Band effect in vibrational dephasing of adatoms bound to surface by central forces
The effect of lateral interactions of adatoms on the spectral line of their local vibrations is analyzed in terms of a simple model which includes only central forces binding adatoms to a surface, so that in a case free of lateral interactions the contribution from the surface- longitudinal vibratio...
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| Datum: | 2001 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Englisch |
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Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine
2001
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| author | Rozenbaum, V. M. Lin, S. H. |
| author_facet | Rozenbaum, V. M. Lin, S. H. |
| author_institution_txt_mv | [
{
"author": "V. M. Rozenbaum",
"institution": "Інститут хімії поверхні НАН України"
},
{
"author": "S. H. Lin",
"institution": "Institute of Atomic and Molecular Sciences, Academia Sinica"
}
] |
| author_sort | Rozenbaum, V. M. |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-11-27T09:42:39Z |
| description | The effect of lateral interactions of adatoms on the spectral line of their local vibrations is analyzed in terms of a simple model which includes only central forces binding adatoms to a surface, so that in a case free of lateral interactions the contribution from the surface- longitudinal vibrational mode to the dephasing process should vanish (K. Burke, D. C. Langreth, M. Persson, Z.-Y. Zhang, Phys. Rev. B 47 (1993) 15869). The lateral interactions are shown to cause the spectral line shift and broadening which are proportional to the cubed and the squared ratio of the band width for collectivized local vibrations to the resonance width for the longitudinal mode; as a result, band effect causes a notable contribution, provided this ratio is of order of unity. |
| first_indexed | 2025-09-24T17:44:39Z |
| format | Article |
| fulltext |
BAND ЕFFЕСT lIч VIBRAТI0I{AL DЕP}IASING oF
ADATol\{sBoLrNDТОSURFAсЕBYсЕ,NTRALFoRCЕs
v. ]\,I. Rozеnbauml,2 and S.H. Lin1
tlrtstitutе o.f ,4tontiс аttd Molесulсtr Sсiепсеs, Асаdеmiа Sitliса
ii вi"' 23-166, Tаtpеi, Tаiwаn, Rеpublic of СHINА
,tn,),,|,',ofsur'fасеСhеmtstrу,|,IаtioпаlАcаdеmуofSсiеnсes
Gеп.Nqumovstr,]7,Kу,it,-lб1,03бs0UKRAINЕ,е-mаil:vrozеn@mаil,kдr.nеt
Abstrасt
Thееffесtoflatетalintеraсtionsofadatomsonthespесtrallinеofthеiгloсalvibrations
is analуzеd in tеrms
"f
; fi;;^;;а^"1 *ьi1' ьсludеs onlу iеntral Гorсеs binding adatoms to a
suгfaсe, so that i" u ;;;; frее of lutе.at intеia.сiio"' iь" сontгibution from thе suгГaсе-
longitudinal viьгationat.,n-oсЪ-io-ш* o.рьu,lne ;,oсеss sьoutа y.anish (K. Burkе, D. C.
Langrеth, М' Pеrsson, z.-i-' zьunc,вьу,, к*'.вii trssзl l5s69) Thе latегal intегaсtions
arе shown to сausе tnе spесtral linе shift.and ь,йa.ning *hi"h u.".р.opoпiona1 to thе сubеd
and thе squагеd ,u,,o # ш.Ъand width for сol'есtivйеd loсal vibrations to thе rеsonanсе
width for thе longitudiJ *oс., "'
a rеsult. b^";;й;;; ..usеs a notablе сontгibution, pгovidеd
this гatio is of ordег of unrtу,
Todatеagrеatvariеtуofadsorbatе.sуstеmshavеbееninv.еstisatedinwhiсhlatегal
dipolе-dipolе int".u"ti*,l';i ;;y **il",, tьJ.,.;;;; i; vibratiоnal spJсtra Il] Ьut also givе
гisеtoсomplехorlеntationalstruсtuтеsp.а1нсьыrеngеgivеnmuсhspaсеinthеlitеraturеts
to analуzе thе сontгibu;ion of latеralint.,u.tion,"i"'"_iь?й*.гa1-linе..i,ift
and bгoadеning foг
loсalvibrations [5.8] ;;];;;;'-;ttaсking tь.Ъl"йl.. has involvеd thе еxсhangе dеphastng
modеl with tье ьiquaoialti;'.;;й;;;. oг tй unй*oniс соupling bеtweеn the high-frequеnсу
loсal vibration and thе low-frequеnсу rе.sonanсе modе responsiblе for tеmpеraturе
depеndenсеs of oьsей,pЪ",*r iin",.-шoi.i^oiiу i'.ьu'.this.appгoaсh included latrrai
intеraсtions both fоr nt;;:f,Jo'йl;' iii *а-low-frеquеncу modеs [6-81.
At thе samе tiйе, сonsidегation of
"
j;.;Ё;'lфч::'*rn.*ъ.ffl"#"l
rеvеalеd a signifiсant lorЪ oг thе сubiс anharmoniсitу whose сontrtot
сomparablе to that ;"i;;.й"а,uti".unь#i]o"i.1'у is,rol Givеn propег weight^in t|е
trеatment of thе d";;";;g";;;.ss,^this й.to, ыЬ*еd to adеouatеlv aссount toг tne
anhaгmoniс "oupringЪ;;"Zn,thе
suгГaсе.',"","..'. i"сai modе anj thе suгfaсе-longitudinal
resonanсе modе uпiiJ-thе сasе of two io."iйшу-o,iеntеd modеs whiсh arе сouplеd еvеn in
thе haгmoniс "po,";;;;;;
*j .ьu, giu. н," io,u-геduсtion faсtor quеnсhing thе dеphasing
bу sеveral ordеrs of rnugnituс., Il l], two.mu;i-dpfp""o]:{..:'i:o"s сould bе еxpесtеd to
""u,"
u matеrial .trJ"?i;;;;..lii. ьi"аi"g or un uаuio,n to a suгfaсе bу сеntral foгсеs g^tvеs
noсontгibutiontothеdephasing.p,o::,:'*j;;iуwеakеrnon-сеntгalforсеsprеvеntlttгom
vanishing at all tro]. йlе adаТtiЬnat 1atеrai-i;;;;сtions of loсa' modеs in a sеnsе rеpresеnt
non-сеntral forсes' ""-йЫ'*
situаtion:.'Щ;;';т^'щ::"сt сan bе investigated in
its purе foгm, as i,^.,;;;lТ;ъrеlу bе absеnt ioг nоt intеraсting аdatoms. In thе prеsеnt
сontгibution, -. u''- u, thе соnsldегation
-or
iш, pu,. еffесt and its сontгibution to thе
dеphasing proсеss ,n.plunar lattiсеs of intеraсting adatoms'
212
GOF
ГoRсЕs
;; i.7
r- es
n1аil.kаr.neI
Е
EI:
r
f..
b,
Wе staгt fгom th.е Hamiltonian oГa systеm of two mutually pеrpеndiсular modеs ut and?/l, pгеsеntеd in Rеf. Il0]:
fт I t r rt l 1 1flR = й\pi + pf
)+ -Inaliu'i + U(l - lo) (l)
with thе potеntial of сеntral forсеs
U(,) = Ф,r2 + Ф.rз + Фo,r ,
whеге
(2)
(3)
r=l-lo=-J(o +ur)r+u,l ,l,l
-/o tur+;uti - *uru,|zto
(/o is thе еquilibгium distanсe bеtwееn thе adatom and thе surfaсе atom bound to it, rи is theгеduсеd mass, С)' and rq aге thе fгеquеnсiеs of thе loсal and thе геsonanсе modеs, with C)L >>
a;1, whiсh is usually thе сasе if adatom is small in mass). Thе potential of thе anhaгmoniс
сoupling bеtwееn the t\^'o modеs, whеn еxpandеd in a powег se.iеЪ in u1 andиil up to the teгmofthе fouпh dеgrее appеaгs as
Uo,h = a\u,|'u] + Ф'!uf u1* Фf и] + of и| (4)
and is сhaгaсteгizеd by thе сoеffiсiеnts
,' I I
Фi = _ . (ЗФ,I^ -2Ф,), оз = iФ,, Фo- = Фt, Ф* = Фз (5)2ц z/, ' |o-,
Latеral intегaсtions bеtwееn adatoms foгming a planar lattiсе геsult in a band of сollесtiйzеd
loсal modеs whiсh is desсribеd in thе haгmoniс approхimation by thе Hamilton ian |6,1,12]
1r
H - = + > |tp (к)l, + Оi iи- (к)r, ]--.L ) L| r1\../l
'
(б)
- k' r
Hеге thе dispersion law Qц is spесifiеd by the frеquеnсy o. and paramеtеrs of dipolе-dipоlе
intеraсtiоn:
оi=о1 т еХp(_,k'R)
L"З
R I\
, / ^ 12IIOIJI*-l--'
I
m\dtt)
o
(7)
ll ailJ
withрandRгеspeсtivеlуdеnоtingthеdipolеmomеntandthеradiusvectorofthеtwo-
Ji,n"n'ionut lattiсе. -^t^.l^nс ^f intеrеst to us whiсh definеd .'h: '': 1,l"^ :,i:
Rеf I l 3 ] геpoгtеd thе
^
rеlations..:l::,.'.u to us
.
whiф ::Н,т J}ffу.-"ll"i ili
ьarмiсiiЬr''", y*'"fu::$l:i'T:.''J'r'*lff:хуlxxH:.lli.,l""'.";;Цiь::|'r::l'
*"ni-"iа* ryIIY'Ьnе simplе 'oс"l
unо.,Ёn,ij.,"ii"" in thе.prеsеnt work invoives ontу
and rеsonanс" Tgo"':,Т}1:lч:':""*жТ: ffi.'Ы;;1h. limii с11 << Г)l, whiсh еnablеs
;;;;;;;.,' of iongitudinal displaсеmеnts
',ц
iь.'.lы"ь"s to gеt simplifiеd:
(s)
A=Qn-,uх-Оо=Ao+A'
n(') =\exp(пс,llnur)
_ il-'
(e)
[?l)
= #а,(,,)[n(, )
-']iТ
"d:*;1[n.
;n-)
.'o,
whеrе 4 is thе full rrsonancе width of thе longitudinal mоdе'
?'l /l-\ -.Ф_.1
a,u _a3. =+}+Фl(k) =oт ;G -о3 /0 ()o
(1 1)
is thе tеmpеraturе.dеpеndrnt
fасtоr of thе Bosе-Еinstеin statistiсs, and
.l
o.ъ оЦ 2tФi ) (l2)
б\(к)=Ф\-#Ъ-#
isthееffесtiv.':lч.::-ff;:1ffi H::l"-:жii:ЩЁ:},##lilTJ;'::.::''}.'"tll]
:::%:::ъ",Тн:."'й';}."iБ";ii.г
isl one сan rеadily si
сoеfIiсiеnt б.l(к) with k=O whiсl sТc1:,.*" *.*,u'"'-^:I:ill;ffiТ;:#:;
o.n*ouuo,, tье1y!1eе Еq. (9)) ::]Tt*:':.j},.}:'::3:"f,""ъТТj'**:ifu*.l"ll;:;
itl"..ЬЪm"i.n.s spесifiеd bу Еq. .!5)'1'll'il'il сaiсulatеd in thе
othеr hand, the sресtral linе shift and nalтu
thеory dеpеnd on thе valuе of бl| (к) at k*0:
(13)
11,1
_ la
-ri the two-
uft and thе
d using thе
Lngs of loсal
rr.olvеs onlу
т;h еnablеs
(8)
(e)
( 14)
f
o')
\г'l
and provе to bе nonzero.
To estimate Ar an.d Г1, lеt us ехpгеss' as in Rеf. [ 1 l ], the сoеfftсiеnt Фз in tегms of thеbond еnеrgy Д of a Могsе potentiai appioхimatingiье,гunсtion U?) and intгoduсе thеparamеtег AС)o"'o = maх|Qр-Q6| сharaсtегizing the width of thе loсal viЬгatiоn band. Тhеn
- 4 B + Ч,('u)|,@u)-']
[lffi : : ?,',)
whеге B : hl2mlo2 is thе гotation сonstant оf thе light atom with thе mass rl геsiding at thе
distаnсе /o fгom thе сoггеsponding hеalry atom ofthе suгfaсе, Foг a hydгogеn atom and /о д: l
.An we oЬtain B - |9 сm-'. Тhе ratio hСlnlЕn for H on thе Si(l11) tl4] and C(ll1) [15,16]suгfaсеs as wеll as that foг Н in hуdгoхуl gгoups on vaгious oхidе suгfaЬеs [17] is uЬout Ь.ron thе othег hand, thе гatio {2oq/а4, foг thе same sуstems оhangеs in a widе гangЪ, from 0.2 to
2 5 Thеn atk,T:h.соand Ae)ь.nа = ?, 1\,е aггivе at Ar - Гr
^,
l - 10 сm-l
Сlеarly thе band еffесt сonсегnеd pгovеs to bе гathеr slight for systеms with wеak
latеral intеraсtions, whiсh сan bе ехеmplifiеd bу thе sуstem I'C(йl): ДQм"а * 1'4 cm-,, rl *
12O сm.| [16], and thе full rvidth is fоund as 2Гr э O 04 .--,. Ho*.uеr, anothег systеm,oFvsio2, pгеsеnts thе сasе whеrе thе low-frequеnсу modе сoгresponds to the гotational
vibration of a hydroryl group around thе Si-o bond with the fтеquЁnсyq - 10O сm.l; this
vibгation is slightly сouplеd with thе phonon spесtrum of thе substraie and hеnсе thе valuе n *4 сm.l tuгns out to bе small еnougй and сoЬpa.ablе tо AО6"n, - z
"n,,....ii;i
.i;
;# ";l;rеlation (13) givеs thе valuе 2Г1х Q сm.I of t!1 samе oгdег of magnitudе asЪхpегimеntally
obsеrvеd onеs [l8] Thе 2х.1 phasе of Сo,lЪIaСl(.lOO) is anothJr eхamplе of a system
сharaсtегizеd Ьу п * 2,8 сm.l, and АС)6un. = 6. сm.l (udging by thе sсalе of thе Davydov
splitting foг thе spесtгal linе of Co loсal vibгations *йi"ь- is-obsеrvеd at tеmpегatuгеs Т <
2s K) [3,4].
Thus, in paгallеl with othеr dеphasing mесhanisms, thе band dephasing еffесt сannotaЬlу сontгibutе to thе shift and width of the spесtгal linе of loоal vibгaiions, |rovided thе
band width foг thesе loсal vibrations is сompaгеd to thе геsonanсе width of thе iй-f,.qu"n.у
modе. Thе modеl involving thе potеntial oГ сеntгal foгоеs pегmittеd thе ..puге'' band еfiесt tЬ
bе trеatеd: thе speсtгal line shift and width aге pгopoгtionaito thе сubеd and thе squaгеd band
width for loоal vibгations, AO6"n6, and vanish at AQ6.n3 :0.
Aсknorvlеdgments
This woгk was finanсiallу suppoгtеd by thе China Pеtгolеum Corpoгation.
Rеfеrenсеs
l. Peгsson B.NJ. and Rуbегg R Vibгational intегaсtioп bеtwееn moleсulеs adsorbеd on a
mеtal suгfaсе: Thе dipole-dipole interaсtion // Phys. Rev' B -l98l. - v 24. - P. 6954 -
697О
2' Tеmpеraturе dеpеndenсе of thе vз absoгption of thе monolayег Co2 adsoгbеd on
NaCl(100). сontinuous сhangе in adsоrbatе 8eomеtry and vibгatiоnal dеphasing /
J' Hеidbегg, Е' Kampshoff , R Krihnеmuth' o. Sсhоnekas // SuгГ Sсi. - lssi. .
У . 269/270. - P. 120 - 12.7
'). \- -.
,J
trol
(11)
(12)
rе сubiс
:q (10)
:malizеd
:-d.ordеr
.rishеs if
on thе
:':
_ jгbation
(13)
215
Fouгiег-tгansfогm infгaгеd spесtra of Сo adsorbed on NaCl(l00): struсtural сhangеs at low_йp..u,.,,"s
/ J Hеidbе.!, в кunlpshoff, R.Ktihnemuth' М.Suhгеn' H. Wеiss // Surf.
Sсi - 1992 - у.26912.7О . P. 128 - 134.
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fеггoеlесtгiс (2 х 1) monolayег- Co adsorbеd on NaСl(001) i J. Hеidbегg, М.Grunwald,
М. Hustеdt, F. Traеger // Suгf. Sсi. - 1996 - v. 368. . P ' |26 - 1з2.
Pегsson B.N.J , Hoffman F.M., Rybегg R. Influеnсе of еxсiton motion on the shape of
optiсa1 absoгption linеs' Appliсations й vibгations at suгfaсеs i/ Phуs. Rеv. B. - 1986. -
V 34. N 4 .P.2266 -228з
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Tvеrd. Tеla. - l99s - V 4ъ. N 1 - P l52 - 155 [Phуs. Sol. Statе. - 1998. . v.40. -
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adsorbеdmolесulеs//Surf. Rеv, t-еtt' - 1998..v 5.N 5. -P 965-970.
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tеst foг vibгational phasе rеlaхation at surfaсеs // Phуs. Rеv. Lеtt. . 19s7. - V. 59. N l9. _
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2t6
|
| id | oai:ojs.pkp.sfu.ca:article-60 |
| institution | Surface |
| keywords_txt_mv | keywords |
| language | English |
| last_indexed | 2025-09-24T17:44:39Z |
| publishDate | 2001 |
| publisher | Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine |
| record_format | ojs |
| resource_txt_mv | surfacezbircomua/e1/e5a2e56089ef71cee65457c2c2edd7e1.pdf |
| spelling | oai:ojs.pkp.sfu.ca:article-602018-11-27T09:42:39Z Band effect in vibrational dephasing of adatoms bound to surface by central forces Band effect in vibrational dephasing of adatoms bound to surface by central forces Band effect in vibrational dephasing of adatoms bound to surface by central forces Rozenbaum, V. M. Lin, S. H. The effect of lateral interactions of adatoms on the spectral line of their local vibrations is analyzed in terms of a simple model which includes only central forces binding adatoms to a surface, so that in a case free of lateral interactions the contribution from the surface- longitudinal vibrational mode to the dephasing process should vanish (K. Burke, D. C. Langreth, M. Persson, Z.-Y. Zhang, Phys. Rev. B 47 (1993) 15869). The lateral interactions are shown to cause the spectral line shift and broadening which are proportional to the cubed and the squared ratio of the band width for collectivized local vibrations to the resonance width for the longitudinal mode; as a result, band effect causes a notable contribution, provided this ratio is of order of unity. The effect of lateral interactions of adatoms on the spectral line of their local vibrations is analyzed in terms of a simple model which includes only central forces binding adatoms to a surface, so that in a case free of lateral interactions the contribution from the surface- longitudinal vibrational mode to the dephasing process should vanish (K. Burke, D. C. Langreth, M. Persson, Z.-Y. Zhang, Phys. Rev. B 47 (1993) 15869). The lateral interactions are shown to cause the spectral line shift and broadening which are proportional to the cubed and the squared ratio of the band width for collectivized local vibrations to the resonance width for the longitudinal mode; as a result, band effect causes a notable contribution, provided this ratio is of order of unity. The effect of lateral interactions of adatoms on the spectral line of their local vibrations is analyzed in terms of a simple model which includes only central forces binding adatoms to a surface, so that in a case free of lateral interactions the contribution from the surface- longitudinal vibrational mode to the dephasing process should vanish (K. Burke, D. C. Langreth, M. Persson, Z.-Y. Zhang, Phys. Rev. B 47 (1993) 15869). The lateral interactions are shown to cause the spectral line shift and broadening which are proportional to the cubed and the squared ratio of the band width for collectivized local vibrations to the resonance width for the longitudinal mode; as a result, band effect causes a notable contribution, provided this ratio is of order of unity. Chuiko Institute of Surface Chemistry National Academy of Sciences of Ukraine 2001-06-10 Article Article application/pdf https://surfacezbir.com.ua/index.php/surface/article/view/60 Surface; No. 4-6 (2001): Chemistry, Physics and Technology of Surface; 212-216 Поверхность; № 4-6 (2001): Химия, физика и технология поверхности; 212-216 Поверхня; № 4-6 (2001): Хімія, фізика та технологія поверхні; 212-216 3154-8091 3154-8083 en https://surfacezbir.com.ua/index.php/surface/article/view/60/59 Авторське право (c) 2001 V.M. Rozenbaum, S.H. Lin |
| spellingShingle | Rozenbaum, V. M. Lin, S. H. Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title | Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title_alt | Band effect in vibrational dephasing of adatoms bound to surface by central forces Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title_full | Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title_fullStr | Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title_full_unstemmed | Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title_short | Band effect in vibrational dephasing of adatoms bound to surface by central forces |
| title_sort | band effect in vibrational dephasing of adatoms bound to surface by central forces |
| url | https://surfacezbir.com.ua/index.php/surface/article/view/60 |
| work_keys_str_mv | AT rozenbaumvm bandeffectinvibrationaldephasingofadatomsboundtosurfacebycentralforces AT linsh bandeffectinvibrationaldephasingofadatomsboundtosurfacebycentralforces |