type (e.g., providing lower energy resolution), and / or the plurality of X-ray diffractors 30 comprises both at least one single crystal type and at least one mosaic crystal type. In certain embodiments, at least two X-ray diffractors 30 (e.g., each X-ray diffractor 30) comprise the same material and diffraction surface (e.g., reflection or Miller index) and are configured to diffract X-rays with less than 10% (e.g., less than 2%, less than 0.1%) of energy overlap with each other. In certain other embodiments, at least two X-ray diffractors 30 (e.g., each X-ray diffractor 30) comprise different materials and / or different diffraction surfaces (e.g., Miller index). In certain embodiments, the X-rays 22 diffracted by the first X-ray diffractor 30a have a first energy and the X-rays 22 diffracted by the second X-ray diffractor 30b have a second energy that differs from the first energy by at least 1 eV (e.g., at least 2 eV, at least 5 eV, at least 15 eV, at least 30 eV).

[0021] Table 1 lists exemplary crystal materials and diffractive surfaces and corresponding diffracted X-ray energy ranges according to certain embodiments described herein. In certain embodiments, at least one crystal material and diffractive surface (e.g., Miller index) is configured to provide an optimal tradeoff between throughput and spectral resolution. In certain embodiments, the diffractive surface (e.g., Miller index) is configured to reduce (e.g., minimize, eliminate) background contributions resulting from high order reflections of high energy X-rays. The presence of these high energy X-rays in the polychromatic X-rays 22 incident on the X-ray diffractor 30 can depend on the selection and design of the X-ray collimator 20.

[0022] [Table 1]

[0023] The at least one X-ray diffractor 30 (e.g., the most upstream X-ray diffractor 30) can have an X-ray transmission of greater than 2% (e.g., greater than 5%). The at least one X-ray diffractor 30 can be thin enough to provide that X-ray transmission. For example, the at least one X-ray diffractor 30 can have a thickness (e.g., thickness in a direction in which the X-rays 22 received by the X-ray diffractor 30 propagate) of less than 500 microns (e.g., less than 200 microns, less than 100 microns, less than 50 microns, less than 20 microns, less than 10 microns, less than 5 microns). The at least one crystalline material can be held by a support structure configured to provide mechanical strength without affecting the X-ray transmission of the X-ray diffractor 30. The thickness of the at least one X-ray diffractor 30 can be selected to provide an optimal tradeoff between diffraction efficiency and transmission (e.g., increasing or maximizing throughput). For example, the thickness of the at least one crystalline material can vary between about 1.5 and 5 times the primary extinction thickness of the X-rays in the crystalline material (e.g., if the primary extinction thickness is 2.5 microns, the thickness of the crystalline material can range from about 3.5 microns to 12.5 microns). The diffraction efficiency can be within a range of about 37% to about 99% of the maximum theoretical diffraction efficiency, and the X-ray transmission can be greater than 2% (e.g., within a range of 2% to 95%).

[0024] In certain embodiments, the X-ray diffractors 30 are asymmetrically cut to either increase the energy bandwidth for higher flux of diffracted X-rays 22 or decrease the energy bandwidth for higher energy resolution. In certain embodiments, at least one of the X-ray diffractors 30 diffracts X-rays 22 with different energies across a crystal surface (e.g., an imperfect crystal), and the corresponding X-ray detector 40 comprises a pixel array detector that records the diffracted X-rays 22 in response to different positions on the X-ray diffractor 30. In certain embodiments, the diffraction plane of at least one X-ray diffractor 30 is substantially parallel to the crystal plane of the at least one X-ray diffractor 30, while in certain other embodiments, the diffraction plane of at least one X-ray diffractor 30 is not substantially parallel to the crystal plane of the at least one X-ray diffractor 30.

[0025] In certain embodiments, at least one X-ray diffractor 30 of the plurality of X-ray diffractors 30 is substantially flat (see, e.g., FIGS. 1A, 1B, 2A, 4, and 5), while in certain other embodiments, at least one X-ray diffractor 30 is curved (e.g., spherically curved, cylindrically curved) in one or two directions (see, e.g., FIGS. 3, 4, 5, and 6).

[0026] In certain embodiments, at least one X-ray diffractor 30 of the plurality of X-ray diffractors 30 comprises multiple layers.

[0027] The multiple X-ray diffractors 30 can comprise at least one single crystal, at least one mosaic crystal, and / or at least one multi-layer. For example, symmetric single crystals, asymmetric single crystals, mosaic crystals, and multi-layers can be mixed and matched to provide a given energy resolution and throughput.

[0028] In certain embodiments, at least one X-ray diffractor 30 (e.g., each X-ray diffractor 30) of the plurality of X-ray diffractors 30 is configured to diffract X-rays 22 having a predetermined energy (e.g., a characteristic X-ray energy or X-ray spectral line corresponding to one or more atoms of interest, an energy of a background contribution near the characteristic X-ray energy or X-ray spectral line). In certain embodiments, at least one X-ray diffractor 30 (e.g., each X-ray diffractor 30) is configured to diffract X-rays 22 within an energy resolution of better than 50 eV (e.g., better than 25 eV, better than 10 eV, better than 5 eV, better than 2 eV, better than 1 eV) and / or a spectral bandwidth of greater than 10 eV (e.g., greater than 25 eV, greater than 50 eV, greater than 100 eV, greater than 200 eV, greater than 1 keV). The spectral bandwidth of the X-ray diffractors 30 can include one or more characteristic X-ray energies or X-ray spectral lines corresponding to one or more atoms of interest, energies of background contributions near the characteristic X-ray energies or X-ray spectral lines, or no X-ray spectral lines. In certain embodiments, at least one X-ray diffractor 30 (e.g., the most downstream X-ray diffractor 30) has a larger spectral bandwidth (e.g., coarser energy resolution) than at least one other X-ray diffractor 30 (e.g., the most upstream X-ray diffractor 30). In certain embodiments, the spectral overlap of the X-rays 22 diffracted by the at least two X-ray diffractors 30 is less than 50% (e.g., less than 25%, less than 10%, less than 5%, no spectral overlap). In certain other embodiments, the spectral overlap of the X-rays 22 diffracted by the at least two X-ray diffractors 30 is greater than 5% (e.g., greater than 10%, greater than 25%). The diffraction energy, energy bandwidth, and spectral overlap of the X-ray diffractors 30 can be selected based on the particular spectroscopic measurement to be performed.

[0029] In certain embodiments, each X-ray diffractor 30 of the plurality of X-ray diffractors 30 has substantially the same energy resolution as one another. In certain other embodiments, the most upstream X-ray diffractor 30 (e.g., the first X-ray diffractor 30a) has the highest energy resolution of all the X-ray diffractors 30 (e.g., capable of resolving fine features at the leading edge of the absorption spectrum of a sample such as TiO2 or rutile), and at least one other X-ray diffractor 30 has substantially the same energy resolution as one another or has substantially different energy resolutions as one another.

[0030] In certain embodiments, the most upstream X-ray diffractor 30 (e.g., first X-ray diffractor 30a) is configured to diffract X-rays having the weakest intensity (e.g., signal) of the spectrum being measured. For example, the most upstream X-ray diffractor 30 can be configured to diffract characteristic X-rays of trace atoms of source 5 (e.g., sample under analysis) having low signal intensity, and the other X-ray diffractors 30 (e.g., second X-ray diffractor 30b and / or third X-ray diffractor 30c) can be configured to diffract characteristic X-rays of other atoms of source 5 (e.g., major atoms, minor atoms) having stronger X-ray signals.

[0031] In certain embodiments, the most downstream X-ray diffractor 30 of the plurality of X-ray diffractors 30 (e.g., the third X-ray diffractor 30c in FIGS. 1A and 1B, the second X-ray diffractor 30b in FIGS. 2A, 3, 4, 5, and 6) is substantially not transparent to the X-rays 22. In certain embodiments, the most downstream X-ray diffractor 30 has a larger spectral bandwidth than at least one other X-ray diffractor 30 of the plurality of X-ray diffractors 30 (e.g., each of the other X-ray diffractors 30) to increase the detected X-ray signal. For example, the most downstream X-ray diffractor 30 can comprise a multilayer while at least one other X-ray diffractor 30 comprises a thin crystalline material.

[0032] Operation stage In certain embodiments, the apparatus 10 further comprises at least one motion stage configured to move at least one X-ray diffractor 30 (e.g., each X-ray diffractor 30) of the plurality of X-ray diffractors 30 to adjust the angle of incidence of the X-rays 22 on the at least one X-ray diffractor 30. For example, a first motion stage (e.g., a rotational motion stage, a linear motion stage) can be configured to move the first X-ray diffractor 30a relative to the X-ray propagation direction 24 (e.g., to adjust the first Bragg angle θ1), a second motion stage (e.g., a rotational motion stage, a linear motion stage) can be configured to move the second X-ray diffractor 30b relative to the X-ray propagation direction 24 (e.g., to adjust the second Bragg angle θ2), and / or a third motion stage (e.g., a rotational motion stage, a linear motion stage) can be configured to move the third X-ray diffractor 30c relative to the X-ray propagation direction 24 (e.g., to adjust the third Bragg angle θ3). The movement of the first, second and third X-ray diffractors 30a, b, c is indicated in Figures 1A and 1B by curved double arrows. The exemplary apparatus 10 of Figures 1A and 1B includes at least one moving stage, and the exemplary apparatus 10 of Figures 2A, 3, 4, 5 and 6 may also include at least one moving stage. Although Figures 1A and 1B show the exemplary apparatus 10 in a schematic manner in which each of the X-ray diffractors 30 is moved by at least one moving stage, in certain other embodiments, at least one of the X-ray diffractors 30 is fixed relative to the X-ray propagation direction 24.

[0033] In certain embodiments, at least one motion stage is configured to change at least one Bragg angle (e.g., at least one of the first, second, and third Bragg angles θ1, θ2, θ3) of the corresponding at least one X-ray diffractor 30 over a predetermined angular range (e.g., an angular range of 0.1 degrees wide, 1 degree wide, 5 degrees wide, or 50 degrees wide). In certain embodiments, at least some of the motion stages are configured to simultaneously change the Bragg angles of the corresponding X-ray diffractors 30 (e.g., by the same angular amount, but with different angular amounts). In certain embodiments, at least one motion stage is configured to hold at least two X-ray diffractors 30 at a predetermined angle relative to each other (e.g., the angle between the diffraction planes of the first and second X-ray diffractors 30a,b is greater than 0.1 mrad). In certain other embodiments, at least one motion stage is configured to adjust (e.g., rotate) the angles of at least two X-ray diffractors 30 relative to each other and / or relative to the X-ray propagation direction 24. For example, the X-ray diffractors 30 can be rotated at the same angular velocity (e.g., rotated simultaneously by the same angular increment) or at different angular velocities (e.g., rotated simultaneously by different angular increments). In certain embodiments, at least one X-ray diffractor 30 is configured to be rotated while the corresponding X-ray detector 40 remains fixed, and in certain other embodiments, the at least one X-ray diffractor 30 and the corresponding X-ray detector 40 are configured to move in tandem with each other (e.g., the X-ray detector 40 is moved in accordance with the rotation of the X-ray diffractor 30 to ensure detection of the diffraction spectral bands of the X-rays).

[0034] By changing at least one Bragg angle of the corresponding at least one X-ray diffractor 30, the X-ray energy diffracted by the X-ray diffractor 30 to the corresponding X-ray detector 40 is changed. In certain embodiments, during the spectrum measurement, each X-ray diffractor 30 remains stationary and is configured (e.g., optimized) to diffract a predetermined X-ray energy or over a predetermined spectral bandwidth (e.g., each X-ray diffractor 30 is configured to diffract one or more corresponding characteristic X-ray spectral lines of one or more corresponding atomic elements), thereby providing simultaneous measurement of multiple characteristic X-ray spectral lines (e.g., of multiple atomic elements). In certain other embodiments, during the spectrum measurement, at least one X-ray diffractor 30 remains stationary and configured to diffract a predetermined X-ray energy, while at least one other Bragg angle of at least one other X-ray diffractor 30 is changed to diffract X-rays having another predetermined discrete X-ray energy or having a predetermined range of X-ray energies (e.g., covering another predetermined spectral bandwidth).

[0035] X-ray detector Examples of X-ray detectors 40 compatible with certain implementations described herein include, but are not limited to, ionization chambers, proportional counters, scintillation counters, pin diodes, silicon drift detectors (SDDs), pixels of pixel array detectors (e.g., charge coupled device (CCD) detectors, complementary metal-oxide semiconductor (CMOS) detectors, photon counting detectors). In certain implementations, the plurality of X-ray detectors 40 comprises at least one X-ray detector 40 having an energy resolution of better than 25% (e.g., better than 5%) of the energy of the detected X-rays.

[0036] In certain embodiments, at least one of the multiple X-ray detectors 40 comprises a pixel array detector extending in at least one dimension and is used with a corresponding X-ray diffractor 30 comprising at least one crystalline material where the X-ray diffractor 30 is substantially non-flat (e.g., warped). The at least one X-ray detector 40 may be pixelated (e.g., includes pixels having pixel sizes in the range of 3 microns to 200 microns in the dispersion direction and 3 microns to 5000 microns in the sagittal direction) or may comprise a strip detector or a two-dimensional detector. The at least one X-ray detector 40 may comprise a direct conversion solid-state X-ray detector (e.g., a pixelated photon counting detector, a CCD detector, a CMOS detector). The at least one X-ray detector 40 may comprise multiple SDD detectors stacked on top of each other.

[0037] In certain implementations, at least one X-ray detector 40 of the plurality of X-ray detectors 40 comprises a photon-counting pixel array detector having at least one energy threshold configured to reject (e.g., remove detection) X-rays having an energy below the at least one energy threshold and / or reject (e.g., remove detection) X-rays having an energy above the at least one energy threshold. For example, the X-ray detector 40 can be configured to reject higher harmonics (e.g., multiples) or lower harmonics (e.g., multiples) of the measured energy recorded by the X-ray detector 40. For example, the photon-counting pixel array detector can have at least two energy thresholds configured to define an energy window between the two energy thresholds (e.g., an energy window at least 1 keV wide) such that X-rays below and above the energy window are not detected. The energy threshold can be preset to a few keV (eg, in the range of 3 keV to 8 keV, in the range of 1 keV to 3 keV) or sub-keV (eg, SDD with an energy window on the order of 100 eV to 250 eV).

[0038] By reducing (e.g., eliminating) the higher harmonics, certain embodiments can reduce (e.g., eliminate) the background contribution in the absorption spectrum, significantly increasing the throughput of the apparatus 10. For example, removing the 10% background contribution arising from the higher harmonics in the spectrum can increase the throughput of the apparatus 10 by about 3 times for XAS measurements. By eliminating higher energy x-rays, the ionizing radiation source (e.g., generating the x-rays in the x-ray source 5) can also be operated at a higher flux (e.g., higher voltage) for higher throughput.

[0039] In certain embodiments in which at least one X-ray detector 40 comprises a pixelated detector, the pixelated detector may comprise a one-dimensional or two-dimensional array of pixels. The pixelated detector may have a long dimension in the range of 30 mm to 50 mm, in the range of 30 mm to 100 mm, in the range of 100 mm to 300 mm, or in the range of more than 300 mm. In the case of a one-dimensional array of pixels, the detector may be oriented such that the long dimension of the array is along the dispersion plane. The pixel size may be large enough (e.g., on the order of 0.5 mm to 10 mm) to accommodate the diffracted X-ray beam in the dispersion plane. In a sagittal plane (e.g., substantially perpendicular to the dispersion plane), the diffracted X-ray beam may be detected by a plurality of pixels, each pixel being independent of adjacent pixels and configured to detect a corresponding portion of the diffracted X-ray beam. In the case of a two-dimensional array detector, the detectors may be used to record diffracted X-rays from different regions of a corresponding X-ray diffractor 30 (e.g., different regions of a substantially flat crystal where the crystallographic plane varies across the crystal), thereby allowing simultaneous detection of a range of X-ray energies.

[0040] In certain embodiments, the apparatus 10 further comprises at least one motion stage configured to move at least one X-ray detector 40 (e.g., each X-ray detector 40) of the plurality of X-ray detectors 40 such that diffracted X-rays from a corresponding X-ray diffractor 30 are received by the X-ray detector 40. For example, a first motion stage (e.g., a rotational motion stage, a linear motion stage) can be configured to move the first X-ray detector 40a, a second motion stage (e.g., a rotational motion stage, a linear motion stage) can be configured to move the second X-ray detector 40b, and / or a third motion stage (e.g., a rotational motion stage, a linear motion stage) can be configured to move the third X-ray detector 40c.

[0041] In certain implementations, at least some of the motion stages are configured to simultaneously move the corresponding X-ray detectors 40. For example, the X-ray detectors 40 can move at the same linear or angular velocity or with different linear or angular velocities. In certain implementations, the at least one X-ray detector 40 and the corresponding at least one X-ray diffractor 30 are configured to move in tandem with one another (e.g., the X-ray detector 40 moves in accordance with the rotation of the X-ray diffractor 30 to ensure detection of the diffraction spectrum bands of the X-rays).

[0042] Exemplary Apparatus 1A and 1B are schematic illustrations of two exemplary apparatuses 10 including multiple substantially flat X-ray diffractors 30 and multiple X-ray detectors 40 according to certain embodiments described herein. The X-ray diffractors 30 are configured to receive substantially collimated X-rays 22 and are arranged sequentially along the X-ray beam propagation direction 24. As shown in FIG. 1A, each X-ray diffractor 30 includes a substantially flat crystal, and each X-ray detector 40 includes at least one active element 42 configured to directly receive a diffracted spectral band of the X-rays 22 from the corresponding X-ray diffractor 30. As shown in FIG. 1B, the first and second X-ray diffractors 30a,b are substantially flat channel-cut crystals, and the third X-ray diffractor 30c is a substantially flat crystal. At least one of the X-ray detectors 40 each includes at least one active element 42, and the first and second X-ray detectors 40a,b each include at least one reflective X-ray optic 44a,b (e.g., an X-ray mirror) configured to receive a diffracted spectral band of X-rays 22 directly from the corresponding X-ray diffractor 30a,b and reflect at least a portion of the diffracted spectral band of X-rays 22 to the corresponding at least one active element 42a,b. In certain embodiments, as shown in FIG. 1B, the third X-ray detector 40c does not include at least one reflective X-ray optic, and in certain other embodiments, the third X-ray detector 40c includes at least one reflective X-ray optic.

[0043] 2A illustrates an exemplary apparatus 10 including multiple substantially flat X-ray diffractors 30 and multiple X-ray detectors 40 according to certain embodiments described herein. The X-ray diffractors 30 are configured to receive diverging X-rays 22 (e.g., from an X-ray source 5 extending less than 100 microns along a dispersive plane) and are arranged sequentially along an X-ray beam propagation direction 24. Each of the first and second X-ray detectors 40a,b may include at least one active element 42a,b (e.g., a pixel array detector) and is configured to detect a corresponding diffracted spectral band of the X-rays 22 from the corresponding X-ray diffractor 30a,b. The angle between the diffraction planes of the two X-ray diffractors 30 may be greater than 0.1 mrad.

[0044] FIG. 3 illustrates an exemplary apparatus 10 including multiple curved (e.g., spherically curved in at least one direction, cylindrically curved) X-ray diffractors 30 and multiple X-ray detectors 40 according to certain embodiments described herein. The X-ray diffractors 30 are configured to receive diverging X-rays 22 and are arranged sequentially along an X-ray beam propagation direction 24. The X-ray diffractors 30 include a first X-ray diffractor 30a including a first von Hamos crystal having a corresponding first longitudinal axis 32a and a second X-ray diffractor 30b including a second von Hamos crystal having a corresponding second longitudinal axis 32b at a non-zero angle Θ (e.g., greater than 0.1 mrad) relative to the first longitudinal axis 30a. In certain embodiments, the non-zero angle Θ is fixed at a predetermined value (e.g., in the range of 0.1 mrad to 0.5 radians) during the spectral measurement, while in certain other embodiments, the non-zero angle Θ varies during the spectral measurement. 3 shows two X-ray diffractors 30, each with a von Hamos crystal, certain other embodiments can include additional X-ray diffractors 30, each with a von Hamos crystal. At least one of the X-ray detectors 40 includes a pixel array detector configured to detect a diffraction spectral band of the X-rays 22 diffracted by the corresponding X-ray diffractor 30 (e.g., a von Hamos crystal). In certain embodiments, the von Hamos crystal of the most upstream X-ray diffractor 30 (e.g., the first X-ray diffractor 30a) has an X-ray transmittance of at least 2% (e.g., at least 5%), and the von Hamos crystal of the most downstream X-ray diffractor 30 (e.g., the second X-ray diffractor 30b) has an X-ray transmittance of less than 5% (e.g., less than 2%). The apparatus 10 of FIG. 3 can be considered to comprise a first von Hamos WDS and one or more second von Hamos WDSs sequentially disposed downstream of the first von Hamos WDS, each second von Hamos WDS configured to intercept at least a portion of the x-rays 22 that are transmitted through the first von Hamos WDS and any other upstream von Hamos WDSs.In certain embodiments, the at least one von Hamos WDS is configured to intercept at least a portion of X-rays 22 that are intercepted and transmitted by at least one other von Hamos WDS (see, e.g., FIG. 3 ), and in certain other embodiments, the at least one von Hamos WDS is configured to intercept at least a portion of X-rays that are not intercepted by at least one other von Hamos WDS.

[0045] FIG. 4 illustrates an exemplary apparatus 10 including at least one substantially flat X-ray diffractor 30, at least one substantially curved (e.g., spherically curved, cylindrically curved in at least one direction) X-ray diffractor 30, and multiple X-ray detectors 40 according to certain embodiments described herein. The X-ray diffractors 30 are configured to receive diverging X-rays 22 and are arranged sequentially along the X-ray beam propagation direction 24. As shown in FIG. 4, the first X-ray diffractor 30a includes a substantially flat crystal having an X-ray transmission of at least 2% (e.g., at least 5%), and the second X-ray diffractor 30b includes a von Hamos crystal downstream of the first X-ray diffractor 30a. At least one of the X-ray detectors 40 includes a pixel array detector configured to detect a diffraction spectral band of the X-rays 22 diffracted by the corresponding X-ray diffractor 30.

[0046] FIG. 5 illustrates another exemplary apparatus 10 including at least one substantially flat X-ray diffractor 30, at least one substantially curved (e.g., spherically curved, cylindrically curved in at least one direction) X-ray diffractor 30, and multiple X-ray detectors 40 according to certain embodiments described herein. The X-ray diffractors 30 are configured to receive diverging X-rays 22 and are arranged sequentially along the X-ray beam propagation direction 24. As shown in FIG. 5, the first X-ray diffractor 30a includes a substantially flat crystal having an X-ray transmittance of at least 2% (e.g., at least 5%), and the second X-ray diffractor 30b includes a spherically or cylindrically curved crystal (e.g., Johann crystal, Johannsson crystal) downstream of the first X-ray diffractor 30a. At least one of the X-ray detectors 40 includes a pixel array detector configured to detect a diffraction spectral band of the X-rays 22 diffracted by the corresponding X-ray diffractor 30. In certain embodiments, the X-ray source 5, the second X-ray diffractor 30b, and the second X-ray detector 40b (e.g., comprising a single active element 42b (e.g., pixel, detector element)) are configured in a Rowland circle geometry. In certain other embodiments, the X-ray source 5, the second X-ray diffractor 30b, and the second X-ray detector 40b are configured in a geometry that deviates from the Rowland circle, with the X-ray source 5 being inside the Rowland circle while the second X-ray diffractor 30b and the second X-ray detector 40b being on the Rowland circle, and with the second X-ray detector 40b comprising a pixel array detector.

[0047] FIG. 6 illustrates another exemplary apparatus 10 including multiple curved (e.g., spherically curved, cylindrically curved in at least one direction) X-ray diffractors 30 and multiple X-ray detectors 40 according to certain embodiments described herein. The X-ray diffractors 30 are configured to receive diverging X-rays 22 and are arranged sequentially along the X-ray beam propagation direction 24. As shown in FIG. 6, the X-ray diffractors 30 include a first X-ray diffractor 30a including a spherically or cylindrically curved first crystal (e.g., Johann crystal, Johannsson crystal) having an X-ray transmittance of at least 2% (e.g., at least 5%), and a second X-ray diffractor 30b including a spherically or cylindrically curved first crystal (e.g., Johann crystal, Johannsson crystal) downstream of the first X-ray diffractor 30a. At least one of the X-ray detectors 40 includes a pixel array detector configured to detect a diffraction spectral band of the X-rays 22 diffracted by the corresponding X-ray diffractor 30. In a particular embodiment, the X-ray source 5, the first X-ray diffractor 30a, and the first X-ray detector 40a are configured in a first Rowland circle geometry, and the X-ray source 5, the second X-ray diffractor 30b, and the second X-ray detector 40b are configured in a second Rowland circle geometry.

[0048] Exemplary XAS, XES and XRF Methods In certain embodiments, the apparatus 10 is configured to perform X-ray absorption spectroscopy (XAS) and / or X-ray emission spectroscopy (XES) of various materials (e.g., catalysts in fuel cells, semiconductor quantum structures, magnetic semiconductor structures, nanotechnology, materials for energy storage and conversion). For example, XAS measurements can be performed by detecting X-ray absorption as a function of X-ray energy across the absorption edge of an atomic element with sufficient energy resolution (e.g., less than 2 eV or less than 1 eV to detect X-ray absorption near edge structure (XANES) indicative of chemical states such as oxidation states, less than 10 eV or less than 5 eV to detect extended X-ray absorption fine structure (EXAFS) indicative of interatomic distances and coordination numbers). In another example, XES measurements can be performed by detecting X-ray emission as a function of X-ray energy with sufficient energy resolution (e.g., less than 2 eV) to determine chemical states such as oxidation states.

[0049] In certain embodiments, the apparatus 10 is configured to perform X-ray fluorescence (XRF) spectroscopy in a variety of applications (e.g., metallurgy, geology and mining, semiconductor metrology, failure analysis, electronics, archaea, and environmental analysis). For example, XRF measurements can be made by detecting the number of characteristic X-rays emitted by atomic elements in a material (e.g., solid, liquid, powder), and in many situations, XRF measurements are made non-destructively.

[0050] Conventional XAS, XES, and / or XRF systems that use crystal-based spectrometers to provide sufficient energy resolution have limited throughput because only a narrow energy bandwidth of X-rays incident on a point on the crystal that satisfies Bragg's law is reflected, and X-rays outside the narrow energy bandwidth are lost or wasted (e.g., absorbed by the crystal), reducing the signal contained in the absorbed X-rays. In contrast, using apparatus 10 according to certain embodiments described herein, a wider energy bandwidth of X-rays can be efficiently used simultaneously, allowing for increased data collection rates.

[0051] In certain embodiments, for XANES measurements, at least one of the X-ray diffractors 30 has an energy bandwidth of better than 3 eV (e.g., better than 2 eV, better than 1 eV), but with a maximum central energy difference of less than 50 eV (e.g., less than 20 eV, less than 10 eV). In certain embodiments, the difference between the average energies of the different X-ray diffractors 30 is between 2 eV and 10 eV, or up to 250 eV. To obtain XANES measurements over an energy range (e.g., 30 eV to 100 eV), the X-ray diffractors 30 can be rotated and the X-rays diffracted by each X-ray diffractor 30 can be recorded. The spectra recorded by all X-ray diffractor 30 / X-ray detector 40 pairs can be normalized to obtain a single spectrum.

[0052] In certain embodiments, for EXAFS measurements, at least one X-ray diffractor 30 has an energy spectrum resolution of better than 50 eV (e.g., better than 10 eV, better than 5 eV, better than 2 eV), and the central energies of the X-ray diffractors 30 differ by more than 1 eV (e.g., more than 2 eV, more than 5 eV, more than 10 eV), but the maximum central energy difference is less than 100 eV (e.g., less than 500 eV). In certain embodiments, the difference between the central energies of the different X-ray diffractors 30 is in the range of 5 eV to 50 eV. To obtain EXAFS measurements over an energy range (e.g., 400 eV to 1000 eV), the X-ray diffractors 30 can be rotated and the X-rays diffracted by each X-ray diffractor 30 can be recorded. The spectra recorded by all X-ray diffractor 30 / X-ray detector 40 pairs can be normalized to obtain a single spectrum.

[0053] In certain embodiments, for XES measurements, at least one of the X-ray diffractors 30 has an energy bandwidth of better than 3 eV (e.g., better than 2 eV, better than 1 eV), and the central energies of the X-ray diffractors 30 differ by more than 1 eV (e.g., more than 2 eV, more than 3 eV, more than 10 eV), but the maximum central energy difference is less than 50 eV. In certain embodiments, the difference between the central energies of the different X-ray diffractors 30 is within the range of 2 eV to 50 eV (e.g., in the range of 2 eV to 10 eV). In certain embodiments, the different X-ray diffractors 30 are configured to measure different characteristic X-ray emission lines (e.g., Kα and Kβ X-ray spectral lines). For example, at least one upstream X-ray diffractor 30 can be configured to diffract a first characteristic X-ray spectral line of lower fluorescence yield (e.g., the Kβ X-ray spectral line or one of its satellite spectral lines), and the X-ray diffractors 30 can be rotated and the X-rays diffracted by each X-ray diffractor 30 can be recorded. The spectra recorded by all X-ray diffractor 30 / X-ray detector 40 pairs can be normalized to obtain a single spectrum.

[0054] In certain embodiments, for XRF measurements, the apparatus 10 can efficiently use a wider energy bandwidth of X-rays simultaneously, increasing the data collection rate. In certain embodiments, the X-rays are generated by a primary X-ray beam or charged particles incident on the sample under analysis. In certain embodiments, at least one of the X-ray diffractors 30 has an energy resolution of better than 50 eV (e.g., better than 25 eV, better than 10 eV). In certain embodiments, the difference between the average energies of the different X-ray diffractors 30 is greater than 10 eV (e.g., greater than 25 eV, greater than 50 eV, greater than 500 eV). In certain embodiments, the different X-ray diffractors 30 are configured to measure characteristic X-ray emission lines of different atomic elements (e.g., X-ray spectral lines of Ca and Cu). In certain embodiments, at least one upstream X-ray diffractor 30 is configured to diffract characteristic X-rays of atomic elements of low concentration or low fluorescence signal. In certain embodiments, at least one upstream X-ray diffractor 30 is configured to diffract characteristic X-rays of the atomic elements of interest, and at least one other X-ray diffractor 30 is configured to diffract X-rays having energies close to the characteristic X-ray spectral lines (e.g., to improve the accuracy of the analysis of the atomic elements). The X-ray diffractors 30 can be rotated, and the X-rays diffracted by each X-ray diffractor 30 can be recorded. The spectra recorded by all X-ray diffractor 30 / X-ray detector 40 pairs can be normalized to obtain a measure of the atomic composition of the material.

[0055] Although commonly used terms are used to describe the systems and methods of certain embodiments for ease of understanding, these terms are used herein with their broadest reasonable interpretation. Although various aspects of the present disclosure are described with respect to illustrative examples and embodiments, the disclosed examples and embodiments should not be construed as limiting. Conditional language such as "can," "could," "might," or "may" is generally intended to convey that certain embodiments include certain features, elements, and / or steps, but not other embodiments, unless otherwise stated or understood otherwise within the context in which it is used. Thus, such conditional language is generally not intended to imply that the features, elements, and / or steps are in any way 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 and indicate 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.

[0056] Conjunctions such as the phrase "at least one of X, Y, and Z," unless otherwise noted, should be understood within the context in which they are generally used to convey that an item, term, etc. can be either X, Y, or Z. Thus, such conjunctives are 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.

[0057] Language of degree as used herein, such as the terms "approximately," "about," "generally," and "substantially," describes 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%, within ±5%, within ±2%, within ±1%, or within ±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. 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.

[0058] 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. Although the present invention has been described with reference to these specific configurations, the description is intended to illustrate the present invention and is not intended to limit it. Various modifications and applications will occur to those skilled in the art without departing from the true spirit and scope of the present invention. Thus, for example, in any method or process disclosed herein, the acts or operations constituting 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 may be combined with each other to generate alternative configurations that are compatible with the embodiments disclosed herein. Various aspects and advantages of the embodiments have been described where appropriate. It should be understood that not all such aspects or advantages are necessarily 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 group of advantages as taught herein without necessarily achieving other aspects or advantages as may be taught or suggested herein.

Claims

1. 1. An apparatus configured to receive x-rays propagating from an x-ray source along an x-ray propagation direction, comprising: a plurality of X-ray diffractors along the X-ray propagation direction, the plurality of X-ray diffractors comprising at least a first X-ray diffractor and a second X-ray diffractor, the second X-ray diffractor being downstream of the first X-ray diffractor; a plurality of X-ray detectors including at least a first X-ray detector and a second X-ray detector; Equipped with the first X-ray diffractor is configured to receive the X-rays, diffract a first spectral band of the X-rays to the first X-ray detector, and transmit at least 2% of the received X-rays to the second X-ray diffractor; the second X-ray diffractor is configured to receive the transmitted X-rays from the first X-ray diffractor and diffract a second spectral band of the X-rays to the second X-ray detector; the first X-ray detector comprises at least one first active element configured to measure a first spectrum of at least a portion of the first spectral band of the X-rays, and the second X-ray detector comprises at least one second active element configured to measure a second spectrum of at least a portion of the second spectral band of the X-rays.

2. The apparatus of claim 1 , wherein the plurality of X-ray diffractors are arranged sequentially along the X-ray propagation direction.

3. 2. The apparatus of claim 1 , wherein the plurality of X-ray diffractors further comprises a third X-ray diffractor, the plurality of X-ray detectors further comprises a third X-ray detector, the third X-ray diffractor downstream of the second X-ray diffractor, the second X-ray diffractor configured to transmit at least 2% of the X-rays received from the first X-ray diffractor to the third X-ray diffractor, the third X-ray diffractor configured to receive the transmitted X-rays from the second X-ray diffractor and diffract a third spectral band of the X-rays to the third X-ray detector, the third X-ray detector comprising at least one third active element configured to measure a third spectrum of at least a portion of the third spectral band of the X-rays.

4. 2. The apparatus of claim 1, further comprising an X-ray collimator configured to receive the X-rays from the X-ray source and collimate at least a portion of the X-rays, the first X-ray diffractometer configured to receive the collimated X-rays from the X-ray collimator.

5. 5. The apparatus of claim 4, wherein the x-ray collimator comprises at least one mirror optic having a functional surface, at least a portion of the surface having a parabolic shape.

6. 5. The apparatus of claim 4, wherein the x-ray collimator comprises a Wolter optic having a hyperboloidal segment and a paraboloidal segment, configured such that a focal point of the hyperboloidal segment is aligned with the x-ray source and a focal point of the paraboloidal segment is aligned with another focal point of the hyperboloidal segment.

7. The apparatus of claim 4 , wherein the x-ray collimator comprises a polycapillary optic or a multiple nested mirror optic.

8. The apparatus of claim 4 , wherein the x-ray collimator comprises at least one Soller slit.

9. 5. The apparatus of claim 4, wherein X-rays from the X-ray collimator are incident on the first X-ray diffractor at a first Bragg angle, the first spectral band of X-rays diffracted by the first X-ray diffractor to the first X-ray detector having a first central X-ray energy, X-rays from the first X-ray diffractor are incident on the second X-ray diffractor at a second Bragg angle, the second spectral band of X-rays diffracted by the second X-ray diffractor to the second X-ray detector having a second central X-ray energy, and the second X-ray energy differs from the first X-ray energy by at least 1 eV.

10. The plurality of X-ray diffractors further comprises a third X-ray diffractor, the plurality of X-ray detectors further comprises a third X-ray detector, the third X-ray diffractor configured to diffract a third spectral band of the X-rays into the third X-ray detector, the third X-ray diffractor being downstream of the second X-ray diffractor, and the X-rays from the second X-ray diffractor diffract at a third Bragg angle θ ３ and the third spectral band of the X-rays 22 incident on the third X-ray diffractor at a third central X-ray energy E ３ 10. The apparatus of claim 9, further comprising:

11. The apparatus of claim 1 , wherein the x-rays received by the first x-ray diffractometer are divergent.

12. 12. The apparatus of claim 11, further comprising an aperture between the X-ray source and the first X-ray diffractor, the aperture having a width in a dispersive plane of the first X-ray diffractor less than 100 microns.

13. The apparatus of claim 1 , wherein at least one X-ray diffractor of the plurality of X-ray diffractors comprises at least one crystalline material.

14. 14. The apparatus of claim 13, wherein the at least one crystalline material is selected from the group consisting of graphite, highly oriented pyrolytic graphite (HOPG), highly annealed pyrolytic graphite (HAPG), diamond, quartz, LiF, Si, and Ge.

15. 14. The apparatus of claim 13, wherein at least one X-ray diffractor of the plurality of X-ray diffractors is a single crystal, at least one X-ray diffractor of the plurality of X-ray diffractors is a mosaic crystal, and / or the plurality of X-ray diffractors comprises both at least one single crystal and at least one mosaic crystal.

16. 10. The apparatus of claim 1, wherein the first X-ray diffractor has a thickness of less than 500 microns in a direction of propagation of the X-rays received by the first X-ray diffractor.

17. The apparatus of claim 1 , wherein at least one X-ray diffractor of the plurality of X-ray diffractors is asymmetrically cut.

18. The apparatus of claim 1 , wherein at least one X-ray diffractor of the plurality of X-ray diffractors is substantially flat.

19. The apparatus of claim 1 , wherein at least one X-ray diffractor of the plurality of X-ray diffractors is curved in at least one direction.

20. 2. The apparatus of claim 1, wherein the first X-ray diffractor is configured to diffract characteristic X-rays of a trace atomic element of the X-ray source and the second X-ray diffractor is configured to diffract characteristic X-rays of other atomic elements of the X-ray source.

21. 2. The apparatus of claim 1, wherein an X-ray diffractor of the plurality of X-ray diffractors that is downstream of every other X-ray diffractor of the plurality of X-ray diffractors is substantially not transparent to the X-rays.

22. 10. The apparatus of claim 1, further comprising at least one motion stage configured to move at least one X-ray diffractor of the plurality of X-ray diffractors to adjust an angle of incidence of the X-rays to the at least one X-ray diffractor.

23. 2. The apparatus of claim 1, wherein at least one X-ray detector of the plurality of X-ray detectors is selected from the group consisting of an ionization chamber, a proportional counter, a scintillation counter, a pin diode, a silicon drift detector, and a pixel of a pixel array detector.

24. The apparatus of claim 1 , wherein at least one X-ray detector of the plurality of X-ray detectors comprises a pixel array detector extending in at least one dimension.

25. 2. The apparatus of claim 1, wherein at least one X-ray detector of the plurality of X-ray detectors comprises a photon-counting pixel array detector having at least one energy threshold configured to reject X-rays having energies below the at least one energy threshold and / or reject X-rays having energies above the at least one energy threshold.

26. The apparatus of claim 1 , wherein the first and second X-ray diffractors each comprise a substantially flat crystal.

27. 2. The apparatus of claim 1, wherein the first X-ray diffractor comprises a first substantially curved crystal and the second X-ray diffractor comprises a second substantially curved crystal.

28. 28. The apparatus of claim 27, wherein the first substantially curved crystal comprises a first von Hamos crystal having a corresponding first longitudinal axis, and the second substantially curved crystal comprises a second von Hamos crystal having a corresponding second longitudinal axis that is at an angle of greater than 0.1 mrad relative to the first longitudinal axis.

29. 28. The apparatus of claim 27, wherein at least one of the first substantially curved crystal and the second substantially curved crystal comprises a von Hamos crystal, a Johann crystal, or a Johannsson crystal.

30. 10. The apparatus of claim 1, wherein the first X-ray diffractor comprises a substantially flat crystal and the second X-ray diffractor comprises a substantially curved crystal.

31. 31. The apparatus of claim 30, wherein the substantially curved crystal comprises a von Hamos crystal, a Johann crystal, or a Johannsson crystal.

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