a),
sham the
mate t ( ~ ,
= 0.891 for BPI1 and All* = 0.175 tor
where
BPI, while E is t h e s d r order para~leterchwicte-g
the local orientation ardering of the moled
c u b In the cubic structures of BP, The theory
a r k with negligible viola
the
oMer fn
~~
of the p h a d the cubic
o f a h U t l 0 1 . Wecanas
stitutss not. mre than 1150 of the ~ o u d -h
ra&$:
predicts P univemd temperatdependence of
F for LC phases: l o
3434 [p2Ba'+96yrea, (TI#-T) J"
(5)
L
l6rra
where B O 1 = 1.031, TO = 1.184, Boa = 1.017,
-
2). The s d v a l u e of E ( T , -2) indimtea
4$
the correctness of the application of the t w o - h :f
appmximatlon in the dynamic t h q of d i f f m
and of allowing for Fourier harmonia of only ong ,
type ~ ( t , 2) in Landau's theory of phase
E(T,
+
rO' = 1. L32, TI 4 is the temperature of the phase
transition from the isotrapic kiquid to the BP, and
a , , 8, r are the coefficients in the expansion of
the free energy in powers of the order p e w t e r .
Figure 4b shows the temperature dependen- of
,-
--
Lion5.
a
the s d a r order parameter, determined by expreslion (4) fmm the experimental values of E ( T , 2 ) .
The continuous curve is the theoretid dependence of the scalar order paramatar obtained fmm
(5) by selection of the parametere Blu and a l l y .
FOP the curve shown in Fig. 4b, f i l y = 0.34;
We see that the value of the
a,ly = 0.012 K ' l .
local orientational order =mains p m c t i d y unchanged in the phase trandtion BPI-BPII.
The narrow diffraction peak in thick specimens
in the region of the d u r n of the main refledon
(Fig. le), not previously observed in a BP of a
LC may be due to diffraction with Fourier harmonic
E ( T , -2)
(not natural). The narmw hdf-width
of the additional peak is evidence of the gwd quality
of the crystal. An estimate of the region af mherent scattering" fmm the width of Ihe a d d tional peak reveals that it is about 102 pm, i . e.,
it corresponds to the thickness of the single
crystal. From the intensity of the narrow-band
peak we can estimate the value of the modulus of
the Fourier harmonic E ( T , -2) = 4.10-*. We must
emphasize that this is the upper h i t of the -ti-
1".
a. B a 1 y b h Y . z. m i t r i d , ucp. Fh. wu, 3&9
'
[Sm.N p . U p .
535 (1985)].
S w y s r , f. B l r a l , A. Wlltrop, t r t sl., Liquid Q y a u
u,
(1985)
1, 3 (1986).
R. n. k n w i c h
8nd S.
J. a m ,
~ h y r .h v . A
-
2 , 635
(1981).
R. U. Eonueich and S. J. &tr-,
Phya. h.A
1791
(1983).
'S. k i h Md U. w,RLys. Rev. Iatt. g,822 ( 1 W ) .
D. L. Johnron, J. 8. Plack, and P. P. W b r ,
Rev.
htt. g
6
, u
1 (1980).
'V. A. fi-1'
and V. V. F~~khortw,
Pi.'= Zb. m.Twr. lit.
283 (1983) [ ~ g p pktt.
337 (1983)l.
' V , A. B a l y b , V. E. h i t r i h , and 3. H. -chi*,
Zb.
b p . Tmr. Fiz. 82, 58S (1982) [Sav. Phy..
322
u,
'
m.
z,
a,
mx,
(1982)J.
R. B a r b e t - b s h a d P. Pieranski, J. do Pby.. 9,
L1 (1965).
''V.
A. Belyalrov,E. I. m i k h m , V . L. b i t r l u r L o , u d V . It.
Dolganw, Zh. %Irsp. Teor. P i z . 89, 2035 (1985) [ h v . PbyL.
u, 1173 (198511.
"E. I. P B m M , V . K. mlpnov,MdS. P. Krylov&,Zh. m.
Tear. Fie. 93, 1 7 5 0 (1987) [SOT. Phys.
%, 998 (1987)j.
Translated by S. G. Kirsch
Dechiralization of cholesteric liquid crystals due to the action of
ionizing radiation
0.D.Lavrentovich and V. A. Linev
Insrirute of Physics Academy of Sciences of the Ukminian SSR
(Submitted Janwry 10, 1988)
Kristallografiya 35.465469 ( March-April 19WI
The authors have studied the influence of ionizing radiation on the sptctra of selective reflection of light by
cholesteric liquid crystals {CLCwerivatives of cholesterol. They show that, under the influence of Y - ( ~ C O )
and proton {E, = 70 MeV)irradiation with d m of up to 200 kGr, in the derivatives of choIcstcrol there is a
marked change in the sptctra of selective reflection of light, which is due to the formation of radiationinduced impurities. The prescncc of t h e impuritits, in the first place. reduces the temperature range of
existence of the CLC, and, in the second place alters the effective twisting capacity of the molccuIcs, leading
to dechiralization of the system as a twhotc.
-
INTRODUCTION
Chiral structures are traditional and very
interesting objects of investigation in optics. The
simples exampies of such structures are cholesteric
liquid crystals (CLC) for which the s p h l twisting
of the supermolecular structure causes selective
tmnsmission and reflection of light, and also gigantic
optical aetlvlty. As established on the bask of
28E
%v. Phys. Crystatlogr. 35t 21, MarchApril 1990
<-
copious experimental material, the pitch of the
spiral of the CLC is very sensitive to various e x t r r
nal actions electromagnetic field, temperature,
pressure, ete.
However, there have been practieally no investigations of the changes of the optical properties of CLC under the Influence of such
an important factor 8s lodztng radiation ( I R ) . The
Importance of such investigations i6 due not only
to possible practical appliatfons but also to the
-
'
0038-5638190102 0268-04 #03.00
O 1990 Amarkan Institute of Physics
26a
of 115 kGr and with 7-quanta in a K100,000 (40Co)
apparatus to a dose of 100 kGr (Grey(Gr) = Jlkg).
Measursments of the selective a c t i o n r p e r
tra vs the tempereture and dose of mdhtion were
made in an SF-16 ~peetmphotometerin tha wavelength m g e ZOOrl2OO nm. For the plimar-orientnted specimens the thickness of the CLC layer
was 15 pin. T h e n n o 6 t a b ~ t i o n(to d t h h O.I0C)
was effected by a special unit which could alsa
vary the temperature at 0.5-5O Clmin
Before p r e ~ n t i n gthe experimental results
it seem pertinent to make one remark. In the
mgion of aebctlve reflection of light in the trans-
.
mission ilpectrum of a p b r layer of CLC we observe a &urn
whlch coinddes in wavelength
with the h u m of the selective ref1ection.l
'rherefore to simpfify with the maximum of the
eelective transmission minimum, but in describing
and discussing the results we use the term "selective reflaction. "
PIG. 1. T m p m t u r a d W a s of -1X of wlwtivs
mflectlan in mixtures of CP + CC (a, b) and CP + CP (e, d).
a, c) m i x m e n of n r m f r r d b t r d eonpanmtr; b) W irradiatd
vlth protons t o
C s s o f llr5 kGr; d) CF i r r a d i r t d w i t h y quanta t o 4 dose of 100 Wr.
general problem of elucidating the influence of IR
on c h i d strvctures both at the maerogtmctural
and at the molecular level.
Theaimof our work was to fill this gap. We
studied the temperature dependences of the wavelengths of selective reflection of CLC and their
alterations under the influence of IR For the
initial and irradiated substencee, and a h for radiation-induced impuritie~, we determined the so-called
mohcular twisting forces, which are a quantitative
measure of the c h i d t y of the CLC. We measured
how the degree of deehLralleatiou of the CLC degends
on the dose of IR.
.
EXPERIMENTAL RESULTS
The family of temperature dependences of the
wavelength A of the maximum of selective reflection over a wide ran@ of concentmtians is shown
in Fig. 1 (mixtures C P i C C a n d CF + CP). As
it follows from Fig. 1, the overatl course of the
h ( T ) dependences in systems with an irradiated
component ia analogous to the ease of an unlrradiated mixture. In particular, for CP-CC mixtures
with h e of ths concentration C of CC the i n c h tion of the dependence X(T) changes twice: when
0 5 C s_ 0.2h(T) it monotonidly decreases, when
0.2 c C c 0.6 it monotonidy increases, and
finally, when 0.6 c C 5 1X(T) it agdn demases.
Momover, as seen from a more detailed cumparison, the behavior of h ( T ) in the two types
of mixture manifests quantitative differences: On
irradiation, the X(T) curves shift to lower temperatures, owing t o the fall in the phase transmission
temperatures as a result of fofmetion of radiationinduced impurities in the system. * ' However, It
mER1MENTA.L METHOD
We etudfed two-component dxtures of three
dmrivatives of cholesterol: cholesteryl formete (CF),
cholesteryi pelargonate ( CP) , and cholesteryl chloride
( C C ) . The. choice of mixtures as objects of inVeatigation was pmmpted, in the first piam, by
their wide practical applications, and, In the eecoad
p h , by the necessity of determination of the
molecular forces of twisting, the conept of which
h e d on the laws of change of the wavelength
of selective reflection with mncent~~tion.
3 In thin
article we give data for two mixture&: CP + CC
and CF + CP. As the irmdiated component in the
CP + CC mixture we used CP (the CC was not
imdiated), and in the CF + CP mixture we first
h d i a t e d the CF. Icradiation of only one comPonent pursued the alm of a more reliable es-tion of the changes in CLC due t o IR.
The substances were irradiated with 70 MeV
Protons in a V-240 isochmnous cyclotron to a doee
289
Sow. Phys. Crystsllogr. 36121. Much-April 1990
o f val-s of affwtive twisting forcu on
p r m t a r r (r = 0.22 TITiq (TIT,) Im. 11)) , &ere Ti is
th -ratof tha p h s s transition of chole~tmrolt m a ~
imtrepic liquid, q ( T / T ~ ) is th. d r parmtnr. l a a)
Mnirrdhtd i
3 (I), irradiated w i t h p r D t m to dm* o f 1C5
bGr (2). radiation-induced wuritias (3); b) mnitrdf.t.d Q
quanta t o a d o u of 10P &r (2).
( I), irrdhtd wLth
FIG. 2.
radbtion-indwed with.,( 3 ) .
0.D. Lsvrentovich and V. A. Linw
269
thane in the #luof the h(T) dependenC€S in the irradiated dxtlmt6
purely on account of the change in the p h
transition tempersturn. ' TbIs is easy to verify
Lf we reckon that the cumw of AIT) in Fig. 1
-not
be cornpamad with one another by a ~imple
tranefer along the temperature d , because as
a result of ifiecliation there i8 a change in the
slope d the l ( T l curve. In fact, this means that
as a result of irradiation themhas hen a change
In the actual twisting capadty of the irradiated
DISCUSSION OF RESULTS
Thus, as a result of the action of IR in
rivatives of* cholesterol, the mapnitud~of
f ective rnoleculnr twisting forces decrease.
us consider the possible causes of this
seems impossible to explain the
As shown in Ref. 3, imdiation leads to
down of the CLC molecules, resulting in the f
tion of radiation-induced impurities in
A chenge in the chemical structure of the mole&of chole~temlderivatives under the influence of
component; a quantitative m u r e of this is the
IR can occur either In the steroid nucleus or ia
m o l m l a r force of twisting 9,
the akyl and isopmpyl chains. Leder ''' studied the influence of, the chemical structure of molecub
The molecular forcehi of twisting are deterof cholesteries on the magnitude of the twisting
+
mined from the shape of the curve of the redprocal
force. In these articles it was shown that the
of the wavelength of selective reflection of the
effectlw twisting force increases with incmasing
mhture ve the concentration of the wrnponents*:
length of the alkyl chain of the compounds of the
homolbgous series of aliphatic estem of cholesterol.
In Ref; 8 Leder obtained interesting results of
where
and b 2
re'ptiTe1y'
the
an investigation of the redpmcal effecdve waveforces of twisting of the first and second commpolengths in relation to the lend of the
L a parameter representing
nents , respectively,
R (Fig. I ) . I t was shown that the r e c i p m efthe mutual influenee of the components of the mixture, Bctive wavelenghs in relation to
Lie a straight
and is the concentra*n
Iirat (Lmdiat*)
both for right-hand& and for ieft-bnded
component, usually expressed in units by weight
cholesterics. This straight line can lxz d y c i d l y
(as shown in Ref. 6, the law A"(C) is better As
expressed by the equmtion '1 = 1 .5d + 15.6.
satisfied with a set of weight mncentratiana)
it ~ollowsProm the expression , the effective molecuw~~hC,"O~8~?&~th2
lar twisting forces are determined by extrapalation
than
1.08
are
left-handed. In other words,
of the dependence x ' ~ ( C ) to the values C = 0 and
variation
of
d
both the absolute values and the
L - +.
signs of the effective t w f s t i n ~forces may dter.
The quantities +,, e t r
were determined
A second important factor determining the
by approximation of dependence (1) by the method
spiral
twisting k the structure of the steroidal
of least squares. The temperature dependences
skeletons of the molecules of cholesterol derivatives
are
given
in
Fig.
2
for
CP
and
CF,
respec$,,
in particular, the position of the double bond C=C
tively. As seen ffom Fig. 2 , in CP and CF under
[Fig. 1). For example, In R e f . 9 it was shown
the influence of IR there is a reduction of the efthat
them la a marked tendency toward increme
fective molecular twisting forces. It is logical to
in the "rightness" of cholesterics when the double
treat this as the result of formation of -tionbonds in positions 7-8 and 5-6 disappear or this
induced imurities in the system, with values @P
bond ia displaced to pdsltlon 8-14.
Now let us
lower than in the initial molecules. The values of
consider what types of structural changes in the
far the impurities can also be estimated if
molecules can bear msponsibility for a change in
we uae the above method for the same irradiated
the sgifal twist under irradiation.
component and consider it ae a mixture of molecules of the initial substance with known o and
Choleetervl pelargonate. As follows from the
"defective" molecules chamcterized by some interesults obtained by us previously by ESR and IR
wl
m e r Q ~ P .
s~ectmsco~v.
under the influence of IR. in CP
them is amc'hangein the geometry of thd steriod
The mrrectness of this approach is confirmed,
nucleus of the molecule, due to changes in its
Firstly, by the w u l t e in Refs. 3 and 4 , which
chemical structure; but there are little or no
indicate the stability of the mdiation-induced imehangr?~in the structure of the alkyl chain.
purities. Secondly, the intmduction of the concept
Analysis of the structure of the staroid nucleus
@P L 8b.o based on the circumstance that the
of the molecules of the cholesterol series suggests
value of F P is gmctidy independent of the
that the weakest link with respect to i d i e t i o n
impurity concentration (dose of radistion) : For
is
the double bond in position 5-6 (Pig. I), joining
example, when the dose is changed from 110 to
quadrupL and triple carbon atoms; eccordfng to
190 kGr, gimp for CP deviates fmm the values
many data (see, e. g. , Ref. lo), in irrediation of
in Fig. 2 (dme 145 kGr) by less than 10%.
hvdrocarbon communds dissmiation of. C. X. h. .n..d..s.
we used a linear variant
To determine
n k quadruple &d tdp'1e earbon atom preponderate.
of approximation ( I ) , in which we put a,, = 0 ,
The probability of dissociation of these b n d a is
and determined the concentration of mdlatlon-induced 5-10 times water than the probability of disimpurities by the method in Ref. 3. In particular,
sociation of other types of C*
bond^. As shown
for CP with a dose of 145 kGr the impurity conby Leder, * change in the structure of the stemid
centration k aggmximately 15%. The obMned temnucleus near bond 5-6 reduces the twisting capacity
perature dependenare also shorn in Fig.
of CP. For example, if the carbon atoms in posi2. Fmm Fig. 2 we see that the value of eimp in
tions 5-6 are joined, not by a double bond, as
CP irradiated with a dose of 145 kGr is about half
in cholesteml derivatives, but by a single bond,
as great as 4 for th* initial CP, and in CF bwp
as in the cholestanol series, then the value of - 4
chenges sign at a redlation dose of 100 kGr.
decreases by a factor of 5-10. Consequently, the
3T?.
'
.
---
'
($f-sE&r
1
f8dBz
.
270
Sow. Phya. Cryatallqr. 35121. March-April 1990
0 . D. Lavrmtovichad V. A. M e V
270
r CP ,exporimentally o b a w e d by
due to & t i o n - h d u d
changee
the h n d 5-6 af the steroid nucleue
cholesteryl fonnete. In contrast with CP,
cons%quenm of mdiolysia of CF, as
lwsfmm ESR data and IR epectrasoopy, in a
w g e in tbe formy1 te-tion
with formation
dCDOH~Upssniththerr6u'tthattha.lot.eu1eg
joined into
by hydmpn ban&.
The
V, this
drhira]imtion of CF is svidenUy
,wm, aince the dime- formed mag poseese a
[dting force of oppaaite a l p .
From the abo-te it follows that under the hn u e n c e ~ fI R t h e - hamarkedchangeinthespectra
refleetion of CLC, which k due to forof
metion of radiation-induced impuritie~. These imprities play a double role: In the first place
they alter the temperature range of exbtence of
the CLC ; and in the second place, they alter the
twisting =padties of the molecules.
firoces
'L. n. rl-,
msetro- md a
w
d
(In b s i . n ] , IW.,
(1978).
v. A. klgrl;op .nd A. S. oni in, o p t l a ~lolrr&
Cryltrl. [inI h u r h ) , K m h ,
(1482).
quid
l l l . ~ . ~ f i , ~ . ~ . ~
um
,p
~
, .
DI. Fit. m. & 16% (1W7).
v. A. b,st al., ~hf..
26 (I=).
0. D. f
a
d V. A. W ,
m. liz. Zh.
8S6 (1988)
a ~ . - ~ ~ . - , ~ l r . ~ t . ~ . ~ t . ~ 1 ( 1 ~ ~ 5
L- B- P'b-.
2649 (1971).
1. 1. kd.r, J. a.
~ry..
4671 (1971).
G. A. ~ o m h v ,0. D. m t o v i c h ,
m- m.
22,
'
'
'
a,
'- ".
a,
*'OG.L. r.h l~d dW., rJ.m
, -.
etryl. x, 11m (1973).
iation miu of
-
[lhusim m-
lrtionl, b t b d r d a t , n o w (1985).
l l ~ . p . ~ , ~ . ~ . t i w t l * f i , a n d ~ . ~ . ~ h i . - ,
m.
~ r i h l l c g r & i y a%, 99% (1979) [*.
cry~mllw.&,
570 (1979)l.
12g. n. ~ v a r ' y a mand v. F. --,
~(ristallogmfiya
wz
(1979) [SW.
wtallogr. &, 567 (19?9)].
a,
m.
Transkted by S . G . Kirsch
Influence of forced magnetoelectric convection on the dopant
impurity distribution in growth of single crystals by the Czochralski
A. L. Goncharov, D. A. Zeinatov, and I. V. Starshinova
Stare Scient~$c-Research and Dexign Institute of the Rare Meiab I~dusrry;and Itu~irurc of Applitd Marhemaricr of rhr
Academy ofsciences of the USliR
(Submitted Septcmkr 26, 1988)
Kristallografiya 35.47-74
(March-April 1990)
The authors have constructed a mathematical model of the procews of hmt and mass transfer in the mtlt
during growth of single crystals by Czochdski's method in a magnetic field with simultaneous pasagc of an
electric current through the mtlt. They compare thc rtsults of numerical and natural cxperimtnts. By the
method of numerical experiment they determine the optimal tahnological parameters or the pracens for
which one achievm the smallest scatter of the impurity concentration along the d i u s of the crystal.
INTRODUCTION
In order to
the processesof heat and
mass transfer in melts, recently i n m i n g use
has h e n made of methods of n u = d d experiment
(NE)-modehg technological pmcesses on a comPuter. Numerical experiments enable us t o obtain
f&rly accurate estimates of the influence of any
Particular technological parameter on the source
of the process' This type of estimate is veFyimportant, bemuse It often enables us t o reduce the
number of costly m t u d experiments.
A number of articles have recently been pubk h e d with descriptions of a mathematid m e 1
of Czochralski gmwth of dngle crystale under magnetohydmdynamlc (MHD) actions. l''
An obvious
consequence of MHD action k d u c t i o n of such
Undesirable phenomena as temperature fluctuations,
t h e m msymmetry, vibration of the melt, etc. 3
1.
?
!
, ;,
'
. &
L 2 .
,
1
I
t
f
I
An interesting principle, in our view, af acon the melt is deadbed in Ref. I . S h u l taneous transmission of an electric curmnt through
the melt end ection of a constant magnetic field
generates in the melt easily controlled msgnetoelectric convection.
The dm of our pmsent work was to hveatigate the f%atures of a mathematical model of the
of heat and -s
t-fer
in *e melt
during growth of single cryst&
of elemental semicondUftors by the Czochraiski methd in magnetfc field with simultaneous transmission of an
electde eu-nt
through the melt,
of numerical e x p e h n t s on the model, comparison
of the results of the natural experiment with those
of dculation based on various p h y s i d pamumten.
and determination of the paths of dnimization of
the nonurdformity of the distribution of the Impurity
dong the radius of the afngle crystal.
2.
FEATURESOF MATHEMATICAL MODEL
It
known that the flow of melt in a m e ible during growth of single crystals by the
Czochralski method m*fies the Navierstokes
equation,
av +
-
tion
27 1
Sou. my.. Crystsllogr. 3612). Mwch-Apra 1990
*
at
( V V ) V-Re-'AV-Vp+t,
Z+(Y
V ) T - R ~ - * ~ - ~ A diu
T , V-o
,..
(1)
at
0033-5033190102 0271 4 4 e03.00
@ 1090 Ammriun Institute of Physics
27 1