Volume 90. number 5
13 August 1982
DEPHASUUC IN MOLECULAR CRYSTALS:
A PICOSECOND CARS STUDY OF NAPHTHALENE
Dana D. DLOIT, Claire L. SCHOSSER and Eric L. CHRONISTER Department Recwed
of Chemistry, Schwl
of Chemical Sclenees, Lhlieersrfy of Ilhnois Urbana, llhnofs 61801.
23 Mxch 1982; m final form 7 June 1982
The temperature dependencr of pwxecond CARS oi wbratlon31 CYCICO~S III mphtiene is presented. Below 030 K relaxation IS dominated by spont;meous cmlsson of phonons. Above 40 K hgh-irequency phonons induce dephtig. The resultsare conswcntwih a phonon-promoled energy wnsier process.
Raman spectroscopy ISan important tool for understandmg vIbrational dephasing m orgamc molecular solids. The decay of vibrational coherence is given by a polarizabdity au:ocormlation function which is the Founer transform of the spontaneous Raman hneshape [ 11. This function can be measured by delayed picosecond probe puke experiments using stunulated Raman  or CARS  spectroscopy. Unhke stimulated Raman spectroscopy,CARS has the advantage of requuing lower laser power and can investigate all the Raman-active modes of a molecule rather thanlust one. In this work, time delayed CARS spectroscopy is used to study temperaturedependent dephasing of three totally symmetric vtbratlons in pure naphthalene crystals. Timedelayed CARS has previously been used to study low-temperature lmeshapes in crystalline N2, H, , benzene , and naphthalene . Th tech;que is experimentally advantageous if the decay of coherence is long relative to the puke width,i.e.if the spontaneous Raman lineshape is narrow. Tcmperaturedependent vibrational dephasing was ;.M tiga:Jted by Harris et al.  in solid durene using q\C-.f;l.,.?l~c Ramtixallering. Thejr iound l!-3: line kosdemng and frequency shilt were character.zed by an Qtivation energy which was the same for both processes. Their results were interpreted using the Kubo lmeshape theory [B] involving energy exchange 386
with a single low-frequency vibration. It was later pointed out that this approach predicted lifetimes for the low-frequency exchanging modes which Here too short to be consistent with the observed lineshape 191. Hess and Prasad [IO] studied the temperature dependence of the 766 cm-1 totally symmetric vibration in crystalline naphthalene with spontaneous Raman scattering. They found a different activation energy for line broadening and line shift. At low temperature they deduced a gaussian lineshape and interpreted this to mean the excitation was locahzed. At 296 K the observed lineshape had homogeneous and inhomogeneous character. Subsequently Hesp and Wiersma  measured the low-temperature lineshape of a few vibrations in naphthalene usmg picosecond CARS. Due to the high resolution of this technique they were able to show that the 766 cm-l line and others were actually lorentzian at low temperature and had relatively long dephasing tunes of * 100 PSOur measurements of the temperature dependence of dephasing of the 5 11,766, and 1385 cm-l modes (since the frequencies shift slightly with temperature these values are not strktly accurate), show these lineshapes are nearly temperature independent below z=40 K and broaden above this temperature. Only very high-frequency phonons participate in the broadening process so that the temperature dependence of dephasing is not as steep as for triplet excitons [l l] 0 009.2614/82kMKlO-OOOO/ooool% 02.75 0 1982 North-Holland
Volume 90, number 5
CHEMICAL PHYSICS LETTERS
or optical phonons [ 12,131.Our improved measurements of the 766 cm-t low-temperature linewidth show that the broadening below 1X K has the sume temperature dependence as the line shift data of Hess and Prasad. Application of the exchange model gves results inconsistent with the observed linewidth of the optical phonon involved in dephasing. The data are, however,consistent with a thermally activated T, process mvolving scattering to a higher lymg vibration.
2. Experimental The CARS FID experiments were performed with tunable 20 ps light pulses generated by a par of cavitydumped, synchronous dye lasrs. The laars are driven by the second harmonic of a continuously pumped Nd : YAG laser which is acousto~ptrcally mode locked and Q swltched [ 141.The dye pulse energy is IOpJ, the frequency band width -0.7 cm-l , and the repetition rate IS 500 Hz. The beams were focused to 250 W. A simultaneous pulse pair of frequencies wL and wL - 6 coherently excites a VIbration of frequency 6. The subsequent decay of vibrational coherence is sampled by a timedelayed wL puke. The scattered CARS signal at frequency wL t 6 rs detected by a photomultiplier and a lockin amplifier. The probe pulse delay was varied by a motorized delay hne and the decay was stored and averaged in a multichannel analyzer and read out on an X-Y recorder. A single decay was obtamed every 2 sand the results represent the averaging of --ZOO decays. The possibility of non-linear effects other than chose due COthe CARS susceptibility was excluded by verifying that the appropriate intensity dependence, linear in each of the three laser beams and cubic in total power, was observed in each case. Naphthalene smgle crystals were prepared from zone-refined material by the Bridgman techmque and were = 1 mm thick. The beams were perpendicular to the ob cleavage plane and were all polarized along the b axis. The crystal was mounted in a copper cuvette which was cooled by a closed&e helium refrigerator. The temperatu-e was measured by a calibrated silicon diode and maintained by a proportional controller. The temperature was hefd constant to iOZ”C and the quoted values are accurate to 05°C. Crystals
13 4ugust 1982
were cycled from room temperature to low temperature only once.
3. Discussion and results 3.1. Low-renrperarure lureshape
At a!l temperatures thus far studied the timedelayed CARS sIgna consuts of an imthl transient and z exponential decay. For example, fig. I shows a log plot of the decay of the 1385 cm-l vrbration at a few temperatures. The decay ISexponential for more than three I/e lIferunes. Thus the center of the frequency domain CARS lineshape ISlorentzian. This has previously been interpreted  3s homogeneous broadening, mdicating the vibration is delocahzed, I e. tt is a vibntlonal exciton [IS] which motionally sverages its environment. The decay constant for the 1385 cm-l vlbrdtion IS identical to that obtained by picosecond CARS by Hesp and Wlerma  and by Decola et al. [ 161 using frequency domam CARS. Our values for the 5 11 and 766 cm-’ vibrations are ~20% faster than Hesp and Wiersma’s picosecond medsurzments. This chscrepancy is not understood. It may be due to lmpunties in the naphthalene. Although our naphthalene was extensirely zone-refeed, it was not fused with potassium. The measured decay parameters and the calculated lorentzian hnewidths are given in table 1.
Fig. 1. Prmsecond tunedcbyed CARS of 1385 cm-t nbranon of cwstdme naph!halene. Euxpt for a np~d u-utul trannSIcnt, tbe decays ate purely svponcnrd for man: thm three l/e hfeumes. The NRdeay ts the measuredtnsttumcntal responsefunftlon obkuncd by turungoff the vibrattonal resonance.
Volume 90, number 5 Table 1 CARS irec-mductlon T (0
30 40 50 70 90 110 130 150
dec3y umes r far naphthslcne
crystalsand calculated lorenu~~~ hnewidth Y 1385 cm-’
13 qugun 1982
r (PS) 4
r (PSI 3
I (ps) a)
125 122 111 96
0.013 0.044 0 048 0.056 0.074 0.078 0.12
61 61 53 51 34 2s 22 17 16
0.087 0 087 0.10 0.11 0.16 0.21 0.24 031 0.33
91 07 87 81 66 54 35 31 24
0.059 0.061 0.061 0.066 0 082 0.099 0.15 0.17 022
72 68 45 -
a)Valuesforr a~cur.~tcto z5 ps.
The nutial transient m the decay rate is due to interactions including two-photon absorption, since both dye lasers are in the two photon regon [ 171. The relative proportion of non-resonant interactIon could be varied somewhat by tuning both dye lasers while mamtaining a constant frequency difference. The non-resonant response is rapidly decaymg and follows the applied laser fields.This is useful to deremune the mstrumental respouse at a given combination of wavelengths. The NR decay in fig. 1 is the measured instrumental response and has an exponentlal trtig edge with a I/e decay time of 12 ps. The shape of the delayed CARS signal around zero delay IScomplicated and not yet completely explained. This corresponds to the wings of the frequency domain CARS lineshape. The low-temperature 766 cm-1 decay, the open circles in fig. ?a, is accurately fit by assummg about equal proportions of resonant and non-resonant interachons. The shape of the initial transient changes with temperature. The 1385 cm-’ decay has an unexplained ripple on the nsing edge which is temperature dependent and vanishes above = 100 K (see fii. 2b). The 5 11 cm-l vibration does not noticeably change shape at the temperatures studied. The measured dephasing rates are temperature independent below ~40 K. This suggests the dephasing is a T, process due to spontaneous emission of phonons caused by cubic or higherarder anharmonicities [ 10,12]. The decay route could be emission of single phonons causmg vibrational Lascqding. Since the vinon-resonant
brational frequencies are greater than twice the Debye frequency (” 140 cm-l), multiphonon emission IS also a possible but less bkely mechanism. 3.2. Temperawe dependence of dephasing The temperaturedependent contribution to the linewidth is characterized by a simple activation energy. If the low-temperature linewidth is subtracted from the observed linewidth using the values in table I, a log plot versus l/Tgives a line whose slope is the activation energy. The solid circles in fg. 3 are such a
plot for the 766 cm-l vibration. The correlation coefficient R > 098 for all three vibrations studied. The activation energies, T= 0 linewidths. and extrapolated T = 0~linewidths are given in table 2. The open circles in fig. 3 are the values obtained for the linewidth by Hess and Prasad [IO] by spontaneous Raman scattering. The data overlap in the region 90-140 K and agree within experimental error. Above 150 K the line changes slope. The lineshapes also change somewhat with temperature as discussed in section 3 .I. At low temperature they are lorentzian whereas at 296 K the 766 cm-* has some inhomogeneous character [IO], implying this exciton is partially localized at high temperature by lattice phonons. The change in slope in fii. 3 may indicate that a localization transition occurs above Z=150 K. However, as fg. 2a shows, there are changes in the wings of the line (peak of the decay) well below 150 K. Hesp and Wiersma  suggested [email protected]
= sition to a localized state occurs gradually, and fast in
Voluine 90, number 5
I3 August 1402
Fg. 3. Temperature dependence of vlbrarlonsl dcphJsmg for the 766 cm-’ vrbmuon of crystallme naphthalcne. The dcph;rong rate. 1snearly tcmpcr&mz mdeprndcnt up to = 40 E and mcrcascs thereafter. The sobd cuclrs arc the Wmpr‘raWrcdependent hnewldth measured by plcosemnd CARS and
grve an ac1Ivatlon cncrgy oi 118 q 12 cm-‘. The open arcler arc the data of Hsss and Prawd [IO], mcarurcd by spontmcous Ran-an sattcring.
The data overlap m the rWon 90-110
K and agree urlthm c~pcnment~l
Ftg. 2. (a) Ptcosecond tunedelayed CARS cm-* vLnuon of cryst&ne naphthalene.
sgnal for the 766 The decay at 9.5 K IS accur;ltely fit by n npldly decaymg non-reson~~~t cuherencc. By 70 peak of the decay changes shape.This correspondsto
response and B slowrr dewy of rlbrsuonal K ttc
of the frequency domsln CARS synal. (b) The
nsmg edge of the 1385 cm-l vrbratlon dcvelopes a “ripple” as the temperature IS decreased below 150 K. The effect LS sull unexpkuned.
the wings of the line. However, a temperature dependence of the intensity of the non-resonant mteraction cannot be ruled out as another mechanism to explain the observed temperature dependence of lineshape. 3.3. Mechanismofthermalb activateddephasing
frequency molecular vibrations.The hlghrst frequency 4 = 0 optical phonons are at 111 cm-t and 141 cm-l and involve hbrations about the long molecular axis[ 121. The lowest-frequency molecular vibration, the ring “butterfly” mode, is ar 173 cm-l. In rhe crystal the butterfly mode is delocalized w2h an exciton bandwidth of 15 cm-t [ 181. It is useful to tltik of this mode as another type of high-frequency phonon. Exammation of the data in table 2 shows that the 5 11 and 766 cm-t vlbratlons are dephased by interaction with long-axis hbrons. The 1385 cm-t vibration is unaffected by these librons but is dephased by the “butterfly” vlbrdtlon. At temperatures greater than those studied (T> 150 K), hgh-frcquency vibrations will be thermally excited. Ii these interact strongly with the vibrational excitons, a more complicated temperature dependence wdl result. Although we have estabhshed that tempenture-
Table 2 Actlvallon frequency ior vlbrdtlonal dephang AU values tn cm-’ Mode
The exponential activation observed for temperaturedependent dephasing indicates this process involves scattering of the high-frequency vibrational exciton by a single lnw-frequency mode. The hkely candidates arc high-frequency optical phonons a Id low-
Low-temparurc linewldth (r=O)
103 t 21
0.087 0 059
118 L 12 175 t 16
0 75 !I.> I
Volume 90, number 5
13 Augurr 1982
dependent dephasing is due to interaction with highfrequency phonons we cannot yet conclus~vcly deter-
This research was supported by the National Science Foundation, Division of Ma&&Is Research grant no. NSF DMR8041630. Acknowledgementis made to the Donors of The Petroleum R&arch Fund, administered by the American Chemical Society, and the Research Corporation for partial support of this research. We wish to thank the referee fdr a critical reading of this manuscript and many helpful suggestions.
higher-lying vibrations via cubic anharmonicity [ 121 or pure dephasing. The scattering mechanism requires a state having energy equal to the sum of the nbrational exciton plus phonon. For example, for the 5 11 cm-t vibration there would have to be such a state at Slit 103(+21)cm-1.Thisshouldbethe618cm-1 Bzu in-plane vibration [ 191. For the 766 cm-l nbratlon there are three closely-spaced modes at 875,876 a;ld 878 cm- 1 [ 191. For the 1385 cm-l vibration there ISan Ag state at 1578 cm-l . Pure dephasing due to energy exchangewith the phonons [7,8] can be ruled out. In this model the energy of the h&-frequency vibrational exciton is modulated by a diagonal quartic interachon. The model predicts the activation energy for line broadening and line shifting wffl be identical. Hess and Prasad [lo) deduced an activation energy for the frequency shift of the 766 cm-’ vibration of 133 f 10 cm-’ by subtracting the calculated effect of thermal expansion from the observed lineshtit. Their results fcr line broadening were about twice tlus value. However, our results in the range 40- 150 K give an energy of 118 + 12 cm-l, the same as for the frequency shift within expertmental error. The reason for this discrepancy is evident from the combined data in fig. 3: the slope mcreases abruptly above =Z150 K. Application of the exchange model to the frequency shift data of Hess and Prasad and the line broadening data of thawwork gives 6~/2a = 10 cm-t and 7 = 0.02 ps, where 60 is the anharmonic frequency shhlftand 7 the lifetime of the 121 cm-t phonon. The observed linewidth of this phonon ranges from 13 to 5 cm-l at thee temperatures [ 121, giving a lower lmr to the hfetime of a few ps. Thus the exchange model is inconsistent with the experimental results for the 766 cm-t vibration below 150 K. The agreement of activation energies may be fortuitous since the contribution of thermal expansion of the hnewidth was not considered. Further work remains to be done on the naphthalene vibrational exciton system. In particular,CARS excitation with resonant (to Sl) probe scattering  should be capable of distinguishing between T1 and pure dephasing processes. We are currently attempting this experiment and others to better elucidate the mechanism of vibrational dephasing. 390
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