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Phase relations and some electrical properties of compounds in TiS2-NbS2 system
hhtaials Resemb Bulletin, Vol. 32, No. 6, pp. 689-699.1997 Copyright 0 1997 Else&r tiencc Ltd F&d in the USA. All ri@s nsscrved 0025-5408/97 $17.00 + .OO
PII SOO25-5408(97)00049-4
PHASE RELATIONS AND SOME ELECTRICAL PROPERTIES OF COMPOUNDS IN TiSz-NbSl SYSTEM
M. Shimakawa’, H. Maki’, H. Nisbihara* and K. Hayash?* ‘Laboratory for Solid State Chemistry, Okayama University of Science l-1 Ridai-cho, Okayama 700, Japan *Faculty of Science and Technology, Ryukoku University, Seta, Ohtsu, 520-21, Japan (Refereed) (Received October 14, 1996; Accepted December 18, 1996)
ABSTRACT The phase relations of the TiSrNbSz system have been studied in the temperature range from 500 to 1100°C. Three polytypes, lT, 2H., and 3R, are observed. The lT-polytype is a high tempemture phase, the 2H,-polytype is a medium temperature phase, and the 3R-polytype is a low temperature phase. The lT-polytype spreads over almost the whole composition range of the system. The 2IGpolytype has a very narrow homogeneity range around 100% NbSz. The 3R-polytype is stable in the composition range between 100% and 96% NbS2. The electrical resistivity has been measured from 30 to 300 K. The magnetic susceptibility has been measured from 5 to 300 K. The samples of the lT-Ti, _ ~Nb~sl (X I 0.90) show the semiconductive behavior caused by an impurity scattering mechanism. Q 1997 E/SMW SCMC~ ~rd KEYWORDS: A. chalcogenides, A. layered compounds, D. crystal structure INTRODUCTION The layered transition metal dichalcogenides are of great interest as model compounds for study of electrical interaction in a quasi-two-dimensional system. In particular, IV,-, V,-, and VI&ransition metal dichalcogenides form the layered structure. The single layer is a Ch-M-Ch sandwich (M: transition metal, Ch: Chalcogen). Each single layer is bound to the *To whom correspondence shouldbe addressed. 689
690
M. SHIMAKAWA
et al.
Vol. 32, No. 6
neighboring layer by a relatively weak Van der Waals force. Generally, there are many polytypes in the layered compounds and the physical properties of the compounds are varied from polytype to polytype [ 11. The factors used to determine the stability of a polytype are a chemical composition and an equilibrium temperature. Also, a quenched sample is often in a metastable phase, which has an inherent instability. Because the physical properties of polytypes depend on the preparation process of the compounds, it is necessary to clarify the phase relation of the system before the preparation of single crystals for physical property measurements. The layered transition metal dichalcogenides exhibit an exotic electrical conductivity due to CDW (charge density wave). IT-TaS2 and IT-TaSe;! have high CDW transition temperatures [2,3]. The CDW in IT-T& - xNbx& was found by DiSalvo et al. [4]. However, details of the phase relation for the Ti, xNb& were not studied previously. In the present study, we have investigated the phase diagram of the system Ti&--NbS2 and the electronic properties of the compounds. Three polytypes, 1T, 2H,, and 3R polytypes, are observed in this system. The samples of the lT-Ti,_xNbxSz (X I 0.90) show semiconductive behavior by an impurity scattering mechanism. EXPERIMENTAL Sample Preparation. The starting materials, Ti-powder (99% pure; Katayama), Nb-powder (99.9% pure; Mitsuwa), and S-blocks (99.9999% pure; Wako), were sealed in an evacuated quartz ampoule. The ampoule was heated at 1000-l 100°C for 2 days to complete the reaction and annealed at the desired temperatures between 500 and 1000°C for one week. Then the sample was obtained after quenching in water. Crystal Structure Determination. The sample powder was processed with an acetate glue to avoid the preferred orientation on the observed powder X-ray diffraction pattern. After drying and grinding, the sample was mounted on the sample holder, and X-ray diffraction on the processed powder was performed [5]. Data were collected by the fixed-time-step scan method with a fixed time of 2 seconds and a step of 28 of 0.05”. The crystal structure parameters were refined by using the Rietveld method with the computer program RIETAN [6]. Magnetic Susceptibility Measurement. For the samples of the 1T-TiI_xNbxS2 (X 5 0.95) the magnetic susceptibility was measured from 5 to 300 K with the SQUID method. The applied magnetic field was 10000 gauss. Electrical Resistivity Measurement. The electrical resistivity was measured on the pressed powder samples by the van der Pauw method in the temperature range between 30 and 300 K. of Stoichiometry. The sulfur/metal ratios of lT-Ti,_xNb& samples were determined by the thermogravimetric analysis, oxidizing the TiI_xNbxS2 into TiOn and NbzOs in air at 900°C. Analysis
TITANIUM NIOBIUM SULFIDE
Vol. 32, No. 6
Identification
1150
100
99.5 99
98 97.5 97 96.7 96.5 96 95 94 93 92 91 90 89 88 87 86 85 84 83
TABLE 1 of Compounds in TiSrNbSz
System
Quenching Temperature(“C)
NbS, (mol%)
691
IT IT
1100
1000
900
800
500
2H, 2H. IT + iH, IT+3R
2H,
2H, 2H. + 3R
3R
3R*
2H, + 3R
2H; + 3R
3R
3R*
3R
IT + 3R 3R
3R
IT IT + 3R IT IT IT IT IT IT IT IT IT IT IT IT IT 1100
80 IT 75 IT 70 IT 68 IT 67 IT 66 IT 60 IT 55 IT 50 IT 45 IT 40 IT 33 IT IT 30 25 IT 20 IT 15 1T IO IT 7 IT 5 1T 3 IT 1 IT 0 IT *small peaks of the NbS, are observed.
IT + 3R lT+3R 1T + 3R
3R* IT + 3R* IT + 3R*
lT+3R IT + 3R* 1T + 3R* IT* IT* lT*
900
700
600
IT IT IT
IT 1T
IT IT .I I‘
692
M. SHIMAKAWA
RESULTS
et al.
Vol. 32, No. 6
AND DISCUSSION
Phase Relation. A phase relation of the Ti&--Nb!$ system in the temperature range between 500 and 1lOO’C is proposed. The identification of the compounds in the TiSrNbSz system is shown in Table 1 and the phase diagram of the TiS2-NbS2 system is shown in Figure 1. The lT-polytype spreads over the whole system at a high temperature and the lT-polytype is stable even at a low temperature below 87 mol% NbS2. The 3R-polytype is stable at a low temperature, in the composition range from 96 mol% NbS2 to 100 mol% Nl& The 2H,-polytype is stable at an intermediate temperature, in the narrow composition range from 99 mol% NbS2 to 100 mol% NbS2. Many small peaks of Nb& are observed for the samples annealed at 500°C. We can estimate that the amount of NbS, mixed with Ti,&Jb& is l%, judging from the intensity ratio of the powder X-ray diffraction peak. As the 1% of Nb& is coproduced, the Ti-ratio of the TirexNbx& at SOO’C increases by about I%, and the S-ratio, decreases by 1%. The NbSz has a phase transition of 3R/2H,. In the present investigation, we could not confirm a phase transition of 2H,/lT. However, the 2HJlT transition possibly exists at a higher temperature. Tie olNbo&& has a phase transition of 3R/lT. Although the samples around this composition are quenchable, the sample of exactly this composition is not quenchable and the ampoule of the sample is always broken during quenching. The exploded sample consists of a large amount of lT-polytype and a small amount of 3R-polytype. Therefore, this composition at the temperature is at a special point in the phase diagram of the TiS-NbS2 system, where the lT-polytype transforms directly into the 3R-polytype, without passing through the two phase region. To investigate lT/3R and 3R/lT transition rates, the 1T sample was annealed at 95O”C, which is below the transition temperature, and the 3R sample was annealed at 1 lOO”C, which is above the transition temperature. After annealing for one day, the samples were quenched in water. The phase of the samples was analyzed by the powder X-ray diffraction method. The IT sample was completely transformed into the 3R-polytype, but the 3R sample was partially transformed into the lT-polytype. By the above experiment, we have found that the 3R/lT transition rate is much lower than the lT/3R transition rate. Moreover, since this transformation skips the 3R/2H, and the 2H,/lT phase transition, the heat of the phase transition may be large. Consequently, the ampoule of TiooNbo9& is heated up by the heat of transformation and the sulfur vapor pressure increases rapidly so that the ampoule is broken by the sulfur vapor pressure during quenching. T(“C)
T(“C)
cv
dJ 1100
T
1100
R
0 TiS,
20
80
800
100
‘85
NIBS,
TiS,
FIG. 1 Phase diagram of the Ti&Nb&
90
95 nwl%
system.
100
NLS,
Vol. 32, No. 6
0
0.2
TITANIUM NIOBIUM SULFIDE
0.4
.0.8
0.6
1.74
+.j1.71 1.68
..
t
. ..-*
0.2
0
‘-0
. . - -
. --
693
0.4
0.6
0.8
1-O
. .rJ’
-
1.65 ’
I
0
0.2
0.4
0.6
0.8
1.0
X of Ti,.,Nb,S,
Lattice parameters Since the observed ratios of the Tii_,Nb&
FIG. 2 and axial ratio vs. chemical composition
for lT-Ti,_xNbx&.
sulfur/metal ratios are 1.98-2.02, we consider that the sulfur/metal are stoichiometric within an experimental accuracy.
Crystal Structure of 1T-TiI_xNbd3~. The crystal structure of lT-Til_xNbxS is studied. The lattice parameters and the axial ratio vs. chemical composition for lT-Tii_xNbxsZ are shown in Figure 2. The a parameter decreases and the c parameter increases as the X value increases. This result suggests that the sample of this composition range is a single phase, because all the peaks observed for the sample are indexed according to lT-phase, with no extra peak. This result is consistent with the result by Furuseth [7]. We consider that the Ti atoms and the Nb atoms in the lT-Tii_xNbx& occupy the metal atom sites randomly. The observed profile, the calculated profile of the X-ray diffraction pattern of lT-T& sNbo.zSz, and the difference profile of both are shown in Figure 3. The fmal RI value is 1.83%. Therefore, the results ensure that the structure of lT-Tii-xNbxS;! is the CdIz structure. The z parameter of the sulfur atom and the metal-sulfur (M-S) bond length vs. chemical composition for lT-Ti,_xNb& are shown in Figure 4. The z parameter of the sulfur atom and the M-S bond length linearly increase as the X value increases. For Ti&, R.WP8.46 R.P-6.26 ILE-10.34 H.I-I.RJ R.F-I.31
I
T g
I 20
I
I
30
40
SO 60 2 0 (deg.)
70
80 CuKa
FIG. 3 Powder X-ray diffraction profile of ~T-T~o.&I~o.~SZ.
M. SHIMAKAWA
694
0.250
’ 0
A-.&
et al.
Vol. 32, No. 6
. -
1
0.2
0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
X of ‘l’i,.,Nb,S,
z parameter of IT-Tii_xNbxSz.
sulfur
atom
and
M-S
FIG. 4 bond
length
vs.
chemical
composition
for
the z parameter of the sulfur atom is almost a regular value, 0.250 1, and the titanium atom is octahedrally coordinated by the sulfur atoms. As the titanium atoms are substituted by the niobium atoms, the MS6 octahedron is distorted along the 3-fold axis. Here, the elongation of an octahedron is measured by the ratio of the height of the octahedron along the 3-fold axis and the M-S bond length. Thus measured value is normalized by that of the regular octahedron. From now, we will call this normalized value “TR value”. The TR values vs. chemical composition for IT-Tii_xNbx& are shown in Figure 5. The TR value increases from 1.02 for TiS2 to 1.078 for Tie &bo9&. The Limitation of Trigonal Distortion of Octahedral Coordination. The TR value of the regular octahedron is 1, and that of the regular trigonal prism is 1.134, where the coordinated atoms are in contact with each other. It is evident that the trigonal prismatic coordination favors more elongated crystal tiled than the octahedral coordination. Is there a clear boundary between them? What value is the boundary, if it exists? To solve this problem, two hypotheses are introduced: (i) The anion is in contact with each other. (ii) The anion can be deformed according to the parabolic potential (harmonically). Therefore, we consider that the trigonal elongation of the coordination octahedron causes the contraction in the plane perpendicular to the 3-fold axis and the elongation in the direction of the 3-fold axis. Let the original ionic radius of the anion be “r”, the contraction “-A?, and the elongation “+Ar” in the 3-fold axis direction, then the M-S bond length “Lot,” can written as L,, = (2r’ + 2A1-~)“~/2 The height of the coordination octahedron the bond length and is represented by
“Hoc,” can be calculated
(1) by using the value of
Vol. 32, No. 6
TITANIUM NIOBIUM SULFIDE
I.08
695
a-
I
9.h
.
1.06
1.00
’ 0.2
0
0.4
0.8
0.6
I 1.0
X of Ti,.,Nb,S,
FIG. 5 TR value vs. chemical composition &
for 1T-Ti,_xNbxs2.
= (2r2/3 + 8Ar x r/3 + 2Ar2/3)“2/2
(2)
Then, the TR value can be written as TR,/3’”
= (2r2/3 + 8Ar x r/3 + 2Ar*/3)“‘/(2r2+
2Ar’)‘” = (l/3 + 4Ar/3r)‘”
(3)
and this formula can be simplified by omitting the Ar* term. For the coordination trigonal prism, the contraction of the coordination trigonal prism causes the contraction of the lattice along the 3-fold axis and the elongation in the plane perpendicular to the axis. The TR values of the trigonal prismatic coordination can be calculated by the same procedure as the elongated octahedron: TRttis/3’” = (r - Ar)/(7r2/3 + 2Ar x r/3 + 7Ar2/3)“* = (1 - Ar/r)/(7/3 + 2Ar/3r)“*
(4)
If the transition from the coordination trigonal prism to the coordination octahedron is caused by the distortion energy of the anion, then the TR-values of the coordination should be equal at the transition point. This condition leads the value of the anion distortion as equation (5). Arlr = l/24
i 1
octahcclral
1 1.00
trigonal prism
:211,-MoS, : I, !2II,-rUS1
p,S, TiSe, IT-TuS, TiS,
(5)
TiTc
I
‘I
2ll,-T&c, 1
1.08
1.16
TR-vnlue FIG. 6 TR value of transition metal dichalcogenides with coordination coordination trigonal prism.
octahedron
and those with
696
M. SHIMAKAWA et al
The TR-value
can be calculated by substituting TRbw+
Vol. 32, No. 6
the value of eq. 5 into eq. 3:
= 1.080
(6)
The TR values of the various transition metal dichalcogenides with the octahedron and the coordination trigonal prism are plotted in Figure 6. The polyhedrons are separated at the expected boundary value of TR = 1.080. It that such a crude energy consideration offers the good separation of. the polyhedron.
coordination coordination is interesting coordination
Impurity Scattering Mechanism of Conduction Electron. The electrical resistivities for the samples of the IT-TLxNb& (X 5 0.90) are studied and the impurity scattering mechanism of conduction electron is found. The electrical resistivity as a function of temperature for lT-Til&IbxSz (X I 0.90) is shown in Figure 7. The electrical resistivity suggests a semiconductive property, and increases monotonously as temperature decreases. However, the electrical resistivity of the sample with CDW transition shows metallic behavior at a high temperature, the electrical resistivity of the samples in this chemical composition range shows a semiconductive behavior at any temperature range. An electrical conductivity mechanism ruled by the thermal excitation of the carrier must be changed by the following equation: p = exp(-El2kT)
(7)
where E is a band gap and k is a Boltzman constant. If the semiconductive behavior for lT-Til_xNbx& is regulated by the thermal excitation of the carrier, a linear relationship between In p vs. l/T should exist. However, such a relationship is not found on the observed electrical resistivity for lT-Til_xNbxS, but a linear relationship between In p vs. In T exists (Fig. 8). In other words, the electrical resistivity is proportional to T”. The n-value of T” vs.
-0.6
t
I
100
150 Temperature(K)
200
250
FIG. 7 Electrical resistivity of 1T-Til_xNb&
300
Vol. 32, No. 6
TITANIUM
NIOBIUM
SULFIDE
697
2.5
2.0
9 0.5
-0.0 4.5
4
5.5
6
Id(K)
FIG. 8 Linear relationship between In p and In T. chemical composition is shown in Figure 9. The n value becomes the maximum value of n = 1.5 at X = 0.83. Also, the n value decreases as the concentration of titanium increases. The band gap for lT-Ti&&& must be narrow to show such a electrical resistivity. When the band gap is narrow, the electrical conductivity is not regulated by the number of carriers, but by the mobility of the carriers. When the mobility of carriers is regulated by the impurity concentration, the mobility pi increases as the temperature increases and obeys the formula pi
T”’
oc
1.5 -
‘s % n
(8)
. .
1.0 -
.
* .
*
:.
.
.
* . 0.5 -
. .
.
.
.
.
. . 0.0
.
t
- -0.5 L0.0
I 0.2
0.4 0.6 X of Ti,,h%&
FIG. 9 n value of T” vs. chemical composition.
0.8
1.0
698
M. SHIMAKAWA
et al.
If the mobility of carriers is regulated by the phonon, temperature increases and will obey the formula.
Vol. 32, No. 6
the mobility
pL decreases
as the
For 1T-Ti,_xNb& the band gap, E, may be very close to zero and the number of carriers may be almost constant, and the electrical resistivity is regulated by the mobility. For the sample of n = 1.5, the electrical resistivity is regulated by the impurity scattering of the carriers. While, for the sample of the range 4.08 I n < 1.5, the contribution of the impurity scattering of the carriers is small and the contribution of the phonon scattering of the carriers is large. If the electrical resistivity is regulated by both scattering mechanisms, total mobility can be represented by eq. 10.
l/p = l/p, + l&L Nb-rich samples show the electrical resistivity the Ti-rich samples by the phonon scattering.
regulated
(10) by the impurity
scattering
and
The magnetic susceptibility for Magnetic Susceptibility for lT-TLxNbxSz . lT-Til_xNbxSz is measured in the temperature range between 5 and 300 K. The magnetic susceptibility as a function of temperature is shown in Figure 10. The magnetic susceptibility of the samples indicates a feature of the weak paramagnetism. At low temperature, the magnetic susceptibility increases as the temperature decreases. This behavior is known as a pronounced “Curie tail.” The paramagnetic behavior of the magnetic susceptibility can be represented by x=C/(T-8)
(11)
x10-’
4
0
50
100
150 Temperature(K)
200
250
FIG. 10 Magnetic susceptibility of ~T-T~I-xN~xSZ.
300
Vol. 32, No. 6
TITANIUMNIOBIUM SULFIDE
699
where C is the Curie constant and 0 is the Weiss constant. We can calculate an effective magnetic moment responsible for the temperature-dependent part of the magnetic susceptibility by plotting x-’ vs. T. The effective magnetic moments of Ti,&&&, TiO.&Ib&G, Ti&&&G, Tio.~~Nbo&, and Ti0.&b&$ are 0.146, 0.093, 0.082, 0.098, and 0,059 pB, respectively; these moments are very small. CONCLUSION 1.
2.
3.
4.
The present investigation has revealed the phase relations of the Ti&-Nb& system. Three polytypes, namely, lT, 2H., and 3R, are observed in this system. The lTpolytype spreads over almost the whole composition range of the system. The 2H,polytype has a very narrow homogeneity range around 100% NbS2. The 3R-polytype is stable in the range between 100% NbSz and 96% NbS2. The partial substitution of Nb atoms by Ti atoms in NbSz enhances the stability of lT-polytype. NbS2 does not crystallize into the 1T structure, however, lT-Tioo2Nbo.& is observed. The electrical resistivity for lT-Ti,_xNb& (X 5 0.90) is regulated by the impurity scattering of carriers. The electrical resistivity is proportional to T”. The n-value becomes the maximum of n = 1.5 around X = 0.83. Also, the n value decreases as the concentration of titanium increases. The magnetic susceptibility for lT-Til_&Jb& indicates a feature of the weak paramagnetism. At low temperature, the magnetic susceptibility increases as the temperature decreases. ACKNOWLEDGMENT
The author would like to thank Mr. Mattheu Main for reading the manuscript and giving me advice on English expressions. REFERENCES 1. 2. 3. 4. 5. 6. 7.
F. Hulliger, Structural Chemisv
ofhyer-Type Phase, Reidel, Holland (1976). J.A. Wilson and A.D. Yoffe,Adv. Phys. 18, 193 (1969). J.A. Wilson, F.J. DiSalvo and S. Mahajan, A&. Phys. 24, 117 (1975). F.J. DiSalvo, J.A. Wilson, B.G. Bagley and J.A. Waszczak, Phys. Rev. B 12,222O (1975). Y. Maruyama, Department of Mineralogy, Okayama University, Okayama, Japan, personal communication, 1989. F. Izumi, J. Cryst. Jpn. 27,23 (1985). S. Furuseth, J. Alloys Comp. 178,211 (1991).
PII SOO25-5408(97)00049-4
PHASE RELATIONS AND SOME ELECTRICAL PROPERTIES OF COMPOUNDS IN TiSz-NbSl SYSTEM
M. Shimakawa’, H. Maki’, H. Nisbihara* and K. Hayash?* ‘Laboratory for Solid State Chemistry, Okayama University of Science l-1 Ridai-cho, Okayama 700, Japan *Faculty of Science and Technology, Ryukoku University, Seta, Ohtsu, 520-21, Japan (Refereed) (Received October 14, 1996; Accepted December 18, 1996)
ABSTRACT The phase relations of the TiSrNbSz system have been studied in the temperature range from 500 to 1100°C. Three polytypes, lT, 2H., and 3R, are observed. The lT-polytype is a high tempemture phase, the 2H,-polytype is a medium temperature phase, and the 3R-polytype is a low temperature phase. The lT-polytype spreads over almost the whole composition range of the system. The 2IGpolytype has a very narrow homogeneity range around 100% NbSz. The 3R-polytype is stable in the composition range between 100% and 96% NbS2. The electrical resistivity has been measured from 30 to 300 K. The magnetic susceptibility has been measured from 5 to 300 K. The samples of the lT-Ti, _ ~Nb~sl (X I 0.90) show the semiconductive behavior caused by an impurity scattering mechanism. Q 1997 E/SMW SCMC~ ~rd KEYWORDS: A. chalcogenides, A. layered compounds, D. crystal structure INTRODUCTION The layered transition metal dichalcogenides are of great interest as model compounds for study of electrical interaction in a quasi-two-dimensional system. In particular, IV,-, V,-, and VI&ransition metal dichalcogenides form the layered structure. The single layer is a Ch-M-Ch sandwich (M: transition metal, Ch: Chalcogen). Each single layer is bound to the *To whom correspondence shouldbe addressed. 689
690
M. SHIMAKAWA
et al.
Vol. 32, No. 6
neighboring layer by a relatively weak Van der Waals force. Generally, there are many polytypes in the layered compounds and the physical properties of the compounds are varied from polytype to polytype [ 11. The factors used to determine the stability of a polytype are a chemical composition and an equilibrium temperature. Also, a quenched sample is often in a metastable phase, which has an inherent instability. Because the physical properties of polytypes depend on the preparation process of the compounds, it is necessary to clarify the phase relation of the system before the preparation of single crystals for physical property measurements. The layered transition metal dichalcogenides exhibit an exotic electrical conductivity due to CDW (charge density wave). IT-TaS2 and IT-TaSe;! have high CDW transition temperatures [2,3]. The CDW in IT-T& - xNbx& was found by DiSalvo et al. [4]. However, details of the phase relation for the Ti, xNb& were not studied previously. In the present study, we have investigated the phase diagram of the system Ti&--NbS2 and the electronic properties of the compounds. Three polytypes, 1T, 2H,, and 3R polytypes, are observed in this system. The samples of the lT-Ti,_xNbxSz (X I 0.90) show semiconductive behavior by an impurity scattering mechanism. EXPERIMENTAL Sample Preparation. The starting materials, Ti-powder (99% pure; Katayama), Nb-powder (99.9% pure; Mitsuwa), and S-blocks (99.9999% pure; Wako), were sealed in an evacuated quartz ampoule. The ampoule was heated at 1000-l 100°C for 2 days to complete the reaction and annealed at the desired temperatures between 500 and 1000°C for one week. Then the sample was obtained after quenching in water. Crystal Structure Determination. The sample powder was processed with an acetate glue to avoid the preferred orientation on the observed powder X-ray diffraction pattern. After drying and grinding, the sample was mounted on the sample holder, and X-ray diffraction on the processed powder was performed [5]. Data were collected by the fixed-time-step scan method with a fixed time of 2 seconds and a step of 28 of 0.05”. The crystal structure parameters were refined by using the Rietveld method with the computer program RIETAN [6]. Magnetic Susceptibility Measurement. For the samples of the 1T-TiI_xNbxS2 (X 5 0.95) the magnetic susceptibility was measured from 5 to 300 K with the SQUID method. The applied magnetic field was 10000 gauss. Electrical Resistivity Measurement. The electrical resistivity was measured on the pressed powder samples by the van der Pauw method in the temperature range between 30 and 300 K. of Stoichiometry. The sulfur/metal ratios of lT-Ti,_xNb& samples were determined by the thermogravimetric analysis, oxidizing the TiI_xNbxS2 into TiOn and NbzOs in air at 900°C. Analysis
TITANIUM NIOBIUM SULFIDE
Vol. 32, No. 6
Identification
1150
100
99.5 99
98 97.5 97 96.7 96.5 96 95 94 93 92 91 90 89 88 87 86 85 84 83
TABLE 1 of Compounds in TiSrNbSz
System
Quenching Temperature(“C)
NbS, (mol%)
691
IT IT
1100
1000
900
800
500
2H, 2H. IT + iH, IT+3R
2H,
2H, 2H. + 3R
3R
3R*
2H, + 3R
2H; + 3R
3R
3R*
3R
IT + 3R 3R
3R
IT IT + 3R IT IT IT IT IT IT IT IT IT IT IT IT IT 1100
80 IT 75 IT 70 IT 68 IT 67 IT 66 IT 60 IT 55 IT 50 IT 45 IT 40 IT 33 IT IT 30 25 IT 20 IT 15 1T IO IT 7 IT 5 1T 3 IT 1 IT 0 IT *small peaks of the NbS, are observed.
IT + 3R lT+3R 1T + 3R
3R* IT + 3R* IT + 3R*
lT+3R IT + 3R* 1T + 3R* IT* IT* lT*
900
700
600
IT IT IT
IT 1T
IT IT .I I‘
692
M. SHIMAKAWA
RESULTS
et al.
Vol. 32, No. 6
AND DISCUSSION
Phase Relation. A phase relation of the Ti&--Nb!$ system in the temperature range between 500 and 1lOO’C is proposed. The identification of the compounds in the TiSrNbSz system is shown in Table 1 and the phase diagram of the TiS2-NbS2 system is shown in Figure 1. The lT-polytype spreads over the whole system at a high temperature and the lT-polytype is stable even at a low temperature below 87 mol% NbS2. The 3R-polytype is stable at a low temperature, in the composition range from 96 mol% NbS2 to 100 mol% Nl& The 2H,-polytype is stable at an intermediate temperature, in the narrow composition range from 99 mol% NbS2 to 100 mol% NbS2. Many small peaks of Nb& are observed for the samples annealed at 500°C. We can estimate that the amount of NbS, mixed with Ti,&Jb& is l%, judging from the intensity ratio of the powder X-ray diffraction peak. As the 1% of Nb& is coproduced, the Ti-ratio of the TirexNbx& at SOO’C increases by about I%, and the S-ratio, decreases by 1%. The NbSz has a phase transition of 3R/2H,. In the present investigation, we could not confirm a phase transition of 2H,/lT. However, the 2HJlT transition possibly exists at a higher temperature. Tie olNbo&& has a phase transition of 3R/lT. Although the samples around this composition are quenchable, the sample of exactly this composition is not quenchable and the ampoule of the sample is always broken during quenching. The exploded sample consists of a large amount of lT-polytype and a small amount of 3R-polytype. Therefore, this composition at the temperature is at a special point in the phase diagram of the TiS-NbS2 system, where the lT-polytype transforms directly into the 3R-polytype, without passing through the two phase region. To investigate lT/3R and 3R/lT transition rates, the 1T sample was annealed at 95O”C, which is below the transition temperature, and the 3R sample was annealed at 1 lOO”C, which is above the transition temperature. After annealing for one day, the samples were quenched in water. The phase of the samples was analyzed by the powder X-ray diffraction method. The IT sample was completely transformed into the 3R-polytype, but the 3R sample was partially transformed into the lT-polytype. By the above experiment, we have found that the 3R/lT transition rate is much lower than the lT/3R transition rate. Moreover, since this transformation skips the 3R/2H, and the 2H,/lT phase transition, the heat of the phase transition may be large. Consequently, the ampoule of TiooNbo9& is heated up by the heat of transformation and the sulfur vapor pressure increases rapidly so that the ampoule is broken by the sulfur vapor pressure during quenching. T(“C)
T(“C)
cv
dJ 1100
T
1100
R
0 TiS,
20
80
800
100
‘85
NIBS,
TiS,
FIG. 1 Phase diagram of the Ti&Nb&
90
95 nwl%
system.
100
NLS,
Vol. 32, No. 6
0
0.2
TITANIUM NIOBIUM SULFIDE
0.4
.0.8
0.6
1.74
+.j1.71 1.68
..
t
. ..-*
0.2
0
‘-0
. . - -
. --
693
0.4
0.6
0.8
1-O
. .rJ’
-
1.65 ’
I
0
0.2
0.4
0.6
0.8
1.0
X of Ti,.,Nb,S,
Lattice parameters Since the observed ratios of the Tii_,Nb&
FIG. 2 and axial ratio vs. chemical composition
for lT-Ti,_xNbx&.
sulfur/metal ratios are 1.98-2.02, we consider that the sulfur/metal are stoichiometric within an experimental accuracy.
Crystal Structure of 1T-TiI_xNbd3~. The crystal structure of lT-Til_xNbxS is studied. The lattice parameters and the axial ratio vs. chemical composition for lT-Tii_xNbxsZ are shown in Figure 2. The a parameter decreases and the c parameter increases as the X value increases. This result suggests that the sample of this composition range is a single phase, because all the peaks observed for the sample are indexed according to lT-phase, with no extra peak. This result is consistent with the result by Furuseth [7]. We consider that the Ti atoms and the Nb atoms in the lT-Tii_xNbx& occupy the metal atom sites randomly. The observed profile, the calculated profile of the X-ray diffraction pattern of lT-T& sNbo.zSz, and the difference profile of both are shown in Figure 3. The fmal RI value is 1.83%. Therefore, the results ensure that the structure of lT-Tii-xNbxS;! is the CdIz structure. The z parameter of the sulfur atom and the metal-sulfur (M-S) bond length vs. chemical composition for lT-Ti,_xNb& are shown in Figure 4. The z parameter of the sulfur atom and the M-S bond length linearly increase as the X value increases. For Ti&, R.WP8.46 R.P-6.26 ILE-10.34 H.I-I.RJ R.F-I.31
I
T g
I 20
I
I
30
40
SO 60 2 0 (deg.)
70
80 CuKa
FIG. 3 Powder X-ray diffraction profile of ~T-T~o.&I~o.~SZ.
M. SHIMAKAWA
694
0.250
’ 0
A-.&
et al.
Vol. 32, No. 6
. -
1
0.2
0
0.2
0.4
0.6
0.8
1.0
0.4
0.6
0.8
1.0
X of ‘l’i,.,Nb,S,
z parameter of IT-Tii_xNbxSz.
sulfur
atom
and
M-S
FIG. 4 bond
length
vs.
chemical
composition
for
the z parameter of the sulfur atom is almost a regular value, 0.250 1, and the titanium atom is octahedrally coordinated by the sulfur atoms. As the titanium atoms are substituted by the niobium atoms, the MS6 octahedron is distorted along the 3-fold axis. Here, the elongation of an octahedron is measured by the ratio of the height of the octahedron along the 3-fold axis and the M-S bond length. Thus measured value is normalized by that of the regular octahedron. From now, we will call this normalized value “TR value”. The TR values vs. chemical composition for IT-Tii_xNbx& are shown in Figure 5. The TR value increases from 1.02 for TiS2 to 1.078 for Tie &bo9&. The Limitation of Trigonal Distortion of Octahedral Coordination. The TR value of the regular octahedron is 1, and that of the regular trigonal prism is 1.134, where the coordinated atoms are in contact with each other. It is evident that the trigonal prismatic coordination favors more elongated crystal tiled than the octahedral coordination. Is there a clear boundary between them? What value is the boundary, if it exists? To solve this problem, two hypotheses are introduced: (i) The anion is in contact with each other. (ii) The anion can be deformed according to the parabolic potential (harmonically). Therefore, we consider that the trigonal elongation of the coordination octahedron causes the contraction in the plane perpendicular to the 3-fold axis and the elongation in the direction of the 3-fold axis. Let the original ionic radius of the anion be “r”, the contraction “-A?, and the elongation “+Ar” in the 3-fold axis direction, then the M-S bond length “Lot,” can written as L,, = (2r’ + 2A1-~)“~/2 The height of the coordination octahedron the bond length and is represented by
“Hoc,” can be calculated
(1) by using the value of
Vol. 32, No. 6
TITANIUM NIOBIUM SULFIDE
I.08
695
a-
I
9.h
.
1.06
1.00
’ 0.2
0
0.4
0.8
0.6
I 1.0
X of Ti,.,Nb,S,
FIG. 5 TR value vs. chemical composition &
for 1T-Ti,_xNbxs2.
= (2r2/3 + 8Ar x r/3 + 2Ar2/3)“2/2
(2)
Then, the TR value can be written as TR,/3’”
= (2r2/3 + 8Ar x r/3 + 2Ar*/3)“‘/(2r2+
2Ar’)‘” = (l/3 + 4Ar/3r)‘”
(3)
and this formula can be simplified by omitting the Ar* term. For the coordination trigonal prism, the contraction of the coordination trigonal prism causes the contraction of the lattice along the 3-fold axis and the elongation in the plane perpendicular to the axis. The TR values of the trigonal prismatic coordination can be calculated by the same procedure as the elongated octahedron: TRttis/3’” = (r - Ar)/(7r2/3 + 2Ar x r/3 + 7Ar2/3)“* = (1 - Ar/r)/(7/3 + 2Ar/3r)“*
(4)
If the transition from the coordination trigonal prism to the coordination octahedron is caused by the distortion energy of the anion, then the TR-values of the coordination should be equal at the transition point. This condition leads the value of the anion distortion as equation (5). Arlr = l/24
i 1
octahcclral
1 1.00
trigonal prism
:211,-MoS, : I, !2II,-rUS1
p,S, TiSe, IT-TuS, TiS,
(5)
TiTc
I
‘I
2ll,-T&c, 1
1.08
1.16
TR-vnlue FIG. 6 TR value of transition metal dichalcogenides with coordination coordination trigonal prism.
octahedron
and those with
696
M. SHIMAKAWA et al
The TR-value
can be calculated by substituting TRbw+
Vol. 32, No. 6
the value of eq. 5 into eq. 3:
= 1.080
(6)
The TR values of the various transition metal dichalcogenides with the octahedron and the coordination trigonal prism are plotted in Figure 6. The polyhedrons are separated at the expected boundary value of TR = 1.080. It that such a crude energy consideration offers the good separation of. the polyhedron.
coordination coordination is interesting coordination
Impurity Scattering Mechanism of Conduction Electron. The electrical resistivities for the samples of the IT-TLxNb& (X 5 0.90) are studied and the impurity scattering mechanism of conduction electron is found. The electrical resistivity as a function of temperature for lT-Til&IbxSz (X I 0.90) is shown in Figure 7. The electrical resistivity suggests a semiconductive property, and increases monotonously as temperature decreases. However, the electrical resistivity of the sample with CDW transition shows metallic behavior at a high temperature, the electrical resistivity of the samples in this chemical composition range shows a semiconductive behavior at any temperature range. An electrical conductivity mechanism ruled by the thermal excitation of the carrier must be changed by the following equation: p = exp(-El2kT)
(7)
where E is a band gap and k is a Boltzman constant. If the semiconductive behavior for lT-Til_xNbx& is regulated by the thermal excitation of the carrier, a linear relationship between In p vs. l/T should exist. However, such a relationship is not found on the observed electrical resistivity for lT-Til_xNbxS, but a linear relationship between In p vs. In T exists (Fig. 8). In other words, the electrical resistivity is proportional to T”. The n-value of T” vs.
-0.6
t
I
100
150 Temperature(K)
200
250
FIG. 7 Electrical resistivity of 1T-Til_xNb&
300
Vol. 32, No. 6
TITANIUM
NIOBIUM
SULFIDE
697
2.5
2.0
9 0.5
-0.0 4.5
4
5.5
6
Id(K)
FIG. 8 Linear relationship between In p and In T. chemical composition is shown in Figure 9. The n value becomes the maximum value of n = 1.5 at X = 0.83. Also, the n value decreases as the concentration of titanium increases. The band gap for lT-Ti&&& must be narrow to show such a electrical resistivity. When the band gap is narrow, the electrical conductivity is not regulated by the number of carriers, but by the mobility of the carriers. When the mobility of carriers is regulated by the impurity concentration, the mobility pi increases as the temperature increases and obeys the formula pi
T”’
oc
1.5 -
‘s % n
(8)
. .
1.0 -
.
* .
*
:.
.
.
* . 0.5 -
. .
.
.
.
.
. . 0.0
.
t
- -0.5 L0.0
I 0.2
0.4 0.6 X of Ti,,h%&
FIG. 9 n value of T” vs. chemical composition.
0.8
1.0
698
M. SHIMAKAWA
et al.
If the mobility of carriers is regulated by the phonon, temperature increases and will obey the formula.
Vol. 32, No. 6
the mobility
pL decreases
as the
For 1T-Ti,_xNb& the band gap, E, may be very close to zero and the number of carriers may be almost constant, and the electrical resistivity is regulated by the mobility. For the sample of n = 1.5, the electrical resistivity is regulated by the impurity scattering of the carriers. While, for the sample of the range 4.08 I n < 1.5, the contribution of the impurity scattering of the carriers is small and the contribution of the phonon scattering of the carriers is large. If the electrical resistivity is regulated by both scattering mechanisms, total mobility can be represented by eq. 10.
l/p = l/p, + l&L Nb-rich samples show the electrical resistivity the Ti-rich samples by the phonon scattering.
regulated
(10) by the impurity
scattering
and
The magnetic susceptibility for Magnetic Susceptibility for lT-TLxNbxSz . lT-Til_xNbxSz is measured in the temperature range between 5 and 300 K. The magnetic susceptibility as a function of temperature is shown in Figure 10. The magnetic susceptibility of the samples indicates a feature of the weak paramagnetism. At low temperature, the magnetic susceptibility increases as the temperature decreases. This behavior is known as a pronounced “Curie tail.” The paramagnetic behavior of the magnetic susceptibility can be represented by x=C/(T-8)
(11)
x10-’
4
0
50
100
150 Temperature(K)
200
250
FIG. 10 Magnetic susceptibility of ~T-T~I-xN~xSZ.
300
Vol. 32, No. 6
TITANIUMNIOBIUM SULFIDE
699
where C is the Curie constant and 0 is the Weiss constant. We can calculate an effective magnetic moment responsible for the temperature-dependent part of the magnetic susceptibility by plotting x-’ vs. T. The effective magnetic moments of Ti,&&&, TiO.&Ib&G, Ti&&&G, Tio.~~Nbo&, and Ti0.&b&$ are 0.146, 0.093, 0.082, 0.098, and 0,059 pB, respectively; these moments are very small. CONCLUSION 1.
2.
3.
4.
The present investigation has revealed the phase relations of the Ti&-Nb& system. Three polytypes, namely, lT, 2H., and 3R, are observed in this system. The lTpolytype spreads over almost the whole composition range of the system. The 2H,polytype has a very narrow homogeneity range around 100% NbS2. The 3R-polytype is stable in the range between 100% NbSz and 96% NbS2. The partial substitution of Nb atoms by Ti atoms in NbSz enhances the stability of lT-polytype. NbS2 does not crystallize into the 1T structure, however, lT-Tioo2Nbo.& is observed. The electrical resistivity for lT-Ti,_xNb& (X 5 0.90) is regulated by the impurity scattering of carriers. The electrical resistivity is proportional to T”. The n-value becomes the maximum of n = 1.5 around X = 0.83. Also, the n value decreases as the concentration of titanium increases. The magnetic susceptibility for lT-Til_&Jb& indicates a feature of the weak paramagnetism. At low temperature, the magnetic susceptibility increases as the temperature decreases. ACKNOWLEDGMENT
The author would like to thank Mr. Mattheu Main for reading the manuscript and giving me advice on English expressions. REFERENCES 1. 2. 3. 4. 5. 6. 7.
F. Hulliger, Structural Chemisv
ofhyer-Type Phase, Reidel, Holland (1976). J.A. Wilson and A.D. Yoffe,Adv. Phys. 18, 193 (1969). J.A. Wilson, F.J. DiSalvo and S. Mahajan, A&. Phys. 24, 117 (1975). F.J. DiSalvo, J.A. Wilson, B.G. Bagley and J.A. Waszczak, Phys. Rev. B 12,222O (1975). Y. Maruyama, Department of Mineralogy, Okayama University, Okayama, Japan, personal communication, 1989. F. Izumi, J. Cryst. Jpn. 27,23 (1985). S. Furuseth, J. Alloys Comp. 178,211 (1991).