Nanostructures in the deep xenolite before and after straining

731

ISSN 1069-3513, Izvestiya, Physics of the Solid Earth, 2009, Vol. 45, No. 9, pp. 731–739. © Pleiades Publishing, Ltd., 2009.Original Russian Text © G.A. Sobolev, S.M. Kireenkova, Yu.A. Morozov, A.I. Smul’skaya, V.A. Tsel’movich, V.I. Vettegren, V.B. Kulik, 2009, published in Fizika Zemli, 2009, No. 9,pp. 3–11.

INTRODUCTION

It is known that there is an interaction of the pro-cesses occurring in rocks and minerals at different scalelevels [Sadovskii and Pisarenko, 1991]. This can alsobe generalized on the process of the development offractures under high thermodynamic parameters. Inconnection with this the problem of studying the struc-ture at the nanolevel is of urgent importance in the earthsciences [Bogatikov, 2003; Kireenkova and Sobolev,2005]. We note that there are very few studies in thisfield and they are at an initial stage of development[Akimtsev et al., 2004; Sobolev, Vettegren, and Kireen-kova, 2007a; 2007b; Sharkov et al., 2003].

The purpose of this work consisted in the search fornanocrystals in deep rock, their identification, the esti-mation of their sizes, internal stresses in nanocrystals,and changes in their properties under the effect ofquasihydrostatic pressure.

SUBJECT OF STUDY

A sample of deep rock, mantle xenolite from thekimberlitic tube Obnazhennaya, located on the north ofthe Yakut kimberlitic province, was selected as the sub-ject of this study. A wide set of deep nodular structuresis discovered in the tube, such as peridotites, garnet-pyroxene rocks, mantle eclogite and others, which werestudied by many researchers [Bobrov et al., 2003a;Lutts, 1968; 1974; 1975; Nikitina, 1993; Simakov,2007; Sobolev, 1968; Udovkina, 1985].

For comparison, a sample of the same rock was stud-ied, subjected to quasihydrostatic pressure of 2.5 GPa.

PETROGRAPHY, MINERALOGY, AND FORMATION CONDITIONS

The sample represents the unstratified rock with aspotted structure. The granularity effect is caused bythe nonuniform distribution of garnet and pyroxenes ofdifferent granularity, from the fine-grained to giant-grained ones. The structure is porphyritic, and is mainlyhypidiomorphic due to the weakly expressed idiomor-phism of pyroxenes; in places there is a reaction, whichfixes the different superimposed processes. Theyinclude the structures of the breakdown of the solidsolution in pyroxenes, lamellas (interpositions) oforthopyroxene in clinopyroxene and vice versa, andalso the recrystallization of clinopyroxene in the fine-grained aggregate, developed along the small cracksand along the grain boundaries of late garnet and sec-ondary minerals: amphibole, biotite, serpentine, apa-tite, and ore minerals. The structure of the samplesbefore and after compression can be seen in the photo-graphs of the sections (Figs. 1 and 2). The average com-position of the rock is 40–50% garnet, 45–55% cli-nopyroxene, and 10–15% orthopyroxene. The chemicalcomposition of the rock is presented in Table 1.According to the ratio of MgO/Fe

2

O

3

+

TiO

2

/

Al

2

O

3

thiscomposition occupies an intermediate position betweenperidotites and eclogites and it is close to the garnetif-erous pyroxenites. It differs from the eclogites by itssmaller content of Al

2

O

3

.The rock was studied in the “Borok” geophysical

observatory, of the Institute of Physics of the Earth,Russian Academy of Sciences, on the “Tescan-Vega-II”scanning electron microscope with an INCA Energy450 energy-dispersion microanalyzer (the absorbing

Nanostructures in the Deep Xenolite before and after Straining

G. A. Sobolev

a

, S. M. Kireenkova

a

, Yu. A. Morozov

a

, A. I. Smul’skaya

a

, V. A. Tsel’movich

a

, V. I. Vettegren

b

, and V. B. Kulik

b

a

Institute of Physics of the Earth, Russian Academy of Sciences, ul. Bol’shaya Gruzinskaya 10, Moscow, 123995 Russia

b

Ioffe Physicotechnical Institute, Russian Academy of Sciences, ul. Krasikova 25a, St. Petersburg, 117218 Russia

Received February 25, 2009

Abstract

—A search for nanocrystals in the sample of deep rock, mantle xenolite from the kimberlitic tube, wascarried out. With the use of the Raman spectroscopy method pyrope nanocrystals measuring ~18 nm andomphacite nanocrystals measuring ~13 nm were identified. The dimensions of the crystallographic cell innanocrystals were increased in comparison with macrocrystals. The internal tensile stresses, which could causethese changes, were evaluated by a value of ~1.1 GPa. The action of quasihydrostatic compression pressure witha value up to 2.5 GPa on a change in the structure and properties of nanocrystals was investigated. As a resultof the compression, the sizes of pyrope nanocrystals did not change, but the dimensions of the crystallographiccell increased. The method applied did not make it possible to reliably determine the changes as a result of thepressure of the internal stresses and the sizes of the omphacite nanocrystals.

PACS numbers: 91.60.Mk

DOI:

10.1134/S1069351309090018

732

IZVESTIYA, PHYSICS OF THE SOLID EARTH

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SOBOLEV et al.

current was 0.2 nA and the accelerating voltage was20 kV). The results of the microprobe analysis are pre-sented in Table 2. The studies showed that garnet consists,mainly of pyrope (up to 77 mol %) with an admixture ofalmandine, grossular, and knorringit. Clinopyroxene con-sists of diopside (up to 85%) with an admixture of jadeite,hedenbergite, and tschermakite and it can be related to

omphacite. Orthopyroxene is represented by enstatite,which contains only 5–7 mol % of ferrosilite. The com-positions of minerals from the different xenolites of theObnazhennaya tube are given in the work [Bobrov,2003a]. The garnets of the studied samples are close incomposition to the garnets from the garnetiferouspyroxenites. Consequently, both in terms of its total

2 mm

CPyr

CPyrOPyr

CPyr

OPyr

CPyr

CPyr

OPyr

OPyr

OPyr

CPyr

OPyr

Gr

Fig. 1.

The petrographic section of an undeformed sample made with an optical polarizing microscope. The Nicoles are crossed.Indices of the minerals: (Gr) garnet, (OPyr) orthopyroxene, and (CPyr) clinopyroxene.

Table 1.

Chemical composition of mantle xenolith

Component SiO

2

TiO

2

Al

2

O

3

Fe

2

O

3

FeO MnO MgO CaO Na

2

O K

2

O

% 441.06 00.90 110.30 22.42 110.56 00.18 119.10 88.55 11.10 00.70

CPyr

OPyr

Gr

2 mm

OPyr

CPyrCPyr

CPyrCPyr

Bi

Fig. 2.

Part of the petrographic section of a sample, deformed under a pressure of 2.5 GPa. Designations are the same as in Fig. 1.


Vol. 45

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2009

NANOSTRUCTURES IN THE DEEP XENOLITE BEFORE AND AFTER STRAINING 733

Table 2.

Microprobe analyses of minerals from the garnetiferous pyroxenite of the Obnazhennaya tube

Undeformed sample 3635-1-1

Mineral Garnet Orthopyroxene Clinopyroxene

Number of point

3/1 3/2 4/1 7/1 10/1 1/1 11/3 11/7 12/2 10/2 11/2 11/4 11/5 12/1

Setting Edge Edge Center Center Edge Edge Lamella Lamella Near lamella Edge Edge Near

lamella Center Lamella

SiO

2

41.62 42.71 42.12 42.84 42.88 57.94 58.37 57.29 58.33 54.05 54.43 53.73 53.29 54.48

Al

2

O

3

22.56 22.69 22.97 21.90 21.82 1.23 0.84 1.75 2.23 2.67 3.37 2.74 5.01 3.66

Cr

2

O

3

1.47 1.41 1.47 1.54 1.98 – – – – 1.12 1.11 1.2 1.64 1.25

FeO 7.30 6.60 6.52 7.04 6.90 3.34 4.23 4.77 4.05 1.44 1.37 1.48 1.42 1.22

MgO 21.84 21.97 21.61 21.51 21.47 36.49 36.56 36.19 35.39 16.76 15.85 16.74 15.18 15.67

CaO 5.21 4.63 5.31 5.17 4.95 0.99 – – – 22.89 22.22 22.83 21.82 22.09

Na

2

O

– – – – – – – – – 1.09 1.66 1.29 1.64 1.64

Crystal-chemical coefficients

Si 2.96 3.05 2.98 3.03 3.03 1.97 1.99 1.96 1.98 1.96 1.96 1.95 1.92 1.96

Al 1.89 1.89 1.91 1.83 1.82 0.05 0.03 0.07 0.09 0.12 0.14 0.12 0.21 0.15

Cr 0.08 0.08 0.08 0.08 0.11 – – – – 0.03 0.04 0.04 0.05 0.03

Fe 0.43 0.39 0.39 0.42 0.41 0.10 0.12 0.14 0.12 0.04 0.04 0.04 0.04 0.04

Mg 2.31 2.31 2.28 2.26 2.26 1.85 1.86 1.84 1.79 0.90 0.85 0.90 0.82 0.84

Ca 0.39 0.35 0.40 0.39 0.38 0.04 – – – 0.89 0.86 0.89 0.84 0.85

Na – – – – – – – – – 0.08 0.12 0.09 0.12 0.12

Deformed sample 3635-2-3

Mineral Garnet Orthopyroxene Clinopyroxene

Number of point

16/1 18/3 19/1 20/1 16/3 17/1 18/5 24/1 16/2 17/2 18/4 23/1 24/2

Setting Guest mineral Edge Edge Center Center Near

lamella Edge Lamella Inclusions in orthopyroxene Lamella Edge Edge Near

lamella

SiO

2

42.46 42.73 42.99 42.20 58.49 57.66 58.04 56.84 54.37 53.84 53.98 54.13 53.93

Al

2

O

3

22.92 22.85 22.48 22.99 1.33 2.03 1.03 3.33 2.84 4.01 3.46 2.51 4.94

Cr

2

O

3

1.21 1.15 1.57 1.69 – – – – 0.80 0.91 0.98 0.84 0.99

FeO 7.73 7.12 6.95 6.74 3.70 4.03 4.31 4.41 1.33 1.10 1.44 1.29 1.41

MgO 20.90 21.11 20.54 21.34 36.47 36.29 36.61 35.41 16.6 14.93 16.06 16.62 14.45

CaO 4.77 5.03 5.47 5.04 – – – – 22.63 22.5 22.53 23.42 22.18

Na

2

O

– – – – – – – – 1.44 2.08 1.55 1.18 2.11

Crystal-chemical coefficients

Si 3.00 3.01 3.03 2.98 1.98 1.96 1.98 1.88 1.96 1.94 1.95 1.96 1.94

Al 1.91 1.90 1.87 1.92 0.05 0.08 0.04 0.13 0.12 0.17 0.15 0.11 0.21

Cr 0.07 0.07 0.09 0.09 – – – – 0.02 0.02 0.03 0.02 0.03

Fe 0.46 0.42 0.41 0.40 0.11 0.12 0.12 0.12 0.04 0.03 0.04 0.04 0.04

Mg 2.20 2.22 2.16 2.25 1.84 1.84 1.86 1.80 0.89 0.80 0.86 0.90 0.78

Ca 0.36 0.38 0.42 0.38 – – – – 0.88 0.87 0.87 0.91 0.85

Na – – – – – – – – 0.10 0.14 0.11 0.08 0.15

734


Vol. 45

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SOBOLEV et al.

chemical composition and its mineral composition, therock relates to the garnetiferous pyroxenites, to the typeof xenolites that are in between the ultrabasic peridot-ites and eclogites and which are close to basic ones. Thecomposition of the rock-forming minerals did notchange after the application of hydrostatic pressure.

For determining the conditions of rock formation,the data of pyroxene-garnet thermometers and barome-ters, included in the TPF program [Fonarev et al.,1994], and in the later development of L.P. Nikitina[Nikitina, 1993] were analyzed. The determinationaccuracy of the temperature and pressure amounts

±

50°ë

and

±

0.27

GPa. As the determinations based onthe centers of the grains of the bulk showed, their crys-tallization began at a temperature of

960°ë

and a pres-sure of 3.8 GPa, and it was completed, judging by theequilibria at the interface of the grains, with a tempera-ture decrease of up to

880°ë

and a pressure decrease ofup to 3.5 GPa. The lamellae of orthopyroxene in cli-nopyroxene were formed at a temperature of 880–930

°

C. A secondary garnet at the interface ofpyroxenic grains was formed at a temperature of

780–790°ë

and a pressure of 3.0 GPa.The results obtained are in agreement with the val-

ues of temperatures and pressures, published earlier forthe garnetiferous websterites of the Obnazhennaya tube[Bobrov et al., 2003b], and with the geotherm along theObnazhennaya tube constructed by Nikitina [Nikitina,1993]. The rock was formed in the graphite, but not inthe diamond depth facies.

PHYSICAL PROPERTIES OF ROCK SAMPLESAT HIGH PRESSURES

The quasihydrostatic compression of the sampleswas accomplished in the installation of the cylinder-piston type, with the recording of the propagation timeof the longitudinal and transverse waves by the pulseultrasonic technique by the well-known methodology[Volarovich et al., 1974; Kireenkova and Safarov,1979]. For the study, several sets consisting of two orthree samples with a diameter of 13.5 mm and with aheight of 20 mm, which were cut in three mutually per-

pendicular directions, were prepared. It turned out thatthe samples are highly heterogeneous because of thenonuniform distribution of heterogranular garnet.Therefore, the mean values of several measurementswere used for subsequent analysis. The samples weresubjected to a hydrostatic pressure of 2.5 GPa for 1.5 h.

As is well-known, the basic rock-forming mineralsof mantle rocks are garnet, pyroxene, and olivine. Thetotal content of these minerals in the rocks is 90–95%,which determines the velocity of the elastic waves[Kireenkova et al., 1989]. The xenolite, which was inves-tigated, contains 95% of pyropic garnet and diopside(omphacite). After hydrostatic compression the densitychanged from 3.33 to 3.42 g/cm

3

, the velocity of the lon-gitudinal waves changed from 7.52 to 9.0 km/s, and thevelocity of the transverse waves changed from 4.01 to5.0 km/s.

In the section of the sample, deformed under theaction of quasihydrostatic pressure of 2.5 GPa, it wasrevealed that the coarse lamellae of orthopyroxene inclinopyroxene (penetrating the entire lamellar interpo-sitions with a width of up to 150

µ

m) turned out to betorn into small fragments. This indicates the essentialdeformations, which occurred in the sample under thequasihydrostatic compression, that, obviously, shouldbe confirmed on a larger number of sample sections.

RAMAN SPECTROSCOPY STUDIES

The Raman spectra of the surface layer of the sam-ples were excited by an 16508 Ar

++

argon laser (

Λ

=488 nm, with radiation power of 0.1 W) were recordedon a Ramalog-5 spectrometer in the photon-countingmode with a scattering angle of

180°

. The laser beamwas directed to the surface of the sample (Fig. 3),mounted on the objective table of the microscope. Thelight scattered in the opposite direction to the incidentlight beam with the help of a mirror and the focusingoptical system was directed to the entrance slit of amonochromator. In the monochromator it was decom-posed into a spectrum by two holographic arrays andwas recorded by a TE-104 TS photomultiplier (FEU),which was cooled up to

–30°ë

to reduce thermal noises.The signal from the photomultiplier (FEU) afterstrengthening the amplification was sent to a computerfor accumulation during repeated recordings and forsubsequent analysis. The methodology and instrumen-tation of conducting the experiment is represented indetail in the work [Sobolev et al., 2007].

The samples had a dark color that was occasionallytinged with pink and green. They had a large number ofsurface irregularities with linear sizes of the order of thewavelength of visible light, which caused the strongRayleigh light scattering. Attempts to decrease the lightscattering via polishing were undertaken; however, theyfailed. It was possible to obtain high-quality spectraonly in three places of each of the samples (before andafter the application of pressure). They are presented in

Sample

Mirror

Laserbeam

Scattered light

To the device

Fig. 3.

Layout of the experiment according to the method ofRaman spectroscopy.


Vol. 45

No. 9

2009


Fig. 4. In the undeformed sample, the spectra of regions

1

and

2

differ greatly from the spectrum of region

3

.The spectra of the deformed sample in regions

5

and

6

differ from the spectrum in region

4

. This means thatthe crystals, which fill regions

1

,

2

,

5

, and 6, differ fromthe crystals, which fill regions

3

and

4

. The spectralbands of the other minerals, except pyrope and ompha-cite, were not observed.

The Raman spectra of garnet depend on its compo-sition, which is used for the semiquantitative estimationof the mineral content in the garnet with an accuracy of5–10% [Lyalina, 2000]. Since the grenades in the sam-ples investigated consist mainly of pyrope, and the con-tent of the remaining minerals is lower than the limitsof the accuracy of the method, only the pyrope spectrawere analyzed. In the works [Brefinger et al., 2004;Kolesov, 1998; 2000; Moor and White, 1971; Ma et al.,2007; Gillet et al., 1992; Wang et al., 2001; Huanget al., 2000], the band assignment is given in the Ramanspectra of the pyrope and minerals of the group of pyrox-ene (in particular, eclogite), respectively (Table 3). It fol-lows from Table 3 that the most intensive bands arecharacteristic for the bending and valence vibrations ofthe Si–O bonds in the pyrope and omphacite crystals.

ESTIMATION OF NANOCRYSTAL SIZES

The spectra of a single crystal of pyrope and unde-formed sample of xenolite in a band of ~920 cm

–1

aregiven in Fig. 5. The maximums of the spectra of xeno-lite are displaced towards the low frequencies and areasymmetrically broadened. In Fig. 6, the same compar-ison is carried out for a single crystal of omphacite andan undeformed sample of xenolite in the band of~670 cm

–1

. Here, the shift of the maximum of the spec-trum of xenolite towards the high frequencies and, also,its asymmetric broadening are observed. There are tworeasons for this phenomenon: (a) the crystals in thesample have nanoscale sizes; and (b) the interatomicbonds in the nanocrystals are deformed.

It is well-known that different lattice vibrations aresubjected to energy exchanges because of the nonlin-earity of the forces of interatomic interaction, and theiramplitude experiences continuous beatings. For thisreason the mean life time

τ

of phonons, the quanta ofvibrations (that is, the time during which their ampli-tude changes by

e

≈

2.7

, where

e

is the base of the nat-ural logarithm, the Naperian base) is approximately

10

2

–10

3

vibration periods. During this time, the vibra-tions have time to run a distance

Λ

of tens of nm. As aresult of the interaction of the laser beam with such avibration with a continuously changing amplitude, aband appears in the spectrum, which has a symmetricaldispersion shape and width, inversely proportional tothe life time of the vibration. The bands in the Ramanspectra of single pyrope and omphacite crystals haveprecisely such a dispersion shape.

Inte

nsity

, arb

itrar

y un

its

400 600 800 1000

Frequency, cm

–1

1

2

3

4

5

6

Fig. 4.

Raman spectra in the frequency range 400–1100 cm

–1

:(

1

)–(

3

) before and (

4

)–(

6

) after compressive load deforma-tion, recorded in the different regions of the samples ofxenolite.

Table 3.

Frequencies of the most intensive band maximums inthe Raman spectra of the samples of xenolith

Frequency, cm

–1

Substance Vibration mode

560 Pyrope Deformation vibrations (Si–O), A

1g

640 Pyrope Deformation vibrations (Si–O), F2g

~670 Pyroxene (omphacite)

Valence vibrations (Si–O), A1g, coupling atom O*

860 Pyrope Valence vibrations (Si–O), F2g

920 Pyrope Valence vibrations (Si–O), A1g

~1015 Pyroxene (omphacite)

Valence vibrations (Si–O), A1g

1055 Pyrope Valence vibrations (Si–O), F2g

Inte

nsity

, arb

itrar

y un

its

900 920 940Frequency, cm–1

21

Fig. 5. Band of 920 cm–1 (1) in the Raman spectra of xeno-lite and (2) of a single bulk pyrope crystal.

736

IZVESTIYA, PHYSICS OF THE SOLID EARTH Vol. 45 No. 9 2009

SOBOLEV et al.

If during the life time τ, the vibration has time to“run up” to the crystal boundary and to be scattered onit, the band’s maximum is displaced, and the bandbecomes asymmetric. This phenomenon can be usedfor evaluating the sizes of nanocrystals. The spectralband shape [Tiong, 1984; Shen, 1984; Ritcher, 1984] isdescribed by the formulas:

(1)

(2)

where ν0 is the frequency of the band’s maximum; ν(q)is the dispersion; q is the phonon wave vector for thequantum of the lattice vibrations; q0 is the phonon wavevector for the vibration being investigated; r is the dis-tance from the point at which the amplitude of thevibrations has the largest value; and C(q0, q) is the Fou-rier coefficient for the wave function Ψ'(q0, r).

We assume that nanocrystals in the rock take theshape of spheres, then [Tiong, 1984; Shen, 1984;Ritcher, 1981]:

(3)

I ν( ) C 0 q,( ) 2d3q

ν0 ν q( )–( )2 Γ0/2( )2+-----------------------------------------------------,∫≅

C q0 q,( ) 1

2π( )3------------- Ψ ' q0 r,( ) iq0r–( )exp r3 ,d∫=

C 0 q,( ) 2 q2L2–

16π2--------------–⎝ ⎠

⎛ ⎞ ,exp=

where L is the size of the nanocrystal (the diameter ofthe sphere).

For nanocrystals, according to [Zhang, 2000], thefollowing frequency dependence on the wave vector ofthe phonon q was accepted:

ν(q) = ν0 ± ∆[1 – cos(∆d)], (4)

where ∆= 20 cm–1 and d ≈ 1 nm is the lattice parameter[Kolesov, 1998]. The signs “–”and “+” were acceptedfor the pyrope and omphacite crystals, respectively.

For determining the sizes of pyrope nanocrystals inthe surface layer of the sample of xenolite, the positionand band shape, assigned to the valence vibrations ofthe SiO bonds in the pyrope crystals of 926 cm–1

(Fig. 5) and in the omphacite crystals of 679.8 cm–1,were analyzed (Fig. 6). Using expressions (1)–(4), wefound the values of the vibration frequency of thenanocrystal ν0 and its size L that best fit the shape of theselected bands. It follows from Table 4 that the changesin the band’s shape in the spectra of the surface layer ofthe xenolite crystals with a thickness of several µm, incomparison with the shape of the macrocrystals, can beattributed to the presence of pyrope and omphacite inxenolite, whose linear sizes vary from 13 to 20 nm.

ESTIMATION OF INTERNAL STRESSES

Our calculations showed that the adjustable valuesof the frequency of valence vibrations of nanocrystalsof pyrope amount to ν0 ≈ 922 cm–1, that is ≈4 cm–1lessthan the crystals of macroscopic sizes of 926 cm–1. Theadjustable values of the frequency of the same vibra-tions ν0 ≈ 667 cm–1 in the spectra of omphacite nanoc-rystals are also ≈2.8 cm–1 less than in the spectra of theomphacite macrocrystals of 679.8 cm–1.

The deformation of the crystallographic cell affectsthe position of the vibration frequency of the atoms. Forexample, the frequency changes under the effect of thehydrostatic pressure. For this case, the value of the dis-placement ∆ν is connected with a change in the volume∆V of the crystallographic cell and in the pressure P bythe relationships:

(5)

or

(6)

where ν0 and V are the vibration frequency and the vol-ume of an undeformed sample, G is the Grueneisen

parameter, E is the modulus of elasticity, and α = =

–G The values G and α are positive. Therefore, the

decrease of the vibration frequency shows that inpyrope nanocrystals the interatomic distances areincreased.

∆νν0------- G

∆VV

-------–=

∆ν GνE---P– αP,= =

dνdP-------

ν0

E-----.

Inte

nsity

, arb

itrar

y un

its


2 1

Fig. 6. Band of 670 cm–1 (1) in the Raman spectra of xeno-lite and (2) of a single bulk single omphacite crystal.

Table 4. Parameters ν0 and L, matched for the shape of A1gbands, corresponding to the vibrations of nanocrystals of (1),(2) pyrope, and (3) omphacite in the samples of xenolith

1 2 3

ν0, cm–1 921.7 922.5 667.4

L, nm 20 16 13



The influence of hydrostatic pressure on the Ramanspectra of the pyrope sample was considered in [Ma etal., 2007; Gillet et al., 1992]. Analyzing the plots, pre-sented in these works, we found that for single pyropecrystals α ≈ 3.5 cm–1/GPa. The conventional tensilestresses σef = (1.1–1.3) GPa, which could cause adecrease of the vibration frequency by 4 cm–1in thepyrope nanocrystal, are presented in Table 5.

As regards the omphacite crystals, the frequency oftheir valence vibrations strongly depends on the quan-titative ratio of the chemical elements, include in theircomposition [Wang, 2001]. Therefore, in this case, itwould be incorrect to evaluate the actual stresses on thebasis of the position of the spectral bands.

The effect of an increase of the dimensions of thecrystallographic cell in nanocrystals, apparently, has ageneral nature. Earlier, it was discovered that thedimensions of the crystallographic cell in the anataseand quartz nanocrystals on the surface of sandstonePV-364 are also increased [Sobolev et al., 2007]. Theconventional tensile stresses Pef in these nanocrystalsturned out to be equal to Pef ≈ 0.1–0.2 GPa. The effect ofan increase of the interatomic distance of carbon in thecrystallographic cell of polyethylene nanocrystals wasobserved in [Titenkov, 1985].

A fundamental reason exists, which causes anincrease of the dimensions of the crystallographic cellin nanocrystals: namely, the scattering of phonons ontheir boundaries. It is well-known that the expansion ofinteratomic bonds with a change in the temperature islinearly connected with the squared amplitude of ther-mal vibrations. As already mentioned, the amplitude ofthe atomic vibrations of crystals experiences beatings.The time dependence of an amplitude takes the form:A(t) = A(0)exp(–t/τr) [Ziman, 1966]. Therefore, themean value of an amplitude is less than the maximumvalue A(0) and depends on the mean life time τ. On theother hand, the mean free path Λ of phonons corre-sponds to the distance, at which the amplitude of vibra-tions during the same time τr is reduced by e ≈ 2.7 times(Â is the base of the natural logarithm) [Ziman, 1966].The scattering on the crystal boundary reduces themean free path of the phonons and thus increases themean value of the squared amplitude of the vibrationsand with the expansion of the crystal lattice linearlyconnected with it. For this reason the dimensions of thecrystallographic cell in nanocrystals are increased, incomparison with their sizes in the crystals of macro-scopic sizes.

ESTIMATION OF STRESSES AFTER THE APPLICATION OF PRESSURE

A detailed analysis of spectral bands showed thattheir maximums and shapes in the samples before andafter the application of pressure application are differ-ent. The vibration band of the Si–O bond in the spectraof pyrope nanocrystals in the surface layer of xenolite

before and after the application of pressure is shown inFig. 7. After the hydrostatic compression stress thevibration frequency decreased by ≈0.5 cm–1, and thebandwidth (at half of the maximum intensity)decreased by ≈1 cm–1 (Table 6). Our calculationsshowed that the sizes of the nanocrystals after theaction of the compressive hydrostatic pressureremained unchanged, and the dimensions of the crystal-lographic cell increased. The hydrostatic tensile stressof ≈0.6 MPa corresponds to this increase.

If for the pyrope nanocrystals the shape of the spec-trum before and after the application of pressurechanged only on the quantitative parameters, then forthe spectra of pyroxene the differences were inferred(Fig. 4). Instead of a single band (≈670 cm–1) two bandsappeared. According to [Burzo, 2006], for klinopy-roxenes (a monoclinic crystal lattice) only one type of

Table 5. Frequency shift ∆ν of the maximum of the A1g band of vibrations and the evaluation of the intensity of internal stresses σef in pyrope nanocrystals in the surface layer of xeno-lith

1 2

N0, cm–1 921.7 922.5

∆ν, cm–1 –4.7 –3.5

σef, GPa 1.3 1.0

Inte

nsity

, arb

itrar

y un

its


960

Before deformationAfter deformation

Fig. 7. Band, assigned to the valence vibrations of pyropenanocrystals in xenolite (1) before and (2) after compressiveload deformation.

Table 6. Parameters ν0 and L, matched for the shape of the A1gbands, corresponding to the vibrations of pyrope nanocrystalsbefore (1), (2) and after (4) compressive load deformation

1 2 4

ν0, cm–1 921.7 922.5 920.4

L, nm 20 16 21

738


SOBOLEV et al.

chains of SiO4-tetrahedrons and, correspondingly, onemode of vibration exist. Whereas in orthopyroxenes (anorthorhombic lattice), two types of such chains exist,which are located at a certain angle to each other andhave different mean lengths of the Si–O bond. There-fore, in orthopyroxenes, there are two modes of vibra-tion with close frequencies.

For pyroxenes the splitting of the bands was pre-cisely related with a change in the space group of sym-metry of the crystal lattice [Burzo, 2006; Rull, 2004].With an increase in the applied pressure (> 3.5 GPa) theauthors observed the transition from orthopyroxenes toclinopyroxenes, while with a pressure decrease thereverse transition was observed. This study was carriedout for macrocrystals. Presumably, such studies werenot carried out for nanocrystals. In our experiment withthe samples of xenolite the deformation occurred at aquasihydrostatic pressure of 2.5 GPa. It is well-knownthat the internal stresses on a scale of the crystal latticeof nanocrystals can exceed by several times the externalstresses applied to the sample. This is recorded, forexample, in the studies of the dynamics of the polymor-phic α–β transition in quartzite by the methods of neu-tron diffractometry [Sobolev et al., 2004].

In the experiments described above it was possibleto obtain high-quality pyroxene spectra only for threepoints of the sample. This is insufficient for making awell-substantiated conclusion about the transition at thescale level of nanocrystals of clinopyroxene to orthopy-roxenes under the action of compression. Additionalexperiments are necessary.

CONCLUSIONS

In the samples of xenolite, the pyrope nanocrystalswith a size of ~18 nm and the omphacite nanocrystalswith a size of ~13 nm are found.

The dimensions of the crystallographic cell innanocrystals are increased in comparison with macroc-rystals. The internal tensile stresses, which could causethese changes, were estimated to be ~1.1 GPa.

As a result of a compression of up to 2.5 GPa, thesizes of pyrope nanocrystals did not change, but thedimensions of the crystallographic cell increased.

ACKNOWLEDGMENTS

This work was supported by program No. 6 of theDivision of Earth Sciences, Russian Academy of Sci-ences.

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Documents

Nanostructures in the deep xenolite before and after straining