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Anomalous thermal expansion in ErFe11.4Nb0.6
Journal Pre-proof Anomalous thermal expansion in ErFe11.4Nb0.6 W.Q. Wang, F. Su, Y.F. Xue, Z.X. Cheng, Q.F. Gu, S.J. Campbell, J.L. Wang PII:
S0925-8388(20)30012-8
DOI:
https://doi.org/10.1016/j.jallcom.2020.153649
Reference:
JALCOM 153649
To appear in:
Journal of Alloys and Compounds
Received Date: 6 July 2019 Revised Date:
13 December 2019
Accepted Date: 2 January 2020
Please cite this article as: W.Q. Wang, F. Su, Y.F. Xue, Z.X. Cheng, Q.F. Gu, S.J. Campbell, J.L. Wang, Anomalous thermal expansion in ErFe11.4Nb0.6, Journal of Alloys and Compounds (2020), doi: https:// doi.org/10.1016/j.jallcom.2020.153649. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
W.Q. Wang, F. Su, X.F. Xue and J.L. Wang prepared the samples and carried out magnetization measurement. Z.X. Cheng, Q.F. Gu and J.L. Wang performed synchrotron xray diffraction experiment. S.J. Campbell provided suggestions for the manuscript. J.L. Wang designed this study and wrote the manuscript. All contribute in completing the manuscript and approved the final manuscript.
Anomalous Thermal Expansion in ErFe11.4Nb0.6
W.Q. Wang1, F. Su1, Y.F. Xue1, Z.X. Cheng2, Q.F. Gu3, S.J. Campbell4 and J.L. Wang1,2,4* 1
2
College of Physics, Jilin University, Changchun 130012, People’s Republic of China
Institute for Superconducting and Electronic Materials, Innovation Campus, University of Wollongong, NSW 2500, Australia 3
4
Australia Synchrotron, 800 Blackburn Road, Clayton 3168, Australia
School of Science, The University of New South Wales at the Australian Defence Force Academy, Canberra, Australian Capital Territory 2600, Australia
*
To whom correspondence should be addressed: Email: [email protected];
The thermal expansion properties of the rare earth transition metal compound ErFe11.4Nb0.6 (Curie temperature Tc = 520(10) K) have been investigated in detail by variable temperature high resolution synchrotron x-ray diffraction measurements over the temperature range 300 K to 640 K. The findings from the Rietveld analyses reveal significant anomalies in the thermal expansion of ErFe11.4Nb0.6 below the Curie temperature with negative thermal expansion also evident around Tc = 520(10) K. The structural changes that occur around the Curie temperature lead to a spontaneous volume magnetostriction of ~ 6.3 ×10−3 at 300 K. The minimum values of the linear thermal expansion coefficients αa and αc for ErFe11.4Nb0.6 around TC are determined to be -3.56×10−6 K-1 and -1.30×10−6 K-1 respectively. Details of the structural features of ErFe11.4Nb0.6 (including Wigner-Seitz cell volumes and average bond lengths for Er atoms (2a site) and Fe atoms (8i, 8j, 8f sites) to neighbouring Fe atoms) that contribute to the thermal expansion behaviour have been investigated in detail. The persistence of finite magnetostriction values λa and λc (along the a-axis and the c-axis respectively) and volume magnetostriction ωs, above the magnetic transition temperature, indicates the likely occurrence of short-range magnetic correlations in this region.
1
Key Words: Rare earth metals and alloys, magnetic phase transition, magnetisation, thermal expansion PACS: 71.20.Eh, 77.80.Bh, 75.30.Cr, 65.60.+a
2
1. Introduction Investigation and characterisation of the thermal expansion properties of materials remain important topics in materials science [1, 2]. Indeed, understanding the thermal expansion properties of materials is of increasing significance, especially given the advent of high-precision instruments and devices that require controlled thermal expansion properties [1-3]. As is well known and understood, most materials expand when heated (positive thermal expansion; PTE) which can lead to degraded performance in high-precision instruments and devices. On the other hand, given that some materials contract upon heating (negative thermal expansion; NTE), such materials can potentially be combined with PTE materials to form composites with controllable positive, negative, or even zero thermal expansion (ZTE) [1-3].While the control of thermal expansion is important for practical applications, such behaviour can be difficult to achieve [3]. Indeed, given that NTE and composite materials have been widely used for precision instruments and the aerospace industry among other fields, many theoretical [4, 5] and experimental [1-3] studies have been carried out. As outlined previously [1, 3], negative thermal expansion can be caused by a variety of mechanisms, such as transverse vibration of bridging atoms, spontaneous volume ferroelectrostriction, charge transfer, and magnetic transition. As is well known, rare earth-based materials play significant roles in basic and applied condensed matter physics [6-8].
For example, they offer an extensive range of fascinating
fundamental physical phenomena such as the Kondo effect, quantum criticality, unconventional superconductivity, magneto-crystalline anisotropy, magnetocaloric effect etc. [6-9]. In addition to their potential application as permanent magnets similar to the Nd2Fe14B system [8], iron-rich rare earth (R) intermetallic compounds such as LaFe13-xSix-based compounds [10], R2Fe17-based compounds [11, 12], R3(Fe, M)29 [13-15] and R(Fe, M)12 [16, 17] have been found to exhibit negative thermal expansion (M represents a stabilizing element such as Ti, V, Cr, Mo, W, Nb, Ta [6]). Indeed, given the continuing demand for high performance magnets and the increasing cost and uncertainties in the supply risks of rare earth metals, there has been renewed interest in R(Fe, 3
M)12 compounds [18-20]. This follows as the large Fe content yields high magnetisation and Curie temperature with a large a/c ratio providing high magneto-crystalline anisotropy [6]. The R(Fe, M)12 compounds crystallise in the ThMn12-type structure in which there are 26 atoms (two molecules) per unit cell. The rare earth atoms occupy Wyckoff site 2a (0, 0, 0), with the Fe atoms occupying three crystallographic inequivalent sites, i.e. the 8i (x8i, 0, 0), 8j (x8j, 0.5, 0), and 8f (0.25, 0.25, 0.25) sites [6]. The average Fe-Fe interatomic distances for the Fe (8i), Fe (8j) and Fe (8f) sites are around ~2.71 Å, ~ 2.59 Å and ~ 2.51 Å respectively. While the M atoms for most R(Fe, M)12 compounds were found to occupy the 8i site, for M=Si, the Si atoms were reported to share 8j and 8f sites with Fe in RFe12Si2 compounds [6]. Previously, it was reported that iron-rich YFe11xCoxTi
compounds [16], YFe12Mo2 and Ho(Fe1-xNix)11.3Nb0.7 compounds [17] with the ThMn12-
type structure exhibit strong magneto-volume effects as determined using the push-rod method. However, no detailed information about the structural changes occurring around the ordering temperature could be determined due to the limited resolution of the push-rod method. The aim of this study is to explore and understand fully the magnetoelastic coupling in R(Fe, M)12-type compounds. ErFe11.4Nb0.6 has been selected for investigation as a typical member of this series of compounds. The thermal expansion behavior and spontaneous magnetostriction of the ErFe11.4Nb0.6 compound have been investigated from 300 K to 640 K by means of high-resolution synchrotron x-ray diffraction measurement. The average bonding lengths and Wigner-Seitz cell volumes for the Er atoms (2a site) and Fe atoms (8i, 8j, 8f sites) at their individual sites have been determined.
2. Experimental A polycrystalline sample of ErFe11.4Nb0.6 (~2 g) was prepared by standard arc melting of the constituent elements of 99.9 % purity under an argon atmosphere. The prepared ingots were wrapped in tantalum foil and sealed in quartz glass tubes under vacuum for annealing. The sample was heated at 1173 K for 7 days and then quenched into water. The temperature dependence of the 4
magnetisation curve M-T was measured under a field of 500 Oe after field cooling process using the vibrating sample magnetometer option of a Quantum Design 14 T physical properties measurement system (PPMS). The Curie temperature TC ~ 520(±10) K was determined by extrapolating a graph of the square of the magnetisation versus temperature (M2 versus T) to zero as described in [11]. The crystal structure and thermal expansion of the sample were investigated by high resolution/intensity x-ray powder diffraction with λ = 0.68809 Å using a quartz capillary at the powder diffraction beamline of Australian Synchrotron. Analysis of the room temperature x-ray diffraction pattern confirmed that the ErFe11.4Nb0.6 sample crystallises in the body-centered tetragonal crystal structure (ThMn12-type, space group: I4/mmm, No. 139) as expected.
3. Results and discussion 3.1 Structural properties The set of variable temperature x-ray diffraction patterns collected on ErFe11.4Nb0.6 are shown in Figure 1(a). A temperature step of ∆T = 20 K was selected to cover the temperature range 300 K - 640 K with a 5 K step used in the region of the magnetic transition temperature, Tc = 520(10) K. The trends of the a – lattice parameter and the c - lattice parameter with temperature in the region of Tc are reflected by the (310) and the (002) reflections (Figure 1(b); i.e. changes of lattice parameters in the a-b plane and the c - axis respectively). It is clear that in the region around Tc = 520(10) K, the positions of both peaks (see the inset of Figure 1(a)) shift to smaller angles and deviate from the behaviour expected of a material exhibiting positive thermal expansion. As discussed fully below (see Figure 3), this behavior indicates anomalies in the thermal expansion of the ErFe11.4Nb0.6 unit cell and is not expected as most materials contract along all three crystallographic directions when cooled due to anharmonic lattice phonon vibrations. The 2a, 8i, 8j, and 8f Wyckoff positions of the ThMn12 structure (symmetries 4/mmm, m2m, m2m and 2/m respectively) are drawn in Figure 2(a). The atomic position parameters for the 8i and 8j sites are x ~ 0.3 [6]. The x-ray data were refined by Rietveld analysis using the FULLPROF 5
program [21] with refinements to the diffraction patterns at T=300 K, 500 K and 560 K shown in Figure 2(b) as typical examples. The pattern factor Rp, the weighted pattern factor Rwp, and the expected pattern factor Rexp for refinement of the 300 K pattern are 4.97, 6.92 and 2.35 respectively. Our results confirm that Nb and Fe atoms share the 8i site while the two other transition metal sites 8j and 8f sites are fully occupied by Fe only, in agreement with previous neutron diffraction studies [22] (moreover their neutron study [22] also found that ErFe12-xNbx compounds exhibit a ferrimagnetic structure below TC). This behaviour can be understood in the terms of the differences in atomic radius and valence configuration between the Fe and Nb atoms. The refinement also indicates that less than 4 wt% of α-Fe and 2 wt% of Fe2Nb are present as impurity phases in our ErFe11.4Nb0.6 sample. In the ErFe11.4Nb0.6 compound (see Table 1) each Er atom located at the 2a site has 20 Fe near-neighbour (NN) atoms (four at the 8i site, eight at the 8j site and eight at the 8f site). The average bond length of an Er atom at the 2a site to the neighbouring Fe atoms at T = 300 K is calculated to be 3.1237 Å. The Fe/Nb atoms at the 8i site has one bond with an Er atom and 13 Fe NN atoms (five atoms at the 8i site and four at each of the 8j and 8f sites) while the Fe atoms at the 8j and 8f sites both have 2 neighbouring Er atoms and 10 Fe NN atoms as listed in Table 1. The average bond length of Fe atom at the 8i, 8j and 8f sites to neighbouring Fe atoms is derived to be 3.1183 Å, 2.7052 Å and 2.5731 Å respectively. The Wigner-Seitz cell (WSC) volumes have been calculated with the BLOKJE program [23] for all of the crystallographic sites in ErFe11.4Nb0.6 at 300 K by using the structural and positional parameters and the 12 coordinate metallic radii of 1.78 Å, 1.26 Å and 1.46 Å for Er, Fe and Nb respectively. The calculated WSC volumes for the 2a, 8i, 8j and 8f sites are 29.244 Å3, 12.680 Å3, 11.785 Å3 and 11.311 Å3 respectively (see details in Table 1), with the same sequence occurring in other R(Fe, M)12 compounds [6, 19, 24]. The temperature dependences of the atomic positions parameters x8i and x8j of the 8i and 8j sites respectively, are shown in Figure 2(c). A distinct change in the temperature variation of the x8i
6
and x8j values is evident in the region around TC, indicating clearly the presence of magnetoelastic coupling around the magnetic transition temperature.
3.2 Thermal expansion and related properties The temperature dependences of the a- and c- lattice parameters of ErFe11.4Nb0.6 as determined from the Rietveld refinements along with the unit cell volume, V, are shown in Figures 3(a) and 3(c) respectively. It is clear from these figures that ErFe11.4Nb0.6 exhibits an invar effect below TC over the approximate temperature range ~ 470 – 520 K. As is well known, the thermal expansion of solids is formally described by the Grüneisen relationship between phonon and thermal expansion α(T) = γCVK/V [1]. Here α(T) is the coefficient of thermal expansion (CTE), CV the specific heat at constant volume, K the isothermal compressibility, V the volume and γ the Grüneisen parameter. According to Debye theory, the pure lattice contribution to thermal expansion can be calculated using the Debye temperature (for ErFe11.4Nb0.6, θD ≈ 350 K as derived for similar systems [24, 25] with the Debye–Grüneisen equation). The temperature dependence of the anharmonic phonon contribution has been fitted to the experimental results in the paramagnetic regime and is shown in Figures 3(a) and 3(c) by the dashed lines. The magnetic contribution to the thermal expansion which gives rise to the invar behaviour can be obtained by subtracting the lattice contribution from the experimental values. As noted in Figure 3(a), the magnetic contribution at 300 K along the a - axis and c - axis has been derived to be ∆a = 0.0274 Å and ∆c = 0.0069 Å, respectively, thus indicating that the negative thermal expansion of ErFe11.4Nb0.6 is anisotropic. The value of ∆V at 300 K is determined to be 2.129 Å3 (Figure 3(c)). The coefficient of thermal expansion along a particular direction is defined as α = (∂L/∂T)L-1 where L and T are the length and temperature respectively. The linear thermal expansion coefficient αa(T) along the a - axis and αc(T) along the c - axis have been calculated as shown in Figure 3(b). Both αa(T) and αc(T) exhibit pronounced minima around TC. If the variation 7
of the a and c lattice parameters is considered in the temperature range of 300 K - 380 K (i.e. the approximately invariant region of αa(T) and αc(T)), the average values of αa(T) and αc(T) are ~ 2.59×10-6 K-1 and ~ 6.13×10-6 K-1 respectively. Reflecting the structural effects taking place in the region of the magnetic transition, as shown in Figure 3(b), the minimum values of the thermal expansion coefficients of αamin(Tc) = - 3.56×10-6/K and αcmin(Tc) = - 1.30×10-6/K are obtained around the transition temperature Tc ~ 520 K. By comparison, the minimum values of line thermal expansion coefficients for Dy2Fe17 [11]， Tb3(Fe, Ti)29 [13] and YFe11Ti [16] were found to be 6.9×10-6 K-1， - 12.1×10-6 K-1 and - 1.3×10-6 K-1, respectively. The calculated values of the spontaneous magnetostriction along the a-axis, λa = ∆a/a, and the c - axis λc = ∆c/c, as well as the spontaneous volume magnetostriction ωs = ∆V/V are show as functions of temperature in Figure 3(d). The values for this set of magnetostriction parameters at 300 K are λa = 3.235×10-3, λc = 1.441×10-3 and ωs = 6.216×10-3. Moreover, it can also be seen from Figure 3(d) that λa, λc and ωs do not become zero at TC and maintain nonzero values to around 600 K (T/TC ∼ 1.15), well above the ordering temperature TC = 520(10) K. It is well accepted that the magnitude and the temperature dependence of the bulk volume magnetostriction of a ferromagnetic compound can be related to the square of the magnetic moment [12]. Given this link between magnetostriction and magnetic moment, the persistence of non-zero spontaneous magnetostrictive deformation above the magnetic transition temperature, indicates the likely occurrence of a short-range magnetic correlations. Indeed, such effects have been reported in other systems such as Dy2Fe17-xMnx [11], Er2Fe17 [12], Tb3(Fe,Ti)29 [13]， Ce3(Fe, M)29 [14] and YFe11xCoxTi
[16].
3.3 Magnetoelastic coupling at individual sites
8
Further insight to the behaviour of the magnetoelastic coupling of ErFe11.4Nb0.6 is provided by the temperature dependences of the calculated values for both the WSC volumes and the average bonding distances for the 2a, 8i, 8j and 8f sites as shown in Figure 4. It is clear that, the WSC volumes at the 2a, 8j and 8f sites exhibit trends with increasing temperature that are similar to those obtained for the lattice parameters of Figure 3(a). Likewise, the WSC volumes and the average bonding distances for the 2a, 8j and 8f exhibit a clear anomaly around TC. On the other hand, compared with atoms at the 2a, 8j and 8f sites, the reduced sensitivity of the WSC volume for the atom at the 8i site to change in temperature around TC, may reflect a reduced magneto-volume effect of the 8i site atom. In considering the relative invariance of the average bonding distances of the 8i site in the temperature region around Tc compared with the 8j and 8f sites, the atom at the 8i site has the largest number of Fe nearest neighbours, NN=13, while the atoms at the 8j and 8f sites have 10 Fe neighbours (Table 1). Given that Fe atoms at 8i sites have the largest average interatomic distances (see Table 1 and Figure 4), a Fe atom at an 8i site is expected to have the largest magnetic moment. This behaviour has been confirmed by a neutron diffraction study of the ErFe11.35Nb0.65 compound in which the moments for Fe at 8i, 8j and 8f site are determined to be 2.0(5) µB, 1.9(5) µB and 1.8(3) µB, respectively [22]. As such, it is surprising to note that atoms at the 8i site exhibit a reduced response to magnetoelastic coupling even though atoms at the 8i site experience the largest degree of orbital overlap with surrounding atoms. The Fe ions at 8i sites have 13 coordination ions which results in a stronger bonding force compared with 8j and 8f site Fe which have 10 coordination ions. The behaviour that Fe ions at 8i sites are more rigid than Fe ions at the 8j and 8f sites around the magnetic transition temperature, could be explained based on the overall interaction of the Fe ions at 8i site bonding with surrounding coordination ions and exchange interaction with adjacent Fe ions. Moreover, the fact that the 8i position is partially occupied by Nb atoms, which are nonmagnetic, indicates that there are fewer magnetic atoms at the 8i site compared with the Fe atoms at 8j and 8f sites. This factor may also play a role in the weaker response of 8i site atoms to magnetoelastic coupling. 9
4. Conclusions
The crystal structural effects and magnetoelastic coupling effects of the rare earth intermetallic compound ErFe11.4Nb0.6 of ferrimagnetic transition temperature Tc = 520(10) K have been studied in detail by variable temperature synchrotron x-ray diffraction measurements over the temperature range 300 K to 640 K. The temperature dependence of the a - and c - lattice parameters reveal a region of anisotropic negative thermal expansion below the ordering temperature resulting from a strong spontaneous magnetostriction in the magnetic state, while ErFe11.4Nb0.6 is found to exhibit an invar effect over the approximate temperature range ~ 470 – 520 K. In addition, the presence of magnetoelastic coupling around the magnetic transition temperature is revealed by the distinct changes in atomic position parameters of the 8i and 8j sites around TC while the persistence of non-zero spontaneous magnetostrictive deformation above the magnetic transition temperature, indicates the likely occurrence of a short-range magnetic correlations. Both the Wigner-Seitz cell volume and the average bonding distances for the 2a, 8j and 8f sites exhibit clear anomalies around TC, thus revealing correlation with the change of magnetic state. Acknowledgements The authors are grateful for the experimental support from staff at the Powder Diffraction beamline, Australian Synchrotron (ANSTO).
10
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[16] J.L. Wang, M.R. Ibarra, C. Marquina, B. Garcia-Landa, O. Tegus, Q.F. Xiao, E. Bruck, F.M. Yang and G.H. Wu, J. Appl.Phys. 91, 8216 (2002). [17] J.L. Wang, C. Marquina, B. Garcıá -Landa, M.R. Ibarra, F.M. Yang and G.H. Wu, Physica B 319, 73 (2002). [18] P. Tozman, H. Sepehri-Amin, Y.K. Takahashi, S. Hirosawa, K. Hono, Acta Materialia 153, 354 (2018). [19] A.M. Schönhöbel, R. Madugundo, O. Yu. Vekilova, O. Eriksson, H.C. Herper, J.M. Barandiarán, G.C. Hadjipanayis, J Alloy. Compd., 786, 969 (2019) [20] Taro Fukazawa, Yosuke Harashima, Zhufeng Hou, and Takashi Miyake, Physical Review Materials 3, 053807 (2019) [21] R.C. Juan, The 15th Congr. Int. Union of Crystallography, Proc. Satellite Mtg On Powder Diffraction (Toulouse, France), 1990, p. 127. [22] B.P. Hu, K.Y. Wang, Y.Z. Wang, Z.X. Wang and Q.W. Yan, Phys. Rev. B 51, 2905 (1995) [23] L. Gelato, J. Appl. Crystallogr. 14, 151 (1981) [24] J.L. Wang, W.D. Hutchison and S.J. Campbell, J. Magn. Magn. Mat. 477, 27 (2019) [25] D.P. Lazar, N. Plugaru, V. Kuncser, M. Valeanu, G. Filoti, J. Bartolomé, J. Rubín, J. Magn. Magn. Mat. 302, 56 (2006)
12
Figures:
(b)
(310)
TC
4.0k
Intensity (arb. unit.)
8.0k
(310)
14.72 14.70
20k
TC
300 400 500 600 T (K)
10k
14.6
14.8
two theta (degree) 8.0k
(002)
TC
T (K)
600
500
T (K)
400 300
4.0k
Intensity (arb. unit.)
(002) TC
16.52 16.50
600 500
400
T (K)
(a)
Intensity (arb. unit.)
Peak position (degree)
600 500
400 300
10
20
30
40
16.4
two theta (degree)
16.6
300
two theta (degree)
Figure 1(a) Synchrotron x-ray diffraction patterns of ErFe11.4Nb0.6 over the temperature range 300 K to 650 K and (b) A set of the (310) and (002) Bragg reflections on expanded scales at selected temperatures over the range 300 K to 650 K. The patterns at the selected temperatures reflect the temperature dependence of the lattice parameters in the ab-plane ((310) reflection) and the c - axis ((002) reflection). The inset of Figure 1(a) shows the variation of the positions of the (310) and (002) reflections as functions of temperature with TC = 520(10) K marked by arrows.
13
(b)
Yobs Ycalc Yobs-Ycalc Bragg_position
30000
T=300 K
Intensity (arb. unit.)
0
0.360
(c) x8i, x8j
0.359
T=500 K
0
20000
x8i
TC
20000
T=560 K
x8j
0.279
0 0.278
TC 300
400
500
10
20
30
two theta (degree)
600
T(K)
Figure 2(a) Schematic diagram of the crystal structure of ErFe11.4Nb0.6 (Er atoms at 2a site - grey circles; Fe and Nb atoms at 8i site - red circles; Fe atoms at 8j site - green circles and Fe atoms at 8f site - blue circles); (b) Refinements of ErFe11.4Nb0.6 at T = 300 K, 500 K and 560 K: experimental data (asterisk symbols); red lines are Rietveld refinements to the data (FullProf); blue vertical lines represent Bragg reflections from ErFe11.4Nb0.6, α-Fe and Fe2Nb from top to bottom respectively; the green horizontal line shows the difference between the experimental and calculated patterns. and (c) atomic position parameters x8i and x8j of the 8i and 8j sites respectively, as a function of temperature.
14
a c
8.46 4.792
3
∆V=2.129 Å
342
αa
-5
αc
-1
αa, αc (K )
1.0x10
(b)
0.0
-2
1.0x10
TC 0.0 400 600 T(K)
ωs
(d)
6 -3
4.784
∆c=0.0069 Å
344
3
(a)
(c)
dV/dT (Å /K)
3
Unit cell volume V (Å )
∆a=0.0274 Å
λa, λc, ωs (10 )
lattice parameter (Å)
8.49
346
λa, λc
3
0
300
400
500 T(K)
300
600
400
500
600
T (K)
Figure 3 Temperature dependences for ErFe11.4Nb0.6 of: (a) the a and c lattice parameters; (b) the linear thermal expansion coefficient; (c) the unit cell volume V, and (d) the spontaneous magnetostriction λa = ∆a/a and λc = ∆c/c along the a - axis and the c - axis respectively, and the spontaneous volume magnetostriction ωs = ∆V/V. The arrows indicate the magnetic transition temperature Tc = 520(10) K. A graph of dV/dT versus T is shown in the inset of Figure 3(c).
15
29.5
300
400
500
600
T (K) Fe at 8j site distance
11.85
(c)
3
2.576
WSC volume
11.82 2.574
3
12.69
2.705
2.704 300
400
500
600
T (K)
Fe at 8f site distance
(d) 11.37
WSC volume 3
3.115
2.706
WSC Volume (Å )
29.3
12.72
Average bond length to neighbouring Fe (Å)
3.120
WSC Volume (Å )
Average bond length to neighbouring Fe (Å)
29.4
(b)
2.707
3
WSC volume
Fe at 8i site distance WSC volume
WSC Volume (Å )
(a) WSC Volume (Å )
3.125
2.708
Er at 2a site distance
2.502
11.34
2.499
11.79
11.31 2.572 300
400
500
600
300
400
500
600
T (K)
T (K)
Figure 4 Temperature dependences of the average bond lengths to neighbouring Fe atoms and Wigner-Seitz cell volumes for: (a) an Er atom at the 2a site and Fe atoms at the (b) 8i, (c) 8j and (d) 8f sites, respectively. The arrows indicate the magnetic transition temperature Tc = 520(10) K.
16
Table1 The numbers of neighbouring atoms, Wigner-Seitz cell volumes (WSC volumes) and bond lengths in ErFe11.4Nb0.6 at 300 K. Atom
Er,
Number of
Number of
Er
Fe
neighbours
neighbours
0
8i
Fe, 8j
Minimum
Maximum
Volume bond length to bond length to (Å3)
Average bond length to
neighbouring
neighbouring
neighbouring
Fe (Å)
Fe (Å)
Fe (Å)
29.244
3.0428
3.2302
3.1183
12.680
2.3957
2.9320
2.7052
11.785
2.4478
2.6620
2.5731
11.311
2.3930
2.6050
2.4997
8×Fe8j, 8×Fe8f)
2a Fe/Nb,
20 (4×Fe8i,
WSC-
1
13 (5×Fe8i,
(1×Er2a)
4×Fe8j, 4×Fe8f)
2
10 (4×Fe8i,
((2×Er2a)
2×Fe8j, 4×Fe8f)
Fe,
2
8f
(2× Er2a)
10 (4×Fe8i, 4×Fe8j, 2×Fe8f)
17
A detailed investigation on magnetoelastic coupling in ErFe11.4Nb0.6 compound by variable temperature high resolution Synchrotron x-ray diffraction is presented. Remarkable magnetovolume anomalies and negative thermal expansion have been detected below the Curie temperature, TC. Short-range magnetic correlations are present above TC. Specific features in thermal expansion have been investigated in detail.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
S0925-8388(20)30012-8
DOI:
https://doi.org/10.1016/j.jallcom.2020.153649
Reference:
JALCOM 153649
To appear in:
Journal of Alloys and Compounds
Received Date: 6 July 2019 Revised Date:
13 December 2019
Accepted Date: 2 January 2020
Please cite this article as: W.Q. Wang, F. Su, Y.F. Xue, Z.X. Cheng, Q.F. Gu, S.J. Campbell, J.L. Wang, Anomalous thermal expansion in ErFe11.4Nb0.6, Journal of Alloys and Compounds (2020), doi: https:// doi.org/10.1016/j.jallcom.2020.153649. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
W.Q. Wang, F. Su, X.F. Xue and J.L. Wang prepared the samples and carried out magnetization measurement. Z.X. Cheng, Q.F. Gu and J.L. Wang performed synchrotron xray diffraction experiment. S.J. Campbell provided suggestions for the manuscript. J.L. Wang designed this study and wrote the manuscript. All contribute in completing the manuscript and approved the final manuscript.
Anomalous Thermal Expansion in ErFe11.4Nb0.6
W.Q. Wang1, F. Su1, Y.F. Xue1, Z.X. Cheng2, Q.F. Gu3, S.J. Campbell4 and J.L. Wang1,2,4* 1
2
College of Physics, Jilin University, Changchun 130012, People’s Republic of China
Institute for Superconducting and Electronic Materials, Innovation Campus, University of Wollongong, NSW 2500, Australia 3
4
Australia Synchrotron, 800 Blackburn Road, Clayton 3168, Australia
School of Science, The University of New South Wales at the Australian Defence Force Academy, Canberra, Australian Capital Territory 2600, Australia
*
To whom correspondence should be addressed: Email: [email protected];
The thermal expansion properties of the rare earth transition metal compound ErFe11.4Nb0.6 (Curie temperature Tc = 520(10) K) have been investigated in detail by variable temperature high resolution synchrotron x-ray diffraction measurements over the temperature range 300 K to 640 K. The findings from the Rietveld analyses reveal significant anomalies in the thermal expansion of ErFe11.4Nb0.6 below the Curie temperature with negative thermal expansion also evident around Tc = 520(10) K. The structural changes that occur around the Curie temperature lead to a spontaneous volume magnetostriction of ~ 6.3 ×10−3 at 300 K. The minimum values of the linear thermal expansion coefficients αa and αc for ErFe11.4Nb0.6 around TC are determined to be -3.56×10−6 K-1 and -1.30×10−6 K-1 respectively. Details of the structural features of ErFe11.4Nb0.6 (including Wigner-Seitz cell volumes and average bond lengths for Er atoms (2a site) and Fe atoms (8i, 8j, 8f sites) to neighbouring Fe atoms) that contribute to the thermal expansion behaviour have been investigated in detail. The persistence of finite magnetostriction values λa and λc (along the a-axis and the c-axis respectively) and volume magnetostriction ωs, above the magnetic transition temperature, indicates the likely occurrence of short-range magnetic correlations in this region.
1
Key Words: Rare earth metals and alloys, magnetic phase transition, magnetisation, thermal expansion PACS: 71.20.Eh, 77.80.Bh, 75.30.Cr, 65.60.+a
2
1. Introduction Investigation and characterisation of the thermal expansion properties of materials remain important topics in materials science [1, 2]. Indeed, understanding the thermal expansion properties of materials is of increasing significance, especially given the advent of high-precision instruments and devices that require controlled thermal expansion properties [1-3]. As is well known and understood, most materials expand when heated (positive thermal expansion; PTE) which can lead to degraded performance in high-precision instruments and devices. On the other hand, given that some materials contract upon heating (negative thermal expansion; NTE), such materials can potentially be combined with PTE materials to form composites with controllable positive, negative, or even zero thermal expansion (ZTE) [1-3].While the control of thermal expansion is important for practical applications, such behaviour can be difficult to achieve [3]. Indeed, given that NTE and composite materials have been widely used for precision instruments and the aerospace industry among other fields, many theoretical [4, 5] and experimental [1-3] studies have been carried out. As outlined previously [1, 3], negative thermal expansion can be caused by a variety of mechanisms, such as transverse vibration of bridging atoms, spontaneous volume ferroelectrostriction, charge transfer, and magnetic transition. As is well known, rare earth-based materials play significant roles in basic and applied condensed matter physics [6-8].
For example, they offer an extensive range of fascinating
fundamental physical phenomena such as the Kondo effect, quantum criticality, unconventional superconductivity, magneto-crystalline anisotropy, magnetocaloric effect etc. [6-9]. In addition to their potential application as permanent magnets similar to the Nd2Fe14B system [8], iron-rich rare earth (R) intermetallic compounds such as LaFe13-xSix-based compounds [10], R2Fe17-based compounds [11, 12], R3(Fe, M)29 [13-15] and R(Fe, M)12 [16, 17] have been found to exhibit negative thermal expansion (M represents a stabilizing element such as Ti, V, Cr, Mo, W, Nb, Ta [6]). Indeed, given the continuing demand for high performance magnets and the increasing cost and uncertainties in the supply risks of rare earth metals, there has been renewed interest in R(Fe, 3
M)12 compounds [18-20]. This follows as the large Fe content yields high magnetisation and Curie temperature with a large a/c ratio providing high magneto-crystalline anisotropy [6]. The R(Fe, M)12 compounds crystallise in the ThMn12-type structure in which there are 26 atoms (two molecules) per unit cell. The rare earth atoms occupy Wyckoff site 2a (0, 0, 0), with the Fe atoms occupying three crystallographic inequivalent sites, i.e. the 8i (x8i, 0, 0), 8j (x8j, 0.5, 0), and 8f (0.25, 0.25, 0.25) sites [6]. The average Fe-Fe interatomic distances for the Fe (8i), Fe (8j) and Fe (8f) sites are around ~2.71 Å, ~ 2.59 Å and ~ 2.51 Å respectively. While the M atoms for most R(Fe, M)12 compounds were found to occupy the 8i site, for M=Si, the Si atoms were reported to share 8j and 8f sites with Fe in RFe12Si2 compounds [6]. Previously, it was reported that iron-rich YFe11xCoxTi
compounds [16], YFe12Mo2 and Ho(Fe1-xNix)11.3Nb0.7 compounds [17] with the ThMn12-
type structure exhibit strong magneto-volume effects as determined using the push-rod method. However, no detailed information about the structural changes occurring around the ordering temperature could be determined due to the limited resolution of the push-rod method. The aim of this study is to explore and understand fully the magnetoelastic coupling in R(Fe, M)12-type compounds. ErFe11.4Nb0.6 has been selected for investigation as a typical member of this series of compounds. The thermal expansion behavior and spontaneous magnetostriction of the ErFe11.4Nb0.6 compound have been investigated from 300 K to 640 K by means of high-resolution synchrotron x-ray diffraction measurement. The average bonding lengths and Wigner-Seitz cell volumes for the Er atoms (2a site) and Fe atoms (8i, 8j, 8f sites) at their individual sites have been determined.
2. Experimental A polycrystalline sample of ErFe11.4Nb0.6 (~2 g) was prepared by standard arc melting of the constituent elements of 99.9 % purity under an argon atmosphere. The prepared ingots were wrapped in tantalum foil and sealed in quartz glass tubes under vacuum for annealing. The sample was heated at 1173 K for 7 days and then quenched into water. The temperature dependence of the 4
magnetisation curve M-T was measured under a field of 500 Oe after field cooling process using the vibrating sample magnetometer option of a Quantum Design 14 T physical properties measurement system (PPMS). The Curie temperature TC ~ 520(±10) K was determined by extrapolating a graph of the square of the magnetisation versus temperature (M2 versus T) to zero as described in [11]. The crystal structure and thermal expansion of the sample were investigated by high resolution/intensity x-ray powder diffraction with λ = 0.68809 Å using a quartz capillary at the powder diffraction beamline of Australian Synchrotron. Analysis of the room temperature x-ray diffraction pattern confirmed that the ErFe11.4Nb0.6 sample crystallises in the body-centered tetragonal crystal structure (ThMn12-type, space group: I4/mmm, No. 139) as expected.
3. Results and discussion 3.1 Structural properties The set of variable temperature x-ray diffraction patterns collected on ErFe11.4Nb0.6 are shown in Figure 1(a). A temperature step of ∆T = 20 K was selected to cover the temperature range 300 K - 640 K with a 5 K step used in the region of the magnetic transition temperature, Tc = 520(10) K. The trends of the a – lattice parameter and the c - lattice parameter with temperature in the region of Tc are reflected by the (310) and the (002) reflections (Figure 1(b); i.e. changes of lattice parameters in the a-b plane and the c - axis respectively). It is clear that in the region around Tc = 520(10) K, the positions of both peaks (see the inset of Figure 1(a)) shift to smaller angles and deviate from the behaviour expected of a material exhibiting positive thermal expansion. As discussed fully below (see Figure 3), this behavior indicates anomalies in the thermal expansion of the ErFe11.4Nb0.6 unit cell and is not expected as most materials contract along all three crystallographic directions when cooled due to anharmonic lattice phonon vibrations. The 2a, 8i, 8j, and 8f Wyckoff positions of the ThMn12 structure (symmetries 4/mmm, m2m, m2m and 2/m respectively) are drawn in Figure 2(a). The atomic position parameters for the 8i and 8j sites are x ~ 0.3 [6]. The x-ray data were refined by Rietveld analysis using the FULLPROF 5
program [21] with refinements to the diffraction patterns at T=300 K, 500 K and 560 K shown in Figure 2(b) as typical examples. The pattern factor Rp, the weighted pattern factor Rwp, and the expected pattern factor Rexp for refinement of the 300 K pattern are 4.97, 6.92 and 2.35 respectively. Our results confirm that Nb and Fe atoms share the 8i site while the two other transition metal sites 8j and 8f sites are fully occupied by Fe only, in agreement with previous neutron diffraction studies [22] (moreover their neutron study [22] also found that ErFe12-xNbx compounds exhibit a ferrimagnetic structure below TC). This behaviour can be understood in the terms of the differences in atomic radius and valence configuration between the Fe and Nb atoms. The refinement also indicates that less than 4 wt% of α-Fe and 2 wt% of Fe2Nb are present as impurity phases in our ErFe11.4Nb0.6 sample. In the ErFe11.4Nb0.6 compound (see Table 1) each Er atom located at the 2a site has 20 Fe near-neighbour (NN) atoms (four at the 8i site, eight at the 8j site and eight at the 8f site). The average bond length of an Er atom at the 2a site to the neighbouring Fe atoms at T = 300 K is calculated to be 3.1237 Å. The Fe/Nb atoms at the 8i site has one bond with an Er atom and 13 Fe NN atoms (five atoms at the 8i site and four at each of the 8j and 8f sites) while the Fe atoms at the 8j and 8f sites both have 2 neighbouring Er atoms and 10 Fe NN atoms as listed in Table 1. The average bond length of Fe atom at the 8i, 8j and 8f sites to neighbouring Fe atoms is derived to be 3.1183 Å, 2.7052 Å and 2.5731 Å respectively. The Wigner-Seitz cell (WSC) volumes have been calculated with the BLOKJE program [23] for all of the crystallographic sites in ErFe11.4Nb0.6 at 300 K by using the structural and positional parameters and the 12 coordinate metallic radii of 1.78 Å, 1.26 Å and 1.46 Å for Er, Fe and Nb respectively. The calculated WSC volumes for the 2a, 8i, 8j and 8f sites are 29.244 Å3, 12.680 Å3, 11.785 Å3 and 11.311 Å3 respectively (see details in Table 1), with the same sequence occurring in other R(Fe, M)12 compounds [6, 19, 24]. The temperature dependences of the atomic positions parameters x8i and x8j of the 8i and 8j sites respectively, are shown in Figure 2(c). A distinct change in the temperature variation of the x8i
6
and x8j values is evident in the region around TC, indicating clearly the presence of magnetoelastic coupling around the magnetic transition temperature.
3.2 Thermal expansion and related properties The temperature dependences of the a- and c- lattice parameters of ErFe11.4Nb0.6 as determined from the Rietveld refinements along with the unit cell volume, V, are shown in Figures 3(a) and 3(c) respectively. It is clear from these figures that ErFe11.4Nb0.6 exhibits an invar effect below TC over the approximate temperature range ~ 470 – 520 K. As is well known, the thermal expansion of solids is formally described by the Grüneisen relationship between phonon and thermal expansion α(T) = γCVK/V [1]. Here α(T) is the coefficient of thermal expansion (CTE), CV the specific heat at constant volume, K the isothermal compressibility, V the volume and γ the Grüneisen parameter. According to Debye theory, the pure lattice contribution to thermal expansion can be calculated using the Debye temperature (for ErFe11.4Nb0.6, θD ≈ 350 K as derived for similar systems [24, 25] with the Debye–Grüneisen equation). The temperature dependence of the anharmonic phonon contribution has been fitted to the experimental results in the paramagnetic regime and is shown in Figures 3(a) and 3(c) by the dashed lines. The magnetic contribution to the thermal expansion which gives rise to the invar behaviour can be obtained by subtracting the lattice contribution from the experimental values. As noted in Figure 3(a), the magnetic contribution at 300 K along the a - axis and c - axis has been derived to be ∆a = 0.0274 Å and ∆c = 0.0069 Å, respectively, thus indicating that the negative thermal expansion of ErFe11.4Nb0.6 is anisotropic. The value of ∆V at 300 K is determined to be 2.129 Å3 (Figure 3(c)). The coefficient of thermal expansion along a particular direction is defined as α = (∂L/∂T)L-1 where L and T are the length and temperature respectively. The linear thermal expansion coefficient αa(T) along the a - axis and αc(T) along the c - axis have been calculated as shown in Figure 3(b). Both αa(T) and αc(T) exhibit pronounced minima around TC. If the variation 7
of the a and c lattice parameters is considered in the temperature range of 300 K - 380 K (i.e. the approximately invariant region of αa(T) and αc(T)), the average values of αa(T) and αc(T) are ~ 2.59×10-6 K-1 and ~ 6.13×10-6 K-1 respectively. Reflecting the structural effects taking place in the region of the magnetic transition, as shown in Figure 3(b), the minimum values of the thermal expansion coefficients of αamin(Tc) = - 3.56×10-6/K and αcmin(Tc) = - 1.30×10-6/K are obtained around the transition temperature Tc ~ 520 K. By comparison, the minimum values of line thermal expansion coefficients for Dy2Fe17 [11]， Tb3(Fe, Ti)29 [13] and YFe11Ti [16] were found to be 6.9×10-6 K-1， - 12.1×10-6 K-1 and - 1.3×10-6 K-1, respectively. The calculated values of the spontaneous magnetostriction along the a-axis, λa = ∆a/a, and the c - axis λc = ∆c/c, as well as the spontaneous volume magnetostriction ωs = ∆V/V are show as functions of temperature in Figure 3(d). The values for this set of magnetostriction parameters at 300 K are λa = 3.235×10-3, λc = 1.441×10-3 and ωs = 6.216×10-3. Moreover, it can also be seen from Figure 3(d) that λa, λc and ωs do not become zero at TC and maintain nonzero values to around 600 K (T/TC ∼ 1.15), well above the ordering temperature TC = 520(10) K. It is well accepted that the magnitude and the temperature dependence of the bulk volume magnetostriction of a ferromagnetic compound can be related to the square of the magnetic moment [12]. Given this link between magnetostriction and magnetic moment, the persistence of non-zero spontaneous magnetostrictive deformation above the magnetic transition temperature, indicates the likely occurrence of a short-range magnetic correlations. Indeed, such effects have been reported in other systems such as Dy2Fe17-xMnx [11], Er2Fe17 [12], Tb3(Fe,Ti)29 [13]， Ce3(Fe, M)29 [14] and YFe11xCoxTi
[16].
3.3 Magnetoelastic coupling at individual sites
8
Further insight to the behaviour of the magnetoelastic coupling of ErFe11.4Nb0.6 is provided by the temperature dependences of the calculated values for both the WSC volumes and the average bonding distances for the 2a, 8i, 8j and 8f sites as shown in Figure 4. It is clear that, the WSC volumes at the 2a, 8j and 8f sites exhibit trends with increasing temperature that are similar to those obtained for the lattice parameters of Figure 3(a). Likewise, the WSC volumes and the average bonding distances for the 2a, 8j and 8f exhibit a clear anomaly around TC. On the other hand, compared with atoms at the 2a, 8j and 8f sites, the reduced sensitivity of the WSC volume for the atom at the 8i site to change in temperature around TC, may reflect a reduced magneto-volume effect of the 8i site atom. In considering the relative invariance of the average bonding distances of the 8i site in the temperature region around Tc compared with the 8j and 8f sites, the atom at the 8i site has the largest number of Fe nearest neighbours, NN=13, while the atoms at the 8j and 8f sites have 10 Fe neighbours (Table 1). Given that Fe atoms at 8i sites have the largest average interatomic distances (see Table 1 and Figure 4), a Fe atom at an 8i site is expected to have the largest magnetic moment. This behaviour has been confirmed by a neutron diffraction study of the ErFe11.35Nb0.65 compound in which the moments for Fe at 8i, 8j and 8f site are determined to be 2.0(5) µB, 1.9(5) µB and 1.8(3) µB, respectively [22]. As such, it is surprising to note that atoms at the 8i site exhibit a reduced response to magnetoelastic coupling even though atoms at the 8i site experience the largest degree of orbital overlap with surrounding atoms. The Fe ions at 8i sites have 13 coordination ions which results in a stronger bonding force compared with 8j and 8f site Fe which have 10 coordination ions. The behaviour that Fe ions at 8i sites are more rigid than Fe ions at the 8j and 8f sites around the magnetic transition temperature, could be explained based on the overall interaction of the Fe ions at 8i site bonding with surrounding coordination ions and exchange interaction with adjacent Fe ions. Moreover, the fact that the 8i position is partially occupied by Nb atoms, which are nonmagnetic, indicates that there are fewer magnetic atoms at the 8i site compared with the Fe atoms at 8j and 8f sites. This factor may also play a role in the weaker response of 8i site atoms to magnetoelastic coupling. 9
4. Conclusions
The crystal structural effects and magnetoelastic coupling effects of the rare earth intermetallic compound ErFe11.4Nb0.6 of ferrimagnetic transition temperature Tc = 520(10) K have been studied in detail by variable temperature synchrotron x-ray diffraction measurements over the temperature range 300 K to 640 K. The temperature dependence of the a - and c - lattice parameters reveal a region of anisotropic negative thermal expansion below the ordering temperature resulting from a strong spontaneous magnetostriction in the magnetic state, while ErFe11.4Nb0.6 is found to exhibit an invar effect over the approximate temperature range ~ 470 – 520 K. In addition, the presence of magnetoelastic coupling around the magnetic transition temperature is revealed by the distinct changes in atomic position parameters of the 8i and 8j sites around TC while the persistence of non-zero spontaneous magnetostrictive deformation above the magnetic transition temperature, indicates the likely occurrence of a short-range magnetic correlations. Both the Wigner-Seitz cell volume and the average bonding distances for the 2a, 8j and 8f sites exhibit clear anomalies around TC, thus revealing correlation with the change of magnetic state. Acknowledgements The authors are grateful for the experimental support from staff at the Powder Diffraction beamline, Australian Synchrotron (ANSTO).
10
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12
Figures:
(b)
(310)
TC
4.0k
Intensity (arb. unit.)
8.0k
(310)
14.72 14.70
20k
TC
300 400 500 600 T (K)
10k
14.6
14.8
two theta (degree) 8.0k
(002)
TC
T (K)
600
500
T (K)
400 300
4.0k
Intensity (arb. unit.)
(002) TC
16.52 16.50
600 500
400
T (K)
(a)
Intensity (arb. unit.)
Peak position (degree)
600 500
400 300
10
20
30
40
16.4
two theta (degree)
16.6
300
two theta (degree)
Figure 1(a) Synchrotron x-ray diffraction patterns of ErFe11.4Nb0.6 over the temperature range 300 K to 650 K and (b) A set of the (310) and (002) Bragg reflections on expanded scales at selected temperatures over the range 300 K to 650 K. The patterns at the selected temperatures reflect the temperature dependence of the lattice parameters in the ab-plane ((310) reflection) and the c - axis ((002) reflection). The inset of Figure 1(a) shows the variation of the positions of the (310) and (002) reflections as functions of temperature with TC = 520(10) K marked by arrows.
13
(b)
Yobs Ycalc Yobs-Ycalc Bragg_position
30000
T=300 K
Intensity (arb. unit.)
0
0.360
(c) x8i, x8j
0.359
T=500 K
0
20000
x8i
TC
20000
T=560 K
x8j
0.279
0 0.278
TC 300
400
500
10
20
30
two theta (degree)
600
T(K)
Figure 2(a) Schematic diagram of the crystal structure of ErFe11.4Nb0.6 (Er atoms at 2a site - grey circles; Fe and Nb atoms at 8i site - red circles; Fe atoms at 8j site - green circles and Fe atoms at 8f site - blue circles); (b) Refinements of ErFe11.4Nb0.6 at T = 300 K, 500 K and 560 K: experimental data (asterisk symbols); red lines are Rietveld refinements to the data (FullProf); blue vertical lines represent Bragg reflections from ErFe11.4Nb0.6, α-Fe and Fe2Nb from top to bottom respectively; the green horizontal line shows the difference between the experimental and calculated patterns. and (c) atomic position parameters x8i and x8j of the 8i and 8j sites respectively, as a function of temperature.
14
a c
8.46 4.792
3
∆V=2.129 Å
342
αa
-5
αc
-1
αa, αc (K )
1.0x10
(b)
0.0
-2
1.0x10
TC 0.0 400 600 T(K)
ωs
(d)
6 -3
4.784
∆c=0.0069 Å
344
3
(a)
(c)
dV/dT (Å /K)
3
Unit cell volume V (Å )
∆a=0.0274 Å
λa, λc, ωs (10 )
lattice parameter (Å)
8.49
346
λa, λc
3
0
300
400
500 T(K)
300
600
400
500
600
T (K)
Figure 3 Temperature dependences for ErFe11.4Nb0.6 of: (a) the a and c lattice parameters; (b) the linear thermal expansion coefficient; (c) the unit cell volume V, and (d) the spontaneous magnetostriction λa = ∆a/a and λc = ∆c/c along the a - axis and the c - axis respectively, and the spontaneous volume magnetostriction ωs = ∆V/V. The arrows indicate the magnetic transition temperature Tc = 520(10) K. A graph of dV/dT versus T is shown in the inset of Figure 3(c).
15
29.5
300
400
500
600
T (K) Fe at 8j site distance
11.85
(c)
3
2.576
WSC volume
11.82 2.574
3
12.69
2.705
2.704 300
400
500
600
T (K)
Fe at 8f site distance
(d) 11.37
WSC volume 3
3.115
2.706
WSC Volume (Å )
29.3
12.72
Average bond length to neighbouring Fe (Å)
3.120
WSC Volume (Å )
Average bond length to neighbouring Fe (Å)
29.4
(b)
2.707
3
WSC volume
Fe at 8i site distance WSC volume
WSC Volume (Å )
(a) WSC Volume (Å )
3.125
2.708
Er at 2a site distance
2.502
11.34
2.499
11.79
11.31 2.572 300
400
500
600
300
400
500
600
T (K)
T (K)
Figure 4 Temperature dependences of the average bond lengths to neighbouring Fe atoms and Wigner-Seitz cell volumes for: (a) an Er atom at the 2a site and Fe atoms at the (b) 8i, (c) 8j and (d) 8f sites, respectively. The arrows indicate the magnetic transition temperature Tc = 520(10) K.
16
Table1 The numbers of neighbouring atoms, Wigner-Seitz cell volumes (WSC volumes) and bond lengths in ErFe11.4Nb0.6 at 300 K. Atom
Er,
Number of
Number of
Er
Fe
neighbours
neighbours
0
8i
Fe, 8j
Minimum
Maximum
Volume bond length to bond length to (Å3)
Average bond length to
neighbouring
neighbouring
neighbouring
Fe (Å)
Fe (Å)
Fe (Å)
29.244
3.0428
3.2302
3.1183
12.680
2.3957
2.9320
2.7052
11.785
2.4478
2.6620
2.5731
11.311
2.3930
2.6050
2.4997
8×Fe8j, 8×Fe8f)
2a Fe/Nb,
20 (4×Fe8i,
WSC-
1
13 (5×Fe8i,
(1×Er2a)
4×Fe8j, 4×Fe8f)
2
10 (4×Fe8i,
((2×Er2a)
2×Fe8j, 4×Fe8f)
Fe,
2
8f
(2× Er2a)
10 (4×Fe8i, 4×Fe8j, 2×Fe8f)
17
A detailed investigation on magnetoelastic coupling in ErFe11.4Nb0.6 compound by variable temperature high resolution Synchrotron x-ray diffraction is presented. Remarkable magnetovolume anomalies and negative thermal expansion have been detected below the Curie temperature, TC. Short-range magnetic correlations are present above TC. Specific features in thermal expansion have been investigated in detail.
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests: