Clays and Clay Minerals, Vol. 21, pp. 465-470. Pergamon Press 1973. Printed in Great Britain
THE CRYSTAL STRUCTURE OF THE DIOCTAHEDRAL
MICA 2M2 DETERMINED BY HIGH VOLTAGE
ELECTRON DIFFRACTION
A, P. ZHOUKHLISTOV,B. B, ZVYAGIN,S. V. SOBOLEVAand A. F. FEDOTOV
Academy of Sciences, Moscow, U.S.S.R.
(Received 6 April 1973)
The structure of a dioctahedral 2M2 mica was defined by high voltage electron diffraction. The
cell parameters are: a = 8-965, b ~ 5-175, c = 20.31 A, fl = 100~ 40', Z = 4, space group C2/c. Despite
the peculiar character of the layer dispogition(or4 as ~r~as), the oxygens of the layers are packed according
to the cubic law. Consequently, the interlayer cations K have a trigonal prismatic coordination. The angle
of tetrahedral twist is 11~ 20'. The interatomic distances T-O indicate ordered replacements of AI for
Si.
Abstract
INTRODUCTION
tetrahedral sheets for such cases. Franzini (1969) has
A STRUCTU~L investigation of the dioctahedral mica found another possibility for the formation of 2M 2
polytype 2M 2 is quite expedient not only because it polytypes by alternation of layers A and B in the strucmay reveal some new data concerning a peculiar mica, ture. In such a condition the interlayers are the same
but also because it is closely connected with problems as for group 1 and the ditrigonal geometry of tetraof crystal chemistry and polytypism of micas in hedral sheets is not an obstacle. As it is difficult to ungeneral. Indeed, in principle six possible mica poly- derstand the reason for differences of adjacent layers in
types consisting of centrosymme.trical layers and saris- one and the same structure, one may suppose that an
fying the homogeneity condition are subdivided into alternation of mode packing takes place inside each
layer in dependence on the relative orientation of the
two distinct groups: 1--1M, 2M 1, 3T; and 2--2M2, 20,
6H which are distinguished by the relative orientation octahedral sheet with the lower and upper tetrahedral
of adjacent layers, differing by even (group 1) or odd sheets. All layers are thus equivalent and the structure
(group 2) numbers of 2n/6. These groups differ diffrac- is homogeneous, but polar. This model has the symtionally by positions and intensities of reflections with metry Cc in accordance with observed reflection
k = 3n (indices correspond to axes with b = a x/3). absences, in contrast with symmetry C[ proposed by
If the formation and existence of polytypes of group Franzini.
Independent of these considerations, the proposals
1 is quiteclear and natural, the same is not so easy to
comprehend for polytypes of group 2. As shown by of Franzini were acceptable only for trioctahedral
Bailey (1967), the action of octahedral cations is in micas, because dioctahedral B-layers would have H:
favor of a "cubic" packing of oxygens in a layer. Such bonds between OH and Ob,s not c0nfirmed by
layers have been designated by Franzini (1969) as i.r.-data. Meanwhile, dioctahedral 2M 2 micas do exist,
layers A in contrast to layers B with "hexagonal" pack- as has been shown by Drits et al. (1966) and Sokolova
ing of oxygens. Orientations of group 1 give nearly a (1966). All this underlines the necessity of a detailed
close packing of oxygens and an octahedral coordina- structural analysis of such a mica and that is the purtion of cations in the interlayers. In contrast to this, in pose of this work.
polytypes of group 2 favorable arrangements of
STRUCTUREDETERMINATION
oxygens both inside the layer and in the interlayers
cannot be simultaneously realized. If, say, all the layers
For a structural study by means of high-voltage
are of type A, the oxygens in the interlayers are directly electron diffraction, a sample kingly given us by
stacked, one over another, forming prismatic poly- Mkhitarian (1969) was chosen from a number of dioctahedra. As a consequence, polytypes of group 2 are less hedral 2M 2 micas of different origin and structural
probable and only 2M2 has been found experimentally order. The sample gave very high quality oblique texand then quite seldom.
ture electron diffraction patterns (see Fig. 1). UnfortunIn order to explain the existence of 2M2, Radoslo- ately, this sample contained some non-separable foreign
rich (1958) supposed a hexagonal geometry of the material. Therefore, the chemical analysis (Table 1)
465
466
A.P. ZHOUKHLISTOV,B. B. ZVYAGIN,S. V. SOBOLEVAand A. F. FEDOTOV
Fig. 1. Oblique-texture electron diffraction pattern of the
mica 2M2 (~o 60~
could not be recalculated directly to give a structural
formula. Electron microprobe analysis established that
a considerable amount of Si was concentrated on areas
greater than 10 #m, and Ca and Fe were related to inclusions about 1 5/~m in dimensions. Areas with constant proportions of K, A1, Si were found, and these
areas should be attributed tO the 2M 2 mica. The surface of the powdered specimen did not satisfy the
requirements for quantitative estimation of the chemical composition.
According to spectral data, the specimen contains
no noticeable amount of Li and cannot be a lepidolite.
It differs from giimbellite by the absence of Mg. Under
such conditions, the structural formula was deduced
by using the subsequently established structural data.
The structural analysis was based on high-voltage
oblique-texture patterns, which are advantageous in
such cases, obtained with multiple exposures at optimum and maximum angles (60 and 70~ It is essential
that reflections, which would coincide i.n an ideal case
when c. cos/3 = -a/3, are distinctly resolved, indicating a deviation of the 2M 2 mica lattice from the ideal
greater than the case for 2M2-1epidolites and trioctahedral micas. This situation helped to provide 504 reflections with non-zero intensities distributed over 14
ellipses(h 2 + 3k 2 ~< 124), in correspondence to a 2M 2
lattice. The cell parameters, measured according to the
reflection positions, are a = 8.965, b = 5.175, c =
20-31 A,/3 = 10W 40'. The monoclinic lattice deformation is expressed by the relation - c cos/3/c~ = .0"419.
Absences 0freflections Okl with l odd indicate a space
group of symmetry C2/c or Cc.
The intensities have been estimated by comparison
of patterns with multiple exposures. The most distinct
reflections were measured with a photometer. The intensities so measured were used as standards for estimation of intensity of other reflections. F2-values were
calculated by means of experimentally justified local
intensity formulas (Vainstein, 1964).
The structure was determined by successive refinements of an initially ideal model constructed of threesheet layers of a muscovite composition KAI2(Si3AI)
O10(OH)2 with a hexagonal geometry of tetrahedral
sheets, disposed in a sequence ~5 a4 as q4. 99 (Zvyagin,
1967). The relative displacements ai are counted off in
a coordinate system with axes a and b = a ~ 3 . Therefore, the structural model has the angle c~ > ~/2. Since
the glide plane c passes outside the previously chosen
origin in a vacant octahedral site, the transition to a
standard setting was realized by an interchange of axes
a,b and by transition of the origin in the position 1/4,
- 1/4. The initial coordinate system (with b = a x/3),
in which all polytypes are considered, is right-handed
and the resulting system is left-handed. In order to use
a right-handed system, the structure is reflected in the
plane bc. The model was also subjected to a homogeneous shearing deformation in a negative direction
along the a-axis, in order to satisfy the real value of/3.
The structure refinement proceeded by means of
plane sections of the three-dimensional potential distribution normal to the b-axis for two variants of the
initial models: with layers having or not having symmetry centers (space groups C2/c or Cc). In the second
case, the tetrahedra were rotated by 5 ~ but differently
for the two tetrahedral sheets of a layer; i.e. according
to the "cubic" law in one sheet and the "hexagonal"
law in the other. Incidentally, this rotation permitted
check of the plausibility of a change in the packing
mode of oxygens inside a layer.
It became evident after several stages of refinement
that the oxygens were being displaced into centrosymmetrical positions, so the subsequent refinement proceeded within the limits of the space group C2/c.
In view of the complete or partial overlapping of
many reflections, o n l y 145 distinct and Well separated
reflections of the first four ellipses were used in the first
stages of refinement. Later, the intensities of composite
reflections were divided in the ratios of Fc,lc2 corresponding to the increasingly refined structure. The
final refinement by means of least squares in an iso-
The crystal structure of mica 2M 2
~
7
~
Y
"
Y
~ 9
;,t "~\".9
b
,,.
--~....
.....
)
)
qr
X6
Otd
2
3
4
5
Fig. 2. The normal projection of the structure on the plane
ab. (1) upper octahedral bases; (2) lower octahedral bases;
(3) upper tetrahedral bases; (4) lower tetrahedral bases;
(5) lower tetrahedral bases of the next (upper) mica layer.
The initial configuration of (3) and (5) characterized the
structure of the interlayer space.
tropic approximation has been taken to a value R -~
11.7 per cent for all reflections. The resulting atomic
coordinates and interatomic distances are given in
Tables 2 and 3. The normal projection of the structure
on the plane ab is schematically drawn in Fig. 2.
DISCUSSION
Even the first steps of refinement made it clear that
a 'cubic' packing of oxygens is preserved inside the
layers of the 2M2 mica; thus, the above mentioned
'unfavorable' stacking of layers is the observed mode.
This peculiarity, a result of the interaction between
tetrahedral oxygens and octahedral cations, has
proved to be energetically 'bearable' and did not prevent the formation of the dioctahedral 2M 2 mica. This
stacking of layers and concomitant repulsion of adjacent O, results in an increase of the interlayer thickness
to a value q = 3'41A. There is also a repulsion
between Si-atoms which leads to the displacement
of layers in the direction of the a-axis by a value
- 0 ' 0 1 8 a = -0"16,~.
Table 1. Chemical analyses of the dioctahedral mica 2M2"
SiO2
TiO2
A1203
Fe203
FeO
CaO
Na20
K20
HO +
85"81%
0"33
7"89
1.60
0.28
0.96
0.17
2.11
1.10
100.25~
*Made on IGEM Ac. Sc. U.S.S.R., Analysts C. A.
Gorbatsheva and E. L. Borodina.
467
As the tetrahedral sheets have a ditrigonal geometry,
the K-cations are inside slightly sloped trigonal prisms,
the average K - O distance being 2.859 A. In the projection 0n ab the edges of the tetrahedral bases are
rotated relative to their ideal hexagonal geometry
through angles indicated in Table 4, the average
rotation angle being 11.5 ~ The oxygens forming the
bases of the tetrahedra have different z-coordinates so
that these bases are inclined to the plane ab by an average of 5-5~ and the surface of the basal oxygens is corrugated. The direction of the corrugations is parallel to
the reflection planes m of single layers, along which
oxygens with the least absolute values of z-coordinates
are lying, with indexes [110] and [110] in the layers
a S and 64, respectively.
Table 2. Atomic coordinates (with standard deviations) and
individual thermal coefficients for the 2M2-structure
Atoms
K
AI
T~
T2
OH
O1
02
03
04
05
x
y
0.0
0.0921(17)
0.0900(10) 0.2468(16)
0.1248(7) 0.5670(15)
0 . 2 9 6 4 ( 7 ) 0.0986(15)
-0.0522(12)
0.0657(23)
0.0853(7) 0.5629(23)
0-2697(16) 0-1313(22)
0.1941(15) 0.3139(22)
0.4788(11) 0.1294(20)
0.2570(14)-0.1986(26)
z
B, A 2
0.25
0.0040(9)
0.1348(8)
0.1339(7)
0.0524(10)
0.0540(10)
0.0539(7)
0.1688(8)
0.1675(7)
0.157l(11)
0.45
0.40
0.34
0.37
0.25
0.29
0.28
0.28
0.22
0.27
As seen from Table 2, the two symmetrically independent tetrahedra T1 and T2 differ in their interatomic
distances. The average bond lengths T-O are 1.619 and
1.654 A, indicating that there is an ordered distribution
of isomorphous replacement of A1 for Si mainly in the
T 2 tetrahedra. Applying the relation d,,, = d s i ~ o ( l - x ) +
dAI_oX, where ds~_o = 1.62 and dAl_O = 1"77, the following contents of tetrahedra are deduced: T~ = Si,
T2= Sio.7sAlo.25.
The cations T1 are essentially in the centers of tetrahedra, while cations T2 approach O,p and move away
from the bases, the distance T2-Oap being even less
than Tj O,p despite the corresponding average T-O
distances being greater for T2 than for T~. This phenomenon, observed also for other layer silicates, accompanies the substitution of A1 for Si. As Aleksandrova et
al. (1972) have indicated, a weaker cation has to
approach closer to O,p in order to saturate its unsatisfied valence. At the same time, the cation is farther
from O b a s and the increasingly unsatisfied valences of
the latter oxygens are partially saturated by Si
approaching closer to them. These shifts cause contraction of the bases of Si-tetrahedra and expansion of
the bases of Al-tetrahedra. The unsatisfied valences are
partially saturated by interlayer cations.
A.P. ZHOUKHLISTOV,B. B. ZVYAGIN,S; V. SOBOLEVAand A. F. FEDOTOV
468
The octahedral sheet has the distortions usual for
dioctahedral micas. The octahedra are flattened and
the surface of the bases has a ditrigonal geometry. The
rotation angles of the edges of the octahedra (Table 4)
are in the range 4.5-7 ~ (the average value is 5-5~
Because of this rotation, the shared octahedral edges
are shortened, The edge O H - O H (2-569 A) is the longest of the shared edges; in muscovite (Gti'ven, 1971)
this edge is the shortest one (2'402 A).
It is essential that, whatever the polyhedra distortions, the average O - O and M - O distances be in the
same relation as for regular polyhedra with centered
cations, in accordance with the conclusions of Drits
(1970).
Table 3. Interatornic distances in 2M2--structure (A)
T-Tetrahedron
T1-O1
-O~
-O,
Os
av. T~-O
O1-O
O-O~
-O5
03-0,,
-02
O4-O5
av. O-O
A1-OH
-OH'
-O1
-O'1
-02
O~
A1-O
1"617
1"643
1"589
1"626
1.619
2:683
2-677
2-662
2.525
2.605
2"695
2-641
T2-O2
-O3
-O,
-O5
av. Tz-O
O2-O3
-O4
-O2
O3-O4
-02
O4-O5
av. O-O
A1-Octahedron*
1.982 O1-OH 2.851
1"974
-Oz
2.779
1 . 9 3 0 O2-OH 2.901
2.035
O ~-O'~ 2 . 5 1 8
1.839 OH-OH 2,569
1 . 9 7 7 O 2 - O ~ 2.948
1.956
av. O-O
O'I-OH
-O~
O~-OH
O's-OH
Oi-O'2
02 OH
2.766
I"605
1"681
1"659
1"666
1-653
2.715
2-693
2.721
2.730
2-731
2"593
2.6972.877
2.851
2.761
2.866
2"924
2.819
K-Prisms
inner
K-O3
-04
-O5
av. K-O
2-849
2-908
2-821
2"859
outer
K-O 3
-O,
-Os
av. K-O
3:265
3-233
3.567
3.356
* O'1, O~, OH!--Atoms of the lower octahedral base.
The relative positions of the origins of the tetrahedral
and octahedral sheets (in the centers of Si- and Al-hexagons) indicates that the real displacements a,z have
components along a,b (in a coordinate system with b
= a~/3(0, +1/3), and are expressed as follows: a5
(0.340, -0.346); ~,~ (-0.340, -0.346); z (0,4.018).
The deviation of the real displacements from ideal is
usual for dioctahedral layer silicates and is the reason
for the lattice distortion manifested by the measured
values of fl and c. cos fl/a
Table 4. Rotation angles ~t of the edges of octahedral and
tetrahedral bases on projection on plane ab
AL-Octahedron
Tetrahedron
T1
Tetrahedron
T2
Upper base
Lowerbase
03-05 13~ ' 03-02 13~ ' O1 OH 6~ ' Ol-OH 7635'
03-04 10~ ' 03-04 11~ ' 02 OH 6~ ' O2-OH 5~ '
04-02 10025, O4-Os 9040' O1 O2 4~ ' Oi-O2 4045`
ear. ll~
11~
5~
The multiplicity values for K and A1, found by least
squares, and the indicated tetrahedral compositions
correspond to a forrriula Ko.sAl~.94 [Si3.5Ai0.5]
Olo.t(OH)l.9. By taking into account the degree of replacement of A1 for Si, the structural formula may be
dedt~ced from the chemical analysis. The calculations
have been carried out for three variants: (a) considering Fe also as an octahedral cation; (b) supposing A1
occupies all octahedral positions: and (c) accepting the
deficiency of octahedral cations (only A1) indicated by
least squares. A lack of O,OH compared to the
required (O,OH)I 2 has been obtained in the first case, a
surplus in the second case. Only the third variant gave,
after a small correction, a satisfactory formula (Ko.6s
Nao.o9) (Alz.oa) [Si3.sAlo.s] Olo.o6 (OH)1.94- On this
basis only 13"3 per cent SiO2, compared to a total
sample silica of 85"8 per cent belongs to the 2M 2 mica.
The remaining 72.5 per cent is present as admixtures,
mainly quartz.
It is interesting to compare the investigated 2M2
structure tO the structure of lepidolite 2M 2 (Takeda et
al., 1971) and muscovite 2M1 (Gfiven, 1971). Lepidolite
belongs to the same 2M2 modification, but differs by
composition. Muscovite is qualitatively of the same
composition, but has another arrangement of layers.
This comparison is aided by Table 5, where structural
formulas and some other features of these minerals are
given.
Lepidolite 2M2 has nearly the same degree of tetrahedral replacement of A1 for Si, but differs by having
Li, as 1/3 of the octahedral cations, randomly distributed over all occupied octahedra. Obviously, the low
degree of replacement for A1 for Si favors the formation of a 2M2 mica with interlayer trigonat prisms. The
anion repulsion between adjacent basal oxygen surfaces is therefore decreased. The 2M2 lepidolite occupies an intermediate position between di- and trioctahedral micas, In both 2M2 micas, the oxygen of the
layers are packed according to the cubic law and form
trigonal prisms in the interlayers. They differ by the
angle of tetrahedral twist, which is much less in lepidolite and favors the formation of a 2M2 -structure
The crystal structure of mica 2M2
469
Table 5. The main structural features of the dioctahedral mica 2M2, lepidolite 2M 2 and muscovite 2Mr
a(b)
O cos fl
a
cq, av.
8.965
0.419
9.032
9.008
-
Mineral
Dioctahedral mica 2M2
(K0.6 sNa0.09)A11.93 Si3.5A10. 5
O 10.o6(OH)1.94
Lepidolite 2M 2 (Takeda, 1971)
(K0. svNa0.12)(All.4Lil.05)
Si3.4Alo. 6 0 lo(F1.2(OH)o, e3
Muscovite 2M1 (Giiven, 1971)
(Ko. 86Nao. 1)(All. 9)(Fe, Mg)o. 1
Si3A1 O10(OH)2
(T-
O).v.
(K-O)~.
~/(A)
0 sin fl
Azo,
i 1'~ '
2-859
3.413
0.22
1.619 1-653 1.605
1.668
0.378
5020'
2.98
3.36
0.09
1.622 1.633
1'604
1.643
0-387
11~ '
2-855
3-391
0.22
1.643 1.643
1.640
1.644
(Radoslovich. 1958 I. T h e basal o x y g e n s Ot o f lepldolite
are m o r e in a plane, w h i c h decreases the interlayer
thickness q. In muscovite, q also h a s a lesser value, b u t
for a n o t h e r reason, the closer p a c k i n g of interlayer
oxygens.
Lepidolite 2M 2 h a s a greater K - O distance despite
the lesser r/-value, obviously a result of a lesser angle
o f tetrahedra] twist c~ a n d a greater a-value. K - O distances in the 2M2 a n d 2 M 1 d i o c t a h e d r a l micas are
nearly the same. Since the angles ~ are equal, the decrease of t / m muscovite 2 M 1 is c o m p e n s a t e d by an mcrease in b (2M1) against a (2M:). B o t h 2M2 micas
have the same k i n d o f lattice distortion as expressed b y
the ratio c . c o s fl/a. b u t this distortion is greater, as it
should be. in the pure dioctahedral case. In b o t h 2M2
micas the t e t r a h e d r a T~ a n d T2 are n o n e q u i v a l e n t . This
n o n - e q u i v a l e n c e is also m o r e p r o n o u n c e d in the dioctahedral case. In b o t h cases the T2 cations are displaced t o w a r d s O~p.
AcknowledoemenrsThe authors wish to express their
thanks to R. G. Mkhitarian for the kind presentation of an
unique sample, and to N. V. Troneva for the micro-probe
investigation of sample homogeneity.
R E F E R E N C E S
Aleksandrova. V. A.. Drits. V. A. and Sokolova. G. V. (1972J
TI-O T2~O Ta-O.~. (T2-O),~.
Structural features of one packet dioctahedral chlorite:
Kristallographia 17, 525-532.
Bailey, S. W. (1967) The status of clay mineral structures:
Clays and Clay Minerals 14.1-23.
Drits, V. A. (19701 On the relation of average anion-anion
and cation-anion distances for the simplest structural
polyhedra, tetrahedra and octahedra: Kristallographia
15. 913-917.
Drits. V. A.. Zvyagin, B. B. and Tokmakov. P. P. (1966)
Gfimbelite--A dioctahedral mica 2M a : Dokl. AN S.S.S.R.
170, 1390-1393.
Franzini. M. (19691 The A and B mica layers and the crystal
structure of sheet silicates: Beitr. Mineral. Petrol. 21,203224.
Gffven. N. I19711 The crystal structures of 2M 1 phengite and
2Mj muscovite: Z. fur Kristall. 134. 196-211.
Mkhitarian. R. G.. Achikgesian. S. O. and Nalbandian. E.
M. (1969) On the find of the structural modification 2Mz
among hydromicas of near-ore metasornatites of some
pyrite deposits of North Armenia: Dokl. A N Arm. S.S.R.
49, 38-41
Radoslovich. E. W. (1958~ Structural control of polyrnorphism in micas: Nature 183, 253.
Sokolova. E. P t1966~ On the structure of gf/mbelite: Zap.
Vses. M ineralog. Obshchestva.. 95. 106-107.
Takeda. H.. Haga. N. and Sadanaga, R. (1971) Structural invesngation of the polymorphic transition between 2M2,
1M lepidolite and 2M 1 muscovite: Mineral. J. (Japan) 6,
203 215.
Vainstein. B. K. 11964~ Structure Analysis by Electron Diffraction: Pergamon Press. Oxford.
Zvyagin, B. B. (1967) Electron-Diffraction Analysis of Clay
Mineral Structures: Plenum Press. New York.
Resume---La structure d'un mica diocta6drique 2M 2 a ~t6 d~finie par diffraction 61ectronique/~ haute tension. Les param&res de la maille sont: a - 8.965. b - 5.175. c = 20.31 A. fl - 100 ~ 40', Z - 4. groupe
spatial C2/c. En d6pit du caract~re particulier de la disposition des feuillets (a4 a5 a4 as), les atornes d'oxyg6ne des feuillets sont ernpil6s selon un arrangement cubique. Ainsi. les cations K interfeuillets ont une
coordination trigonale prismatique. L'angle de rotation du t6tra6dre est 11 ~ 20'. Les distances interatomiques T-O indiquent l'existence de remplacements A1-Si ordonnes.
Kurzreferat--Die Struktur eines dioktaedrischen 2M2-Glimmers wurde durch Hochspannungselektronenbeugung bestimmt. Die Zellparameter sind: a = 8.965. b - 5.175. c = 20.31A. fl = 100 ~ 40'. Z = 4.
Raumgruppe C 2 c. Trotz des eigenartigen Charakters der Schichtgliederung (a 4 a5 a4 as) sind die Sauerstoffe der Schichten nach dem kubischen Gesetz angeordnet Die Zwischenschichtkaliumionen besitzen
infolgedessen eine trigonale prisrnatische Zuordnung. Der Winkel der Tetraederdrehung betr~/gt 11 o 20'.
Die Atomabstande T O weisen auf geordneten Ersatz von Si durch A1 hin.
470
A.P.
ZHOUKHLISTOV,B. B. ZVYAGIN,S. V. SOBOLEVAand A. F. FEDOTOV
PealoMe- ]~HdppaKtt~ell 3BCKTpOIIOB B],ICOKOrO Hanpaxcemm onpe~enrmacb cTpyKTypa ]IHOKTa3apanbaoll cnlo~bi 2M2. 1-IapaMCTpSl aqefllm cne~ytoml~e: a=8,965, b~5,175, c=20,31 /~,
~ = 100~ ', Z = 4 , npoerpaacTScHHaa rpylma C2/c. HCCMOTpa ~a cncttrlqbH~eczaB xapazTcp
pacnonomcrma cnocB (o'4aso, o's), cnozxerme ZHc.rfopo~oB B C.IIOJtX c.qe]IyeT Ky6H~IeCKOMy 3axoHy.
Cne]~oBaTenbao, KaTaOnbI npoMe~yTo~moro cno~ K HMCIOT Tpeyronbriyro IlpH3MftTHtleCZyIO
KOOp]/HaaI~rlIO. YFYlOM TeTpa3]IpaYlbHOrO BtITKa ~IB2IJIeTC~I 11~ '. Me)KaTOMHbIe rlpOCTpaHcTBa
T - O yi~a3],maroT Ha ynop~]Iosern~yro 3aMeHy Si Ha AI.
Note
cnio~a = mica