Synthetic Metals, 11 (1985) 85 - 100

85

X-RAY STUDY OF THE NEW CHARGE-DENSITY-WAVE PHASE IN
1T-TaS2SATOSHI TANDA* and TAKASHI SAMBONGI
Department of Physics, Hokkaido University, Sapporo 060 (Japan)(Received February 22, 1985;accepted March 9, 1985)

Abstract
Positions of both the first- and second-order satellite reflections in the
newly found charge<lensity-wave phase of 1T-TaS2 are measured by x-ray
diffraction. The discommensuration network with a lower s y m m e t r y and its
stacking sequence are determined. This phase appears on cooling from thenearly-commensurate phase as well as on heating from the commensurate
phase, in contrast with results of previous measurements.

1. Introduction
In 1T-TaS2, one of the layered transition-metal dichalcogenides, threecharge-density-wave (CDW) phases have been observed [1, 2]. The CDW in
the incommensurate (IC) phase above 350 K is characterized by three wave
vectors, 120 ° apart from each other, qi = 0.283Gi where the Gis are theshortest reciprocal lattice vectors (a , - - b , ~* ~*). As a result, the CDW
forms a triangular lattice within the layer. The stacking period perpendicular
to the layer is 3c, where c is the spacing of the host lattice layer; the electrostatic interaction between the charge density triangular lattice is believed tobe minimized in the fcc-like stacking. In the nearly-commensurate (NC)phase, between ~ 3 5 0 K and 200 K, the trigonal s y m m e t r y is still found inthe ( ~ ) , but they rotate by ~ ~ 12 ° from the Gis and Jqi] = 0.285a* is a little
larger than that in the IC phase. Because reflection intensities of the higher
order satellites are relatively large, the lattice distortion is not sinusoidal inspace, but the commensurate domains form a lattice with the h o n e y c o m b
network of discommensurations (DC). The detailed structure of the DC
network and the stacking sequence have been studied theoretically byNakanishi and Shiba [3].
The transition to the commensurate (C) phase at ~ 2 0 0 K is of firstorder; both ]~] and ~ change discontinuously. In the C-phase ~ = 13.9 ° and*Present address: Research Center, Komatsu Ltd., Shinomiya, Hiratsuka 254 (Japan)
0379-6779/85/$3.30© Elsevier Sequoia/Printed in The Netherlands

86~[ = 0.277a*. The commensurability is satisfied by the relation 3qi --q1 =• In a previous paper [4] we reported that, while the C-CDW structure isdeveloped within each layer, x-ray satellite reflections are broad along thec* direction; the stacking of the C-CDW layers is disordered• Nakanishi andShiba [5] succeeded in analysing the lineshape of super-lattice reflections•
Their result is that the stacking is realized by an alternate repeat of thestacking vector c and 2a + c, where na + c means that a layer stacks on theadjacent one with its origin shifted by n G i + c. The disorder comes from therandom orientation of Gi.
Near 280 K anomalies have been observed, only on heating but notduring cooling, in the electrical resistivity [6], the thermoelectric power[6] and the thermal expansion along the c-axis [7 ]. Changes in the backward
scattering rate of high energy ions [8] and a peak in the differential scanningcalorimetry [9] are indicative of a phase transition at that temperature• Funge t al. [10] found that below 280 K there exists a new phase and proposedthat the stacking period in that phase is 7c. We observed that the new phasebetween ~ 2 0 0 K and 280 K is incommensurate and triclinic [4], and iscalled the T-phase hereafter.
Nakanishi and Shiba [5] extended the Landau-Ginzburg-McMillan
approach to elucidate the three dimensional triple-q CDW structure bytaking into account the interlayer coupling up to the next nearest neighbour
layers. They predicted that the structure of the T-phase is approximately
striped. Although this feature of the new phase has been reported briefly[4], its details together with the experimental procedure are described here
because this is the first observation of the triclinic h o n e y c o m b DC lattice.
Results of a supplementary experiment on the C-phase are also included•
Before experimental results are presented, possible types of CDW
domain configuration are classified, though not comprehensively, because
considering their presence is indispensable in analysing the experimental
data. The width of the x-ray beam is possibly large compared with the size ofan individual domain, so reflection profiles do not always give the internal
structure of a single domain but correspond to an ensemble of several typesof domains.
(i) ~- a n d ~J-.domains

In both NC- and C-phases and also in the T-phase presented in the later
section, the CDW wave vectors are not parallel to the shortest reciprocal
vectors, Gi, but rotate clockwise or anticlockwise. Existence of these two
types of rotational degrees of freedom was first observed by Wilson e t al.
[1] in the C-phase of 1T-TaSe2.
The domain in which wave vectors rotate anticlockwise has been called
the s-domain and clockwise the ~-domain.
(ii) I n - l a y e r 1 2 0 ° d o m a i n s

In the striped phase of 2H-TaSe 2 [11], which appears on heating fromthe C-phase, the trigonal symmetry is broken. One out of three wave vectors

87remains unchanged at the transition, but the other two shrink by ~20% androtate in opposite directions. Therefore, three kinds of domain are possible
with the direction of the commensurate wave vector +120 ° apart from eachother. In real space the stripe DCs run parallel to each other within a domain
but +120 ° away from that in the neighbouring domains. In other structureswith broken trigonal symmetry, three kinds of in-layer 120 ° domains are also
possible as long as the host lattice has trigonal symmetry.
(iii) Possible types o f domain arising from the stacking sequence
As long as the triple-q CDWs are developed, they form the trigonallattice of charge density within each layer. The electrostatic interaction
between layers of point charges is minimized by the fcc-like stacking. For
example, in the C-phase of 1T-TaSe2 the stacking sequence of the superlattice layers is specified by the stacking vector 2a + c; the layers are stacked
successively with the equivalent positions of the next layer displaced by
2L i + c, where L i is one of the shortest lattice vectors d, /~ and --(~ + 6)
(specified as Oc_~ by [5]). Therefore, there can exist three types of domain
with different Lis. Larger variety comes from the operation/:i -~ --/~i {specified as aci by [5]). In the IC-phase of 1T-TaS2 the two types, oci and 0ci, aredistinguished by the c*-positions of the first-order satellite at +1/3. If both--ABCABC-- and --ACBACB-- sequences are possible in both a- and j3domains, there will appear two reflections in a scan along the c*-axis, at+1/3 and --1/3. On the other hand, if the choice of ~- or H-domain is coupledwith the stacking sequence as screw, there will appear only one reflection at+1/3 or --1/3.
2. Experimental procedure
Single crystals used in this work were selected from three stocks
prepared by T. Tani, with pll(4.5K) = 2 × 10 -2, 6.8 × 10 -2 and 8.8 ~ cm. A
few crystals supplied by R. Inada at ISSP were also used for comparison. As
is well known, the transport properties of 1T-TaS2 at low temperature arestrongly dependent on the growth conditions. For example, the electricalresistivity within the layer Pll below ~ 1 0 0 K is much larger for crystals
grown at relatively low temperature (~750 °C) in an atmosphere with excess
sulphur compared with crystals grown at 900 ~ 950 °C without excess
sulphur. Since anomalous properties at low temperature have been attributed
to the Anderson localization, some disorder in the crystal may be found by,e.g., diffraction experiments. This is the reason why we used various samples
of different P lI(4.5K). The results reported in this paper are, however, essentially c o m m o n to all samples used; no systematic variation beyond experimental uncertainty has been found. Moreover, the results are quite reproducible; no change was observed after thermal cycling between room temperature and 100 K.
Crystals that were fiat and relatively thin were selected for the measurements. Most crystals in stock were not flat but slightly curved. They were

88

•

7"

• J:
•

/• /

°

"S
•

o //•~ '.,".'.

;

';• *

.

,.

• /•' / ' .

.'

;o£ :

• super~tticeFig. 1. Reciprocal lattice. The satellite reflections near L1 and L2 are used to determine
the wave vectors.

discarded because they show broad reflection peaks along the c*-axis. The
sample was fixed by Apiezen N grease to a sample holder with the c*-axis
perpendicular to the c~-a~.is. Reflection intensity was measured within theregions of the reciprocal lattice shown in Fig. 1. The first- and second-ordersatellite/super-lattice reflections are observed near Lz and L2, respectively.
These regions were selected for experimental convenience; they are near the(1, 1, 0) plane. The positions of satellite reflections can be determinedaccurately by referring to those of the Bragg (1, 1, l) reflections. Details of
the x-ray apparatus used in this work are described in ref. 12.

3. C-phase
Although diffraction profiles in the C-phase have been reported in ourprevious paper [4], measurements were repeated with different samples to
examine whether the profile, especially its width, is dependent on pit(4.5K).
Because it has been established by electron and x-ray experiments[1, 2] that the in-layer positions of the super-lattice reflections* are(10/13)a* + (12/13)b* near Ll and (18/13)a* + (19/13)b* near L2, we aresolely concerned with their c* positions.
The profile t at 150 K along {10/13, 12/13, ~') is shown in Fig. 2 for asample of P i t ( T = 4.5 K) = 8.8 £2 cm and in Fig. 3 for P l l ( T = 4.5 K) = 2.0 ×
10 -2 ~2 cm. No difference is found between the two samples; the differencein P i l ( T = 4.5 K), an indication of the degree of disorder which results in theAnderson localization, has no effect on the diffraction profile.

*To examine the reliability of our results, the distance ]ql between (1, 1, 0) and(10/13, 12/13, 0) was measured by assuming the angle between ql and ~* is 13.9°. Theo b t a i n e d value Iqi = (0.277 + 0.001)a* is in good agreement with Iq] = ( 1 / \ / 1 3 ) a * =0.27735a* required by the commensurability.
t T h e s e satellites are of the s - d o m a i n . The H-satellites are observed by rotating thesample around the X-axis, which is perpendicular to both co- and c*-axes, by - 3 °.

89

L1
T=150.1K

300)°tt ----8.8~.cm(at4.5K)

200
0

Z

o
o

100

0

-0 2

0

0.2

0.4

Fig. 2. Profiles o f super-lattice reflections in the c o m m e n s u r a t e phase, at 150 K, near L1

for a sample w i t h t h e high electrical resistivity at - 4 K.

0.02 ~cm

-0.~

i

~ 0.4

Fig. 3. Profiles of super-lattice r e f l e c t i o n s in t h e c o m m e n s u r a t e phase, at 150 K, near L1
for a low-resistivity sample.

Important features of the C-phase are:(1) along (10/13, 12/13, ~) two broad peaks appear at ~" = (0.310 +0.003)c* and (0.825 + 0.003)c* and the intensity of the latter is about fourtimes as large as the former;(2) along (18/13, 19/13, ~) a peak appears at ~" = (0.020 + 0.003)c*
with a width larger than that near L 1;(3) everywhere on both lines (10/13, 19/13, ~) and (18/13, 19/13, ~*)the intensity is larger than the background;(4) the broadness is c o m m o n to all samples examined and independentof the cooling rate from room temperature and of thermal cycling. Between~ 1 0 0 K and 200 K the profile is independent of temperature.

90
The broadness of the superlattice reflections is intrinsic because thewidth of the Bragg reflection (1, 1, 0) is ~0.001c* in the C-phase as well as
in the NC-phase; the stacking of the CDW layers is disordered in spite of thegood quality of the crystal.
We assume t h a t the stacking sequence of the CDW layers can be specified by assigning a single stacking vector,(1)
The structure factor is t h e n given by
F(/~) =~
pi

exp 2rriI~. ~i + ~ A jsin(21rq~-(~i--pU))

j=l
.-}

where the CDW p a t t e r n is displaced by pU in the p t h layer. Satellite reflections appear at/~ = (h~* + k 6* + l~*) + (aq I + fl42 "1- 3'q 3) -- { (aq 1 + tic]2 + 7q 3)" U} e(2)where a, fl, ~, are integers.
In the C-phase, only £r = nGi with n = 0, 1, 2 is possible. If n = 1 as
proposed by Scruby et al. [2], reflections would appear near L1 at ~"=--(1/13)c*, --(3/13)c* and (4/13)c* and near L2 at f = (2/13)c*, (5/13)c*and (6/13)e* because of the three kinds of in-layer 120 ° d o m a i n .
Similarly, neither the case n = 0 nor n = 2 is w h a t is observed. Nakanishiand Shiba succeeded in reproducing our experimental results as fully dis2
cussed in [5]. In their model~ every two adjacent layers are coupled by S = c
and the pair is stacked by U = 2Gi, b u t the direction of Gi is c o m p l e t e l y
r a n d o m . The agreement with the observed profiles is d e m o n s t r a t e d in Fig. 8o f their paper [5].

4. I n t e r m e d i a t e phase (T-phase)
On heating the sample from below 200 K, the super-lattice reflections
disappear at ~ 2 2 0 K and three sharp new reflections are observed near L 1
and a n o t h e r three near L 2. These reflections are hereafter called T-satellites.
Near 280 K these T-satellites disappear and the NC-satellites are recovered.
This transition has been d e t e c t e d as anomalies of various properties [6 - 9].
Between 220 K and 280 K o n l y the T-satellites are observable b u t n o t theNC-satellite nor the C-super-lattice reflection, even after thermal cycling, inall samples e x a m i n e d (irrespective of the resistivity at - 4 K). The T-satellites
are sharp; widths are of the same order of those of Bragg reflections along
the c*-direction as well as parallel to the a*-b* plane. After keeping the sample at 150 K for several hours positions o f the T-satellites were measured withreference to the positions of Bragg (1, 1, 0) and (1, 1, 1). The results are
summarized in Table 1.

91
TABLE 1
In-layer wave vectors (absolute magnitude IQil and its angle ~ from Gi) in the T-phaseand ~, the c*-position of the T-satellites
225 K

Q/a*

270 K

~/c*

¢ (o)

Q/a*

~ (o)

(+0.001)
Q1
Q2
Q3

0.286
0.299
0.285

15.8
14.1
12.62

~/c*
(+-0.001)

0.439
0.242
0.319

0.288
0.303
0.286

15.6
13.4
11.84

0.434
0.264
0.302

300
¢D
I,Z

200

o

0
>.
Z
I,g
I.Z

100

I

I

.10

.20

~

I

.30

i

I

.40

a

i

.50
.60
"--*C

Fig. 4. First-order satellite reflections in the T-phase, at 225 K, on heating from the commensurate phase.

Three T-satellites are observed near L1, as shown in Fig. 4. Their c*c o m p o n e n t s (qci) are incommensurate and qcl + q~2 + qca = 1.000 as expected from the relation (3) below and (2). The second-order T-satellites
observed near L : are shown in Fig. 5. Their c*-components, - - 0 . 1 8 4 + 0.003,+0.115 + 0.003, +0.061 + 0.003, are equal to qc2-- qcl, q~l -- qc3 and qca-q~2 respectively. Therefore, these three second-order satellites come fromthree kinds of in-layer 120 ° domain (of a-orientation). Both the in-layer andthe c*-components show weak temperature dependence, as summarized inTable 1.
In-layer wave vectors Qi were obtained after the procedure explained
below. More direct determination was impossible because the rot at i on anglesof the sample around two mutually perpendicular axes (× and ~), bot h o fwhich are perpendicular to the ~o-axis, were n o t measured accurately
enough. The measured quantities are:(1) in-layer distances between the first-order T-satellites and the origino f the reciprocal space, 11, l: and la ;92(2) in-layer distances between the second-order T-satellites and theorigin, m l, m 2 and m 3;(3) the distance between, the Bragg (1, 1, 0) and the origin, L.
The angle between Qi and G i is denoted by 0 i. Using 01 (02) as an adjustable parameter, the magnitude Q](Q2) is calculated from L, ll(l:) and 01(02).
Both Q3 and 03 are then calculated using the above Q1 and Q2 assuming thatthe relation
Q] + Q2 + Q3 = 0(3)holds inside a domain. By comparing l 3 calculated from the above Q3, 03 andL with the measured values, probable values of 01 and 02 are selected by the
restriction that the difference of 13 must be smaller than ~0.05% (experimental reproducibility). Next, the positions of the second-order satellites arecalculated and compared with the measured mi. The most probable values of
the wave vectors are selected by the condition that the positions of all of thesecond-order satellites must be reproduced within ~0.3%, which is thelargest scatter of our experimental data.
The most probable Q i s a r e shown in Fig. 6, and in Table 1 together
with qcS. In the Figure, the Qis are numberedclockwise. If they are arranged
anticlockwise, the second-order satellites Q i - Q j
become degenerate inspace in conflict with the experimental finding.
If the incommensurate structure b u i l t b y the Qis is r e g ~ d e d as the commensurate one but modulated by 6Qi = Qi - Qc~, where Qci is the nearest
commensurate wave vector, and if the modulation is not uniform but concentrated in space, the discommensuration (DC) network can be constructedusing 5Qis. In cases where the 5Qis are parallel to each other, the phase isstriped with parallel DCs arranged periodically. As shown in Fig. 6, thedeviations 5~i are not parallel to each other. Therefore, the T-phase is not(}1 - Q3

3
o

100
Z
-j

o

~ Q2-Q1

0

bZ
~J
I,.Z

t_~

50

-.20

-.10

0

.10 ,

I
.20
----* l:Fig. 5. S e c o n d - o r d e r s a t e l l i t e r e f l e c t i o n s in t h e T - p h a s e , at 2 2 5 K , o n h e a t i n g f r o m t h ecommensurate phase.

93

Q3

b,_a~

225K

!/

/

Oc: -"" "~,~_-b" ~,

'~O2

~Q2

-)

Fig. 6. Inflayer wave vectors, Qi, of the T-phase at 225 K (thick arrows) and the differences, 5Qi, from the c o m m e n s u r a t e ones (thin, d o t t e d arrows). The relation between~Qis are also shown.

striped but a two-dimensional DC network with broken hexagonal s y m m e t r y
is developed in this phase.
Because this is the first observation of such a low s y m m e t r y DC network, we examine below how the present experimental findings are incompatible with t h e condition 5QilISQi within the limits of experimental
reliability. First, Q l a n d 9 2 are calculated using 01 and 02 as parameters andthe restraint that 5QIIISQ: within a domain is used to determine the relation
between possible values of 01 and 02. That restraint is equivalent to the condition that the observed angle between 5Q1 and 5Q: is +60 ° near L 1 because
the observed Q1 comes from a kind of in-layer 120 ° domain different fromthat of Q2. Then la and the mis are calculated as explained above and compared with the experimental values. Figures 7 and 8 show the differences
between the calculated and the observed values with 01 as the parameter.
These differences are larger than allowable for any value of 01. For example,
if 01 >~16.0 °, the differences of 13 between the measured and the calculated
values are three times as large as the allowable value and two out of threemis deviate from the measured values by more than 0.4%, which is twice theallowed amount. Thus we conclude that the T-phase is not striped, as long as
condition (3) is strictly satisfied.
-4

5. Stretched h o n e y c o m b structure of the T-phaseI n this section the commensurate domain lattice is constructed fromthe Qis obtained above. It is assumed that the domain boundary, DC, has theminimum possible phase shift. At 225 K,
Q1 = 0.230~* + 0.090b , Q: = 0.084h ~* - 0.3325*.

(4)

94
1.0%

J
o 830216

I

i

I
16.5

I
17.0

/~/

0.8%

0.4%

/
0%

13

o 830216

0.6%

-0.4%

• 830306
0.3%
-0.8~

0%
- 1.0%

-03,t

5

1

A

16,0

15.5

16.5

I
16.0

----> 8~Fig. 7. Difference between the position of the first-order satellite Q3 assuming the striped
structure and that measured in the present experiment.
Fig. 8. Differences between the positions of the second-order satellites assuming thestriped structure and the measured ones.

The corresponding translation vectors in real space are"4T = 3.955 + 1.00/~,~W = 1 . 0 7 5 - - 2.74/~.

(5)-4

If the CDW is uniform in space and sinusoidal, A T and B w span the incommensurate triangular lattice. On the other hand, if the modulation is discommensurate, a DC can be found where the distances between the charge
density maxima spanned by (AT, BT) and those of the commensurate superlattice, spanned by
l~c = 4~+/~B c = ~ - - 3/~(~c1=(3/13)~*+(1/13) ~)*Qc2( 1 / 1 3 ) ~ * - - (4/13)/~*,(6)>~a/2.

becomeTo find the domain configuration we temporarily assume thatthe DC has no width and no surface tension. Starting from the origin of the(-4c,/~c) lattice, we put the (-4T,/~W) lattice points on the former. We remain
within the same domain as long as
IKSAT+ LSBT + 51
. + LSBTI.
. < IKSAT
.

(7)

95
/

r 11
...............-o25........

...........

6,

' /

/

.

/ ~
/

~

12

Fig. 9. Domain configuration in the T-phase at 225 K. Full lines show DC constructedassuming that a negligible energy is associated with its length. The dotted lines illustrate
an example of probable modifications with reduced DC length.
where a.,~T = - 4 T - - 4 C , a/3T = / 3 T - / 3 C , both K and L are integers, and /~ is
one of the lattice translation vectors (]~] = a). If the inequality in (7) isreversed, we have crossed a DC and arrived at one of the neighbouring
domains specified by A, the translation vector of the peak of the C-CDW
with respect to the super-lattice.
In Fig. 9, the domain configuration in the T-phase at 225 K is shown.
Every domain shows the identical commensurate CDW pattern (and theassociated lattice modulation of hexagon star [13]) within it, but the distances between its origin and the super-lattice points increase by la] as one
passes through the domain boundary, DC. The domain lattice has the 3 X 1
structure as the super-lattice in the C-phase. The domain numbered n ischaracterized by A = n(--/~) (cf. Fig. 1 of [5]). It must be remarked that theconfiguration constructed as above is commensurate in its strict sense
because the vectors connecting the neighbouring domains,-4

15=83d+216,

W=--24d+6/~(at 2 2 5 K )(8)are linear combinations of lattice vectors ~ and 6 with integer coefficients.
From Fig. 9, the vectors~ connecting the nearest 0th domains, lattice v e c t o ~corresponding, to 5Qi, must be equal to 13W, V - - 3 W . . . . . or n V - - 3 n W(modulus 13W). From the measured Qi and (6), the lattice vectors reciprocal
to 5Q 1 and 5Q: are given as,4 = 303.5~ + 89.5/~,/~ = 161.9~ + 6.76

(at 225 K)(9)Numerical comparison gives the following relations:
= 43

+

=

(10)

However, substitution of (8) into (10) gives
IQll = 0.269,~1 = 12.08 °IQ:I = 0.325,~2 = 12.76°

which are different from the measured ones (Table 1) beyond the experimental uncertainty. Therefore, we use the relations (10) but V and W must
be obtained directly from (9) and (10), instead of (8):

96
= 82.5~ + 21.2/~,(8')

W = --26.5~ + 4.8/~

which means that a finite fluctuation must be allowed in the domain size.
It must be remembered that the actual shape of a domain is altered tosome extent when a finite surface tension is taken into account. For example, if the length of DC is minimized with the nodes of DCs fixed, thedomain is hexagonal but distorted, as shown in Fig. 9 by dotted lines. A
variety of its variant, hexagonal or tetragonal, can be found with the same
size. In any case, the configuration is approximately striped but DCs make a
two-dimensional network.
The stacking sequence of the domain lattice layer can be obtained fromthe measured c*-components of the T-satellites. The domain la~/er can be
regarded as the commensurate lattice layer modulated by_~5Qi. Let thestacking vector be U + ~. The in-layer displacement vector U is calculated
from t h e r e l a t i o n--5~)i" t) = [i(2)'where ~i is the c*-position of the satellite Qi, or[7=--(~,A + ~2B)

(2)"

At 225 K, t) = --1.998V + 0.287W. The corresponding stacking sequence isillustrated in Fig. 10. In this configuration the boundary between the 5th
and 6th domains in the first layer is near the centre of the 0th domain in thesecond layer; 2a + c stacking is realized locally (c.f. Fig. 7(a) of [5]). Theinteraction between DCs is repulsive and long-range interaction cannot be
neglected; the W-component of U would be approximately equal to 0.5 if
only the nearest neighbour interaction is dominant.
As shown in Table 1, both the in-layer wave vectors and the c*components are weakly dependent on temperature. The 3 × 1 stretchedhoneycomb structure can be found from a similar analysis at 270 K. The Tdomain becomes smaller with increasing temperature; the area of a domain
at 270 K, ~7 × 103 A 2, is smaller than that at 225 K, ~ 9 X 103 A 2. The/....................................

........
~7"-......

. . . . . . . . . . . /_.__; . . . . . . . . . . . . . . . . . . . . . . . . .
S

/

"

'

" ---:"-\- . . . . . . . . . . . . . . . . .

~ 1 i"- ........

.............. i .......... ~.~.- ................ 41

7/!
...................

................

\' ".-t-I•..........

/ \6/............

°- .......

10'-/-7--.
i/- .........

.......

first

~ -

layer

. . . . . . second layer

Fig. 10. S t a c k i n g s e q u e n c e o f t h e DC n e t w o r k in t n e T - p h a s e at 225 K.

97former is approximately equal to t h e area of. the NC-honeycomb domain.
The stacking vector at 270 K is --2V + 0.358W, where1)= 70.0~ + 7.8/~

and

I~ = - - 1 6 . 5 ~ + 8.76.

6. Observation of the T-phase on cooling
Up to now, the transition to the T-phase has been observed only onheating from the C-phase; no anomaly has been detected in various properties associated with the transition on cooling. However, we found that theT-satellites are observable on cooling below ~250 K. We used four samples,
two with p11(4.5 K) = 2.0 X 10 _2 and the other two with 8.8 ~ cm. In all
samples examined, the T-satellites were observed even after thermal cycling
down to ~ 1 5 0 K. The experimental findings are summarized below.
(1) On cooling from room temperature, the T-satellites are observed
below ~ 2 5 0 K, but the NC-satellites are observed simultaneously. Intensitiesof the latter are reduced to {1/2) ~ (1/3) compared with those at room temperature and are comparable with the T-satellites.
(2) No temperature dependence of their widths or intensities is
detected down to ~ 2 0 0 K. Both types of satellites are sharp, like the NCsatellites at higher temperature. On further cooling, both disappear and only
the C-super-lattice reflections are observable.
(3) The satellites observed in a low-resistivity sample are shown in
Figs. 11, 12 and 13 and summarized in Table 2. Both ~ - a n d ~-rotational
domains are present, but only QI is observed; the in-layer orientational
degree of freedom is lost. Identical results were obtained using another lowI

I

I

i

T:Q,

0( domain

I

i

i

i

i

~domain

"•

T:Q

80o

NC

"3
¢D
¢N

400

g
600
Z

uJ

I-Z

0

>I--

NC

100

200
Z
LU
I.Zm

0

/
-O.8

-017

-0.8

-0.5

-0.4

I
-0.6

I
I F ~
-0.5-0.4-0.3-0.2

I-0.1

Fig. 11. First-order s a t e l l i t e r e f l e c t i o n s o b s e r v e d o n c o o l i n g near L 1 of s - d o m a i n .
Fig. 12. First-order satellites observed on cooling of/~-domain.

98
300

,.

,

,

,

~

II

,

,

,

oro,

200

O(

100

NC

z_

o
-0.2

-o.1

o

o,1

0.2

0.9

1.o

1.1

Fig. 13. Second-order satellite ~eflections on cooling.
TABLE 2c*~components of the satellites observed at 230 K on cooling (in units of c*)

First order
Second order

T-

NC-

T-

NC-

--0.5630.05--(2/3)0--0.436--0.06--(1/3)0resistivity sample and a high-resistivity one. Only in one high-resistivity
sample was the T-satellite Q3, instead of Q1, observed within the ~-domain.
The satellites observed near L2 are the second harmonics of the T- and of theNC-phases; the T- and NC-domains are separated in space.
(4) When the temperature is raised from the coexistence temperature
range without further cooling, all the T-satellites vanish at 283 K and theintensities of the NC-satellites increase to the values before cooling.

7. Discussion
The most important problem, why the T-domain is stretched, remains
unsolved. In general, the actual domain configuration should be determinedtaking into consideration the self-energy of DC and the interaction between
DCs within the layer as well as on neighbouring layers. Evaluation of thesecontributions is left for future theoretical studies.
Three problems must be considered.
(1) Appearance of the T-phase on cooling is observed reproducibly inthe present work, while no corresponding anomaly has been detected in

99various properties. The observed intensities of the T-satellites are not so low,
and the intensities of the NC-satellites are halved. Therefore, the total
volume of the T-domains must be fairly large, for example, half of thesample size. Moreover, because the T-satellites are sharp, the size of eachT-phase region must be large. There is no reason, in principle, why a change
in bulk properties cannot be detected as the T-phase appears on cooling.
(2) The T-phase appears on cooling but always in coexistence with the
NC-phase. In our experimental arrangement one side of the sample iscemented to a lead holder by Apiezon N grease. Because the sample environment is evacuated and no exchange gas is used, there is an inevitable temperature gradient inside the sample. But the local temperature variation does
not exceed - 5 K; the observed transitions are completed within a narrowtemperature range and the intensities of the T-satellites do not increase on
further cooling. A possible explanation for the incomplete transition is that
the NC-T transition is associated with some kind of local distortion and thestress accumulated as a T-phase region grows impedes its further growth.
(3) Only one in-layer 120 ° domain is observed on cooling, while onheating from the C-phase all three domains are observed. We speculate that
the T-domain first appears near the a-~3 boundary and the orientation of the
T-domain has a close relation to the direction of the latter. Electronmicroscopic observation would be most promising for studying thenucleation/transition kinetics, but it must be mentioned that the a*-b* diffraction pattern in the T-phase is quite similar to that in the C-phase.
Some inexplicable phenomena observed during the measurements are
mentioned below.
(i) At the NC-C transition, the Bragg reflections were almost completely missing for some minutes. In such a case the intensity was recoveredby changing the angle w (orientation of the sample) by a few degrees. On
lowering the temperature by ~5 K, the Bragg peak appeared again at theoriginal position, with the shift of ¢~ less than 0.5 °. Far from the transition
temperature the Bragg peaks are observable even by rotating the sample bymore than 0.5 °. A similar phenomenon was observed at the C-T transition.
The above observation suggests that at the transitions the crystal suffers
temporal macroscopic rotation.
(ii) Just before the NC-C transition the satellite intensity showedstrong fluctuation in time even though the temperature was kept constantwithin 0.1 K. A NC-satellite disappeared for ~ 1 0 seconds and appeared
repeatedly and another reflection, not yet assigned, was observed near theNC-satellites for seconds. Their appearance or disappearance was aperiodic.

Acknowledgements
We wish to thank K. Nakanishi and H. Shiba for valuable critical discussions and sending us their theoretical work prior to publication, T. Tani
and R. Inada for supplying samples and M. Ido for valuable discussions andcomments.

100

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