IAOe?IIAEUeIA AEAAeAI?ss IAOE OE?A?IE

O?CEEI-OAOI?*IEE ?INOEOOO IECUeEEO OAIIA?AOO? ?i. A.?.A??E?IA

Ia i?aaao ?oeiieno

Naaio/aiei Na?a?e ?aaaiiae/

OAeE 539.2

Iniaeeaino? oiiiiieo niaeo??a oa ?aciiainieo aeanoeainoae e?enoae?a c
ieineeie aeaoaeoaie

01.04.02 — oai?aoe/ia o?ceea

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy eaiaeeaeaoa
o?ceei-iaoaiaoe/ieo iaoe

Oa?e?a — 1998 ?.

Aeena?oaoe?y ? ?oeiienii.

?iaioa aeeiiaia o O?ceei-oaoi?/iiio ?inoeooo? iecueeeo oaiia?aoo? ?i.
A.?. A??e?ia IAI Oe?a?ie.

Iaoeiaee ea?iaiee — Einaae/ A?iieueae Ia?eiae/, /eai-ei?. IAI Oe?a?ie
aeieoi? oiceei-iaoaiaoe/ieo iaoe i?ioani?, caaiaeoth/ee aiaeaeieii OO?IO
?i. A.?. A??e?ia IAI Oe?a?ie.

Io?oe?ei? iiiiaioe:

?aaiia Ieoaeei Ieaen?eiae/, ae. o.-i. i. i?ioani?, caa?aeoth/ee
a?aeae?eii ?inoeoooo iaoaeio?ceee ?i. A.A.Eo?aethiiaa IAI Oe?a?ie;

Ainiiaea?ueia ?ai? Ieaenaiae?iae/, e. o.-i. i., iaoeiaee ni?a?ia?oiee
OO?IO ?i. A.?.A??e?ia IAI Oe?a?ie.

I?iaiaeia onoaiiaa: Oa?e?anueeee aea?aeaaiee oi?aa?neoao, eaoaae?a
oai?aoe/ii? o?ceee.

Caoeno a?aeaoaeaoueny 16 aa?aciy 1999 ?. i 15 aiaeei? ia can?aeaii?
Niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.175.02 ii caoenoo aeieoi?nueeeo
aeena?oaoe?e i?e O?ceei-oaoi?/iiio ?inoeooo? iecueeeo oaiia?aoo? ?i.
A.?. A??e?ia IAI Oe?a?ie ca aae?anith: 310164, i.Oa?e?a, i?.Eai?ia, 47.

C aeena?oaoe??th iiaeia iciaeiieoeny a a?ae?ioaoe? OO?IO ?i. A.?.
A??e?ia IAI Oe?a?ie (i.Oa?e?a, i?.Eai?ia, 47).

Aaoi?aoa?ao ?ic?neaii 16 ethoiai 1999 ?.

A/aiee nae?aoa? Niaoe?ae?ciaaii? a/aii? ?aaee Ae 64.175.02

Aeieoi? o?ceei-iaoaiaoe/ieo iaoe Eiaaeueia I.N.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie

Aea/aiiy eieeaaeueieo oa?aeoa?enoee ??cieo oei?a iiaa?oiaaeo oaeeue a
e?enoaeao iaiao?aeia aeey iieno iiaa?oiaaeo yaeu o oaa?aeeo o?eao ? aeey
aaeineiiaeaiiy i?eno?i?a, a yeeo aeei?enoiaothoueny iiaa?oiaa? oaee?, a
oaeiae aeey ?icoe?aiiy iaeanoae ?o oaoi?/iiai canoinoaaiiy. Iaea?eueo
oe?iea canoinoaaiiy ia i?aeoeoe? io?eiaee oaee? ?aea?anueeiai oeio, ui
iathoue eiiiiiaioo aaeoi?a ci?uaiiy, ia?iaiaeeeoey?io aei iiaa?oi?
e?enoaeo. Oey inoaiiy ianoaaeia ?iaeoue oaee? ?aea?anueeiai oeio
c?o/ieie aeey aea/aiiy aenia?eiaioaeueieie iaoiaeaie, ao?oeeaee ?icaeoie
yeeo a?aeaoaa?oueny i?ioyaii inoaii?o aeanyoee?oue. Iniaeeaee ?ioa?an a
iao /an aeiee aei aea/aiiy ?aciiainii? aca?iiae?? oaeeue c ieineei
aeaoaeoii o e?enoae?. I?eeeaaeaie ieineeo aeaoaeo?a a e?enoaeao iiaeooue
aooe aea?eieeia? iaae?, i?aeoaci? iaae?, aeaiaei??i? aeaoaeoe oiaeiaee
oa ?io?. Aeei?enoaiiy aaaaoioa?iaeo e?enoae?/ieo nenoai a aeaeo?ii?oe?
oa aeonoiaeaeo?ii?oe?, yea /anii a?oioo?oueny ia ?aciiainieo
aeanoeainoyo oaeeo nenoai, aeiaaa? aiae?co iniaeeainoae niaeo?o
eieeaaiue, ye? aeieeathoue ca ?aooiie aeaiaei??ieo iaae, ui
?icae?eythoue iiiie?enoae?/i? oa?e. Iniaeeaino? ?iciianthaeaeaiiy ??cieo
oei?a eieae?ciaaieo oaeeue iiaeeco ieineeo aeaoaeo?a oa aca?iiae?y
ia’?iieo oaeeue c iiaa?oiath iiaeii? a?aoiaoaaoeny a oeueo?acaoeia?e
aeaoaeoineii??, nenoaiao ia?iaee neaiae?a, aenia?eiaioaeueieo iaoiaeao
aea/aiiy aeanoeainoae oaa?aeeo o?e ? iiaa?oiaaeo yaeu. Ana ia?ae?/aia
aeua ?iaeoue aeooaeueiei ?icaeoie aeine?aeaeaiue niaeo?aeueieo
oa?aeoa?enoee ??cieo oei?a oaeeue o e?enoaeao c ieineeie aeaoaeoaie.

Ca’ycie ?iaioe c iaoeiaeie i?ia?aiaie, ieaiaie, oaiaie

?iaioa aeeiiaia o O?ceei-oaoi?/iiio ?inoeooo? iecueeeo oaiia?aoo?
?i.A.?.A??e?ia IAI Oe?a?ie o a?aeae?eo eaaioiaeo aeanoeainoae oa
iae?i?eieo yaeu o iae?ineii?/ieo nenoaiao o iaaeao oaiaoe/iiai ieaio
aeine?aeaeaiue ca oaiith “Aaceaaeaey o e??ie?enoaeao”, ? aea?ae. ?a?no?.
0196U0002950, a oaeiae ca i?iaeoaie “No?oi”, ? 4.2/88 oa “Aea?eiee”, ?
2.3/624 i?ia?ai AeEIO Oe?a?ie (oiiae ooiaeaiaioaeueieo aeine?aeaeaiue).

Iaoa oa iniiai? caaea/? aeine?aeaeaiiy

Iaoith aeena?oaoe?eii? ?iaioe aoei oai?aoe/ia aeine?aeaeaiiy aieeao
ciai?oiuei? iiaa?oi? oa ieineeo aeaoaeo?a ia niaeo?e ??cieo oei?a
oiiii?a o e?enoaeao. Aea/aiiy i?iaiaeeeinue iaoiaeaie aeeiai?ee
e?enoae?/ii? a?aoee ia iniia? ii??aiyii i?inoeo iiaeaeae e?enoae?a c
ieineeie aeaoaeoaie. I?aaeiaoii ?icaeyaeo aoee oaee? ?aea?anueeiai oeio,
ci?uaiiy a yeeo ia? ii?iaeueio aei ieiueie aeaoaeoo eiiiiiaioo, oae ye
aiie aeia?a niinoa??aathoueny a aenia?eiaioao ? io?eiaee oe?iea
canoinoaaiiy a oaoi?/ieo i?eno?iyo. Iniiaio oaaao iaiao?aeii i?eae?eeoe
iniaeeainoyi eieeaaiue c /anoioaie a nooe?eueiiio niaeo??, oaeei ye
inaaaeieieae?ciaai? eieeaaiiy (eaac?iiaa?oiaa? oiiiie) oa oaee?
o?ainoi?iaoe??, oiio ui ?ai?oa ia aoei ?icaeyiooi oaee eieeaaiiy o
aaeoi?ieo aeene?aoieo iiaeaeyo. Inaaaeieieaeueieie iaceaathoue
noaoe?iia?i? eieeaaiiy, o yeeo iaeia eiiiiiaioa eieae?ciaaia iiaeeco
ieineiai aeaoaeoo, a ae?oaa — ia eieae?ciaaia. I?ae o?ainoi?iaoe??th
?icoi?thoue i?ioean, i?e yeiio ia iiaa?oith e?enoaeo iaaea? oaeey
iaei??? iiey?ecaoe?? (iai?eeeaae, iiia?a/ia), a a?aeaeaa?oueny — ?ioi?
(iai?eeeaae, iiacaeiaaeiy).

Aeey aeinyaiaiiy iinoaaeaii? iaoe a aeai?e aeena?oaoe?ei?e ?iaio? aoei
iaiao?aeii ?ica’ycaoe oae? caaea/?:

1) ia i?eeeaae? i?inoi? iiaeae? aaenaaiiaeueiiai 2D e?enoaeo aea/eoe
niaeo?e iiaa?oiaaeo oa eaac?iiaa?oiaaeo oiiii?a, a oaeiae aieea
iaieeaiiai ia iiaa?oith e?enoaeo iiiioa?o ?cioii?/ieo aeii?oie ia
niaeo?e /anoio eieaeueieo eieeaaiue;

2) o aeene?aoi?e iiaeae? aeine?aeeoe i?ioeane o?ainoi?iaoe?? oiiii?a i?e
a?aeaeoo? a?ae iiaa?oi? e?enoaeo;

3) aea/eoe iniaeeaino? ?aciiainii? aca?iiae?? oiiii?a c ieineei
aeaoaeoii a /anoioiiio ae?aiacii?, aea ?niothoue inaaaeieieae?ciaai?
iiaee eieeaaiue.

Iaoeiaa iiaecia iaea?aeaieo ?acoeueoao?a

Aia?oa ia aac? aeeiai?ee e?enoae?/ii? a?aoee a iai?aiaiaaeaiiio
aaenaaiiaeueiiio e?enoae? aea/aii iniaeeaino? nooe?eueiiai niaeo?o
ia’?iieo eieeaaiue, ui iia’ycai? c o?ainoi?iaoe??th aeonoe/ieo oaeeue.
?ic?aoiaaii aeenia?n?ei? e?ea? (caeaaeiino? /anoio a?ae oaeeueiaiai
aaeoi?a) aeey oaeeue o?ainoi?iaoe??. Canoinoaaiiy iaoiae?a aeeiai?ee
e?enoae?/ii? a?aoee aeicaieeei aea/eoe iia? iniaeeaino? eieeaaiue, ye?
ia iiaeooue aooe io?eiaii ca aeiiiiiaith ??aiyiue oai??? i?oaeiino?. A
?acoeueoao? aaeaeinue aeyaeoe iia? oe?eaa? ?ene niaeo?o eieeaaiue a
ei?ioeioaeeueia?e iaeano?, ye? iia’ycai? c i?iaeiaaeaiiyi aeenia?n?eieo
e?eaeo iiaa?oiaaeo oaeeue a nooe?eueiiio niaeo?? o aeaeyae? e?i?e
/anoio oaeeue o?ainoi?iaoe??.

Aia?oa aoei aea/aii i?iaeaio ?nioaaiiy eaac?iiaa?oiaaeo oiiii?a
(inaaaeieieae?ciaaieo eieeaaiue) a aeene?aoi?e iiaeae? oa aecia/aii
iaeanoue, o iaaeao yei? eaaeeoue iaia?a?aiee niaeo? inaaaeieieaeueieo
noai?a, oiaoi eieeaaiue, iiacaeiaaeia eiiiiiaioa yeeo eieae?ciaaia eiei
aeaoaeoo, a iiia?a/ia ia? aeaeyae noiy/i? oaee? a ia’?i? e?enoaeo.
?nioaaiiy inaaaeieieaeueieo eieeaaiue oeiiaa aeey aaaaoieiiiiiaioieo
iie?a ? oiio oe? ?acoeueoaoe ?iaioe iiaeooue aooe ?iciianthaeaeaieie ia
aeiaaeee ?ioeo o?ce/ieo aaaaoieiiiiiaioieo iie?a.

Anoaiiaeaii, ui i?e /anoioao, ye? oa?aeoa?i? aeey inaaaeieieaeueieo
noai?a, aeieeathoue yaeua ?aciiainiiai ?icn?yiiy oiiii?a ieineei
aeaoaeoii a e?enoae?. ?aciiainia ?icn?yiiy noa? iiaeeeaei ca ?aooiie
aca?iiae?? oiiii?a iaei??? c a?eie ia’?iieo eieeaaiue ?c eieae?ciaaieie
eiei aeaoaeoo eieeaaiiyie ?ioi? a?eee nooe?eueiiai niaeo?o. *anoioa
oiiiia, ui ?icn?th?oueny, ni?aiaaea? c /anoioith inaaaeieieaeueiiai
eieeaaiiy. Oaea ?aciiainia ?icn?yiiy aeonoe/ieo oaeeue aoei oai?aoe/ii
ia?aaeaa/aii cian?i iaaeaaii, ? eiai aiae?c a aeene?aoi?e iiaeae?
e?enoaeo aoa aia?oa i?iaaaeaiee aeena?oaioii. Iaeiei c oe?eaaeo
?acoeueoao?a, iaea?aeaieo a ?iaio?, ? aeieac iiaeeeaino? iiaiiai
a?aeaeooy aai iiaiiai i?ioiaeaeaiiy oiiii?a i?e iaaieo /anoioao e??cue
ieineee aeaoaeo. Caeiie aeenia?n?? oaeeo oiiii?a aeey aeia?eueieo
cia/aiue oaeeueiaiai /enea a iaaeao ciie A?eeethaia ?ic?aoiaaii aia?oa,
a oaeiae aeine?aeaeaii aieea oa?aeoa?enoee aeaoaeoo ia iiaaae?ieo
?aciiainieo /anoio.

Iaoeiaa iiaecia iaea?aeaieo a aeena?oaoe?ei?e ?iaio? ?acoeueoao?a
aecia/a?oueny oaeeie iieiaeaiiyie:

1. A ?aieao iiaeae? aeaiaei??iiai aaenaaiiaeueiiai e?enoaeo c
aca?iiae??th iaeaeeae/eo non?ae?a aea/ai? iiaa?oiaa? oaee? ?aea?anueeiai
oeio i?e iayaiino? aeii?oeiaeo aoii?a ia iiaa?oi? e?enoaeo.

2. Aia?oa a aeene?aoi?e aaeoi?i?e iiaeae? aea/aii inaaaeieieae?ciaai?
eieeaaiiy. Ciaeaeaii iaia?a?aiee niaeo? /anoio eaac?iiaa?oiaaeo oiiii?a
oa aecia/aii iaae? ?o ?nioaaiiy.

3. Aeyaeaii nenoaio iniaeeaeo e?i?e a niaeo?? ia’?iieo eieeaaiue, eio?a
iia’ycaia c ??ciiai ?iaeo o?ainoi?iaoe?yie oiiii?a i?e a?aeaeoo? a?ae
iiaa?oi? e?enoaeo. E?ea? o?ainoi?iaoe?? ?ic?aoiaai? a oe?ieiio ?ioa?aae?
aeiaaeei oaeeue a iiaeae?, ui ?icaeyaea?oueny.

4. Aea/aii yaeua ?aciiainiiai a?aeaeooy ? i?ioiaeaeaiiy oiiii?a e??cue
ieineee aeaoaeo a AOeE e?enoae?. Aia?oa ?ic?aoiaai? niaeo?e oaeeo
?aciiainii aca?iiae?th/eo c aeaoaeoii oaeeue a iaeano? inaaaeieieaeueieo
eieeaaiue ye iecueei/anoioiiai, oae ? aeniei/anoioiiai oei?a.

I?aeoe/ia cia/aiiy ?acoeueoao?a aeena?oaoe??

A aeai?e ?iaio? i?iaaaeaii aiae?c iniaeeainoae niaeo??a eieaeueieo
eieeaaiue, ye? nooo?ai aieeaathoue ia oa?iiaeeiai?/i? oa?aeoa?enoeee
oaa?aeeo o?e i?e iecueeeo oaiia?aoo?ao. ?ic?aoiaai? /anoioi? caeaaeiino?
?aciiainii? aca?iiae?? oaeeue c ieineei aeaoaeoii iiaeooue aooe
aeei?enoai? i?e aeine?aeaeaii? i?ioean?a ?icn?yiiy ??cieo aeae?a
ciai?oiueiai aei?ii?ithaaiiy a e?enoaeao c aeaoaeoaie aai a
aaaaoioa?iaeo e?enoaeao, a oaeiae aeey iiaeaeueoiai aaeineiiaeaiiy
iaoiae?a ia?oeioth/iai eiio?ieth oa noai?aiiy iiaeo aeonoiaeaeo?iiieo
i?eeaae?a.

Iniaenoee aianie aeena?oaioa

Aeena?oaio i?eeiaa aeoeaio oa aaciina?aaeith o/anoue ia an?o aoaiao
aeeiiaiiy oeueiai aeine?aeaeaiiy: ?ic?iaoe? i?aeoiae?a oa iaoiae?a
ae??oaiiy iinoaaeaieo caaea/, iaoaiaoe/iiio iiaeaethaaii? oa i?iaaaeaii?
/eneiaeo ?ic?aooie?a, ia?iaoe? io?eiaieo ?acoeueoao?a, a oaeiae
iaienaii? iaoeiaeo noaoae oa i?aeaioiaoe? aeiiia?aeae ia eiioa?aioe?yo.
Iniaenoi caeiaoaa/ai aoei i?iaaaeaii ?ic?aooiee niaeo??a iiaa?oiaaeo oa
eaac?iiaa?oiaaeo oiiii?a, a oaeiae eieae?ciaaieo eiei ieineiai aeaoaeoo
eieeaaiue.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??

Iniiai? iaoeia? ?acoeueoaoe aoee ai?iaiaai? ia I?aeia?iaeieo
eiioa?aioe?yo: III eiioa?aioe?y “O?ce/i? yaeua o oaa?aeeo o?eao”,
Oa?e?a, 1997; 7-a eiioa?aioe?y e?a?i NIAe “?aaeeaoeeiiiay
iia?aaeaeaaiinoue e ?aaioiniiniaiinoue eiino?oeoeeiiiuo iaoa?eaeia” a
iaaeao nai?ia?o “Iaeeiaeiua e iiaa?oiinoiua aieiu”, A?eai?iae, 1997; III
EUROMECH Solid Mechanics Conference (IV:W9), Stockholm, Sweden, 1997;
9-th International Conference on Phonons Scattering in Condensed Matter
(DE2, PosC22), Lancaster, UK, 1998, a oaeiae iaaiai?thaaeenue ia
iaoeiaeo nai?ia?ao a?aeae?eo eaaioiaeo aeanoeainoae oa iae?i?eieo yaeu o
iae?ineii?/ieo nenoaiao O?ceei-oaoi?/iiai ?inoeoooo iecueeeo oaiia?aoo?
?i.A.?.A??e?ia IAI Oe?a?ie.

Ioae?eaoe??

?acoeueoaoe aeine?aeaeaiue ca oaiith aeena?oaoe?? aoee iioae?eiaai? o 7
iaoeiaeo i?aoeyo, c ieo 4 noaoo?:

1. A.I.Einaae/, Ae.A.Iaoeieei, N.A.Naaio/aiei. Eieaaaiey ?yeaaaneiai
oeia, eieaeeciaaiiua o naiaiaeiie iiaa?oiinoe AOeE e?enoaeea. OIO, 1997,
23, N1, n. 92-96.

2. A.I.Einaae/, N.A.Naaio/aiei, Ae.A.Iaoeieei. Eieaeeciaaiiua e
eaaceeieaeeciaaiiua aieiu a AOeE e?enoaeea. Iao/iua aaaeiiinoe AAO,
1998, Aaeai?iae: ecae-ai AAO, N1(6), n. 191-198.

3. A.I.Einaae/, Ae.A.Iaoeieei, N.A.Naaio/aiei. Iiaa?oiinoiua e
eaaceiiaa?oiinoiua oiiiiu e aieiu o?ainoi?iaoeee a aaenaaiiaeueiii
e?enoaeea. OIO, 1998, 24, N10, n. 992-1002.

4. A.I.Einaae/, Ae.A.Iaoeieei, N.A.Naaio/aiei. Iniaaiiinoe ?aciiainiiai
?annayiey oiiiiia ieineei aeaoaeoii a AOeE e?enoaeea. OIO, 1999, 25, N1,
n.63-71,

oa 3 oace aeiiia?aeae ia I?aeia?iaeieo eiioa?aioe?yo:

1. A.I.Einaae/, N.A.Naaio/aiei, Ae.A.Iaoeieei. Eieaeeciaaiiua e
eaaceeieaeeciaaiiua eieaaaiey aaeece naiaiaeiie iiaa?oiinoe aeene?aoiie
e?enoaeee/aneie ?aoaoee. Iaoa??aee III eiioa?aioe?? “O?ce/i? yaeua o
oaa?aeeo o?eao”, 1997, Oa?e?a, n.40.

2. A.I.Einaae/, N.A.Naaio/aiei, Ae.A.Iaoeieei. Eieaeeciaaiiua eieaaaiey
aaeece ieineiai aeaoaeoa a AOeE e?enoaeea. Iaoa??aee 7-i? eiioa?aioe??
e?a?i NIAe “?aaeeaoeeiiiay iia?aaeaeaaiinoue e ?aaioiniiniaiinoue
eiino?oeoeeiiiuo iaoa?eaeia”, 1997, A?eai?iae: ecae-ai AAO, n.158.

3. A.M.Kosevich, S.E.Savotchenko and D.V.Matsokin. Localized and
pseudolocalized waves at a free surface of FCC crystal. Book of
Abstracts III EUROMECH Solid Mechanics Conference, 1997, Stockholm,
Sweden, p.344.

No?oeoo?a oa ianya aeena?oaoe??

Aeena?oaoe?eia ?iaioa neeaaea?oueny c anooio, o?ueio ?icae?e?a,
aeniiae?a, nieneo aeei?enoaieo aeaea?ae ( c? 101-ai iaeiaioaaiiy) oa
aeaio aeiaeaoe?a. Ci?no ?iaioe aeeeaaeaii ia 123 noi??ieao oa 26
iaethieao.

INIIAIEE CI?NO ?IAIOE

O anooi? iaa?oioiaaii aea?? oaie aeena?oaoe?eii? ?iaioe oa ??
aeooaeuei?noue. Iniaeeao oaaao i?eae?eaii oiio oaeoo, ui aea?ai? ca
i?aaeiao aeine?aeaeaiiy oaee? ?aea?anueei? iiey?ecaoe?? ciaeoee oe?iea
canoinoaaiiy a oaoi?oe? ? iiaeooue aeia?a aea/aoeny aenia?eiaioaeueieie
iaoiaeaie, a oaeiae aeei?enoiaoaaoeny aeey io?eiaiiy ?ioi?iaoe?? a
iaeano? o?ceee iiaa?oiaaeo yaeu. Noi?ioeueiaaii iaoo ? caaea/?
aeine?aeaeaiue, i?iaaaeaieo a aeai?e ?iaio?, iaoeiao iiaecio iaea?aeaieo
?acoeueoao?a oa ?o i?aeoe/ia cia/aiiy.

O ia?oiio ?icae?e? iaaaaeaii ei?ioeee iien iniiaieo oei?a iiaa?oiaaeo
oaeeue o oaa?aeeo o?eao oa ?o aeanoeainoae. C?iaeaii e?oa?aoo?iee iaci?
?nioth/eo oai?aoe/ieo oa aenia?eiaioaeueieo ?acoeueoao?a. Iniaeeaee
aeoeaio c?iaeaii ia ?aea?anueeeo oaeeyo, eieae?ciaaieo iiaeeco iiaa?oi?
[1,2] oa ieineiai aeaoaeoo a e?enoaeao [3,4]. I?iaiae?ciaaii aieea
ai?cio?ii?? ia iniia? ?ia?o [5,6,7] oa aeene?aoiino? e?enoae?/ii? a?aoee
ia oa?aeoa?enoeee iiaa?oiaaeo oaeeue [8,9,10].

, (a iaeano? ?nioaaiiy eaac?iiaa?oiaaeo oiiii?a).

Aaeeeo oaaao a inoaiiueiio ioieo? ia?oiai ?icae?eo i?eae?eaii
iiaeeeainoyi canoinoaaiiy iiaa?oiaaeo oaeeue a no/anieo oaoiieia?yo ?
noi?ioeueiaaii iniiai? aeanoeaino? iiaa?oiaaeo oaeeue, ye? ? iaea?eueo
aaaeeeaeie aeey aeei?enoaiiy ?o c i?aeoe/iith iaoith.

O iiia?aaeieo aeine?aeaeaiiyo ia?icaeyiooeie caeeoeeenue ieoaiiy i?i
aeanoeaino? eieae?ciaaieo eiei ieineiai aeaoaeoo eieeaaiue ?aea?anueeiai
oeio oa ?aciiaini? iniaeeaino? i?ioean?a ?icn?yiiy aeaieiiiiiaioieo
oiiii?a aeaoaeoii, a oaeiae i?ioeane o?ainoi?iaoe?? oaeeue i?e a?aeaeoo?
a?ae iiaa?oi? e?enoaeo o aaeoi?ieo aeene?aoieo iiaeaeyo. Ianooii?
?icae?ee ?iaioe i?noyoue ?acoeueoaoe i?iaaaeaieo aeena?oaioii
aeine?aeaeaiue oaeeo oei?a oaeeue a e?enoaeao c ieineeie aeaoaeoaie.

Ae?oaee ?icae?e i?enay/aii aea/aiith iniaeeainoae niaeo??a iiaa?oiaaeo
oiiii?a a e?enoae?. ?icaeyiooi i?inoo iiaeaeue ?cio?iiii?
aaenaaiiaeueii? a?aoee [8] c oeaio?aeueiith aca?iiae??th iaeaeeae/eo
non?ae?a, ui oa?aeoa?eco?oueny ia?aiao?ii a. Aaenaaiiaeueio a?aoeo
aea?aii oiio, ui /a?ac eiaeai ?? aocie ia?iaiaeeeoey?ii aaceni?e ieiuei?
i?ioiaeeoue a?nue neiao??? oinoiai ii?yaeeo. Oea icia/a?, ui
oa?aeoa?enoeee aeiaaioaeeueiaeo eieeaaiue oaei? aeene?aoii?
aaenaaiiaeueii? a?aoee aoaeooue aea?aaeaioi? a?aeiia?aeiei
oa?aeoa?enoeeai eieeaaiue ?cio?iiiiai na?aaeiaeua, ui i?aeoaa?aeaeaii
?ic?aooieaie. Nooe?eueiee niaeo? eieeaaiue aaenaaiiaeueiiai e?enoaeo
(cao?eoiaai? iaeano? ia iae. 1-3) neeaaea?oueny c aeaio a?eie, ye?
aoaeaii iaceaaoe iiia?a/iith (t) oa iiacaeiaaeiith (l).

Iieacaii, ui a aeiaaioaeeueiaiio iaaeeaeaii? ak<<1 (oa?aeoa?ia aeiaaeeia oaee? i?oaeieo eieeaaiue iaaaaaoi a?eueoa ca i?aeaoiiio a?aenoaiue a) aeenia?n?eia ??aiyiiy i?eaiaeeoueny aei a?aeiiiai ??aiyiiy ?aea?anueeeo oaeeue [16] (1) , ui a?aeiia?aeathoue oaeaeeinoyi oaeeue o?ainoi?iaoe?? c? ci?uaiiyi aeaeo , aea (2) ?aae?co?oueny i?ioean, i?e yeiio ia iiaa?oith e?enoaeo iaaea? iiia?a/ia oaeey, a a?aeaeaa?oueny iiacaeiaaeiy. *anoioi? caeaaeiino? oaeeue o?ainoi?iaoe?? oa iiaa?oiaaeo oaeeue ?ic?aoiaai? aeey aeia?eueieo cia/aiue oaeeueiaiai /enea a iaaeao a?aieoe? ia?oi? ciie A?eeethaia (iae. 1). Anoaiiaeaii, ui e?eaa /anoio oaee? o?ainoi?iaoe?? A1, aeiaaioaeeueiaa oaciaa oaeaee?noue yei? n1, i?eoiaeeoue a oi/eo u?eeie nooe?eueiiai niaeo?o, a ye?e ia?ao?auothoueny aa?oiy a?aieoey t- oa ieaeiy a?aieoey l- a?eie ia'?iieo eieeaaiue, ? ca?aeee ii/eia?oueny aeenia?n?eia e?eaa u?eeiii? iiaa?oiaai? oaee? S2. E?i?y /anoio oaee? o?ainoi?iaoe?? B2, a aeiaaioaeeueiaiio iaaeeaeaii? oaeaee?noue yei? n2 , ia?aoiaeeoue ii/eiath/e c i?e k=2p/3 a iaeanoue l-a?eee nooe?eueiiai niaeo?o (e?i?y A3 ia iae. 1), aea ia?a??ce ?ci/anoioieo iiaa?oiiue ieiueiith kOkz ? iaiioeeeie, ? eiaeiiio oaeeueiaiio /eneo k a?aeiia?aeathoue aea? ia?e iiia?a/ieo oaeeueiaeo /enae . A oe?e iaeano? nooe?eueiiai niaeo?o cae?enith?oueny i?ioean o?ainoi?iaoe??, i?e yeiio ia iiaa?oith iaaea? iiacaeiaaeia oaeey c iaeiei oaeeueiaei /eneii , a a?aeaeaa?oueny c ?ioei : . (3) ?icaeyiooi noaoe?iia?i? inaaaeieieae?ciaai? noaie (eaac?iiaa?oiaa? oiiiie), c /anoioaie a nooe?eueiiio niaeo??, ui i?aaenoaaeythoue niaith noia?iiceoe?th iaaeath/i? oa a?aeaeoi? ia'?iieo t-oaeeue ? eieae?ciaaio a?ey iiaa?oi? l-iiaeo. Aaeoi? ci?uaiiy oaei? oaee? ia? aeaeyae: . (4) Ciaeaeaii iaia?a?aiee niaeo? /anoio inaaaeieieaeueieo eieeaaiue, ui oa?aeoa?eco?oueny oacith oaee? j, yea aecia/a?oueny ye Rt =exp(2ij). Iaaiai?th?oueny oaeiae i?iaeaia ia/eneaiiy aeeaaeo iiaa?oi? a niaeo?aeueio aonoeio aeiaaioaeeueiaeo inaaaeieieae?ciaaieo eieeaaiue. Iaoiae ciaoiaeaeaiiy aonoeie inaaaeieieaeueieo noai?a aeeeaaeaii a?eueo aeaoaeueii a Aeiaeaoeo A ia i?eeeaae? iiaeae? oa?oaaoiai na?aaeiaeua, ui i?noyoue aeaa ieineeo aeaoaeoe ?icoaoiaai? ia a?aenoai? iaaaaaoi a?eueo?e ca oiaueio aeaoaeoieo oa??a. A ?iaio? aeine?aeaeaii aieea aaeni?aiaaiiai ia iiaa?oith e?enoaeo iiiioa?o aeii?oeiaeo aoii?a, ye? iathoue iano I, a?aei?iio a?ae iane aoii?a aioo??oi?o oa??a m, ia niaeo?e iiaa?oiaaeo eieeaaiue. O?aooaaiiy oaeiai iiaa?oiaaiai aeaoaeoiiai oa?o i?eaiaeeoue aei iiyae i?e Mk*. A oi/oe? k* e?i?y SO2 i?eoiaeeoue aei
aa?oii? a?aieoe? nooe?eueiiai niaeo?o oa i?iaeiaaeo?ony i?e km/2
(e?i?y SR ia iae. 3), ? oaeiae aeieea? ae?oaa eieae?ciaaia
iecueei/anoioia oaeey i?e M>3m/2 (e?i?y ST ia iae. 3). *anoeio iiae?aieo
?acoeueoao?a aoei io?eiaii a [17], aea ?icaeyaeaeanue iiaeaeue
eaaae?aoii? a?aoee. Aeenia?n?eia e?i?y ST i?eoiaeeoue aei ieaeiuei?
a?aieoe? nooe?eueiiai niaeo?o oa i?iaeiaaeo?oueny aeae? e?i??th /anoio
oaee? o?ainoi?iaoe??. Iayai?noue aaaeeiai aeii?oeiaiai oa?o ia iiaa?oi?
i?eaiaeeoue aei neaaei? aeenia?n?? oaeaeeino? ?aea?anueei? oaee?.

O?ao?e ?icae?e i?enay/aiee aeine?aeaeaiith aca?iiae?? oiiii?a c ieineei
aeaoaeoii a AOeE e?enoae? c oeaio?aeueiith aca?iiae??th iaeaeeae/eo
non?ae?a. sseui aea?aoe aenieineiao?e/iee iai?yiie ?iciianthaeaeaiiy
oaee? a ieiuei? aeaoaeoo, yea ni?aiaaea? c e?enoaeia?ao?/iith ieiueiith
(001), oi noa? iiaeeeaei ie?aiee iien aeeiai?ee cnoaii? oaee?
ai?eciioaeueii? iiey?ecaoe?? [10] ? aeeiai?ee aa?oeeaeueii
iiey?eciaaii? oaee? ?aea?anueeiai oeio . A ?iaio? aeine?aeaeothoueny
eieeaaiiy ?aea?anueei? iiey?ecaoe??. Nooe?eueiee niaeo? oaeeo eieeaaiue
e?enoaeo (cao?eoiaai? iaeano? ia iae. 4-6, ) neeaaea?oueny c aeaio
a?eie, ye? aoaeaii iaceaaoe iiia?a/iith (t-) oa iiacaeiaaeiueith (l-).
I?iiiio?oueny oaea iiaeaeue ieineiai aeaoaeoo: aca?iiae?y aoii?a i?ae
aeaiia non?aei?ie ieiueiaie oa?aeoa?eco?oueny b, a?aei?iiith a?ae
neeiai? eiinoaioe a a ?aoo? a?aoee. Io?eiaii niaeo?e eieae?ciaaieo eiei
aeaoaeoo oaeeue aeaio aeae?a, ye? a?ae??ciythoueny oacith eieeaaiue
a?aie/ieo aoiiieo oa??a: neiao?e/i? c oa aioeneiao?e/i? c (e?i??
/anoio neiao?e/ieo eieeaaiue iicia/aie e?oa?aie “S”, aioeneiao?e/ieo —
“A” ia iae. 4-6). O aeiaaeeo ineaaeaiiy aca?iiae?? i?ae aeaoaeoieie
oa?aie o ii??aiyii? c aca?iiae??th ?aooe aoii?a e?enoaeo (ba)
ciaeaeaii /anoioe eieae?ciaaieo eieeaaiue, ui eaaeaoue aeua nooe?eueiiai
niaeo?o. Oae? eieeaaiiy ia iiaeooue ?nioaaoe a aeiaaioaeeueia?e iaeano?
niaeo?o ? ia iiaeooue aooe io?eiai? c ??aiyiue oai??? i?oaeiino?. A
u?eei? niaeo?o ia’?iieo eieeaaiue io?eiai? /anoioe eieae?ciaaieo
neiao?e/ieo oa aioeneiao?e/ieo oaeeue o aeiaaeeao ye ineaaeaiiy, oae ?
iineeaiiy aca?iiae?? i?ae a?aie/ieie aoiiieie oa?aie.

Io?eiaii aeenia?n?eia ni?aa?aeiioaiiy, ui aecia/a? /anoioe
inaaaeieieae?ciaaieo a?ey ieineiai aeaoaeoo eieeaaiue, oa ciaeaeaii
a?aieoe? iaeano? ?o ?nioaaiiy.

A ?aieao iiaeae?, ui ?icaeyaea?oueny a oeueiio ?icae?e? i?iaiae?ciaaii
caaea/o ?icn?yiiy ieineei aeaoaeoii oiiii?a aa?oeeaeueii? iiey?ecaoe??.
O oaee? c /anoioith ia ??cieo ae?eyieao ia’?iiiai niaeo?o
eieae?ciaaiith iiaea aooe aai l — , aai t -a?eea. Aoaeaii oiiaii
iicia/aoe ?iaeaenii «a» aaee/eie, ui a?aeiinyoueny aei ia’?iii? a?eee, a
?iaeaenii «b» — aei eieae?ciaaii?. I?e /anoioao b=l, a=t, a i?e b=t,
a=l. Eiiiiiaioe aaeoi?a ci?uaiue oaeeo oiiii?a ia? aeaeyae:

(5)

aea aiie?ooaee iaaeath/i?, a?aeaeoi?, i?ieoiaoi? oa eieae?ciaaieo oaeeue
a?aeiia?aeii , , , , ; (m=a,b) — aeani? aaeoi?e ia’?iieo ??aiyiue
?ooo; — ae?enia, a kb — eiiieaenia aeani? /enea ia’?iieo ??aiyiue a
iaeanoyo ?nioaaiiy inaaaeieieae?ciaaieo eieeaaiue. Iaoiaeaie aeeiai?ee
a?aoee ?ic?aoiaaii /anoioe ?aciiainiiai i?ioiaeaeaiiy (ca oiiae |T |2
=1) oa a?aeaeooy (ca oiiae |R |2 =1) oaee?. O aeiaaeeo iineaaeaiiy
aeaoaeoiiai ca’yceo ?aciiaini? /anoioe iiaiiai a?aeaeooy (e?i?y 1 ia
iae. 4) eaaeaoue a ieaei?e /anoei? inaaaeieieaeueiiai niaeo?o. O
aeiaaeeo a?aenooiino? aeaoaeoo (b=a) e?i?y /anoio iiaiiai a?aeaeooy
ni?aiaaea? c ieaeiueith iaaeath l-a?eee. Aiaeia?/i? aeniiaee o
aeiaaioaeeueiaiio iaaeeaeaii? aoei c?iaeaii a [13,14,16] c ??aiyiue
oai??? i?oaeiino?. Aeaoaeueii ?icaeyiooi a?eueio iiaa?oith ye aeiaaeie
iiaiiai ?ic?eao ca’yceo i?ae a?aie/ieie aoiiieie oa?aie (b=0).
?ic?aoiaaii caeiie aeenia?n?? oaeeue, ui a?aeaeaathoueny a?ae a?eueii?
iiaa?oi? e?enoaeo. Anoaiiaeaii, ui i?e a?aeaeoo? oaee? iiaeooue
ci?ithaaoe iiey?ecaoe?th, oiaoi cae?eniththoueny i?ioeane
o?ainoi?iaoe??, aiaeia?/i? iienaiei o ae?oaiio ?icae?e?. O aeiaaeeo
iineeaiiy aca?iiae?? i?ae a?aie/ieie ieiueiaie e?enoaeo aeieeathoue iia?
?aciiaini? eieeaaiiy c /anoioaie, ui eaaeaoue a iaaeao l-a?eee, aeua
ia’?iii? t-iiaee (e?i?? 2-4 ia iae. 4).

?aciiaini? /anoioe i?ioiaeaeaiiy e??cue ieineee aeaoaeo o aeiaaeeo
iineaaeaiiy aeaoaeoiiai ca’yceo (e?i?y T1ia iae. 5) eaaeaoue a
ei?ioeioaeeueia?e iaeano? iaae ieaeiueith a?aieoeath l-a?eee a?ae oi/ee
ia?ao?auoaaiiy a?eie nooe?eueiiai niaeo?o aei aeayeiai cia/aiiy
oaeeueiaiai /enea k*, ii/eiath/e c yeiai e?ea? /anoio i?ioiaeaeaiiy
ia?aoiaeyoue a aeenia?n?ei? e?ea? u?eeiieo eieae?ciaaieo eieeaaiue
neiao?e/iiai oeio (e?i?y S1 ia iae. 5). O aeiaaeeo iineeaiiy aca?iiae??
i?ae a?aie/ieie oa?aie aeieeathoue aea? a?eee /anoio iiaiiai
i?ioiaeaeaiiy i?e iaeiiio ? oiio aea cia/aii? ia?aiao?a aeaoaeoo. Iaeia
a?eea /anoio i?ioiaeaeaiiy (e?i?y O ia iae. 6) ?nio? a nooe?eueiiio
niaeo?? (a aeniei/anoioi?e iaeano? inaaaeieieaeueieo noai?a) aei
aeayeiai cia/aiiy oaeeueiaiai /enea k*, ii/eiath/e c yeiai aeoiaeeoue ?c
niaeo?o ia’?iieo eieeaaiue o aeaeyae? eieaeueieo /anoio neiao?e/ieo
aeniei/anoioieo iiae (e?i?y S ia iae. 6) i?e oiio ae b. ?aciiainia
i?ioiaeaeaiiy iiaea cae?enithaaoeny a oe?e iaeano? niaeo?o o?eueee i?e
cia/aiiyo ia?aiao?a aeaoaeoo a ?ioa?aae?. Ae?oaa a?eea /anoio
i?ioiaeaeaiiy (e?i?y O2 ia iae. 5) ciaoiaeeoueny a ieaei?e iaeano?
?nioaaiiy inaaaeieieae?ciaaieo noai?a. C ?inoii ia?aiao?a b oae? e?i??
iiiaaeathoue a u?eeio nooe?eueiiai niaeo?o, aea i?iaeiaaeothoueny
aeenia?n?eieie e?eaeie u?eeiieo eieaeueieo neiao?e/ieo eieeaaiue (e?i?y
S2 ia iae. 5) i?e oiio ae cia/aii? b.

?nioaaiiy ?aciiainieo /anoio i?ioiaeaeaiiy aai a?aeaeooy oiiii?a a?ae
aeaoaeoo iia’ycaii c iniaeeainoyie nooe?eueiiai niaeo?o ia’?iieo
eieeaaiue. ?aciiaini? yaeua iiaeeea? i?e iayaiino? aeaio a?eie
nooe?eueiiai niaeo?o, ? o?eueee o cacia/aieo aeua /anoioieo ae?aiaciiao
(iaeanoyo ?nioaaiiy inaaaeieieaeueieo eieeaaiue). ?aciiain
cae?enith?oueny caaaeyee aca?iiae?? eiei aeaoaeoo ia’?iieo oaeeue
iaei??? a?eee nooe?eueiiai niaeo?o c eieae?ciaaiith iiaeith, ui
a?aeuaieeany a?ae ae?oai? a?eee. ?aciiaini? iniaeeaino? i?ioeano
?icn?yiiy iiaeia o?aeooaaoe ye ianeiao?e/i? a?aeiinii ieiueie aeaoaeoo
aeani? eieeaaiiy. Iiaiiio a?aeaeooth, iai?eeeaae, iiaeia ni?anoaaeoe
ianeiao?e/ia ??oaiiy, yea yaey? niaith ?nioth/o o?eueee a iaeiiio c
iai?ai?inoi??a noiy/o oaeeth iaei??? c ia’?iieo a?eie, oa eieae?ciaai? c
iaio aie?a a?ae aeaoaeoo eieeaaiiy ae?oai? a?eee. *anoioe ? oaeeueia?
aaeoi?e oaeeo noai?a ciaoiaeyoueny a iaeanoyo ?nioaaiiy
eaaceeieae?ciaaieo eieeaaeueieo noai?a. ?aciiain cae?enith?oueny ca
o??? oiiae, eiee /anoioa iae?oath/iai oiiiia ni?aiaaea? c /anoioith
inaaaeieieaeueiiai eieeaaiiy.

O aeniiaeao iaaaaeaii iniiai? ?acoeueoaoe, io?eiai? a aeena?oaoe?ei?e
?iaio?:

1. A iai?aiaiaaeaiiio aaenaaiiaeueiiio e?enoae? ia aac? aeeiai?ee
e?enoae?/ii? a?aoee aea/aii iiaa?oiaa? oaee? i?e iayaiino? ia iiaa?oi?
e?enoaeo iiiioa?o ?cioii-aoii?a. Iieacaii, ui e??i iiaa?oiaaeo oaeeue, a
e?enoae? aeieeathoue aeae?eai? e?i?? /anoio a nooe?eueiiio niaeo??
ia’?iieo eieeaaiue. Oea /anoioe oaeeue o?ainoi?iaoe??, ye?
?icn?ththoueny iiaa?oiath e?enoaeo. Anoaiiaeaii, ui aeenia?n?ei? e?ea?
iiaa?oiaaeo oaeeue i?iaeiaaeothoueny a nooe?eueiiio niaeo?? o aeaeyae?
e?i?e /anoio oaeeue o?ainoi?iaoe??.

2. ?icaeyiooi a aeene?aoi?e iiaeae? i?iaeaio ?nioaaiiy eaac?iiaa?oiaaeo
oiiii?a (inaaaeieieae?ciaaieo eieeaaiue), aaeoi? ci?uaiiy a yeeo ia?
ii?iaeueio aei iiaa?oi? e?enoaeo eiiiiiaioo. Aecia/aii iaeanoue a
niaeo?? ia’?iieo eieeaaiue, o iaaeao yei? eaaeeoue iaia?a?aiee niaeo?
inaaaeieieaeueieo noai?a, ui ia?aiao?eco?oueny oacith eaac?iiaa?oiaai?
oaee?.

3. Noi?ioeueiaaii i?e?ineii?/i? a?aie/i? oiiae ia ieineiio aeaoaeo? a
aeeaei? e?enoaeo oa aeiaaaeaii, ui a aeiaaioaeeueiaiio iaaeeaeaii? aiie
ia?aoai?ththoueny ia a?aie/i? oiiae oai??? i?oaeiino?.

4. A ?aieao iiaeae? AOeE e?enoaeo c aca?iiae??th iaeaeeae/eo non?ae?a
aeyaeaii ?aciiaini? iniaeeaino? i?ioeano ?icn?yiiy; aeiaaaeaii
iiaeeea?noue iiaiiai a?aeaeooy oa i?ioiaeaeaiiy oiiii?a /a?ac ieineee
aeaoaeo i?e iaaieo /anoioao a ae?aiacii? niaeo?o inaaaeieieaeueieo
noai?a. ?ic?aoiaaii caeiie aeenia?n?? oaeeo oiiii?a a iaaeao ciie
A?eeethaia oa aeine?aeaeaii aieea oa?aeoa?enoee aeaoaeoo ia iiaaae?ieo
?aciiainieo /anoio.

5. Io?eiaii niaeo?e eieae?ciaaieo oa inaaaeieieae?ciaaieo a?ey ieineiai
aeaoaeoo aeanieo eieeaaiue. I?iaiae?ciaaii oiiae eieae?caoe??
iecueei/anoioieo oaeeue ?aea?anueeiai oeio, u?eeiieo oa aeniei/anoioieo
eieae?ciaaieo oaeeue a caeaaeiino? a?ae ia?aiao??a aeaoaeoo.
Anoaiiaeaii, ui aeenia?n?ei? e?ea? /anoio eieae?ciaaieo eieeaaiue
i?iaeiaaeothoueny a na?aaeei? nooe?eueiiai niaeo?o e?i?yie ?aciiainieo
/anoio oiiii?a, ui iiai?noth i?ioiaeyoue e??cue aeaoaeo.

Nienie aeei?enoaieo aeaea?ae

1. R.Allen, G.Aldredge, F.de Wette. Studies of vibrational surface
modes. Phys. Rev. B, 1971, 4, N6, p.1648-1697.

2. A.I.Ia?anaaea, A.N.Nu?eei. Iiaue iaoiae iaoiaeaeaiey eieaeeciaaiiuo o
iiaa?oiinoe e?enoaeea eieaaaoaeueiuo ninoiyiee. OIO, 1977, 3, N2
,c.229-236.

3. A.I.Einaae/, A.I.Oioeia. I iaeioi?uo iniaaiiinoyo niaeo?a eieaaaiee
e?enoaeea n ieineei aeaoaeoii OOO, 1968, 10, N1, c.56-61.

4. A.I.Einaae/, A.I.Oioeia. Aieiu ?yeay eae i?aaeaeueiue neo/ae
eieaaaiee e?enoaeea n ieineei aeaoaeoii. OOO, 1970, 12, N8, c.2507-2509.

5. A.I.Einaae/, TH.A.Einaae/, A.N.Nu?eei. Iaiauaiiua aieiu ?yeay e
aaiiao?ey eci/anoioiuo iiaa?oiinoae caoeiauo eieaaaiee a e?enoaeea.
AEYOO, 1985, 88, N3, c.1089-1097.

6. TH.A.Einaae/, A.N.Nu?eei. E?eoa?ee nouanoaiaaiey e naienoaa
aeoaieii?iieeathueo aiei ?yeay. AEYOO,1985, 89, N6(12), c.2221-2229.

7. D.Gazis, R.Herman, R.Wallis. Surface elastic waves in cubic crystal.
Phys. Rev., 1960, 119, N2, p.533-544.

8. A.I. Einaae/. Oai?ey e?enoaeee/aneie ?aoaoee. O.: Aeua Oeiea, 1988,
304c.

9. A.I.Ia?anaaea, E.I.Aaeueoaao. Iiaa?oiinoiua eieaaaiey
a?aiaoeaio?e?iaaiiiai eoae/aneiai e?enoaeea. OEN, 1974, N33, Oa?.:
OOEIO, c.22-29.

10. A.I.Einaae/, A.N.Nu?eei, A.A.Oooia. Aeonoe/aneea naeaeaiaua aieiu,
eieaeeciaaiiua aaeece ieineiai aeaoaeoa a AOeE e?enoaeea. OIO, 1996, 22,
N7, c.804-813.

11. J.Strocio, M.Persson, S.Bare, W.Ho. Observation of structure-induced
surface vibrational resonances. Phys. Rev. Lett., 1985, 54, N13,
p.1428-1431.

12. A.I.Einaae/, A.A.Oooia. Eaaceeieaeeciaaiiua iiaa?oiinoiua aieiu o
ieineiai aeaoaeoa a e?enoaeea. OIO, 1993, 19, N11, c.1273-1276.

13. A.N.Darynskii and G.A.Maugin. The elastic wave resonance reflection
from a thin solid layer in a crystal. Wave Motion, 1996, 23, N4,
p.363-385.

14. A.M.Kosevich and A.V.Tutov. Peculiarities of elastic wave scattering
from a planar crystal defect and pseudolocalized vibrations. Phys. Lett.
A, 1998, 248, N2-4, p.271-277.

15. A.I.Einaae/. Iniaaiiinoe aeaoeaiaeueiiai ?aciiainiiai ?annayiey
aieiu eee /anoeoeu ia ieineii aeaoaeoa. AEYOO, 1999, 111, N1, n. 1.

16. E.A.Aeeoi?ia. Caoeiaua iiaa?oiinoiua aieiu a oaa?aeuo oaeao. I.:
Iaoea, 1981, 287 n.

17. H.Kaplan. Effect of an impurity layer on surface waves. Phys. Rev.,
1962, 125, N4, p.1271-1276.

18. A.M.Kosevich, A.V.Tutov. Localized and pseudolocalized at a plane
defect elastic waves. Phys. Lett. A, 1996, 213, p. 265-272.

Naaio/aiei Na?a?e ?aaaiiae/. Iniaeeaino? oiiiiieo niaeo??a oa
?aciiainieo aeanoeainoae e?enoae?a c ieineeie aeaoaeoaie. – ?oeiien.
Aeena?oaoe?y ia caeieaoooy nooiaiy eaiaeeaeaoa o?ceei-iaoaiaoe/ieo iaoe
ca niaoe?aeueiinoueth 01.04.02 – oai?aoe/ia o?ceea. — O?ceei-oaoi?/iee
?inoeooo iecueeeo oaiia?aoo? ?i. A.?. A??e?ia. 1998 ?. Oa?e?a,
Oe?a?ia.

A aeena?oaoe?ei?e ?iaio? i?iaaaeaii oai?aoe/iee aiae?c eieeaaeueieo
niaeo??a e?enoae?a c ieineeie aeaoaeoaie iaoiaeaie aeeiai?ee
e?enoae?/ii? a?aoee. Aea/aii aieea iaieeaiiai ia iiaa?oith e?enoaeo
iiiioa?o ?cioii-aoii?a ia /anoioi? caeaaeiino? iiaa?oiaaeo oiiii?a.
Ciaeaeaii niaeo? /anoio inaaaeieieae?ciaaieo eieeaaiue oa aecia/aii
iaeanoue ?o ?nioaaiiy. I?iaiae?ciaaii a aeene?aoi?e iiaeae? i?ioeane
o?ainoi?iaoe?? oiiii?a i?e a?aeaeoo? a?ae iiaa?oi? e?enoaeo. Aeyaeaii
iniaeeaino? ?aciiainiiai ?icn?yiiy oiiii?a ieineei aeaoaeoii a AOeE
e?enoae?, /anoioe yeeo ?icoaoiaai? a iaeano? ?nioaaiiy inaaaeieieaeueieo
eieeaaiue. ?ic?aoiaaii niaeo?e oaeeo oaeeue ca ?aciiainieo oiia iiaiiai
a?aeaeooy ? i?ioiaeaeaiiy.

Eeth/ia? neiaa: e?enoae?/ia a?aoea, oiiiie, eieaeuei? eieeaaiiy, ieineee
aeaoaeo, iiaa?oiy, oaee? o?ainoi?iaoe??, ?aciiainia ?icn?yiiy,
inaaaeieieaeuei? noaie.

Naaio/aiei Na?aae Aaaaiueaae/. Iniaaiiinoe oiiiiiuo niaeo?ia e
?aciiainiuo naienoa e?enoaeeia, niaea?aeaueo ieineea aeaoaeou. —
?oeiienue. Aeenna?oaoeey ia nieneaiea o/aiie noaiaie eaiaeeaeaoa
oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.04.02 — oai?aoe/aneay
oeceea. — Oeceei-oaoie/aneee einoeooo ieceeo oaiia?aoo? ei. A.E.
Aa?eeia, 1998, Oa?ueeia, Oe?aeia.

A aeenna?oaoeeiiiie ?aaioa i?iaaaeai oai?aoe/aneee aiaeec eieaaaoaeueiuo
niaeo?ia e?enoaeeia n ieineeie aeaoaeoaie iaoiaeaie aeeiaieee
e?enoaeee/aneie ?aoaoee. A iieoia?aie/aiiii aaenaaiiaeueiii e?enoaeea
?ann/eoaiu niaeo?u iecei/anoioiuo e uaeaauo iiaa?oiinoiuo eieaaaiee,
/anoiou eioi?uo eaaeao aia nieioiiai niaeo?a iauaiiuo eieaaaiee.
Onoaiiaeaii, /oi i?e iaee/ee a?aieoeu a e?enoaeea aicieeatho auaeaeaiiua
eeiee /anoio a nieioiii niaeo?a iauaiiuo eieaaaiee. Yoi /anoiou, i?e
eioi?uo aeaeathony aiciiaeiuie i?ioeannu o?ainoi?iaoeee aiei i?e
io?aaeaiee io iiaa?oiinoe e?enoaeea. ?ann/eoaiu niaeo?u /anoio oaeeo
aiei o?ainoi?iaoeee aeey i?iecaieueiuo cia/aiee aieiiaiai /enea a
i?aaeaeao ciiu A?eeethyia. Iieacaii, /oi oa aeenia?neiiiua e?eaua
iiaa?oiinoiuo aiei, eioi?ua iiiaaeatho a nieioiie niaeo?,
i?iaeieaeathony a iai a aeaea auaeaeaiiuo eeiee /anoio aiei
o?ainoi?iaoeee.

?anniio?aia a aeene?aoiie iiaeaee i?iaeaia nouanoaiaaiey
eaaceiiaa?oiiniuo oiiiiia (inaaaeieieaeeciaaiiuo eieaaaiee), aaeoi?
niauaiey a eioi?uo eiaao ii?iaeueioth e iiaa?oiinoe e?enoaeea
eiiiiiaioo. Ii?aaeaeaia iaeanoue a niaeo?a iauaiiuo eieaaaiee, a
i?aaeaeao eioi?ie eaaeeo iai?a?uaiue niaeo? inaaaeieieaeueiuo ninoiyiee,
oa?aeoa?ecothueeny oacie eaaceiiaa?oiinoiie aieiu.

Eco/aiu iiaa?oiinoiua aieiu i?e iaee/ee ia iiaa?oiinoe e?enoaeea
iiiineiy ecioiie/aneeo i?eianiuo aoiiia. Iieacaii, /oi ianna i?eianiuo
aoiiia iiaa?oiinoiiai neiy, ioee/iay io iannu aoiiia aioo?aiieo neiaa,
nouanoaaiii aeeyao ia niaeo?u iiaa?oiinoiuo aiei. Iiiineie oyaeaeuo
ecioiiia i?eaiaeeo e iiyaeaieth aeaoo aeaeia iiaa?oiinoiuo aiei n
/anoioaie, eaaeaueie ieaea nieioiiai niaeo?a i?e iaeiie e oie aea ianna
i?eiane. A neo/aa eaaeie i?eiane aicieeatho nouanoaaiii ei?ioeiaieiiaua
iiaa?oiinoiua eieaaaiey aeaoo aeaeia n /anoioaie, eaaeaueie auoa
nieioiiai niaeo?a. *anoiou aoi?uo eieaeeciaaiiuo ninoiyiee ia?acothony
ii?iaiaui ia?acii eae iiae, oae e iaae nieioiui niaeo?ii iauaiiuo
eieaaaiee.

Noi?ioee?iaaiu iee?ineiie/aneea a?aie/iua oneiaey ia neo/ae ieineiai
aeaoaeoa a aeoaeia e?enoaeea, ec eioi?uo iieo/aiu i?aaeaeueiui
ia?aoiaeii a aeeeiiiaieiiaoth iaeanoue a?aie/iua oneiaey oai?ee
oi?oainoe, oi?ioee?iaaaoeany ?aiaa oaiiiaiieiae/anee. Iieacaii, /oi
aeeeiiiaieiiaua aeenia?neiiiua niioiioaiey iiaa?oiinoiuo aiei a iiaeaee
aaenaaiiaeueiiai 2D e?enoaeea niaiaaeatho n aeenia?neiiiuie
niioiioaieyie aiei aiaeiae/iiai oeia [12,18] a ecio?iiiii
iieoi?ino?ainoaa, eioi?ia oa?aeoa?ecoaony oeene?iaaiiuie cia/aieyie
oi?oaeo iiaeoeae.

A ?aieao iiaeaee AOeE e?enoaeea n acaeiiaeaenoaeai aeeaeaeoeo ninaaeae
iaia?oaeaiu ?aciiainiua iniaaiiinoe i?ioeanna ?annayiey; iieacaia
aiciiaeiinoue iieiiai io?aaeaiey e i?ioiaeaeaiey oiiiiia /a?ac ieineee
aeaoaeo a ieineinoe (001) i?e ii?aaeaeaiiuo /anoioao a aeeaiaciia
niaeo?a inaaaeieieaeueiuo ninoiyiee. ?ann/eoaiu caeiiu aeenia?nee oaeeo
aiei a i?aaeaeao ciiu A?eeethyia e enneaaeiaaii aeeyiea oa?aeoa?enoee
aeaoaeoa ia iiaaaeaiea ?aciiainiuo /anoio. Iieacaii, /oi ?aciiain
aiciiaeai i?e iaee/ee aeaoo aaoaae nieioiiai niaeo?a, eioi?ua iiaoo
acaeiiaeaenoaiaaoue aaeece aeaoaeoa a /anoioiii aeeaiaciia
inaaaeieieaeueiuo eieaaaiee.

Iieo/aiu niaeo?u eieaeeciaaiiuo e inaaaeieieaeeciaaiiuo o ieineiai
aeaoaeoa nianoaaiiuo eieaaaiee ?yeaaaneiai oeia, ?ani?ino?aiythueony
aaeieue aunieineiiao?e/iuo e?enoaeeia?aoe/aneeo iai?aaeaiee a AOeE
e?enoaeea. Iieacaii, /oi aicieeatho neiiao?e/iua e aioeneiiao?e/iua
ioiineoaeueii ieineinoe aeaoaeoa eieaaaiey. I?iaiaeece?iaaiu oneiaey
eieaeecaoeee iecei/anoioiuo aiei ?yeaaaneiai oeia, uaeaauo e
auniei/anoioiuo eieaeeciaaiiuo aiei a caaeneiinoe io ia?aiao?ia
aeaoaeoa. Onoaiiaeaii, /oi aeenia?neiiiua e?eaua /anoio eieaeeciaaiiuo
eieaaaiee i?iaeieaeathony aioo?e nieioiiai niaeo?a eeieyie ?aciiainiuo
/anoio iieiinoueth i?ioiaeyueo /a?ac aeaoaeo oiiiiia.

Eeth/aaua neiaa: e?enoaeee/aneay ?aoaoea, oiiiiu, eieaeueiua eieaaaiey,
ieineee aeaoaeo, iiaa?oiinoue, aieiu o?ainoi?iaoeee, ?aciiainiia
?annayiea, inaaaeieieaeueiua ninoiyiey.

Savotchenko S. E. Peculiarities of the phonon spectra and resonance
properties of crystals with planar defects. — Manuscript. Thesis for a
candidate’s degree in physical and mathematical sciences by speciality
01.04.02 — theoretical physics. — B.Verkin Institute for Low Temperature
Physics and Engineering, 1998, Kharkov, Ukraine.

The vibrational spectra of a crystal with a planar defect are analized
in the thesis within the framework of the lattice dynamics. The effect
of a surface monolayer of impurity atoms on localized vibrations is
investigated. The dispersion relationship of the quasi-surface phonons
is derived. The region of existence of quasi-surface phonons is
determined. The processes of transformation of phonons reflected from
the crystal surface are investigated within the framework of discrete
lattice model. The resonance peculiarities of phonon scattering on the
plane defect in fcc are obtained. The spectra of such phonons are
calculated under resonance condition of total reflection and total
transmission.

Key words: crystal lattice, phonons, localized vibrations, plane defect,
surface, transformation waves, resonance scattering, pseudolocalized
states.

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