Beating Darwin-Bragg losses in lab-based ultrafast x-ray experiments

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Beating Darwin-Bragg losses in lab-based ultrafast x-ray experiments Fullagar, Wilfred K.; Uhlig, Jens; Mandal, Ujjwal; Kurunthu, Dharmalingam; Nahhas, Amal El; Tatsuno, Hideyuki; Honarfar, Alireza; Gustafsson, Fredrik Parnefjord; Sundström, Villy; Palosaari, Mikko; Kinnunen, Kimmo; Maasilta, Ilari; Miaja-Avila, Luis; O'Neil, Galen C.; Joe, Young Il; Swetz, Daniel S.; Ullom, Joel N. Fullagar, W. K., Uhlig, J., Mandal, U., Kurunthu, D., Nahhas, A. E., Tatsuno, H., Honarfar, A., Gustafsson, F. P., Sundström, V., Palosaari, M., Kinnunen, K., Maasilta, I., Miaja-Avila, L., O'Neil, G. C., Joe, Y. I., Swetz, D. S., & Ullom, J. N. (2017). Beating Darwin-Bragg losses in lab-based ultrafast x-ray experiments. Structural Dynamics, 4(4), Article 044011. https://doi.org/10.1063/1.4978742 2017 Beating Darwin-Bragg losses in lab-based ultrafast x-ray experiments Wilfred K. Fullagar, Jens Uhlig, Ujjwal Mandal, Dharmalingam Kurunthu, Amal El Nahhas, Hideyuki Tatsuno, Alireza Honarfar, Fredrik Parnefjord Gustafsson, Villy Sundström, Mikko R. J. Palosaari, Kimmo M. Kinnunen, Ilari J. Maasilta, Luis Miaja-Avila, Galen C. O'Neil, Young Il Joe, Daniel S. Swetz, and Joel N. Ullom Citation: Structural Dynamics 4, 044011 (2017); doi: 10.1063/1.4978742 View online: http://dx.doi.org/10.1063/1.4978742 View Table of Contents: http://aca.scitation.org/toc/sdy/4/4 Published by the American Institute of Physics Articles you may be interested in Pulse length of ultracold electron bunches extracted from a laser cooled gas Structural Dynamics 4, 044010044010 (2017); 10.1063/1.4978996 Dynamic diffraction effects and coherent breathing oscillations in ultrafast electron diffraction in layered 1T- TaSeTe Structural Dynamics 4, 044012044012 (2017); 10.1063/1.4979643 Beating Darwin-Bragg losses in lab-based ultrafast x-ray experiments Wilfred K. Fullagar, 1,2 Jens Uhlig, 1 Ujjwal Mandal, 1,3 Dharmalingam Kurunthu, 1,4 Amal El Nahhas, 1 Hideyuki Tatsuno, 1 Alireza Honarfar, 1 Fredrik Parnefjord Gustafsson, 1 Villy Sundstr€ om, 1 Mikko R. J. Palosaari, 5 Kimmo M. Kinnunen, 5 Ilari J. Maasilta, 5 Luis Miaja-Avila, 6 Galen C. O’Neil, 6 Young Il Joe, 6 Daniel S. Swetz, 6 and Joel N. Ullom 6 1 Department of Chemical Physics, Lund University, Box 124, Lund SE-22100, Sweden 2 Department of Applied Mathematics, RSPE, Australian National University, Canberra, ACT 2601, Australia 3 Department of Chemistry, The University of Burdwan, Golapbag, Burdwan 713104, WB, India 4 Department of Physics, Chemistry and Biology (IFM), Link€ oping University, 58183 Link€ oping, Sweden 5 Nanoscience Center, Department of Physics, University of Jyv€ askyl€ a, P.O. Box 35, FI-40014 Jyv€ askyl€ a, Finland 6 National Institute of Standards and Technology, Boulder, Colorado 80305, USA (Received 18 November 2016; accepted 6 March 2017; published online 24 March 2017) The use of low temperature thermal detectors for avoiding Darwin-Bragg losses in lab-based ultrafast experiments has begun. An outline of the background of this new development is offered, showing the relevant history and initiative taken by this work. V C2017 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution (CC BY) license (http:// creativecommons.org/licenses/by/4.0/).[http://dx.doi.org/10.1063/1.4978742] INTRODUCTION: A CENTRAL REQUIREMENT Crystallographic Darwin-Bragg losses are a leading cause of low detectable flux in X-ray spectroscopy studies, which study the energy exchange (x) of photons of incident energy E with samples. The frustration is most acute where high x-resolution is needed in broadband measurements. The corresponding loss is typically a factor 10 5 , according to the Darwin spectral (or angular) acceptance width, with the possibility of greater throughput if lower resolution will suffice, but in any case relative to the spectral region of interest (ROI). 1,2 A huge variety of conventional Bragg-based spectroscopic arrangements exists, whereby samples, monochromators, analysers, and instrument topology each have more or less bearing on diffraction widths and efficiency. In that collective sense, spectral ROIs are both arbitrary and potentially very broad. For X-ray spectroscopy then, accurate energy-resolving approaches are sought that can accommodate diverse needs without incurring Darwin-Bragg losses at any level. In another very broad class of X-ray techniques, diffraction-based measurements from substantial volumes of reciprocal (momentum transfer, Q-) space are sought that correspond to elastic scatter (x¼0). In these, a basic requirement is again the knowledge of the photon energy. This is seen in the relationships Q¼jk f k i j¼2p/d ¼(4p/k)sin h¼(4pE/hc)sin hfor initial and final momentum vectors k i and k f , diffraction angle 2h, and correlations of size din real space. Note that directions of k i and k f are both defined by knowledge of the places where generation, scatter, and detection occur. For this Bragg diffraction situation, broadband and/or high divergence (i.e., reduced brilliance) sources can address large volumes of reciprocal space for any particular sample orientation (e.g., in individual radiation shots), 3–6 while extreme brilliance sources cannot. The variables Eand hcontribute to Qdeviation according to dQ ¼(@Q/@h)dhþ(@Q/@E)dE. Here the first term shows the need for a low angular uncertainty in diffraction measurements. Traditional divergent and convergent beam geometries typically 2329-7778/2017/4(4)/044011/17 V CAuthor(s) 2017.4, 044011-1 STRUCTURAL DYNAMICS 4, 044011 (2017) use the common angle theorem of cyclic quadrilaterals to avoid losses while accurately knowing hin diffraction setups. Different diffraction measurements have different needs for Q- resolution, such that geometric design compromises are generally possible. More conveniently for pump-probe diffraction measurements, the incident beam may be collimated, as per the laser wakefield-based 7–9 and FemtoMAX 10–12 investments made as part of this work. 5 But in any case, the second factor again shows the simultaneous need to accurately know photon energies in polychromatic diffraction contexts, to enable Q-resolution. In limited flux situations, diffracted photon energies must be established efficiently. More generally, momentum changes (Q) and energy changes (x) are not mutually exclusive. In this broader sense, spectroscopy and diffraction together constitute the scattering function S(Q,x)containing all that can be learned about the sample from scattered radiation. S(Q,x)relates directly to the sample’s structure correlations and their dynamics. This comes about via a Fourier transform in space and time, which connects S(Q,x)to its time-dependent pair correlation function G(d,t). 13–16 It applies to neutrons and other de Broglie wave quanta as well as X-rays. 17 The combination of conceptual need and practical constraint described above often motivates the use of polychromatic radiation; but then the knowledge of the energy of quanta is effectively a requirement. Brilliant sources require a sequential approach to mapping out S(Q,x). That is a problem for ultrafast work, since samples cannot be reoriented within a single shot. Together with an optical excitation pulse, a single shot can be all it takes to damage or destroy a sample. Yet a representative sampling of S(Q,x)space is essential to enable the Fourier transform to G(d,t). Neutron work addressed the latter need around low brilliance sources aided by time of flight (TOF) detection methods. Building on TOF neutron structural dynamics studies, this work introduced low temperature thermal detectors to the lab-based ultrafast laser-driven X-ray field, for those reasons. The manuscript is structured as follows. The “Constraints of Brilliance” section gives a description of the sample structure and spectroscopy features whose observation is lost in ultrabrief collimated monochromatic radiation shots. It is followed by a short discussion of the foundational role that polychromatic neutron time of flight approaches continue to play in molecular structural dynamics contexts, in which they avoid the same losses. Then, the underpinning thermodynamic approach and considerations required by energy dispersive and low temperature thermal detectors to achieve the same outcomes for X-rays is addressed. We close with a brief prospectus and indication of the current state of developments for the first couplings of lab-based ultrafast laser driven X-ray sources with such detectors, which this collaboration has initiated on two continents. CONSTRAINTS OF BRILLIANCE Figure 1offers a graphical representation of the situation discussed in the following paragraphs. A metric often applied to X-ray sources is brilliance. It is the number of photons produced, normalised by their spectral bandwidth, the time interval in which they are produced, the physical dimensions of the source, and their angular divergence from it. Minimising the normalisation terms without overly compromising the total number of photons is often desirable, and increases the metric. Doing so accommodates the narrow acceptance conditions of diffractive and refractive X-ray optics, and the need to address small samples. It also makes spatial coherence effects more easily observable in the absence of energy resolving detectors that could otherwise determine structural effects via polychromatic Q-measurements. The resulting developments have led from low through moderate to high and extreme brilliance sources. In Figure 1, the temporal extension of the du Mond diagram roughly sketches a comparison of single pulses from three sources in terms of their bandwidth, divergence, and pulse duration contributions to single-shot brilliance. Another potential normalising parameter likely to become of increasing interest is the degree of polarisation (linear or circular), for examinations of spin and topological systems. Other factors also critically affect the practical usefulness of a source and could be incorporated in a metric. A partial list would include: repetition rate and temporal 044011-2 Fullagar et al. Struct. Dyn. 4, 044011 (2017) structure; broadband energy span; capacity for integration with other contemporary work; routine accessibility; safety; and affordability. The incorporation of low-T thermal X-ray photon detectors can go a very long way towards enabling X-ray structural dynamics autonomy in groups that have investments in moderate and high power ultrafast laser technologies and the desire to use hard radiations for ultrafast chemical examinations. It is the reason for our investments in this lab-based development, subsequent to and in parallel with major facilities, which can also benefit from them. The advantage comes about by these detectors’ removal of Darwin losses suffered by Bragg diffraction instrument topologies, which was the only way to foresee adequate X-ray progress during its first century. In 2006, a confluence of the rationales described in this work was used to motivate the introduction of low temperature thermal detectors in lab-based ultrafast X-ray contexts. Their combination achieved “first light” in 2010 through the international collaboration represented in this work. 18,19 When tied to the use of a high brilliance source for monochromatic photocrystallography, 20 compromises are either in the temporal domain, 21,22 or by measurements that necessitate vast serial acquisitions of individual shots to ensure due representation of every sample orientation with respect to its symmetry. This may be done stochastically, requiring extensive computational reconstruction. 23 Due to their tight monochromation and power, X-ray free electron laser (XFEL) beams can also be used for spectroscopy when different energies are presented in different shots, thereby effectively sampling x-space. 24 Temporally chirped schemes are another possibility. 25 Such workarounds are achievable in the cited S(Q,x)explorations by applying major facility resources. Yet as earlier demonstrated, 3,4,6,13,25,26 it is true that where the need is FIG. 1. Energy dispersive X-ray array and neutron TOF detectors avoid Darwin losses, opening efficient and comprehensive views of samples’ Q- and x-space. Bragg scattering traces a sinusoid line on a du Mond diagram (panel (a)). Phase space occupancy of radiation sources can be roughly shown by its extension with a time axis (panel (b)). In panel (a) an energy dispersive array captures the highlighted angle range allowing efficient spectroscopy (x-studies), 18,19,139,142,163,164 while Bragg diffraction analyses transmit only what is under the width of the sinusoid line. The Bragg equation can also be shown in momentum transfer space (Q¼ð4p=kÞsin h¼2p=d; panel (c)), where crystal reflections appear as dots. The geometrical size of line and dots in panels (a) and (c) correspond to the Darwin width 68 in the limiting case of infinite ideal crystals (panel (d)). 1,2 Measuring structural dynamics via scattering problems requires representative observation of a sample’s Q- and x-space intensity features, impossible when probing structured samples with just one membrane-thin monochromatic Ewald sphere. Lowering brilliance by increasing divergence or bandwidth permits parallel collection of entire volumes of Q-space intensity features in single shots; the Laue sketch in panel (c) diffracts different colours of a small divergence but polychromatic beam. 3,4,96,196 044011-3 Fullagar et al. Struct. Dyn. 4, 044011 (2017) asample examination in S(Q,x) space, then the tightly squeezed parametric phase space of brilliant sources can be a severe handicap. Monochromatic interests are on one hand a concession to the challenge of photon energy resolvability in the X-ray field, which we deal with here. On the other hand they have meanwhile opened the door to interesting approaches appealing to speckle correlation in spatially coherent sources, phase conjugation/time reversal, and other suggestions and demonstrations that often end up motivating polychromatic approaches. 25,27–31 There is a problem of phase preservation for X-rays in detectors, that is accepted in our broadband approaches and which does not apply at optical energies. Physically, the loss of phase information in detectors corresponds to the inability to preserve the spatial beat structure of interference fringes 32 for short wavelength quanta at high Q. For high resolution this needs a fringe fidelity on vanishingly small length scales (recall Q¼2p/d); however, the finer the fringes, the more they are smeared by the relatively huge physical dimensions of observable radiation event phenomena. 33–35 This constraint was seemingly recognised by the Braggs, noting text by Wilson 36 and relevant for their development of optically reconstructed X-ray diffraction approaches. 37–40 Preservation of X-ray phase in detectors at high Qcorresponding to molecular distances may never find a generally practical solution, while source coherence developments do not change that situation. At optical energies, Ewald spheres cannot access molecular dimensions (Figure 1(c)), but optical wavelengths are long and photon energies low compared to X-rays, so the interference fringe fidelity is preservable. That has been the basis for Lippmann colour photography, 41–45 holography 32,46–48 and optical phase conjugation, 49–53 leading among other things 54,55 to the coherent multidimensional spectroscopies 56 now widely practiced in ultrafast laser labs. 57–61 Optical laser technologies have stimulated efforts to allow comparable effects at higher photon energies, in particular, X-rays, 62–65 where matter and its ultrafast molecular movements are accessible. Phase retrieval approaches in neutron and X-ray measurements are mathematically motivated in textbooks 1,2 without revealing the eventual role of event size, possibly as insurance against a solution being found. Phase retrieval methods are highly diverse and the following are just two relevant examples. Multi-wavelength anomalous diffraction (MAD) near elements’ absorption edges gives an adjustable reference wave within unit cells for phasing. 1 This requires multiple X-ray energies, potentially motivating good photon energy resolvability in detectors; it is otherwise the same as conventional X-ray diffraction of von Laue and the Braggs. Neutron and ultrafast X-ray Laue work demonstrates that exceptional source coherence properties are not needed for protein-scale structural dynamics diffraction studies, 6,66,67 but again motivate a capacity for photon energy resolvability in detector arrays. Those features are a central theme of this work. X-ray sources including synchrotrons were originally motivated in terms of brilliance largely because it allows increasingly efficient diffraction through the DE/E ¼Dh/tan h (3冑2/p)(d/n) 2 (r 0 jFj/v c )10 5 Darwin 68 rocking curves of typical monochromator crystals (here dis interplanar spacing, nis the order of the Bragg reflection, r 0 is the Thomson scattering length, and Fis the structure factor for the unit cell of volume v c ). 1 The idea was that the user may then do as they please in S(Q,x)space, if they can address particular membrane-thin cuts through that space in any representative way, with freedom to scan hand/or Ewhen necessary. We sum up this section with reference to Figure 1. A brilliance-based approach overlooks the alternative of addressing volumes of the same space in parallel using short pulsed but polychromatic and potentially divergent sources, and using these features to spatially resolve the energy of received quanta by the detector. This work’s incentives of atomic and small molecule motions that occur on femtosecond timescales 69 accept ongoing needs for hard radiation phase retrieval, with conventional models and other constraint-based methods. Rather than adding confusion to that problem, its strategy is instead the accumulation of large volumes of ultrafast S(Q,x)space via energy dispersive approaches, which very efficiently use the colour of individual X-ray photons. Semiconductor arrays have for many years offered a powerful opening in this regard. Their capability is now extended in a thermodynamically thorough way, by low temperature thermal X-ray detector arrays. 044011-4 Fullagar et al. Struct. Dyn. 4, 044011 (2017) NEUTRON–X-RAY OVERLAPS Without prospects of extreme brilliance sources, the neutron community’s approach to the S(Q,x)observations it had fostered and extended 13,14,17,70,71 took the necessary path. Their needs for accurate low-loss broadband quantum energy measurement were answered by TOF developments, 72–74 soon aided by cold war pressures and consequently available resources. The same need had no comparable answer for the relatively mature international X-ray community when lasers and synchrotrons were developing. This despite the dawning of some relevant thermal detection technologies, 75–77 strong awareness of statistical mechanics considerations, 78 and many examples of pulsed broadband X-ray sources developed before, during, and since that time. 79–82 This work’s suggestion 83 to combine the ultrafast laser-driven X-rays and low temperature thermal detection was thus built on a heritage 26,84,85 of neutron structural dynamics studies of molecular, 70,86,87 crystalline 71,88,89 and superconducting 90 systems involving fundamental chemical timescales. A confluence occurred of backgrounds in TOF neutron usage, 84 time-resolved X-ray diffraction development, 21 lab-based X-ray source development, 83 and X-ray detector characterization. 34 A connection was built from ultrafast laser physics communities to low temperature thermal physics communities by attaining the Fano resolution limit in semiconductor arrays, recognising its physical cause and initiating action to surpass it while knowing the potential. Today it increasingly offers inroads to many known and contemporary ultrafast X-ray developments. 5,9,91,92 In structural dynamics, neutrons complement X-ray work, especially for studies of light atom, isotope contrast, and magnetic/spin systems. Neutron TOF results are often co-refined or in parallel refined 93 with X-ray data from tuneably monochromated broadband sources. 85,94 The lower noise of X-ray data in the latter studies arises from the greater eventual number of detected quanta despite narrow bandpass monochromation (Darwin width), showing the value of X-ray brilliance there. From the outset, molecular structure determinations using TOF neutron techniques 4,95 practiced atomic resolution polychromatic phase retrieval, just as X-ray Laue techniques also did even in the absence of direct quantum wavelength information. 3,6,96 The high cost of neutron facilities requires instruments to make the most of fluxes that struggle to match what can be provided by simple lab-based ultrafast laser-driven X-ray sources. 81,83 A great diversity of neutron techniques avoid Darwin-Bragg loss using TOF methods in polychromatic S(Q,x)measurements. 97 In relative terms, TOF is inapplicable to X-rays because of the essentially fixed (light speed) velocity of X-ray quanta, noting that the narrow phase space utility of refractive and reflective X-ray optics and line gratings severely restricts their application. Achievements by TOF neutron communities have fully demonstrated the viability of accurately observing large volumes of S(Q,x)space in setups based on energy measurements of individual quanta. That is also the potential opened by combining ultrafast laser driven X-ray sources and low-temperature thermal array detectors, in lab-based ultrafast measurements. 5,83 Looking beyond individual event measurement, links between neutron and X-ray needs also appear in the very relevant “unfolding” of neutron and X-ray spectra. 98–102 In these, a combination of prior knowledge and statistics is used to extract spectra from within measurable inner product integrals (typically pileup intensities). While uncertainties do propagate, 103 the approach is capable of broad applicability. A similar situation applies to Bayesian spectral analyses. 90,104 ENERGY DISPERSIVE X-RAY DETECTORS For polychromatic X-rays, Darwin-Bragg losses are avoidable using energy-dispersive semiconductor array detectors. 105–108 In favourable cases, these show a Fano/bandgap-limited energy resolution. 34,109 Depending on the application, that level of resolution can suffice for quantitative spectroscopic identification of elements in samples, and interpretation of polychromatic diffraction data 105–107 analogous to earlier TOF techniques for neutrons. Cryogenic microcalorimeter arrays make a deeper appeal to statistical physics and take the long-term scope of such X-ray detectors to a new level. 76,110–112 In effect they replace the 044011-5 Fullagar et al. Struct. Dyn. 4, 044011 (2017) semiconductor bandgap-related Fano energy resolution bound for partial measurement of incident X-ray photons’ energy, with a temperature-related bound for their complete measurement. The growing use of cryogenic microcalorimeter arrays for X-ray photon measurement corresponds more directly to the introduction of TOF techniques for neutrons, since both open access to S(Q,x)space using philosophies that permit bypassing the Darwin handicap of Bragg diffraction at high energy resolution. By doing so, they allow gainful examinations of very low radiation levels. The energy range for thermal detectability spans the full X-ray region as well as the rest of the electromagnetic spectrum and includes the measurement of energetic particles. 111 In low temperature microcalorimeters, the range from terahertz 113 to gamma 114 photon energies may be considered. There it can be broadly stated that at the low energy end, photon wavelengths become larger than the pixel size; while at the high energy end, the cross-section for radiation absorption and opening of new radiation-loss channels become troublesome. Low cross-section requires physically larger absorbers, with reduced pixel density, greater heat capacities, and longer thermal conduction timescales. In the X-ray range, the losses have several potential causes, most notably non-thermalised photoelectron escape 34 and X-ray fluorescence (XRF). 115 These lead to partial energy registry by the detector (“spectral redistribution” 116 ), in which the observed spectrum may betray other loss mechanisms, too (see, e.g., the inverted Bi absorber L-edges in the low energy tail on page 67 of Ref. 18). Where suitably quantified, the losses can be largely compensated by suitable stripping algorithms. 117 The desirability of suppressing such losses in microcalorimeters and some ways to do it were identified early. 76 As radiation energies get higher, more energy escape mechanisms become possible. Those loss channels open up, and the spectral redistribution becomes more complex at the expense of the incident spectrum whose observation is sought. THERMAL AND NOISE BOUNDS ON X-RAY ENERGY RESOLUTION Following the theoretical accounting for the photoelectric effect in 1905 (Ref. 118), it was recognised that individual X-ray quanta may be decomposed into a very large number of lower energy excitations, that collectively obey energy conservation. Bolometry is a limiting case and invokes the final thermalisation temperature for the average energy of the eventual excitations (kT). With sufficient instrument design, the thermal effects from a single X-ray photon are quantitatively measurable in pixels of small size and known location. Two aspects of this are important here. First, it is a zero loss alternative to Bragg diffraction selection for accurately determining the energy Eof individual X-ray quanta. Second, that accuracy is fundamentally constrained by the detector’s temperature. In a naive first-order argument, a number N av ¼E/kT of low energy excitations are generated in an absorber initially at absolute zero (0 K). This number fluctuates statistically as N av 1= 2 due to the many combinations of ways to distribute that energy. 119,120 (An analogous treatment effectively estimates the number and energy of quanta in shot-noise limited radiation measurements. 121 ) Applying this somewhat impractical argument to determine the energy of the parent X-ray photon, Poisson statistics applied to the limiting case of Planck distributions in Figure 2then suggest a limiting X-ray energy resolution vs. temperature scaling as DE=E/T 1= 2 . Corresponding X-ray measurement temperatures are necessarily very low. In practice, energy flow to a reservoir at finite temperature is indicated in order to allow physical measurement, which in this context motivates calorimetry. Calorimetry leads to a still lower thermodynamic bound with a stronger temperature dependency 76,77,111 according to thermal fluctuations of magnitude (kT 2 C) 1 = 2 at the temperature of the receiving bath. 120,122 Pixels’ absorber materials and their physical dimensions are constrained by the stopping power for incident radiation and the need to avoid energy trapping and loss mechanisms (i.e., nonthermalisation channels). Thermalisation must occur on timescales briefer than the readout. Moreover, noise is invariably contributed by other aspects of the apparatus used to convey the measured thermal signal. That leads to ongoing efforts to witness, account for, and eventually remedy any excess noise. 123–128 Noise sources generally have spectral dependence 129,130 which further constrains the eventual measurement bandwidth. Signal transfer typically involves nonlinear 044011-6 Fullagar et al. Struct. Dyn. 4, 044011 (2017) amplifiers (e.g., superconducting quantum interference devices (SQUIDs) in transition edge sensor (TES) systems 112 ) and multiplexing arrangements, with the various noise sources convolved at the output. There is consequently a high art in the design procedure for any such detector. Different approaches, including several technologies described in Ref. 111 and perhaps one day the optical damping suggested in Ref. 5, are developing in parallel, each with corresponding noise considerations. Figure 2and the approach above to a “first-guess” upper bound of detection temperature already make it clear that when in a single photon mode, a comparable DE/E measurement of lower photon energies will require lower temperatures. Base temperatures in the range 0.05–0.1 K have often been used in 1–50 keV X-ray work to date. When in pileup mode, spectral information may be extractable through unfolding procedures, as mentioned earlier. This approach can have value when photon energies are too low to make discernible individual contributions, while their pileup does not exceed the dynamic range of readout components. For visible photons and much of the range below it, photons can be dispersed without loss using line gratings or on the basis of refractive dispersion (prisms). In the X-ray range, the restrictive capabilities of refractive, reflective, and line grating optics give low temperature thermal measurements a unique role. PROSPECTUS IN CONTEMPORARY CONTEXTS For X-rays, the key appeals of cryogenic microcalorimetry as an alternative to Bragg diffraction are that it does not similarly constrain instrument geometry and topologies. Like TOF for neutrons, it is free from any Darwin-Bragg throughput loss in broadband measurements, FIG. 2. The statistical manipulation of quantum energies is central to our avoidance of Darwin-Bragg losses. A photon may be assembled from lower energy ones (e.g., laser generated X-rays), or broken into lower energy quanta by thermalisation. When heat is measured in a way that includes all the fragmentary quanta, their number places a statistical limit on the accuracy of knowing the parent photon’s energy. Planck blackbody distributions allow an idealisation, here on a logarithmic energy scale with Wien maxima spanning equivalent temperatures in experiments to date. Temperatures shift in proportion to the quantum energy, anticipating DE/E /T 1 = 2 and offering a first upper bound on measurement temperatures. For example, DE/E ¼10 4 for 1 eV resolution of a 10 keV photon (510 7 K Wien maximum) would need a 10 8 effective temperature change for its measurement, i.e., a Wien maximum no greater than 0.5 K. Treatment of thermal flows in calorimetry imposes a stronger temperature dependence, scaling as (kT 2 C) 1= 2 due to fluctuations at the receiving bath temperature. Convolutions with instrument noise require somewhat lower temperatures still. 111,112 X-rays’ passage through samples, here at relatively ambient temperatures, leaves its S(Q,x)imprint on their ensemble before thermalisation. 044011-7 Fullagar et al. Struct. Dyn. 4, 044011 (2017) 69 A. H. Zewail, “Femtochemistry: Chemical reaction dynamics and their control, chemical reactions and their control on the femtosecond time scale,” in XXth Solvay Conference on Chemistry, Free University of Brussels, edited by P. Gaspard and I. Burghardt (Advances in Chemical Physics, 1995), Vol. 101, pp. 3–45. 70 G. F. Longster and J. W. White, “Neutron scattering and far infra-red spectra of a heavy hindered rotator: CH 2 Br- CHFBr,” Mol. Phys. 17, 1–16 (1969). 71 P. A. Reynolds and J. W. White, “Inelastic neutron scattering from molecular and crystal excitations in aromatic molecular crystals,” Discuss. Faraday Soc. 48, 131–147 (1969). 72 L. W. Alvarez, “The production of collimated beams of monochromatic neutrons in the temperature range 300-10K,” Phys. Rev. 54, 609–617 (1938). 73 R. F. Bacher, C. P. Baker, and B. D. McDaniel, “Experiments with a slow neutron velocity spectrometer II,” Phys. Rev. 69, 443–451 (1946). 74 C. P. Baker and R. F. Bacher, “Experiments with a slow neutron velocity spectrometer,” Phys. Rev. 59, 332–348 (1941). 75 D. H. Andrews, W. F. Brucksch, W. T. Ziegler, and E. R. Blanchard, “Superconducting films as radiometric receivers,” Phys. Rev. 59, 1045–1046 (1941). 76 S. H. Moseley, J. C. Mather, and D. McCammon, “Thermal detectors as X-ray spectrometers,” J. Appl. Phys. 56, 1257–1262 (1984). 77 R. L. M€ ossbauer, “New detector developments for nuclear radiation,” J. Phys. G: Nucl. Part. Phys. 17, S1 (1991). 78 R. B. Barnes and S. Silverman, “Brownian motion as a natural limit to all measuring processes,” Rev. Mod. Phys. 6, 162–192 (1934). 79 E. L. Criscuolo and D. T. Connor, “The development of a fine-focus flash X-ray tube,” Rev. Sci. Instrum. 24, 944–948 (1953). 80 J. D. Craggs and J. M. Meek, High Voltage Laboratory Technique (Butterworths Scientific Publications, 1954). 81 P. J. Mallozzi et al., “Laser-generated plasmas as a source of X-rays for medical applications,” J. Appl. Phys. 45, 1891–1895 (1974). 82 C. N. Boyer, G. E. Holland, and J. F. Seely, “Portable hard X-ray source for nondestructive testing and medical imaging,” Rev. Sci. Instrum. 69, 2524–2530 (1998). 83 W. K. Fullagar et al., “A broadband laser plasma x-ray source for application in ultrafast chemical structure dynamics,” Rev. Sci. Instrum. 78, 115105 (2007). 84 W. K. Fullagar, “Molecular fullerides,” Ph.D. thesis (Australian National University, 1997), available at http:// hdl.handle.net/1885/47059. 85 R. Durand, W. K. Fullagar, G. Lindsell, P. A. Reynolds, and J. W. White, “X-ray and neutron powder diffraction from Rb 3 C 60 (NH 3 ) x and Li 3 C 60 (NH 3 ) x ,” Mol. Phys. 86, 1–17 (1995). 86 J. W. White and C. J. Wright, “Metal atom vibrations in transition metal clusters and complexes by inelastic neutron scattering spectroscopy,” J. Chem. Soc. A 1971, 2843–2847. 87 S. H. Chen and S. Yip, “Neutron molecular spectroscopy,” Phys. Today 29(4), 32–41 (1976). 88 L. Brillouin, Wave Propagation in Periodic Structures: Electric Filters and Crystal Lattices (McGraw-Hill, 1946). 89 D. J. Cebula, R. K. Thomas, and J. W. White, “Diffusion of water in Li-montmorillonite studied by quasielastic neutron scattering,” Clays Clay Miner. 29, 241–248 (1981). 90 C. J. Carlile et al., “Inelastic neutron scattering and superconductivity of Rb 3 C 60 (NH 3 ) x ,” Mol. Phys. 86, 19–37 (1995). 91 M. Schnell et al., “Characterization and application of hard X-ray betatron radiation generated by relativistic electrons from a laser-wakefield accelerator,” J. Plasma Phys. 81, 475810401 (2015). 92 S. Corde et al., “Femtosecond X-rays from laser-plasma accelerators,” Rev. Mod. Phys. 85, 1–48 (2013). 93 P. Coppens, “Comparative X-ray and neutron diffraction study of bonding effects in s-triazine,” Science 158, 1577–1579 (1967). 94 W. K. Fullagar, K. A. Aberdeen, D. G. Bucknall, P. A. Kroon, and I. R. Gentle, “Conformational changes in SP-B as a function of surface pressure,” Biophys. J. 85, 2624–2632 (2003). 95 A. J. Schultz et al., “Argonne intense pulsed neutron source used to solve the molecular structure of a novel organometallic complex,” Science 220, 197–199 (1983). 96 L. Pauling, “The determination with x-rays of the structures of crystals,” Ph.D. thesis (California Institute of Technology, Pasadena California, 1925), available at http://resolver.caltech.edu/CaltechETD:etd-05142003-141307. 97 A.-J. Dianoux and G. Lander, Neutron Data Booklet, 2nd ed. (Institut Laue-Langevin, 2003). 98 R. Sanna and K. O’Brien, “Monte-Carlo unfolding of neutron spectra,” Nucl. Instrum. Methods 91, 573–576 (1971). 99 M. Matzke, “Unfolding procedures,” Radiat. Prot. Dosim. 107, 155–174 (2003). 100 H. Sekimoto and N. Yamamuro, “Unfolding methods with the prior knowledge and integral data of neutron spectrum,” Nucl. Sci. Eng. 80, 101–112 (1982), available at http://www.ans.org/pubs/journals/nse/a_21407. 101 B. Mukherjee, “A high-resolution neutron spectra unfolding method using the genetic algorithm technique,” Nucl. Instrum. Methods Phys. Res. Sect. A 476, 247–251 (2002). 102 J. M. Ortiz-Rodriguez and H. R. Vega-Carrillo, “Unfolding code for neutron spectrometry based on neural nets technology,” in International Symposium on Solid State Dosimetry 2012 (2012), available at http://www.iaea.org/inis/ collection/NCLCollectionStore/_Public/44/048/44048960.pdf. 103 M. Matzke, “Propagation of uncertainties in unfolding procedures,” Nucl. Instrum. Methods Phys. Res. Sect. A 476, 230–241 (2002). 104 D. S. Sivia and C. J. Carlile, “Molecular spectroscopy and Bayesian spectral analysis—how many lines are there?,” J. Chem. Phys. 96, 170–178 (1992). 105 R. Caminiti and V. R. Albertini, “The kinetics of phase transitions observed by energy-dispersive X-ray diffraction,” Int. Rev. Phys. Chem. 18, 263–299 (1999). 106 R. F. Garrett, J. W. White, D. J. King, T. L. Dowling, and W. K. Fullagar, “An energy dispersive time resolved liquid surface reflectometer,” Nucl. Instrum. Methods Phys. Res. Sect. A 467–468(Part 2), 998–1000 (2001). 107 A. Higginbotham et al., “Single photon energy dispersive X-ray diffraction,” Rev. Sci. Instrum. 85, 033906 (2014). 108 E. Danielsson, “Evaluation of a new experimental geometry for ultra-fast time resolve diffraction experiments using a laser-produced plasma source: experimental set-up and image processing (LRAP-309),” M.S. thesis (Lund University, 2003), available at http://www.atomic.physics.lu.se/fileadmin/atomfysik/Ultrafast_X-ray_Science/evadxjobb.pdf. 044011-14 Fullagar et al. Struct. Dyn. 4, 044011 (2017) 109 U. Fano, “Ionization yield of radiations. II. The fluctuations of the number of ions,” Phys. Rev. 72, 26 (1947). 110 C. D. Reintsema et al., “Prototype system for superconducting quantum interference device multiplexing of large-format transition-edge sensor arrays,” Rev. Sci. Instrum. 74, 4500–4508 (2003). 111 C. Enss, Cryogenic Particle Detection (Springer-Verlag, 2005), Topics in Applied Physics Vol. 99. 112 J. N. Ullom and D. A. Bennett, “Review of superconducting transition-edge sensors for X-ray and gamma-ray spectroscopy,” Supercond. Sci. Technol. 28, 084003 (2015). 113 D. Becker et al., “Standoff passive video imaging at 350 GHz with 251 superconducting detectors,” Proc. SPIE 9078, 907804 (2014). 114 D. A. Bennett et al., “A high resolution gamma-ray spectrometer based on superconducting microcalorimeters,” Rev. Sci. Instrum. 83, 093113 (2012). 115 J. H. Hubbell et al., “A review, bibliography, and tabulation of K, L, and higher atomic shell X-ray fluorescence yields,” J. Phys. Chem. Ref. Data 23, 339–364 (1994). 116 G. Prigozhin, S. Jones, M. Bautz, G. Ricker, and S. Kraft, “The physics of the low-energy tail in the ACIS CCD: The spectral redistribution function,” Nucl. Instrum. Methods Phys. Res. Sect. A 439, 582–591 (2000). 117 R. H. Redus, J. A. Pantazis, T. J. Pantazis, A. C. Huber, and B. J. Cross, “Characterization of CdTe detectors for quantitative X-ray spectroscopy,” IEEE Trans. Nucl. Sci. 56, 2524–2532 (2009). 118 A. B. Arons and M. B. Peppard, “Einstein’s proposal of the photon concept—A translation of the Annalen der Physik paper of 1905,” Am. J. Phys. 33, 367–374 (1965). 119 L. D. Landau and E. M. Lifshitz, Statistical Physics (Pergamon Press, 1969), p. 9. 120 F. Mandl, Statistical Physics, 2nd ed. (John Wiley & Sons, 1988). 121 J. Uhlig, C.-G. Wahlstr€ om, M. Walczak, V. Sundstr€ om, and W. Fullagar, “Laser generated 300 keV electron beams from water (obs Fig. 2 and its discussion),” Laser Part. Beams 29, 415–424 (2011). 122 E. Schr€ odinger, Statistical Thermodynamics (Dover Publications, Inc., 1952, republished by Dover 1989). 123 H. F. C. Hoevers et al., “Thermal fluctuation noise in a voltage biased superconducting transition edge thermometer,” Appl. Phys. Lett. 77, 4422–4424 (2000). 124 J. N. Ullom et al., “Characterization and reduction of unexplained noise in superconducting transition-edge sensors,” Appl. Phys. Lett. 84, 4206–4208 (2004). 125 I. J. Maasilta and K. M. Kinnunen, “New analysis method for I-V and complex impedance data of transition-edge sensors,” AIP Conf. Proc. 1185, 38–41 (2009). 126 K. M. Kinnunen, M. R. J. Palosaari, and I. J. Maasilta, “Normal metal-superconductor decoupling as a source of thermal fluctuation noise in transition-edge sensors,” J. Appl. Phys. 112, 034515 (2012). 127 I. J. Maasilta, “Complex impedance, responsivity and noise of transition-edge sensors: Analytical solutions for two- and three-block thermal models,” AIP Adv. 2, 042110 (2012). 128 M. R. J. Palosaari et al., “Analysis of impedance and noise data of an X-ray transition-edge sensor using complex thermal models,” J. Low Temp. Phys. 167, 129–134 (2012). 129 P. Horowitz and W. Hill, The Art of Electronics, 2nd ed. (Cambridge University Press, 1989). 130 F. N. H. Robinson, Noise in Electrical Circuits (Oxford University Press, 1962). 131 B. A. Mazin et al., “ARCONS: A 2024 pixel optical through near-IR cryogenic imaging spectrophotometer,” Publ. Astron. Soc. Pac. 125, 1348 (2013). 132 F. R aksi et al., “Ultrafast X-ray absorption probing of a chemical reaction,” J. Chem. Phys. 104, 6066–6069 (1996). 133 I. V. Tomov, D. A. Oulianov, P. Chen, and P. M. Rentzepis, “Ultrafast time-resolved transient structures of solids and liquids studied by means of X-ray diffraction and EXAFS,” J. Phys. Chem. B 103, 7081–7091 (1999). 134 T. Lee, Y. Jiang, C. G. Rose-Petruck, and F. Benesch, “Ultrafast tabletop laser-pump–X-ray probe measurement of solvated [Fe(CN) 6 ] 4 ,” J. Chem. Phys. 122, 084506 (2005). 135 H. G. Ahlstrom, in Laser-Plasma Interaction - Les Houches Session XXXIV, edited by R. Balian and J. C. Adam (North- Holland, 1982), Chap. 1. 136 L. Miaja-Avila et al., “Laser plasma X-ray source for ultrafast time-resolved X-ray absorption spectroscopy,” Struct. Dyn. 2, 024301 (2015). 137 S. M. Hooker, D. A. Jaroszynski, and K. Burnett, “Laser-driven particle accelerators: new sources of energetic particles and radiation,” Philos. Trans. R. Soc. A 364, 553–778 (2006). 138 G. L. Betancourt-Martinez et al., “The transition-edge EBIT microcalorimeter spectrometer,” Proc. SPIE 9144, 91443U (2014). 139 M. R. J. Palosaari et al., “Broadband ultrahigh-resolution spectroscopy of particle-induced X-rays: Extending the limits of nondestructive analysis,” Phys. Rev. Appl. 6, 024002 (2016). 140 J. N. Ullom et al., “Transition-edge sensor microcalorimeters for X-ray beamline science,” Synchrotron Radiat. News 27, 24–27 (2014). 141 S. Okada et al., “First application of superconducting transition-edge sensor microcalorimeters to hadronic atom X-ray spectroscopy,” Prog. Theor. Exp. Phys. 2016, 091D01. 142 J. Uhlig et al., “High-resolution X-ray emission spectroscopy with transition-edge sensors: present performance and future potential,” J. Synchrotron Radiat. 22, 766–775 (2015). 143 T. C. B. Harlang et al., “Iron sensitizer converts light to electrons with 92% yield,” Nat. Chem. 7, 883–889 (2015). 144 S. E. Canton et al., “Visualizing the non-equilibrium dynamics of photoinduced intramolecular electron transfer with femtosecond X-ray pulses,” Nat. Commun. 6, 6359 (2015). 145 B. Br€ uggemann, J. A. Organero, T. Pascher, T. Pullerits, and A. Yartsev, “Control of electron transfer pathways in a dye-sensitized solar cell,” Phys. Rev. Lett. 97, 208301 (2006). 146 F. Ma et al., “Ultrafast excited state dynamics of [Cr(CO) 4 (bpy)]: Revealing the relaxation between triplet chargetransfer states,” RSC Adv. 6, 20507–20515 (2016). 147 A. H. Zewail, “Femtochemistry: Atomic-scale dynamics of the chemical bond,” J. Phys. Chem. A 104, 5660–5694 (2000). 148 A. H. Zewail, “Curiouser and curiouser: Managing discovery making,” Nature 468, 347 (2010). 149 A. H. Zewail and V. Lobastov, “Method and system for ultrafast photoelectron microscope,” U.S. patent 7,154,091 B2 (2006). 044011-15 Fullagar et al. Struct. Dyn. 4, 044011 (2017) 150 A. Mandelis, “Focus on photonics and biomedical optics,” Phys. Today 67(2), 53 (2014). 151 D. J. Flannigan and A. H. Zewail, “4D electron microscopy: Principles and applications,” Acc. Chem. Res. 45, 1828–1839 (2012). 152 J. C. Williamson, M. Dantus, S. B. Kim, and A. H. Zewail, “Ultrafast diffraction and molecular structure,” Chem. Phys. Lett. 196, 529–534 (1992). 153 A. H. Zewail, “Diffraction, crystallography and microscopy beyond three dimensions: Structural dynamics in space and time,” Philos. Trans. R. Soc. A 363, 315–329 (2005). 154 M. Chergui and A. H. Zewail, Phys. Today 69(12), 69–70 (2016). 155 R. Ovsyannikov et al., “Principles and operation of a new type of electron spectrometer – ArTOF,” J. Electron Spectrosc. Relat. Phenom. 191, 92–103 (2013). 156 B. Wannberg, “Electron optics development for photo-electron spectrometers,” Nucl. Instrum. Methods Phys. Res. Sect. A601, 182–194 (2009). 157 D.-S. Yang, P. Baum, and A. H. Zewail, “Ultrafast electron crystallography of the cooperative reaction path in vanadium dioxide,” Struct. Dyn. 3, 034304 (2016). 158 L. Miaja-Avila et al., “Sub-picosecond, table-top X-ray absorption spectroscopy using superconducting microcalorimeters,” in 2013 Conference on Lasers and Electro-Optics (CLEO) (2013). 159 C. Bressler and M. Chergui, “Ultrafast X-ray absorption spectroscopy,” Chem. Rev. 104, 1781–1812 (2004). 160 C. Bressler and M. Chergui, “Molecular structural dynamics probed by ultrafast X-ray absorption spectroscopy,” Ann. Rev. Phys. Chem. 61, 263–282 (2010). 161 G. Vank oet al., “Spin-state studies with XES and RIXS: From static to ultrafast,” J. Electron Spectrosc. Relat. Phenom. 188, 166–171 (2013). 162 J. N. Ullom et al., “X-ray absorption spectroscopy of iron tris(bipyridine) using superconducting microcalorimeters,” in 2014 Conference on Lasers and Electro-Optics (CLEO) - Laser Science to Photonic Applications (2014), pp. 1–2. 163 L. Miaja-Avila et al., “Ultrafast time-resolved hard X-ray emission spectroscopy on a tabletop,” Phys. Rev. X 6, 031047 (2016). 164 G. O’Neil et al., “Ultrafast time-resolved X-ray absorption spectroscopy of ferrioxalate photolysis with a laser plasma X-ray source and microcalorimeter array,” J. Phys. Chem. Lett. 8, 1099–1104 (2017). 165 M. Bargheer et al., “Comparison of focusing optics for femtosecond X-ray diffraction,” Appl. Phys. B 80, 715–719 (2005). 166 A. Thoss, “X-ray emission and particle acceleration from a liquid jet target using a 1-kHz ultrafast laser system,” Ph.D. thesis (Free University of Berlin, 2003), available at http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_ 000000001074. 167 L. Rymell, “A new laser-plasma X-ray source for microscopy and lithography,” Ph.D. thesis (Lund University, LRAP- 214, 1997). 168 J. Carlsson, in PP Mekanik Workshop, S€ odra Sandby, Sweden (2016). 169 F. Parnefjord Gustafsson, “Investigation of the laser pointing and intensity fluctuations for a laser-based plasma x-ray source,” BSc thesis (Lund University, 2015), available at http://www.lu.se/lup/publication/8778049. 170 F. Gatti, F. Fontanelli, M. Galeazzi, A. M. Swift, and S. Vitale, “Detection of environmental fine structure in the lowenergy b-decay spectrum of 187 Re,” Nature 397, 137–139 (1999). 171 M. R. J. Palosaari et al., “Transition-edge sensors for particle induced X-ray emission measurements,” J. Low Temp. Phys. 176, 285–290 (2014). 172 Y. I. Joe et al., “Observation of iron spin-states using tabletop x-ray emission spectroscopy and microcalorimeter sensors,” J. Phys. B: At., Mol. Opt. Phys. 49, 024003 (2016). 173 L. J. P. Ament, M. van Veenendaal, T. P. Devereaux, J. P. Hill, and J. van den Brink, “Resonant inelastic x-ray scattering studies of elementary excitations,” Rev. Mod. Phys. 83, 705–767 (2011). 174 J. Tomkinson, J. Penfold, and J. Howard, “Molecular vibrational spectroscopy with neutrons, recent results from the spallation neutron source,” J. Mol. Struct. 142, 1–3 (1986). 175 S. F. Parker and J. Tomkinson, “Vibrational spectroscopy on TFXA,” Neutron News 9, 33–39 (1998). 176 G. E. Ice and C. J. Sparks, “Mosaic crystal X-ray spectrometer to resolve inelastic background from anomalous scattering experiments,” Nucl. Instrum. Methods Phys. Res. Sect. A 291, 110–116 (1990). 177 L. V. H amos, “R€ ontgenspektroskopie und Abbildung mittels gekr€ ummter Kristallreflektoren. I. Geometrisch-optische Betrachtungen,” Ann. Phys. 409, 716–724 (1933). 178 A. P. Shevelko, “X-ray spectroscopy of laser-produced plasmas using a von Hamos spectrograph,” Proc. SPIE 3406, 91–108 (1998). 179 H. Legall et al., “A new generation of X-ray optics based on pyrolytic graphite (FRAAU04),” in Proceedings of the FEL 2006, BESSY, Berlin, Germany (2006), pp. 798–801, available at https://accelconf.web.cern.ch/AccelConf/f06/PAPERS/ FRAAU04.PDF. 180 G. M. Stiehl et al., “Code-division multiplexing for x-ray microcalorimeters,” Appl. Phys. Lett. 100, 072601 (2012). 181 D. R. Schmidt et al., “A superconductor–insulator–normal metal bolometer with microwave readout suitable for largeformat arrays,” Appl. Phys. Lett. 86, 053505 (2005). 182 A. Zangwill, “A half century of density functional theory,” Phys. Today 68(7), 34–39 (2015). 183 J. W. Fowler, “Maximum-likelihood fits to histograms for improved parameter estimation,” J. Low Temp. Phys. 176, 414–420 (2014). 184 J. W. Fowler et al., “When “optimal filtering” isn’t,” IEEE Trans. Appl. Supercond. 27, 1–4 (2017). 185 A. E. Szymkowiak, R. L. Kelley, S. H. Moseley, and C. K. Stahle, “Signal processing for microcalorimeters,” J. Low Temp. Phys. 93, 281–285 (1993). 186 H. Tatsuno et al., “Absolute energy calibration of X-ray TESs with 0.04 eV uncertainty at 6.4 keV in a hadron-beam environment,” J. Low Temp. Phys. 184, 930–937 (2016). 187 J. W. Fowler et al., “The practice of pulse processing,” J. Low Temp. Phys. 184, 374–381 (2016). 188 J. W. Fowler et al., “Microcalorimeter spectroscopy at high pulse rates: A multi-pulse fitting technique,” Astrophys. J. Suppl. Ser. 219, 35 (2015). 044011-16 Fullagar et al. Struct. Dyn. 4, 044011 (2017) 189 K. Karafasoulis et al., “Gamma spectroscopic measurements using the PID350 pixelated CdTe radiation detector,” in IEEE Nuclear Science Symposium & Medical Imaging Conference (2010), pp. 3816–3820. 190 K. Spartiotis et al., “A photon counting CdTe gamma- and X-ray camera,” Nucl. Instrum. Methods Phys. Res. Sect. A 550, 267–277 (2005). 191 C. Hall, K. Spiers, W. Fullagar, and R. Lewis, “Assessment of a MEDIPIX2 detector for coherent X-ray diffractive imaging,” AIP Conf. Proc. 1234, 235–239 (2010). 192 A. J. Minnich et al., “Thermal conductivity spectroscopy technique to measure phonon mean free paths,” Phys. Rev. Lett. 107, 095901 (2011). 193 I. Maasilta and A. J. Minnich, “Heat under the microscope,” Phys. Today 67(8), 27–32 (2014). 194 N. Zen, T. A. Puurtinen, T. J. Isotalo, S. Chaudhuri, and I. J. Maasilta, “Engineering thermal conductance using a twodimensional photonic crystal,” Nat. Commun. 5, 3435 (2014). 195 P. Coppens et al., “The use of synchrotron radiation in chemical crystallography: Charge density analysis, resonance diffraction and the study of transient species,” Trans. Am. Crystallogr. Assoc. 34, 51 (1999), available at http://harker. chem.buffalo.edu/group/publication/acaproc_99_51.pdf. 196 W. Friedrich, P. Knipping, and M. Laue, “Interferenzerscheinungen bei R€ ontgenstrahlen,” Ann. Phys. 346, 971–988 (1913). 044011-17 Fullagar et al. Struct. Dyn. 4, 044011 (2017)