M. Prager- Rotational tunneling in a disordered system: nonequilibrium methane CN4 II

8/3/2019 M. Prager- Rotational tunneling in a disordered system: nonequilibrium methane CN4 II

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Rotational tunneling in a disordered system: nonequilibrium methane CN4 I1

M . PRAGERInstitut fur Festkbrperjorschung der Kernforschutzgsanlage Julich, Po sfa ch 1913,D-5170 Jul ich, WestGermany

Received July 2 1, 1987This paper is dedicated to Professor J. A. Morrison

M. PRAGER. an . J . Chem. 66,570 (1988).A pure methane sample was condensed onto a cold surface(T = 5 K) under conditions used in matrix-isolation spe ctroscopy .The sam ple shows a disturbed long range orientational order ofCH 411. Th e free rotor and tunneling transitions are considerablybroadened. Stacking faults and defects are believed to cause the disorder. The disorder is largely reduced with increasinannealing temperaturesTabut, surprisingly, even atT, -- 0.7Tmhe long range ord er is not fully reestablished.

M. PRAGER. an. J . Chem. 66,570 (1988).On a condens e un Cchantillon de m ttha ne pu r sur une surface froide(T = 5 K),dans des conditions identiquesi celles utilisees

en spectrosco pie par isolation en matrice. L 'echantillon presente un ordre d'orientationi ongue distance perturb6 de CH,11. Lestransitions dSes i la rotation libre et i l'effet tunnel sont trks Clargies. On considkre que des failles et des dCfauts dansl 'empilement sont i l'origine du dCsordre. Le desordre est beaucoup moins important lorsqu'on augmente la temperature drecuisson, T,; toutefois, mkme lorsque Ta - 0,7T,, on observe avec surprise que l 'ordre i longue distance n'est pascomplktement rCtabli.

[Traduit par la revue]

I. IntroductionDisorder is caused by the partial or com plete loss of the three

dimensional periodicity of a physical property. In classicalglasses the relevant property is the center-of-mass position. Inmagnetic glassy systems the center of mass structure is stillperiodic but the magnetic periodicity is removed due to a statis-tical replacement of magnetic atoms by nonmagnetic ones.Glasses show universal low temperature properties, which arewell described by the generally accepted "tunneling model".The physical structure of these tunneling states, however, isprobably characteristic for every special system (1).

In molecular solids orientational disorder can be produced ife.g. a part of the anisotropically interacting molecules is re-placed by isotropic units (2-4). Usually for low concentrationsof the isotropic species (4) and/or weak anisotropic coupling( 9 , he effects of disorder can be considered as a perturbation ofthe ordered state. For highly diluted systems(6, 7), however,the long range orientational order can be comp letely removed ,which in some cases is discussed under the aspect of an orienta-tional glass (2) or "frozen-in" orientational disorder( 3 , 4 ) .

There is the question whether pure m olecular systems can bestabilized in an orientationally disordered s tate also. Long rangeorientational order can be disturbed if the solid is produced in anonequilibrium procedure, e .g. by very fast cooling (analogousto glassy metals) or by con densing it from the gas phase onto acold substrate directly in the solid phase. Such sam ples are usedespecially in the matrix-isolation spectroscopy technique tostudy individual molecules or molecular aggregates. They areknown to be composed of small crystallites and to containdefects and stacking faults in rather large concentrations(8).Stacking faults lead to inequivalent m olecular sites (fcc and hcpsurrounding) and are often used to explain the spectroscopicobservations (9). D efects interrupt the long range orientationalinteraction (as an isotropic impu rity) and lead to a relaxed localorientational order. In the present work we tried to get anorientationally disordered sam ple using a m atrix-isolation tech-nique of preparation.

In some materials the effect of disorder can be monitored viaits influence on the quantum transitions of a weakly hinderedrotor. Rotational tunneling, observable in various molecular

solids by incoherent neutron scattering, offers an extsensitive probe. B esides solid hydrogen ( l o ), methanemost intensively studied quan tum ro tor system (1 1, thermal equilibrium methane first crystallizes in an fcc otionally disordered phase, CH4 I. Below T , = 20.4 Kmolecules partially order while the center of mass struunchanged. The ordering is caused by the octopole-ocinteraction (13). The topology is such that this intevanishes at 25% of the sites for symmetry reasons. These432 symm etry feel only a weak crystalline field and the mmolecules are almost free quan tum rotors. Th e remaininare orientationally ordered at sites of symmetry J2rn inatively strong rotational potential. Due to this potent

observes a tunnel splitting of the librational ground statransitions at 75 and 140 p.eV. Bo th, free rotors (FRtunneling m olecules(TM), will be affected by disorder different ways. Th e more sensitive probes certainly arebecause the relaxation o f orientations around a defect rethe compensation of the octopole-octopole interactionTM , on the other hand , will feel only a rather weak changbasic potential.

11. Experiments and resu ltsInelastic and elastic neutron scattering experiments w

formed using light and heavy methane of 99.99% anpurity, respectively.

11.1. Sample preparationBoth samples were prepared under similar condition

same special inlet system described elsewhere (14),allows the condensation of large size m atrix-isolation sfor neutron scattering experiments. A reference volumewas filled up to a pressure of 2 bar with CH4 or C D4volume is connected with the sample holder via a regvalve. The inlet line is heated toT = 110 K up to the scontainer consisting of A1 which was atT = 5 K. Dcondensation a very slow flux of 10 cm3 /min was mainThus the adsorbed methane had enough time to come cthermal equilibrium with the cold surface despite the bmal conductivity of the matrix. Th e sam ple temperaturecondensation was always below 15K (see below).


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11.2 Inelastic spe ctraThe quantum rotor states of the methane molecules were

measured using the high resolution neutron time-of-flight spec-trometer IN5 of the Institut Laue-Langevin (ILL) in Grenoble.Two setups with energy resolutions of 34/59 peV FW HM atincident wavelengths of 8.516.0A were used. Standard datacorrections were performed and the measured spectra trans-formed into S(0,o) using the ILL-program package

PRIME/CR OSSX (15). Figure 1, bottom, shows the spectrumin the energy range up to 1.5 meV (Ai= 6 A) as taken im-mediately after condensation at a samp le temperatureT = 2 K.Various characteristic chang es compared to equilibrium CH4 I1are found: (i) The free rotor states at EFR= 1.09 meV arestrongly suppressed and asymmetrically broadened to lowerenergy transfers. (ii) The tunneling transitions, sFown withbetter energy resolution in Fig. 2, b ottom (Ai= 8.5 A ), are alsostrongly asymm etric with the tail to higher energy tran sfer. (iii)The energy region between tunneling and free rotor lines con-tains a large number of new states. (iv) The energy levels are notin thermal equilibrium. A parametrization of the spec trum hasbeen tried by using various lineshapes in potential space (Gaus-sian, Lorentzian, constant in a range, linear in a range, expo nen-

tial, power-function, all may be asymmetric) to extract theintensities. The relation between rotational potentials V andquantum transition energy OTM ,W FR was taken from Hiiller andRaich (16) for the TM

[ l ] hwTM= 143 peV exp (0.0758(37- V/B))and was just extended phenomenologically to the FR-range aswas done in ref. 6

[2] hwFR= 1.3 1 meV exp - -(

where B is the rotational constant of a methane molec ule.The solid lines in Figs. 1 and 2 are fits with asymmetric

Lorentzians. The distributions of rotational potentials in the

freshly prepared sam ple had widths ofrFR 8 B and rTM 6B. G aussians do not reproduce the large intensity between thetunneling and free rotor lines while constant lineshapes over-emphasize it. Using the results from the fit with Lorentzians w esee that the spin temperatureT , describing the intensities of theFR lines is consid erably high er( T , = (8 2 2) K) than the samp letemperatureT = 2 K . In the tunnel system the population of theE and T states relative to the A states corresponds to a spintemperature aroundT , -- 4 K. Th e spin temperature approachessomewhat the sample temperature with increasing annealing.However, all these numbers suffer from the problem that it israther difficult to attribute the intensities of broad distributionsunambiguously toFR and TM.

At T = 10 K the described spectra have changed slightly,

mainly by broadening. AtT = 15 K we observ e a broad quasi-elastic line beside the elastic line which is characteristic forrotational diffusion in CH4I.

Spectra taken during the condensation of the methane showan intermediate shape. No well-defined inelastic lines can bedetected but the broad in elastic intensity is not yet quasi-elastic.

The sample was ann ealed at temperaturesTa = 30, 50, 70 Kfor 30 min each. After each annealing, spectra were again m ea-sured at a samp le temperatureT = 2 K . Annealing atT = 3 0 Kdid not change the spectra. After heat treatment atT , = 50 K thetunneling lines are considerably sharpened and the free rotorlines get much more pronoun ced. T he broad intensity betweenthe free rotor and tunneling energ ies is reduced (Figs. 1 and 2 ,

4 I 1 I I ICH411 matrix

energy t r ans fe r (meV)FIG. 1. Inelastic neutron scattering spectra of condensed methane a

measured with the high resolution time-of-flight spectrometer INusing a wavelengthX i = 6 A (energy resolution 6 E = 59 p,eV). Top:annealed atT , = 50 K fo r 30 min; bottom: not annealed. The nonzerbackground is an artefact due to an incomplete em pty can sub traction

top). The sharpening of the inelastic features in the spectrumfurther increases after annealing atT a = 70 K. Although thistemperature is only 22% below the melting point this annealinis not sufficient to produce an equilibrium CH 4 I1 samp le (17).

11.3 Dirractio n experimentsTo characterize the structure of our sample neutron powde

diffraction patterns were m easured using the diffractometer D1of the ILL, Grenoble, with an incoming wav tlength h i= 2.98 Ain a range of momentu m transfers 1. 6< Q (A-') < 3.3. Spectrawere taken at three different temperaturesT = 7, 15, 25 K fromthe unannealed sam ple and after annealing for 30 min atT , = 60K . To get pronounced d iffraction peaks , the coherent scattereCD4 had to be used instead of C H4. Unfortun ately, CD 4 has phase diagram some what different from that of CH, (for detailsee e.g. ref. 18). Th e pattern atT = 7 (15, 25) K are found, bycomparison with earlier unpublished measu remen ts, to be characteristic of ph ase I11 (11, I). W e only show parts of the diffrac

tion pattern taken atT = 7 K an d 25 K before and after annealing(Fig. 3). The essential difference between the two spectra consists in a considerable sha rpening of the lines originating fromthe methane sample. If one assumes that a finite crystal sizcauses the line broadening in the cold condensed sample onestimates a characteristic diam eter of the crystallites D= 400 Afrom the standard expression (19).

[3] D - " 'PI112 CO S 6

6 being the Bragg angle and p the vdW-radius of a methanemolecule.

Additional Bragg peaks are du e to the A1 container and to N


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572 C A N . I. CHEM.

-400 0 400energy transfer (peV)

FIG . 2. Inelastic neutron scattering spectra of condensed methane.Spectrometer: IN5.X i = 8.5 A (6E = 34 keV) . Top: annealed atT, =50 K for 30 min; bottom: not annealed . The nonzero background is anartefact due to an incomplete empty can subtrac tion.

scattering angle 2 0 ( O )FIG. 3. Neutron diffraction patterns of condensed methaneCD 4 in

the range of the (111) and (200) reflections as measured with thepowder diffractometer D la of theILL with a wavelengthX i = 2.98 A .The shaded peaks are due to a N2 surface contamination. Left:T = 25K, CD 4I; right: T = 7 K , CD 4111. Top: Sample annealed atT , = 60 Kfor 30 rnin; bottom; Sample not annealed .

probably condensed on the outer surface of our sampltainer.

111. Discussion

The data we have presented o n a one-component disoquantum system would be difficult to obtain by methodsthan INS. In particular, w e have investigated:

(i) Control of pre pa rat ion conditions

To prevent annealing of a matrix during condensationlow condensation rate s are usually used in the matrix prodprocedure. The temperature in the sample, however, really be mea sured. In o ur system this is possible via an iprobe since the tunneling transitions ofCH4 molecules shcharacteristic temperature dependence in the range frotemperature to the phase transition temperatureT , (1 1above which the molecule is orientationally disordered.paring the spectrum taken during condensation with obtained later under conditions of thermal equilibrium wclude that the sample temperature during preparation wa(12 + 2) K, even for such large sam ples as necessary for nscattering experiments. Temperature gradients in the scertainly affect some wha t the accuracy of this statemen t.

( ii) Perturbed long range orientational order a nd rotapotentials

In spite of strong differences, the inelastic spectrum unannealed sample is qualitatively similar to spectra fromI1 cooled dow n from the liquid. The crude diffraction pare also characteristic for long-range-ordered methane phases 111, 11, I. T he finite linewidth of th e B ragg p eaks attributed to finite crystallite size s. Thu s it seems possibsurface effects are influencing the rotational potentials.assume s that they are significant in a depth of about3 molediameters below the surface one expects, from the revolumes, disorder for 5% of the molecules. This is much sthan the observed value. W e note that in particular the fre

states which in an undisturbed lattice represent already 25 %molecules are nearly completely suppressed. Thu s, the dmust be of different origin . The m atrices used in matrix isspectroscopy are known to represent nonequilibrium containing stacking faults, dislocations, and so on(8 , 9methane, rather low concentrations of such statisticallybuted defects will remove the compensation of the octoctopole interaction at the FR sites and modify the postrengths at the tunneling sites. The general effects spectra thus should be similar to those found in the CH4 /Kr where the anisotropic octopole-octopole intebetween methane molecules is diluted by som e percentisotropic Kr atom s (4). Indeed, the spectra resemble eachbut there are also differences. In the m ixed CH 4/Kr sam

distinction between FR and tunneling states, both weaccording to the probabilities found in the undisturbed could be maintained u p to rather large Kr concentrations0.1) while the disorder in the present cold condensed strongly suppresses the FR states ccmpared to the TMsystem thus seems to be closer to a fully disorder ed state

It is a question whether an orientationa l "glassy state"described by a general distribution function as in the tunstandard model (STM ) of normal glasses (21). There msome fundamental differences, how ever. It is a symmetrerty of rotational potentials that their minima are equThis means an asymmetry parameter, calledA is the STalways zero. On the other hand, the tunneling parame


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PRAGER 573

related to the potential strength V since the tunneling frequen-cy depends almost exponentially on V according to [I ]. Apossible function for molecular system analogous to the STMthus would read sim ply

[4] p(V) dV = constant dV

and yields a distribution of tunneling splittings

[51 p(w ,)a exp (- PV )

In some matrix isolation systems we have indeed found a dis-tribution compatible with [5]. The tunneling states are o b s e ~ e das wings close to the elastic line. The shape of this spectrumremained unchanged if the instrumental resolution was im-proved (22). In the present case, however, such a distributionfunction is not able to d escribe the spectra. Instead rather broadLorentzians in potential space with cutoffs at the free rotorenergy on the one side and at the tunneling energy on the otheryield the best fits.

(iii) InJluence of disord er on the ph as e diag ramDue to the presence of disorder the phase diagram of m ethane

is somewhat changed. W hile the equilibrium sample show s thephase transition to orientationally disordered CH 4 I at T,= 20.4K , we o b s e ~ elready the quasielastic spectra corresponding todisordered methane at T = 15 K. Thus the phase transitiontemperature T, is lowered by more than 25 % du e to disorder, asin the CH 4/Kr m ixtures (4). Th e diffraction patterns reflect thesame effect for CD4. We did not try, however, to get moreaccurate values of the transition temperatures.

(iv) Effects of a nn ea lin gWith increasing annealing the inelastic intensity is more and

more concentrated into the FR and tunneling lines, which ha vegrown much sh arper. But even after annealing at T,= 70 K thespectrum reflects disorder. T he inelastic lines still have asym -metric tails and the intensity of the FR transitions is still con-siderably below the 25% of the inelastic scattering measured for

an equilibrium structure of CH 411. Th e remaining defects clear-ly have to overcome rather large activation barriers. T his is incontrast to the assumption that the onset of diffusion fullyreconstructs a matrix at annealing temperatures T, = 0.4T,,.With annealing, the size of the methane crystallites has con-siderably increased, yielding sharp Bragg peaks. All theseeffects prove that the disorder in our sy stem is not due to surfaceeffects.

(v) Spin conv ersionIn the unannealed and the ann ealed matrix the quantum rotor

levels, especially theFR, are not in thermal equilibrium with thelattice. While in disordered CH4 /Kr m ixtures with rather largeKr concentrations spin conversion is accelerated (23), this

seems to be not the case for the matrix system. T hu s, it is not thedisorder but the p resence ofKr atoms that m ust be responsiblefor the effect in the CH4/Kr system. The deviation from thethermal equilibrium, however, is also different to that ofquenched CH 4 I1 (24). In the quenched material E-state mole-cules do not convert, w hile in our matrix an increased popula-t ion of T-s ta tes is found. This ob se ~ at io n , owever, needs amore detailed study .

The interpretation of the present spectra arising from a three-dimensionally-coupled, diso rdered quantum rotor system mustremain incomplete. T heoretical models usually use a m olecularfield theory to describe the system in a single-particle pictureand hence cannot explain the present ob se ~ a ti o n s . ere compu-

ter simulation seems to be possible and helpful for a deepeunderstanding of our data.

The single-particle picture is certainly m ore adapted to singlmolecular defects in an atomic matrix. Thus, complementaryinformation can be obtained by investigating C H4 matrixisolated in rare gases. Such experim ents w ere already performedwith limited energy resolution and fo r equilibrium sam ples (5)In a cold condensed sample several transitions belonging tinequivalent sites (9 ,2 5) an d an additional broad distribution ostates is found (25 ). This is d irect evidence fo r the existence othe defects used to explain the present results.

IV . ConclusionsMethane condensed slowly (10 cm3/min) on to a cold surfac

(T = 5 K) maintains a long range orientational structure as iCH4 I1 but displays orientational disorder, w hich m anifestitself in a significant broadening and weakening of the quantumtransitions compared to the undisturbed material. In the disturbed structure the transition temperature into the orientationaly ordered phase I1 is reduced by m ore than 2 5% . T he disordeshows remarkable differences to that produced by diluting thorientation-dependent interaction with sm all percentages of rargases . 'The free rotor states are strongly sup presse d and represent more a broad band of states at energies below that of the frerotor, but no system with random orientations is formed. Thdisorder, m ost probably , is caused by stackin g faults and defecand is considerably reduced with increasing annealing. Surprsingly even at the h ighest an nealing temperatures T,/T,,- .7 i tcould not be completely removed.

AcknowledgementsW. Langel made available his matrix isolation setup. H

Blank and G . Kearly helped with the experiments on IN5. AHewat provided measuring t ime for a short run on Dla.H.Lauter supplied the CH 4. I thank all these colleagues for thecollaboration.

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M. Prager- Rotational tunneling in a disordered system: nonequilibrium methane CN4 II