- Email: [email protected]
Study on velocity mode of 57Fe Mӧssbauer spectroscopy and determination of lattice dynamics in Fe3S4
Results in Physics 12 (2019) 1214–1217
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Microarticle
Study on velocity mode of 57Fe Mӧssbauer spectroscopy and determination of lattice dynamics in Fe3S4 Wenbin Zuoa, Vasiliy Pelenovicha, Qidong Lib, Xiaomei Zenga, Dejun Fua, a b
T
⁎
Key Laboratory of Artificial Micro- and Nano-Materials of Ministry of Education of China, School of Physics and Technology, Wuhan University, Wuhan 430072, China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Spinel structure Mӧssbauer Spectroscopy Lattice dynamics Debye temperature
57 Fe Mӧssbauer spectroscopy studies on chemically synthesized greigite Fe3S4 have been conducted with a unique velocity mode, known as constant velocity with slope, which allows detection of subtle changes and indepth details of sextets in the spectra. Accurate determination of the overlapped sub-spectra corresponding to tetrahedral Fe3+ (A) and octahedral Fe2.5+ (B) sub-lattices has been made based on the special velocity mode. Estimation of Debye temperature θD from the temperature dependent central shift (CS) values gives the values: 805 ± 10 K and 760 ± 10 K for A- and B-sites, respectively. The discrepancy of two θD values reveals different lattice vibration between A- and B-sites. The Lamb-Mӧssbauer factor ratio fB/fA is found to be 0.98 at room temperature. The different low-temperature behaviors of hyperfine magnetic field for tetrahedral A- and octahedral B-sites are observed.
Introduction Greigite Fe3S4 is an important magnetic material with inverse spinel structure as a counterpart of magnetite Fe3O4 [1]. There are two sublattices of iron atoms where Fe3+ ions occupy tetrahedral A-sites and both Fe2+ and Fe3+ ions occupy octahedral B-sites. Natural greigites are widely distributed in sedimentary rocks all over the world and now are recognized as a recorder of the ancient geomagnetic field and environmental processes, which are important for paleomagnetic and environmental magnetic studies [2–5]. Artificial greigites have been broadly used in electrochemistry, biomedicine, and environmental magnetic studies [6–8]. 57Fe Mӧssbauer spectroscopy study of Fe3S4 is started from 1960s by Morice et al. [9], and two sextets in Mӧssbauer spectra for Fe3S4 has been revealed [10–16]. However, assignments of tetrahedral A-site and octahedral B-site are ambiguous in literature. Some researchers attribute A- and B-sites to two sextets with similar central shift (0.51 mm/s and 0.60 mm/s) but different hyperfine field (308 kOe and 29.1 kOe) [10,11,13] while the others claim two different central shift (0.28 mm/s and 0.53 mm/s) and same hyperfine field (313 kOe) [12,14–16]. The reason is the huge overlap of sub-spectra, which is completely different from magnetite. In this study, in an attempt to solve this problem, we make use of the “constant velocity with slope” mode to carefully examine the most informative 1st and 6th peaks of the sextet, trying to separate the two sub-spectra. Although such velocity mode is known in Mӧssbauer community, very few work ⁎
is reported. Once the determination of tetrahedral A site and octahedral B site in Fe3S4 is clear, study on lattice dynamics from Mӧssbauer parameters can be performed. One of the most important parameters in lattice dynamics, Debye temperature θD, can be calculated from temperature dependent central shift (CS) values in the framework of Debye model. Only after the θD of a material is determined would the terms ‘‘high temperature’’ and ‘‘low temperature’’ be meaningful. However, few work is focused on the lattice dynamics of Fe3S4. This study intends to fill this gap. In the present work, we carry out 57Fe Mӧssbauer spectroscopy using a special velocity mode to accurately determine the local order of iron atoms in Fe3S4. Mӧssbauer spectra at various temperatures from 300 K to 15 K are recorded to study the dynamics and magnetic structure of the tetrahedral and octahedral sub-lattices of greigite. Experimental details Fe3S4 powder was synthesized in a typical reaction as reported in our previous work [8]. The Mössbauer spectra of Fe3S4 with ideal absorber thickness of 22.9 mg/cm2 were collected by a conventional spectrometer (Germany, Wissel MS500) in transmission geometry with a 25 mCi gamma ray source 57Co in Rh matrix. The waveform of the source motion was provided by the Mӧssbauer driving system (Digital Function Generator DFG-1200). An α-Fe foil at room temperature was
Corresponding author. E-mail address: [email protected] (D. Fu).
https://doi.org/10.1016/j.rinp.2019.01.010 Received 5 December 2018; Received in revised form 4 January 2019; Accepted 4 January 2019 Available online 08 January 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 12 (2019) 1214–1217
W. Zuo et al. 1.01
1.00
1.00 0.99
Transmission
0.98
0.98
0.96 0.97
0.94
0.92
0.96 0.95
1
0.94
6 0.90
Velocity (mm/s)
8
0.93 8
constant acceleration
6
6
constant velocity with 20% slope
6
4
4
2
2
0
0
-2
-2
-4
-4
(a)
-6
1
(c)
-6
-8
-8
A Peak 6
(b)
(c)
B
(d)
Peak 6
Fig. 1. Typical constant velocity mode for full spectra (a) and peak 6 (b), constant velocity-20% slope mode for full spectra (c) and peak 6 (d).
used as the absorber for velocity calibration. The spectra were fitted by Recoil code using Lorentzian site analysis [17].
Fe3S4 sample are presented in Fig. 3 as a function of temperature. The CS values relative to the reference absorber α-Fe foil show an abrupt increase at the beginning of cooling and then a platform after 100 K. It can be expressed by the following formula:
Results and discussion
δCS (T ) = δIS + δSOD (T ) = δIS + c1 −
A typical Mӧssbauer spectrum with constant acceleration mode for Fe3S4 powder recorded at room temperature is shown in Fig. 1(a). The spectrum is obtained by scanning the velocity range ± 7 mm/s, thereby allocating about 15 channels to peaks 1 and 6 out of the 512 channels used to store the γ-ray data. The enlarged peak 6 presented in Fig. 1(b) shows good symmetry, from which it is difficult to get the accurate position of subspectra. Using a unique velocity mode, the two outer peaks 1 and 6 are extremely broadened with allocation of about 37 channels to collect the data and more valid data appear, as shown in Fig. 1(c). It results in asymmetry of peak 6 in Fig. 1(d) showing the accurate positions of two sub-spectra. After that, a Lorentzian fitting according to the position in Fig. 1(d) can be performed to obtain Mӧssbauer parameters. A Lorentzian fitting of Mӧssbauer spectra at room temperature and 15 K are shown in Fig. 2, consisting of two magnetic sextets and one paramagnetic doublet. The two six-line magnetic patterns are ascribed to tetrahedral Fe3+ (A-site) and octahedral Fe2.5+ (B-site), respectively. The central doublet can be attributed to the secondary phase γ-Fe2S3 with inverse spinel structure, which often appears in chemically prepared greigite [16]. The hyperfine parameters including CS and hyperfine field (H) obtained from the fitting of 57Fe Mӧssbauer spectra for
〈v 2〉 2c
(1)
where c1 is a constant and 〈v 2〉 indicates the mean-square velocity of iron nuclei. δIS is a temperature independent value only related to the s electron charge density at nuclei, which reveals the valence state of iron. Temperature dependent 〈v 2〉 can be written as:
〈v 2〉 =
9kB θD ⎡ 1 T +⎛ ⎞ M ⎢ ⎝ θD ⎠ ⎣8 ⎜
⎟
4
∫0
θD / T
x3 dx⎤ ex − 1 ⎥ ⎦
(2)
where M is the mass of a Mössbauer atom, kB is the Boltzmann constant, θD is the Debye temperature, T is absolute temperature, and x is equal to θD/T. Thus, analysis of CS versus temperature allows estimation of the Debye temperature. The fittings of CS–T curves are shown as blue and red solid lines in Fig. 3(a), giving the calculated Debye temperature values 805 ± 10 K and 760 ± 10 K corresponding to A- and B-site lattices, respectively. θD of B-site is found to be 6% lower than that of A-site, resulting in the discrepancy of iron atom vibration as well as different Lamb–Mössbauer factor (f). Under the Debye model and harmonic approximation: 1215
Results in Physics 12 (2019) 1214–1217
W. Zuo et al.
1.02
-Fe2S3
0.98 0.96 0.94
Doublet site 19%
0.92
Fe3S4
1.00
Transmission
Transmission
1.00
1.02
B-site A-site
Fe3S4
0.96 0.94
Doublet site 18% (b)
RT
0.90 -10
-5
0
5
15K
0.90 -10
10
-5
Velocity (mm/s) Fig. 2.
57
5
10
Velocity (mm/s)
328
2.5+
octahedral Fe 3+ tetrahedral Fe
0.7 D
0.6
=760 10K
0.5 0.4 D
2.5+
octahedral Fe 3+ tetrahedral Fe
324
Hyperfine field (kOe)
0.8
CS (mm/s)
0
Fe Mӧssbauer spectra of greigite recorded at room temperature (a) and 15 K (b). Assignments of A- and B-site sub-spectra are shown.
0.9
=805 10K
320 2
316
R =0.99
312
R2=0.93
308 304 300
0.3 0.2
-Fe2S3
0.98
0.92
(a)
B-site A-site
(a)
(b)
296 0
50
100
150
200
250
300
0
50
Temperature (K)
100
150
200
250
300
Temperature (K)
Fig. 3. Hyperfine parameters including CS (a) and hyperfine magnetic field (b) obtained from the fitting of Mӧssbauer spectra versus temperature.
ln f = −k 2 〈u2〉 = −
3Eγ2
2
⎡1 + 4 ⎛ T ⎞ 4Mc 2kB θD ⎢ ⎝ θD ⎠ ⎣ ⎜
⎟
∫0
θD / T
x dx⎤ ex − 1 ⎥ ⎦
Table 1 Debye temperatures of magnetite and greigite obtained from different methods.
(3)
Compound
where 〈u2〉 is the mean-square displacement. Hereby, the Lamb–Mössbauer factor ratio fB/fA is found to be 0.98 at room temperature, which gives a good agreement with the work of van Loef where it is demonstrated that the mean-square displacement of the iron at B site is larger than that of the A-site iron for spinel structure compounds [18]. Comparison of θD values in greigite Fe3S4 and magnetite Fe3O4 helps to understand the difference of physical properties in spinel compounds, as listed in Table 1. The θD values of Fe3O4 derived from different methods are not the same, however, it is still meaningful to find that our θD value obtained from Mossbauer spectroscopy for Fe3S4 is much higher than that for Fe3O4. This divergence of θD values between greigite and magnetite can be attributed to a different interatomic force of the iron, which is related to the exchange interaction between Fe ions in A and B sub-lattices. In conclusion, the dynamics of Fe ions in tetrahedral A- and octahedral B-sub-lattices of greigite are quite different and it is surprising to find different lattice dynamics between magnetite and greigite despite the same lattice structure. The hyperfine magnetic fields presented in Fig. 3(b) for A- and Bsites in greigite increase with temperature decreasing due to the ordering of magnetic moments. A crossover is observed at about 250 K,
Fe3O4
A-site B-site
Fe3O4 Fe3O4 Fe3S4
A-site B-site
Debye temperature (K)
Method
Reference
θD (−2) : 334 ± 10 θD (−2) : 314 ± 10
RAA of MS
[19]
θD (−3) : 660 θD (−3) : 570
Heat capacity Heat capacity
[20] [21]
θD (1) : 805 ± 10 θD (1) : 760 ± 10
SOD of MS
This study
“RAA of MS” indicates the resonant absorption area of Mossbauer spectra; “SOD of MS” indicates the second order Doppler shift of Mossbauer spectra.
which is slightly lower than the value (290 K) reported by Vandenberghe et al. [12]. Saturation value H(0) (320 ± 1 kOe) for A-site is smaller than that for B-site (325.1 ± 0.8 kOe), which gives a good agreement with literature [10,11]. Hyperfine magnetic field can be expressed as [18]:
H (T ) = A (T ) M (T )
(4)
where A(T) is the hyperfine constant which may impede a close connection between H and magnetization (M) described by Brillouin function. van Loef studied the hyperfine magnetic field obtained from 1216
Results in Physics 12 (2019) 1214–1217
W. Zuo et al.
Acknowledgements
Mossbauer measurement and the sublattice magnetization from neutron diffraction data for ferrimagnets. For A-site ions, hyperfine constant is temperature independence as a consequence of all the ions in S states while for B-site ions, it is temperature dependence because fast electron exchange occurs [22]. Hereby, contribution of A(T) are tentatively taken account into the fitting of H–T curves and it would be worthwhile to conduct a more careful study of A(T) in greigite, which is excluded in the present work. The slow temperature variation of A-site fields may imply a high Curie temperature. An accurate determination of TC by extrapolation here is not possible because of the lack of information about the complex exchange interactions and the formal valences of Fe [12]. On the other hand, the hyperfine magnetic field is much lower than that in magnetite due to a strong reduction of covalency effects.
This work was supported by the National Natural Science Foundation of China under the grant # 11875210 and by the Shenzhen Science and Technology Innovation Committee under the grant JCYJ20170818112901473. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
Conclusion We have applied a specific velocity mode, constant velocity with 20% slope, to conduct Mӧssbauer spectroscopy study on the synthesized greigite samples. This velocity mode helps to observe details and subtle changes of sextets in Mӧssbauer spectra, which can give accurate determination of the complex overlapping subspectra corresponding to tetrahedral and octahedral sub-lattice sites in greigite. It has been found that the Debye temperatures θD obtained from the temperature dependent CS values are 805 ± 10 K and 760 ± 10 K for tetrahedral Fe3+ and octahedral Fe2.5+ sites, respectively, and the Lamb–Mӧssbauer factor ratio fB/fA is equal to 0.98 at room temperature. The discrepancy of lattice dynamics between inverse spinel greigite and magnetite has also been demonstrated from Mӧssbauer spectroscopy. The different temperature variations of A-site and B-site fields are revealed.
[13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
1217
Skinner BJ, Erd RC, Grimaldi FS. Am Mineral 1964;49:543. Snowball IF, Thompson R. J Geophys Res 1990;95:4471. Roberts AP, Reynolds RL, Verosub KL, Adam DP. Res Lett 1996;23:2859. Jiang WT, Horng CS, Roberts AP, Peacor DR. Earth Planet Sci Lett 2001;193:1. Roberts AP, Jiang WT, Florindo F, Horng CS, Laj C. Res Lett 2005;32:L05307. He Z, Yu SH, Zhou X, Li X, Qu J. Adv Funct Mater 2006;16:1105. Yamaguchi S, Wada H. J Appl Phys 1973;44:1929. Li QD, Wei QL, Zuo WB. Chem Sci 2017;8:160. Morice JA, Rees LVC, Rickard DT. J Inorg Nucl Chem 1969;31:3797. Spender MR, Coey JMD, Morrish AH. Can J Phys 1972;50:2313. Coey JMD, Spender MR, Morrish AH. Solid State Commun 1970;8:1605. Vandenberghe RE, Grave ED, Bakker PMA, Krs M, Hus JJ. Hyperfine Interact 1991;68:319. Vaughan DJ, Ridout MS. J Inorg Nucl Chem 1971;33:741. Chang L, Rainford BD, Stewart JR, Ritter C, Roberts AP, Tang Y, et al. J Geophys Res 2009;114:B07101. Chang L, Roberts AP, Tang Y, Rainford BD, Muxworthy AR, Chen QW. J Geophys Res 2008;113:B06104. Lyubutin IS, Starchikov SS, Lin CR, et al. J Nanopart Res 2013;15:1397. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in C: the art of scientific computing. 2nd ed. Cambridge University Press; 1992. van Loef JJ. Physica 1966;32:2102. Sawatzky GA, Van Der Woude F, Morrish AH. Phys Rev 1969;183:383. Kouvel JS. Phys Rev 1956;102:1489. Millar RW. J Am Chem Soc 1929;51:215. van der Woude F, Sawatzky GA, Morrish AH. Phys Rev 1968;169:533.
Contents lists available at ScienceDirect
Results in Physics journal homepage: www.elsevier.com/locate/rinp
Microarticle
Study on velocity mode of 57Fe Mӧssbauer spectroscopy and determination of lattice dynamics in Fe3S4 Wenbin Zuoa, Vasiliy Pelenovicha, Qidong Lib, Xiaomei Zenga, Dejun Fua, a b
T
⁎
Key Laboratory of Artificial Micro- and Nano-Materials of Ministry of Education of China, School of Physics and Technology, Wuhan University, Wuhan 430072, China State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Spinel structure Mӧssbauer Spectroscopy Lattice dynamics Debye temperature
57 Fe Mӧssbauer spectroscopy studies on chemically synthesized greigite Fe3S4 have been conducted with a unique velocity mode, known as constant velocity with slope, which allows detection of subtle changes and indepth details of sextets in the spectra. Accurate determination of the overlapped sub-spectra corresponding to tetrahedral Fe3+ (A) and octahedral Fe2.5+ (B) sub-lattices has been made based on the special velocity mode. Estimation of Debye temperature θD from the temperature dependent central shift (CS) values gives the values: 805 ± 10 K and 760 ± 10 K for A- and B-sites, respectively. The discrepancy of two θD values reveals different lattice vibration between A- and B-sites. The Lamb-Mӧssbauer factor ratio fB/fA is found to be 0.98 at room temperature. The different low-temperature behaviors of hyperfine magnetic field for tetrahedral A- and octahedral B-sites are observed.
Introduction Greigite Fe3S4 is an important magnetic material with inverse spinel structure as a counterpart of magnetite Fe3O4 [1]. There are two sublattices of iron atoms where Fe3+ ions occupy tetrahedral A-sites and both Fe2+ and Fe3+ ions occupy octahedral B-sites. Natural greigites are widely distributed in sedimentary rocks all over the world and now are recognized as a recorder of the ancient geomagnetic field and environmental processes, which are important for paleomagnetic and environmental magnetic studies [2–5]. Artificial greigites have been broadly used in electrochemistry, biomedicine, and environmental magnetic studies [6–8]. 57Fe Mӧssbauer spectroscopy study of Fe3S4 is started from 1960s by Morice et al. [9], and two sextets in Mӧssbauer spectra for Fe3S4 has been revealed [10–16]. However, assignments of tetrahedral A-site and octahedral B-site are ambiguous in literature. Some researchers attribute A- and B-sites to two sextets with similar central shift (0.51 mm/s and 0.60 mm/s) but different hyperfine field (308 kOe and 29.1 kOe) [10,11,13] while the others claim two different central shift (0.28 mm/s and 0.53 mm/s) and same hyperfine field (313 kOe) [12,14–16]. The reason is the huge overlap of sub-spectra, which is completely different from magnetite. In this study, in an attempt to solve this problem, we make use of the “constant velocity with slope” mode to carefully examine the most informative 1st and 6th peaks of the sextet, trying to separate the two sub-spectra. Although such velocity mode is known in Mӧssbauer community, very few work ⁎
is reported. Once the determination of tetrahedral A site and octahedral B site in Fe3S4 is clear, study on lattice dynamics from Mӧssbauer parameters can be performed. One of the most important parameters in lattice dynamics, Debye temperature θD, can be calculated from temperature dependent central shift (CS) values in the framework of Debye model. Only after the θD of a material is determined would the terms ‘‘high temperature’’ and ‘‘low temperature’’ be meaningful. However, few work is focused on the lattice dynamics of Fe3S4. This study intends to fill this gap. In the present work, we carry out 57Fe Mӧssbauer spectroscopy using a special velocity mode to accurately determine the local order of iron atoms in Fe3S4. Mӧssbauer spectra at various temperatures from 300 K to 15 K are recorded to study the dynamics and magnetic structure of the tetrahedral and octahedral sub-lattices of greigite. Experimental details Fe3S4 powder was synthesized in a typical reaction as reported in our previous work [8]. The Mössbauer spectra of Fe3S4 with ideal absorber thickness of 22.9 mg/cm2 were collected by a conventional spectrometer (Germany, Wissel MS500) in transmission geometry with a 25 mCi gamma ray source 57Co in Rh matrix. The waveform of the source motion was provided by the Mӧssbauer driving system (Digital Function Generator DFG-1200). An α-Fe foil at room temperature was
Corresponding author. E-mail address: [email protected] (D. Fu).
https://doi.org/10.1016/j.rinp.2019.01.010 Received 5 December 2018; Received in revised form 4 January 2019; Accepted 4 January 2019 Available online 08 January 2019 2211-3797/ © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/BY-NC-ND/4.0/).
Results in Physics 12 (2019) 1214–1217
W. Zuo et al. 1.01
1.00
1.00 0.99
Transmission
0.98
0.98
0.96 0.97
0.94
0.92
0.96 0.95
1
0.94
6 0.90
Velocity (mm/s)
8
0.93 8
constant acceleration
6
6
constant velocity with 20% slope
6
4
4
2
2
0
0
-2
-2
-4
-4
(a)
-6
1
(c)
-6
-8
-8
A Peak 6
(b)
(c)
B
(d)
Peak 6
Fig. 1. Typical constant velocity mode for full spectra (a) and peak 6 (b), constant velocity-20% slope mode for full spectra (c) and peak 6 (d).
used as the absorber for velocity calibration. The spectra were fitted by Recoil code using Lorentzian site analysis [17].
Fe3S4 sample are presented in Fig. 3 as a function of temperature. The CS values relative to the reference absorber α-Fe foil show an abrupt increase at the beginning of cooling and then a platform after 100 K. It can be expressed by the following formula:
Results and discussion
δCS (T ) = δIS + δSOD (T ) = δIS + c1 −
A typical Mӧssbauer spectrum with constant acceleration mode for Fe3S4 powder recorded at room temperature is shown in Fig. 1(a). The spectrum is obtained by scanning the velocity range ± 7 mm/s, thereby allocating about 15 channels to peaks 1 and 6 out of the 512 channels used to store the γ-ray data. The enlarged peak 6 presented in Fig. 1(b) shows good symmetry, from which it is difficult to get the accurate position of subspectra. Using a unique velocity mode, the two outer peaks 1 and 6 are extremely broadened with allocation of about 37 channels to collect the data and more valid data appear, as shown in Fig. 1(c). It results in asymmetry of peak 6 in Fig. 1(d) showing the accurate positions of two sub-spectra. After that, a Lorentzian fitting according to the position in Fig. 1(d) can be performed to obtain Mӧssbauer parameters. A Lorentzian fitting of Mӧssbauer spectra at room temperature and 15 K are shown in Fig. 2, consisting of two magnetic sextets and one paramagnetic doublet. The two six-line magnetic patterns are ascribed to tetrahedral Fe3+ (A-site) and octahedral Fe2.5+ (B-site), respectively. The central doublet can be attributed to the secondary phase γ-Fe2S3 with inverse spinel structure, which often appears in chemically prepared greigite [16]. The hyperfine parameters including CS and hyperfine field (H) obtained from the fitting of 57Fe Mӧssbauer spectra for
〈v 2〉 2c
(1)
where c1 is a constant and 〈v 2〉 indicates the mean-square velocity of iron nuclei. δIS is a temperature independent value only related to the s electron charge density at nuclei, which reveals the valence state of iron. Temperature dependent 〈v 2〉 can be written as:
〈v 2〉 =
9kB θD ⎡ 1 T +⎛ ⎞ M ⎢ ⎝ θD ⎠ ⎣8 ⎜
⎟
4
∫0
θD / T
x3 dx⎤ ex − 1 ⎥ ⎦
(2)
where M is the mass of a Mössbauer atom, kB is the Boltzmann constant, θD is the Debye temperature, T is absolute temperature, and x is equal to θD/T. Thus, analysis of CS versus temperature allows estimation of the Debye temperature. The fittings of CS–T curves are shown as blue and red solid lines in Fig. 3(a), giving the calculated Debye temperature values 805 ± 10 K and 760 ± 10 K corresponding to A- and B-site lattices, respectively. θD of B-site is found to be 6% lower than that of A-site, resulting in the discrepancy of iron atom vibration as well as different Lamb–Mössbauer factor (f). Under the Debye model and harmonic approximation: 1215
Results in Physics 12 (2019) 1214–1217
W. Zuo et al.
1.02
-Fe2S3
0.98 0.96 0.94
Doublet site 19%
0.92
Fe3S4
1.00
Transmission
Transmission
1.00
1.02
B-site A-site
Fe3S4
0.96 0.94
Doublet site 18% (b)
RT
0.90 -10
-5
0
5
15K
0.90 -10
10
-5
Velocity (mm/s) Fig. 2.
57
5
10
Velocity (mm/s)
328
2.5+
octahedral Fe 3+ tetrahedral Fe
0.7 D
0.6
=760 10K
0.5 0.4 D
2.5+
octahedral Fe 3+ tetrahedral Fe
324
Hyperfine field (kOe)
0.8
CS (mm/s)
0
Fe Mӧssbauer spectra of greigite recorded at room temperature (a) and 15 K (b). Assignments of A- and B-site sub-spectra are shown.
0.9
=805 10K
320 2
316
R =0.99
312
R2=0.93
308 304 300
0.3 0.2
-Fe2S3
0.98
0.92
(a)
B-site A-site
(a)
(b)
296 0
50
100
150
200
250
300
0
50
Temperature (K)
100
150
200
250
300
Temperature (K)
Fig. 3. Hyperfine parameters including CS (a) and hyperfine magnetic field (b) obtained from the fitting of Mӧssbauer spectra versus temperature.
ln f = −k 2 〈u2〉 = −
3Eγ2
2
⎡1 + 4 ⎛ T ⎞ 4Mc 2kB θD ⎢ ⎝ θD ⎠ ⎣ ⎜
⎟
∫0
θD / T
x dx⎤ ex − 1 ⎥ ⎦
Table 1 Debye temperatures of magnetite and greigite obtained from different methods.
(3)
Compound
where 〈u2〉 is the mean-square displacement. Hereby, the Lamb–Mössbauer factor ratio fB/fA is found to be 0.98 at room temperature, which gives a good agreement with the work of van Loef where it is demonstrated that the mean-square displacement of the iron at B site is larger than that of the A-site iron for spinel structure compounds [18]. Comparison of θD values in greigite Fe3S4 and magnetite Fe3O4 helps to understand the difference of physical properties in spinel compounds, as listed in Table 1. The θD values of Fe3O4 derived from different methods are not the same, however, it is still meaningful to find that our θD value obtained from Mossbauer spectroscopy for Fe3S4 is much higher than that for Fe3O4. This divergence of θD values between greigite and magnetite can be attributed to a different interatomic force of the iron, which is related to the exchange interaction between Fe ions in A and B sub-lattices. In conclusion, the dynamics of Fe ions in tetrahedral A- and octahedral B-sub-lattices of greigite are quite different and it is surprising to find different lattice dynamics between magnetite and greigite despite the same lattice structure. The hyperfine magnetic fields presented in Fig. 3(b) for A- and Bsites in greigite increase with temperature decreasing due to the ordering of magnetic moments. A crossover is observed at about 250 K,
Fe3O4
A-site B-site
Fe3O4 Fe3O4 Fe3S4
A-site B-site
Debye temperature (K)
Method
Reference
θD (−2) : 334 ± 10 θD (−2) : 314 ± 10
RAA of MS
[19]
θD (−3) : 660 θD (−3) : 570
Heat capacity Heat capacity
[20] [21]
θD (1) : 805 ± 10 θD (1) : 760 ± 10
SOD of MS
This study
“RAA of MS” indicates the resonant absorption area of Mossbauer spectra; “SOD of MS” indicates the second order Doppler shift of Mossbauer spectra.
which is slightly lower than the value (290 K) reported by Vandenberghe et al. [12]. Saturation value H(0) (320 ± 1 kOe) for A-site is smaller than that for B-site (325.1 ± 0.8 kOe), which gives a good agreement with literature [10,11]. Hyperfine magnetic field can be expressed as [18]:
H (T ) = A (T ) M (T )
(4)
where A(T) is the hyperfine constant which may impede a close connection between H and magnetization (M) described by Brillouin function. van Loef studied the hyperfine magnetic field obtained from 1216
Results in Physics 12 (2019) 1214–1217
W. Zuo et al.
Acknowledgements
Mossbauer measurement and the sublattice magnetization from neutron diffraction data for ferrimagnets. For A-site ions, hyperfine constant is temperature independence as a consequence of all the ions in S states while for B-site ions, it is temperature dependence because fast electron exchange occurs [22]. Hereby, contribution of A(T) are tentatively taken account into the fitting of H–T curves and it would be worthwhile to conduct a more careful study of A(T) in greigite, which is excluded in the present work. The slow temperature variation of A-site fields may imply a high Curie temperature. An accurate determination of TC by extrapolation here is not possible because of the lack of information about the complex exchange interactions and the formal valences of Fe [12]. On the other hand, the hyperfine magnetic field is much lower than that in magnetite due to a strong reduction of covalency effects.
This work was supported by the National Natural Science Foundation of China under the grant # 11875210 and by the Shenzhen Science and Technology Innovation Committee under the grant JCYJ20170818112901473. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12]
Conclusion We have applied a specific velocity mode, constant velocity with 20% slope, to conduct Mӧssbauer spectroscopy study on the synthesized greigite samples. This velocity mode helps to observe details and subtle changes of sextets in Mӧssbauer spectra, which can give accurate determination of the complex overlapping subspectra corresponding to tetrahedral and octahedral sub-lattice sites in greigite. It has been found that the Debye temperatures θD obtained from the temperature dependent CS values are 805 ± 10 K and 760 ± 10 K for tetrahedral Fe3+ and octahedral Fe2.5+ sites, respectively, and the Lamb–Mӧssbauer factor ratio fB/fA is equal to 0.98 at room temperature. The discrepancy of lattice dynamics between inverse spinel greigite and magnetite has also been demonstrated from Mӧssbauer spectroscopy. The different temperature variations of A-site and B-site fields are revealed.
[13] [14] [15] [16] [17] [18] [19] [20] [21] [22]
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Skinner BJ, Erd RC, Grimaldi FS. Am Mineral 1964;49:543. Snowball IF, Thompson R. J Geophys Res 1990;95:4471. Roberts AP, Reynolds RL, Verosub KL, Adam DP. Res Lett 1996;23:2859. Jiang WT, Horng CS, Roberts AP, Peacor DR. Earth Planet Sci Lett 2001;193:1. Roberts AP, Jiang WT, Florindo F, Horng CS, Laj C. Res Lett 2005;32:L05307. He Z, Yu SH, Zhou X, Li X, Qu J. Adv Funct Mater 2006;16:1105. Yamaguchi S, Wada H. J Appl Phys 1973;44:1929. Li QD, Wei QL, Zuo WB. Chem Sci 2017;8:160. Morice JA, Rees LVC, Rickard DT. J Inorg Nucl Chem 1969;31:3797. Spender MR, Coey JMD, Morrish AH. Can J Phys 1972;50:2313. Coey JMD, Spender MR, Morrish AH. Solid State Commun 1970;8:1605. Vandenberghe RE, Grave ED, Bakker PMA, Krs M, Hus JJ. Hyperfine Interact 1991;68:319. Vaughan DJ, Ridout MS. J Inorg Nucl Chem 1971;33:741. Chang L, Rainford BD, Stewart JR, Ritter C, Roberts AP, Tang Y, et al. J Geophys Res 2009;114:B07101. Chang L, Roberts AP, Tang Y, Rainford BD, Muxworthy AR, Chen QW. J Geophys Res 2008;113:B06104. Lyubutin IS, Starchikov SS, Lin CR, et al. J Nanopart Res 2013;15:1397. Press WH, Teukolsky SA, Vetterling WT, Flannery BP. Numerical recipes in C: the art of scientific computing. 2nd ed. Cambridge University Press; 1992. van Loef JJ. Physica 1966;32:2102. Sawatzky GA, Van Der Woude F, Morrish AH. Phys Rev 1969;183:383. Kouvel JS. Phys Rev 1956;102:1489. Millar RW. J Am Chem Soc 1929;51:215. van der Woude F, Sawatzky GA, Morrish AH. Phys Rev 1968;169:533.