Characterization of framework and extra-framework aluminum species in non-hydrated zeolites Y by 27Al spin-echo, high-speed MAS, and MQMAS NMR spectroscopy at B0 = 9.4 to 17.6 T

27Al spin-echo, high-speed MAS (nu(rot) = 30 kHz), and MQMAS NMR spectroscopy in magnetic fields of B0 = 9.4, 14.1, and 17.6 T were applied for the study of aluminum species at framework and extra-framework positions in non-hydrated zeolites Y. Non-hydrated gamma-Al2O3 and non-hydrated aluminum-exchanged zeolite Y (Al,Na-Y) and zeolite H,Na-Y were utilized as reference materials. The solid-state 27Al NMR spectra of steamed zeolite deH,Na-Y/81.5 were found to consist of four signals. The broad low-field signal is caused by a superposition of the signals of framework aluminum atoms in the vicinity of bridging hydroxyl protons and framework aluminum atoms compensated in their negative charge by aluminum cations (delta(iso) = 70 +/- 10 ppm, C(QCC) = 15.0 +/- 1.0 MHz). The second signal is due to a superposition of the signals of framework aluminum atoms compensated by sodium cations and tetrahedrally coordinated aluminum atoms in neutral extra-framework aluminum oxide clusters (delta(iso) = 65 +/- 5 ppm, C(QCC) = 8.0 +/- 0.5 MHz). The residual two signals were attributed to aluminum cations (delta(iso) = 35 +/- 5 ppm, C(QCC) = 7.5 +/- 0.5 MHz) and octahedrally coordinated aluminum atoms in neutral extra-framework aluminum oxide clusters (delta(iso) = 10 +/- 5 ppm, C(QCC) = 5.0 +/- 0.5 MHz). By chemical analysis and evaluating the relative solid-state 27Al NMR intensities of the different signals of aluminum species occurring in zeolite deH,Na-Y/81.5 in the non-hydrated state, the aluminum distribution in this material was determined.     

67Zn solid-state and single-crystal NMR spectroscopy and X-ray crystal structure of zinc formate dihydrate.

The crystal structure, quadrupole coupling parameters, and the orientation of the electric field gradient tensors for each site of zinc formate dihydrate have been determined. There are two distinct sites in the asymmetric unit: one containing four in-plane waters with two bridging formats, the other containing six bridging formates. The solid-state NMR lineshapes have been assigned to their respective sites by using isotopic labeling and cross-polarization methods. The hydrated site corresponds to the lineshape having a quadrupole coupling constant (Cq) of 9.6 MHz and the anhydrous site has a Cq of 6.2 MHz. The absence of chemical shielding contributions to the observed lineshapes has been verified with a high-field solid-state NMR experiment performed at 18.8 T.     

Solid-state NMR detection, characterization, and quantification of the multiple aluminum environments in US-Y catalysts by (27)Al MAS and MQMAS experiments at very high field.

The detection of all of the aluminum present in steamed zeolite H-Y catalysts by (27)Al MAS NMR at 14.4 T (600 MHz for (1)H) and 18.8T (800 MHz for (1)H) is reported. Further, it is shown that it is possible by (27)Al MAS and MQMAS NMR measurements to clearly identify four separate aluminum environments which are characteristic of these materials and to unambiguously assign their coordinations. Average chemical shift and quadrupolar coupling parameters are used to accurately simulate the (27)Al MAS NMR spectra at 9.4 T (400 MHz for (1)H), 14.4 T (600 MHz for (1)H) and 18.8 T (800 MHz for (1)H) in terms of these four aluminum environments. In addition, these average chemical shift and quadrupolar coupling parameters are used to calculate peak positions in the (27)Al MQMAS isotropic dimension that are in good agreement with the experimental data acquired at 9.4 and 18.8 T.     

Theoretical and experimental investigation of the effect of proton transfer on the (27)al MAS NMR line shapes of zeolite-adsorbate complexes: an independent measure of solid Acid strength

Assessing the degree of proton transfer from a Br?nsted acid site to one or more adsorbed bases is central to arguments regarding the strength of zeolites and other solid acids. In this regard certain solid-state NMR measurements have been fruitful; for example, some (13)C, (15)N, or (31)P resonances of adsorbed bases are sensitive to protonation, and the (1)H chemical shift of the Br?nsted site itself reflects hydrogen bonding. We modeled theoretically the structures of adsorption complexes of several bases on zeolite HZSM-5, calculated the quadrupole coupling constants (Q(cc)) and asymmetry parameters (eta) for aluminum in these complexes and then in turn simulated the central transitions of their (27)Al MAS NMR spectra. The theoretical line width decreased monotonically with the degree of proton transfer, reflecting structural relaxation around aluminum as the proton was transferred to a base. We verified this experimentally for a series of adsorbed bases by way of single-pulse MAS and triple quantum MQMAS (27)Al NMR. The combined theoretical and experimental approach described here provides a strategy by which (27)Al data can be applied to resolve disputed interpretations of proton transfer based on other evidence.     

铝在MCM-22分子筛骨架上分布的27Al MQ MAS NMR研究

利用二维多量子魔角旋转（2D MQ MAS）技术并结合量子化学计算，研究了铝在MCM-22分子筛骨架上的分布，并对铝的不等价四面体位进行了归属.在27Al 2D 5Q MAS NMR谱中骨架四配位铝的范围内观察到3个信号，证明MCM-22分子筛有3种骨架铝.经计算这3种骨架四配位铝的各向同性化学位移和四极作用常数分别为：δ 50.5、δ 57.3、δ 62.4和1.74、1.68、1.92 MHz. MCM-22分子筛结构中有8种结晶学不等价四面体（T）位.我们通过模拟MCM-22分子筛的27Al 2D 5Q MAS NMR谱，认为8种不等价T位分为3组. T2、T6位上的铝分别与δ 61、δ 49处的信号相关， T1、T3、T4、T5、T7、T8位上的铝对δ 56处的共振峰有贡献.当硅铝原子数比(Si/Al)在10～15之间变化时，铝在MCM-22分子筛的骨架上是无规占据的.     

DFT计算结合固体NMR研究富铝SSZ-13的铝分布和Br?nsted酸性

具有菱沸石(CHA)结构的SSZ-13分子筛在甲醇制烯烃(MTO)及柴油机车尾气氨选择性催化还原(NH_3-SCR)反应中具有重要的应用,采用富铝SSZ-13可以调节MTO反应的烯烃选择性和提升NH_3-SCR的低温脱硝活性,因此SSZ-13中的铝含量和分布与对应的酸性决定了其催化性能。本文采用密度泛函理论结合固体核磁共振实验研究了富铝和富硅HSSZ-13的Al位置与Br?nsted酸强度的内在关系。通过计算取代能发现,对于孤立Al位,质子位于Al周围4个不同O位时能量差异较小,最稳定的B酸位点是O(1)―H。对于富铝SSZ-13,两个Al原子位于同一六元环的对位是Al-Si-Si-Al (NNNN)序列中最稳定的结构,而Al-Si-Al (NNN)序列中能量最优的Al分布是两个铝原子排布于六棱柱上下不同的六元环上。通过计算最稳定构型下的质子亲和势、NH3脱附能和吸附氘代乙腈后的1H NMR化学位移,发现富铝SSZ-13中含有Si(2Al)分布的NNN序列导致了其Br?nsted酸强度弱于高硅的分子筛。分峰拟合29Si魔角旋转核磁共振(MASNMR)谱图表明富铝SSZ-13中Si(2Al)的含量在43%以上,而吸附氘代乙腈后的1H MAS NMR实验显示富铝SSZ-13的桥羟基化学位移向低场移动,进一步证明富铝SSZ-13具有较弱的Br?nsted酸强度。     

“NMR invisible” aluminum species in dealuminated mordenite zeolite: a1H/27 AI TRAPDOR NMR study

Various kinds of aluminum species in dealuminated mordenite were investigated in detail, and the quadrupole coupling constants (QCCs) for aluminum atoms associated with these species were obtained by means of the newly introduced¹H/²⁷ AI TRAPWR method as well as²⁷Al magic angle spinning (MAS) nuclear magnetic resonance (NMR). QCC values of 11.3, 15.3, 13.3 and (14.0± 0.6) MHz were determined from the TRAPDOR profiles for Lewis acid sites, Bronsted acid sites (SiOHAl) and two kinds of non-framework aluminum species Al(OH) _n , respectively. The source of the “invisible Al” is discussed on the basis of the NMR experimental results.     

Structural characterization of MAO and related aluminum complexes. 1. Solid-state (27)Al NMR with comparison to EFG tensors from ab initio molecular orbital calculations.

Experimental and ab initio molecular orbital techniques are developed for study of aluminum species with large quadrupole coupling constants to test structural models for methylaluminoxanes (MAO). The techniques are applied to nitrogen- and oxygen-containing complexes of aluminum and to solid MAO isolated from active commercial MAO preparations. (Aminato)- and (propanolato)aluminum clusters with 3-, 4-, and 6-coordinate aluminum sites are studied with three (27)Al NMR techniques optimized for large (27)Al quadrupole coupling constants: field-swept, frequency-stepped, and high-field MAS NMR. Four-membered (aminato)aluminum complexes with AlN(4) coordination yield slightly smaller C(q) values than similar AlN(2)C(2) sites: 12.2 vs 15.8 MHz. Planar 3-coordinate AlN(2)C sites have the largest C(q) values, 37 MHz. In all cases, molecular orbital calculations of the electric field gradient tensors yields C(q) and eta values that match with experiment, even for a large hexameric (aminato)aluminum cage. A D(3d) symmetry hexaaluminum oxane cluster, postulated as a model for MAO, yields a calculated C(q) of -23.7 MHz, eta = 0.7474, and predicts a spectrum that is too broad to match the field-swept NMR of methylaluminoxane, which shows at least three sites, all with C(q) values greater than 15 MHz but less than 21 MHz. Thus, the proposed hexaaluminum cluster, with its strained four-membered rings, is not a major component of MAO. However, calculations for dimers of the cage complex, either edge-bridged or face-bridged, show a much closer match to experiment. Also, MAO preparations differ, with a gel form of MAO having significantly larger (27)Al C(q) values than a nongel form, a conclusion reached on the basis of (27)Al NMR line widths in field-swept NMR spectra acquired from 13 to 24 T.     

Theoretical Study of Ethanethiol Adsorption on HZSM-5 Zeolite

The density functional theory and the cluster model methods have been employed to investigate the interactions between ethanethiol and HZSM-5 zeolites. Molecular complexes formed by the adsorption of ethanethiol on silanol H3SiOH with two coordination forms, model Bronsted acid sites of zeolite cluster H3Si(OH)Al(OH)2SiH3 interaction with ethanethiol, aluminum species adsorbed ethanethiol have been comparatively studied. Full optimization and frequency analysis of all cluster models have been carried out using B3LYP hybrid method at 3-21G basis level for hydrogen atoms and 6-31G(d) basis set level for silicon, aluminum, oxygen, carbon, and sulfur atoms. The structures and energy changes of different coordination forms of H3Si(OH)Al(OH)2SiH3-ethanethiol, silanol-ethanethiol and Al(OH)3-ethanethiol have been studied. The calculated results showed the nature of interactions was van der Waals force as exhibited by not much change in geometric structures and properties. The preference order of ethanethiol adsorbed on HZSM-5 zeolite may be residual aluminum species, bridging hydroxyl groups and silanol OH groups from the adsorption heat. The adsorbed models of protonized ethanethiol on bridging hydroxyl OH groups and linear hydrogen bonded ethanethiol on bridging OH groups suggested in literature might not exist as revealed by this theoretical calculation. Possible adsorption models were obtained for the first time.     

Anisotropic NMR interaction tensors in the decamethylaluminocenium cation

Solid-state NMR experiments, analytical and numerical simulations of solid NMR powder patterns, ab initio self-consistent field and hybrid density functional theory calculations, and single-crystal X-ray diffraction are used to characterize the molecular structure and anisotropic NMR interaction tensors in the bis(pentamethylcyclopentadienyl)aluminum cation, [Cp(2)Al](+). This highly symmetric main group metallocene has a structure analogous to that of ferrocene and the cobaltocenium cation. The single-crystal X-ray diffraction structure is reported for [Cp(2)Al][AlCl(4)]. Solid-state (27)Al[(1)H] magic-angle spinning and static NMR experiments are used to study the aluminum chemical shielding and electric field gradient tensors, revealing axial symmetry in both cases with a large chemical shielding span of Omega = 83(3) ppm and a small nuclear quadrupole coupling constant, C(Q)((27)Al) = 0.86(10) MHz. Carbon-13 CPMAS NMR experiments in combination with ab initio calculations and simulations of the effects of chemical exchange on (13)C static powder patterns reveal dynamic rotation of rings and suggest a low internal rotational barrier for this process. Theoretical computations of interaction tensors using the Gaussian 98 and Amsterdam Density Functional software packages are in good agreement with experiment and lend insight into the molecular origin of these NMR interactions. Orientations of the NMR tensors determined from theory, the large chemical shielding span, and the very small value of C(Q)((27)Al) can all be rationalized in terms of the high molecular symmetry.     

Distribution of aluminum and boron in the periodical building units of boron-containing Beta zeolites

Various boron only ([B]-BEA) as well as aluminum- and boron-containing beta zeolites ([Al,B]-BEA) have been prepared and modified by ion exchange of ammonium, sodium, and nickel ions. The zeolite samples have been characterized by 11B, 27Al, and 29Si MAS as well as three of them by 11B and 27Al 3Q-MAS NMR spectroscopy. The quantitative contributions of defect-free Si(nX) (n = 2, 1, 0; X = Al, B) and Si(OH)x (x = 2, 1) sites to the NMR signal intensities were calculated from the various Si/(Al + B) ratios and relative 11B, 27Al, and 29Si NMR signal intensities using the special distribution of aluminum and boron in different periodical building units of the zeolite framework. The boron atoms are sitting exclusively in diagonal positions in the four-membered rings of [B]-BEA zeolites, while the aluminum atoms are situated both in diagonal and lone positions in the four-membered rings of [Al,B]-BEA zeolites. A higher part of boron atoms are positioned in framework-related deformed tetrahedral boron species than in lattice positions in the [B]-BEA than in the [Al,B]-BEA zeolites. All extraframework octahedral aluminum species are transformed back to lattice positions due to ion exchange from the protonated form to ammonium-, sodium-, or nickel-ions containing zeolites. Oppositely, trigonal boron leaves the zeolite structure completely during ion exchange.     

On the structures of X- and Y-type zeolites. Structural changes within the cavities of Na-Y during dehydration and contrasts with Na-X systems

Samples of dehydrated and partially dehydrated Na-Y were examined by X-ray diffraction methods revealing the progressive structural changes which occur as water is removed and the different behaviour compared with Na-X. The differences between Na-Y and Na-X reflect the reduced Al content of Na-Y and the consequential lower average capability of each framework oxygen atom for balancing cation charges. In the small-pore region of Na-Y, the total number of Na atoms remains relatively constant during dehydration (ca. 15 per unit cell compared withca. 18 in Na-X); unlike Na-X, Na-Y, has no site I atoms. Significant dehydration of the small-pore region, and the change from low to high site II occupancy, do not occur until the total water content of the sample is less than that which pertains under atmospheric conditions. In the 12-ring regionn of Na-Y, [Na(H₂O)₂]⁺ units are observed at an intermediate level of dehydration, possibly linked by water molecules astride the site III region to networks in adjacent 12-rings. There is no build-up, as in Na-X, of Na at site III, and site IIB (=III) is (at least partially) occupied by H₂O rather than Na. Further dehydration progressively removes H₂O but there is little rearrangement of Na atom positions, except the build-up in site II which accounts for much of the loss of Na from the mobile phase.     

Convergence of electric field and electric field gradient versus atomic basis sets in all-siliceous and Mg substituted phillipsites

Electrostatic potential (EP), electric field (EF), and electric field gradient (EFG) values are calculated in periodic models of magnesium substituted phillipsite (MgPHI) zeolite forms using periodic DFT (PDFT) hybrid B3LYP level with fourteen different basis sets. Relative root mean square differences between the EP, EF, or EFG values estimated between different basis sets are evaluated in several spatial domains available for adsorbate molecules in the zeolite. In these areas, the EF increase in MgPHI is evaluated relative to all-siliceous PHI types. The EP is interpreted in terms of framework ionicity for MgPHI and all-siliceous PHI models. Angular Si-O-Si dependence of the EFG asymmetry at (17)O atoms in all-siliceous zeolites is discussed.     

The rotational spectrum,nuclear spin—spin coupling,nuclear quadrupole coupling,and molecular structure of KrHF

Rotational spectra have been assigned for the ⁸²Kr, ⁸³Kr, ⁸⁴Kr, and ⁸⁶Kr isotopic species of the KrHF and KrDF van der Waals molecules by using pulsed microwave Fourier transform spectroscopy in a Fabry—Perot cavity with a pulsed supersonic nozzle molecular source. The rotational, centrifugal distortion, nuclear spin—spin, and nuclear quadrupole coupling constants are used to determine the structure and obtain intramolecular potential binding information. The ⁸³Kr nuclear quadrupole coupling constants are 10.28 ± 0.08 MHz and 13.83 ± 0.13 MHz for KrHF and KrDF respectively. The electric field gradient at the krypton nucleus is calculated from the coupling constant and the known nuclear quadrupole moment and explained by Sternheimer shielding and formation of the van der Waals bond. There is a negligible charge transfer in the KrHF bond.     

Incorporation of metallocenes into the channel structured Metal-Organic Frameworks MIL-53(Al) and MIL-47(V)

A selection of metallocene inclusion compounds with channel structured MOFs (MOF = Metal-Organic Framework) were obtained via solvent-fee adsorption of the metallocenes from the gas-phase. The adsorbate structures ferrocene(0.5)@MIL-53(Al) (MIL-53(Al) = [Al(OH)(bdc)](n) with bdc = 1,4-terephthalate), ferrocene(0.25)@MIL-47(V) (MIL-47(V) = [V(O)(bdc)](n)), cobaltocene(0.25)@MIL-53(Al), cobaltocene(0.5)@MIL-47(V), 1-formylferrocene(0.33)@MIL-53(Al), 1,1'dimethylferrocene(0.33)@MIL-53(Al), 1,1'-diformylferrocene(0.5)@MIL-53(Al) were determined from powder X-ray diffraction data and were analyzed concerning the packing and orientation of the guest species. The packing of the ferrocene guest molecules inside MIL-47(V) is significantly different compared to MIL-53(Al) due to the lower breathing effect and weaker hydrogen bonds between the guest molecules and the host network in the case of MIL-47(V). The orientation of the metallocene molecule is also influenced by the substituents (CH(3) and CHO) at the cyclopentadienyl ring and the interaction with the bridging OH group of MIL-53(Al). The inclusion of redox active cobaltocene into MIL-47(V) leads to the formation of a charge transfer compound with a negatively charged framework. The reduction of the vanadium centers is stoichiometric. The resulting material is a mixed valence compound with a V(3+)/V(4+) ratio of 1:1. The new compounds were characterized via thermal gravimetric analysis, infrared spectroscopy, solid state NMR, and differential pulse voltammetry. Both systems are 1D-channel pore structures. The metallocene adsorbate induced breathing effect of MIL-53(Al) is more pronounced compared to MIL-47(V), this can be explained by the different bridging groups between the MO(6) clusters.     

Influence of hydrogen bonding on the properties of water molecules adsorbed in zeolite frameworks

Three hydrated aluminosilicate frameworks—LiABW, NaNAT, and BaEDI—are partly optimized with the periodic Hartree–Fock CRYSTAL95 code. In particular, we optimized the positions of the adsorbed water molecules including the positions of the framework cations (ABW, NAT) or part of the framework atomic positions (ABW). This allowed us to compare cation–water clusters in the gas and adsorbed states and discuss the influence of hydrogen bonding to the framework oxygen atoms or to the neighbor water molecules on the atomic properties (quadrupole coupling constant, anisotropy of electric field gradient) of the adsorbed water molecules. The LiBIK structure obtained from X‐ray diffraction is also considered to illustrate the hydrogen bonds occurring between adsorbed water molecules. © 2003 Wiley Periodicals, Inc. Int J Quantum Chem, 2003     

MCM-22分子筛酸性的DFT理论计算研究

本文利用量子力学中的密度泛函理论(DFT)计算，研究了MCM-22分子筛上骨架Al在8个不同的T位的分布和Br?nsted酸的落位及强度。所有计算基于分子筛的8T簇模型 (H₃SiO)₃Si-O(H)-T(OSiH₃)₃(T=Si，Al)，采用DFT的BLYP方法，所有原子均应用DNP基组。通过计算(Al，H)/Si替代能和质子亲和势，得出推论：MCM-22分子筛中骨架Al的最有利落位在T1，T4，T3和T8位。而形成Br?nsted-酸的最可能的位置为Al1-O3-Si4，Al4-O3-Si1，Al3-O11-Si2和Al8-O10-Si2桥基。Al1-O3H-Si4和Al4-O3H-Si1位的酸性强度接近，Al3-O11H-Si2和Al8-O10H-Si2位的酸性分别略低于和略高于前两个酸位。通过计算模板剂分子六次甲基亚胺(HMI)与B-酸中心的相互作用，进一步探讨了HMI对分子筛中Al落位的靶向作用。     

17O magic angle spinning NMR studies of Brønsted acid sites in zeolites HY and HZSM-5

High-resolution 17O/1H double resonance NMR spectra were obtained for two zeolites, one with a low Si/Al ratio (zeolite HY) and one with a high Si/Al ratio (HZSM-5), to investigate their local structure and Br?nsted acidity. Two different oxygen signals, corresponding to Br?nsted acid sites in supercages and sodalite cages of zeolite HY were readily resolved in the two-dimensional (2-D) 1H-17O heteronuclear correlation (HETCOR) NMR spectra allowing the 17O isotropic chemical shift (deltaCS) and quadrupolar coupling parameters (quadrupolar coupling constant, QCC, and asymmetry parameter, eta) for the two oxygen atoms to be extracted. Similar experiments for HZSM-5 showed that the sites in this system are associated with a much larger distribution in NMR parameters than found in HY. 17O-1H rotational echo double resonance (REDOR) NMR was applied to probe the O-H distances in zeolites HY and HZSM-5. Weaker 17O-1H dephasing was observed for zeolite HZSM-5 in comparison to that of HY, consistent with longer O-H bonds and/or increased proton mobility.     

沸石桥羟基和硅羟基与噻吩相互作用的理论研究

采用密度泛函理论和模型簇法研究了噻吩和沸石分子筛桥羟基和硅羟基的相互作用.对噻吩吸附在硅羟基H3SiOH可能的两种配位方式及吸附在沸石模型簇H3Si(OH)Al(OH)2OSiH3桥羟基B酸上可能的两种配位方式进行了比较分析.所有模型簇采用B3LYP混合方法对氢原子在6-31G基组水平上,对硅原子、铝原子、氧原子、碳原子、硫原子在6-31 G(d)基组水平上进行了全优化和频率分析.着重考察了噻吩与硅羟基及分子筛桥羟基模型簇不同配位方式所形成的配合物的结构及能量变化.计算结果表明由于在形成沸石-噻吩和硅羟基-噻吩配合物的结构和性质变化不明显,所以它们之间的相互作用为范德华作用力.从噻吩在沸石分子筛的桥羟基和硅羟基与噻吩的相互作用的吸附热可以推断,噻吩优先吸附在桥羟基上,只有桥羟基吸附饱和后方吸附在硅羟基上.由频率分析结果和实验结果的一致性可以证明所推测吸附模型的正确性.     

Structure of Framework Aluminum Lewis Sites and Perturbed Aluminum Atoms in Zeolites as Determined by 27Al{1H} REDOR (3Q) MAS NMR Spectroscopy and DFT/Molecular Mechanics

Zeolites are highly important heterogeneous catalysts. Besides Brønsted SiOHAl acid sites, also framework Al_FR Lewis acid sites are often found in their H‐forms. The formation of Al_FR Lewis sites in zeolites is a key issue regarding their selectivity in acid‐catalyzed reactions. The local structures of Al_FR Lewis sites in dehydrated zeolites and their precursors—“perturbed” Al_FR atoms in hydrated zeolites—were studied by high‐resolution MAS NMR and FTIR spectroscopy and DFT/MM calculations. Perturbed framework Al atoms correspond to (SiO)₃AlOH groups and are characterized by a broad ²⁷Al NMR resonance (δ_i=59–62 ppm, C_Q=5 MHz, and η=0.3–0.4) with a shoulder at 40 ppm in the ²⁷Al MAS NMR spectrum. Dehydroxylation of (SiO)₃AlOH occurs at mild temperatures and leads to the formation of Al_FR Lewis sites tricoordinated to the zeolite framework. Al atoms of these (SiO)₃Al Lewis sites exhibit an extremely broad ²⁷Al NMR resonance (δ_i≈67 ppm, C_Q≈20 MHz, and η≈0.1).