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Thermal expansion of a Au−Al−Yb intermediate valence quasicrystal
Solid State Communications 211 (2015) 19–22
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Thermal expansion of a Au Al Yb intermediate valence quasicrystal T. Watanuki a,n, S. Kashimoto b, T. Ishimasa b, A. Machida a, S. Yamamoto b, Y. Tanaka b, M. Mizumaki c, N. Kawamura c, S. Watanabe d a
Condensed Matter Science Unit, Quantum Beam Science Center, Japan Atomic Energy Agency, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan c Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan d Department of Basic Sciences, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 February 2015 Accepted 8 March 2015 Communicated by S. Miyashita Available online 14 March 2015
The thermal expansion of a Au Al Yb intermediate-valence quasicrystal has been studied. X-ray diffraction measurements showed zero thermal expansion below 50 K. By comparison with an isostructural Au Al Tm quasicrystal, the contribution of the Yb valence variation was extracted, and it was shown that its negative thermal expansion component compensated for the positive thermal expansion of the original lattice. On cooling, the Yb contribution grew steeply below approximately 155 K down to the lowest experimental temperature of 5 K, due to enlargement of the Yb atomic radius, which was caused by the valence shift toward the divalent state. Additionally, a larger Yb contribution to the thermal expansion was demonstrated in a crystalline approximant to this quasicrystal. The magnitude of this contribution was approximately 1.4 times larger than in the case of the quasicrystal itself, resulting in a slight negative thermal expansion below 50 K. A heterogeneous valence model for the quasicrystal that we proposed previously accounts for this magnitude difference. & 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Quasicrystal A. Intermediate valence compounds D. Thermal expansion
1. Introduction Icosahedral Au Al Yb quasicrystal [1] (q-Au Al Yb) is an intermediate-valence compound [2]. The Yb of valence of 2.61 þ exhibits an intermediate state between a divalent state (4f14, J ¼0) and a trivalent one (4f13, J ¼7/2) [2]. It is expected to have rich physical properties due to the variable character of the Yb state. Non-Fermi-liquid behavior—namely, quantum critical phenomena —has been observed at very low temperatures below several Kelvin without either doping, pressure, or field tuning [2,3]. This behavior has been explained by the theory of quantum-critical valence fluctuations of Yb [3–5]. It is expected that other interesting physical properties caused by the Yb valence variation will be shown in other temperature ranges. We focused on the thermal expansion character of qAu Al Yb. Since the Yb valence can vary as a function of temperature, we expected that it would have an effect on the thermal expansion. Yb valence change induces variation of the Yb atomic radius, and consequently, modification of the lattice volume. The temperature scale of this effect should correspond to the Kondo temperature (TK). The magnetic susceptibility of qAu Al Yb shows a Curie–Weiss behavior above approximately 100 K [2,3,6], and the TK value is estimated to be around the n
Corresponding author. E-mail address: [email protected] (T. Watanuki).
http://dx.doi.org/10.1016/j.ssc.2015.03.008 0038-1098/& 2015 Elsevier Ltd. All rights reserved.
value of the paramagnetic Curie temperature of absolute θp ¼ 138 K [2]. The q-Au Al Yb Au51Al34Yb15, with a sixdimensional lattice parameter of a6D ¼7.448 Å [1], has an isostructural Tm-based quasicrystal of Au46Al38Tm16 alloy (q-Au Al Tm), with a6D ¼7.411 Å [7], where Tm has an integer valence of 3 þ [8]. A comparative study between them enabled us to extract the contribution of the Yb valence variation. Additionally, a periodic counterpart to q-Au Al Yb is available for obtaining an insight into the Yb valence state of q-Au Al Yb by contrastive investigation between them. The 1/1 cubic crystalline approximant of Au51Al35Yb14 (c-Au Al Yb) consists of the same atomic cluster as q-Au Al Yb, but in a different arrangement, i.e., a bcc packing structure with a lattice parameter a0 ¼ 14.500 Å [1]. This approximant also has an isostructural Tm-based compound, Au48Al38Tm14 (c-Au Al Tm), with a0 ¼ 14.458 Å [7]. In this study, we demonstrate zero thermal expansion of qAu AlYb at low temperatures due to the intermediate-valence Yb contribution. Additionally, a larger Yb contribution to the thermal expansion in c-Au Al Yb than in q-Au Al Yb is shown, and the origin of the difference is discussed.
2. Experiment Thermal expansion measurements of q-Au Al Yb at low temperatures were performed using X-ray diffraction (XRD). In
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T. Watanuki et al. / Solid State Communications 211 (2015) 19–22
order to extract the Yb contribution, q-Au Al Tm was also measured as a reference. An as-cast specimen of q-Au Al Yb was prepared from highpurity materials [Au (purity 99.99 wt%), Al (purity 99.999 wt%), and Yb (purity 99.9 wt%)] in an arc furnace with an argon atmosphere, as described in Ref. [1] Another as-cast specimen of qAu Al Tm was prepared by a similar method [7]. Each specimen was respectively confirmed to be q-Au Al Yb or q-Au Al Tm by XRD measurements using Cu Kα radiation. Low temperature XRD experiments were performed at BL22XU in SPring-8 [9]. Thermal expansion was determined by measuring the temperature dependence of the d-values of the specimens in the temperature range between 5 and 300 K. Oscillation photographs of each cracked piece of q-Au Al Yb and q-Au Al Tm alloy were taken using a monochromatized incident X-ray of 20 keV (λ ¼0.6199 Å) and an imaging plate detector in the two theta range up to 331. Sharp diffraction spots were obtained from each specimen piece of several tens of microns in size that consisted of single-crystalline domains, which enabled us to acquire high-precision d-value data. The oscillation photographs were converted into the two theta intensity plots, as shown in Fig. 1, and the d-values of the reflection peaks were obtained. In order to perform highprecision comparative measurements between q-Au Al Yb and q-Au Al Tm, the two specimen pieces were mounted on the same diamond plate at the cold head of a He 4 K closed cycle cryostat. XRD data of the two specimens were acquired in the same cooling and heating process. Additionally, the thermal expansions of c-Au Al Yb and c-Au Al Tm were measured by a similar procedure to the above.
3. Results and discussions Fig. 2 shows the temperature dependence of averaged, normalized d-value, dðTÞ=d300 K , of q-Au AlYb along with that of qAu AlTm. Normalization was done based on the values at 300 K.
Fig. 1. (Color online) X-ray diffraction patterns of (a) icosahedral Au Al Yb quasicrystal (q-Au Al Yb) and (b) icosahedral Au Al Tm quasicrystal (qAu Al Tm) at 5 K. The oscillation photographs of each specimen piece that consisted of single-crystalline domains were converted into the two theta intensity plots. Major reflections are indicated by six-dimensional indices.
Fig. 2. (Color online) Temperature dependence of averaged, normalized d-values, dðTÞ=d300 K , of q-Au Al Yb (red closed circles), q-Au Al Tm (orange open circles), c-Au Al Yb (blue closed squares), and c-Au Al Tm (light-blue open squares). Normalization was done based on the values at 300 K. Solid lines denote polynomial fits.
The linear thermal expansion normalized by the length at 300 K,
ΔlðTÞ=l300 K , is related to dðTÞ=d300 K by the equation ΔlðTÞ=l300 K ¼
dðTÞ=d300 K 1. dðTÞ=d300 K was obtained by averaging the normalized d-values of several sharp diffraction peaks at a higher angle between 201 and 301, where the temperature dependencies of the normalized d-values were basically identical to each other. On cooling, the dðTÞ=d300 K value of q-Au Al Yb decreases monotonically; however, the decreasing ratio becomes remarkably smaller at low temperatures. dðTÞ=d300 K shows nearly constant behavior below approximately 50 K. By contrast, the dðTÞ=d300 K value of q-Au Al Tm shows typical behavior for an alloy. By comparing the dðTÞ=d300 K value of q-Au Al Yb with that of q-Au Al Tm, no difference appears above approximately 200 K. On cooling below 200 K, however, the dðTÞ=d300 K value of q-Au Al Yb turns upward compared with that of q-Au Al Tm. The upward shift gradually becomes larger as the temperature decreases. Eventually, nearly zero thermal expansion appears below 50 K. Above 200 K, nearly linear temperature dependence is observed. The linear thermal expansion coefficient was evaluated to be 12:8ð3Þ 10 6 K 1 . The upward shift of the dðTÞ=d300 K value of q-Au Al Yb from that of q-Au AlTm is attributed to the valence decrease of the Yb atoms in q-Au AlYb as the temperature decreases. Because the Yb atomic radius becomes larger as the valence decreases from a trivalent state to a divalent one, the upward shift is interpreted as the lattice expansion component due to the Yb atomic radius enlargement that is caused by the valence shift toward the divalent state. Fig. 3 shows the upward shift component, namely a linear thermal expansion of the Yb contribution, ΔlYb ðT Þ=l300 K . It was obtained by subtracting the polynomial fit of the dðTÞ=d300 K data for q-Au AlTm from that for q-AuAl Yb. On cooling, ΔlYb ðT Þ=l300 K starts to increase around 200 K. It grows steeply below a temperature, Tnq-Au Al Yb, of approximately 155 K down to the lowest temperature of 5 K, and reaches 3:9 10 4 ; i.e., 13% of the counter-contribution to the original lattice contraction. This additional Yb contribution to the negative thermal expansion component compensates for the positive thermal expansion of the original lattice, and causes zero thermal expansion at low temperatures. TnqAu Al Yb is a characteristic temperature of ΔlYb ðT Þ=l300 K , and
T. Watanuki et al. / Solid State Communications 211 (2015) 19–22
Fig. 3. (Color online) Linear thermal expansion of the Yb contribution, ΔlYb ðT Þ=l300 K , of q-Au Al Yb (red solid line) and c-Au Al Yb (blue dotted line). Arrows indicate the characteristic temperatures, T*q-Au Al Yb and T*c-Au Al Yb.
roughly corresponds to the Kondo temperature, TK. Here, we defined the Tnq-Au Al Yb value as the temperature where the second derivative of ΔlYb ðT Þ=l300 K takes the maximum value. The Kondo screening effect on the magnetic character of the trivalent component appears below Tnq-Au Al Yb, and causes the Yb valence shift toward the nonmagnetic divalent state. The Tnq-Au Al Yb value is consistent with our previous magnetic measurement of θp ¼ 138 K, as mentioned above [2]. The Yb valence shift has been directly confirmed by Xray absorption spectroscopy near the Yb-L3 edge. According to the preliminary valence measurements at BL39XU in SPring-8, the shift value by cooling from room temperature down to 5 K is estimated to be 0.05. The effects of Yb on thermal expansion have been reported in other intermediate-valence Yb compounds. For example, YbCu2Si2, whose Yb valence is 2.89 at 300 K [10], shows a negative volume thermal expansion below approximately 80 K [11] along with the Yb valence decrease as the temperature decreases [10,12]. The ΔlYb ðT Þ=l300 K value of q-Au Al Yb increases continuously by cooling, even at the lowest temperatures. This result indicates that the electronic specific heat coefficient of the Yb–4f contribution, γYb, increases even at the lowest temperatures. The ΔlYb ðT Þ=l300 K value is related to the specific heat of the Yb–4f contribution, CYb, by the following expression that was derived from the Grüneisen relation on the assumption that the temperature dependencies of the bulk modulus and the sample volume are negligible at the lowest temperatures 1 d C ðT Þ ΔlYb ðT Þ=l300 K Yb : T dT T Because d=dT ΔlYb ðT Þ=l300 K remains at a non-zero value, the left side of the expression increases divergently with decreasing temperature, which indicates divergent growth of C Yb ðT Þ=T, namely γYb, at the lowest temperatures. This consequence is consistent with the nonFermi-liquid behavior of q-Au Al Yb. Our previous specific heat measurement showed the divergent growth of the C Yb ðT Þ=T at very low temperatures down to 0.38 K [2]. Next, the results for c-Au Al Yb, i.e., the periodic counterpart of q-Au Al Yb, are shown. In Fig. 2, the dðTÞ=d300 K values of c-AuAl Yb and c-Au Al Tm are displayed. The upward shift of the dðTÞ=d300 K value of c-Au Al Yb away from that of
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c-Au Al Tm is again observed, but the magnitude is larger than it was in the case of q-Au Al Yb. As a result, slight negative thermal expansion of c-Au Al Yb appears below approximately 50 K. As shown in Fig. 3, the ΔlYb ðT Þ=l300 K value of c-Au AlYb exhibits similar behavior to that of q-Au AlYb, but it reaches 5:6 10 4 (larger than that of q-Au Al Yb). The characteristic temperature, Tnc-Au Al Yb, of approximately 135 K is close to Tnq-AuAlYb, but the magnitude of ΔlYb ðT Þ=l300 K is approximately 1.4 times larger than was the case for q-Au Al Yb in the temperature region between 5 and 100 K. The difference of the magnitude is discussed below. The Tnc-Au Al Yb value is again consistent with our previous magnetic measurement on c-Au AlYb of θp ¼ 127 K [2]. The continuous increase in the ΔlYb ðT Þ=l300 K value of c-Au Al Yb at the lowest temperatures is also consistent with the non-Fermi-liquid behavior of c-Au Al Yb [2,3]. Comparison of c-Au Al Tm with q-Au AlTm shows that their dðTÞ=d300 K values are very close to each other. The local structural similarity between the quasicrystal and its crystalline approximant is reflected in the very close nature of the thermal expansion. By comparing the Yb-based compounds (q-Au Al Yb and c-Au AlYb) with the Tm-based compounds (q-Au Al Tm and c-Au Al Tm), no difference in dðTÞ=d300 K is shown in the higher temperature region above approximately 200 K. This result indicates that the Tm-based compounds work well as reference systems for the Yb-based compounds. We examined the difference in the magnitudes of ΔlYb ðT Þ=l300 K between q-Au Al Yb and c-Au Al Yb. Previously, we proposed a heterogeneous valence model for q-Au Al Yb [2], which is responsible for the magnitude difference. In this model, the major Yb sites in q-Au Al Yb exhibit a high valence, similar to the c-Au Al Yb valence of 2.8 þ, and the remaining minor sites exhibit a low valence, estimated at 2.2 þ. By contrast, all Yb sites in c-Au Al Yb that are crystallographically equivalent to each other homogeneously exhibit the same valence of 2.8 þ [2]. The major sites in q-Au Al Yb are located in the atomic cluster, as is also the case in all Yb sites of c-Au Al Yb, and the minor sites in qAu Al Yb are located in the gaps of the cluster packing [1,13– 15]. The population ratio of major sites to minor ones in q-Au Al Yb is approximately 7:3 [16]. Note that q-Au Al Yb contains the minor sites, but c-Au Al Yb does not have them. The existence of the minor sites in q-Au Al Yb may cause the magnitude difference between these two systems. According to this model, the high-valence Yb at the major sites in q-AuAl Yb accounts for the similarity of Tnq-Au Al Yb to Tnc-Au Al Yb. Because TK that corresponds to Tn depends greatly on the Yb valence, the close Tn values indicate similarity in the Yb valence, which is ensured by the high-valence Yb. It is reasonable to expect that the high-valence Yb in q-Au Al Yb exhibits a similar valence shift due to cooling to that of c-Au Al Yb. By contrast, the low-valence Yb at the minor sites in q-Au Al Yb is considered to show no valence shift. As mentioned in Ref [2], low-valence Yb close to the divalent state typically shows a nonmagnetic character. This indicates that TK is much higher than room temperature, and consequently, no temperature variation due to the Kondo screening effect is shown at low temperatures. The coexistence of these two kinds of Yb in qAu AlYb accounts for the smaller valence shift as a result of averaging the two effects of the valence shift sites and the non-shift ones, and consequently for the smaller magnitude of ΔlYb ðT Þ=l300 K than in c-Au Al Yb. By employing the population ratio of these two sites, the magnitude ratio of ΔlYb ðT Þ=l300 K of q-Au Al Yb to that of c-Au Al Yb is calculated to be 0.7, with an inverse ratio of approximately 1.4. The estimate with the heterogeneous valence model agrees with the experimental result of 1.4, as shown above. To summarize, we have found anomalous thermal expansion behavior in intermediate-valence compounds of q-Au Al Yb and c-Au Al Yb at low temperatures due to the temperature variation of their Yb valence. It was also shown that their thermal
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expansion character at the lowest temperatures is consistent with their non-Fermi-liquid behavior. Additionally, a larger anomaly has been demonstrated in c-Au Al Yb than in q-Au Al Yb. The difference would be originated from the existence of the additional kind of Yb sites in q-Au Al Yb that does not exist in c-Au Al Yb. Acknowledgments This work was performed under Proposals nos. 2011B3701, 2011B2092, 2012A3701 and 2012B0046 at SPring-8, and was partially supported by a Grant-in-aid for Scientific Research (No. 24540386) from the Japan Society for Promotion of Science. References [1] T. Ishimasa, Y. Tanaka, S. Kashimoto, Philos. Mag. 91 (2011) 4218. [2] T. Watanuki, S. Kashimoto, D. Kawana, T. Yamazaki, A. Machida, Y. Tanaka, T.J. Sato, Phys. Rev. B 86 (2012) 094201. [3] K. Deguchi, S. Matsukawa, N.K. Sato, T. Hattori, K. Ishida, H. Takakura, T. Ishimasa, Nat. Mater. 11 (2012) 1013. [4] S. Watanabe, K. Miyake, J. Phys. Soc. Jpn. 82 (2013) 083704. [5] S. Watanabe, K. Miyake, Phys. Rev. Lett. 105 (2010) 186403.
[6] S. Jazbec, S. Vrtnik, Z. Jagličić, S. Kashimoto, J. Ivkov, P. Popčević, A. Smomtara, H.J. Kim, J.G. Kim, J. Dolinsěk, J. Alloy. Compd. 586 (2014) 343. [7] K. Tanaka, Y. Tanaka, T. Ishimasa, M. Nakayama, S. Matsukawa, K. Deguchi, N.K. Sato, Acta. Phys. Pol. A 126 (2014) 603. [8] M. Nakayama, K. Tanaka, S. Matsukawa, K. Deguchi, K. Imura, T. Ishimasa, N.K. Sato, J. Phys. Soc. Jpn. 84 (2015) 024721. [9] T. Watanuki, A. Machida, T. Ikeda, A. Ohmura, H. Kaneko, K. Aoki, T.J. Sato, A.P. Tsai, Philos. Mag. 87 (2007) 2905. [10] J.M. Lawrence, G.H. Kwei, P.C. Canfield, J.G. DeWitt, A.C. Lawson, Phys. Rev. B 49 (1994) 1627. [11] N.D. Dung, T.D. Matsuda, Y. Haga, S. Ikeda, E. Yamamoto, T. Ishikura, T. Endo, S. Tatsuoka, Y. Aoki, H. Sato, T. Takeuchi, R. Settai, H. Harima, Y. Ōnuki, J. Phys. Soc. Jpn. 78 (2009) 084711. [12] L. Moreschini, C. Dallera, J.J. Joyce, J.L. Sarrao, E.D. Bauer, V. Fritsch, S. Bobev, E. Carpene, S. Huotari, G. Vank´o, G. Monaco, P. Lacovig, G. Panaccione, A. Fondacaro, G. Paolicelli, P. Torelli, M. Grioni, Phys. Rev. B 75 (2007) 035113. [13] H. Takakura, C.P. Gómez, A. Yamamoto, M. de Boissieu, A.P. Tsai, Nat. Mater. 6 (2007) 58. [14] A.P. Tsai, C.P. Gómez, in: T. Fujiwara, Y. Ishii (Eds.), Handbook of Metal Physics: Quasicrystals, Elsevier, Amsterdam, 2008, p. 75. [15] T. Ishimasa, in Ref. 13, p. 49. [16] H. Takakura (private communication).
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Solid State Communications journal homepage: www.elsevier.com/locate/ssc
Thermal expansion of a Au Al Yb intermediate valence quasicrystal T. Watanuki a,n, S. Kashimoto b, T. Ishimasa b, A. Machida a, S. Yamamoto b, Y. Tanaka b, M. Mizumaki c, N. Kawamura c, S. Watanabe d a
Condensed Matter Science Unit, Quantum Beam Science Center, Japan Atomic Energy Agency, 1-1-1 Kouto, Sayo, Hyogo 679-5148, Japan Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan c Japan Synchrotron Radiation Research Institute, 1-1-1 Kouto, Sayo, Hyogo 679-5198, Japan d Department of Basic Sciences, Kyushu Institute of Technology, Kitakyushu 804-8550, Japan b
art ic l e i nf o
a b s t r a c t
Article history: Received 14 February 2015 Accepted 8 March 2015 Communicated by S. Miyashita Available online 14 March 2015
The thermal expansion of a Au Al Yb intermediate-valence quasicrystal has been studied. X-ray diffraction measurements showed zero thermal expansion below 50 K. By comparison with an isostructural Au Al Tm quasicrystal, the contribution of the Yb valence variation was extracted, and it was shown that its negative thermal expansion component compensated for the positive thermal expansion of the original lattice. On cooling, the Yb contribution grew steeply below approximately 155 K down to the lowest experimental temperature of 5 K, due to enlargement of the Yb atomic radius, which was caused by the valence shift toward the divalent state. Additionally, a larger Yb contribution to the thermal expansion was demonstrated in a crystalline approximant to this quasicrystal. The magnitude of this contribution was approximately 1.4 times larger than in the case of the quasicrystal itself, resulting in a slight negative thermal expansion below 50 K. A heterogeneous valence model for the quasicrystal that we proposed previously accounts for this magnitude difference. & 2015 Elsevier Ltd. All rights reserved.
Keywords: A. Quasicrystal A. Intermediate valence compounds D. Thermal expansion
1. Introduction Icosahedral Au Al Yb quasicrystal [1] (q-Au Al Yb) is an intermediate-valence compound [2]. The Yb of valence of 2.61 þ exhibits an intermediate state between a divalent state (4f14, J ¼0) and a trivalent one (4f13, J ¼7/2) [2]. It is expected to have rich physical properties due to the variable character of the Yb state. Non-Fermi-liquid behavior—namely, quantum critical phenomena —has been observed at very low temperatures below several Kelvin without either doping, pressure, or field tuning [2,3]. This behavior has been explained by the theory of quantum-critical valence fluctuations of Yb [3–5]. It is expected that other interesting physical properties caused by the Yb valence variation will be shown in other temperature ranges. We focused on the thermal expansion character of qAu Al Yb. Since the Yb valence can vary as a function of temperature, we expected that it would have an effect on the thermal expansion. Yb valence change induces variation of the Yb atomic radius, and consequently, modification of the lattice volume. The temperature scale of this effect should correspond to the Kondo temperature (TK). The magnetic susceptibility of qAu Al Yb shows a Curie–Weiss behavior above approximately 100 K [2,3,6], and the TK value is estimated to be around the n
Corresponding author. E-mail address: [email protected] (T. Watanuki).
http://dx.doi.org/10.1016/j.ssc.2015.03.008 0038-1098/& 2015 Elsevier Ltd. All rights reserved.
value of the paramagnetic Curie temperature of absolute θp ¼ 138 K [2]. The q-Au Al Yb Au51Al34Yb15, with a sixdimensional lattice parameter of a6D ¼7.448 Å [1], has an isostructural Tm-based quasicrystal of Au46Al38Tm16 alloy (q-Au Al Tm), with a6D ¼7.411 Å [7], where Tm has an integer valence of 3 þ [8]. A comparative study between them enabled us to extract the contribution of the Yb valence variation. Additionally, a periodic counterpart to q-Au Al Yb is available for obtaining an insight into the Yb valence state of q-Au Al Yb by contrastive investigation between them. The 1/1 cubic crystalline approximant of Au51Al35Yb14 (c-Au Al Yb) consists of the same atomic cluster as q-Au Al Yb, but in a different arrangement, i.e., a bcc packing structure with a lattice parameter a0 ¼ 14.500 Å [1]. This approximant also has an isostructural Tm-based compound, Au48Al38Tm14 (c-Au Al Tm), with a0 ¼ 14.458 Å [7]. In this study, we demonstrate zero thermal expansion of qAu AlYb at low temperatures due to the intermediate-valence Yb contribution. Additionally, a larger Yb contribution to the thermal expansion in c-Au Al Yb than in q-Au Al Yb is shown, and the origin of the difference is discussed.
2. Experiment Thermal expansion measurements of q-Au Al Yb at low temperatures were performed using X-ray diffraction (XRD). In
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T. Watanuki et al. / Solid State Communications 211 (2015) 19–22
order to extract the Yb contribution, q-Au Al Tm was also measured as a reference. An as-cast specimen of q-Au Al Yb was prepared from highpurity materials [Au (purity 99.99 wt%), Al (purity 99.999 wt%), and Yb (purity 99.9 wt%)] in an arc furnace with an argon atmosphere, as described in Ref. [1] Another as-cast specimen of qAu Al Tm was prepared by a similar method [7]. Each specimen was respectively confirmed to be q-Au Al Yb or q-Au Al Tm by XRD measurements using Cu Kα radiation. Low temperature XRD experiments were performed at BL22XU in SPring-8 [9]. Thermal expansion was determined by measuring the temperature dependence of the d-values of the specimens in the temperature range between 5 and 300 K. Oscillation photographs of each cracked piece of q-Au Al Yb and q-Au Al Tm alloy were taken using a monochromatized incident X-ray of 20 keV (λ ¼0.6199 Å) and an imaging plate detector in the two theta range up to 331. Sharp diffraction spots were obtained from each specimen piece of several tens of microns in size that consisted of single-crystalline domains, which enabled us to acquire high-precision d-value data. The oscillation photographs were converted into the two theta intensity plots, as shown in Fig. 1, and the d-values of the reflection peaks were obtained. In order to perform highprecision comparative measurements between q-Au Al Yb and q-Au Al Tm, the two specimen pieces were mounted on the same diamond plate at the cold head of a He 4 K closed cycle cryostat. XRD data of the two specimens were acquired in the same cooling and heating process. Additionally, the thermal expansions of c-Au Al Yb and c-Au Al Tm were measured by a similar procedure to the above.
3. Results and discussions Fig. 2 shows the temperature dependence of averaged, normalized d-value, dðTÞ=d300 K , of q-Au AlYb along with that of qAu AlTm. Normalization was done based on the values at 300 K.
Fig. 1. (Color online) X-ray diffraction patterns of (a) icosahedral Au Al Yb quasicrystal (q-Au Al Yb) and (b) icosahedral Au Al Tm quasicrystal (qAu Al Tm) at 5 K. The oscillation photographs of each specimen piece that consisted of single-crystalline domains were converted into the two theta intensity plots. Major reflections are indicated by six-dimensional indices.
Fig. 2. (Color online) Temperature dependence of averaged, normalized d-values, dðTÞ=d300 K , of q-Au Al Yb (red closed circles), q-Au Al Tm (orange open circles), c-Au Al Yb (blue closed squares), and c-Au Al Tm (light-blue open squares). Normalization was done based on the values at 300 K. Solid lines denote polynomial fits.
The linear thermal expansion normalized by the length at 300 K,
ΔlðTÞ=l300 K , is related to dðTÞ=d300 K by the equation ΔlðTÞ=l300 K ¼
dðTÞ=d300 K 1. dðTÞ=d300 K was obtained by averaging the normalized d-values of several sharp diffraction peaks at a higher angle between 201 and 301, where the temperature dependencies of the normalized d-values were basically identical to each other. On cooling, the dðTÞ=d300 K value of q-Au Al Yb decreases monotonically; however, the decreasing ratio becomes remarkably smaller at low temperatures. dðTÞ=d300 K shows nearly constant behavior below approximately 50 K. By contrast, the dðTÞ=d300 K value of q-Au Al Tm shows typical behavior for an alloy. By comparing the dðTÞ=d300 K value of q-Au Al Yb with that of q-Au Al Tm, no difference appears above approximately 200 K. On cooling below 200 K, however, the dðTÞ=d300 K value of q-Au Al Yb turns upward compared with that of q-Au Al Tm. The upward shift gradually becomes larger as the temperature decreases. Eventually, nearly zero thermal expansion appears below 50 K. Above 200 K, nearly linear temperature dependence is observed. The linear thermal expansion coefficient was evaluated to be 12:8ð3Þ 10 6 K 1 . The upward shift of the dðTÞ=d300 K value of q-Au Al Yb from that of q-Au AlTm is attributed to the valence decrease of the Yb atoms in q-Au AlYb as the temperature decreases. Because the Yb atomic radius becomes larger as the valence decreases from a trivalent state to a divalent one, the upward shift is interpreted as the lattice expansion component due to the Yb atomic radius enlargement that is caused by the valence shift toward the divalent state. Fig. 3 shows the upward shift component, namely a linear thermal expansion of the Yb contribution, ΔlYb ðT Þ=l300 K . It was obtained by subtracting the polynomial fit of the dðTÞ=d300 K data for q-Au AlTm from that for q-AuAl Yb. On cooling, ΔlYb ðT Þ=l300 K starts to increase around 200 K. It grows steeply below a temperature, Tnq-Au Al Yb, of approximately 155 K down to the lowest temperature of 5 K, and reaches 3:9 10 4 ; i.e., 13% of the counter-contribution to the original lattice contraction. This additional Yb contribution to the negative thermal expansion component compensates for the positive thermal expansion of the original lattice, and causes zero thermal expansion at low temperatures. TnqAu Al Yb is a characteristic temperature of ΔlYb ðT Þ=l300 K , and
T. Watanuki et al. / Solid State Communications 211 (2015) 19–22
Fig. 3. (Color online) Linear thermal expansion of the Yb contribution, ΔlYb ðT Þ=l300 K , of q-Au Al Yb (red solid line) and c-Au Al Yb (blue dotted line). Arrows indicate the characteristic temperatures, T*q-Au Al Yb and T*c-Au Al Yb.
roughly corresponds to the Kondo temperature, TK. Here, we defined the Tnq-Au Al Yb value as the temperature where the second derivative of ΔlYb ðT Þ=l300 K takes the maximum value. The Kondo screening effect on the magnetic character of the trivalent component appears below Tnq-Au Al Yb, and causes the Yb valence shift toward the nonmagnetic divalent state. The Tnq-Au Al Yb value is consistent with our previous magnetic measurement of θp ¼ 138 K, as mentioned above [2]. The Yb valence shift has been directly confirmed by Xray absorption spectroscopy near the Yb-L3 edge. According to the preliminary valence measurements at BL39XU in SPring-8, the shift value by cooling from room temperature down to 5 K is estimated to be 0.05. The effects of Yb on thermal expansion have been reported in other intermediate-valence Yb compounds. For example, YbCu2Si2, whose Yb valence is 2.89 at 300 K [10], shows a negative volume thermal expansion below approximately 80 K [11] along with the Yb valence decrease as the temperature decreases [10,12]. The ΔlYb ðT Þ=l300 K value of q-Au Al Yb increases continuously by cooling, even at the lowest temperatures. This result indicates that the electronic specific heat coefficient of the Yb–4f contribution, γYb, increases even at the lowest temperatures. The ΔlYb ðT Þ=l300 K value is related to the specific heat of the Yb–4f contribution, CYb, by the following expression that was derived from the Grüneisen relation on the assumption that the temperature dependencies of the bulk modulus and the sample volume are negligible at the lowest temperatures 1 d C ðT Þ ΔlYb ðT Þ=l300 K Yb : T dT T Because d=dT ΔlYb ðT Þ=l300 K remains at a non-zero value, the left side of the expression increases divergently with decreasing temperature, which indicates divergent growth of C Yb ðT Þ=T, namely γYb, at the lowest temperatures. This consequence is consistent with the nonFermi-liquid behavior of q-Au Al Yb. Our previous specific heat measurement showed the divergent growth of the C Yb ðT Þ=T at very low temperatures down to 0.38 K [2]. Next, the results for c-Au Al Yb, i.e., the periodic counterpart of q-Au Al Yb, are shown. In Fig. 2, the dðTÞ=d300 K values of c-AuAl Yb and c-Au Al Tm are displayed. The upward shift of the dðTÞ=d300 K value of c-Au Al Yb away from that of
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c-Au Al Tm is again observed, but the magnitude is larger than it was in the case of q-Au Al Yb. As a result, slight negative thermal expansion of c-Au Al Yb appears below approximately 50 K. As shown in Fig. 3, the ΔlYb ðT Þ=l300 K value of c-Au AlYb exhibits similar behavior to that of q-Au AlYb, but it reaches 5:6 10 4 (larger than that of q-Au Al Yb). The characteristic temperature, Tnc-Au Al Yb, of approximately 135 K is close to Tnq-AuAlYb, but the magnitude of ΔlYb ðT Þ=l300 K is approximately 1.4 times larger than was the case for q-Au Al Yb in the temperature region between 5 and 100 K. The difference of the magnitude is discussed below. The Tnc-Au Al Yb value is again consistent with our previous magnetic measurement on c-Au AlYb of θp ¼ 127 K [2]. The continuous increase in the ΔlYb ðT Þ=l300 K value of c-Au Al Yb at the lowest temperatures is also consistent with the non-Fermi-liquid behavior of c-Au Al Yb [2,3]. Comparison of c-Au Al Tm with q-Au AlTm shows that their dðTÞ=d300 K values are very close to each other. The local structural similarity between the quasicrystal and its crystalline approximant is reflected in the very close nature of the thermal expansion. By comparing the Yb-based compounds (q-Au Al Yb and c-Au AlYb) with the Tm-based compounds (q-Au Al Tm and c-Au Al Tm), no difference in dðTÞ=d300 K is shown in the higher temperature region above approximately 200 K. This result indicates that the Tm-based compounds work well as reference systems for the Yb-based compounds. We examined the difference in the magnitudes of ΔlYb ðT Þ=l300 K between q-Au Al Yb and c-Au Al Yb. Previously, we proposed a heterogeneous valence model for q-Au Al Yb [2], which is responsible for the magnitude difference. In this model, the major Yb sites in q-Au Al Yb exhibit a high valence, similar to the c-Au Al Yb valence of 2.8 þ, and the remaining minor sites exhibit a low valence, estimated at 2.2 þ. By contrast, all Yb sites in c-Au Al Yb that are crystallographically equivalent to each other homogeneously exhibit the same valence of 2.8 þ [2]. The major sites in q-Au Al Yb are located in the atomic cluster, as is also the case in all Yb sites of c-Au Al Yb, and the minor sites in qAu Al Yb are located in the gaps of the cluster packing [1,13– 15]. The population ratio of major sites to minor ones in q-Au Al Yb is approximately 7:3 [16]. Note that q-Au Al Yb contains the minor sites, but c-Au Al Yb does not have them. The existence of the minor sites in q-Au Al Yb may cause the magnitude difference between these two systems. According to this model, the high-valence Yb at the major sites in q-AuAl Yb accounts for the similarity of Tnq-Au Al Yb to Tnc-Au Al Yb. Because TK that corresponds to Tn depends greatly on the Yb valence, the close Tn values indicate similarity in the Yb valence, which is ensured by the high-valence Yb. It is reasonable to expect that the high-valence Yb in q-Au Al Yb exhibits a similar valence shift due to cooling to that of c-Au Al Yb. By contrast, the low-valence Yb at the minor sites in q-Au Al Yb is considered to show no valence shift. As mentioned in Ref [2], low-valence Yb close to the divalent state typically shows a nonmagnetic character. This indicates that TK is much higher than room temperature, and consequently, no temperature variation due to the Kondo screening effect is shown at low temperatures. The coexistence of these two kinds of Yb in qAu AlYb accounts for the smaller valence shift as a result of averaging the two effects of the valence shift sites and the non-shift ones, and consequently for the smaller magnitude of ΔlYb ðT Þ=l300 K than in c-Au Al Yb. By employing the population ratio of these two sites, the magnitude ratio of ΔlYb ðT Þ=l300 K of q-Au Al Yb to that of c-Au Al Yb is calculated to be 0.7, with an inverse ratio of approximately 1.4. The estimate with the heterogeneous valence model agrees with the experimental result of 1.4, as shown above. To summarize, we have found anomalous thermal expansion behavior in intermediate-valence compounds of q-Au Al Yb and c-Au Al Yb at low temperatures due to the temperature variation of their Yb valence. It was also shown that their thermal
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expansion character at the lowest temperatures is consistent with their non-Fermi-liquid behavior. Additionally, a larger anomaly has been demonstrated in c-Au Al Yb than in q-Au Al Yb. The difference would be originated from the existence of the additional kind of Yb sites in q-Au Al Yb that does not exist in c-Au Al Yb. Acknowledgments This work was performed under Proposals nos. 2011B3701, 2011B2092, 2012A3701 and 2012B0046 at SPring-8, and was partially supported by a Grant-in-aid for Scientific Research (No. 24540386) from the Japan Society for Promotion of Science. References [1] T. Ishimasa, Y. Tanaka, S. Kashimoto, Philos. Mag. 91 (2011) 4218. [2] T. Watanuki, S. Kashimoto, D. Kawana, T. Yamazaki, A. Machida, Y. Tanaka, T.J. Sato, Phys. Rev. B 86 (2012) 094201. [3] K. Deguchi, S. Matsukawa, N.K. Sato, T. Hattori, K. Ishida, H. Takakura, T. Ishimasa, Nat. Mater. 11 (2012) 1013. [4] S. Watanabe, K. Miyake, J. Phys. Soc. Jpn. 82 (2013) 083704. [5] S. Watanabe, K. Miyake, Phys. Rev. Lett. 105 (2010) 186403.
[6] S. Jazbec, S. Vrtnik, Z. Jagličić, S. Kashimoto, J. Ivkov, P. Popčević, A. Smomtara, H.J. Kim, J.G. Kim, J. Dolinsěk, J. Alloy. Compd. 586 (2014) 343. [7] K. Tanaka, Y. Tanaka, T. Ishimasa, M. Nakayama, S. Matsukawa, K. Deguchi, N.K. Sato, Acta. Phys. Pol. A 126 (2014) 603. [8] M. Nakayama, K. Tanaka, S. Matsukawa, K. Deguchi, K. Imura, T. Ishimasa, N.K. Sato, J. Phys. Soc. Jpn. 84 (2015) 024721. [9] T. Watanuki, A. Machida, T. Ikeda, A. Ohmura, H. Kaneko, K. Aoki, T.J. Sato, A.P. Tsai, Philos. Mag. 87 (2007) 2905. [10] J.M. Lawrence, G.H. Kwei, P.C. Canfield, J.G. DeWitt, A.C. Lawson, Phys. Rev. B 49 (1994) 1627. [11] N.D. Dung, T.D. Matsuda, Y. Haga, S. Ikeda, E. Yamamoto, T. Ishikura, T. Endo, S. Tatsuoka, Y. Aoki, H. Sato, T. Takeuchi, R. Settai, H. Harima, Y. Ōnuki, J. Phys. Soc. Jpn. 78 (2009) 084711. [12] L. Moreschini, C. Dallera, J.J. Joyce, J.L. Sarrao, E.D. Bauer, V. Fritsch, S. Bobev, E. Carpene, S. Huotari, G. Vank´o, G. Monaco, P. Lacovig, G. Panaccione, A. Fondacaro, G. Paolicelli, P. Torelli, M. Grioni, Phys. Rev. B 75 (2007) 035113. [13] H. Takakura, C.P. Gómez, A. Yamamoto, M. de Boissieu, A.P. Tsai, Nat. Mater. 6 (2007) 58. [14] A.P. Tsai, C.P. Gómez, in: T. Fujiwara, Y. Ishii (Eds.), Handbook of Metal Physics: Quasicrystals, Elsevier, Amsterdam, 2008, p. 75. [15] T. Ishimasa, in Ref. 13, p. 49. [16] H. Takakura (private communication).