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Chemical doping effect on the crystal structure and superconductivity of MgB2
Physica C 386 (2003) 588–592 www.elsevier.com/locate/physc
Chemical doping effect on the crystal structure and superconductivity of MgB2 C.H. Cheng a, Y. Zhao a,*, X.T. Zhu a, J. Nowotny a, C.C. Sorrell a, T. Finlayson b, H. Zhang c a
Superconductivity Research Group, School of Materials Science and Engineering, University of New South Wales, P.O. Box 1, Sydney, NSW 2052, Australia b School of Physics and Materials Engineering, Monash University, Melbourne, Victoria 3800, Australia c Materials Physics Laboratory, State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
Abstract Substituent alloys of Mg1x Mx B2 with M ¼ Ti, Zr, Mo, Mn, Fe, Ca, Al, Ag, Cu, Y, and Ho and 0 6 x 6 10% have been synthesized by the solid-state reaction. The solid solubility for most of these dopants at Mg site is found to be very low except for M ¼ Al. In most of these alloys, the Vegard relationship holds as the doping level is low. The lattice constants for the fictitious compounds such as AgB2 , CuB2 , FeB2 have been extrapolated. The superconductivity transition temperature, Tc , shows a systematic changes with the doping level in some of these substituent alloys. Relevant mechanisms of superconductivity suppression have been discussed. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 74.62.Bf; 74.62.Dh Keywords: MgB2 ; Chemical doping; Vegard relationship; Superconductivity
1. Introduction The newly discovered superconductor MgB2 [1] has attracted considerable interest from theoretical and experimental points of view since MgB2 has achieved a record high Tc in the conventional superconductors. Theory indicates that MgB2 can be treated as phonon-mediated superconductor with strong coupling [2,3]. Photoemission spectroscopy
*
Corresponding author. Tel.: +61-2-9385-5986; fax: +61-29385-5956. E-mail address: [email protected] (Y. Zhao).
[4], tunneling spectroscopy [5], isotope effect measurements [6,7], and inelastic neutron scattering measurement [8] also support that MgB2 is a typical BCS superconductor with a strong electron– phonon (e–p) interaction. It is found that electron doping is deleterious to superconductivity in MgB2 , as demonstrated in Al-doped MgB2 [9]. Superconductivity can also be greatly suppressed by pressure [10,11]. On the other hand, the chemical doping effect on MgB2 is not very clear although some very preliminary results show a suppression of Tc by Liþ and Al doping [9,12]. Therefore, it is necessary to provide clearer results of both the hole and electron doping effects in MgB2 to understand why MgB2 has such a high Tc
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4534(02)02167-6
C.H. Cheng et al. / Physica C 386 (2003) 588–592
compared to other conventional superconductors, especially other diborides with an isostructure to MgB2 . In this paper, we report the structure and superconductivity of MgB2 doped with various chemical dopants. We find that most of the dopants have a very low solid solubility in the Mg site of MgB2 except for Al. The Vegard relations holds for all these dopants. The lattice constants for fictitious compounds such as AgB2 , CuB2 , FeB2 have been extrapolated from the Vegard relationship, the corresponding lattice constants are different from what have been predicted by theoretical calculation [13]. Our results also suggest that the suppression of superconductivity by chemical doping originates largely from the chemical pressure effect.
589
3. Results and discussion The doping level dependence of the lattice constants for the Ag-doped MgB2 is shown in Fig. 1(a). At x < 0:5%, the lattice constants decrease linearly with increasing doping level. However, the decrease of the lattice constants is getting saturated as the doping level is higher than x > 0:5%, showing a sharp turn at x 0:5%, as shown in the inset of Fig. 1(a). For convenience, hereinafter, the doping level at the turning point is denoted as xL . Similar phenomenon was also observed for the samples doped with Ti, Mo, Mn, Fe, or Cu although the values of xL change with the doping element (see Table 1). For the dopants Ca, Zr, Y, and Ho, the lattice constants exhibit a random
2. Experimental Mg1x Mx B2 samples with M ¼ Ti, Zr, Mo, Mn, Fe, Ca, Al, Ag, Cu, Y, and Ho and 0 6 x 6 1:0% have been synthesized by the solid-state reaction using fine powders of Mg, B, Ti, Zr, Mo, Mn, Fe, Al, Ag, Cu, and Y, and granular Ca with high purity ( P 99.9%) as starting materials. Powders of the raw materials with the stoichiometry composition were mixed in argon atmosphere for 1 h, pressured into bar shape, placed on a MgO plate, and first heated at 600 °C for 1 h, and then sintered in a range of temperature between 700 and 850 °C within sealed quartz tube for 5 h. The vapor pressure of Mg was kept at 500–600 Torr during the sintering. Finally, the samples were annealed at 600 °C for 5 h in flowing argon. The crystal structure was examined by the X-ray diffraction (XRD) using an XÕpert MRD high-resolution X-ray diffractometer with Cu Ka radiation. The microstructural and compositional analyses were carried out by scanning electron microscope (SEM) equipped with electron energy dispersive analyses (EDS). The lattice parameters were calculated from the indexed reflections of XRD patterns with a least-squared method. The onset superconducting transition temperature, Tc , was determined by electrical resistivity measurement using four-probe method.
a
Fig. 1. (a) Doping level dependence of the lattice constants for Ag-doped MgB2 . Inset: enlarged view around xL . (b) XRD patterns for three samples around xL . # and indicate the impurity phases.
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Table 1 Relevant physical parameters for Mg1x Mx B2 alloys Element
xL (at.%)
aex (nm)
aXRD (nm)
dTc =dx (K/at.%)
ba (1/at.%)
bc (1/at.%)
dp=dxja (GPa/at.%)
dp=dxjc (GPa/at.%)
dTc =dP jc (K/GPa)
Al Y Ho Ca Ti Zr Mo Mn Fe Cu Ag
>1.0 0 0 0 0.2 0 0.28 0.46 0.48 0.26 0.44
0.3003 – – – 0.3032
0.30054 0.3299 0.3273
)9.9 – – – )7.2 – )5 )13.1 )14.2 )7.6 )4.8
)0.0253 – – – )0.0175 – )0.0107 )0.024 )0.0262 )0.0204 )0.0150
)0.027 – – – )0.0204 – )0.0143 )0.0332 )0.0335 )0.0241 )0.0207
13.53 – – – 9.36 – 5.72 12.83 14.01 10.91 8.02
8.79 – – – 6.65 – 4.66 10.81 10.91 7.85 6.74
1.13 – – – 1.08 – 1.07 1.21 1.30 0.968 0.712
a
0.3053 0.3012 0.3006 0.3023 0.3040
0.30292 0.31687 0.304 0.3007 – 0.296a 0.298a
Calculated data [13].
variation with doping level, suggesting that these dopants cannot occupy the Mg site in MgB2 . For Al-doped MgB2 the lattice constants show a linear dependence on the doping level in the whole doping range up to x ¼ 1:0%. As revealed previously [14], the turning point in Fig. 1(a) reflects the reach of the solid solubility limit of the dopants at the Mg site in MgB2 crystal. This is confirmed by XRD and SEM analyses for the samples with the doping level around xL . For example, Fig. 1(b) shows the XRD patterns for three samples whose lattice constant data are plotted in the inset of Fig. 1(a) (see the solid circles). The impurity phases gradually appear when the doping level passes through the xL from a lower value (x ¼ 0:4%) to a higher value (x ¼ 0:75%). The results of SEM analyses (not given here) are also consistent with the XRD analyses mentioned above. In substituent alloys, the Vegard relationship holds as the doping level is low [15], and gives a linear dependence between the lattice constant and the doping level in the form: a ¼ a1 þ ða2 a1 Þx
ð1Þ
where a is the lattice constant of the alloy, a1 and a2 are the lattice constants of the solute and the solution, respectively, and x is the doping level. The linear dependence of the lattice constants with the doping level at low doping levels reveals that the Vegard law holds for the substituent alloys of Mg1x Mx B2 . Fig. 2(a) shows the comparison of the experimental data with the Vegard relationship for Al- and Ag-doped MgB2 samples. Based on
Fig. 2. (a) Vegard relationship for Ag- and Al-doped MgB2 . (b) Fitness of the relationship of the lattice constants with doping level by Eq. (2). The lines are theoretic values according to Vegard relationship.
Eq. (1) and using a1 ¼ 0:3086 nm (the length of aaxis of the MgB2 unit cell), the values of the lat-
C.H. Cheng et al. / Physica C 386 (2003) 588–592
tices constants of the corresponding diborides, such as AlB2 , MoB2 , TiB2 , etc. have been extrapolated from the experimental data of the lattice constant of the alloys at low doping levels. As shown in Table 1, the extrapolated lattice constant of a-axis for these diborides (denoted as aex ) are very close to the values determined directly from the XRD data on pure-phase diborides, demonstrating the validity of the Vegard relationship for the MgB2 system. For elements such as Ag, Cu, and Fe whose corresponding diborides do not exist, the lengths of the a-axis of the unit cells for the fictitious diborides are, by extrapolation, 0.3041 nm for AgB2 , 0.3013 nm for CuB2 , and 0.2981 nm for FeB2 . The extrapolated data provide references for synthesizing these compounds in future, and a test for the theoretical calculation of the lattice constants of these fictitious compounds [13]. It is worthy to note that there is a significant discrepancy between our experimentally-extrapolated and theoretically-calculated values of the lattice constant for the fictitious AgB2 and CuB2 . Further study is necessary to explain this discrepancy. For M ¼ Al, Ti, Mo, Mn, Fe, Cu, Ag, the doping level dependencies of the lattice constants a and c for Mg1x Mx B2 alloys can be generally expressed as: a ¼ a0 ð1 þ ba xÞ
ð2aÞ
c ¼ c0 ð1 bc xÞ
ð2bÞ
where a0 and c0 are the lattice constants at zero doping level, ba and bc are chemical axial compressibility, defined as ba ¼ ð1=a0 Þðda=dxÞ and bc ¼ ð1=c0 Þðdc=dxÞ for the a- and c-axis, respectively. For example, for M ¼ Ag, ba ¼ 0:0150/ at.% and bc ¼ 0:0207/at.%, as shown in Fig. 2(b). It is evident that the lattice constant along the c-axis decreases with doping level more rapidly than that along the a-axis, resulting in a reduced c=a ratio for Ag-doped MgB2 . For some other dopants, similar results are obtained and listed in Table 1. The above-shown chemical pressure effect on the lattice constants is very similar to the mechanical isostatic pressure effect which also obeys a linear relationship between the lattice constants and the pressure [16], as shown below
591
a ¼ a0 ð1 þ aa P Þ
ð3aÞ
c ¼ c0 ð1 þ ac P Þ
ð3bÞ
where P is the mechanical pressure; aa and ac are mechanical axial compressibility, defined as aa ¼ ð1=a0 Þðda=dP Þ and ac ¼ ð1=c0 Þðdc=dP Þ for the a- and c-axis, respectively. Using the relationship of dP =dx ¼ ðdR=dxÞ=ðdR=dP Þ (where R ¼ a and c) and taking aa ¼ 0:00187/GPa and ac ¼ 0:00307/GPa [16], we can establish a bridge between the mechanical and chemical pressure. For M ¼ Ag, we have dP =dxja ¼ 8:02 GPa/at.% for R ¼ a and dP =dxjc ¼ 6:73 GPa/at.% for R ¼ c. The corresponding results for other dopants are listed in Table 1. We have seen previously in the text that the response of the crystal structure to the chemical pressure is anisotropic, similar to the mechanical pressure effect, now we find that the chemical pressure exerting to the crystal structure by chemical doping is also anisotropic. This is one of the unique features of the chemical pressure which differs from mechanical isostatic pressure. Using the above-established relationship between the chemical and mechanical pressure, we can compare the Tc suppression induced by the chemical pressure with that by the mechanical pressure. The typical variations of Tc with the axial pressure in a- and c-axis for the Ag-doped MgB2 are plotted as the filled marks in Fig. 3(a) and (b), respectively. As expected from the anisotropic chemical pressure, the suppression of Tc under the axial pressure in a- and c-direction is also different from each other. Tc drops more dramatically under the c-axial pressure than under the a-axial pressure, giving dTc =dP ¼ 0:72 K/GPa under the caxial pressure and )0.60 K/GPa under the a-axial pressure. The corresponding results for other dopants are also listed in Table 1. The suppression rates of Tc for the case of M ¼ Ag are smaller than the value of dT0 =dP ¼ 1:1 K/GPa, generated from the hydrostatic pressure measurements (see the dashed lines in Fig. 3(a)) [10,11]. However, for M ¼ Al, Mn, etc., the suppression rate of Tc by chemical pressure effect is larger than that by the mechanical pressure. The above-mentioned discrepancies may be attributed to the additional effects, such as hole doping, hole filling, and
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C.H. Cheng et al. / Physica C 386 (2003) 588–592
nation of these effect leads to a more rapid decrease of Tc with increasing chemical doping level. 4. Summary
Fig. 3. Variation of Tc with axial pressure in (a) a-axis and (b) c-axis. The filled and open marks represent the data before and after subtracting the contribution of the hole doping, respectively. The dashed lines are plotted using dTc =dP ¼ 1:1 K/ GPa.
magnetic pair-breaking, which are superposed on the chemical pressure effect. For example, for M ¼ Ag, the replacement of Agþ for Mg2þ gives rise to hole doping effect which enhances the superconductivity of MgB2 slightly [14], and thus compensates the chemical pressure effect to a certain extent. This has been confirmed by the fact that, after taking away the hole doping effect, the chemical pressure effect is almost the same as the mechanical pressure effect on Tc (see the open marks in Fig. 3). Our result of the Ag doping effect on Tc of MgB2 is different from the prediction [13] that Ag doping enhances Tc . The discrepancy originates from the calculation which only considers the hole doping effect but omits the chemical pressure effect. In fact, the latter effect is a dominant one in Ag-doped MgB2 . For Al-doped MgB2 , the hole-filling effect of Al3þ for Mg2þ provides an extra Tc suppression effect, and thus decreases Tc more seriously. For magnetic dopants such as Mn and Fe, besides the hole filling and chemical pressure effects, pair-breaking effect of Mn or Fe is an additional Tc suppression mechanism. Combi-
In summary, we have prepared Mg1x Mx B2 compounds with M ¼ Ti, Zr, Mo, Mn, Fe, Ca, Al, Ag, Cu, Y, and Ho using solid state reaction method and studied the doping effect on structure and superconductivity of MgB2 . The solid solubility for most of these dopants at Mg site is found to be very low except for M ¼ Al. In most of these alloys, the Vegard relationship holds in the low doping level region. The lattice constants for the fictitious compounds such as AgB2 , CuB2 , FeB2 have been extrapolated. The superconductivity transition temperature, Tc , shows a systematic decrease with the doping level in Ti-, Mo-, Mn-, Fe-, Al-, Ag-, or Cu-doped MgB2 . Chemical pressure effect is the common reason for the Tc suppression in these alloys. References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimistu, Nature 410 (2001) 63. [2] J. Kortus, I.I. Mazin, K.D. Belashchenko, V.P. Antropov, L.L. Boyer, Phys. Rev. Lett. 86 (2001) 4656. [3] J.M. An, W.E. Pickett, Phys. Rev. Lett. 86 (2001) 4366. [4] T. Takahashi, T. Sato, S. Souma, T. Muranaka, J. Akimitsu, Phys. Rev. Lett. 86 (2001) 4915. [5] G. Rubio-Bollinger et al., Phys. Rev. Lett. 86 (2001) 5582. [6] S.L. BudÕko et al., Phys. Rev. Lett. 86 (2001) 1877. [7] D.G. Hinks, H. Claus, J.D. Jorgensen, Nature 411 (2001) 457. [8] R. Osborn et al., Phys. Rev. Lett. 87 (2001) 017005. [9] J.S. Slusky et al., Nature 410 (2001) 343. [10] T. Vogt et al., Phys. Rev. B 63 (2001) 220505 (R). [11] B. Lorenz, R.L. Meng, C.W. Chu, Phys. Rev. B 63 (2001) 1000. [12] Y.G. Zhao et al., Physica C 361 (2001) 91. [13] S.K. Kwon, S.J. Youn, K.S. Kim, B.I. Min, cond-mat/ 0106483 (2001). [14] C.H. Cheng, L. Wang, Y. Zhao, H. Zhang, Physica C 378– 381 (2002) 244. [15] B.K. Xu, W.P. Yan, D.M. Liu, in: Crystallography, Press of Jilin University, 1991, p. 151. [16] J.D. Jorgensen, D.G. Hinks, S. Short, Phys. Rev. B 63 (2001) 224522.
Chemical doping effect on the crystal structure and superconductivity of MgB2 C.H. Cheng a, Y. Zhao a,*, X.T. Zhu a, J. Nowotny a, C.C. Sorrell a, T. Finlayson b, H. Zhang c a
Superconductivity Research Group, School of Materials Science and Engineering, University of New South Wales, P.O. Box 1, Sydney, NSW 2052, Australia b School of Physics and Materials Engineering, Monash University, Melbourne, Victoria 3800, Australia c Materials Physics Laboratory, State Key Laboratory for Mesoscopic Physics, Department of Physics, Peking University, Beijing 100871, China
Abstract Substituent alloys of Mg1x Mx B2 with M ¼ Ti, Zr, Mo, Mn, Fe, Ca, Al, Ag, Cu, Y, and Ho and 0 6 x 6 10% have been synthesized by the solid-state reaction. The solid solubility for most of these dopants at Mg site is found to be very low except for M ¼ Al. In most of these alloys, the Vegard relationship holds as the doping level is low. The lattice constants for the fictitious compounds such as AgB2 , CuB2 , FeB2 have been extrapolated. The superconductivity transition temperature, Tc , shows a systematic changes with the doping level in some of these substituent alloys. Relevant mechanisms of superconductivity suppression have been discussed. Ó 2002 Elsevier Science B.V. All rights reserved. PACS: 74.62.Bf; 74.62.Dh Keywords: MgB2 ; Chemical doping; Vegard relationship; Superconductivity
1. Introduction The newly discovered superconductor MgB2 [1] has attracted considerable interest from theoretical and experimental points of view since MgB2 has achieved a record high Tc in the conventional superconductors. Theory indicates that MgB2 can be treated as phonon-mediated superconductor with strong coupling [2,3]. Photoemission spectroscopy
*
Corresponding author. Tel.: +61-2-9385-5986; fax: +61-29385-5956. E-mail address: [email protected] (Y. Zhao).
[4], tunneling spectroscopy [5], isotope effect measurements [6,7], and inelastic neutron scattering measurement [8] also support that MgB2 is a typical BCS superconductor with a strong electron– phonon (e–p) interaction. It is found that electron doping is deleterious to superconductivity in MgB2 , as demonstrated in Al-doped MgB2 [9]. Superconductivity can also be greatly suppressed by pressure [10,11]. On the other hand, the chemical doping effect on MgB2 is not very clear although some very preliminary results show a suppression of Tc by Liþ and Al doping [9,12]. Therefore, it is necessary to provide clearer results of both the hole and electron doping effects in MgB2 to understand why MgB2 has such a high Tc
0921-4534/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-4534(02)02167-6
C.H. Cheng et al. / Physica C 386 (2003) 588–592
compared to other conventional superconductors, especially other diborides with an isostructure to MgB2 . In this paper, we report the structure and superconductivity of MgB2 doped with various chemical dopants. We find that most of the dopants have a very low solid solubility in the Mg site of MgB2 except for Al. The Vegard relations holds for all these dopants. The lattice constants for fictitious compounds such as AgB2 , CuB2 , FeB2 have been extrapolated from the Vegard relationship, the corresponding lattice constants are different from what have been predicted by theoretical calculation [13]. Our results also suggest that the suppression of superconductivity by chemical doping originates largely from the chemical pressure effect.
589
3. Results and discussion The doping level dependence of the lattice constants for the Ag-doped MgB2 is shown in Fig. 1(a). At x < 0:5%, the lattice constants decrease linearly with increasing doping level. However, the decrease of the lattice constants is getting saturated as the doping level is higher than x > 0:5%, showing a sharp turn at x 0:5%, as shown in the inset of Fig. 1(a). For convenience, hereinafter, the doping level at the turning point is denoted as xL . Similar phenomenon was also observed for the samples doped with Ti, Mo, Mn, Fe, or Cu although the values of xL change with the doping element (see Table 1). For the dopants Ca, Zr, Y, and Ho, the lattice constants exhibit a random
2. Experimental Mg1x Mx B2 samples with M ¼ Ti, Zr, Mo, Mn, Fe, Ca, Al, Ag, Cu, Y, and Ho and 0 6 x 6 1:0% have been synthesized by the solid-state reaction using fine powders of Mg, B, Ti, Zr, Mo, Mn, Fe, Al, Ag, Cu, and Y, and granular Ca with high purity ( P 99.9%) as starting materials. Powders of the raw materials with the stoichiometry composition were mixed in argon atmosphere for 1 h, pressured into bar shape, placed on a MgO plate, and first heated at 600 °C for 1 h, and then sintered in a range of temperature between 700 and 850 °C within sealed quartz tube for 5 h. The vapor pressure of Mg was kept at 500–600 Torr during the sintering. Finally, the samples were annealed at 600 °C for 5 h in flowing argon. The crystal structure was examined by the X-ray diffraction (XRD) using an XÕpert MRD high-resolution X-ray diffractometer with Cu Ka radiation. The microstructural and compositional analyses were carried out by scanning electron microscope (SEM) equipped with electron energy dispersive analyses (EDS). The lattice parameters were calculated from the indexed reflections of XRD patterns with a least-squared method. The onset superconducting transition temperature, Tc , was determined by electrical resistivity measurement using four-probe method.
a
Fig. 1. (a) Doping level dependence of the lattice constants for Ag-doped MgB2 . Inset: enlarged view around xL . (b) XRD patterns for three samples around xL . # and indicate the impurity phases.
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Table 1 Relevant physical parameters for Mg1x Mx B2 alloys Element
xL (at.%)
aex (nm)
aXRD (nm)
dTc =dx (K/at.%)
ba (1/at.%)
bc (1/at.%)
dp=dxja (GPa/at.%)
dp=dxjc (GPa/at.%)
dTc =dP jc (K/GPa)
Al Y Ho Ca Ti Zr Mo Mn Fe Cu Ag
>1.0 0 0 0 0.2 0 0.28 0.46 0.48 0.26 0.44
0.3003 – – – 0.3032
0.30054 0.3299 0.3273
)9.9 – – – )7.2 – )5 )13.1 )14.2 )7.6 )4.8
)0.0253 – – – )0.0175 – )0.0107 )0.024 )0.0262 )0.0204 )0.0150
)0.027 – – – )0.0204 – )0.0143 )0.0332 )0.0335 )0.0241 )0.0207
13.53 – – – 9.36 – 5.72 12.83 14.01 10.91 8.02
8.79 – – – 6.65 – 4.66 10.81 10.91 7.85 6.74
1.13 – – – 1.08 – 1.07 1.21 1.30 0.968 0.712
a
0.3053 0.3012 0.3006 0.3023 0.3040
0.30292 0.31687 0.304 0.3007 – 0.296a 0.298a
Calculated data [13].
variation with doping level, suggesting that these dopants cannot occupy the Mg site in MgB2 . For Al-doped MgB2 the lattice constants show a linear dependence on the doping level in the whole doping range up to x ¼ 1:0%. As revealed previously [14], the turning point in Fig. 1(a) reflects the reach of the solid solubility limit of the dopants at the Mg site in MgB2 crystal. This is confirmed by XRD and SEM analyses for the samples with the doping level around xL . For example, Fig. 1(b) shows the XRD patterns for three samples whose lattice constant data are plotted in the inset of Fig. 1(a) (see the solid circles). The impurity phases gradually appear when the doping level passes through the xL from a lower value (x ¼ 0:4%) to a higher value (x ¼ 0:75%). The results of SEM analyses (not given here) are also consistent with the XRD analyses mentioned above. In substituent alloys, the Vegard relationship holds as the doping level is low [15], and gives a linear dependence between the lattice constant and the doping level in the form: a ¼ a1 þ ða2 a1 Þx
ð1Þ
where a is the lattice constant of the alloy, a1 and a2 are the lattice constants of the solute and the solution, respectively, and x is the doping level. The linear dependence of the lattice constants with the doping level at low doping levels reveals that the Vegard law holds for the substituent alloys of Mg1x Mx B2 . Fig. 2(a) shows the comparison of the experimental data with the Vegard relationship for Al- and Ag-doped MgB2 samples. Based on
Fig. 2. (a) Vegard relationship for Ag- and Al-doped MgB2 . (b) Fitness of the relationship of the lattice constants with doping level by Eq. (2). The lines are theoretic values according to Vegard relationship.
Eq. (1) and using a1 ¼ 0:3086 nm (the length of aaxis of the MgB2 unit cell), the values of the lat-
C.H. Cheng et al. / Physica C 386 (2003) 588–592
tices constants of the corresponding diborides, such as AlB2 , MoB2 , TiB2 , etc. have been extrapolated from the experimental data of the lattice constant of the alloys at low doping levels. As shown in Table 1, the extrapolated lattice constant of a-axis for these diborides (denoted as aex ) are very close to the values determined directly from the XRD data on pure-phase diborides, demonstrating the validity of the Vegard relationship for the MgB2 system. For elements such as Ag, Cu, and Fe whose corresponding diborides do not exist, the lengths of the a-axis of the unit cells for the fictitious diborides are, by extrapolation, 0.3041 nm for AgB2 , 0.3013 nm for CuB2 , and 0.2981 nm for FeB2 . The extrapolated data provide references for synthesizing these compounds in future, and a test for the theoretical calculation of the lattice constants of these fictitious compounds [13]. It is worthy to note that there is a significant discrepancy between our experimentally-extrapolated and theoretically-calculated values of the lattice constant for the fictitious AgB2 and CuB2 . Further study is necessary to explain this discrepancy. For M ¼ Al, Ti, Mo, Mn, Fe, Cu, Ag, the doping level dependencies of the lattice constants a and c for Mg1x Mx B2 alloys can be generally expressed as: a ¼ a0 ð1 þ ba xÞ
ð2aÞ
c ¼ c0 ð1 bc xÞ
ð2bÞ
where a0 and c0 are the lattice constants at zero doping level, ba and bc are chemical axial compressibility, defined as ba ¼ ð1=a0 Þðda=dxÞ and bc ¼ ð1=c0 Þðdc=dxÞ for the a- and c-axis, respectively. For example, for M ¼ Ag, ba ¼ 0:0150/ at.% and bc ¼ 0:0207/at.%, as shown in Fig. 2(b). It is evident that the lattice constant along the c-axis decreases with doping level more rapidly than that along the a-axis, resulting in a reduced c=a ratio for Ag-doped MgB2 . For some other dopants, similar results are obtained and listed in Table 1. The above-shown chemical pressure effect on the lattice constants is very similar to the mechanical isostatic pressure effect which also obeys a linear relationship between the lattice constants and the pressure [16], as shown below
591
a ¼ a0 ð1 þ aa P Þ
ð3aÞ
c ¼ c0 ð1 þ ac P Þ
ð3bÞ
where P is the mechanical pressure; aa and ac are mechanical axial compressibility, defined as aa ¼ ð1=a0 Þðda=dP Þ and ac ¼ ð1=c0 Þðdc=dP Þ for the a- and c-axis, respectively. Using the relationship of dP =dx ¼ ðdR=dxÞ=ðdR=dP Þ (where R ¼ a and c) and taking aa ¼ 0:00187/GPa and ac ¼ 0:00307/GPa [16], we can establish a bridge between the mechanical and chemical pressure. For M ¼ Ag, we have dP =dxja ¼ 8:02 GPa/at.% for R ¼ a and dP =dxjc ¼ 6:73 GPa/at.% for R ¼ c. The corresponding results for other dopants are listed in Table 1. We have seen previously in the text that the response of the crystal structure to the chemical pressure is anisotropic, similar to the mechanical pressure effect, now we find that the chemical pressure exerting to the crystal structure by chemical doping is also anisotropic. This is one of the unique features of the chemical pressure which differs from mechanical isostatic pressure. Using the above-established relationship between the chemical and mechanical pressure, we can compare the Tc suppression induced by the chemical pressure with that by the mechanical pressure. The typical variations of Tc with the axial pressure in a- and c-axis for the Ag-doped MgB2 are plotted as the filled marks in Fig. 3(a) and (b), respectively. As expected from the anisotropic chemical pressure, the suppression of Tc under the axial pressure in a- and c-direction is also different from each other. Tc drops more dramatically under the c-axial pressure than under the a-axial pressure, giving dTc =dP ¼ 0:72 K/GPa under the caxial pressure and )0.60 K/GPa under the a-axial pressure. The corresponding results for other dopants are also listed in Table 1. The suppression rates of Tc for the case of M ¼ Ag are smaller than the value of dT0 =dP ¼ 1:1 K/GPa, generated from the hydrostatic pressure measurements (see the dashed lines in Fig. 3(a)) [10,11]. However, for M ¼ Al, Mn, etc., the suppression rate of Tc by chemical pressure effect is larger than that by the mechanical pressure. The above-mentioned discrepancies may be attributed to the additional effects, such as hole doping, hole filling, and
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nation of these effect leads to a more rapid decrease of Tc with increasing chemical doping level. 4. Summary
Fig. 3. Variation of Tc with axial pressure in (a) a-axis and (b) c-axis. The filled and open marks represent the data before and after subtracting the contribution of the hole doping, respectively. The dashed lines are plotted using dTc =dP ¼ 1:1 K/ GPa.
magnetic pair-breaking, which are superposed on the chemical pressure effect. For example, for M ¼ Ag, the replacement of Agþ for Mg2þ gives rise to hole doping effect which enhances the superconductivity of MgB2 slightly [14], and thus compensates the chemical pressure effect to a certain extent. This has been confirmed by the fact that, after taking away the hole doping effect, the chemical pressure effect is almost the same as the mechanical pressure effect on Tc (see the open marks in Fig. 3). Our result of the Ag doping effect on Tc of MgB2 is different from the prediction [13] that Ag doping enhances Tc . The discrepancy originates from the calculation which only considers the hole doping effect but omits the chemical pressure effect. In fact, the latter effect is a dominant one in Ag-doped MgB2 . For Al-doped MgB2 , the hole-filling effect of Al3þ for Mg2þ provides an extra Tc suppression effect, and thus decreases Tc more seriously. For magnetic dopants such as Mn and Fe, besides the hole filling and chemical pressure effects, pair-breaking effect of Mn or Fe is an additional Tc suppression mechanism. Combi-
In summary, we have prepared Mg1x Mx B2 compounds with M ¼ Ti, Zr, Mo, Mn, Fe, Ca, Al, Ag, Cu, Y, and Ho using solid state reaction method and studied the doping effect on structure and superconductivity of MgB2 . The solid solubility for most of these dopants at Mg site is found to be very low except for M ¼ Al. In most of these alloys, the Vegard relationship holds in the low doping level region. The lattice constants for the fictitious compounds such as AgB2 , CuB2 , FeB2 have been extrapolated. The superconductivity transition temperature, Tc , shows a systematic decrease with the doping level in Ti-, Mo-, Mn-, Fe-, Al-, Ag-, or Cu-doped MgB2 . Chemical pressure effect is the common reason for the Tc suppression in these alloys. References [1] J. Nagamatsu, N. Nakagawa, T. Muranaka, Y. Zenitani, J. Akimistu, Nature 410 (2001) 63. [2] J. Kortus, I.I. Mazin, K.D. Belashchenko, V.P. Antropov, L.L. Boyer, Phys. Rev. Lett. 86 (2001) 4656. [3] J.M. An, W.E. Pickett, Phys. Rev. Lett. 86 (2001) 4366. [4] T. Takahashi, T. Sato, S. Souma, T. Muranaka, J. Akimitsu, Phys. Rev. Lett. 86 (2001) 4915. [5] G. Rubio-Bollinger et al., Phys. Rev. Lett. 86 (2001) 5582. [6] S.L. BudÕko et al., Phys. Rev. Lett. 86 (2001) 1877. [7] D.G. Hinks, H. Claus, J.D. Jorgensen, Nature 411 (2001) 457. [8] R. Osborn et al., Phys. Rev. Lett. 87 (2001) 017005. [9] J.S. Slusky et al., Nature 410 (2001) 343. [10] T. Vogt et al., Phys. Rev. B 63 (2001) 220505 (R). [11] B. Lorenz, R.L. Meng, C.W. Chu, Phys. Rev. B 63 (2001) 1000. [12] Y.G. Zhao et al., Physica C 361 (2001) 91. [13] S.K. Kwon, S.J. Youn, K.S. Kim, B.I. Min, cond-mat/ 0106483 (2001). [14] C.H. Cheng, L. Wang, Y. Zhao, H. Zhang, Physica C 378– 381 (2002) 244. [15] B.K. Xu, W.P. Yan, D.M. Liu, in: Crystallography, Press of Jilin University, 1991, p. 151. [16] J.D. Jorgensen, D.G. Hinks, S. Short, Phys. Rev. B 63 (2001) 224522.