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Charge ordering in Eu3S4 determined by the valence-difference contrast of synchrotron X-ray diffraction
ARTICLE IN PRESS
Physica B 350 (2004) 353–365
Charge ordering in Eu3S4 determined by the valence-difference contrast of synchrotron X-ray diffraction Hiroki Oharaa,1, Satoshi Sasakia,*, Yukiko Konoikea,2, Takeshi Toyodaa,3, Kouji Yamawakia, Masahiko Tanakab a
Materials and Structure Laboratory, Tokyo Institute of Technology, Nagatsuta 4259, Midori-ku, Yokohama 226-8503, Japan b Photon Factory, Institute of Materials Structure Science, KEK, Oho 1-1, Tsukuba 305-0801, Japan Received 20 January 2004; accepted 26 April 2004
Abstract Synchrotron X-ray diffraction study for single crystals of Eu3S4 has revealed that a Th3P4-type I 4% 3d structure transforms to a charge-ordered I 4% 2d one at Tc ¼ 188:5 K. The crystal structures of Eu3S4 at T ¼ 300; 180 and 160 K were determined in the least-squares refinements with the Mo Ka intensity data. The valence-difference contrast method was applied at the LII absorption edge of Eu, utilizing a large difference in anomalous scattering factors between Eu2+ and Eu3+. The cation distribution of Eu2+ and Eu3+ was determined by crystal-structure analyses based on the ( intensity data collected at two wavelengths of l ¼ 1:6312 and 1.6298 A.The least-squares structural refinements suggest that the most plausible atomic arrangement is [Eu3+]4a[Eu2+Eu3+]8dS4. The charge-ordering scheme is that a half of Eu3+ ions occupy the whole 4a sites in the I 4% 2d crystal structure, while the remaining half of Eu3+ ions mix with Eu2+ in the 8d sites. The scheme is also supported by the energy dependence of Bragg intensities for 400 and 004 reflections. r 2004 Elsevier B.V. All rights reserved. PACS: 61.10.Nz; 61.66.Fn; 61.50.Ks; 78.70.Ck Keywords: Charge ordering; Valence contrast; Eu3S4; Mixed-valence compound; X-ray anomalous scattering; Synchrotron radiation
1. Introduction *Corresponding author. Tel.: +81-45-924-5308; fax: +8145-924-5339. E-mail address: [email protected] (S. Sasaki). 1 Present address: Semiconductor Energy Laboratory, Co. Ltd., Atsugi 243-0036, Japan. 2 Present address: Fujitsu System Solutions, Ltd., Honkomagome, Tokyo 113-0021, Japan. 3 Present address: Industrial Research Institute of Ishikawa, Kanazawa 920-8203, Japan.
A mixed-valence compound Eu3S4 has divalent Eu2+ (4f 7 5s2 5p6 6s2 ; S ¼ 7=2; L ¼ 0; J ¼ 7=2) and trivalent Eu3+ (4f 6 5s2 5p6 5d1 6s2 ; S ¼ L ¼ 3; J ¼ 0) ions in the ratio 1:2 and is recognized as a unique system including divalent rare-earth ions. The room-temperature phase has a Th3P4 structure, as shown in Fig. 1, where all Eu ions occupy a kind of crystallographic site in a BCC lattice
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.04.072
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Fig. 1. (a) Projection and (b) schematic drawing of the crystal structure of a room-temperature phase of Eu3S4 (Th3P4-type structure). Solid circle=Eu, open circle=S. The heights of atoms along the a3-axis are given by integer after multiplied by 100. The bond distances ( for Eu polyhedron are given in A.
[1–4]. The cell dimension and space group are ( and I 4% 3d; respectively. Eu3S4 has the a ¼ 8:516 A transport property as intrinsic semiconductor by a hopping of 4f electrons between adjacent Eu sites. The origin of the hopping motion of charge carriers is considered as either thermally activated drift mobility or electron tunneling, based on the observations of different isomer shift in . Mossbauer spectra [5] and constant charge carrier concentration [6]. Eu3S4 has a non-magnetic phase transition at the temperature of 175 or 168 K, which was reported from the measurements of the electrical conductivity and Seebeck coefficients [6,7]. The exact temperature of the phase transition is considered to depend on the purity of the sample. A maximum temperature of Tc ¼ 185 K [8] or 188.5 K [9] was observed for purer single crystals synthesized by the chemical vapor deposition (CVD) technique with more stoichiometric composition. There is a report on the M.ossbauer experiments that Eu3S4 becomes ferromagnetic below Tc ¼ 3:8 K by freezing the 4f configuration [10]. . In Mossbauer spectra of 151Eu3S4 below T ¼ 210 K, two absorption peaks were observed and interpreted as electron hopping between Eu2+
and Eu3+ ions [5]. X-ray powder diffraction study found a cubic to tetragonal phase transition, having a 0.4% distortion in the ratio of a=c in the low-temperature phase [7]. Based on an approach to derive from the Th3P4 structure and construct a charge-ordering model between Eu2+ and Eu3+, a tetragonal cell was proposed with the I 4% 2d crystal structure, where Eu2+ occupies the 4a sites, Eu3+ occupies the 8d sites and S does the 16e sites (Carter model) [11]. From the study on the temperature-independent susceptibility, Eu3S4 was suggestively considered to have partial charge ordering of Eu2+ and Eu3+ and to be interpretable as a simple sum of Van Vleck-type Eu3+ and Curie–Weiss-type Eu2+ [12]. On the other hand, based on the analogy of the similar compounds such as La3S4, La3Se4, Pr3S4 and Pr3Se4, the firstorder transition was proposed for Eu3S4 [13]. The existence of the first-order transition at Tc ¼ 186 K in Eu3S4 was supported by the measurement of the configuration entropy [14]. In the Raman scattering study, any new phonon mode was not observed for single crystals of Eu3S4, which is inconsistent with the charge order–disorder transition [15].
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Thus, the occurrence of the charge ordering in Eu3S4 still remains in dispute. The valenceselective structure determination would be the best way to examine the charge order–disorder mechanism [16]. In this paper, we first determine the crystal structure of a low-temperature phase of Eu3S4 because of the lack of the crystal-structure data. Then, the cation distribution of Eu2+ and Eu3+ of low-temperature phase will be determined by the recent developed technique, which utilizes the valence contrast in X-ray anomalous scattering.
2. Sample Powder crystals of Eu3S4 were prepared by reacting stoichiometric proportions of EuS (Soekawa Rikagaku Co. Ltd., 99.9%) and sulfur (Wako Pure Chemical Industries, Ltd., 99.9999%) in an evacuated silica capsule at 1073 K for 4 days. Single crystals of Eu3S4 were synthesized from the powder sample with 0.06 g NH4I flux by the vapor growth. The starting materials were put on an end of 165 mm silica tube, NH4I flux was placed in the middle of the silica tube with oliphis (30 mm in diameter) and single crystals were grown at the other end of the silica tube. The evacuated silica tube as preheated at 673 K and kept in vapor growth between 923 and 973 K for 9 days. Single crystals having dimensions up to 0.2 mm were successfully obtained.
3. Conventional X-ray measurements X-ray single-crystal diffraction experiments were first carried out using a conventional Rigaku AFC5 four-circle diffractometer. Mo Ka radiation ( was used after monochromatized (l ¼ 0:7107 A) by graphite (0 0 2). Each of two single crystals was mounted on the glass fiber and used for X-ray studies: one is a parallel-piped crystal having the dimensions of 140 85 50 mm3 (specimen #1) and the other is a spherical crystal of 60 mm in diameter (specimen #2). Low-temperature experiments were performed with the Oxford Cryostream Cooler, where cold
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and dry nitrogen gas is directly blown onto the crystal. The temperature at the sample position was calibrated using two sets of chromel-constantan thermocouple wires. The temperature was controlled within 71 K during the intensity measurements. In order to avoid the formation of twinning, the cooling operation was accomplished in the magnetic field of 1.5 T along the [0 0 1] direction of Eu3S4, by using a pair of rareearth magnet. The integrated intensity data were collected up to 2y ¼ 90 , in the o22y scan mode with maximum five scans. The scan speeds in intensity measurements were 0.5 /min for specimen #2 and 1 /min for specimen #1. The scan width was 1.2+0.3 tan y in o: The experimental conditions for X-ray measurements are summarized as follows: (1) specimen #1, measured at T ¼ 296 K in one-eighth of reciprocal space; the number of reflections measured, Nm ¼ 1444 and the number of reflections averaged and used in refinements, Na ¼ 199; (2) specimen #2, at T ¼ 296 K in a hemisphere; Nm ¼ 5300 and Na ¼ 181; (3) specimen #1, at T ¼ 180 K in one-eighth space; Nm ¼ 5305 and Na ¼ 507; (4) specimen #2, at T ¼ 160 K in a hemisphere, Nm ¼ 2357 and Na ¼ 205: The fluctuations in the integrated intensities for three standard reflections were held less than 71.4%, 74.0% and 74.0% during the data collections at 296, 180 and 160 K, respectively. The Lorentz-polarization and absorption effects were corrected. A linear absorption coefficient is 30.5 mm1 for the Mo Ka radiation. Since specimen #1 is not a spherical crystal, the absorption correction was made by the grid-integration method for the arbitrary-shape crystal [17]. The calculation software called ACACA was installed in a full matrix least-squares program of RADY [18] and used for this purpose. In the absorption correction for specimen #1 the transmitted factor ranges from 0.056 to 0.107.
4. Crystal structures of Eu3S4 The room-temperature phase of Eu3S4 was reconfirmed to be the BCC Th3P4 structure with the space group of I 4% 3d (Fig. 1). The cell
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( at T ¼ 296 K. dimension was a ¼ 8:53470:003 A Final structural parameters and bond distances are listed in Table 1. Only x-coordinate of sulfur (u parameter) is a variable among positional parameters. The u parameter obtained in this study was 0.0713, which was comparable with the reported value (u ¼ 0:0721) [4]. It gives a slight deviation from an ideal Th3P4 structure (u ¼ 1=12=0.0833). The crystal structure of Th3P4 is well approximated as the octahedral configuration with the FCC structure of NaCl. A kind of Eu ion exists in the 12a site, having a 4% inversion axis without a center of symmetry. A Eu ion is coordinated by eight sulfur ions in a distorted cube. The Eu–S distances estimated in ( which are this study are 2.846 and 3.068 A, indicated with the respective bonds in Fig. 1. In the other view from anions, a sulfur ion is coordinated by six Eu ions.
Table 1 Atomic parameters and bond distances for a room-temperature phase of Eu3S4 #1
#2
Eu (12a) b11 b22 ( 2) Bequiv: (A
0.00315(5) 0.00251(3) 0.793(7)
0.00231(5) 0.00151(3) 0.517(8)
S (16c) X b11 b12 ( 2) Bequiv: (A
0.0713(5) 0.00428(9) 0.0004(1) 1.248(9)
0.0713(6) 0.0038(1) 0.0000(1) 1.10(1)
R factor Weighted R factor
0.029 0.041
0.054 0.052
Bond distances ( Eu–S (A) ( Eu–S (A) ( Eu–Eu (A) ( S–S (A) ( S–S (A)
2.846(1) 3.068(1) 3.991(1) 3.284(2) 3.695(3)
Note: The standard deviation is given for the last digit in parenthesis. Eu sites: x ¼ 3=8; y ¼ 0; z ¼ 1=8; b22 ¼ b33 ; b12 ¼ b13 ¼ b23 ¼ 0: S sites: x ¼ y ¼ z; b11 ¼ b22 ¼ b33 ; b12 ¼ b13 ¼ b23 :
In the early 1970s, the X-ray data for chargeordered Eu3S4 or Sm3S4 taken at low temperature were interpreted as a tentative tetragonal structure derived from the Th3P4 one, where the c=a ratio ( and c ¼ 8:539 A ( [7]. was 1.004 with a ¼ 8:505 A From the theoretical study on cation-vacancy ordering in the Th3P4 structure, the tetragonal structural model was in accordance with the space group of I 4% 2d or I 4% [11]. The calculation of Madelung potentials preferred the I 4% 2d structural model, taking into account the ionic size increased when divalent cations occupy the 4a sites. A recent single-crystal X-ray diffraction study has confirmed the tetragonal deformation from the observation of the discontinuity in Bragg intensity at the phase transition of Eu3S4 [9]. The crystal structure of the low-temperature phase of Eu3S4 was determined for the first time in this study by the X-ray single-crystal diffraction method. The crystal symmetry was tetrahedral with a space group of I 4% 2d: The cell dimensions ( and c ¼ 8:51470:002 A ( were a ¼ 8:50870:001 A at T ¼ 180 K. The crystal structure of the lowtemperature phase can be well represented with the I 4% 2d structure proposed by Carter [11]. Table 2 shows the final atomic parameters of Eu3S4 at 180 and 160 K, determined by the crystal structure analyses with the Mo Ka diffraction data. The schematic projection of the crystal structure for the low-temperature phase is shown in Fig. 2. Both Eu sites are coordinated by eight sulfur ions. The 4a sites distributes like the diamond structure. The interatomic distances on Eu–S are given in Fig. 2 for two kinds of non-equivalent Eu sites: 4a and 8d sites. The Eu–S bond distances are 2.852 ( for the 4a polyhedron, which are well and 3.033 A ( for the polycompared with 2.846 and 3.068 A hedron of the room-temperature phase, respectively. The EuS8 polyhedron is more distorted through the phase transition, where the Eu–S bonds shrink with 0.2% shorter for the shorter bond and extend 1.2% longer for the longer bond. The 8d sites are surrounded with eight sulfur atoms, too. The EuS8 polyhedron is similar to the distorted cube of the room-temperature phase. When the temperature decreases through the phase transition, four shorter Eu–S bonds in Eu– ( extend a little and split into two bonds S=2.846 A
ARTICLE IN PRESS H. Ohara et al. / Physica B 350 (2004) 353–365 Table 2 Atomic parameters for a low-temperature phase of Eu3S4 Temperature (K)
#1 180
#2 160
Eu (4a) b11 b33 ( 2) Bequiv: (A
0.00325(5) 0.00363(8) 0.98(1)
0.00178(9) 0.0013(1) 0.47(2)
Eu (8d) X b11 b22 b33 b23 ( 2) Bequiv: (A
0.3755(3) 0.00348(6) 0.00331(6) 0.00363(4) 0.00018(5) 0.96(2)
0.3749(3) 0.0019(1) 0.0023(1) 0.00128(7) 0.00003(8) 0.53(3)
S (16e) X Y Z b11 b22 b33 b12 b13 b23 ( 2) Bequiv: (A
0.572 (1) 0.823 (1) 0.449 (1) 0.0053(3) 0.0060(3) 0.0077(3) 0.0007(2) 0.0016(2) 0.0005(2) 1.84(8)
0.573(1) 0.823(1) 0.448(1) 0.0064(5) 0.0045(4) 0.0033(3) 0.0023(3) 0.0014(3) 0.0011(3) 1.4(1)
R factor Weighted R factor
0.073 0.082
0.047 0.050
4a sites: x ¼ y ¼ z ¼ 0; b11 ¼ b22 ; b12 ¼ b13 ¼ b23 ¼ 0: 8d sites: y ¼ 1=4; z ¼ 1=8; b12 ¼ b13 ¼ 0:
( while the other four bonds of of 2.849 and 2.864 A, ( split into 3.042 and 3.047 A. ( The mean 3.068 A ( is 0.2% shorter Eu–S distance estimated as 2.951 A ( of room-temperature phase. than 2.957 A ( The mean Eu–S distance for 4a sites is 2.943 A, which is about 0.3% shorter than that of the 8d sites. As mentioned from the above structural view, there is no drastic change between low- and room-temperature phases in the size of the sites occupied by cations. It suggests that the cation distribution of Eu2+ and Eu3+ ions cannot be estimated from the only information on the crystal structure. Now, our study requires introducing the valence-difference contrast (VDC) method in order to discuss the charge ordering in the I 4% 2d structure.
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5. Valence-difference contrast X-ray scattering power within a Bragg peak at the hkl reciprocal lattice point is kinematically given by a square of the crystal-structure factor. The structure factor can be written as Fhkl ¼ Sj fj expf2piðhxj þ kyj þ lzj Þ;
ð1Þ
where xj ; yj and zj are the fractional coordinates of the jth atom and fj is the atomic scattering factor. In the VDC method, the atomic scattering factor must be different between two kinds of cation in different valence states. The valence difference on the effect of X-ray anomalous scattering becomes dominant at the absorption edge by a chemical shift between different oxidation states [16]. In the dominant condition near the absorption edge, the atomic scattering factor for an X-ray energy E can be given by f ðsin y=l; EÞ ¼ f0 ðsin y=lÞ þ f 0 ðEÞ þ if 00 ðEÞ;
ð2Þ
where l and y are the wavelength and a half of scattering angle, respectively, and f0 ; f 0 and f 00 are the Thomson elastic scattering term and real and imaginary terms of anomalous scattering factor, respectively. The strong contrast at the absorption edge makes the cation distinguish because of the large difference in f 0 ðEÞ: The f 00 ðEÞ term is generally estimated from the absorption spectra of the X-ray absorption near-edge structure (XANES). The f 0 ðEÞ and f 00 ðEÞ values have the relation of Kramers–Kronig’s dispersion, where one of them can be transformed from the other (e.g., Ref. [19]): Z N f 0 ðoÞ ¼ ð2=pÞ fo0 f 00 ðo0 Þ½o2 ðo0 Þ2 1 g do0 ; 0
ð3Þ 0
where o and o are angular frequency. The program DIFFKK [20] was used in this study to calculate the experimental-base f 0 values from the f 00 ones, by using Eq. (3) and the theoretical approximation on unobserved f 0 : Synchrotron experiments to measure the XANES spectra were performed at the beamline BL-3A of the Photon Factory. The X-rays were monochromatized by the Si(1 1 1) double-crystal monochromator. The absorption measurements
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Fig. 2. (a) Projection and (b) schematic drawing of the crystal structure of a low-temperature phase of Eu3S4. Solid circle=Eu(4a), hatched circle=Eu(8d), open circle=S. The heights of atoms along the c-axis are given by integer after multiplied by 100. The bond ( for Eu(4a) and Eu(8d) polyhedra are given only for independent bonds. All standard deviations for Eu–S distances in this distances [A] ( The other characteristic distances are: Eu(4a)I–Eu(8d)II=3.980(1) A; ( Eu(4a)I–Eu(8d)III=3.983(2) A; ( figure are equal to 70.009 A. ( Eu(8d)III–Eu(8d)IV=3.978(2) A.
were made at the Eu LII edge with two ionization chambers with N2 (monitor) and 75% N2+25% Ar gas. A reason to use the LII edge was that the diffraction experiment at Eu LIII (E ¼ 6:980 keV) was beyond its ability on the monochromator angle in the beamline BL-10A. The beam size was 1 2 mm2. A thickness of samples was adjusted for the suitable absorption, where two or three sheets of transparent tape were piled up. The incident and absorbed intensities were measured at a measuring time of 30 s for 851 steps of the monochromator angle with variable step-widths from 0.2 to 11 eV. The energy calibration on Eu LII edge was carefully made, by using an iron metal foil of 5 mm in thickness at the Fe Kabsorption edge. The first inflection point of the Fe foil was assigned to be E ¼ 7:112 keV [21,16]. X-ray energy in keV was converted to wavelength ( with a factor of 12.3985. in A Powder samples of EuS and Eu2O3 (Koch Chemical Ltd., 99.9%) were used as standards of Eu2+ and Eu3+ spectra, respectively. Fig. 3(a) shows f 00 curves estimated from the XANES spectra observed for EuS (cubic, NaCl structure) and Eu2O3 (cubic, bixbyite structure) at the Eu LII absorption edge. A chemical shift of 7 eV was
clearly observed between Eu2+ (E ¼ 7:601 keV) and Eu3+ (E=7.608 keV). Fig. 3(b) shows the energy-dependence curves of f 0 ; which were calculated through the Kramers–Kronig transformation. There is a sharp negative peak in each of f 0 curves of Eu2+ and Eu3+, corresponding to the individual absorption edge. Two typical wave( (E ¼ 7:6010 keV) and lengths of l ¼ 1:6312 A ( (E ¼ 7:6075 keV) were selected for our 1.6298 A crystal-structure study with the VDC technique. As the resolving power in VDC depends on the difference in f 0 ; the wavelengths to have the f 0 values in the opposite sign were chosen to examine the validity of the valence estimation. Anomalous scattering factors of Eu2+ and Eu3+ for the two wavelengths are summarized in Table 3. For example, the f 0 values for Eu2+ and Eu3+ have a remarkably large difference between –2.706 and ( +2.890 at wavelengths of 1.6312 and 1.6298 A, respectively. Since f 0 is independent on the scattering angles (or sin y=l), the VDC gives more powerful contrast for the higher-order reflection with higher scattering angle. Thus, the VDC technique with sufficient number of reflections promises the accurate determination of the site occupancy for Eu2+ and Eu3+ ions.
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Table 3 Scattering factors and absorption coefficients for Eu ions at wavelengths near Eu LII absorption edge ( Wavelength l (A) Energy E (keV)
1.6312 7.6010
Anomalous scattering factors Real part f0 (Eu2+) 14.820 f0 (Eu3+) 12.114 0.334 f0 (S) f0 (Eu2+)f0 (Eu3+) 2.706 Imaginary part f00 (Eu2+) f00 (Eu3+)
11.224 10.180
Atomic absorption coefficients ma (Eu2+) (mm2) 1.03 1015 3+ 2 ma (Eu ) (mm ) 0.93 1015 Linear absorption coefficients m (mm1) 200.8
Fig. 3. Anomalous scattering factors of Eu2+ and Eu3+ ions in the vicinity of Eu LII absorption edge: (a) imaginary part, f 00 ; obtained from XANES absorption spectra and (b) real part, f 0 ; transformed by the Kramers–Kronig relation. The dE gives a chemical shift of 7 eV between the different valence states of Eu ions.
6. Energy and temperature dependence of Bragg intensity The existence of the VDC was verified by the measurements of Bragg intensity of Eu3S4 at the Eu LII edge and T ¼ 180 K. Fig. 4 shows the energy dependence of diffraction intensities measured for 400 and 004 reflections by using a vertical-type four-circle diffractometer at BL-10A. There is a double negative peak, which has a deep valley and a shallow hollow on the energydependent intensity curves. A chemical shift of about 2 eV was observed between the curves for
1.6298 7.6075
10.735 13.625 0.334 +2.890
13.417 11.121
1.23 1015 1.02 1015
225.3
400 and 004 reflections, which indicates a difference in occupation of Eu2+ and Eu3+ for 4a and 8d sites. The appearance of the energy dependence can be interpreted that Eu ions with different valence prefer different sites in the I 4% 2d structure. The 8d and 4a sites locates on the atomic planes of (4 0 0) and (2 0 0), respectively. And both of them influence the 400 intensity. On the other hand, the 004 intensity has the only contribution from the 4a sites on (0 0 4) (Fig. 2). According to the cation distribution estimated in Chapter 8, both Eu2+ and Eu3+ ions occupy the 8d sites while only Eu3+ does the 4a sites. Therefore, it is reasonable in Fig. 2 that the 400 curve related to both Eu2+ and Eu3+ ions locates at lower energy side than the 004 one with the only Eu3+ ions. Thus, it is clear that the X-ray intensity used in the VDC structural analysis reflects the distribution difference between Eu2+ and Eu3+ ions. The phase transition of Eu3S4 was observed on the temperature-dependent measurements of the X-ray intensity, using the same diffractometry at the BL-10A. The phase transition from a cubic lattice to a tetragonal one was clearly detected in the change of X-ray intensity. Fig. 5 shows the
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Fig. 5. Temperature dependence of 400, 040 and 004 Bragg intensities of Eu3S4. A discontinuity at T ¼ 188:5 K is clearly seen for the 004 reflection.
7. VDC experiments Fig. 4. Energy dependence of normalized integrated intensity for 400 (open circle) and 004 (solid circle) reflections of Eu3S4 measured at Eu LII absorption edge at T ¼ 180 K. The intensity ratio of I(4 0 0)/2I(0 0 4) is also given in cross.
temperature dependence of the reflection intensities for 400, 040 and 004 within the temperature range between 176 and 196 K. There is a clear intensity jump for the 004 reflection at Tc ¼ 188:5 K, which is deeply related to the structural change on the c-axis. The 400 and 004 reflections have almost constant intensities within the above temperature range. The intensity curve related to the a-axis changes smoothly with the tetragonal symmetry. The temperature dependence can be interpreted as reflecting a difference in atomic arrangements between the I 4% 3d and I 4% 2d structures. Namely, the difference is that the Eu sites in the I 4% 3d structure locate near the planes of (4 0 0) and (0 0 4), while the 8d sites of the I 4% 2d structure are far from the (0 0 4). Although, the phase-transition temperature first reported was Tc ¼ 168 K [7], it historically increased higher and higher up to 186 K with purer samples close to the stoichiometric composition [8]. The phase-transition temperature of Tc ¼ 188:5 K is the highest among the reported values.
The crystal-structure determination for the lowtemperature phase gives an interpretation that Eu ions occupy the 4a and/or 8d sites in the tetragonal I 4% 2d structure. The energy-dependence study in the Bragg intensity suggests the existence of a charge ordering. Thus, it is highly expected that the site occupancy of Eu2+ and Eu3+ should be estimated with a close connection of the VDC method. In Eq. (1) on the structure factor, the intensity contribution from a kind of sites is given by a sum of atomic scattering factors for all atoms occupying the sites. In a binary system of Eu2+ and Eu3+ ions averaged in space and time, the mole fraction of a kind of Eu ions gives the occupation for the examined sites, and simultaneously the other kind of Eu ions occupies the remaining part of the same sites. Therefore, the atomic scattering factor for the ions occupying the 4a sites can be written as f4a ¼ 4½xðEu2þ ÞfEu2þ ðsin y=l; EÞ þ xðEu3þ ÞfEu3þ ðsin y=l; EÞ ¼ 4½xðEu2þ ÞfEu2þ ðsin y=l; EÞ þ f1 xðEu2þ ÞgfEu3þ ðsin y=l; EÞ
ð4Þ
within a unit cell, where x(A) is the mole fraction of A ions in the 4a sites and xðEu2þ Þ þ xðEu3þ Þ ¼ 1:
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Similarly, the scattering factor for the 8d sites can be given by f8d ¼ 8½f1 xðEu2þ ÞgfEu2þ ðsin y=l; EÞ þ f2 xðEu3þ ÞgfEu3þ ðsin y=l; EÞ ¼ 8½f1 xðEu2þ ÞgfEu2þ ðsin y=l; EÞ þ f1 þ xðEu2þ ÞgfEu3þ ðsin y=l; EÞ :
ð5Þ
The least-squares calculation needs only one parameter of xðEu2þ Þ to be solved. X-ray intensity measurements for the VDC crystal-structure analysis were made with the spherical crystal (specimen #2) at l ¼ 1:6312 and ( Slightly longer wavelengths from the 1.6298 A. minima of f 0 were selected in order to keep the anomalous scattering effect intense but the absorption effect small. The anomalous scattering factors and linear absorption coefficients are listed in Table 3. The occupancy of Eu2+ and Eu3+ ions was doubly determined with the values of (1) 0 0 fEu and fEu for 2þ ¼ 14:820 3þ ¼ 12:114 0 0 ( l ¼ 1:6312 A and (2) f 2þ ¼ 10:7350 and f 3þ ¼ Eu
Eu
( The charge effect in 13:625 for l ¼ 1:6298 A. total atomic scattering factor is schematically shown in Fig. 6 for the experiment at ( l ¼ 1:6312 A. The intensity data were collected up to 2y ¼ 90 in the o22y step-scan mode with a step-interval of 0.01 in o and a measuring time of 1 s per step. The intensity decreasing of the incident X-rays was monitored and normalized with the intensity variation for a standard reflection at every 50 reflections. The polarization factor was assumed to be unity because the electric vector of the incident beam from the bending magnet is about 100% polarized perpendicular to the scattering plane. The integrated intensity was calculated from the profile data after the background correction. After averaging of 412 and 79 reflections within a half of the reciprocal space, 51 and 18 independent reflections were used for the site-occupancy analysis, respectively. The occupancy parameter was determined in the least-squares calculation based on the synchrotron radiation data, where a scale factor and an extinction parameter were simultaneously refined: R ¼ 0:108; wR ¼ 0:120 and R ¼ 0:106; wR ¼ 0:123 for the analyses at l ¼
Fig. 6. Total atomic scattering factors for Eu2+ and Eu3+ at ( The sin y=l range for the collection of intensity l ¼ 1:6312 A. data is shown by an arrow.
( respectively. The relatively 1:6312 and 1.6298 A, large R-values may be due to the severe absorption. Because of the 2y independence on f 0 ; the least-squares calculation was well converged in the site-occupancy refinement with high confidence. In the estimation on the occupancy parameter, atomic coordinates and anisotropic temperature factors were fixed to the values refined with the Mo Ka data. 8. Determination of site preference of Eu2+ and Eu3+ Associated with two powerful merits of (1) a large f 0 difference between Eu2+ and Eu3+ and (2) a constant value of f 0 through siny=l; the leastsquares calculations on site-occupancy refinements were converged well. In the refinements, the shift/ error value for a variable on the occupancy was smaller than 0.4 106. Two sets of data obtained with different wavelengths (l ¼ 1:6312 and ( gave very similar results as shown in 1.6298 A) Table 4. The results on the site preference of Eu2+ and Eu3+ ions are summarized in Table 4. It is our conclusion that Eu2+ ions do not occupy the 4a
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Table 4 Results of the site preference on Eu2+ and Eu3+ ions ( Wavelength used (A)
1.6312 1.6298
Occupancy in 4a sites
Occupancy in 8d sites
Eu2+
Eu3+
Eu2+
Eu3+
0.04 0.00
0.96 1.00
0.96 1.00
1.04 1.00
( are 70.11 and 70.17 for Eu2+ in 4a sites, respectively. Note: The standard deviations for the refinements on l ¼ 1:6312 and 1.6298 A
sites within the error. The ordering scheme is that the Eu3+ ions occupy the 4a sites, while both Eu2+ and Eu3+ ions occupy the 8d sites in the ratio of 1:1. The chemical formula involving the information on the valence is simply given as [Eu3+]4a[Eu2+Eu3+]8dS4. The cation distribution of Eu2+ and Eu3+ quite resembles such mixedvalence compounds as magnetite and inversespinel compounds. However, it should be emphasized that the charge ordering is quite different from that of the Carter model previously reported. The model was characterized by the full occupation of Eu2+ ions in 4a sites and constructed on the basis of the empirical knowledge that divalent Eu ions are larger than trivalent ones. The ionic ( in radii of Eu2+ and Eu3+ ions are 1.25 and 1.07 A the coordination number of 8, respectively [22]. As described in Chapter 4, the mean Eu–S distance for the 8d sites are about 0.3% larger than that of 4a sites. The small difference in the site size is the reason that the Carter model does not come true. On the other hand, our site-occupancy result is consistent with the fact that larger Eu2+ ions occupy slightly larger 8d sites. In the least-squares calculations, the residuals of SwðjFobs j jFcalc jÞ2 are minimized to fit the best parameters, where Fobs and Fcalc are observed and calculated crystal-structure factors and the weight w is 1=s2F : The variation of residual factors is plotted in Fig. 7 as a function of Eu2+ contents in 4a sites. The curve of the residual factors has a minimum, which locates very close to zero in occupancy of Eu2+ ions on the 4a sites. Thus, it strongly supports that Eu2+ ions do not occupy the 4a sites. The crystal-structure factors were calculated based on the structural parameters of the low-
Fig. 7. Residual factors in the refinements with the Synchro( and T ¼ 180 K, tron X-ray data measured at l ¼ 1:6312 A which are given against the mole ratio of Eu2+ ions occupied in the 4a sites in the I 4% 2d structure.
temperature phase obtained in this study. Table 5 shows the variation of crystal-structure factors against the occupancy of Eu2+ ions in the 4a and 8d sites. A systematic correlation exists between occupancy parameter and reflection intensity. For example, as increasing the Eu2+ contents in the 4a sites, the calculated structure factor of the 400 reflection, F ð4 0 0Þ; decreases systematically, while F (0 0 4) increases. In the observed structure factors, there exists a relation that F ð4 0 0Þ is larger than F (0 0 4). The calculated structure factors for a pair of 400 and 004 reflections fit into the observed ones more and more when it approaches to the condition that Eu2+ does not occupy the 4a sites.
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Table 5 ( Comparison of observed and calculated structure factors for some reflections to be equivalent in cubic symmetry (.e ¼ 1:6312 A) Reflection
400 004 220 202 620 602 206 321 312 213 a
F(obs)
104.2 89.1 122.4 110.6 203.2 170.6 154.9 253.5 222.8 197.6
F(calc)a F(calc) Eu2+ in 4a sites (%)
F(calc)
F(calc)
F(calc)
F(calc)
F(calc)
4
0
20
40
60
80
100
107.2 103.1 101.3 96.1 182.2 178.0 181.6 216.4 218.0 211.9
107.5 102.5 101.6 95.9 182.5 177.9 181.4 216.6 218.3 211.4
105.8 105.7 100.0 96.8 180.8 178.7 182.3 215.7 216.7 213.9
104.1 109.1 98.3 97.6 179.0 179.6 183.2 214.8 215.0 216.4
102.5 112.5 96.7 98.4 177.2 180.5 184.1 213.9 213.4 219.0
100.8 116.1 95.1 99.2 175.5 181.3 185.0 213.1 211.8 221.4
99.2 119.6 93.5 100.1 173.7 182.2 185.9 212.3 210.3 223.9
Final results in refinement.
9. Discussion The determination of the site occupancy for Eu ions resulted the existence of a charge ordering of [Eu3+][Eu2+Eu3+]S4 below Tc ¼ 188:5 K. All Eu2+ and a half of Eu3+ ions occupy the 8d sites in the I 4% 2d crystal structure, while the remaining half of Eu3+ ions occupy the 4a site. It was found that larger Eu2+ ions prefer slightly larger 8d sites, although both sites are surrounded by eight sulfur atoms in the coordination of a distorted cube, respectively. Eu2+ has the outer electronic structure of 4f75d06s2. The 4f7 levels are relatively atomic with the hybridization of d–s electrons. It is well known that Eu2+ has the largest Hund’s-rule coupling in the rare-earth series, where the 5d level is over 1 eV above the final occupied 4f state [23]. On the other hand, the 4f6 levels in Eu3+ cannot hybridize with the d levels (4f65d16s2, total J ¼ 0). It is probably natural that one electron of 4f7 in Eu2+ occupies a part of unoccupied 5d band. Valence mixture with the 5d level between Eu2+ and Eu3+ is important from our experimental results within the temperature range so far examined, where both Eu2+ and Eu3+ equally occupy the 8d sites. The broadening and merging into a single intermediate isomer-shift peak were observed above 228 K, which is consistent with an electron hopping transport model [5]. Our results suggest that even in the low-temperature phase of
Eu3S4, the hopping electrons can move through the lattice via the Eu3+ ions. Then, the extra electron of the Eu2+ ions leads to the hopping due to the localized distortion in the 8d sites of a crystal lattice (small polaron). The arrangement of [Eu3+]4a[Eu2+Eu3+]8dS4 for the low-temperature phase is similar to that of [Fe3+][Fe2+Fe3+]O4 for the room-temperature phase of magnetite with the inverse-spinel structure. In the structural aspect at lower temperature, both Eu2+ and Eu3+ ions exist together in the same kind of crystallographic 8d sites. It means that the charge ordering gives no significant difference in chemical bonding with the nearest neighbors. The circumstance accords with small structural change through the phase transition: Eu– ( Eu–S–Eu=162.2 at 296 K; Eu(8d)– Eu=3.991 A, ( Eu(8d)=3.978 A, Eu(8d)–S–Eu(8d)=162.9 at 180 K. In the crystal structure of the low-temperature phase, the interatomic Eu–S distances are close in occupation of Eu3+ ions to have Eu(8d)– ( and Eu(4a)–S=2.943 A. ( Small differS=2.951 A ence in bond distances between cation sites of 8d and 4a suggests that another type of the charge order transition the phase transition is expected to exist at a lower temperature than Tc ¼ 188:5 K. A ferromagnetic phase transition reported at T ¼ 3:8 K [10] might be one candidate. . Two isomer-shift peaks of Mossbauer spectra of Eu3S4 supports the separation of Eu2+ and Eu3+
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ions below T ¼ 228 K [5]. Since the observation temperature is higher than Tc (=188.5 K), the gradual freezing of electron hopping occurs independently on the crystal-structural change, where the crystal still maintains the Th3P4-type structure. The frequency of hopping can be described as a relaxation time t to exchange the . electrons in the observation of the Mossbauer spectra. Exponential temperature dependence of t was reported with a continuous change through the phase transition. The t values are 1.0107, 3.5 108, 3.5 109, 1.7 109, 8.5 1010 and 3.5 1011 sec at T ¼ 83; 200, 213, 228, 250 and 325 K, respectively [5]. It should be noted that the hopping of electrons still exists at T ¼ 83 K even below the phase-transition temperature of Tc ¼ 188:5 K. On the other hand, the t value of 1.7 109 s at T ¼ 228 K is well compared to the relaxation time of magnetite (t=1.1 109 at 300 K) [24]. The temperature to give the t value of 1.1 109 s for Eu3S4 can be roughly estimated as T ¼ 240 K. It leads to a temperature difference of 60 K on t between the two compounds. And, magnetite transforms into a low-temperature phase at the Verwey temperature Tv ¼ 123 K, having the monoclinic distortion and charge ordering [27–29]. Since the energy barrier to enable the electron hopping is relatively small even in the low-temperature phase so far examined, a new charge ordering between Eu2+ and Eu3+ ions may exist for Eu3S4. In the view of the distribution of valence ions, the low-temperature phase of Eu3S4 can correspond to the room-temperature one of magnetite. It is meaningful that the nature of the phase transition of Eu3S4 is examined to compare with the Verwey transition and to search another phase transition of Eu3S4 around TE60 K. Thus, the search for another phase transition and the explanation of the ferromagnetic phase would become a new frontier in Eu3S4 researches. Because of the technical difficulty to determine accurately the crystal structure below T ¼ 3:8 K, X-ray diffuse scattering study at the relatively higher temperature is indispensable to observe the Huang scattering by the VDC method. Similar gradual freezing of electron hopping was observed in the neutron and X-ray Huang scattering of magnetite [25,26].
10. Conclusion We conclude that an I 4% 3d phase of Eu3S4 transforms to a charge-ordered I 4% 2d phase at Tc ¼ 188:5 K. From the crystal-structure determination with the VDC technique near a Eu LII absorption edge, the existence of a charge ordering was confirmed with the arrangement of [Eu3+]4a[Eu2+Eu3+]8dS4. Namely, all Eu2+ ions mix with a half of Eu3+ in the 8d sites in the I 4% 2d crystal structure, where the remaining Eu3+ ions occupy the 4a sites.
Acknowledgements We thank N. Shibuichi, K. Ohkubo, F. Saito and N. Kita of our group for their experimental help. We also thank Prof. M. Yoshimura of Tokyo Institute of Technology for his valuable discussion. This study was performed under the auspices of the Photon Factory (PAC Nos. 97G169, 99G196) and partly supported by JSPSRFTF96P00205.
References [1] K. Meisel, Z. Anorg. Allg. Chem. 240 (1939) 300. [2] L. Domage, J. Flahaut, M. Guittard, C.R. Acad. Sci. Paris 249 (1959) 697. [3] F. Holtzberg, S. Methfessel, J. Appl. Phys. 37 (1966) 1433. [4] M. Palazzi, S. Jaulmes, Mater. Res. Bull. 13 (1978) 1153. [5] O. Berkooz, M. Malamud, S. Shtrikman, Solid State Commun. 6 (1968) 185. [6] I. Bransky, N.M. Tallan, A.Z. Hed, J. Appl. Phys. 41 (1970) 1787. [7] H.H. Davis, I. Bransky, N.M. Tallan, J. Less-Common Met. 22 (1970) 193. [8] W. Wickelhaus, A. Simon, K.W.H. Stevens, P.J. Brown, K.R.A. Ziebeck, Philos. Mag. B 46 (1982) 115. [9] Y. Konoike, T. Toyoda, K. Yamawaki, S. Sasaki, Proc. Symp. Atomic-Scale Surf. Interf. Dynam. 4 (2000) 437. . [10] E. Gorlich, H.U. Hrynkiewicz, R. Kmie!c, K. Latka, K. Tomala, Phys. Status Solidi B 64 (1974) 147. [11] F.L. Carter, J. Solid State Chem. 5 (1972) 300. [12] O. Massenet, J.M.D. Coey, F. Holtzberg, J. Phys. 37 (1976) C4-297. [13] P.D. Dernier, E. Bucher, L.D. Longinotti, J. Solid State Chem. 15 (1975) 203. [14] R. Pott, G. Guntherodt, . W. Wichelhaus, M. Ohl, H. Bach, Phys. Rev. B 27 (1983) 359.
ARTICLE IN PRESS H. Ohara et al. / Physica B 350 (2004) 353–365 [15] G. Guntherodt, . W. Wichelhaus, Solid State Commun. 39 (1981) 1147. [16] S. Sasaki, Rev. Sci. Instrum. 66 (1995) 1573. [17] B.J. Wuensch, C.T. Prewitt, Z. Kristallogr. 122 (1965) 24. [18] S. Sasaki, KEK Internal, Vol. 87, No. 3, National Laboratory for High-Energy Physics, Tsukuba, Japan, 1987, p. 1. [19] G.R. Screaton (Ed.), Dispersion Relation, Oliver and Boyd, Edinburgh, 1960. [20] J.O. Cross, M. Newville, J.J. Rehr, L.B. Sorensen, C.E. Bouldin, G. Watson, T. Gouder, G.H. Lander, M.I. Bell, Phys. Rev. B 58 (1998) 11215. [21] J.A. Bearden, A.F. Burr, Rev. Mod. Phys. 39 (1967) 125. [22] R.D. Shannon, C.T. Prewitt, Acta Crystallogr. B25 (1969) 925.
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[23] C.M. Varma, Rev. Mod. Phys. 48 (1976) 219. [24] W. Kundig, . R.S. Hargrove, Solid State Commun. 7 (1969) 223. [25] Y. Fujii, G. Shirane, Y. Yamada, Phys. Rev. 11 (1975) 2036. [26] T. Toyada, S. Sasaki, M. Tanaka, Jpn. J. Appl. Phys. 36 (1997) 2247. [27] E.J.W. Verwey, P.W. Haayman, Physica 8 (1941) 979. [28] M. Iizumi, T.F. Koetzle, G. Shirane, S. Chikazumi, M. Matsui, S. Todo, Acta Crystallogr. B38 (1982) 2121. [29] S. Sasaki, T. Toyoda, M. Tanaka, Y. Noda, T. Shobu, N. Ikeda, Proceedings of the Eighth International Conference on Ferrites. (ICF-8), 2000, Japan, Japan Society of Powder and Powder Metals, 2000, p. 135.
Physica B 350 (2004) 353–365
Charge ordering in Eu3S4 determined by the valence-difference contrast of synchrotron X-ray diffraction Hiroki Oharaa,1, Satoshi Sasakia,*, Yukiko Konoikea,2, Takeshi Toyodaa,3, Kouji Yamawakia, Masahiko Tanakab a
Materials and Structure Laboratory, Tokyo Institute of Technology, Nagatsuta 4259, Midori-ku, Yokohama 226-8503, Japan b Photon Factory, Institute of Materials Structure Science, KEK, Oho 1-1, Tsukuba 305-0801, Japan Received 20 January 2004; accepted 26 April 2004
Abstract Synchrotron X-ray diffraction study for single crystals of Eu3S4 has revealed that a Th3P4-type I 4% 3d structure transforms to a charge-ordered I 4% 2d one at Tc ¼ 188:5 K. The crystal structures of Eu3S4 at T ¼ 300; 180 and 160 K were determined in the least-squares refinements with the Mo Ka intensity data. The valence-difference contrast method was applied at the LII absorption edge of Eu, utilizing a large difference in anomalous scattering factors between Eu2+ and Eu3+. The cation distribution of Eu2+ and Eu3+ was determined by crystal-structure analyses based on the ( intensity data collected at two wavelengths of l ¼ 1:6312 and 1.6298 A.The least-squares structural refinements suggest that the most plausible atomic arrangement is [Eu3+]4a[Eu2+Eu3+]8dS4. The charge-ordering scheme is that a half of Eu3+ ions occupy the whole 4a sites in the I 4% 2d crystal structure, while the remaining half of Eu3+ ions mix with Eu2+ in the 8d sites. The scheme is also supported by the energy dependence of Bragg intensities for 400 and 004 reflections. r 2004 Elsevier B.V. All rights reserved. PACS: 61.10.Nz; 61.66.Fn; 61.50.Ks; 78.70.Ck Keywords: Charge ordering; Valence contrast; Eu3S4; Mixed-valence compound; X-ray anomalous scattering; Synchrotron radiation
1. Introduction *Corresponding author. Tel.: +81-45-924-5308; fax: +8145-924-5339. E-mail address: [email protected] (S. Sasaki). 1 Present address: Semiconductor Energy Laboratory, Co. Ltd., Atsugi 243-0036, Japan. 2 Present address: Fujitsu System Solutions, Ltd., Honkomagome, Tokyo 113-0021, Japan. 3 Present address: Industrial Research Institute of Ishikawa, Kanazawa 920-8203, Japan.
A mixed-valence compound Eu3S4 has divalent Eu2+ (4f 7 5s2 5p6 6s2 ; S ¼ 7=2; L ¼ 0; J ¼ 7=2) and trivalent Eu3+ (4f 6 5s2 5p6 5d1 6s2 ; S ¼ L ¼ 3; J ¼ 0) ions in the ratio 1:2 and is recognized as a unique system including divalent rare-earth ions. The room-temperature phase has a Th3P4 structure, as shown in Fig. 1, where all Eu ions occupy a kind of crystallographic site in a BCC lattice
0921-4526/$ - see front matter r 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.physb.2004.04.072
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Fig. 1. (a) Projection and (b) schematic drawing of the crystal structure of a room-temperature phase of Eu3S4 (Th3P4-type structure). Solid circle=Eu, open circle=S. The heights of atoms along the a3-axis are given by integer after multiplied by 100. The bond distances ( for Eu polyhedron are given in A.
[1–4]. The cell dimension and space group are ( and I 4% 3d; respectively. Eu3S4 has the a ¼ 8:516 A transport property as intrinsic semiconductor by a hopping of 4f electrons between adjacent Eu sites. The origin of the hopping motion of charge carriers is considered as either thermally activated drift mobility or electron tunneling, based on the observations of different isomer shift in . Mossbauer spectra [5] and constant charge carrier concentration [6]. Eu3S4 has a non-magnetic phase transition at the temperature of 175 or 168 K, which was reported from the measurements of the electrical conductivity and Seebeck coefficients [6,7]. The exact temperature of the phase transition is considered to depend on the purity of the sample. A maximum temperature of Tc ¼ 185 K [8] or 188.5 K [9] was observed for purer single crystals synthesized by the chemical vapor deposition (CVD) technique with more stoichiometric composition. There is a report on the M.ossbauer experiments that Eu3S4 becomes ferromagnetic below Tc ¼ 3:8 K by freezing the 4f configuration [10]. . In Mossbauer spectra of 151Eu3S4 below T ¼ 210 K, two absorption peaks were observed and interpreted as electron hopping between Eu2+
and Eu3+ ions [5]. X-ray powder diffraction study found a cubic to tetragonal phase transition, having a 0.4% distortion in the ratio of a=c in the low-temperature phase [7]. Based on an approach to derive from the Th3P4 structure and construct a charge-ordering model between Eu2+ and Eu3+, a tetragonal cell was proposed with the I 4% 2d crystal structure, where Eu2+ occupies the 4a sites, Eu3+ occupies the 8d sites and S does the 16e sites (Carter model) [11]. From the study on the temperature-independent susceptibility, Eu3S4 was suggestively considered to have partial charge ordering of Eu2+ and Eu3+ and to be interpretable as a simple sum of Van Vleck-type Eu3+ and Curie–Weiss-type Eu2+ [12]. On the other hand, based on the analogy of the similar compounds such as La3S4, La3Se4, Pr3S4 and Pr3Se4, the firstorder transition was proposed for Eu3S4 [13]. The existence of the first-order transition at Tc ¼ 186 K in Eu3S4 was supported by the measurement of the configuration entropy [14]. In the Raman scattering study, any new phonon mode was not observed for single crystals of Eu3S4, which is inconsistent with the charge order–disorder transition [15].
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Thus, the occurrence of the charge ordering in Eu3S4 still remains in dispute. The valenceselective structure determination would be the best way to examine the charge order–disorder mechanism [16]. In this paper, we first determine the crystal structure of a low-temperature phase of Eu3S4 because of the lack of the crystal-structure data. Then, the cation distribution of Eu2+ and Eu3+ of low-temperature phase will be determined by the recent developed technique, which utilizes the valence contrast in X-ray anomalous scattering.
2. Sample Powder crystals of Eu3S4 were prepared by reacting stoichiometric proportions of EuS (Soekawa Rikagaku Co. Ltd., 99.9%) and sulfur (Wako Pure Chemical Industries, Ltd., 99.9999%) in an evacuated silica capsule at 1073 K for 4 days. Single crystals of Eu3S4 were synthesized from the powder sample with 0.06 g NH4I flux by the vapor growth. The starting materials were put on an end of 165 mm silica tube, NH4I flux was placed in the middle of the silica tube with oliphis (30 mm in diameter) and single crystals were grown at the other end of the silica tube. The evacuated silica tube as preheated at 673 K and kept in vapor growth between 923 and 973 K for 9 days. Single crystals having dimensions up to 0.2 mm were successfully obtained.
3. Conventional X-ray measurements X-ray single-crystal diffraction experiments were first carried out using a conventional Rigaku AFC5 four-circle diffractometer. Mo Ka radiation ( was used after monochromatized (l ¼ 0:7107 A) by graphite (0 0 2). Each of two single crystals was mounted on the glass fiber and used for X-ray studies: one is a parallel-piped crystal having the dimensions of 140 85 50 mm3 (specimen #1) and the other is a spherical crystal of 60 mm in diameter (specimen #2). Low-temperature experiments were performed with the Oxford Cryostream Cooler, where cold
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and dry nitrogen gas is directly blown onto the crystal. The temperature at the sample position was calibrated using two sets of chromel-constantan thermocouple wires. The temperature was controlled within 71 K during the intensity measurements. In order to avoid the formation of twinning, the cooling operation was accomplished in the magnetic field of 1.5 T along the [0 0 1] direction of Eu3S4, by using a pair of rareearth magnet. The integrated intensity data were collected up to 2y ¼ 90 , in the o22y scan mode with maximum five scans. The scan speeds in intensity measurements were 0.5 /min for specimen #2 and 1 /min for specimen #1. The scan width was 1.2+0.3 tan y in o: The experimental conditions for X-ray measurements are summarized as follows: (1) specimen #1, measured at T ¼ 296 K in one-eighth of reciprocal space; the number of reflections measured, Nm ¼ 1444 and the number of reflections averaged and used in refinements, Na ¼ 199; (2) specimen #2, at T ¼ 296 K in a hemisphere; Nm ¼ 5300 and Na ¼ 181; (3) specimen #1, at T ¼ 180 K in one-eighth space; Nm ¼ 5305 and Na ¼ 507; (4) specimen #2, at T ¼ 160 K in a hemisphere, Nm ¼ 2357 and Na ¼ 205: The fluctuations in the integrated intensities for three standard reflections were held less than 71.4%, 74.0% and 74.0% during the data collections at 296, 180 and 160 K, respectively. The Lorentz-polarization and absorption effects were corrected. A linear absorption coefficient is 30.5 mm1 for the Mo Ka radiation. Since specimen #1 is not a spherical crystal, the absorption correction was made by the grid-integration method for the arbitrary-shape crystal [17]. The calculation software called ACACA was installed in a full matrix least-squares program of RADY [18] and used for this purpose. In the absorption correction for specimen #1 the transmitted factor ranges from 0.056 to 0.107.
4. Crystal structures of Eu3S4 The room-temperature phase of Eu3S4 was reconfirmed to be the BCC Th3P4 structure with the space group of I 4% 3d (Fig. 1). The cell
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( at T ¼ 296 K. dimension was a ¼ 8:53470:003 A Final structural parameters and bond distances are listed in Table 1. Only x-coordinate of sulfur (u parameter) is a variable among positional parameters. The u parameter obtained in this study was 0.0713, which was comparable with the reported value (u ¼ 0:0721) [4]. It gives a slight deviation from an ideal Th3P4 structure (u ¼ 1=12=0.0833). The crystal structure of Th3P4 is well approximated as the octahedral configuration with the FCC structure of NaCl. A kind of Eu ion exists in the 12a site, having a 4% inversion axis without a center of symmetry. A Eu ion is coordinated by eight sulfur ions in a distorted cube. The Eu–S distances estimated in ( which are this study are 2.846 and 3.068 A, indicated with the respective bonds in Fig. 1. In the other view from anions, a sulfur ion is coordinated by six Eu ions.
Table 1 Atomic parameters and bond distances for a room-temperature phase of Eu3S4 #1
#2
Eu (12a) b11 b22 ( 2) Bequiv: (A
0.00315(5) 0.00251(3) 0.793(7)
0.00231(5) 0.00151(3) 0.517(8)
S (16c) X b11 b12 ( 2) Bequiv: (A
0.0713(5) 0.00428(9) 0.0004(1) 1.248(9)
0.0713(6) 0.0038(1) 0.0000(1) 1.10(1)
R factor Weighted R factor
0.029 0.041
0.054 0.052
Bond distances ( Eu–S (A) ( Eu–S (A) ( Eu–Eu (A) ( S–S (A) ( S–S (A)
2.846(1) 3.068(1) 3.991(1) 3.284(2) 3.695(3)
Note: The standard deviation is given for the last digit in parenthesis. Eu sites: x ¼ 3=8; y ¼ 0; z ¼ 1=8; b22 ¼ b33 ; b12 ¼ b13 ¼ b23 ¼ 0: S sites: x ¼ y ¼ z; b11 ¼ b22 ¼ b33 ; b12 ¼ b13 ¼ b23 :
In the early 1970s, the X-ray data for chargeordered Eu3S4 or Sm3S4 taken at low temperature were interpreted as a tentative tetragonal structure derived from the Th3P4 one, where the c=a ratio ( and c ¼ 8:539 A ( [7]. was 1.004 with a ¼ 8:505 A From the theoretical study on cation-vacancy ordering in the Th3P4 structure, the tetragonal structural model was in accordance with the space group of I 4% 2d or I 4% [11]. The calculation of Madelung potentials preferred the I 4% 2d structural model, taking into account the ionic size increased when divalent cations occupy the 4a sites. A recent single-crystal X-ray diffraction study has confirmed the tetragonal deformation from the observation of the discontinuity in Bragg intensity at the phase transition of Eu3S4 [9]. The crystal structure of the low-temperature phase of Eu3S4 was determined for the first time in this study by the X-ray single-crystal diffraction method. The crystal symmetry was tetrahedral with a space group of I 4% 2d: The cell dimensions ( and c ¼ 8:51470:002 A ( were a ¼ 8:50870:001 A at T ¼ 180 K. The crystal structure of the lowtemperature phase can be well represented with the I 4% 2d structure proposed by Carter [11]. Table 2 shows the final atomic parameters of Eu3S4 at 180 and 160 K, determined by the crystal structure analyses with the Mo Ka diffraction data. The schematic projection of the crystal structure for the low-temperature phase is shown in Fig. 2. Both Eu sites are coordinated by eight sulfur ions. The 4a sites distributes like the diamond structure. The interatomic distances on Eu–S are given in Fig. 2 for two kinds of non-equivalent Eu sites: 4a and 8d sites. The Eu–S bond distances are 2.852 ( for the 4a polyhedron, which are well and 3.033 A ( for the polycompared with 2.846 and 3.068 A hedron of the room-temperature phase, respectively. The EuS8 polyhedron is more distorted through the phase transition, where the Eu–S bonds shrink with 0.2% shorter for the shorter bond and extend 1.2% longer for the longer bond. The 8d sites are surrounded with eight sulfur atoms, too. The EuS8 polyhedron is similar to the distorted cube of the room-temperature phase. When the temperature decreases through the phase transition, four shorter Eu–S bonds in Eu– ( extend a little and split into two bonds S=2.846 A
ARTICLE IN PRESS H. Ohara et al. / Physica B 350 (2004) 353–365 Table 2 Atomic parameters for a low-temperature phase of Eu3S4 Temperature (K)
#1 180
#2 160
Eu (4a) b11 b33 ( 2) Bequiv: (A
0.00325(5) 0.00363(8) 0.98(1)
0.00178(9) 0.0013(1) 0.47(2)
Eu (8d) X b11 b22 b33 b23 ( 2) Bequiv: (A
0.3755(3) 0.00348(6) 0.00331(6) 0.00363(4) 0.00018(5) 0.96(2)
0.3749(3) 0.0019(1) 0.0023(1) 0.00128(7) 0.00003(8) 0.53(3)
S (16e) X Y Z b11 b22 b33 b12 b13 b23 ( 2) Bequiv: (A
0.572 (1) 0.823 (1) 0.449 (1) 0.0053(3) 0.0060(3) 0.0077(3) 0.0007(2) 0.0016(2) 0.0005(2) 1.84(8)
0.573(1) 0.823(1) 0.448(1) 0.0064(5) 0.0045(4) 0.0033(3) 0.0023(3) 0.0014(3) 0.0011(3) 1.4(1)
R factor Weighted R factor
0.073 0.082
0.047 0.050
4a sites: x ¼ y ¼ z ¼ 0; b11 ¼ b22 ; b12 ¼ b13 ¼ b23 ¼ 0: 8d sites: y ¼ 1=4; z ¼ 1=8; b12 ¼ b13 ¼ 0:
( while the other four bonds of of 2.849 and 2.864 A, ( split into 3.042 and 3.047 A. ( The mean 3.068 A ( is 0.2% shorter Eu–S distance estimated as 2.951 A ( of room-temperature phase. than 2.957 A ( The mean Eu–S distance for 4a sites is 2.943 A, which is about 0.3% shorter than that of the 8d sites. As mentioned from the above structural view, there is no drastic change between low- and room-temperature phases in the size of the sites occupied by cations. It suggests that the cation distribution of Eu2+ and Eu3+ ions cannot be estimated from the only information on the crystal structure. Now, our study requires introducing the valence-difference contrast (VDC) method in order to discuss the charge ordering in the I 4% 2d structure.
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5. Valence-difference contrast X-ray scattering power within a Bragg peak at the hkl reciprocal lattice point is kinematically given by a square of the crystal-structure factor. The structure factor can be written as Fhkl ¼ Sj fj expf2piðhxj þ kyj þ lzj Þ;
ð1Þ
where xj ; yj and zj are the fractional coordinates of the jth atom and fj is the atomic scattering factor. In the VDC method, the atomic scattering factor must be different between two kinds of cation in different valence states. The valence difference on the effect of X-ray anomalous scattering becomes dominant at the absorption edge by a chemical shift between different oxidation states [16]. In the dominant condition near the absorption edge, the atomic scattering factor for an X-ray energy E can be given by f ðsin y=l; EÞ ¼ f0 ðsin y=lÞ þ f 0 ðEÞ þ if 00 ðEÞ;
ð2Þ
where l and y are the wavelength and a half of scattering angle, respectively, and f0 ; f 0 and f 00 are the Thomson elastic scattering term and real and imaginary terms of anomalous scattering factor, respectively. The strong contrast at the absorption edge makes the cation distinguish because of the large difference in f 0 ðEÞ: The f 00 ðEÞ term is generally estimated from the absorption spectra of the X-ray absorption near-edge structure (XANES). The f 0 ðEÞ and f 00 ðEÞ values have the relation of Kramers–Kronig’s dispersion, where one of them can be transformed from the other (e.g., Ref. [19]): Z N f 0 ðoÞ ¼ ð2=pÞ fo0 f 00 ðo0 Þ½o2 ðo0 Þ2 1 g do0 ; 0
ð3Þ 0
where o and o are angular frequency. The program DIFFKK [20] was used in this study to calculate the experimental-base f 0 values from the f 00 ones, by using Eq. (3) and the theoretical approximation on unobserved f 0 : Synchrotron experiments to measure the XANES spectra were performed at the beamline BL-3A of the Photon Factory. The X-rays were monochromatized by the Si(1 1 1) double-crystal monochromator. The absorption measurements
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Fig. 2. (a) Projection and (b) schematic drawing of the crystal structure of a low-temperature phase of Eu3S4. Solid circle=Eu(4a), hatched circle=Eu(8d), open circle=S. The heights of atoms along the c-axis are given by integer after multiplied by 100. The bond ( for Eu(4a) and Eu(8d) polyhedra are given only for independent bonds. All standard deviations for Eu–S distances in this distances [A] ( The other characteristic distances are: Eu(4a)I–Eu(8d)II=3.980(1) A; ( Eu(4a)I–Eu(8d)III=3.983(2) A; ( figure are equal to 70.009 A. ( Eu(8d)III–Eu(8d)IV=3.978(2) A.
were made at the Eu LII edge with two ionization chambers with N2 (monitor) and 75% N2+25% Ar gas. A reason to use the LII edge was that the diffraction experiment at Eu LIII (E ¼ 6:980 keV) was beyond its ability on the monochromator angle in the beamline BL-10A. The beam size was 1 2 mm2. A thickness of samples was adjusted for the suitable absorption, where two or three sheets of transparent tape were piled up. The incident and absorbed intensities were measured at a measuring time of 30 s for 851 steps of the monochromator angle with variable step-widths from 0.2 to 11 eV. The energy calibration on Eu LII edge was carefully made, by using an iron metal foil of 5 mm in thickness at the Fe Kabsorption edge. The first inflection point of the Fe foil was assigned to be E ¼ 7:112 keV [21,16]. X-ray energy in keV was converted to wavelength ( with a factor of 12.3985. in A Powder samples of EuS and Eu2O3 (Koch Chemical Ltd., 99.9%) were used as standards of Eu2+ and Eu3+ spectra, respectively. Fig. 3(a) shows f 00 curves estimated from the XANES spectra observed for EuS (cubic, NaCl structure) and Eu2O3 (cubic, bixbyite structure) at the Eu LII absorption edge. A chemical shift of 7 eV was
clearly observed between Eu2+ (E ¼ 7:601 keV) and Eu3+ (E=7.608 keV). Fig. 3(b) shows the energy-dependence curves of f 0 ; which were calculated through the Kramers–Kronig transformation. There is a sharp negative peak in each of f 0 curves of Eu2+ and Eu3+, corresponding to the individual absorption edge. Two typical wave( (E ¼ 7:6010 keV) and lengths of l ¼ 1:6312 A ( (E ¼ 7:6075 keV) were selected for our 1.6298 A crystal-structure study with the VDC technique. As the resolving power in VDC depends on the difference in f 0 ; the wavelengths to have the f 0 values in the opposite sign were chosen to examine the validity of the valence estimation. Anomalous scattering factors of Eu2+ and Eu3+ for the two wavelengths are summarized in Table 3. For example, the f 0 values for Eu2+ and Eu3+ have a remarkably large difference between –2.706 and ( +2.890 at wavelengths of 1.6312 and 1.6298 A, respectively. Since f 0 is independent on the scattering angles (or sin y=l), the VDC gives more powerful contrast for the higher-order reflection with higher scattering angle. Thus, the VDC technique with sufficient number of reflections promises the accurate determination of the site occupancy for Eu2+ and Eu3+ ions.
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Table 3 Scattering factors and absorption coefficients for Eu ions at wavelengths near Eu LII absorption edge ( Wavelength l (A) Energy E (keV)
1.6312 7.6010
Anomalous scattering factors Real part f0 (Eu2+) 14.820 f0 (Eu3+) 12.114 0.334 f0 (S) f0 (Eu2+)f0 (Eu3+) 2.706 Imaginary part f00 (Eu2+) f00 (Eu3+)
11.224 10.180
Atomic absorption coefficients ma (Eu2+) (mm2) 1.03 1015 3+ 2 ma (Eu ) (mm ) 0.93 1015 Linear absorption coefficients m (mm1) 200.8
Fig. 3. Anomalous scattering factors of Eu2+ and Eu3+ ions in the vicinity of Eu LII absorption edge: (a) imaginary part, f 00 ; obtained from XANES absorption spectra and (b) real part, f 0 ; transformed by the Kramers–Kronig relation. The dE gives a chemical shift of 7 eV between the different valence states of Eu ions.
6. Energy and temperature dependence of Bragg intensity The existence of the VDC was verified by the measurements of Bragg intensity of Eu3S4 at the Eu LII edge and T ¼ 180 K. Fig. 4 shows the energy dependence of diffraction intensities measured for 400 and 004 reflections by using a vertical-type four-circle diffractometer at BL-10A. There is a double negative peak, which has a deep valley and a shallow hollow on the energydependent intensity curves. A chemical shift of about 2 eV was observed between the curves for
1.6298 7.6075
10.735 13.625 0.334 +2.890
13.417 11.121
1.23 1015 1.02 1015
225.3
400 and 004 reflections, which indicates a difference in occupation of Eu2+ and Eu3+ for 4a and 8d sites. The appearance of the energy dependence can be interpreted that Eu ions with different valence prefer different sites in the I 4% 2d structure. The 8d and 4a sites locates on the atomic planes of (4 0 0) and (2 0 0), respectively. And both of them influence the 400 intensity. On the other hand, the 004 intensity has the only contribution from the 4a sites on (0 0 4) (Fig. 2). According to the cation distribution estimated in Chapter 8, both Eu2+ and Eu3+ ions occupy the 8d sites while only Eu3+ does the 4a sites. Therefore, it is reasonable in Fig. 2 that the 400 curve related to both Eu2+ and Eu3+ ions locates at lower energy side than the 004 one with the only Eu3+ ions. Thus, it is clear that the X-ray intensity used in the VDC structural analysis reflects the distribution difference between Eu2+ and Eu3+ ions. The phase transition of Eu3S4 was observed on the temperature-dependent measurements of the X-ray intensity, using the same diffractometry at the BL-10A. The phase transition from a cubic lattice to a tetragonal one was clearly detected in the change of X-ray intensity. Fig. 5 shows the
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Fig. 5. Temperature dependence of 400, 040 and 004 Bragg intensities of Eu3S4. A discontinuity at T ¼ 188:5 K is clearly seen for the 004 reflection.
7. VDC experiments Fig. 4. Energy dependence of normalized integrated intensity for 400 (open circle) and 004 (solid circle) reflections of Eu3S4 measured at Eu LII absorption edge at T ¼ 180 K. The intensity ratio of I(4 0 0)/2I(0 0 4) is also given in cross.
temperature dependence of the reflection intensities for 400, 040 and 004 within the temperature range between 176 and 196 K. There is a clear intensity jump for the 004 reflection at Tc ¼ 188:5 K, which is deeply related to the structural change on the c-axis. The 400 and 004 reflections have almost constant intensities within the above temperature range. The intensity curve related to the a-axis changes smoothly with the tetragonal symmetry. The temperature dependence can be interpreted as reflecting a difference in atomic arrangements between the I 4% 3d and I 4% 2d structures. Namely, the difference is that the Eu sites in the I 4% 3d structure locate near the planes of (4 0 0) and (0 0 4), while the 8d sites of the I 4% 2d structure are far from the (0 0 4). Although, the phase-transition temperature first reported was Tc ¼ 168 K [7], it historically increased higher and higher up to 186 K with purer samples close to the stoichiometric composition [8]. The phase-transition temperature of Tc ¼ 188:5 K is the highest among the reported values.
The crystal-structure determination for the lowtemperature phase gives an interpretation that Eu ions occupy the 4a and/or 8d sites in the tetragonal I 4% 2d structure. The energy-dependence study in the Bragg intensity suggests the existence of a charge ordering. Thus, it is highly expected that the site occupancy of Eu2+ and Eu3+ should be estimated with a close connection of the VDC method. In Eq. (1) on the structure factor, the intensity contribution from a kind of sites is given by a sum of atomic scattering factors for all atoms occupying the sites. In a binary system of Eu2+ and Eu3+ ions averaged in space and time, the mole fraction of a kind of Eu ions gives the occupation for the examined sites, and simultaneously the other kind of Eu ions occupies the remaining part of the same sites. Therefore, the atomic scattering factor for the ions occupying the 4a sites can be written as f4a ¼ 4½xðEu2þ ÞfEu2þ ðsin y=l; EÞ þ xðEu3þ ÞfEu3þ ðsin y=l; EÞ ¼ 4½xðEu2þ ÞfEu2þ ðsin y=l; EÞ þ f1 xðEu2þ ÞgfEu3þ ðsin y=l; EÞ
ð4Þ
within a unit cell, where x(A) is the mole fraction of A ions in the 4a sites and xðEu2þ Þ þ xðEu3þ Þ ¼ 1:
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Similarly, the scattering factor for the 8d sites can be given by f8d ¼ 8½f1 xðEu2þ ÞgfEu2þ ðsin y=l; EÞ þ f2 xðEu3þ ÞgfEu3þ ðsin y=l; EÞ ¼ 8½f1 xðEu2þ ÞgfEu2þ ðsin y=l; EÞ þ f1 þ xðEu2þ ÞgfEu3þ ðsin y=l; EÞ :
ð5Þ
The least-squares calculation needs only one parameter of xðEu2þ Þ to be solved. X-ray intensity measurements for the VDC crystal-structure analysis were made with the spherical crystal (specimen #2) at l ¼ 1:6312 and ( Slightly longer wavelengths from the 1.6298 A. minima of f 0 were selected in order to keep the anomalous scattering effect intense but the absorption effect small. The anomalous scattering factors and linear absorption coefficients are listed in Table 3. The occupancy of Eu2+ and Eu3+ ions was doubly determined with the values of (1) 0 0 fEu and fEu for 2þ ¼ 14:820 3þ ¼ 12:114 0 0 ( l ¼ 1:6312 A and (2) f 2þ ¼ 10:7350 and f 3þ ¼ Eu
Eu
( The charge effect in 13:625 for l ¼ 1:6298 A. total atomic scattering factor is schematically shown in Fig. 6 for the experiment at ( l ¼ 1:6312 A. The intensity data were collected up to 2y ¼ 90 in the o22y step-scan mode with a step-interval of 0.01 in o and a measuring time of 1 s per step. The intensity decreasing of the incident X-rays was monitored and normalized with the intensity variation for a standard reflection at every 50 reflections. The polarization factor was assumed to be unity because the electric vector of the incident beam from the bending magnet is about 100% polarized perpendicular to the scattering plane. The integrated intensity was calculated from the profile data after the background correction. After averaging of 412 and 79 reflections within a half of the reciprocal space, 51 and 18 independent reflections were used for the site-occupancy analysis, respectively. The occupancy parameter was determined in the least-squares calculation based on the synchrotron radiation data, where a scale factor and an extinction parameter were simultaneously refined: R ¼ 0:108; wR ¼ 0:120 and R ¼ 0:106; wR ¼ 0:123 for the analyses at l ¼
Fig. 6. Total atomic scattering factors for Eu2+ and Eu3+ at ( The sin y=l range for the collection of intensity l ¼ 1:6312 A. data is shown by an arrow.
( respectively. The relatively 1:6312 and 1.6298 A, large R-values may be due to the severe absorption. Because of the 2y independence on f 0 ; the least-squares calculation was well converged in the site-occupancy refinement with high confidence. In the estimation on the occupancy parameter, atomic coordinates and anisotropic temperature factors were fixed to the values refined with the Mo Ka data. 8. Determination of site preference of Eu2+ and Eu3+ Associated with two powerful merits of (1) a large f 0 difference between Eu2+ and Eu3+ and (2) a constant value of f 0 through siny=l; the leastsquares calculations on site-occupancy refinements were converged well. In the refinements, the shift/ error value for a variable on the occupancy was smaller than 0.4 106. Two sets of data obtained with different wavelengths (l ¼ 1:6312 and ( gave very similar results as shown in 1.6298 A) Table 4. The results on the site preference of Eu2+ and Eu3+ ions are summarized in Table 4. It is our conclusion that Eu2+ ions do not occupy the 4a
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Table 4 Results of the site preference on Eu2+ and Eu3+ ions ( Wavelength used (A)
1.6312 1.6298
Occupancy in 4a sites
Occupancy in 8d sites
Eu2+
Eu3+
Eu2+
Eu3+
0.04 0.00
0.96 1.00
0.96 1.00
1.04 1.00
( are 70.11 and 70.17 for Eu2+ in 4a sites, respectively. Note: The standard deviations for the refinements on l ¼ 1:6312 and 1.6298 A
sites within the error. The ordering scheme is that the Eu3+ ions occupy the 4a sites, while both Eu2+ and Eu3+ ions occupy the 8d sites in the ratio of 1:1. The chemical formula involving the information on the valence is simply given as [Eu3+]4a[Eu2+Eu3+]8dS4. The cation distribution of Eu2+ and Eu3+ quite resembles such mixedvalence compounds as magnetite and inversespinel compounds. However, it should be emphasized that the charge ordering is quite different from that of the Carter model previously reported. The model was characterized by the full occupation of Eu2+ ions in 4a sites and constructed on the basis of the empirical knowledge that divalent Eu ions are larger than trivalent ones. The ionic ( in radii of Eu2+ and Eu3+ ions are 1.25 and 1.07 A the coordination number of 8, respectively [22]. As described in Chapter 4, the mean Eu–S distance for the 8d sites are about 0.3% larger than that of 4a sites. The small difference in the site size is the reason that the Carter model does not come true. On the other hand, our site-occupancy result is consistent with the fact that larger Eu2+ ions occupy slightly larger 8d sites. In the least-squares calculations, the residuals of SwðjFobs j jFcalc jÞ2 are minimized to fit the best parameters, where Fobs and Fcalc are observed and calculated crystal-structure factors and the weight w is 1=s2F : The variation of residual factors is plotted in Fig. 7 as a function of Eu2+ contents in 4a sites. The curve of the residual factors has a minimum, which locates very close to zero in occupancy of Eu2+ ions on the 4a sites. Thus, it strongly supports that Eu2+ ions do not occupy the 4a sites. The crystal-structure factors were calculated based on the structural parameters of the low-
Fig. 7. Residual factors in the refinements with the Synchro( and T ¼ 180 K, tron X-ray data measured at l ¼ 1:6312 A which are given against the mole ratio of Eu2+ ions occupied in the 4a sites in the I 4% 2d structure.
temperature phase obtained in this study. Table 5 shows the variation of crystal-structure factors against the occupancy of Eu2+ ions in the 4a and 8d sites. A systematic correlation exists between occupancy parameter and reflection intensity. For example, as increasing the Eu2+ contents in the 4a sites, the calculated structure factor of the 400 reflection, F ð4 0 0Þ; decreases systematically, while F (0 0 4) increases. In the observed structure factors, there exists a relation that F ð4 0 0Þ is larger than F (0 0 4). The calculated structure factors for a pair of 400 and 004 reflections fit into the observed ones more and more when it approaches to the condition that Eu2+ does not occupy the 4a sites.
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Table 5 ( Comparison of observed and calculated structure factors for some reflections to be equivalent in cubic symmetry (.e ¼ 1:6312 A) Reflection
400 004 220 202 620 602 206 321 312 213 a
F(obs)
104.2 89.1 122.4 110.6 203.2 170.6 154.9 253.5 222.8 197.6
F(calc)a F(calc) Eu2+ in 4a sites (%)
F(calc)
F(calc)
F(calc)
F(calc)
F(calc)
4
0
20
40
60
80
100
107.2 103.1 101.3 96.1 182.2 178.0 181.6 216.4 218.0 211.9
107.5 102.5 101.6 95.9 182.5 177.9 181.4 216.6 218.3 211.4
105.8 105.7 100.0 96.8 180.8 178.7 182.3 215.7 216.7 213.9
104.1 109.1 98.3 97.6 179.0 179.6 183.2 214.8 215.0 216.4
102.5 112.5 96.7 98.4 177.2 180.5 184.1 213.9 213.4 219.0
100.8 116.1 95.1 99.2 175.5 181.3 185.0 213.1 211.8 221.4
99.2 119.6 93.5 100.1 173.7 182.2 185.9 212.3 210.3 223.9
Final results in refinement.
9. Discussion The determination of the site occupancy for Eu ions resulted the existence of a charge ordering of [Eu3+][Eu2+Eu3+]S4 below Tc ¼ 188:5 K. All Eu2+ and a half of Eu3+ ions occupy the 8d sites in the I 4% 2d crystal structure, while the remaining half of Eu3+ ions occupy the 4a site. It was found that larger Eu2+ ions prefer slightly larger 8d sites, although both sites are surrounded by eight sulfur atoms in the coordination of a distorted cube, respectively. Eu2+ has the outer electronic structure of 4f75d06s2. The 4f7 levels are relatively atomic with the hybridization of d–s electrons. It is well known that Eu2+ has the largest Hund’s-rule coupling in the rare-earth series, where the 5d level is over 1 eV above the final occupied 4f state [23]. On the other hand, the 4f6 levels in Eu3+ cannot hybridize with the d levels (4f65d16s2, total J ¼ 0). It is probably natural that one electron of 4f7 in Eu2+ occupies a part of unoccupied 5d band. Valence mixture with the 5d level between Eu2+ and Eu3+ is important from our experimental results within the temperature range so far examined, where both Eu2+ and Eu3+ equally occupy the 8d sites. The broadening and merging into a single intermediate isomer-shift peak were observed above 228 K, which is consistent with an electron hopping transport model [5]. Our results suggest that even in the low-temperature phase of
Eu3S4, the hopping electrons can move through the lattice via the Eu3+ ions. Then, the extra electron of the Eu2+ ions leads to the hopping due to the localized distortion in the 8d sites of a crystal lattice (small polaron). The arrangement of [Eu3+]4a[Eu2+Eu3+]8dS4 for the low-temperature phase is similar to that of [Fe3+][Fe2+Fe3+]O4 for the room-temperature phase of magnetite with the inverse-spinel structure. In the structural aspect at lower temperature, both Eu2+ and Eu3+ ions exist together in the same kind of crystallographic 8d sites. It means that the charge ordering gives no significant difference in chemical bonding with the nearest neighbors. The circumstance accords with small structural change through the phase transition: Eu– ( Eu–S–Eu=162.2 at 296 K; Eu(8d)– Eu=3.991 A, ( Eu(8d)=3.978 A, Eu(8d)–S–Eu(8d)=162.9 at 180 K. In the crystal structure of the low-temperature phase, the interatomic Eu–S distances are close in occupation of Eu3+ ions to have Eu(8d)– ( and Eu(4a)–S=2.943 A. ( Small differS=2.951 A ence in bond distances between cation sites of 8d and 4a suggests that another type of the charge order transition the phase transition is expected to exist at a lower temperature than Tc ¼ 188:5 K. A ferromagnetic phase transition reported at T ¼ 3:8 K [10] might be one candidate. . Two isomer-shift peaks of Mossbauer spectra of Eu3S4 supports the separation of Eu2+ and Eu3+
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ions below T ¼ 228 K [5]. Since the observation temperature is higher than Tc (=188.5 K), the gradual freezing of electron hopping occurs independently on the crystal-structural change, where the crystal still maintains the Th3P4-type structure. The frequency of hopping can be described as a relaxation time t to exchange the . electrons in the observation of the Mossbauer spectra. Exponential temperature dependence of t was reported with a continuous change through the phase transition. The t values are 1.0107, 3.5 108, 3.5 109, 1.7 109, 8.5 1010 and 3.5 1011 sec at T ¼ 83; 200, 213, 228, 250 and 325 K, respectively [5]. It should be noted that the hopping of electrons still exists at T ¼ 83 K even below the phase-transition temperature of Tc ¼ 188:5 K. On the other hand, the t value of 1.7 109 s at T ¼ 228 K is well compared to the relaxation time of magnetite (t=1.1 109 at 300 K) [24]. The temperature to give the t value of 1.1 109 s for Eu3S4 can be roughly estimated as T ¼ 240 K. It leads to a temperature difference of 60 K on t between the two compounds. And, magnetite transforms into a low-temperature phase at the Verwey temperature Tv ¼ 123 K, having the monoclinic distortion and charge ordering [27–29]. Since the energy barrier to enable the electron hopping is relatively small even in the low-temperature phase so far examined, a new charge ordering between Eu2+ and Eu3+ ions may exist for Eu3S4. In the view of the distribution of valence ions, the low-temperature phase of Eu3S4 can correspond to the room-temperature one of magnetite. It is meaningful that the nature of the phase transition of Eu3S4 is examined to compare with the Verwey transition and to search another phase transition of Eu3S4 around TE60 K. Thus, the search for another phase transition and the explanation of the ferromagnetic phase would become a new frontier in Eu3S4 researches. Because of the technical difficulty to determine accurately the crystal structure below T ¼ 3:8 K, X-ray diffuse scattering study at the relatively higher temperature is indispensable to observe the Huang scattering by the VDC method. Similar gradual freezing of electron hopping was observed in the neutron and X-ray Huang scattering of magnetite [25,26].
10. Conclusion We conclude that an I 4% 3d phase of Eu3S4 transforms to a charge-ordered I 4% 2d phase at Tc ¼ 188:5 K. From the crystal-structure determination with the VDC technique near a Eu LII absorption edge, the existence of a charge ordering was confirmed with the arrangement of [Eu3+]4a[Eu2+Eu3+]8dS4. Namely, all Eu2+ ions mix with a half of Eu3+ in the 8d sites in the I 4% 2d crystal structure, where the remaining Eu3+ ions occupy the 4a sites.
Acknowledgements We thank N. Shibuichi, K. Ohkubo, F. Saito and N. Kita of our group for their experimental help. We also thank Prof. M. Yoshimura of Tokyo Institute of Technology for his valuable discussion. This study was performed under the auspices of the Photon Factory (PAC Nos. 97G169, 99G196) and partly supported by JSPSRFTF96P00205.
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