Electron spin resonance of 65-million-year-old glasses and rocks from the Cretaceous–Tertiary...

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Electron spin resonance of 65-million-year-old glasses and rocks from the Cretaceous–Tertiary boundary David L. Griscom a, * ,1 , Virgilio Beltr an-L opez b , Celia I. Merzbacher a , Elizabeth Bolden a a Optical Sciences Division, Naval Research Laboratory, Washington, DC 20375, USA b Instituto de Ciencias Nucleares, Universidad Nacional Aut onoma de M exico, C.U., A. Postal 70-543, 04510, Mexico DF, Mexico Abstract Glasses and rocks produced or altered by the colossal impact of an asteroid or comet with the earth 65 million years ago have been studied by electron spin resonance (ESR) and thin-section photomicroscopy. The ESR spectra reveal the presence of 1.9 0.5 wt% single-domain (SD) titanomagnetite particles (sizes in the range 10–60 nm) in shock-melted rocks drilled from the floor of the giant Chicxulub crater ( P 180 km diameter) buried 1 km below the surface of Mexico’s Yucat an peninsula. These ferrimagnetic (ferrite) particles account for 37 9% of the total iron in the once- vitreous crater-floor rocks. Similar ferrites in particle sizes 3 nm and amounts 0.13 0.03 wt% are found in coeval tektite glasses from Haiti. Additional SD titanomagnetite phases in particle sizes ranging from 3 to 4.5 nm and amounts 0.045 0.020 wt% are identified by ESR as markers of the Cretaceous–Tertiary (K/T) boundary in limestones from two sites in Spain, where their ESR intensities rise above background by factors 14. The latter K/T-boundary ‘marker’ ferrites are hypothesized to have precipitated in vitreous materials ejected from the Chicxulub crater and to have survived aqueous weathering which converted their original glassy matrices to clays. Spherules from K/T- boundary beds in Mexico and New Jersey were found to contain amounts of ferrites not exceeding background levels; rather, their ESR spectra exhibit spectral components characteristic of Fe 3 in glasses and of previously reported ra- diation-induced paramagnetic species in crystalline quartz and calcite (CaCO 3 ). Thin-section studies, including energy- dispersive spectroscopy, show the Mexican spherules to be fine-particle agglomerates (component grain sizes 1–100 lm) of calcite, dolomite (MgCa(CO 3 ) 2 ), and glass, with interstitial flint (a polycrystalline form of quartz assumed to have been deposited hydrolytically after the spherules fell to earth). It is argued that the carbonate-containing spherules originally condensed within a ‘warm fireball’ composed of water vapor and 2000 km 3 of shock-vaporized limestone proposed by others to have been generated by the Chicxulub impact. Ó 1999 Elsevier Science B.V. All rights reserved. 1. Introduction The impact of a massive asteroid or comet (10 15 kg) into a shallow sea 65 million years ago (Ma) is now widely believed to have brought about the abrupt extinctions of the dinosaurs and many marine species [1,2]. The impacting object and an equivalent mass of the target rock (a 3 km-deep accumulation of limestones and sulfates lying on Journal of Non-Crystalline Solids 253 (1999) 1–22 www.elsevier.com/locate/jnoncrysol * Corresponding author. Tel.: +1-202 404 7087; fax: +1-202 767 5792; e-mail: [email protected] 1 Fulbright–Garc ıa Robles Fellow at Universidad Nacional Aut onoma de M exico (UNAM), M exico DF, 5 May–29 July 1997. 0022-3093/99/$ – see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 3 4 0 - 3

Transcript of Electron spin resonance of 65-million-year-old glasses and rocks from the Cretaceous–Tertiary...

Electron spin resonance of 65-million-year-old glasses androcks from the Cretaceous±Tertiary boundary

David L. Griscom a,*,1, Virgilio Beltr�an-L�opez b, Celia I. Merzbacher a,Elizabeth Bolden a

a Optical Sciences Division, Naval Research Laboratory, Washington, DC 20375, USAb Instituto de Ciencias Nucleares, Universidad Nacional Aut�onoma de M�exico, C.U., A. Postal 70-543, 04510, Mexico DF, Mexico

Abstract

Glasses and rocks produced or altered by the colossal impact of an asteroid or comet with the earth 65 million years

ago have been studied by electron spin resonance (ESR) and thin-section photomicroscopy. The ESR spectra reveal the

presence of 1.9 � 0.5 wt% single-domain (SD) titanomagnetite particles (sizes in the range �10±60 nm) in shock-melted

rocks drilled from the ¯oor of the giant Chicxulub crater ( P 180 km diameter) buried �1 km below the surface of

Mexico's Yucat�an peninsula. These ferrimagnetic (ferrite) particles account for 37 � 9% of the total iron in the once-

vitreous crater-¯oor rocks. Similar ferrites in particle sizes �3 nm and amounts 0.13 � 0.03 wt% are found in coeval

tektite glasses from Haiti. Additional SD titanomagnetite phases in particle sizes ranging from �3 to �4.5 nm and

amounts 0.045 � 0.020 wt% are identi®ed by ESR as markers of the Cretaceous±Tertiary (K/T) boundary in limestones

from two sites in Spain, where their ESR intensities rise above background by factors �14. The latter K/T-boundary

`marker' ferrites are hypothesized to have precipitated in vitreous materials ejected from the Chicxulub crater and to

have survived aqueous weathering which converted their original glassy matrices to clays. Spherules from K/T-

boundary beds in Mexico and New Jersey were found to contain amounts of ferrites not exceeding background levels;

rather, their ESR spectra exhibit spectral components characteristic of Fe3� in glasses and of previously reported ra-

diation-induced paramagnetic species in crystalline quartz and calcite (CaCO3). Thin-section studies, including energy-

dispersive spectroscopy, show the Mexican spherules to be ®ne-particle agglomerates (component grain sizes �1±100

lm) of calcite, dolomite (MgCa(CO3)2), and glass, with interstitial ¯int (a polycrystalline form of quartz assumed to

have been deposited hydrolytically after the spherules fell to earth). It is argued that the carbonate-containing spherules

originally condensed within a `warm ®reball' composed of water vapor and �2000 km3 of shock-vaporized limestone

proposed by others to have been generated by the Chicxulub impact. Ó 1999 Elsevier Science B.V. All rights reserved.

1. Introduction

The impact of a massive asteroid or comet(�1015 kg) into a shallow sea 65 million years ago(Ma) is now widely believed to have brought aboutthe abrupt extinctions of the dinosaurs and manymarine species [1,2]. The impacting object and anequivalent mass of the target rock (a 3 km-deepaccumulation of limestones and sulfates lying on

Journal of Non-Crystalline Solids 253 (1999) 1±22

www.elsevier.com/locate/jnoncrysol

* Corresponding author. Tel.: +1-202 404 7087; fax: +1-202

767 5792; e-mail: [email protected] Fulbright±Garc�õa Robles Fellow at Universidad Nacional

Aut�onoma de M�exico (UNAM), M�exico DF, 5 May±29 July

1997.

0022-3093/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved.

PII: S 0 0 2 2 - 3 0 9 3 ( 9 9 ) 0 0 3 4 0 - 3

top of a basement of andesite granite) were va-porized within a second, and at least 10 times asmuch target rock was shock melted within minutes[3]. Thus, in an instant of geologic time, the earthbecame blanketed with more than 1016 kg of glass.Exploratory wells drilled by the Mexican oilcompany, Petr�oleos Mexicanos (PEMEX), helpedto con®rm of the existence of the gigantic Chic-xulub crater (180±300 km in diameter [4]) buriedbeneath the present-day surface of Mexico's Yu-cat�an peninsula. The PEMEX drill cores retrievedsamples of polymict impact breccias at depths �1km, de®ning the topographic ¯oor of the crater asit existed �10 min [5] after the impact. At depths�1.3 km shock-melted rocks of andesitic compo-sition [6] were encountered. These crater `meltrocks' and glassy tektites [7] from Beloc, Haiti,have been found to exhibit nearly identical com-positions (see Table 1) and both have been radio-metrically dated at 65.0 Ma [8]. Thus, the Beloctektites are concluded to be Chicxulub impactejecta ballistically launched (typically at angles6 45° to the horizon [3]) by shock overpressures(>60 gigapascals (GPa) [9,10]) su�cient to causewhole rock melting. More di�cult to understand,however, has been the fact that unmelted quartzgrains evidently subjected to pressures of no morethan a few tens of GPa [11] have been recoveredfrom sites as far as 10 000 km from the Chicxulubcrater, whereas ballistic transport by shock accel-eration would require overpressures in the range

�50±100 GPa su�cient to either erase any recordof lower levels of shock or to melt the quartz tosilica glass [3]. It has been hypothesized recently [3]that these moderately shocked quartz grains wereboosted into high-angle (>70°) trajectories by abuoyantly rising `warm ®reball' consisting of CO2

and water vapor released from �2000 cubic kilo-meters of shock-decomposed wet limestone.

The materials ejected from the Chicxulub im-pact are theorized to have fallen back to earth inthe sequence [3]: (i) `curtain ejecta' consisting ofjets of molten and fragmented rock launched atangles �45°, (ii) warm-®reball-lofted particles, and(iii) hot-®reball ®ne dust condensates (including astill unidenti®ed chemical component enriched iniridium [1,2]). This rain of debris formed a multi-layer mantle on top of continental surfaces and sea¯oors at what was to be the ®nal moment of theCretaceous period, coinciding with the end of the150-million-year reign of the dinosaurs. Immedi-ately above this stratum are now found the oldestrocks of the Tertiary period, deposited while themammals which survived the catastrophe began toradiate into ecological niches left vacant by thegiant reptiles. On the basis of available evidence[8±10,12], most of the glassy materials originallypresent in this Cretaceous±Tertiary (`K/T') boun-dary layer either crystallized during cooling orwere subsequently subjected to hydrolytic altera-tion. The Haitian tektites [7,8] and a small pro-portion of the melt rock from the PEMEX drill

Table 1

Average chemical compositions in weight% of some rocks and glasses related to the K/T impact event, with comparison to andesite

Oxides Beloc tektites Chicxulub Andesitea

Yellow glassb Black glassc Y6 altered rockc C1 glassc

SiO2 49.06 63.09 61.85 59.08 59.5

Al2O3 13.19 15.21 13.10 14.81 17.2

FeOd 5.14 5.44 4.75 3.93 6.1

MgO 4.09 2.74 3.15 4.74 3.4

CaO 24.54 7.26 10.35 10.30 7.1

K2O 0.63 1.59 1.9 2.24 1.6

Na2O 2.10 3.63 4.35 4.35 3.7

TiO2 0.64 0.67 0.4 0.13 0.7

MnO 0.14 0.16 0.1 0.14 0.12

a Ref. [6].b Ref. [7].c Ref. [8].d Iron-oxide contents are formally listed as FeO; in fact, all these materials prove to be characterized by Fe3�/Fe2� ratios ~0.4 (see

[6,37], and this work).

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cores [8,9] are among the few known exceptions.Indeed, most of the glassy crater ejecta depositedin the K/T boundary rocks has probably beenweathered to clays [3,12].

The present study was initially undertaken withthe object of using the technique of electron spinresonance (ESR) to search for single-domain (SD)ferrite particles (i.e., ferrimagnetic minerals inparticle sizes 6 60 nm [13]) which may be relics ofthe Chicxulub impact event. This search was in-spired by the discovery [14±17] of Ni-rich (Ni2�/total cations� 0.15), high-Fe3� (Fe3�/Fetotal�0.75±0.90) magnesioferrite particles in sizes >1 lmwhich form a world-wide horizon at the K/Tboundary and are characterized by concentrationpro®les more sharply de®ned than those of thebetter-known iridium layer [1,2]. Strong evidencehas been given that these (multi-domain) Ni-rich,high-Fe3� ferrites are ablation products of the in-falling impactor, implying them to be `cosmicmarkers' [14±17]. In principle, therefore, the pres-ent ESR investigation could reveal SD members ofthe same `cosmic ferrites' previously elucidated inlarger particle sizes [14±17] or SD ferrites precipi-tated in glassy components of the Chicxulub craterejecta, or both. Below we provide the ®rst full re-port of our ESR investigations of SD ferrite phasesassociated with the K/T impact event. We alsoinclude a preliminary report of ESR measurementsof several paramagnetic species present in thecrystalline carbonate portions of the K/T boun-dary rocks.

2. Experimental details

X-band (9.1±9.5 GHz) ESR spectra were re-corded on Varian E-Line and Bruker ER200spectrometers. Sample temperatures in the range100±570 K were regulated by means of N2-gas¯ow-through accessories. By recording spectra atmicrowave power levels low enough to avoidsaturation, ESR spin concentrations were mea-sured with reference to Varian `strong pitch'standard samples. These `line sample' standardscontain 3 ´ 1015 spin-1/2 states per linear cm ofsample tube length. Most experimental sampleswere in powder form and were loaded into fused

quartz sample tubes to depths P 3 cm andweighed to establish their lineal mass densities forcomparison to the standard. A few materials wereso magnetic that the use of linear samples causedthe detector current to move o� scale duringbroad ®eld sweeps. To avoid inaccuracies associ-ated with this condition, samples of such materialswere limited to total masses �2±10 mg, makingthem approximately `point samples'. However,point samples positioned at the center of a TE102

microwave cavity can be compared to a line-sample standard by recognizing that the `e�ectivelength' of any line sample in the X-band cavity is 1cm [18]. Based on interlaboratory comparisons,we believe the absolute accuracy of recent Varianstrong pitch samples to be �15% (better than the�25% quoted 38 years ago [18]). The accuracies inintegrating the areas under the experimental ab-sorption curves depend on several factors includ-ing signal-to-noise ratios and establishingbaselines. We estimate random errors from allsources to be no greater than �10% for the SDdomain ferrites of the present study. By contrast,our attempts to quantify Fe3� in glasses appear tohave given numbers which are systematically lessthan actual values determined by other means(vide infra).

Thin sections for photomicroscopy were pre-pared using a precision polishing system (Logi-tech). Scanning electron microscopy (SEM) andenergy-dispersive spectroscopy (EDS) were carriedout on a limited area of one of the thin sectionsusing an SEM instrument (Zeiss-Cambridge LEO1550) operated at 15 keV in the secondary-electrondetection mode and an EDS analyzer (EDAX).

The following geologic samples stratigraphi-cally associated with the K/T boundary were in-vestigated: (1) a specimen of dark-matrix meltrock from the PEMEX Y6-N19 drill core ex-tracted from 1.3 km below Mexico's Yucat�anpeninsula, (2) 80 mg of tektite glasses �1 mmpicked from a single sample of spherulitic materialfrom a site in Beloc, Haiti, (3) two series of pow-dered rock samples from selected stratigraphicintervals transecting the K/T boundary at two sitesin Spain (Caravaca and Sopelana), (4) a single1:2� 0:6 cm2 oblate spheroid from El Guayal,State of Tabasco, Mexico, (5) specimens of

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 3

boundary clay from Gubbio, Italy, and Bidart,France, and (6) an aliquot of sub-mm spherulesfrom a 6 cm-thick K/T-boundary stratum coredfrom 384 m beneath the coastal plane at BassRiver, NJ [19]. For comparison purposes, a num-ber of geologic materials collected from strata re-mote from the K/T boundary were also studied,including Australasian tektites and a sample offusion crust (USNM No. 5575) from a meteoritewhich fell on 8 February 1969 at Pueblito de Al-lende in northern Mexico.

Sub-samples of all K/T-age materials (exceptfor some members of the Sopelana sequence) wereweighed and treated in 25% HCl to remove car-bonates. After washing in distilled water to removeresidual CaCl2, drying, and reweighing, the massfraction of carbonates in the original material wasassumed to be equal to the resulting weight loss. Inthe case of the the Guayal spherule, where thecarbonates were evidently encapsulated in ¯int(vide infra), iterative grinding and acid treatmentswere performed after which the ESR signal ofMn2� in the calcite fraction [20] was monitored inorder to extrapolate the amount of carbonate notdissolved.

3. Results

Fig. 1 displays the room-temperature ESRspectra of a collection of 65 Ma geologic speci-mens, i.e., ones either radiometrically dated by40Ar/39Ar methods (i.e., the Chicxulub crater meltrock and the Beloc tektites [8]) or stratigraphicallylinked to the K/T event (e.g., the Caravaca [14]and Gubbio [1] boundary clays and the Bass Riverspherules [19]). These `K/T marker' signals can becompared with the spectra of Fig. 2 recorded forseveral reference materials of diverse non-K/T-boundary geologic provenances. In both ®gures,ampli®cation factors are provided to convey asense of the relative strengths of these signals.These factors comprise the products of all perti-nent parameters to which the intensities of thedisplayed spectra were linearly proportional,namely, the ®eld modulation amplitude, the squareroot of microwave power, the ampli®er gain, andthe sample mass. For spectra of similar line shapes

and equal amplitudes, a smaller ampli®cationfactor generally implies a greater signal strengthper unit sample mass. The most intense spectra inFigs. 1 and 2 are those of the Chicxulub crater-¯oor dark-matrix melt rock and the Allende me-teorite fusion crust, respectively. Photomicro-graphs of 30 lm thin sections of the formermaterial are presented in Fig. 3.

Fig. 1. X-band ESR spectra of several 65-Ma-old rocks and

glasses created or altered by the K/T impact event: (a) and (b)

impact-derived tektite glasses from Beloc Haiti; (c) the acid-

insoluble fraction of K/T-boundary clay from Caravaca, Spain;

(d) a whole-rock sample of red clay from the K/T boundary in

Gubbio, Italy; (e) dark-matrix melt rock from the Y6-N19 drill

core extracted from below the ¯oor of the Chicxulub crater,

Yucat�an, M�exico. Gain factors are the product mMGp

P,

where m, M, G, and P are sample mass, magnetic-®eld modu-

lation amplitude, ampli®er gain, and microwave power, re-

spectively. All spectra recorded at room temperature.

4 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

4. Discussion

Although most of the materials of Fig. 1 tracetheir origins to glasses formed in the K/T impact,only the mm-sized tektites, (a) and (b), are stillglassy. Due to devitri®cation and/or aqueous al-teration, little or no glass remains in the othersamples (see Ref. [8] for pertinent observationsconcerning drill-core specimen Y6-N19). Theg� 4.3 features in the spectra of the Haitianspecimens are characteristic of paramagnetic Fe3�

in many types of glasses [21], and also in someminerals such as plagioclase [22]. (The g value is

de®ned by the equation hm� gbH, where h isPlanck's constant, m the spectrometer frequency, bthe Bohr magneton, and H is the magnitude of theapplied magnetic ®eld at resonance.) In particular,the ESR spectra of the Haitian tektites bearqualitative resemblances to those of tektites ofmore recent origin [23], e.g., the 0.8 Ma-old in-dochinite represented by the spectrum of Fig. 2(g).The faint 6-line spectrum centered at g� 2 in Fig.2(g) arises from Mn2�. The g� 2 signal of Fig. 1(a)must also include a contribution from the knownamount of Mn2� present in this sample (Table 1),but its rounded shape and poorly resolved 55Mnhyper®ne structure indicates that Fe3� ions ± and/or something else ± also contributes to this part ofthe spectrum. As will be discussed below, part ofthe g� 2 spectrum of Fig. 1(a) ± and certainlymost of the much stronger signals near g� 2 inFig. 1((b)±(e)) may be due to near-spherical SDferrite particles originally precipitated in glasses[24].

A ferrite is a material possessing a spontaneousmagnetization below a certain temperature as aresult of an exchange-coupled assemblage ofatomic dipoles, at least some of which are alignedantiparallel to the net magnetic moment [25,26].The particular class of ferrites considered here arematerials having the structure of the mineral spinel(MgAl2O4) but with compositions closer toMeOáFe2O3, where Me is a divalent cation. Eachunit cell in the spinel structure possesses eighttetrahedral (A) and 16 octahedral (B) sites whichcan be occupied by cations. If the divalent cationsMe occupy the A sites, the material is known as anormal spinel. But, if all eight divalent ions arefound in eight of the 16 B sites, these ferrites arecalled inverse spinels. The magnetic moments of alllike ions on a given coordination sublattice aregenerally aligned mutually parallel and are anti-ferromagnetically opposed by the mutually alignedmoments of ions of the same type found in theother sublattice. Magnetite (Me�Fe) and ma-gnesioferrite (Me�Mg) are examples of inversespinels wherein the magnetic moments of the Fe3�

ions, evenly divided between the A and B sites,exactly cancel in the ideal case. However, in realmaterials the site preferences of individual ions aregoverned by activation energies, leading to

Fig. 2. X-band ESR spectra of rocks and glasses mostly unre-

lated to the K/T event 65 million years ago: (a) fusion crust

from the Allende meteorite; (b) acid-insoluble clay fraction of

limestone from the interval 21 to 26 cm below the K/T boun-

dary at Caravaca, Spain; (c) acid-insoluble fraction of

spherulitic material from the K/T-boundary at Bass River, NJ;

(d) volcanic ash from a recent eruption of Mt. Popocatepetl,

Mexico; (e) yellow clay from Northern Virginia; (f) a specimen

of the iron-hydroxide-hydrate mineral limonite; and (g) a 0.8-

million-year-old tektite glass from Indochina. Gain factors are

as de®ned in Fig. 1. All spectra recorded at room temperature.

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 5

quench-temperature-dependent degrees of mixingbetween A and B sites. Thus, ideal magnesioferritehas no spontaneous magnetization, whereas thereal materials typically have about 10% of theMg2� ions in A sites, displacing an equal numberof Fe3� ions to B sites and so producing a small netmagnetic moment [25,26]. By contrast, irrespectiveof quench temperature, magnetite always possessesa strong net magnetization arising from the Fe2�

ions residing mostly on the B sublattice. Magneticresonance of ferrites, though recorded on standardESR spectrometers, is commonly referred to asferromagnetic resonance (FMR). The application

of FMR methods to ®ne-particle metallic-iron andferrite precipitates in natural glasses is reviewed inRef. [24].

4.1. ESR quantitative analysis of paramagnetic ionsand ferrimagnetic particles in glasses

By double numerical integration of a ®rst-de-rivative ESR spectrum such as those of Figs. 1 and2 and division by the appropriate ampli®cationfactor, a raw measure of ESR intensity per unitsample mass can be obtained. For an experimentalsample we denote this raw intensity as Imeas

Fig. 3. Thin-section photomicrographs of Chicxulub crater-¯oor melt rock from the PEMEX Y6-N19 drill core from 1.3 km below the

Yucat�an Peninsula, M�exico: Dark-matrix melt material, (a), (b), and (c), photographed in linearly polarized light and (d) a 2 mm

fractured quartz grain viewed under crossed polarizers. The 1 mm crystal in the lower left quadrant of (c) is identi®ed as plagioclase.

6 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

(experimental sample) and note that it has di-mensions gÿ1 (or cm gÿ1 in the case of a linesample) due to inclusion of the sample mass (orlineal mass density) in the ampli®cation factor. Toconvert this raw intensity to an absolute spin countit is ®rst necessary repeat the procedure for astandard sample, obtaining Imeas (standard sam-ple). However, in the case of the standard sample,sample mass is not included in the ampli®cationfactor. Thus, Imeas(standard sample) is dimension-less. Absolute numbers of resonators per gram (anindividual resonator being, e.g., an isolated para-magnetic Fe3� ion or a single ferrite particle pre-cipitated in a glass) can then be estimated by use ofthe formula

Nmeas�experimental sample; J�

� Imeas�experimental sample�Imeas�standard sample�

G1=2�x�GJ �x�

� Nknown�standard sample; 1=2�; �1�where Nmeas(experimental sample, J) is the numberdensity of resonators having quantum mechanicalspin J and Nknown(standard sample, 1/2) is theknown number of J� 1/2 spins per centimeter inthe `line' standard sample [18]. Here, GJ (x) is thestatistical mechanical average of the ESR transi-tion probabilities of the centers or particles withspin angular momentum J, evaluated under the setof experimental conditions speci®ed by x� hm/kT(k is Boltzmann's constant and T is temperature inKelvin) (see Appendix A and Ref. [27]):

Gj�x� � 2J1ÿ eÿ2Jx

1ÿ eÿ�2J�1�x

� ��1ÿ eÿx�

� eÿx

1ÿ eÿx�2J� ÿ 2��1ÿ eÿ2Jx�

ÿ 2Jeÿx�1ÿ eÿ�2Jÿ2�x��: �2�In the case of paramagnetic centers, J is simply thespin state of the center, e.g., J�S� 1/2 for acarbon pitch standard sample or J�S� 5/2 forFe3� or Mn2�. But in the case of ferrite particles, Jis taken to be J 0g, where gJ 0 is the e�ective numberof Bohr magnetons per formula unit measured inthe bulk material and g is the number of formulaunits per particle of diameter d. That is, g� (p/6)d3qA/FW, where A is Avogadro's number and q

and FW are the density and formula weight, re-spectively, of the magnetic material. For puremagnetite at T� 0 K, it is known that J 0�0� � 2(e.g., [25,26]). However, due to the ®nite strengthof the Weiss exchange ®elds coupling the spinmagnetic moments of the individual transition-group ions in the crystal, thermal agitation willfrustrate complete alignment of all spins [25,26].Thus, J 0 is a decreasing function of increasingtemperature, being in fact proportional to thesaturation magnetization, Ms(T), which decreasesto 0 at the Curie temperature. Whence, the valuesof J to be used in Eq. (2) are

J � J 0�0�gMs�T �=Ms�0�; �3�where a suitable analytic approximation to litera-ture data for Ms(T)/Ms(0) may be employed, suchas Ms(T)/Ms(0)� 1ÿ4.05 ´ 10ÿ6T1:75 used here formagnetite.

Critical to the application of Eqs. (1)±(3) tosmall-particle ferrites is the ability to assign aparticle diameter, d. While this might be accom-plished, e.g., by transmission electron microscopy,it is generally more convenient to ®t the tempera-ture dependence of the FMR intensity to Eq. (2),using d as a ®tting parameter [24,27]. This ®ttinghas been done in Fig. 4 for several samples of thepresent study.

4.2. ESR signals of crater-¯oor rocks and coevaltektite glasses

The crater-¯oor melt-rock spectrum of Fig. 1(e)is seen to be �500 times more intense than thespectrum of Fig. 1(a), which is due to paramag-netic resonance of Fe3� in a tektite glass of virtu-ally the same composition (Table 1). Thisobservation alone indicates that the spectrum ofFig. 1(e) must arise from ferromagnetic phases.Moreover, the asymmetric shape (narrower andhigher on the low-®eld side) and g value (nearg� 2.0) of this line are speci®cally suggestive[24,28] that it arises from spherical, SD (6 60 nm[29]) particles of magnetite. To verify this hy-pothesis, the temperature dependence of the in-tensity and of the peak-to-peak linewidth of thisresonance have been plotted in Fig. 5(a) and (b),respectively, where they are compared with

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 7

predictions based on literature data for bulkmagnetite. Indeed, above the Verwey temperatureof magnetite (�118 K in pure, stoichiometricmagnetite [30]), the intensity data (circles in Fig.5(a)) follow the behavior of 60 nm particles of puremagnetite (smooth curve) predicted by Eqs. (2)and (3). With falling temperature in the vicinity ofthe Verwey transition, the FMR intensity datadecrease precipitously in a manner similar to staticmagnetization data (crosses [31]) measured for anapplied magnetic ®eld strength (358 mT) close tog� 2 ®eld (325 mT) of the present experiment.Consistent with the physics upon which Eq. (2) isbased, the FMR intensity should be congruentwith the actual magnetization whenever it shouldbe di�erent from Ms(0).

The sense of the spectral asymmetry of the g� 2component of Fig. 1(e) implies (e.g., [24,28]) a

negative ®rst-order magnetocrystalline anisotropyconstant, K1, as expected for pure magnetite at 300K. For this reason, the linewidth data of Fig. 5(b)(circles) have been assigned algebraic signs ac-cording to the inferred sign of K1. The continuouscurve in Fig. 5(b) represents the predicted anisot-ropy-determined linewidth, (5/3)2K1/Ms [24,28],based on K1 data [32] for pure magnetite, ne-glecting other line-broadening e�ects. Qualitativeagreement is seen between experiment and pre-diction, particularly as regards the change in al-gebraic sign of K1 near the transition. The fact thatthe magnitudes of the measured FMR linewidths(circles) are greater than those predicted (particu-larly at high temperatures) is reasonably attribut-

Fig. 4. Temperature dependence of the FMR intensities of Y6-

N19 Chicxulub crater dark-matrix rock (circles), separated

fractions of acid-insoluble K/T-boundary clays from Caravaca,

Spain (squares and triangles), and opaque tektites from Beloc,

Haiti (diamonds). Solid curves are the normalized predicted

behaviors of spherical, single-domain particles of pure magne-

tite of selected diameters, d, calculated by means of Eqs. (2) and

(3). A calculated curve for d� 10 nm (not shown for clarity) was

10% lower than the curve for d� 60 nm at 500 K. Each of the

data sets, which do not include points below 100 K, is arbi-

trarily normalized to match a calculated curve over a substan-

tial temperature range. The dashed curve is passed through the

data points as an aid to the eye.

Fig. 5. Temperature dependence of (a) the FMR intensity and

(b) the FMR linewidth of dark-matrix melt rock from the Y6-

N19 drill core. In (b), the linewidth data have been assigned

algebraic signs corresponding to the sign of the magnetocrys-

talline anisotropy constant, K1, inferred from inspection of the

spectral asymmetry of the resonance line. The circles in (b) have

been connected with straight-line segments as an aid to the eye;

the dashed line spans a temperature interval where the obtained

spectra appeared to be superpositions of spectral types char-

acterized by both positive and negative K1 values. Crosses and

curves without symbols represent predicted behaviors of the

FMR spectra of ideal assemblages of spherical, single-domain

particles of pure magnetite of diameters �60 nm based on data

[31,32] for large single crystal samples.

8 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

able to dipole±dipole interactions [33] among the(3.2 � 0.8) ´ 1013 60 nm-diameter magnetite parti-cles per cubic centimeter measured (vide infra) inthe examined piece of dark-matrix melt rock.Consistent with this interpretation, a sample ofone of the abundant light gray altered-melt-rockclasts [34] from the Y6-N19 drill core exhibited aroom-temperature FMR spectrum which was �5times weaker than that of Fig. 1(e) and, corre-spondingly, �15% narrower (i.e., closer to theprediction of Fig. 5(b)). In Fig. 5(b), the apparentshift of the isotropy point (K1 zero crossing) to atemperature lower than that for pure magnetite isconsistent with �5% titanium substitution [35].These results thus con®rm the earlier identi®cationof SD titanomagnetite particles in the Chicxulubcrater rocks based on measurements of severalbulk magnetic properties [34].

By making use of the Y6 composition data ofTable 1 and Eqs. (1)±(3), our ESR intensity datareveal that �37 � 9% of the total iron in thestudied sample of dark-matrix melt rock is presentas particles of magnetite in sizes �10±60 nm. Thisresult implies that at least 25 � 6% of the total ironin this crater-¯oor rock is in the trivalent state. TheESR signal of any isolated Fe3� in the crater rockis masked by the much more intense magnetitesignal (note the progressive obscuration of theg� 4.3 signals in Fig. 1 from top to bottom) andtherefore was not measurable in this experiment.However, by assuming that only 20% of the ironnot associated with magnetite remains in the tri-valent state, the present measurement becomesconsistent with the Chicxulub crater-¯oor meltrock retaining the ratio Fe3�/Fetotal P 0.40, astypically observed for andesites [6]. An unchangedredox ratio would imply that the crater-¯oor meltrock was not heated hot enough nor exposed longenough to a gas phase of di�ering oxygen fugacityto have e�ected such a change. On the other hand,the high degree of single-domain magnetite pre-cipitation (1.9 � 0.5 wt% or 37 � 9% of total iron)is undoubtedly linked to cooling times su�cientlyrapid to have hindered ripening of the precipitatedmagnetite particles into size ranges �60 nm [13].Perhaps accelerated cooling of the uppermostChicxulub crater-¯oor materials (of which Y6-N19is a member) resulted from immediate ¯ooding of

the crater with sea water. If so, larger-grainedmagnetite may yet be found nearer to the bottomof the immense lens of crater-¯oor glass calculated[36] to be �5 km deep for Chicxulub.

By contrast with the crater-¯oor rock, wemeasure only 0.13 � 0.03 wt% magnetite (particlesizes �3 nm) in the opaque tektite glasses of Fig.1(b). Assuming that the spectrum of Fig. 1(a)arises only from paramagnetic Fe3� and Mn2�

(and taking the Mn2� content to be as given bychemical analyses [7,8]), we measure the Fe3�/Fetotal ratio in our dark-yellow Beloc tektites to be0.081 � 0.020. This ratio is roughly twice thatpreviously determined by ESR for the geologicallyyounger Australasian tektites [23]. However, ourFe3� estimates disagree with M�ossbauer determi-nations of Fe3�/Fetotal falling in the range 0.39±0.43 for black Beloc tektites and 0.74 for a re-portedly rare yellow glass separate [37]. Since ourown dark-yellow glasses were not uncommon inthe single aliquot of Beloc spherules to which wehad access and they di�ered from our separate ofopaque glasses only in possessing perceptibletransparency in sizes 6 1 mm, we suppose thatthey may fall in the group of `black' tektites of Ref.[37]. Even so, there remains a discrepancy of afactor of �5 between our ESR Fe3� determina-tions and the M�ossbauer results of Ref. [37]. Since,in an earlier study of Australasian tektites [23],ESR tended to underestimate Fe3� contents rela-tive to M�ossbauer by factors of �3, we supposethat ESR (as we have used it) must systematicallyunderestimate the paramagnetic Fe3� contents ofoxide glasses. This failing could be due to a largefraction of the Fe3� ESR intensity calculated [38]to fall above 1000 mT, a range inaccessible to ourelectromagnets. (Note that this situation does notseem to pertain to Fe3� in heavy-metal ¯uorideglasses where crystal-®eld splittings are �10 timesless [39]).

Since the amounts of magnetite we measure inour Haitian tektites account for no more than�4% of the total iron, the amplitudes of the g� 4.3signals in these samples should be about propor-tional to the total paramagnetic Fe3� contents,even though we cannot measure them absolutely.Therefore, a comparison of the spectra of Fig. 1(a)and (b) implies that the Fe3� content of our

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 9

opaque tektite glasses may be �4.5 times less thanthat of our dark-yellow ones, leading us to suggestthe possibility that our opaque glasses may bechemically reduced relative to the black glasses ofRef. [37].

4.3. ESR signals of limestones and clays

Limestones are typically composed of CaCO3

(calcite) plus clay minerals and minor detritalquartz [40]. For rocks formed of materials depos-ited on the ¯oors of seas shallower than �4 km[41], the calcite fraction comprises mostly the shellsand secretions of single-cell biota (e.g., zooplank-ton, and planktonic algae) while the clays andquartz derive from weathered rock carried into theoceans by rivers [40,42]. The K/T boundary claysare found [12] to be mineralogically distinct fromthe layers above and below them, being relativelyfree of detrital quartz and largely composed ofsmectite, a clay mineral [43] which can be formedby aqueous alteration of certain types of glasses.The sharp multi-line spectrum centered on g� 2 inFig. 1(d), when examined on an expanded mag-netic ®eld scale, was found to be identical in shapeto that of Mn2� in synthetic calcite powders [20].The same Mn2� spectrum should be easily detect-able in all marine limestones, given its propensityto substitute for Ca2� in CaCO3 and the fact thatthe concentration of manganese in sea water isrelatively independent of time, depth, or geo-graphic location [42].

The calcite fractions of limestones and theirassociated ESR signals can be removed by disso-lution in acid. An HCl-treated K/T-boundary clayfrom Caravaca, Spain, exhibits a ferrite compo-nent in its ESR spectrum, Fig. 1(c), which is vir-tually identical in shape and intensity to thespectrum recorded for the untreated whole rockexcept that the sharp multi-line manganese signalis removed. By contrast, when the boundary clayfrom Gubbio, Italy, was treated in acid, the ferritesignal was reduced by a factor of �5 below that ofthe whole-rock spectrum of Fig. 1(d), leaving asignal (not shown) similar in shape to that of Fig.1(c). We surmise that the magnetic phases in theGubbio clay which succumbed to acid treatmentincluded iron hydroxides, e.g., G�othite (a-Fe-

OOH) [43], which are common HCl-soluble min-erals in clays. Based on a comparison of ESRspectral line shapes, the acid-soluble ferrimagneticminerals in the Gubbio boundary clay (principallyresponsible for the line shape of Fig. 1(d)) maydi�er little from the iron hydroxides present in claytaken from one of the authors' back yards (seespectrum of Fig. 2(e)). Limonite, a common iron-hydroxide-hydrate mineral (see Fig. 2(f)), maycontribute weakly to the spectrum of Fig. 2(e).

The acid-insoluble ferrimagnetic componentspresent in K/T-boundary clays from Caravaca andSopelana in Spain, Gubbio in Italy, and Bidart inFrance all displayed nearly identical ESR lineshapes, i.e., close to that of Fig. 1(c). These lineshapes, and the g values of their zero crossings(�2.13±2.19), di�ered from those of the back-ground signals present in the rocks above andbelow the boundary at both Spanish sites, asepitomized by the spectrum Fig. 2(b) for whichg� 2.04. (Rocks from above or below the K/Tboundary at Gubbio or Bidart were not studied.)Based on these observations, we propose thatspectra of the type shown in Fig. 1(c) may becharacteristic of particular SD ferrites whichoriginated in, and are surviving relics of, impact-derived glasses which have long ago succumbed toaqueous alteration.

Fig. 6(a) shows the FMR spectrum of a par-ticulate component mechanically separated fromthe acid-insoluble fraction of a Caravaca K/T-boundary clay in the following way: The acid-treated and dried sample was placed in a �20 cm-long, vertically oriented silica tube with a glass-wool plug near the top. The tube was then con-nected by a hose and valve to a vacuum pump. Asthe valve was slowly opened, water moleculesoutgassing from the clays levitated a fraction ofthe material into the glass wool where it wascaptured for study. Fig. 6(b) is a computer line-shape simulation carried out by means of an al-gorithm given in Ref. [28] assuming that the FMRspectrum is due to SD ferrite particles (6 60 nm).The parameters used to simulate this room-tem-perature spectrum (primarily g� 2.2; 2K1/Ms�ÿ48 mT, but including smaller contributionsdue to ferrites with the same g value but morenegative values of 2K1/Ms) are in reasonable

10 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

agreement with those for pure synthetic magnetite(g� 2.12 [30], 2K1/Ms�ÿ46 mT [32]) and naturaltitanomagnetites (g� 2.17 [30] and 2K1/Ms�ÿ80mT for 10% Fe2TiO4 substitution [35]). Sincesubstitution of either Ni2� or Mg2� for Fe2� inFe3O4 is known to decrease the absolute magni-tude of K1 [25,26], the parameters used in thesimulation of Fig. 6(b) are inconsistent with ex-pectation for SD (6 60 nm) particles of the Ni-richmagnesioferrites which have been identi®ed inmulti-domain 2 sizes (>1 lm) in numerous K/T-boundary clays and attributed to aerodynamicablation products of infalling impactor(s) [14±17].Thus, the contribution of `cosmic' ferrites to thespectra of Figs. 1(c) and 6(a) may be minimal.

The `®ne-structure' modulation seen imposedupon the broader spectral envelope of Fig. 6(a) isattributed to the presence of an insu�cient num-ber of ferrite particles to de®ne a smooth powderpattern and a ®nite number of di�erent ferritecompositions with di�ering values of 2K1/Ms (ascontrasted with the smooth bell-shaped distribu-tions of 2K1/Ms values observed for ferrite parti-cles precipitated in homogeneous glasses, e.g., inRef. [46]). The simulation of Fig. 6(b), accom-plished with a coarse grid in solid-angle space andjust a few discrete anisotropy constants, con®rmsthis conclusion.

The temperature dependence of the intensity ofthe signal of Fig. 6(a) is plotted as the triangles inFig. 4. These data, pertaining to the levitatedfraction of acid-insoluble Caravaca boundary clay(vide supra), match well with the predicted tem-perature dependence of 4.6 nm magnetite particles(continuous curve) generated by means of Eq. (2).On the other hand, the intensity of the spectrum of

the residual fraction of this acid-insoluble Cara-vaca sample (squares in Fig. 4) follows the calcu-lated curve for 3 nm magnetite at highertemperatures but, as indicated by the dashedcurve, there is evidence of an additional phase witha magnetic transition near 325 K. We suspect thatit is fortuitous that this temperature happens to beclose to the N�eel point of G�othite (�380 K) [47],since most iron hydroxides originally present in thesample should have been removed by the HCltreatment. In any event, the ESR intensity of the(acid-washed) Haitian opaque tektite glasses (dia-monds in Fig. 4) follow the calculated curve for 3nm magnetite over the entire range of temperaturestudied. Recent M�ossbauer studies [37] of theHaitian tektites carried out at 78 K demonstratedthe absence of magnetite particles larger than �10nm. M�ossbauer measurements at liquid helium

2 Given that multi-domain broadening e�ects for magnetite

lead to spectra resembling that of Fig.2(d) [24,44,45], it is clear

that particles >1 lm cannot be contributing greatly to the

essentially SD FMR signals of Figs. 1 or 6. A small hysteresis

near zero ®eld seen in Fig. 1(e) may be due to a small fraction of

the magnetite being present as few-domain (60 < d <100 nm)

particles in analogy to the case of 2-domain particles of metallic

iron in lunar glasses [44]. In Fig. 1(e), the dashed curve was

obtained during the ®rst magnetic ®eld scan; the solid curves

were recorded for subsequent scans, one of them after rotating

the sample 180o.

Fig. 6. Experimental (a) and computer simulated (b) X-band

ESR spectra of single-domain ferrite particles in a mechanical

separate of acid-insoluble clay from the K/T boundary in Ca-

ravaca, Spain. Fine structure `modulation' riding on top of the

central part of (a) is believed to be an e�ect of an insu�cient

number of magnetic grains to give a smooth powder pattern.

Noise riding on the simulation (b) results partly from an at-

tempt to simulate a small number of grains and partly from the

Monte-Carlo method of simulating the Lorentzian line broad-

ening (width 44 mT).

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 11

temperature would be necessary to con®rm theexistence of 3 nm magnetite particles [45].

4.4. FMR read-out of the record in the rocks

Fig. 7(a) illustrates the variation of SD FMRintensity per unit mass of whole rock (i.e., cal-cite + clay) as a function of sampling height, h,across the K/T boundary at Caravaca, Spain.Here, a height interval of 1 cm represents �1700years in geologic time [14], and h� 0 correspondsto the K/T boundary as de®ned by the iridiumlayer [1,2,14], as well as by a sharp peak in theconcentration of Ni-rich `cosmic' ferrite particles

in sizes >1 lm [14]. The non-zero `background'intensity apparent in Fig. 7(a) above and below theK/T boundary is associated with FMR signalsessentially identical with the one illustrated in Fig.2(b). We believe it is important to understand theorigin of this qualitatively di�erent `background'FMR signal, particularly in view of the fact thatan analogous background was not found in SEM/EDS searches for Ni-rich ferrite particles >1 lm[14±17]. Since the latter surveys deliberately ex-cluded Ni-poor ferrite particles of likely terrestrialorigin, the default view would be that the presentbackground signals are due to SD particles ofterrestrial magnetite. However, the symmetricalline shape of Fig. 2(b) does not match the classicalasymmetrical shape expected for dilute assem-blages of SD particles of Fe3O4 such as that of Fig.1(e), and the room-temperature g value seems tobe wrong (being �2.04 instead of falling in therange �2.12±2.17 for synthetic and natural mag-netites, respectively [30]). Hence, we consider be-low the possibility that the background spectrumof Fig. 2(b) might be due to `cosmic dust' (mi-crometeorites which bombard our planet at a rateof �30 Gg [48] to 78 Gg [49] per year).

The background resonance of Fig. 2(b) super-®cially resembles the spectrum of the Allendemeteorite fusion crust, Fig. 2(a), except that thelatter has a much larger e�ective g value (�2.5)than the former (�2.04). In general, the g values offerrites are the weighted averages of the g values ofthe magnetic transition-metal ions found on the Aand B sites. The room-temperature g values foriron-group ions on the octahedral (B) sites are 2.00for Fe3�, 2.12 for Fe2�, 2.3 for Ni2�, and 1.97 forCr3� [25,26,50]. The spinels formed in meteoritefusion crusts (and in cosmic dust) comprise solidsolutions of eight end members, including 22 to 54(57) mol% Fe3O4, 29 to 61 (23) mol% MgFe2O4, 9to 11 (4) mol% NiFe2O4, 1 to 4 (3) mol%MgAl2O4, and 1 to 3 (3) mol% FeCr2O4 [15]; (thenumbers in parentheses are for cosmic dust). TheFe3�/Fetotal ratios of extraterrestrial materials en-tering the earth's atmosphere at speeds >11 km sÿ1

(escape velocity [10]) are determined by the alti-tudes (and hence oxygen partial pressures) atwhich they are decelerated and melted by aerody-namic friction [15]. Micrometeorites are deceler-

Fig. 7. FMR intensities (a) and carbonate contents (b) of a

series of whole-rock samples transecting the K/T Boundary at

Caravaca, Spain. Data of (a) represent amplitudes of the ESR

derivative spectra measured at a ®xed value magnetic ®eld (225

mT) selected to be representative of the FMR intensity of sin-

gle-domain ferrites and to exclude the paramagnetic resonance

spectrum of Mn2� in CaCO3 (see Fig. 1(d)). Errors along the

horizontal axes are in all cases about the size of the data points.

Sampling increments on the vertical axis were equal to the size

of the data points at h�+5, 0,ÿ1, andÿ3 but about twice the

size of the data points at the other heights. Height h� 0 cor-

responds to the K/T boundary as identi®ed both biostrati-

graphically and by large Ir and Ni-rich spinel anomalies [14].

Geologic time increases from bottom (earliest) to top (latest),

with 1 cm in column height corresponding to �1700 years of

sedimentation at Caravaca [14].

12 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

ated in the upper atmosphere and hence are lessoxidized (leading to smaller MgFe2O4 contents)than fusion crusts and ablation droplets fromlarger meteorites [15].

We now consider a possible explanation of therelatively large g value (�2.5) exhibited by the SDferrites in the Allende fusion crust by taking intoaccount their normative composition, which in-cludes 36% Fe3O4, 38% MgFe2O4, 11% NiFe2O4,4% MgAl2O4, and 3% FeCr2O4 [15]. It can be re-called that, for inverse spinels, the Fe3� (and Cr3�)ions are partitioned approximately equally be-tween A and B sublattices and are antiferromag-netically aligned so that their magnetic momentstend to cancel [25,26]. Thus, if the Allende-fusion-crust ferrites are presumed to be ideal inversespinels, they would possess magnetic momentsarising only from Fe2� (in Fe3O4 and FeCr2O4)and Ni2� (in NiFe2O4), all located on B sites. The gvalue for this situation can be calculated from theformula [26,50]

geff �P

i wigiSiPi wiSi

; �4�

where the summation is taken over all magneticion types on the B sublattice except Fe3� and Cr3�,Si and gi are, respectively, the spin and g value ofion type i, and wi is the weighting factor deter-mined by chemical analysis. Using the g values andnormative compositional data cited above andtaking S� 2 for Fe2� and S� 1 for Ni2�, thevalue of geff obtained by means of Eq. (4) is �2.14± much too small to match our observation.However, this calculation neglects the chemicaldisorder quenched into real ferrites, which is inturn a function of the di�erent types of metal ionsincorporated [25,26]. It has been shown that the gvalues of real ferrites with as many as three typesof ions can be calculated as functions of quenchtemperature provided that the g values of each ofthese ions are known for both the A and B sites[51]. For comparison with experiment, the exampleof NiOáFe�2ÿt�AltO3 was examined [51], leading tothe determination that Ni2� ions on A sites arecharacterized by g� 4.0. While the larger numberof cation types (seven) in the Allende fusion-crustferrites clearly precludes a g-value calculation in

the present case, it seems noteworthy that themeasured value for an Al-containing nickel ferritewith t� 0.25 was geff � 2.7 [51]. Given that morethan enough aluminum is present in the Allendeferrite compositions to support formation of nickelferrites with t� 0.25, we suppose that Ni2� ions inA sites are responsible for the large positive g shiftof the FMR spectrum of the Allende fusioncrust. 3

The micrometeorites which comprise the cosmicdust contain 2±3 times less Ni than typical mete-orite fusion crusts [15]. Thus, other conditionsbeing equal (e.g., quench rates from the melt), anyprecipitated SD ferrites in micrometeorites shouldbe characterized by g values closer to 2 than is thecase for the Allende fusion crust. It is an openquestion, however, whether these g values could beas low as the value (2.04) measured for back-ground signals, such as the one of Fig. 2(b), arisingfrom acid-insoluble fractions of limestones notfrom the K/T boundary.

Assuming a world-wide ¯ux of cosmic dust of78 Gg per year [49] and an estimated depositionrate of limestones at Caravaca ca. 65 Ma ago of�0.6 cm kaÿ1 [14], the acid-insoluble fractions ofthe Caravaca rocks above and below the K/Tboundary would contain �4 ´ 10ÿ5 g/g of cosmicdust. By comparison, the admixture of Allendemeteorite fusion crust (see spectrum of Fig. 2(a))required to account for the FMR intensity of thebackground signal in the Caravaca clays (Fig.2(b)) would be �1.6 ´ 10ÿ3 g/g. This factor-of-40discrepancy might seem to weigh heavily against acosmic-dust origin for the background signal of

3 Another conceivable explanation for this large g shift would

be the interfering contribution of a multi-domain (MD)

spectrum arising from those ferrite particles in sizes >1 lm

shown to exist in meteorite fusion crusts [15]. Presumably, this

MD component would have a shape similar to that illustrated

in Fig. 2(d). However, we have tried without success to ®t the

Allende fusion-crust spectrum of Fig. 2(a) with a linear

combination of the spectra of Fig. 2(b) and (d). Thus, while

there must exist an underlying MD spectrum which contributes

at least slightly to the spectrum of Fig. 2(a), we conclude that:

(i) SD ferrite particles exert the dominant in¯uence on the

Allende fusion-crust ESR line shape and (ii) the measured value

of g� 2.5 is typical of these SD particles and is not an artifact

superimposed by the co-present MD particles.

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 13

Fig. 2(b), even though recent evidence [52] hasbeen interpreted as indicating that the in¯ux ofmeteoroids may be larger than previous estimates.However, the additional possibility remains thatmicrometeorites in the size range �10±100 lm maycontain larger mass fractions of single-domainferrites than do the fusion crusts of larger bodiessuch as Allende whose decelerations take place atlower altitudes. Clearly, an FMR study of a clay-free separate of cosmic dust (e.g., as recovered bymelting glacial ice from arctic regions [53]) wouldbe the best means to determine the g values of anySD ferrites in them, together with their signalstrengths per gram. Until such data are obtainedwe reserve judgement on whether or not the FMRbackground signals of limestones away from theK/T boundary arise from cosmic dust.

Fig. 7(b) shows that the carbonate fraction, f, ofthe rocks at Caravaca undergoes a precipitousdrop in the interval h� 0 to h�+3 cm. This de-crease is due principally to the extinction of thecarbonate-producing marine protozoa in this in-terval of geologic time [1,2,14]. We expect that thedeposition rates of clays resulting from continentalweathering and erosion were una�ected by thevicissitudes of the marine biota (although theymight have been momentarily increased as a resultof the destruction of continental ¯ora in wild®resignited by reimpacting K/T crater ejecta [54]). Inany event, if we assume for the sake of argumentthat the `background' ferrite phases are mineralcomponents of the rocks from which the clayswere derived (as opposed to being cosmic dust),then the total amounts of these phases in anylimestone sample would be simply proportional toits clay fraction, 1ÿ f. In fact, within experimentalaccuracy, the FMR intensity plotted in Fig. 7(a)appears to be proportional to the clay fraction atCaravaca everywhere except at the K/T boundary.Indeed, at h� 0 � 1 cm the FMR intensity in-creases above background by a factor of �14,whereas 1ÿ f increases only by a factor of �2.9(and at h�ÿ1 � 1 cm the FMR intensity increasesby a factor of �2 while 1ÿ f increases by a factorof �1.2). Thus, the amounts of SD ferrites de-tected by ESR in materials from the K/T boundaryat Caravaca (and also at Sopelana, for which wehave recorded a similar intensity spike at

h� 1.5 � 0.5 cm) cannot be explained in terms ofuniformitarian geologic processes.

We conclude that K/T-boundary SD ferriteshaving FMR spectra similar to that of Fig. 1(c)probably had their genesis in the K/T impactevent. Taking into consideration the fact that theirline shapes and g values (vide supra) are consistentwith those of terrestrial magnetites, we infer thatthese SD `marker' ferrites are not primarily de-rived from extraterrestrial materials. Rather, wepropose that they were precipitated in glassy ejectafrom the Chicxulub crater. Thus, our experimentmay be less de®nitive as an indicator of majorimpacts of extraterrestrial bodies on the earth thanis the iridium anomaly [1,2] or the sharp spike inthe number density of Ni-rich `cosmic' spinels [14±17] found at K/T boundary sites. However, ourESR methods may prove useful to the emerging®eld of global ballistic sedimentology [55], i.e., forestimating the world-wide distributions of ejectaresulting from major cratering events. For exam-ple, we propose that the 0.045 � 0.020 wt% SDmagnetite we measure in the Caravaca boundaryclay results from an approximate 65:35 mixture oflocally derived clay sediments with materials bal-listically emplaced as glasses containing 0.13 � 0.03wt% SD magnetite (i.e., glasses similar to oursample of opaque Beloc tektites), since weatheredto clays.

4.5. ESR spectra of some K/T spherules

ESR spectra were recorded for material from asingle cm-sized spheroid collected from a K/T-re-lated spherule bed at El Guayal, Mexico [56], andalso for a 300 mg unsorted aliquot of materialfrom the Bass River, NJ, K/T spherule layer [19].The amounts of SD ferrites detected in both thesesamples were comparable to or lower than thebackground levels in the Spanish limestones. Infact, the broad spectrum of the acid-insolublefraction of the Bass River spherules (Fig. 2(c))resembles the Caravaca background spectrum ofFig. 2(b), except that the g� 2 part is smaller by afactor of �0.67 and the g value of the derivativezero crossing has shifted from �2.04 to �2.11. Thespectrum of the whole-rock Guayal spherule ma-terial had no components clearly attributable to

14 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

ferrites; rather, its ESR spectra are characteristicof calcite (e.g., of Mn2� impurities therein [20]) andof quartz and `glass'. The ubiquitous g� 4.3 res-onance, typical of Fe3� in glasses, was present inboth spherulitic samples. In each of these cases,this g� 4.3 signal was broader than those recordedfor australasian tektite glasses (e.g., Fig. 2(g)) andin fact resembled more the g� 4.3 lines recordedfor the clay fractions of the Spanish limestones.The amplitude of the g� 4.3 line in the Caravacalimestones (data not shown) correlated moderatelywell with the clay fraction, 1ÿ f. We supposetherefore that the g� 4.3 component in the claysarises from Fe3� present in some acid-insolubleclay mineral of terrestrial origin ± or from glassycomponents of cosmic dust.

Fig. 8 shows that the part of the spectrum of theGuayal spheroid near to g� 2 includes the signalsof E0 centers [57] in quartz and of the so-far-un-identi®ed `N2' center commonly observed in nat-ural and (irradiated) synthetic calcites (e.g., [58]).Both these signals are known to be induced in theirrespective host minerals by decays of naturallyoccurring 238U and 232Th. The dashed curve in Fig.8 approximates the contributions to the spectrum

of peroxy radicals, which are radiation-induceddefects in glassy silica [59], as well as in naturalquartz [60]. For comparison, the spectrum of c-ray-induced E0c centers in a high-purity silica glassis also shown in Fig. 8. We have computer simu-lated the E0-center signal of the Guayal spheroidusing the published principal-axis g values for theE01 center in single-crystal a quartz [61], con®rmingthat the SiO2 phases in the spheroid are polycrys-talline as opposed to glassy, since statistical dis-tributions of g values are required to simulate thespectra of various E0 centers (such as E0c) inamorphous forms of silica [62]. Using the previ-ously determined g values of the E01 center inquartz [61] as a point of reference allowed us todetermine g values of the centers in the co-presentcalcite components of Fig. 8 to within an accuracyof �0.0001.

The ESR spectrum of an unsorted sample ofBass River spherules exhibited an N2 componentthat was �2 times greater per unit mass than thatof the Guayal spheroid, although by acid disso-lution the calcite fraction was found to be �0.35 inboth samples. On the other hand, there were �10times fewer E0 centers in the Bass River material

Fig. 8. X-band ESR spectrum of a 65-million-year-old spheroid from El Guayal, State of Tabasco, M�exico, recorded at room tem-

perature. This material, shown by X-ray di�raction to comprise polycrystalline quartz and calcite, exhibits a `back-to-back' pair of

resonances arising from the E01 center in a quartz [57,61] and the N2 center in calcite [58], superimposed on part of the spectrum of

peroxy radicals in quartz (approximated by the dashed curve). Each of these signals was induced in its respective host material by

natural radiations. For comparison, the inset shows the spectrum of c-ray-induced E0c centers in synthetic silica.

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 15

than in the Guayal spheroid, implying that theirrespective quartz contents may di�er by this fac-tor. A major component of the Bass River spher-ules is thought to be clays (possibly smectite) [19].

4.6. Photomicroscopy, X-ray di�raction and SEM

Inspection of the photomicrographs of Fig. 3give insight into the mineralogy of the dark-matrixmelt rock from the PEMEX Y6-N19 core. Undercrossed polarizers, the dark matrix was determinedto be polycrystalline with crystallite sizes 6 10 lmand to contain partially digested grains of quartz,feldspar (Fig. 3(c)) and other minerals in the sizerange �0.1±5 mm. The quartz grain in Fig. 3(b) isseen to be surrounded by double halos; the darker,inner-most corona is identi®ed as pyroxene, inagreement with the conclusions of other workers[9]. The lighter corona may be clear glass depletedin the iron lost to the pyroxene [10]. Veins of darkmaterial penetrating the fractured quartz singlecrystal in Fig. 3(d), when inspected under cross-polarized illumination, appeared to be isotropicand hence still glassy. The opaque grains �10±150lm seen in Fig. 3(c) appeared bright white in re-¯ected light and may be magnetite. (The magnet-ically pervasive 60 nm magnetite particles cannotbe seen in visible-light microscopy.)

X-ray di�raction showed the principal crystal-line phases in the cm-sized Guayal spheroid to becalcite and a quartz, con®rming the inferencesdrawn above from ESR. However, the transmis-sion photomicrograph of Fig. 9(a) depicts a com-plex agglomerate of individual fragments ofdiverse shapes, sizes and colors with concentriczoning patterns (the geometric center of thespheroid is near the lower left). Most of the brightspots ranging from �40 to �70 lm in diameterseen in this image are transparent mineral frag-ments equal to or larger than the thickness of thinsection (�40 lm). Although some of these grainsmay be quartz, we were unable to conclusivelyidentify any of them by inspection under cross-polarized light. Fig. 9(c) shows a hollow spherule�33 lm in diameter, while arcuate features seennear the bottom of Fig. 9(d) appear to be frag-ments of hollow spherules whose original diame-ters were �40±60 lm. Fig. 9(d) represents the same

®eld of view as Fig. 9(b) but is imaged in coaxiallyre¯ected light. Since frontal illumination has thee�ect of obscuring most mineral grains smallerthan the sample thickness, Fig. 9(d) reveals apervasive inter-grain matrix, textureless on thisscale of magni®cation.

Fig. 10 reproduces an SEM image encompass-ing the same ®eld of view as Figs. 9((b),(d)) andindicates the mineralogical natures of some of theobjects in these views as inferred from their EDSspectra. The rhomboidal grain prominent in thephotomicrographs of Figs. 9((b),(d)) was di�cultto discern against the background of the inter-grain matrix when imaged by SEM in the sec-ondary-electron detection mode wherein contrastis determined by di�erences in atomic mass. Thiscentral grain, outlined by the dashed rhombus inFig. 10, was determined by EDS to be dolomite,CaMg(CO3)2. Several other clasts which areclearly visible in Fig. 9(d) but exhibit poor contrastin Fig. 10 were also identi®ed as consisting pri-marily of dolomite. The arcuate structure to thelower right of Fig. 10 probably is (or was) glass,based on its cationic composition which includesSi, Mg, Al, Ca, and possibly Na and Fe. Surpris-ingly, however, the morphologically similar struc-ture to the lower left of the ®gure is calcite. Alarger, irregularly shaped calcite grain is identi®edbelow and to the right of the dolomite rhomboid.One of the bright spots �4 lm in diameter seen inFigs. 9((c),(d)) was examined by EDS and found todisplay a series of strong lines due to lanthanumand cerium and a small but discernable peak dueto phosphorus. Thus, we identify this particle and,tentatively, the rest of the 4 lm bright specks asmonazite (Ce, La, Th)PO4. The arrowhead-shapedobject to the left center of Fig. 10 is composi-tionally complex, including internal clasts of do-lomite, calcite, and glass and a rind of MgO-richaluminosilicate glass. Finally, focussing the elec-tron beam on areas of the inter-grain matrix freeof resolved grain structure (located within thedashed ovals in Fig. 10) gave EDS spectra con-sistent with �95% silicon dioxide and �5% calcite.We suggest that most of this pervasive micro-crystalline SiO2 binder is authigenic, i.e., that itdeveloped in place after deposition of the spherulebed. In this view, the inter-grain material would be

16 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

¯int, i.e., quartz precipitated from solutions whicheventually penetrated void spaces inevitably pres-ent in spheroids which had accreted at tempera-tures low enough (<900°C) to avert decompositionof the included calcite grains or remelting of theincluded glass spherules.

5. Conclusions regarding the geology of major

impacts on the earth

Computer modeling of extreme cratering events[5,63] indicate that the Chicxulub crater-¯oor

glasses and breccias should comprise shock-meltedmaterial from a transient crater punched as deeplyas 50 km into the earth by a �10 km-diameterimpactor arriving with a velocity �25 km sÿ1.After vaporization of the impactor, the transientcrater ¯oor would, according to some calculations[5,63], rebound in the shape of a massive `droplet'to an altitude of �50 km. Successive fallbacks andrebounds of this central peak are calculated to bedamped so rapidly that the crater reaches its �1km-deep `®nal' morphology in a time of only �10min. Thus, by glass-making standards a result ofthe Chicxulub impact would have been a very large

Fig. 9. Photomicrographs of a Guayal spheroid: (a) and (b) views in transmitted plane-polarized light; (c) and (d) views in coaxially

illuminated re¯ected light. Photomicrographs (b) and (d) represent approximately the same ®eld of view. Bright spots in (a) and (b) are

most likely crystals of calcite, dolomite, or quartz; those in (c) and (d) are most likely monazite.

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 17

quantity of extremely poor grade glass. The `holdtime' at the ®nal melting temperature(s) wouldcertainly not have been long enough to have ho-mogenized a glass batched from poorly co-mminuted andesite, limestone, dolomite, andevaporites (mainly CaSO4). Indeed, the claststhemselves, being at lower initial temperatures,tend to exert a quenching e�ect which slows theirdigestion and frustrates gravitational separation ofany partially crystallizing phases [36]. The heter-ogeneous nature of the crater-¯oor dark-matrixmelt rock apparent in the photomicrographs ofFig. 3 is consistent with this expectation, as is the(unchanged) oxidation state of the iron determined

here from the FMR intensity of the precipitatedSD magnetite.

Our ESR, photomicroscopic, and SEM/EDSresults discussed above are consistent with the as-sessment of Grajales and coworkers [56] that theGuayal spheroids are accretionary lapilli. Wesuppose that these lapilli condensed within a warm®reball [3] composed of vaporized calcium car-bonate and water with entrained grains of pul-verized platform rocks (calcite, dolomite, andevaporites) and glass microspherules swept out ofthe ejecta curtain or condensed from the coaxiallyrising hot ®reball. We remark that the Guayalspheroids share their size and (2:1) aspect ratio

Fig. 10. Scanning electron microscope image encompassing the same ®elds of view as Figs. 9((b) and (d)). Dashed polyhedra highlight

three crystal fragments which are readily discerned in Fig. 9(d) but exhibit low contrast under SEM viewing. Dashed ovals are areas of

the inter-grain matrix selected to be free of resolvable inclusions. The indicated mineral phases are inferred from EDS determinations

of major-element chemistry.

18 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

with the Australite button tektites, which are al-uminosilicate glass spheres sculpted by unidirec-tional aerodynamic friction (e.g., [64,65]). Wesuggest that both types of objects self-assembledinto nearly identical aerodynamic shapes, the tek-tites by remelting and viscous ¯ow of the leadingsurfaces during atmospheric re-entry of solidi®edspherical droplets of glass and the Guayal spher-ules by attitude-selective accretion of particulatematerial during ®reball-borne ascent.

El Guayal is located in the State of Tabasco,M�exico, about 500 km southwest of the Chic-xulub epicenter. This site is likely to have beensubmerged in shallow coastal waters at the timeof the impact [56,66]. The Guayal spheroids,together with minor amounts of glass andshocked quartz, were discovered in a bed severalcentimeters thick located about �2 m below theK/T boundary, as determined biostratigraphically[56] and further demarcated by maxima in mag-netic susceptibility and induced remanent mag-netization likely associated with SD magnetite orother low coercivity ferrites [67]. This spheroidbed is sandwiched between two sandstone layers,each �2 m thick [56], which in turn overlay �50m of calcarious breccias containing limestoneclasts of both shallow- and deep-water origins[56]. We tentatively propose that these breccias,resting on top of undisturbed late-Cretaceousshallow-water limestones, comprise Chicxulubcurtain ejecta greatly diluted by local sea-¯oorsediments jointly emplaced by a nearby second-ary cratering event (reimpact of a fragment ofprimary curtain ejecta >10 m). The chronologyof the emplacement of these `K/T-transition'rocks at El Guayal is tentatively interpreted asfollows: (i) primary and secondary crater ejectaimpact and churn up the sea ¯oor, creating a 50m-deep layer of breccia within �10 min; (ii)earthquake-triggered mass ¯ows transport anddeposit sand from near-shore areas [68]; (iii) theGuayal accretionary spheroids impact and settlethrough the water column; (iv) waning tsunamiwaves crisscrossing deeper parts of the Gulf ofMexico deposit additional ®ne sand for manyhours; and (v) hot-®reball ®ne dust (enriched inIr and Ni-magnesioferrites) falls out of thestratosphere over a period of weeks.

Only the warm-®reball phenomenon postulatedby Alvarez et al. [3] seems capable of explainingthe nature and stratigraphic position of the Guayalspheroids, since only this process could supportaccretion of fragile calcite/dolomite/glass lapilliand provide a mechanism for launching them intothe relatively high-velocity, high-angle trajectories[55] required to delay their fallback (potentially formore than 1 h [3,55]) until after settling of themassive breccia layers created by reimpactingChicxulub curtain ejecta and the superposition ofsand layers transported by seismic mass ¯ows.

Acknowledgements

The authors are greatly indebted to a number ofindividuals for the provision of samples. Speci®-cally, we wish to thank E. Robin (Centre des Fa-ibles Radioactivit�es, Lab. CEA/CNRS, France)for K/T boundary rocks from Spain and France,L. Mar�õn (Inst. de Geof�õsica, UNAM, M�exico) forsamples of the PEMEX Y6-N19 drill core andBeloc tektites, J. Urrutia-Fucugauchi (Inst. deGeof�õsica, UNAM, M�exico) for the Guayal sphe-rule, the Gubbio clay sample and other K/T-boundary materials, R.K. Olsson (Department ofGeological Sciences, Rutgers U.) for the BassRiver spherules, and T. McCoy (Department ofMinerals, Smithsonian Museum of Natural His-tory) for the Allende fusion crust sample. Wefurther thank Dr McCoy for his assistance withthe photomicroscopy, Professor Urrutia for kindlymaking available what is known about the stra-tigraphy of the El Guayal site, and G. Villalobos(Naval Research Laboratory) for SEM/EDSmeasurements.

Appendix A

The origin of Eq. (2) can be understood byreference to the in-depth development of themagnetic resonance phenomenon in the book byAbragam and Bleaney [69], whose treatment of thesubject will be sketched below in a most minima-listic fashion. Assumed is a quantum-mechanicalsystem composed of an aggregation of atoms ormolecules each having the same spin J. The spin

D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22 19

vector J is quantized along the z direction de®nedby the orientation of an applied static magnetic®eld H. The only matrix element of Jz isáM|Jz|Mñ�M. The energy of a stationary state isWM �ÿgbHM, where H is the magnitude of H.Upon exposure to a weak oscillating magnetic ®eldof magnitude H1 perpendicular to H, transitionsare induced between magnetic sublevel M and theadjacent levels M � 1. The transition probabilityper unit time is given by

wM�1$M � 2p3�gbH1=h�2

�hM � 1jJ�jMi2f �m�; �A:1�where f(m) is a line-shape function and J� areraising and lowering operators. The matrix ele-ments of J� are given by áM � 1|J�|Mñ�p

{J(J + 1)ÿM(M � 1)}, leading to the selectionrule M M M � 1. The oscillating magnetic ®eld in-duces transitions in both directions with equalprobability, but in general there will be a net ab-sorption of energy because the states with lowerenergy have greater populations if relaxation issuitably e�cient. Hence, considering only transi-tions M M Mÿ 1 and assuming no signi®cant de-parture from thermal equilibrium, the netabsorption of energy per unit time between anadjacent pair of stationary states can be expressed:

dW =dt � wMÿ1$M�hm��NM ÿ NMÿ1�� wMÿ1$M�hm�� fexp�ÿWM=kT �ÿ exp�ÿWMÿ1=kT �g;

�A:2�where NM and NM ÿ 1 are the populations of thelower and upper states, respectively. In principle,the transitions given by Eq. (A.2) can be summedover all values of M to get the total power ab-sorption. Abragam and Bleaney [69], in treatingthe case of a circularly polarized microwave ®eldH1, made several approximations based on theassumption that hm/kT� 1 which obviated theneed to perform the sum exactly. This led to thefamiliar result

dWdT� N2p3m2�gbH1�2J�J � 1�f �m�

3kT� 4p3m2v0H 2

1 f �m�; �A:3�

where N is the total number of centers of spin Jand v0 is the static susceptibility which can bemeasured by non-resonance methods in the hightemperature limit (hm/kT� 1).

In Ref. [27], Griscom undertook to obtain aclosed-form expression for the sum of the terms ofEq. (A.2) over all values of M in the manifold of J,properly normalized by division by the partitionfunction Z �P exp�ÿWM=kT �:dWdT� 2p3m2�gbH1�2f �m�

XJ

M�ÿJ�1

fJ�J�1�ÿM�Mÿ1�g eMx ÿ e�Mÿ1�x� �XJ

M�ÿJ

eMx: �A:4�,

(Here again, x� hm/kT). It was perceived [27] thatEq. (A.4) could be reduced to sums of a geometricprogression and two additional series identi®ableas the ®rst and second derivatives of the ®rstgeometric progression. Since closed-form expres-sions for the sums of geometric series are wellknown (and the particular one of concern herehad been used in the classic derivation of theBrillouin function BJ (Jx)), it became possible toobtain closed-form expressions for the sums of theother two progressions by di�erentiation of theoriginal closed-form expression. Nevertheless,care was taken to prove the correctness of thesederived formulae by the method of mathematicalinduction (see, e.g., [70]). Disregarding the factor2p3m3(gbH1)2f(m) in Eq. (A.4), the result after somerearrangement of terms is that given by Eq. (2). Itshould be noted that this function is 2J times thenormalized version of the same function given inRef. [27]. Also, it is pointed out that the use ofEq. (3) to make J a function of temperature issuperior to the approximate method proposed inRef. [27] for taking into account the temperaturedependence of Ms when treating ferromagneticparticles.

Eq. (2) reduces identically to GJ (x)� tanh(x/2)for the case J� 1/2, thus agreeing with the well-known exact result (e.g., [69]) in the low-spin limit.It has been noted [27] that Eq. (2) approaches theBrillouin function in the low temperature limit

20 D.L. Griscom et al. / Journal of Non-Crystalline Solids 253 (1999) 1±22

(hm/kT� gbH/kT� 1), a seldom-discussed regimein the context of magnetic resonance intensity.

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