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Mössbauer spectroscopic studies on FexNbS2 single crystals
Journal of Alloys and Compounds 383 (2004) 259–264
Mössbauer spectroscopic studies on Fex NbS2 single crystals Toshihide Tsuji∗ , Hirokazu Watanabe School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Tatsunokuchi, Ishikawa 923-1292, Japan
Abstract Single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) were synthesized by a chemical transport reaction using iodine as a transport agent. Lattice parameters of c-axis increased linearly with increasing x content, due to intercalated iron atoms, but lattice parameters of a-axis increased slightly. A change of the slope in the lattice parameters of c- and a-axes was observed at around x = 1/4. Mössbauer spectra of all single crystals were composed of a paramagnetic quadrupole doublet of asymmetric shape. The isomer shift increased from 0.700 mm s−1 at x = 0.159 to 0.786 mm s−1 at x = 0.325 with increasing x content, accompanying the discontinuity in isomer shift at around x = 1/4. These values of isomer shift are ascribed to formally high-spin Fe2+ state. The electric field gradient for the composition x > 1/4 was positive and increased with increasing x content, whereas that for the composition x < 1/4 was negative and increased slightly. © 2004 Elsevier B.V. All rights reserved. Keywords: Mössbauer spectroscopy; Electric field gradient; Intercalated compounds; Layered compounds; Fex NbS2
1. Introduction A number of transition metal dichalcogenides form layered compounds, and a weak van der Waals bonding between chalcogen atoms of adjacent layers allows easy to intercalate the metallic atoms. Among intercalated layered compounds, the iron atoms in Fex NbS2 can occupy the vacant octahedral sites situated between the prismatic [S–Nb–S] layers, and form ordered super-lattices for the compositions of x = 1/4 and 1/3. The electrical, magnetic and thermodynamic properties of Fex NbS2 have been studied mainly for two compositions of x = 1/4 and 1/3 [1–8], but physical properties for other compositions are lacking. From 57 Fe-Mössbauer spectroscopy of powder samples in the temperature range from 4.2 to 300 K, Katada et al. [9] and Katada and Herber [10] reported that the electronic configuration of the iron in Fex NbS2 (x = 1/4, 1/3 and 1/2) was ascribed to formally high-spin Fe2+ state and the guest atoms sit in a three-dimensional sulfur–metal network. Gorochov et al. [4] studied Mössbauer spectroscopy of single crystals of Fex NbS2 (x = 1/4 and 1/3) at 4.2 K and reported that the principal component of the electric field gradient was ∗ Corresponding author. Tel.: +81-761-51-1520; fax: +81-761-51-1149. E-mail address: [email protected] (T. Tsuji).
0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2004.04.044
negative for Fe1/4 NbS2 , whereas positive for Fe1/3 NbS2 . However, for other compositions except x = 1/4, 1/3 and 1/2, the effects of intercalated iron on the lattice parameters and Mössbauer parameters of Fex NbS2 single crystals have not been systematically studied yet. In this study, Mössbauer spectroscopic studies on the single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) were carried out systematically at room temperature, and the results of Mössbauer parameters were compared with those of the lattice parameters by X-ray diffraction method.
2. Experimental 2.1. Sample preparation Starting powders of Fex NbS2 were prepared by heating the desired compositions of high-purity iron (99.998%), niobium (99.9%) and sulfur (99.99%) at 673 K for 12 h, and then at 1173 K for 24 h. We prepared the single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) by a chemical transport reaction between the starting powders of Fex NbS2 and iodine as a transport agent in a sealed silica tube with an inner diameter of 14 mm and a length of 200 mm. The silica tube was placed in a two-zone furnace with the charge at 1223 K and the growth zone held at 1123 K. After 60 h, the crystals were obtained as hexagonal platelets with di-
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ameter of about 5 mm and a thickness of about 0.05 mm. All of the crystals synthesized were confirmed to be a single crystal with hexagonal crystal structure by Laue X-ray transmission method. The iron content, x, in Fex NbS2 was determined by an electron probe micro-analyzer method. 2.2. Mössbauer spectroscopy
Fig. 1. Lattice parameters of a- and c-axes for single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) at room temperature as a function of x content.
Mössbauer spectroscopy was carried out by a conventional constant acceleration spectrometer using the 57 Co source diffused in Rh matrix. The isomer shift was referred to a metallic iron absorber. An incident ␥-ray direction was in parallel to the c-axis of the single crystal. Mössbauer spectroscopy was also carried out at various angles of ␣ between c-axis of the single crystal and incident ␥-ray. A computer program was used to calculate the fitted Lorenzian lines and all required parameters.
Fig. 2. (a) and (b) Mössbauer spectra obtained at 295 K for single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325). An incident ␥-ray direction is in parallel to the c-axis of a single crystal.
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261
3. Results and discussion 3.1. Lattice parameters of single crystals Fex NbS2 (0.159 ≤ x ≤ 0.325) Lattice parameters of a- and c-axes for single crystals Fex NbS2 (0.159 ≤ x ≤ 0.325) at room temperature are plotted in Fig. 1 as a function of x content. Lattice parameters of c-axis increase linearly with increasing x content, due to intercalated iron atoms in the vacant octahedral sites situated between the prismatic layers [S–Nb–S] of 2s niobium disulfide, but a change of the slope in lattice parameter is seen at around x = 1/4. On the other hand, the lattice parameters of a-axis increase slightly with increasing iron content, though a small change in the slope is also seen at x = 1/4. 3.2. Mössbauer spectra of single crystals Fex NbS2 (0.159 ≤ x ≤ 0.325) The Mössbauer spectra obtained at 295 K are shown for single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) in Fig. 2(a) and (b), where the incident ␥-ray direction is in parallel to the c-axis of a single crystal. All of the single crystals are composed of a paramagnetic quadrupole doublet with asymmetric shapes, though it seems to be a single peak in the composition near x = 1/4. The intensity ratios of two absorption lines IL /IH for the composition x > 1/4 are reverse to those for the composition x < 1/4, where IL and IH are the absorption intensities for low and high energies, respectively. The isomer shift (IS) and the electrical field gradient, EQ , values were calculated for Mössbauer spectra of Fex NbS2 (0.159 ≤ x ≤ 0.325) shown in Fig. 2(a) and (b), and the results are plotted as a function of iron content in Fig. 3(a) and (b), respectively. The sign of EQ was determined from Mössbauer spectroscopy carried out at various angles of α between c-axis of single crystal and incident ␥-ray, as will be discussed later. In the figure, the values of IS and EQ for the compositions of x = 0.25 and 0.333 reported by Katada et al. [9] and those for x = 0.333 reported by Gorochov et al. [4] are also shown for the comparison. Our results are in good agreement with those reported by other workers [4,10]. The isomer shift increases from 0.700 mm s−1 at x = 0.159 to 0.786 mm s−1 at x = 0.325 with increasing x content, accompanying the discontinuity in isomer shift at around x = 1/4. These values of isomer shift are ascribed to formally high-spin Fe2+ state in the octahedral sites situated between the prismatic layers [S–Nb–S] of 2s niobium disulfide. This fact agrees well with the results by magnetic susceptibility measurements [3–6] and those reported by Mössbauer spectroscopy [4,9,10]. The discontinuity in isomer shift seen at around x = 1/4 in Fig. 3(a) corresponds to the change in the slope of the lattice parameter of c- and a-axes in Fig. 1. The values of EQ vary considerably, though the iron atoms in these intercalated compounds are seemed to be surrounded octahedrally by six sulfur atoms and the nearest neighbor-
Fig. 3. (a) Isomer shift (IS) and (b) electric field gradient, EQ , values calculated for Fex NbS2 (0.159 ≤ x ≤ 0.325) as a function of iron content: (䊊) this work; (䉲) Katada and Herber [10]; (䉱) Gorochov et al. [4].
ing environments of iron atoms are essentially identical. The electric field gradient for the composition x < 1/4 is negative and increases slightly with increasing x content, and suddenly changes the sign of electric field gradient at x = 0.25. On the other hand, the electric field gradient for the composition x > 1/4 is positive and increased with increasing x content. The observed quadrupole splitting for these compounds may be mainly caused by the trigonal distortion, which may be related to the observed lattice parameters of a- and c-axes in Fig. 1(a) and (b). Mössbauer spectra were measured at 295 K by changing the angle, α, between c-axis of the single crystal and incident ␥-ray in order to know the origin of asymmetry and the sign of EQ . All of the several single crystals were aligned for the direction of c-axis, but placed randomly for the direction of a-axis. Fig. 4(a) and (b) shows the intensity ratio of two lines, IH /IL , for Mössbauer spectra of Fe0.325 NbS2 as a function of the angle α. In figure, the intensities of high and low energy absorption peaks in Fig. 4 are defined as IH and IL , respectively. The intensity ratio of IH /IL is changed remarkably for the angle of α, and becomes the reverse at the angle between α = 45 and 60◦ .
262 T. Tsuji, H. Watanabe / Journal of Alloys and Compounds 383 (2004) 259–264
Fig. 4. (a) and (b) Mössbauer spectra of Fe0.325 NbS2 as a function of angle, α, between the c-axis of the single crystal and incident ␥-ray.
T. Tsuji, H. Watanabe / Journal of Alloys and Compounds 383 (2004) 259–264
263
Let us calculate the transition A from (3/2, ±3/2) to (1/2, ±1/2) and the transition B from (3/2, ±1/2) to (1/2, ±1/2). Here, we define ϕ as the angle between the principle axis of the electric field gradient and the incident ␥-ray, θ as the angle between the principle axis of electric field gradient and c-axis of a single crystal, and Ψ as the angle between one particular single crystal and the other several single crystals, which were placed randomly for the direction of a-axis and were aligned for the direction of c-axis. The cos ϕ is given by the following equation:
Table 1 The angle of θ between the principle axis of electric field gradient and c-axis of a single crystal for Fex NbS2 is shown for various compositions
cos ϕ = sin θ sinψ cos α + cos θ sin α
The electric field gradients (EQ ) of upper and lower columns in table are negative (EQ < 0) and positive (EQ > 0), respectively.
(1)
If we define the absorption intensities of the transitions A and B as IA and IB , respectively, the absorption intensities of IA and IB are calculated by using Eq. (1) as follows: 2π 3 IA = (1 + cos2 ϕ) dψ 2 0 3π (2) (2 + sin2 θ sin2 α + 2cos2 θ cos2 α), = 2 3 2 + (sin2 ϕ) dψ 2 3 0 3π 10 = − sin2 θ sin2 α − 2cos2 θ cos2 α . (3) 2 3
IB =
2π
The theoretical intensity ratios of IH /IL = IA /IB and the experimental values of IH /IL for Mössbauer spectra for the composition x = 0.281, 0.309 and 0.325 are calculated and plotted as a function of the angle α in Fig. 5. The theoretical intensity ratios of IH /IL = IA /IB calculated from Eqs. (2) and (3) are fitted well to the experimental values, as seen in the Fig. 5, and the electric field gradient (EQ ) for three
x in Fex NbS2
θ (◦ )
0.159 42.5 0.199 45.3 0.239 52.2 ................................................................... 0.281 22.6 0.309 17.1 0.325 20.1
compositions is positive. The angles of θ are calculated to be 22.6, 17.1 and 20.1 for the compositions of x = 0.281, 0.309 and 0.325, respectively. The same theoretical calculation was carried out for the compositions of x = 0.159, 0.199 and 0.239, and the results are summarized in Table 1, where the angles of θ for various compositions of Fex NbS2 are also shown. In table, the electric field gradients (EQ ) of upper and lower columns for the compositions of x < 1/4 and x > 1/4 are negative (EQ < 0) and positive (EQ > 0), respectively.
4. Conclusions Single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) were synthesized by chemical transport reaction using iodine as a transport agent, and the following conclusions are obtained. (1) Lattice parameters of c-axis increased linearly with increasing x content, due to intercalated iron atoms, but the lattice parameters of a-axis increased slightly. A change of the slope in lattice parameters of c- and a-axes was observed at around x = 1/4. (2) Mössbauer spectra of all single crystals were composed of a paramagnetic quadrupole doublet of asymmetric shape. (3) The isomer shift increased from 0.700 mm s−1 at x = 0.159 to 0.786 mm s−1 at x = 0.325 with increasing x content, but the discontinuity in isomer shift was obtained at around x = 1/4. These values of isomer shift are ascribed to formally high-spin Fe2+ state. (4) The electric field gradient for the composition x > 1/4 was positive and increased with increasing x content, whereas that for the composition x < 1/4 was negative and increased slightly. (5) The lattice parameters of a- and c-axes, isomer shift and the sign of the electric field gradient remarkably were changed in the composition of x = 1/4. References
Fig. 5. Intensity ratios of IH /IL of Mössbauer spectra for the composition x = 0.281, 0.309 and 0.325 as a function of the angle α. In figure, θ is the angle between the principle axis of the electric field gradient and c-axis of the single crystal.
[1] J.M. van den Berg, P. Cossee, Inorg. Chim. Acta 2 (1968) 143. [2] F. Hulliger, E. Pobitschka, J. Solid State Chem. 1 (1970) 117. [3] R.H. Fried, A.R. Beal, A.D. Yoffe, Phil. Mag. 35 (1977) 1269.
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[4] O. Gorochov, A. Le Blanc-Soreau, J. Rouxel, P. Imbert, G. Jehanno, Phil. Mag. 43 (1981) 621. [5] N. Doi, Y. Tazuke, J. Phys. Soc. Jpn. 60 (1991) 3980. [6] M. Koyano, H. Watanabe, Y. Yamamura, T. Tsuji, S. Katayama, Proc. Int. Symp. Intercalat. Comp. (1990) 164. [7] T. Tsuji, Y. Yamamura, H. Watanabe, S. Saito, M. Sorai, J. Thermal Anal. Calorimetry 57 (1999) 839.
[8] T. Tsuji, Y. Yamamura, M. Koyano, S. Katayama, M. Ito, J. Alloys Compd. 317–318 (2001) 213. [9] M. Katada, S. Sato, Y. Hirasawa, H. Sano, Radiochem. Radioanal. Lett. 54 (1982) 293. [10] M. Katada, R.H. Herber, J. Solid State Chem. 33 (1980) 361.
Mössbauer spectroscopic studies on Fex NbS2 single crystals Toshihide Tsuji∗ , Hirokazu Watanabe School of Materials Science, Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Tatsunokuchi, Ishikawa 923-1292, Japan
Abstract Single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) were synthesized by a chemical transport reaction using iodine as a transport agent. Lattice parameters of c-axis increased linearly with increasing x content, due to intercalated iron atoms, but lattice parameters of a-axis increased slightly. A change of the slope in the lattice parameters of c- and a-axes was observed at around x = 1/4. Mössbauer spectra of all single crystals were composed of a paramagnetic quadrupole doublet of asymmetric shape. The isomer shift increased from 0.700 mm s−1 at x = 0.159 to 0.786 mm s−1 at x = 0.325 with increasing x content, accompanying the discontinuity in isomer shift at around x = 1/4. These values of isomer shift are ascribed to formally high-spin Fe2+ state. The electric field gradient for the composition x > 1/4 was positive and increased with increasing x content, whereas that for the composition x < 1/4 was negative and increased slightly. © 2004 Elsevier B.V. All rights reserved. Keywords: Mössbauer spectroscopy; Electric field gradient; Intercalated compounds; Layered compounds; Fex NbS2
1. Introduction A number of transition metal dichalcogenides form layered compounds, and a weak van der Waals bonding between chalcogen atoms of adjacent layers allows easy to intercalate the metallic atoms. Among intercalated layered compounds, the iron atoms in Fex NbS2 can occupy the vacant octahedral sites situated between the prismatic [S–Nb–S] layers, and form ordered super-lattices for the compositions of x = 1/4 and 1/3. The electrical, magnetic and thermodynamic properties of Fex NbS2 have been studied mainly for two compositions of x = 1/4 and 1/3 [1–8], but physical properties for other compositions are lacking. From 57 Fe-Mössbauer spectroscopy of powder samples in the temperature range from 4.2 to 300 K, Katada et al. [9] and Katada and Herber [10] reported that the electronic configuration of the iron in Fex NbS2 (x = 1/4, 1/3 and 1/2) was ascribed to formally high-spin Fe2+ state and the guest atoms sit in a three-dimensional sulfur–metal network. Gorochov et al. [4] studied Mössbauer spectroscopy of single crystals of Fex NbS2 (x = 1/4 and 1/3) at 4.2 K and reported that the principal component of the electric field gradient was ∗ Corresponding author. Tel.: +81-761-51-1520; fax: +81-761-51-1149. E-mail address: [email protected] (T. Tsuji).
0925-8388/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.jallcom.2004.04.044
negative for Fe1/4 NbS2 , whereas positive for Fe1/3 NbS2 . However, for other compositions except x = 1/4, 1/3 and 1/2, the effects of intercalated iron on the lattice parameters and Mössbauer parameters of Fex NbS2 single crystals have not been systematically studied yet. In this study, Mössbauer spectroscopic studies on the single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) were carried out systematically at room temperature, and the results of Mössbauer parameters were compared with those of the lattice parameters by X-ray diffraction method.
2. Experimental 2.1. Sample preparation Starting powders of Fex NbS2 were prepared by heating the desired compositions of high-purity iron (99.998%), niobium (99.9%) and sulfur (99.99%) at 673 K for 12 h, and then at 1173 K for 24 h. We prepared the single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) by a chemical transport reaction between the starting powders of Fex NbS2 and iodine as a transport agent in a sealed silica tube with an inner diameter of 14 mm and a length of 200 mm. The silica tube was placed in a two-zone furnace with the charge at 1223 K and the growth zone held at 1123 K. After 60 h, the crystals were obtained as hexagonal platelets with di-
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ameter of about 5 mm and a thickness of about 0.05 mm. All of the crystals synthesized were confirmed to be a single crystal with hexagonal crystal structure by Laue X-ray transmission method. The iron content, x, in Fex NbS2 was determined by an electron probe micro-analyzer method. 2.2. Mössbauer spectroscopy
Fig. 1. Lattice parameters of a- and c-axes for single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) at room temperature as a function of x content.
Mössbauer spectroscopy was carried out by a conventional constant acceleration spectrometer using the 57 Co source diffused in Rh matrix. The isomer shift was referred to a metallic iron absorber. An incident ␥-ray direction was in parallel to the c-axis of the single crystal. Mössbauer spectroscopy was also carried out at various angles of ␣ between c-axis of the single crystal and incident ␥-ray. A computer program was used to calculate the fitted Lorenzian lines and all required parameters.
Fig. 2. (a) and (b) Mössbauer spectra obtained at 295 K for single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325). An incident ␥-ray direction is in parallel to the c-axis of a single crystal.
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261
3. Results and discussion 3.1. Lattice parameters of single crystals Fex NbS2 (0.159 ≤ x ≤ 0.325) Lattice parameters of a- and c-axes for single crystals Fex NbS2 (0.159 ≤ x ≤ 0.325) at room temperature are plotted in Fig. 1 as a function of x content. Lattice parameters of c-axis increase linearly with increasing x content, due to intercalated iron atoms in the vacant octahedral sites situated between the prismatic layers [S–Nb–S] of 2s niobium disulfide, but a change of the slope in lattice parameter is seen at around x = 1/4. On the other hand, the lattice parameters of a-axis increase slightly with increasing iron content, though a small change in the slope is also seen at x = 1/4. 3.2. Mössbauer spectra of single crystals Fex NbS2 (0.159 ≤ x ≤ 0.325) The Mössbauer spectra obtained at 295 K are shown for single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) in Fig. 2(a) and (b), where the incident ␥-ray direction is in parallel to the c-axis of a single crystal. All of the single crystals are composed of a paramagnetic quadrupole doublet with asymmetric shapes, though it seems to be a single peak in the composition near x = 1/4. The intensity ratios of two absorption lines IL /IH for the composition x > 1/4 are reverse to those for the composition x < 1/4, where IL and IH are the absorption intensities for low and high energies, respectively. The isomer shift (IS) and the electrical field gradient, EQ , values were calculated for Mössbauer spectra of Fex NbS2 (0.159 ≤ x ≤ 0.325) shown in Fig. 2(a) and (b), and the results are plotted as a function of iron content in Fig. 3(a) and (b), respectively. The sign of EQ was determined from Mössbauer spectroscopy carried out at various angles of α between c-axis of single crystal and incident ␥-ray, as will be discussed later. In the figure, the values of IS and EQ for the compositions of x = 0.25 and 0.333 reported by Katada et al. [9] and those for x = 0.333 reported by Gorochov et al. [4] are also shown for the comparison. Our results are in good agreement with those reported by other workers [4,10]. The isomer shift increases from 0.700 mm s−1 at x = 0.159 to 0.786 mm s−1 at x = 0.325 with increasing x content, accompanying the discontinuity in isomer shift at around x = 1/4. These values of isomer shift are ascribed to formally high-spin Fe2+ state in the octahedral sites situated between the prismatic layers [S–Nb–S] of 2s niobium disulfide. This fact agrees well with the results by magnetic susceptibility measurements [3–6] and those reported by Mössbauer spectroscopy [4,9,10]. The discontinuity in isomer shift seen at around x = 1/4 in Fig. 3(a) corresponds to the change in the slope of the lattice parameter of c- and a-axes in Fig. 1. The values of EQ vary considerably, though the iron atoms in these intercalated compounds are seemed to be surrounded octahedrally by six sulfur atoms and the nearest neighbor-
Fig. 3. (a) Isomer shift (IS) and (b) electric field gradient, EQ , values calculated for Fex NbS2 (0.159 ≤ x ≤ 0.325) as a function of iron content: (䊊) this work; (䉲) Katada and Herber [10]; (䉱) Gorochov et al. [4].
ing environments of iron atoms are essentially identical. The electric field gradient for the composition x < 1/4 is negative and increases slightly with increasing x content, and suddenly changes the sign of electric field gradient at x = 0.25. On the other hand, the electric field gradient for the composition x > 1/4 is positive and increased with increasing x content. The observed quadrupole splitting for these compounds may be mainly caused by the trigonal distortion, which may be related to the observed lattice parameters of a- and c-axes in Fig. 1(a) and (b). Mössbauer spectra were measured at 295 K by changing the angle, α, between c-axis of the single crystal and incident ␥-ray in order to know the origin of asymmetry and the sign of EQ . All of the several single crystals were aligned for the direction of c-axis, but placed randomly for the direction of a-axis. Fig. 4(a) and (b) shows the intensity ratio of two lines, IH /IL , for Mössbauer spectra of Fe0.325 NbS2 as a function of the angle α. In figure, the intensities of high and low energy absorption peaks in Fig. 4 are defined as IH and IL , respectively. The intensity ratio of IH /IL is changed remarkably for the angle of α, and becomes the reverse at the angle between α = 45 and 60◦ .
262 T. Tsuji, H. Watanabe / Journal of Alloys and Compounds 383 (2004) 259–264
Fig. 4. (a) and (b) Mössbauer spectra of Fe0.325 NbS2 as a function of angle, α, between the c-axis of the single crystal and incident ␥-ray.
T. Tsuji, H. Watanabe / Journal of Alloys and Compounds 383 (2004) 259–264
263
Let us calculate the transition A from (3/2, ±3/2) to (1/2, ±1/2) and the transition B from (3/2, ±1/2) to (1/2, ±1/2). Here, we define ϕ as the angle between the principle axis of the electric field gradient and the incident ␥-ray, θ as the angle between the principle axis of electric field gradient and c-axis of a single crystal, and Ψ as the angle between one particular single crystal and the other several single crystals, which were placed randomly for the direction of a-axis and were aligned for the direction of c-axis. The cos ϕ is given by the following equation:
Table 1 The angle of θ between the principle axis of electric field gradient and c-axis of a single crystal for Fex NbS2 is shown for various compositions
cos ϕ = sin θ sinψ cos α + cos θ sin α
The electric field gradients (EQ ) of upper and lower columns in table are negative (EQ < 0) and positive (EQ > 0), respectively.
(1)
If we define the absorption intensities of the transitions A and B as IA and IB , respectively, the absorption intensities of IA and IB are calculated by using Eq. (1) as follows: 2π 3 IA = (1 + cos2 ϕ) dψ 2 0 3π (2) (2 + sin2 θ sin2 α + 2cos2 θ cos2 α), = 2 3 2 + (sin2 ϕ) dψ 2 3 0 3π 10 = − sin2 θ sin2 α − 2cos2 θ cos2 α . (3) 2 3
IB =
2π
The theoretical intensity ratios of IH /IL = IA /IB and the experimental values of IH /IL for Mössbauer spectra for the composition x = 0.281, 0.309 and 0.325 are calculated and plotted as a function of the angle α in Fig. 5. The theoretical intensity ratios of IH /IL = IA /IB calculated from Eqs. (2) and (3) are fitted well to the experimental values, as seen in the Fig. 5, and the electric field gradient (EQ ) for three
x in Fex NbS2
θ (◦ )
0.159 42.5 0.199 45.3 0.239 52.2 ................................................................... 0.281 22.6 0.309 17.1 0.325 20.1
compositions is positive. The angles of θ are calculated to be 22.6, 17.1 and 20.1 for the compositions of x = 0.281, 0.309 and 0.325, respectively. The same theoretical calculation was carried out for the compositions of x = 0.159, 0.199 and 0.239, and the results are summarized in Table 1, where the angles of θ for various compositions of Fex NbS2 are also shown. In table, the electric field gradients (EQ ) of upper and lower columns for the compositions of x < 1/4 and x > 1/4 are negative (EQ < 0) and positive (EQ > 0), respectively.
4. Conclusions Single crystals of Fex NbS2 (0.159 ≤ x ≤ 0.325) were synthesized by chemical transport reaction using iodine as a transport agent, and the following conclusions are obtained. (1) Lattice parameters of c-axis increased linearly with increasing x content, due to intercalated iron atoms, but the lattice parameters of a-axis increased slightly. A change of the slope in lattice parameters of c- and a-axes was observed at around x = 1/4. (2) Mössbauer spectra of all single crystals were composed of a paramagnetic quadrupole doublet of asymmetric shape. (3) The isomer shift increased from 0.700 mm s−1 at x = 0.159 to 0.786 mm s−1 at x = 0.325 with increasing x content, but the discontinuity in isomer shift was obtained at around x = 1/4. These values of isomer shift are ascribed to formally high-spin Fe2+ state. (4) The electric field gradient for the composition x > 1/4 was positive and increased with increasing x content, whereas that for the composition x < 1/4 was negative and increased slightly. (5) The lattice parameters of a- and c-axes, isomer shift and the sign of the electric field gradient remarkably were changed in the composition of x = 1/4. References
Fig. 5. Intensity ratios of IH /IL of Mössbauer spectra for the composition x = 0.281, 0.309 and 0.325 as a function of the angle α. In figure, θ is the angle between the principle axis of the electric field gradient and c-axis of the single crystal.
[1] J.M. van den Berg, P. Cossee, Inorg. Chim. Acta 2 (1968) 143. [2] F. Hulliger, E. Pobitschka, J. Solid State Chem. 1 (1970) 117. [3] R.H. Fried, A.R. Beal, A.D. Yoffe, Phil. Mag. 35 (1977) 1269.
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[4] O. Gorochov, A. Le Blanc-Soreau, J. Rouxel, P. Imbert, G. Jehanno, Phil. Mag. 43 (1981) 621. [5] N. Doi, Y. Tazuke, J. Phys. Soc. Jpn. 60 (1991) 3980. [6] M. Koyano, H. Watanabe, Y. Yamamura, T. Tsuji, S. Katayama, Proc. Int. Symp. Intercalat. Comp. (1990) 164. [7] T. Tsuji, Y. Yamamura, H. Watanabe, S. Saito, M. Sorai, J. Thermal Anal. Calorimetry 57 (1999) 839.
[8] T. Tsuji, Y. Yamamura, M. Koyano, S. Katayama, M. Ito, J. Alloys Compd. 317–318 (2001) 213. [9] M. Katada, S. Sato, Y. Hirasawa, H. Sano, Radiochem. Radioanal. Lett. 54 (1982) 293. [10] M. Katada, R.H. Herber, J. Solid State Chem. 33 (1980) 361.