16 Kon

06beJlMHeHHbiM MHCTMTYT RJl ePHbl X

Mccn eJlOBaHMA

JlY6Ha

P 17 B5 411

AMlaJl J j VI)(lB Illloml r II ( BimiddotII

~ M M F TI )J1~lIl bI H AIIAm1l

l TPYKTYIhl

PeAaKTOp E E Kon eC OB a bull Ha KeT I IAlWlJI1I1l11

nOAnHcaHO 9 ne ~arb 0107 85 ~op~aT 60x9016 O~ceTHaR ne 4aTb Y 4 -~3A nHcTo8 108

THpa 3 3 0 3aKa3 3 6 4 0 7

H3AaTenbcKH~ OTAen 06~eA~HeHHoro HHCTHTYTa RAep H~X HccneAbBaHH~ ay6Ha MoCK08CKO~ 06naCTH

II WI J ( )1l MIII1 ATYJgt1I0M IOMUlilotl

1 IImiddotII () tl1 ( 1l1KI LiKSO t

II(UIP(IIHltIHI j) l ys i e1 ~1 t ill l1 tl fin li di

19 8 5

B noc~~ee BpeMH nOHBKnOCb donowos qnCAO 3KCnepHMeHTanbHHX

padOT nocTaMemwx IVIff BWICHeHIDI OCodeHHOCTeH Hll3KOTSMllSpaTypHIiX

qaSOBllX nepeXOIOB B KPHCTaJIJIaX Li K SO~ B HCCASllOBaHHRX 71+8 IpOBeIeHHIiX CaMIiMH paSJllftlliHMB MeTOuaMH B odJIaCTll TeMnepaTyp OT KOMshy

BaTHO uo 150 K HaIt9EHO YCTaHOBJIeHO CYllIeCTBOBaHIe no KpaiHSH Mepe

uByx TOleK nepaxoll1l llepBail TOtma HaXOnRTCS MeJUlY 198 K B 21O K H

COOTBeTCTBYST nepexouy a3 ~3H ill ) B KOTOpO~ KPICTaAA BaxOuKTCR

upI KOMHaTHOit TeMIIepaType B qa3Y IYj BTOpaJI - B6JIHSB 190 K rlle

npOICXOIlllT nepexoI 1Y - Y Oda nepexolla RJIYT C TeMIIepaTypHIiM rHCTeshy

peSICOM OC06SHHO 60ADIlll4M ( 50 K) npn nepexone ill- IY ltPaSH 1Y B Y

cerneTo3AeKTpJrecKlle 8 1OI a qa3a Y eme II ifePP03JlllCTRieCKM 34 KaK CAeucTBHe HXKe 190 KKPHCTaAn pa36KBaSTCR Ha ~C~pNBUHOHHHe

uBoimmtll ( nOMeHH ) Ha6~SCH l)Blt B 0 11T1feCKKX TaR H B ~ltIgtshypaItItROHHIDt 9KCllSp IIM8HTax 6 II I 2 bull

ATOMHM CTPYKTypa Li KS0t HSBeCTHR lOJlhlW B qase ill (uprp

PG3 II) ~ a naHHH8 0 CHMMSTPKH ifa3 IY II Y no c n nop upoTHBOpetmshy

BH TaR B 1 npennOAOZEIHH 6 m WI H m vn 2 COOT BeTCTOOHHO I4JIR qa3 1Y

H Y a B II nepexou I1 Y rsTSpnpSTlIPyelCJ[ KaK 6rvrn-+ 2 PesYADshy

TaTH OIITJ[TSCKIlX KCCJIenoBaH1lit 8 npOT]UlOpelaT odSIIM rpynnaM 6 WI rn H

rt W 2 H nepexonH ill -gt 11 -gt Y B STOlt pa60Te paCCMaTPJmamCH KaK

6 - 2 - I OIllJ[T8CKYJ) aKTIBHOCTD B L ~ K S 0i CKaJIH K B pa60Te 1 HO He 06aapyDJlll K wm qaSH BOS~a HlDIte 198r rrpennoJIolDlJIH

rpynoy 3m B HenaBHsJi He~TpoHorpaqMqscKolt pa60Te I~ YTBePJtllasTc R

iTO UPOCTpaHCTBeHHM rpynna KPBCT8JLJIa B ilBse 1Y ecTO P31c a I4JIR

crt3i Y npennOJIaraSTCR nceBuopotfjBiecKBJI cHMMeTpHR B 3TO 1t6 padoTe

I2 o6paIIlaeTCR BHlIMaHH8 Ha 3aMSIJ1ISHHYJ) KlUiSTKKY nepexOIOB (epsMH

YCTaHOBJleHllJi paBHOOOCHR - CYTKH II 60Ase) ITO B03MOlDiO B KaKOfi-TO

CTeneHB od~CHReT rrpOTBBOpeqanOCTb ~HHX pa3HIiX 3KCnepHMeHTOB

M3BeCTHO ITO uOM9HHaR CTPYKTypa Odpa3~CS B ~ppOSJlllCTBshy

IecKol qass OTpaltBeT CHMMeTpHI) KaK rrapa- TaK H ~ppoqnSH Ee reOMeTpIR YOEeT 6HTb HCCJIeIOBaHa ItH~OHHUMK M8TO~ nOSBOJInmshy

~ OCYllISCTBITb CKaHKpOBaHIe OKpeCTHOCTH YSAOB 06paTHOH pemeTKB

KpaCTaJUIa HaI60ASe yn06HllMi1 MeTOllBMK CKaHJrpOBaHIR cpaBHIITeJllHO

60JIbmBX 06~CTS2 06paTlloro npOCTpaHCTBa HBJIHDTCS peHTreHrOHHOMeTPBshy

~eCKaS C~YKa no BeAceH6epry H HSTpOHHRS uH~TOM8TPBH ITO M8TOny

~) 0608Haleaaa ~ I8HH no pa60Te 9

B noc~~ee BpeMH nOHBKnOCb donowos qnCAO 3KCnepHMeHTanbHHX

padOT nocTaMemwx IVIff BWICHeHIDI OCodeHHOCTeH Hll3KOTSMllSpaTypHIiX

qaSOBllX nepeXOIOB B KPHCTaJIJIaX Li K SO~ B HCCASllOBaHHRX 71+8 IpOBeIeHHIiX CaMIiMH paSJllftlliHMB MeTOuaMH B odJIaCTll TeMnepaTyp OT KOMshy

BaTHO uo 150 K HaIt9EHO YCTaHOBJIeHO CYllIeCTBOBaHIe no KpaiHSH Mepe

uByx TOleK nepaxoll1l llepBail TOtma HaXOnRTCS MeJUlY 198 K B 21O K H

COOTBeTCTBYST nepexouy a3 ~3H ill ) B KOTOpO~ KPICTaAA BaxOuKTCR

upI KOMHaTHOit TeMIIepaType B qa3Y IYj BTOpaJI - B6JIHSB 190 K rlle

npOICXOIlllT nepexoI 1Y - Y Oda nepexolla RJIYT C TeMIIepaTypHIiM rHCTeshy

peSICOM OC06SHHO 60ADIlll4M ( 50 K) npn nepexone ill- IY ltPaSH 1Y B Y

cerneTo3AeKTpJrecKlle 8 1OI a qa3a Y eme II ifePP03JlllCTRieCKM 34 KaK CAeucTBHe HXKe 190 KKPHCTaAn pa36KBaSTCR Ha ~C~pNBUHOHHHe

uBoimmtll ( nOMeHH ) Ha6~SCH l)Blt B 0 11T1feCKKX TaR H B ~ltIgtshypaItItROHHIDt 9KCllSp IIM8HTax 6 II I 2 bull

ATOMHM CTPYKTypa Li KS0t HSBeCTHR lOJlhlW B qase ill (uprp

PG3 II) ~ a naHHH8 0 CHMMSTPKH ifa3 IY II Y no c n nop upoTHBOpetmshy

BH TaR B 1 npennOAOZEIHH 6 m WI H m vn 2 COOT BeTCTOOHHO I4JIR qa3 1Y

H Y a B II nepexou I1 Y rsTSpnpSTlIPyelCJ[ KaK 6rvrn-+ 2 PesYADshy

TaTH OIITJ[TSCKIlX KCCJIenoBaH1lit 8 npOT]UlOpelaT odSIIM rpynnaM 6 WI rn H

rt W 2 H nepexonH ill -gt 11 -gt Y B STOlt pa60Te paCCMaTPJmamCH KaK

6 - 2 - I OIllJ[T8CKYJ) aKTIBHOCTD B L ~ K S 0i CKaJIH K B pa60Te 1 HO He 06aapyDJlll K wm qaSH BOS~a HlDIte 198r rrpennoJIolDlJIH

rpynoy 3m B HenaBHsJi He~TpoHorpaqMqscKolt pa60Te I~ YTBePJtllasTc R

iTO UPOCTpaHCTBeHHM rpynna KPBCT8JLJIa B ilBse 1Y ecTO P31c a I4JIR

crt3i Y npennOJIaraSTCR nceBuopotfjBiecKBJI cHMMeTpHR B 3TO 1t6 padoTe

I2 o6paIIlaeTCR BHlIMaHH8 Ha 3aMSIJ1ISHHYJ) KlUiSTKKY nepexOIOB (epsMH

YCTaHOBJleHllJi paBHOOOCHR - CYTKH II 60Ase) ITO B03MOlDiO B KaKOfi-TO

CTeneHB od~CHReT rrpOTBBOpeqanOCTb ~HHX pa3HIiX 3KCnepHMeHTOB

M3BeCTHO ITO uOM9HHaR CTPYKTypa Odpa3~CS B ~ppOSJlllCTBshy

IecKol qass OTpaltBeT CHMMeTpHI) KaK rrapa- TaK H ~ppoqnSH Ee reOMeTpIR YOEeT 6HTb HCCJIeIOBaHa ItH~OHHUMK M8TO~ nOSBOJInmshy

~ OCYllISCTBITb CKaHKpOBaHIe OKpeCTHOCTH YSAOB 06paTHOH pemeTKB

KpaCTaJUIa HaI60ASe yn06HllMi1 MeTOllBMK CKaHJrpOBaHIR cpaBHIITeJllHO

60JIbmBX 06~CTS2 06paTlloro npOCTpaHCTBa HBJIHDTCS peHTreHrOHHOMeTPBshy

~eCKaS C~YKa no BeAceH6epry H HSTpOHHRS uH~TOM8TPBH ITO M8TOny

~) 0608Haleaaa ~ I8HH no pa60Te 9

Bp 8MBHlt IIjJonaTa C np Jlll19H9HJ6M nOSJl1I0HHO-qyBCTBlfTSJThHOrO I8TeRTOpa

lleUTponorpa1lHIHl CKBit 1r19 I On YJIO YCllalWlO poundHMeHrGH B nCCJle~OBaHIDIX ~oshy

MdHHoi CTlYKtY1lIJ pl3JllrltD fWC ltPHCTmOB 3 11 B TOM lHCJIe H lliIH

1tO~J1 IQllOHIUI lIOMClfOfJ B Li K S0 4 Ill 0ll11aKO B OJIYIOO li KSO He

yTV IJIOC1J JJ1L OJllIOSIlIltHOTO O1136Tlt1 Ha BtmpOO 0 CHMMelp1m 1m3ROTeMllepashy

lYI HflX laa H3-31 UIlmIIWI H60KOJIbKIDC BOSMOlltHOCTBi ll)UI KH TepnpeTauHI

jlll3YJlbTLlTOD 123M9pelUtil D HaCTOJllllel pa6 0T6 JJpOBBIell ClMN8TpHlbmft aIIashy

Jrn3 onnueMillC p9 symmlToB nIrIqtpaKuHOlllioro 3Kcnep llMlHTa no na6JIDIeHHD

~OMe lion B Li K 5 0 ~ )l1Ul Tpex lHlIOTB3 OTIIOCllTeJIbHO H3M9HBlfHil TOlSI shy

1I0il CJiMIleTPBIf KPHClaJLlB npH nepex one B rInay Y Gtl IIl-+ Mnt2 6m VYI- 2 llJIlI ( 2 - I (B0 3MOltUiOCTh rrepex ona B rpynny 3 WI OTBePI89TCli B 60JIhshy

lillUICTBO palSOT) )Jml aHaJIH3a ncn OJIbaOBaHO n p6lUlOJIOJlteIlK6 0 BOSI~fOBSshy

Jilllf n rlepPo 3JIac TlM8CKol tIase co CTaBHol1 06paTHOI pewa f RlI 15 iTO

cM3aHo C COxpaHelH8 M rrplf rrspex ons MaJl)OCKOrmltfBCROit CIDt1eTplUl ltPB CTaJIshy

JIa 16 B IIBl)BOM paSI8J1S nOJIYI8 Hb1 OCHOmtJlS COOTIIOlUelLHII OnpBlBJIJiJJIIHB

mCJIO 11 110JIOJlt8FfM ROMlTOHeHT lIlLIi mOOoro y3JIa 06paTIIOA PO ueT10i ~8e aHaJI113KpyJOTCR B03MOJKHbl8 CJIYI1lli paC1lI8IIJIeHHB YSJIOB IIpK jlti30BOM nepexons

IY- Y B UK SOlj 113 np OB9IeHHOr O paCCMOTpe l fIDl CJlBJUBT ITO B )ltCIIBpmt)~lTe no

Ha j mle HHIO B03HHKaKll18 r o B ltPaS8 Y p aCllI8IDWHWI y 3JIOD o6pa11I 0~ peWSl1UI

Ha KOMllOH8HTbI BOSMOllHO rrpaKTWleOKH 0ro10SHaIJIO YCTWIOmtTL rOlGllfyll

Ol1MMeTpIDD HCXOUHoB Ii IPePP03JIaCTlflB CRoit Ila3 ltPMOTaJlJI3 LlK5Ott I Coc Ta rug n 06paTHM pemsTM H en WlaJllTWlecKoB

rrp8lIcTw emw E CJIl ns pex on KpnCT3JlJIa K 3 rrapa- B tJcppocasy conpoBOJtnaBTcH

pa3iSnemmM ero Ha IO~Hbl C n p a3JllUlliWt OPH8 HTauwIMH TO B 06paTHOM

rrpOCTpaIlCTBe rrpOKCXO~T pac m8nneHHC J~oro y3JIa 06paTHOi peweTKH B

061118M CJIYi8e TaRJK8 Ha y RmmOHeBTOB it3 ROMIlOH8HTOB Y M OB MOlKHO

COOTaBlITb Yl un8HTWlliHX TpaFlCJImJilOllliHX peID8 TOK ruunaa KS KOT OPliX

COOT BeTCTayST KaROMY-TO OUHOMY IO~HY H HMe8T CHMM8 TpHD qepP~SbI Jry COBORYJlHOCTL n p81l1STrr ~06HO paCCM1TpMBaTh RaJ( OW K HaSbIshy

BaTh COCTnBllOii pewe rKo~ 15 JrSl)eCTHO ITO M8ltPOC~TEr llOJIHshy

nOMB1ll10r o Rp aCTaJJJla Trult8Jl Jlte RaJ( K CHMM8TPHH napartasbI I CJIs nOBashy

T8JlloHO TOleUM CHMMSTPM c OCTa BHoi1 peW8TRH lI 06paTBoA peJU8TKfI rrapashyl1nSbI KPKCTaJIJJa I(OlllfDllll 61gt1Th O~OBbl COXpaHBHlS CHMMB TPIm B n OM

cnyqaB He06xoIllMo paCCMaTPRBaT h B CTPOr OM CMliCJI8 T e KaK c OxpaHeshy

IIH8 He TOJIbKO CaMIU orrepauID CBMMeTpm HO H l(8l( COXpaH9ID9 opHeHTa shy

IliH B npoCTpaBCTM COOTBe TCTBYJWtHX 11M 3JIeMBHTOB CHMMe Tpml T e

2

nOBopoTHIiX 0r8~ I rrJlOC10CTeH 3epKaJILlIOr O OTp aJte mm OnepaH CY-MMOTshy

p rJl qlepp$SIl o jpa3ym T01JS1JHYKl rpyuny (F) KOTopaJt 5UlJJW fCH WJT(shy

rpynnoH TOlelHoi4 rpyl1Iill ( P) n ar-arGSll lleJWT oplJO lf3 ( F ) -3J1(~ II0 l T(j R

CUMM8 TpMH MoryT JlISM6HHTh CBOIO OPI1J8HTat lI1JO OCTaJIhfille iRC COXP W 51 1(JCR

npn l1epexoIe B c TporoM CMiOJID I oopc3ym (I ) - rpynn q BJUIlOOlYlAfI n c nshy

rpYI1IIoli RaJ( (P ) - TaJ n ( F ) -rpyn n

OnspauHH ( I )-rpYllllli ne1tcTBy m B IIl-tnBJJaX OIlHo r o n0 M31ia 1 Onel)8shy

WUI (P ) -rpymIhl H8 BOWeI(llIUe B (1 )-r pynrry CB5l3b1BalVT UorltJl ~iIl 1Ipy r c rwyIOM Ii B 06meM crryqa8 He oripa3JlT rpynny Od03Ha1JHM m YYl If

m 1 IlOP5IJOltyen rpyl1Il (P ) ( F ) JIJ ( l) COOTBeTCTneJ-fllO Torrra 11fCJO

CB5l3liBaIOOlHX nOMBHli o nepalPfl1 Ge T VfI f -W 1 HO T OJlLyenO

n = VYl p VVl r 9 WI WI ( 1) H3 HIDe Iam H8 3KBHBaJIeHTHble nOMOHlL )le iklBHTeJ[bHO e rJll 51 - 3Jlelo1e fl T

(I ) - rpYTlIIbl a SE- MBliUOMtJHHUJI Ol1epaUKfI TO S~ 51middot Se TaJOite

MSlillOMellJiaJi OIl8pat(I1H HO OHa naeT nOM3H 3KBImaJleHTFl Il H nOJlYlCIIHOMY

no O IIS~ Se l K UorolleHhI HHBapHaHTHli OTHO CI1T8JThHO onepaloill

( I )-rpymIhl

rrOR~eM RaJ YCJlo BJle COXPaHSJUUI Cl1tIIM9IPIHl l1ap rul a3h1 MOlmO npliMeshy

HilTh nJUl Hax01Kll8HRH pacm8IlJ1eHI1H UUIHor o Y3M o6parIl 0 i1 pCWeTKI1 E CJIl1

0603HalHTh OCH SJI8MellTapllOH HIi1KH KjJHCTaJlJlB B 111JilMOM ~ 06paTHOM

npOCTpaHCTOO Jepe3 ( a() 11 ( b) TO JIOO oi4 3J1eIleHT SN T01Je1JllOn

rpymru ( r) MOlKHO 3arrnCaTh B B11lI8

SN ~ ~ S t blit -+ (2) rne ~ ~ - USJlbIe DICM (0 plusmnI) a CHMBOJI bt tl- - UH3UHll il one shy

paTOp 17 N = 12 ~p bull

)Jml JJK6 0 ro B8KTOpa peill8 TKJIJ ~

- -- - h b H~ h4 b ~ 20 b -+ 1 ~ ( 3 ) rne h~ - HHneKCll MlUlJIepa SKBIBaJIeHTRble C TOIKH 3peRIDl CHMMeTpJIIH

pellleTKH B9RTOPIgtI nO~aJOTCR C n OMOllhD COOTHoweHH~ -+ --9

-iN 5 1-1 ~ 2 HIol t ~ Ht = L h_ S w t (4)

ITPH qa30BOM n8pexone pacCrBTpJlIBae MOM B KakOM-TO O)tHOM ilCXOlJHOM

nOMeHe rrpOlllCXOlHT TpaHccIJoPMaUIDI ( MaJJaR) CHCTe Mli KoopmmaT- ( it B CHCTSMY ( -A1) ii COOTBeTCTBSIUlO CHCT9Mli ( b ) B ( B~ ) RBJIH])shy

lI1ellcR 06paTHOB n o OTHOlDeHHKl R CHCTSMe ( A ) BeKTOPhl H~ KOTOshy

phl8 no nspexona B rronperusTKS HcxOllllOro UOMeHa 6 wrn 3KBRBaJI8UTHll

BBKTOPY -H4 t 3allJlICllBalOTCR T8 rr8ph B BHne

H~ L ~Nt Bt ( 5)

3

ITp TtHlIMaH BO B1mMaKHe aJIOC Tb nellJOp MaqHH ICXO~lOfi CHCTe~ ROOpnlIHaT

MO o lTIWaTb _ -igt

= 2 ( gt~-+o(e() b( (6 )Bt rIt~ ~e K - CZMBOJI KpOn 6K8p1 a l o(el(ltClt I n TaKHM oClpa30M

H~ ~ ~ XK 61( XNIlt =L Ht lX-til + o(tK) _ (7)

roCJllI TeIlepb none~tCTBOBaTb on spaopOM s~~ Ha BBKTOPbl H~ TO

rroJJY4a1c~ B6KlOPH _ ~

H -= S~I H~ -= L yj bS y Nj L Xtl SNij ( 8 )

KOHlQgtl RO TOpUX pacn OJIOlltellli B OKpeCTHOCTI KOHIa B8KTOpa -ti H KOTOshy

pHS C~~IOBaTe~bHO rrpenCTaBnff~ KOMrrOHeHT~ pacms nnSHHoro ys~ ~~ ( Scmf S - onep3JllliI He H3 (I )-r pynlTll ) IIonc TaBJIIiII B ( 8 ) COOTHOIll9HI1H - (7 ) H ( 4 ) lIOJIYllIM OKOHlaTeJIbHO HCKOllle paClleIIJIeHHS Y3Jl8 HI B BRDe

COBOKYllHOCTH B0KTOpDB

H = I YNjbj lIj =~) + ~ hlol (~ t Sr4ft1eO(ti S~~j ) (9)

3neCb HHneKC N rrpo6erae T VI WI f r 3Ha leHirl T e ytrnTIlBamCH

eIUflfWiHaF orrep~IDI 11 Bce MelKllOMeIDme oITepauHH Ia KJqHe n e 3KBHBaJIeHTHlle

IlO~llli bull

aTpwume 3JIe MeHTll olt j sarulCfIT OT HeKoTopor o tmCJIa napaMS TpDB

OIlHC~BaIDmKX H3M8HSHRe 3~eMeHTapHO~ fIleRKH KpHcTaa~ rrpH nepeXOIe 113

rrapa- B qeppcxpasy J T napaMeTpll MOJKHO pa3ISJmTb no TpeM TmIaM H3MeH8shy

HKlt Bpallefffie BCen 3~eMeuroHTapHOli fIlIeiiru KStf3H6mle MEl o calt HSMeHeshy

Iille B0JIlfIKHIl MelKOCeBllX yrJIOB B CaMOM 06UleM CJryqaa MOJlte T Cl llTb rro TpiII

rralBMeTpa KrutUoro THna ecJm rrpmW XOIJHT nepex on c rrOHU elHeM CHMMe Tshy

pHH no TP~HO~ Ho HeROToplle R3 HEX MorYT paBHRTbCH ByRD a HSKOTOshy

PIlS - dllTb CBfISaHHWlli IWyr C IWyroMIIpH paCCMOTpeHHH KORKpeTHOro ~30-

Bor o rrepexo~ H~O ytmTIlBaTb ellie ~TO npe06p a ay eMYD 3~eM8HTapl~

fIlI8ifilty SalaCTyID YIl06HO Bbl6paTb He CTaHIJaPTHOl IT1lH IqlHCTaJlJIorpa4lHlecshy

KOit CHCTeMli napaqaSIi a TaKO~ ~T06bl R3MeHeHRe e e CHMMeTpID 6~0

MHlWM1JIbHO B 3TOM CJIYlIie HHIl9KCH lmmrepa _HNA 1-1 1 -l oll (qxp-MY~ ( 4raquo ROMIIOH8HTOB paClleMeHlIOr o y 3Jl8 H~ TaKlIte IJOJllltHH 6ElTb

rrpe06paa oBaHli B RHISKCIl HeCTaHnapTHOil fIleitK3

2 lIoMeHll B LL K lt014

IIpHMeHRM Terrep b nOJIYeHHH8 COOTHomeHKH K HaxoneHHD paCmeMeHRa

Y3JIOB 06paTHOH pemeTKH LiK SO- TlpR rrepexone 6W1 1 KOTOpldt

BKJIIJm8T (no 1tI3M9HeHHD CHMM6TpO ) Bee IijlyrltIe BoaMOlIIHbIe rrepexoroi

4

TO~SlHaF rpynna 6 WI YY MOlKe T 6ElTb SallHC8Jia KaE rrpOlI3BenslIHe nByx ~eCKHX rpynn (6) H ( II ) 17 lbR r eHspaTopbl (B nH~OM IIpeIshy

CTaBJISHHH) aCTb - ___ ~A

o ~ 1(I -+ ALu) - ~ Ix M ( lOa)

~ -Ii --

2 = I - 2 JJt~ ( lOd ) - --- --

3neCb 1 z b o~ - eltIDlKUfllH 3JleMeHT u - enmIjftffillil BeKTOP

BItOJIb OCK me CToro nOpHDKa AI - enKH-wrnH~ BeKTOP BIOJIb OIHOi R3 -~ ) _ - ~

oceJ1 BTop oro lTopHJKa ( AL u = 0 bull ITOJIarafI Al tl~ ~ K u = 1t4 ol-t rro~ liS (10)

6 b~ il4 +bA~l- - ~ 4~ -+ 63 X ( Ira) -- - - b~

T - 101 0 b~lz+ b a4 + 1 ~ ( Ird)

Bce IUleH~aTb a~eM8 HTOB rpyIIIru ( P) MOlY 6liTb JlerJltO n oryqeHll 33

(II ) noc~e IlOBaTeJIbHIlM rrepeMH OXGHHeM

lJruI paCCMOTpeHlffi rrepexona B TpHKJl1lli1Iy1O (p0M6KI8CKy1O rum MOHOshy

KJmHHyIO) p eme TKY YIOdHO RCXOIU~Tb HS P OrlaquoWlIl C(01t SlIf) ibm HCXOlJUOH la3H

o6pasOBaHHoJ1 BeKTOpaMR ( PlIc I)

deg1

PuC I CBfISb 061llHOH ISKcaroHaJIhlfoii fIle~H ( tt 0 ) C poM6m ecshy

K Oti fIle iiRo~ ( ~ iil~ ) KOTOpaR paCCMaTpHBaeTCff ITp H rrep ex oshy

Ie KPIICTaJIJl8 3 ( P )- B ( F )-qa3Y bull -+ __ -I) - -+ ~ 11 - dl_~ = ~ + d t ) d 1 - III + z 3 - -3 (2 )

rns It - B8RTOpL r eKCar OHaJIbHol p emS TIUi

OCS 03HamM ltlepe3 f~ =b~~ lt - OTHOCliTeJllHOS 1I3M6HeHHe IIJm-

RbI 1 lepe3 w~ - MSJIoe BpamelllIe fIlIefuui ItaK leJIoro BOKPyr ( - it OCH 1I ~epe 3 2 X - MalIoe K3M9HeIDfe yrJIa Melt1ly ocmm TIpOTJrnOnoshy

l

JlOJCHoro aJ BeKTOPIi HOBOn CHCTeJlru A~ MOryT d liTb 3annCaHN T e nepb

epe B8KT OpU CilVOl ~lft~Te~ ~~ middot1 nOOIJEmme rrapaMe TpIi CJle~

06ra30M (pl1C ~a 6 )

w

a ~

PUC r1 SIwH91m9 HaITpaBJIBHHM ocei1 3Jle MeHTaplloti iIleltIm npH

a ) npamemiY fiieilliIl IHu lelor o d ) npH 113MeHeHllH yrnoB ~ -r I -- - I

~JKJJY OCffiiJil ( lLi -= 0-- a j IN Iti A i) bull

f ( ) - 0

A~ == (4-~~) (1 + -fi X3 +cI3 ttl + c ( Xl-L) 1L3

I (13 ) ( )-+ ~ A ) -Az =- f3 1 3-3 ILl +(H[)ll1 +~ -lt ( 1 +4 43

~lt )-~ A shyA3 A [17+cJ1 dl + A fi(X~-W1)dll +CA+i1)~

rne 0 =- I (l1 Iit A -=-- I ~ TIPHIIHMaH BO BHHMaH19 (12 ) J DOJIYa8 11 M1Tpm 1Y (0lt ) rrp eo6paSOBaFJJ1 (6 )

- 1 2u3 - 3 -1()3+2t~ ~(- tr - t +~ - tt ) l 2 3 3 ( 4)

(0lt ) - 1+fS~-2i3 -1- 2Gi + t3 ~l (-U1 - Il--1 +~)

- 02 -- f2 +~+ti - fS~ + I-O-f~ -~~

6

3 neCb HCIIom30Bam~ OdO SHa lJeHlF

- = (~a)t 1 (l - i 2)2- ~= Vi -lt-Ashy(1 5 ) + ~ A cJ (2-G) +1 A ~L I(t lt-) If) w) J34

ltli =n tI 1- 4 (1 lt) a jJ 1t (tc) (j5 =- 1- 3 Pi

T e n epb C n OMolIlb JO ( 9) MOJCHO ilflffiCJIHT h nOJlOJli9HH5 KONITIOIl ~ HTO B IJ1CliO lLJl9 1shy

Hor o Y3Jla 3 TH nB9HaIllaTh K Oh1I10H9HTon ynOO HO c rpynm1p0BlTh B 113p11

CJl9 IJyll1lRM OdpaSOM A = (14) n == (2 5 ) == ( 3 G) D = (7 IO~ E == ( 8 II) bull F == (9 I 2 ) BoK TOP IWMnOH9 HTa Jmloro Y31l3 06paTlIoii

pellieTRu ~mnneM T~9Pb RaJlt 4 ~ -gt

H~plusmn - H~ + h 3 01~3ba+ RIj plusmn h3 UN 1 VN b3 (If)

r ne N 3ne Clgt rrpo6er ae1 3I1a i91HlfI II n F a + ~J11 - OOTBCTC~llYKn

n ep BoMY Hlill BTOPOMY lJJleHY napll I3e1 TOPU R UII 11 tI([UI5lPII VIJ eCTlgt

~ -gt RA =(~4oH1Lo(L4) b~ to (~1b(42+ 2t(H)~- ~ ~ Rs Eo(~-(u) - ~1c(4~1 b4 +[kl(gt(14-~4-tlaquo2-O(Ll) + h (0( t 0lt2)] b~- ( 17)Re=[~l~~-tolL~-ll(o(4 -~+o(el-O(ll)l b4+[-II~14 +hl (Oltw lJlz 4)] ~ Rl) [h(Dl I1- Dltl) - ~2 OlL41 h~ +[- h~ (0( -~4 +0(12-0lt12)+ ~_ (0(lt4 ton )] 62shyRE~ (h oz2 + ~z0(11) 6 + (h o(H + hl oH ) 62shyR1= [h (11(+1 -+11(42) + hL (o(Il -~Htltl(U-Dlz)]rt[-I~ o(u - h~(o(12- D(21)] 1 - -- - - U = o(~1 b + 0(1 2 b~ Ub =-o($~ bl + (o(H +ol ) bl (I6 )

~ Tgt ~ - ~ ~ Ua -0(31 + (~~+C32)~2 U E ~ 0(32 101 + OltHl shy- 1gt -gt U - (middotH+ o(31) ~1 +OIl 1 b z U F -=- (1)1 H +o(2) 6 - ltX31 Igtz

VA he O(I~ +- h2 c(l~ Vb - (0lt43 - 0( ) + 4 o(n

Vp =hf (D(q-0(23)+ ~ 1O( O Vf z hl O(l +~L 0(1)

(19)

Vc -=-1o(13+2(O( n -0lt23) ) Vp - ~1o(13+~ 2 (o(n- o(2 ~)

7

shyB Ti(1IJT~G pdffiICaHU 31FJ Me lT~ Cfv18 TP I1ll 3 l8JJi~e paCme JW1eHRe

11D nep exo1e 6 1Y 1I~ I II yenll1Otchl iYLJJlI0pa HI H2 H3 CBR3aHHhle c Y3JIaMU

l JellU Tlm 13 ( P) Jl ( j ) lo3ax Ta6JOOa

(P) (F) 5middot-t Hi 1-2- ~11-1 Hz H3

1 h~ IL 1 3 h4 + ~2bull L G hl +h2 - I-)l ~~ 12shy

6A

1shy3 h2 - ~1- ~ l ~3 -3 - hi~

S ( ~ h - hl Z5 -h1shyb - 1shy -

~ 6 Gmiddot 2 ~2

G2middot i hi + hl~ ~

10 1

t t4 A1 ~ t i - hl ~ L - ~I - lG~ f

hi - hz hl - hi - ~ 2

hi ~3 - ~2 h-+h2 ~l hi hi h2- ~3 h2 h~ ~l hlt 11shy

-12- ~3 h~ - ~1 - ~1- h3 - ~l - ~1 h -~i - hl

1 2 13 - 4

lleHTpll TIDKe CTH nay- AB bullbull F KOTop ble Y106 HO --gt --gt

6yKBOJ rramCH BeRToparrn Hi -t h3 0( 3~ b3 -t Ri

- h4 + ~2 hl - ~-~2 h3 - ~i - 2 hl ~ l

~ - hl (

2 hi -+ ~2 ~ J 1~212 ~J

2 hl -t ~l h ~1- hL h)

-1i -21-2shy ~l -21--hl ~ l

- hi + kl ~3 ~i -+ 11~ hs

0 6 03HalHTb TOll lite

8 TH lUeCTI TOlelt

o6naurmI oco6mm c BoilcTBaMll OUR K OMI1JIaHapHli 1 MoryT 6ltTb crpYIIIllIposhy

Ba110 B nEB paBHOCIOPOBJ1X TpeyrOJIhHIDlta ABC Ii b E F CO CTOPOHaMH

Ae DE fi b (hgt ~~ -+ hl)llt ( 1 1 + Cll ) f~2 (20)

UeHTp li RlieCTH TpeyrOJIhHlmOB JIeltaT Ha Ko~e OOKTOPOB (+ l1JIH ABC H

- 1m DE F )

~H-3~b~+ [- (1plusmnr3)h ~2t~~J61+[=2t3~i- (~+YJ ~Jb2 (21) 3TH DB8 rOiKH ClfMMBTpKlliLI OTHOCHTeJIbHO IIJI OCK OCTII rrpOXOlHmeJt iepe 3

Hi gt t I paCCTomm8 NaiKlIY HIDm

) t-G =2 f3b~ ( ~~ +h~+h~ h1)~ 2 1 l3 (22 )

8

BSKTop 06Ulero ~eHTpa T~eCTH TpeyrOJIhHHKOD

G Hi - ~~ 23 ~ - 1 (16 + ~ l -C ) (23 ) -

Mff BSKTOPOB HI pacIlClI10llte HHhIX 13 ILllOCKOCTIX 3SpKaJ1bHOrO OTpaKOHIDI

~31i ( P) l KOMIIOHen TIl y 3JIa Ii CaMH Tpey r OJIhHIDlli CHMM9Tp lPUill OTHOCR-

TSJIhHO 3TltX ILllOCK o CTSf )2JuI

nBa C130~CTEB o~ i13 CTopon

ITJIOCKOCTH ecmr HI JIe )(lT~

eCJlli If3 = 0 ~ JIJOOoro HI BOKTOp~ plusmn U N 1I8JKaT B

() = 0 JiI lt53 = 1 rrORBJIfIFJr CH Om9

TpeyrOJTbHflKa n sprreHwmYJJHpHa 3CPKaJIbllOii

STOll IDIOCKOCTHj Tpe yrOJIbHfOOI COBMe lJlClKYrCfl

bull IlJIOCKOCH rrByx TpeyrOJIbIlITKOE H rrEW

rrOrrOJJHHTeJIhHOS paCmeITJISHHS T oeK A il F TOJIhK0IVill

w~ - - X 4 W z i- X~ TIoCJlenrme rrBa YCJIOBIDI 03Ha alOI iTO

( i poundt~ ) H3MeHR9 T CBOKl OpHe IITaI~)fIO 3 TH BSRTOPbI HMem

nmmy 12-4 L LIUII -=- 11(3 + ch + tgt(3 ~ tgt(12 -+

B 3epKMhHott llIOCK OCTH

BeJIi1Ilffill plusmn 11 na1OT

TOJIbKOrrJIR h h2 0 BID 03HaaIOT ITO OCb iiJ CJIYa8 BCe KOMIIOHSHTII JIeltaT

TIpoBenSM T8rrSpb aHaJIH3

H3MeHeHID TOlellloit CJiIMMeTPHH rrp11

a ) 6 t71W1 -+VWI2 6) 6 m Wl-gt 2 R

JlJm cJIYmeB a) r~ 6) (1 = 1- 1 --~3 H3MSHRST CBOIO opHeHT~IO TO

h3 0 IlJIOCKOCT b

OrrHHaKOBYIO

_ ( 24 )

R 0 6pa3ym nEB rryqKa ( plusmn ( lilt I Ue I Uc ) l t( UbI U euro ) U F) ) CliM-

MeTpgtrIHble OTHOCJ1TeJIbHO 3eprCaJlbHOlt lTJlOCROCTH B lltaruJOM flY1Ke coce lI)-me

BSKTOPIl OOpa3ym yrOJI GOO E CJm JJYfKI1 Hrr0HTUtUII1 T O BCO BSKTOPIl JI8ltaT

_

lOrrOJJHllTeJIbllOe paCm8IlJIe llH8 DlOJIb b3

Wi 1=- 1- f If Wl -I- - Xl TIoCJIe ll)-ll1e nBa yCJIOshy

H3MeHRST CBOIO OpH8HTartHIO B rrpOTHBHOM

B ITJIOCKOCTll (00 h3( ~ -pound3 raquo TpeX

-1 -gt -r-gt MOCKOCTH ( Qi dt~ ) II KaK UN TaR 11 VIII bj BSKTOplt oTJIIftUill

OT HyJ1f BHyTPHllOMeHHM TOIellfM rpyrrrra (I ) eCTb 1 H paC1l18ITJIeffil8

rrp01l30iUleT TaR KaK paCCMOTPSHO BlffiIe T e Ha nBeHanuaTb KOMllOHeHT

B 06IyenlM cJJYlae ECJIH lIB a~ coxpaHReT CBOe HarrpaBJISHHe ( W = =W2 = 0) TO OpHSHT~ ITJIOCKOCTR ( ill ill ) TaKlKe HS113M9HHa 11

rpyrrrra (I ) SCTb 2 rrpH 1gt fo 0 wm WI Wl2 llpH X3 = 0 rrJIR CJIYM

a) 11 2 Ip11 JIJOOOM X 3 JVlff CJIYlasI 6) TaK11M 06pa30M MOllteT 6uTb pacshy

meIIJIeHHS Ha me CT b aJIl1 TpR KOMTIOHeHTIl KaEnoro y3na B cJIYtIae a) H

meCTb KOMIIOHeHT B CJIYlle 6 ) ECJIH OORTOpll 11i R V ~ paBHH HyJllO

TO KOMIIOHeHT~ CO~KYI C TOtIKaMl A B bullbullbull F Bo3MOlKHOCTh pa9JIK1mTb

9

cymecTB~ r RTIOTe3 OTHOCHT8JIbHO

nepexorre B tpa3Y Y B LL KSO B) 6- 2-1 = 0 ll CJIe rrOBaTeJIbH0 ecmr OCh

O~OBpSMSHHO K3MeHReTCR OpRSHT~

shyB Ti(1IJT~G pdffiICaHU 31FJ Me lT~ Cfv18 TP I1ll 3 l8JJi~e paCme JW1eHRe

11D nep exo1e 6 1Y 1I~ I II yenll1Otchl iYLJJlI0pa HI H2 H3 CBR3aHHhle c Y3JIaMU

l JellU Tlm 13 ( P) Jl ( j ) lo3ax Ta6JOOa

(P) (F) 5middot-t Hi 1-2- ~11-1 Hz H3

1 h~ IL 1 3 h4 + ~2bull L G hl +h2 - I-)l ~~ 12shy

6A

1shy3 h2 - ~1- ~ l ~3 -3 - hi~

S ( ~ h - hl Z5 -h1shyb - 1shy -

~ 6 Gmiddot 2 ~2

G2middot i hi + hl~ ~

10 1

t t4 A1 ~ t i - hl ~ L - ~I - lG~ f

hi - hz hl - hi - ~ 2

hi ~3 - ~2 h-+h2 ~l hi hi h2- ~3 h2 h~ ~l hlt 11shy

-12- ~3 h~ - ~1 - ~1- h3 - ~l - ~1 h -~i - hl

1 2 13 - 4

lleHTpll TIDKe CTH nay- AB bullbull F KOTop ble Y106 HO --gt --gt

6yKBOJ rramCH BeRToparrn Hi -t h3 0( 3~ b3 -t Ri

- h4 + ~2 hl - ~-~2 h3 - ~i - 2 hl ~ l

~ - hl (

2 hi -+ ~2 ~ J 1~212 ~J

2 hl -t ~l h ~1- hL h)

-1i -21-2shy ~l -21--hl ~ l

- hi + kl ~3 ~i -+ 11~ hs

0 6 03HalHTb TOll lite

8 TH lUeCTI TOlelt

o6naurmI oco6mm c BoilcTBaMll OUR K OMI1JIaHapHli 1 MoryT 6ltTb crpYIIIllIposhy

Ba110 B nEB paBHOCIOPOBJ1X TpeyrOJIhHIDlta ABC Ii b E F CO CTOPOHaMH

Ae DE fi b (hgt ~~ -+ hl)llt ( 1 1 + Cll ) f~2 (20)

UeHTp li RlieCTH TpeyrOJIhHlmOB JIeltaT Ha Ko~e OOKTOPOB (+ l1JIH ABC H

- 1m DE F )

~H-3~b~+ [- (1plusmnr3)h ~2t~~J61+[=2t3~i- (~+YJ ~Jb2 (21) 3TH DB8 rOiKH ClfMMBTpKlliLI OTHOCHTeJIbHO IIJI OCK OCTII rrpOXOlHmeJt iepe 3

Hi gt t I paCCTomm8 NaiKlIY HIDm

) t-G =2 f3b~ ( ~~ +h~+h~ h1)~ 2 1 l3 (22 )

8

BSKTop 06Ulero ~eHTpa T~eCTH TpeyrOJIhHHKOD

G Hi - ~~ 23 ~ - 1 (16 + ~ l -C ) (23 ) -

Mff BSKTOPOB HI pacIlClI10llte HHhIX 13 ILllOCKOCTIX 3SpKaJ1bHOrO OTpaKOHIDI

~31i ( P) l KOMIIOHen TIl y 3JIa Ii CaMH Tpey r OJIhHIDlli CHMM9Tp lPUill OTHOCR-

TSJIhHO 3TltX ILllOCK o CTSf )2JuI

nBa C130~CTEB o~ i13 CTopon

ITJIOCKOCTH ecmr HI JIe )(lT~

eCJlli If3 = 0 ~ JIJOOoro HI BOKTOp~ plusmn U N 1I8JKaT B

() = 0 JiI lt53 = 1 rrORBJIfIFJr CH Om9

TpeyrOJTbHflKa n sprreHwmYJJHpHa 3CPKaJIbllOii

STOll IDIOCKOCTHj Tpe yrOJIbHfOOI COBMe lJlClKYrCfl

bull IlJIOCKOCH rrByx TpeyrOJIbIlITKOE H rrEW

rrOrrOJJHHTeJIhHOS paCmeITJISHHS T oeK A il F TOJIhK0IVill

w~ - - X 4 W z i- X~ TIoCJlenrme rrBa YCJIOBIDI 03Ha alOI iTO

( i poundt~ ) H3MeHR9 T CBOKl OpHe IITaI~)fIO 3 TH BSRTOPbI HMem

nmmy 12-4 L LIUII -=- 11(3 + ch + tgt(3 ~ tgt(12 -+

B 3epKMhHott llIOCK OCTH

BeJIi1Ilffill plusmn 11 na1OT

TOJIbKOrrJIR h h2 0 BID 03HaaIOT ITO OCb iiJ CJIYa8 BCe KOMIIOHSHTII JIeltaT

TIpoBenSM T8rrSpb aHaJIH3

H3MeHeHID TOlellloit CJiIMMeTPHH rrp11

a ) 6 t71W1 -+VWI2 6) 6 m Wl-gt 2 R

JlJm cJIYmeB a) r~ 6) (1 = 1- 1 --~3 H3MSHRST CBOIO opHeHT~IO TO

h3 0 IlJIOCKOCT b

OrrHHaKOBYIO

_ ( 24 )

R 0 6pa3ym nEB rryqKa ( plusmn ( lilt I Ue I Uc ) l t( UbI U euro ) U F) ) CliM-

MeTpgtrIHble OTHOCJ1TeJIbHO 3eprCaJlbHOlt lTJlOCROCTH B lltaruJOM flY1Ke coce lI)-me

BSKTOPIl OOpa3ym yrOJI GOO E CJm JJYfKI1 Hrr0HTUtUII1 T O BCO BSKTOPIl JI8ltaT

_

lOrrOJJHllTeJIbllOe paCm8IlJIe llH8 DlOJIb b3

Wi 1=- 1- f If Wl -I- - Xl TIoCJIe ll)-ll1e nBa yCJIOshy

H3MeHRST CBOIO OpH8HTartHIO B rrpOTHBHOM

B ITJIOCKOCTll (00 h3( ~ -pound3 raquo TpeX

-1 -gt -r-gt MOCKOCTH ( Qi dt~ ) II KaK UN TaR 11 VIII bj BSKTOplt oTJIIftUill

OT HyJ1f BHyTPHllOMeHHM TOIellfM rpyrrrra (I ) eCTb 1 H paC1l18ITJIeffil8

rrp01l30iUleT TaR KaK paCCMOTPSHO BlffiIe T e Ha nBeHanuaTb KOMllOHeHT

B 06IyenlM cJJYlae ECJIH lIB a~ coxpaHReT CBOe HarrpaBJISHHe ( W = =W2 = 0) TO OpHSHT~ ITJIOCKOCTR ( ill ill ) TaKlKe HS113M9HHa 11

rpyrrrra (I ) SCTb 2 rrpH 1gt fo 0 wm WI Wl2 llpH X3 = 0 rrJIR CJIYM

a) 11 2 Ip11 JIJOOOM X 3 JVlff CJIYlasI 6) TaK11M 06pa30M MOllteT 6uTb pacshy

meIIJIeHHS Ha me CT b aJIl1 TpR KOMTIOHeHTIl KaEnoro y3na B cJIYtIae a) H

meCTb KOMIIOHeHT B CJIYlle 6 ) ECJIH OORTOpll 11i R V ~ paBHH HyJllO

TO KOMIIOHeHT~ CO~KYI C TOtIKaMl A B bullbullbull F Bo3MOlKHOCTh pa9JIK1mTb

9

cymecTB~ r RTIOTe3 OTHOCHT8JIbHO

nepexorre B tpa3Y Y B LL KSO B) 6- 2-1 = 0 ll CJIe rrOBaTeJIbH0 ecmr OCh

O~OBpSMSHHO K3MeHReTCR OpRSHT~

- CJJY-l[U a) I Ci ) l8 aaillcm OT lTOB8JleHllli Bel1Opa a3 11 Orrpen8JUIeTCR

OIJl1811raUl1e i1 TpeYlOJThHillWH AOC 1 DE F OTHOCl1T8mHO B8KTOPl ht -- ~~1 e cm1 810] B HTOP neJKl1T B 80PKalbJIOit IJIJOC]()CTll IlJIq C1JYIaR a) (1-3 = 0) o~a cTopoHa TpGyrOJlhHImOB neprrenmfiJI3IlpHa 8TOMY Be]Topy bull n7IR 6) - B

cXJ rneM cJIYae 3 TO He f3llt RPOM8 Cl1TYaJJIDf ](orna 1 3 plusmn f31 ECJIH lK8

13 = plusmn 0 1 T O HaJIh8R pa3JLTrnTh CJIYl8l a) 0 r5 ) lICX OlJFI TOJIhKO H3

r e OMpTplnt nOMOEROit c Tp y wrypli

lIer-axoJI ( ~ 2 -71 MOlRHO p a c mAATpHnaTh ](are G-0 1 ITO CJIeny8T liS

rrplml tTdITa c y rreprr0 31WIIl 13 OT )n c JIiae rpyrma (P ) COCTOI~T TOlIhK0 113

[8C1U 318M8HTon (rrepBll8 U8 CTL 31J8M8HTOB TacJJllIll1 ) T 8 B 06 mGM

CJIYlse nOJllt1O Ha6JIiDl1arbCR Ul8 CTh ](t)MIIOHeHT paCIIl8lIJOHHOIO ySJIa H

TOJIhKO f~n I JpeyroJUJillli ABC Bce npe 1llUJY1118 e paccMOTpeHm~ CHMMeTplill

IW WIOlefIT Te rreph H8 crrpanenmmo TK KOMIIOH8HfH 7 8 12 He CYl1eCTshy

Bym TilK )aJ CHM18TPUiI Ila3bl (F ) TpllliJIRHHaq ~o 1 4 2 = 0 lil ~ -gt

Y1Yill OCh at lUll IIJIOCKOCTh ( a( fL~ ) lum Od8 BMP- CTC M8PJIlOl CBOIO -- 0PHOHTRnUIO IIpH rrepeXOJl8 n CJI8JOBaT8JIbHO B cnyqa8 B) B8YTOp U U 11lJH VN ~ lllIt OCla BMe CTO He paBThl HYJlIO

v3 rrpOBenGHHOTO paCCMOTpGHIDl CJlellYeT ITO rrepexo~ rrpHHaIJ7lellUT R

CnyqMM a) U1IIi 6) 8CJrn BC8 B8RTOPH B rpyrrrrax LIr YI Vpj 1 HYlJeBble

ECIDI B8KTOpa ~ IiYJI8Bbl8i J 111 He paBl-ll HyJllO llJUI HaoaopT

TO rrep oxoJ H8COMHelmo rrplmaIJ7le JilliT CJiYaIO B) ECJrn JiW ~ 11 VN ~ HO l~BHH Hy JllO T O rrepexoJ MOlKeT rrpHH~1J8zaTb a) a) llJUI B) CTfIarnM

npH 3TOM Pil3JllHlITb cnyqaH B) 11 a) Cl) M8He o rrpOCTO HO B rrpHHUIDIe

p Cmiddot 3lOro-lO eCJ1H Tj)HHRTh DO BHl1Mllime ITO IJ7IR a ) II 6 ) IJ1CJlO KOMlIOH8HT

BGernrl (j OJ1hrue meC Tl a U1lli B) I1CilhUle Iillli paBlIO lllOCTH (JIB8 rum aowe IwmOI8HT MorY COnITanaTb rro CJIYalfrlW1 npllIIDIaM) BeKTOPbl

UIII n VN b MOLHO 0 rrrCJ6 TIITL i I821llH rMO 4pyr OT lJ)yra J(e tlCTBlIshy

Te lLHO ill5 Y3lOB (0 0 ~ 3 ) paCll18J1J1eHlle orrl18)lCJIfl8TCH TOJU]O OOKTOshy-cgt

pawl UN a UlFl Y8JIOB ( ~~ hl 0 ) IU BRJIa)l P100H IIYJIJ(

Ila p HC 3 rrpencTann8 m HeKoTopble B0 3MOllUUle paCIl10 IJ1CHl151 )lJIl1 Tpex

CJIYIaeB a) 6) If B) PIle 3 HMC(T TOJIhKO JJIJIJOCTpaTIUlllhl ii CMHCJJ TR

OOJlwnUlli napnIle TpOB ITO ROTOPl1M paCCllITHroJIOCL paCI~eJ1Jle H1l8 owrn W OPaHbl C7JYIrutllliM 06pa30M

PaccMOTpeHI18 pealJbHbIX 3Kcrr8pmleHTaJlhHbIX p83YJllgtTaToB MOJK8T

3aTpywmTbcH pa3JIU1HblMH oClCT0HT8lbCT3BMIL JlarrpUMep n8KoTopbl8 THTII1

IlOI1eHOB MOryT 38HRM3Th TOJlhKO OIeHh MaJIeHhKlIll odbeM B 06pa3lO lJill

COBceM OTCYTCTBOBaTh H8)lOCTaTotHaR pa3peliIaJOOl8Q CIIOCOOIlOCTh 3ItcnepHshy

MeHTaJIhHoLl YCTaHOBltYl HJIYI CSOJIhUlM M033JNHOCTh oCSpa3l~a Mory-f C)l8JIaTh

10

Y

Jfl s B I5)e 2 Tgt eli 110) shy

4 ~AI4)

~B1gt 7 C

6~

fl

Pgtc 3 HSKoTope OO3M(mJillr~ pac[~nJ11lellM

) ysaJI (lDO) rrepexoll 6tyW rn VV Mllal1tl 1p N i co 0 1 = 5 ~ = 3 OCTaJI1Jie pam[~ lIyJlK)

6) y S8Jl ( 100) rr6p ElXon 6 A W1_ 2 T1Up8MtlTpii i = 7 == 0 If3 == ()l = 3 OCTaJIblflieurol lilBHH lIymoi

B) Y 3e JI ( IOI) llep exon 6 ~ I TlapaMeTpU i = () ~ = 4 11 = 2 ~2 = 1 5 1) = 11 ~ = ui CJi == 1 tij == 2 ~ = 2 2 + rom - 0 3HaIaeT V(CM TaRcT ) BeJJlllJHHa V

yxa3aHa B cKoCSKax nmppll 0 3Ra I8lCTJ 1l0Mepa IWMnOIWIlT 1 - I ~

CTpeJIK8 03HaIa8 T IIp09KltHFl KOHla B8ItTOpa Il l b + hI 11 1 11

Ha ILIOCROCTh pncyHRa OOJlJftIHUll rrapaMelp()B rtpKBeltCll1I B eJHHHshy

lax npenCTaJlJl8mrux OTpG31WM AL

Hepasp emeHHllMH OTJeJlbHbl8 KOMlIOH81PJ bI IIOCKOJllgtKY M0 38l1IHOCTb rrplffiOlIKT

llt pa3M1iTRIO ysna no cclBPlfl8cROH nossp x llOCTK c patJlyCOM HI TO

KOMIlOHOHTU JIe~e Ha n OBBp XHOCTZ n eprreHIHKy1IRpHoi -R MOryT

CJIHThCf BOSMOJIHO ITO IDA8HHO no 3TO~ rrpKmHO OTnOJIhHHOHe jJmllll K OMIlOH8HTil Ha pHC 4 ( JI9BaR cTopoaa) U3 pa60 TIi 6 bull O1lI03HalffiBJI

IrnT8prrpeT~ naHIDlXr~ll1eIIJIeHHJl Y3JIoll peUl9TKU Li k S 0lt bull IIpe1lshyCTaBJJeHIillX B paaoT8 II TaRlle 3aTPY1lHUI8JIlHa KS-sa H9nOCTa TOlffioro

pasp eWeHlfJI KOMIlOHeHT ]JJIR ycnelllHoro rrpJilMeHeHllR KSJIOlkSHH OlO B HaCTOHshy

lleil pa6 0T8 ~TOna JKeJraTeJIhHo YJIYIDIlilIl p83pellalClQYl) cnocoCSHoCTb IIpOshy

BeCTB R3M9peIm6 pacmeIUraHM no KpruUleft Mepe HeCKOJIIJltllC Y3JIOB o6paToll

peme TKB Li KSOIj Pa60Ta B aTOM HaIIpaBJI9HID1 1Iampm ne~eTCH

ABTOPbI 6JIaIO~pHY ~ AillyBaHOBY 3a RHTepec K pa60Te H nOJI93HHe

06CY1KII8HliH bull

11

JIwrepaTypa

1 B~nD~t M L cL a l S~ Jd ~L Comm 0 1~ 1 1 10 4

2 S~1 m D P 1 mlIln 1979 1J ~ gt~3

J 01 middot ~c~middotcs l-i T Krd J wl kl ir I JOb f~_ FtHi l fJ J I _~ ct r middotic~ 198 1 3 3

p

1 11 01 II ( cd rr I Il III(ctr i cl I 1BI )~ I 319

) II l u fo Orls Joll3 k 1 iErrodl(tr l c 19B1 JIo p 379

6 Tomzesld P E Luk$ze -licgt K Phas Tra n s itions 19 B3 4 p 37

7 reh R et 31 Ferroele c tr ic 198 1 53 p 337

1 Iva n o v II Ferroe l e c trics 19 85 62 p 43 1

l q~llsal -1 1 middott al Prrma na 1983 20 p 133

10 FU iot o S e t a l JPhys I) AIPl Phy s 198 1 17 P 135

11 Ral su r o v n a l ph ys dL aL ~ol ( a l 19 B4 83 p K I 17

1 6h lk ay - Tamha ne S elra A C~idamb r a m R H~II B4 1 1 fl rli n

19 84 p 1 6 3

13 Ba l agu ro v A lt e t a l F e r ro e l~ctl i cs 1983 18 1 163

14 h aJJ a r yp ol1 A1 H up OVlRl1 14- 84 -69 )lyfH8 1984

15 Pa rr y CS Ac La CImiddoty st 1962 15 1gt 59gt

16 Sh u va l ol Lr J PhysSo c J apan 1 9~9 l ( SlIpl1 l p 3~

17 Zach riase n N H Th eo r y or X- Sa y DifrracLlun in Cr ys La ls J Wil ey

Np YOlk 1945

PyKOilHCb llOCTyrrKna B H3~aTaabCKHi OT~aH 14 HDaH 1984 ro~a

12

BanapYPOB AM TIona H CaBeHKo BH PI7-85-450 CIiMMeTpHHHbIH aHaJIH3 HH3KOTeMnepaTYPHOH oOMeHHOH CTPYKTYPbl B cPepp03JIaCTJiKe LiKS0

4

Ha 0CHOBe npHHUHTIa coxpaHeHHH MaKpOCKOna4eCKOH CHMMeTshyPliH npH cPa30BoM n (~pexooe npOBeneu a llaJIH3 noMemlOH CTPYKTYPbl B03HHKaID~eH B ~epp03JIaCTa4eCKHX KpHCTaJIJIaX LiKS04 npH T S 190 K PaC CMoTpeHbl CJIYliaH ne pexooOB H3 KPHC TaJIJIOppa(lHshyH CKHX KJIaCCOB 6mm HJIH 6 B KJIaCCbI mm2 2 HI TIoKa3aHO 110 R 3KCnepHMeHTe no Ha5JIIDoeHHIO paCDJenJIeHHR Y3JIOB 06paTHOH pe wcTKH LiKS04 Ha KOMTIOHeHTbI B03MO~HO npaKTH4e CKH 0oHo3Ha4HO YCTaHOBHTb T04eliHYID CHMMeTpHID HCXOAHOH H cPe pp03JIaCTa4eCKOH cPa 3 KpHCTaJIJIa

PaeioTa BbmOJIHeHa B J1aeiopaTopHH He ffTpOHHOH cPH3HKH mum

npenpHHT O5beJVIHeHHoru HHCTHTYT8 IIAepHbIX HccneAoB8HHR llytlH8 1985

nepeBoA TIlllp03ooBoH

Balagurov AM Popa NC Savenko B ~ P17-8 i- 450 Symmetry Ana lysis of Low Tempera ture Domain Structure in Ferroelasti c Li KS04

The doma in s tructure appearing in f e r r oc l a st l c Li KS04 at T $ 190 K has heen analys ed s t a rtin g from t he pr i nc lpl e of mac r oscopic symme try cons e rvati on The t r ansi tions [ r om the poin t groups 6mm or 6 into mm2 2 o r 1 I r e cons id r ed in deta i l It is shown that by t he measurement of l h~ s p l i t of r ec iprocal lattice node it is pos s i bl e t o det e r mine the point gr ou p of thc para- and ferroe l as t i c phase in l iKS0 4

The inve s tigati on has been pe r f ormed at the Laborator y of Neutron Phys ics JINR

Preprint of the Joint Institute for Nucl ea r Research Dubna 198 5