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Nuclear Resonance Vibrational Spectroscopy: a Modern Tool to Pinpoint Site-Specific Cooperative Processes

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Nuclear Resonance Vibrational Spectroscopy: a Modern Tool to Pinpoint Site-Specific Cooperative Processes crystals Review Nuclear Resonance Vibrational Spectroscopy: A Modern Tool to Pinpoint Site-Specific Cooperative Processes Hongxin Wang 1,* , Artur Braun 2,* , Stephen P. Cramer 1 , Leland B. Gee 3 and Yoshitaka Yoda 4 1 SETI Institute, Mountain View, CA 94043, USA; [email protected] 2 Laboratory for High Performance Ceramics, Empa. Swiss Federal Laboratories for Materials Science and Technology, Überlandstrasse 129, CH-8600 Dübendorf, Switzerland 3 LCLS, SLAC National Accelerator Laboratory, Menlo Park, CA 94025, USA; [email protected] 4 Precision Spectroscopy Division, SPring-8/JASRI, Sayo 679-5198, Japan; [email protected] * Correspondence: authors: [email protected] (H.W.); [email protected] (A.B.) Abstract: Nuclear resonant vibrational spectroscopy (NRVS) is a synchrotron radiation (SR)-based nu- clear inelastic scattering spectroscopy that measures the phonons (i.e., vibrational modes) associated with the nuclear transition. It has distinct advantages over traditional vibration spectroscopy and has wide applications in physics, chemistry, bioinorganic chemistry, materials sciences, and geology, as well as many other research areas. In this article, we present a scientific and figurative description of this yet modern tool for the potential users in various research fields in the future. In addition to short discussions on its development history, principles, and other theoretical issues, the focus of this article is on the experimental aspects, such as the instruments, the practical measurement issues, the data process, and a few examples of its applications. The article concludes with introduction to non-57Fe NRVS and an outlook on the impact from the future upgrade of SR rings. Citation: Wang, H.; Braun, A.; Cramer, S.P.; Gee, L.B.; Yoda, Y. Keywords: nuclear resonant vibrational spectroscopy; NRVS; Mössbauer spectroscopy; isotope- Nuclear Resonance Vibrational specific; site-specific; vibrational modes; phonons; partial vibrational density of state; PVDOS; Spectroscopy: A Modern Tool to inelastic scattering; high-resolution monochromator; HRM; real sample temperature; an almost Pinpoint Site-Specific Cooperative zero background Processes. Crystals 2021, 11, 909. https://doi.org/10.3390/ cryst11080909 1. Introduction Academic Editor: Giacomo Saielli Nuclear resonant vibrational spectroscopy (NRVS) is a synchrotron radiation (SR)- based nuclear inelastic scattering (NIS) spectroscopy that measures the phonons (i.e., Received: 31 May 2021 vibrational modes) associated with the nuclear transition [1–9]. NRVS has distinguished Accepted: 16 July 2021 advantages and has been used by physicists, chemists, materials scientists, etc. for more Published: 2 August 2021 than 25 years. While chemists call it NRVS, per historical reasons, physicists often call it by another name—nuclear resonant inelastic X-ray scattering (NRIXS) [10–13]. In this Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in article, we present a scientific but figurative description of the experimental aspects of this published maps and institutional affil- wonderful modern tool to the potential future users working in various research fields. iations. 1.1. NRVS Transitions and Selection Rules Figure1a shows the basic principle of NRVS transitions; while an incident X-ray beam scans through an interested energy region to cover the nuclear transition and the associated vibrations (e.g., E ~ 14.41425 keV for 57Fe), the nuclear back radiation can be Copyright: © 2021 by the authors. 1 monitored as the scattering energy (E = hν ). The total intensities collected from both the Licensee MDPI, Basel, Switzerland. 2 1 ν This article is an open access article direct nuclear fluorescence at h 1 and the internally converted electron K shell fluorescence distributed under the terms and at hν2 vs. the vibrational energy Evib = (E1–E2) is a raw NRVS spectrum. In this sense, conditions of the Creative Commons it is similar to resonant optical Raman spectroscopy where vibrational information is Attribution (CC BY) license (https:// extracted in an inelastic scattering from laser light excitation. An NRVS spectrum includes creativecommons.org/licenses/by/ Stokes (creation of phonons) and anti-Stokes (annihilation of phonons) branches, although 4.0/). Figure1a only illustrates the Stokes transitions. It is also similar to Mössbauer spectroscopy Crystals 2021, 11, 909. https://doi.org/10.3390/cryst11080909 https://www.mdpi.com/journal/crystals Crystals 2021, 11, x FOR PEER REVIEW 2 of 44 Crystals 2021, 11, 909 2 of 42 Figure 1a only illustrates the Stokes transitions. It is also similar to Mössbauer spectros- (MS),copy except(MS), except that MS that measures MS measures the recoilless the recoilless hyperfine hyperfine interactions, interactions, while NRVS while measures NRVS themeasures recoiled the transitions recoiled transitions due to vibrations. due to vibrations. The raw NRVS The raw spectra NRVS can spectra be transformed can be trans- to partialformed vibrational to partial vibrational density of statedensity (PVDOS), of state which(PVDOS), is independent which is independent of any experimental of any ex- conditionsperimental and conditions is calculable and viais calculable theory-based via mathematicaltheory-based simulations.mathematical Figure simulations.1b provides Fig- anure example 1b provides of such an example PVDOS. of such PVDOS. 57 FigureFigure 1.1. ((aa)) AnAn illustrationillustration ofof NRVSNRVS transitions;transitions; ( (bb))57 Fe NRVS spectraspectra forfor DvMFDvMF NiFeNiFe hydrogenasehydrogenase (reaction(reaction center center structure structure = = insert)insert) inin aa hydridehydride (blue)(blue) andand deuterateddeuterated samplesample (red).(red). TheThe peakpeak assign-assign- ments (bold black text) and peak counts per second (the blue numbers) are given for the hydride ments (bold black text) and peak counts per second (the blue numbers) are given for the hydride sample (blue curves). sample (blue curves). OneOne ofof thethe centralcentral relationsrelations forfor anyany spectroscopyspectroscopy isis thethe algebraicalgebraic selectionselection rule(s),rule(s), whichwhich telltell wherewhere thethe allowedallowed transitionstransitions occuroccur and,and, thus,thus, whatwhat thethe spectralspectral profileprofile isis like.like. ForFor NRVS,NRVS, therethere areare majormajor factorsfactors thatthat governgovern itsits intensity intensity distribution distribution[ 14[14].]. SinceSince thisthis articlearticle focusesfocuses onon thethe experimentalexperimental science,science, wewe omitomit thethe detailsdetails ofof thethe formulaformula deductiondeduction butbut summarizesummarize thethe conclusionsconclusions instead.instead. AsAs forfor anyany spectroscopy,spectroscopy, thethe intensityintensity forfor NRVSNRVS isis proportionalproportional toto thethe sample’ssample’s con-con- centrationcentration andand thethe populationpopulation distributeddistributed onon thethe groundground statestate (e.g.,(e.g., thethe groundground vibrationalvibrational level).level). TheThe ground-stateground-state populationpopulation distributiondistribution is is also also a a function function of of the the ambient ambient tempera- temper- tureature T T of of the the statistical statistical ensemble. ensemble. ∝ vib SimilarSimilar toto other other inelastic inelastic scattering scattering process, process, NRVS NRVS also also has has a general a general∝ 1/E vib 1/Edepen- de- dencependence that that reduces reduces its signal its signal for higher-energy for higher-energy transitions. transitions. SimilarSimilar toto MössbauerMössbauer transition,transition, thethe NRVSNRVS signalsignal levellevel isis proportionalproportional toto thethe Lamb–Lamb– MössbauerMössbauer factorfactor (f (fLMLM or LM factor for short). The LM factorfactor (f(fLMLM)) signifies signifies the the probability, probability, i.e.,i.e., whetherwhether or how likely a a nu nuclearclear resonance resonance will will take take place. place. For For example, example, free free atoms atoms or orgaseous gaseous samples samples have have almost almost zero zero LM LM factor factorss and and have have no nuclearnuclear resonance,resonance, neitherneither MössbauerMössbauer nornor NRVS.NRVS. IsotopeIsotope typetype andand samplesample temperaturetemperature TT areare alsoalso thethe factorsfactors thatthat affectaffect thethe LMLM factor.factor.57 57Fe isis oneone ofof thethe fewfew isotopesisotopes thatthat showshow aa significantsignificant nuclearnuclear effecteffect eveneven atat roomroom temperaturetemperature (RT),(RT), whilewhile thethe nuclearnuclear transitiontransition forfor mostmost otherother isotopesisotopes cancan onlyonly be observed at at a a cryogenic cryogenic temperature. temperature. This This poses poses a fundamental a fundamental problem problem for oper- for operandoando investigationsinvestigations of materials, of materials, which which function function only only at ambient at ambient or orhigh high temperatures. temperatures. In Inaddition, addition, the the LM LM factors factors depend depend on on the the molecular molecular environment environment of the probed nuclei.nuclei. ForFor example,example, the the iron iron in in lithium lithium iron iron phosphate phosphate undergoes undergoes changes changes in thein th oxidatione oxidation state state during dur- de-lithiation,ing de-lithiation, and soand does so does its LM its factor,LM factor, which which Aldon Aldon et al. et have al. have demonstrated demonstrated recently
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