Positron annihilation spectroscopy and specific heat study of Neon ion irradiated MgB2

Physics Letters A 372 (2008) 1521–1526 www.elsevier.com/locate/pla

Positron annihilation spectroscopy and specific heat study of Neon ion irradiated MgB2 A. Talapatra a , S.K. Bandyopadhyay a,∗ , P.M.G. Nambissan b , Pintu Sen a , V. Ganesan c a Variable Energy Cyclotron Centre, 1/AF, Bidhan Nagar, Kolkata 700064, India b Saha Institute of Nuclear Physics, 1/AF, Bidhan Nagar, Kolkata 700064, India c UGC-DAE Consortium for Scientific Research, Khandwa Road, Indore 452017, India

Received 30 August 2007; received in revised form 14 September 2007; accepted 1 October 2007 Available online 5 October 2007 Communicated by V.M. Agranovich

Abstract Specific heat studies under magnetic field and positron annihilation spectroscopy were carried out on 160 MeV Ne ion irradiated polycrystalline MgB2 samples. There is an unusual decrease in positron lifetime in the irradiated sample which may be due to neon ion implantation. This was also indicated by change in cell volume. Coincidence Doppler Broadening Spectra of Mg, B, irradiated and unirradiated MgB2 show that positrons primarily annihilate in boron sublattice in the unirradiated sample whereas there is some similarity of the spectrum of the irradiated sample with that of Mg. There is Mg deficiency in the unirradiated sample whereas predominantly boron vacancies exist in Ne ion irradiated MgB2 sample. Specific heat measurements show that there is a small increase in electronic part of the specific heat and electron–phonon coupling constant. © 2007 Elsevier B.V. All rights reserved. PACS: 74.70.Ad; 61.80.-x; 75.40.Cx; 78.70.Bj Keywords: MgB2 ; Ion irradiation; Specific heat; Positron annihilation

1. Introduction MgB2 is a simple binary superconductor with Tc around 39 K. The observation of the boron isotope effect [1] shows that it is a phonon-mediated superconductor. Optical phonon modes play a crucial role for the superconductivity in this compound [2]. It has been established that it is a two-gap superconductor [3]. These two gaps arise from quasi two-dimensional σ band and three-dimensional π band at the Fermi surface. The analysis of specific heat data in superconducting state using phenomenological two-gap α model gives the value of one gap above and the other gap below the BCS limit [4]. This model assumes both the gaps to follow the usual temperature

* Corresponding author. Tel.: +91 33 2337 1230 Ext 2401; fax: +91 33 2334 6871. E-mail address: [email protected] (S.K. Bandyopadhyay).

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dependence of the BCS theory, but 2i0 /kB Tc (= αi ; i = 1, 2) differ from the BCS value of 3.5 and are used as fitting parameters. In the case of a two-gap superconductor, non-magnetic impurity scattering has pair breaking effect in contrast to single gap superconductor [5]. In MgB2 , the inter-band impurity scattering between σ and π bands is negligible due to the orthogonality of σ and π wave functions. Defects introduced in the system (by irradiation, for example) are expected to bring about changes in inter-band and intra-band scattering rates. In the case of high dose of neutron irradiation, it has been observed that Tc decreases drastically and two gaps merge to give a single gap [6]. In such cases, the electronic density of states (EDOS) at Fermi surface changes. Irradiation of MgB2 with heavy and moderately heavy ions increases the residual resistivity (ρ0 ) and temperature variation of resistivity (dρ/dT ) without affecting Tc appreciably [7,8]. In this Letter, we present the studies on specific heat of MgB2 irradiated with Ne ions at moder-

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Table 1 The lattice parameters and occupancies of Mg and B as obtained from Rietveld analysis. The transition temperature, residual resistivity and room temperature resistivity as obtained from resistivity measurement are also given Sample

a (Å)

c (Å)

Mg occupancy (%)

B occupancy (%)

Tc (R = 0) (K)

ρ0 (µ cm)

ρ300 (µ cm)

A B

3.081 3.090

3.523 3.533

93.2 87.3

99.2 83.5

38.0 37.1

19.02 38.74

54.82 86.59

ate dose. The defects were characterised by highly sensitive techniques of positron annihilation spectroscopy and X-ray diffraction (XRD). 2. Experimental Polycrystalline MgB2 samples were prepared using solid state reaction starting from Mg and B powders [9]. The samples were irradiated with 160 MeV Ne6+ ions to a dose of 2 × 1015 cm−2 . They were irradiated from both sides to have fairly uniform damage. The irradiation was carried out at Variable Energy Cyclotron Centre, Kolkata. The samples were characterised by XRD and resistivity measurements. The resistivity parameters and Tc of the samples are reported in Table 1. The unirradiated and irradiated samples are denoted as A and B, respectively. The specific heat measurements of the samples were performed in the temperature range of 2.5 K to 300 K at 0 T and 14 T by a 14 T Quantum Design Physical Properties Measurement System (QD PPMS) using relaxation method at UGCDAE Consortium for Scientific Research, Indore. Measurement of bare calorimeter with exact amount of Apiezon N grease, used for thermal contact, was performed in order to extract the contribution of addenda. To characterise the defects, positron annihilation spectroscopy was done. Positron annihilation lifetime spectroscopy (PALS) is a tool to detect the presence of vacancies. When positrons annihilate with electrons, their rest masses are converted into energy and emitted in the form of γ -rays. Positrons are localised in open volume regions of a solid. The γ -rays carry the information about the electron density and momentum at the annihilation site. PALS gives the size and concentration of defects in the solids but it cannot provide direct information on chemical environment around the annihilation site. Coincidence Doppler Broadening Spectroscopy (CDBS), which utilises two detectors, gives the momentum distribution of the core electrons that otherwise lie submerged under the nuclear background. Two-detector technique helps in improving the peak to background ratio [10]. The core electrons give the high momentum part of the spectrum. Even when the atoms form solids, the core electrons retain their atomic identity. Thus CDBS gives information about the chemical surrounding of the annihilation site. PALS and CDBS are complementary to each other and simultaneous measurements give a complete picture of the size, concentration and type of defects present in the system. For positron annihilation studies, a positron source (22 NaCl with activity of 15 µCi) was sandwiched between the samples. Annihilation γ -rays were detected using two BaF2 detec-

tors. The measurements were carried out using slow-fast coincidence technique. The time resolution of the measurement system is 200 ps. RESOLUTION programme was used to deconvolute the experimental resolution and POSITRONFIT [11] programme was used to extract the components. CDBS was measured using two high purity Ge (HPGe) detectors having high energy resolution (1.3 keV at 511 keV). The annihilated γ quanta with energies E1 and E2 were coincidentally measured with these HPGe detectors located at 180◦ to each other. The total energy of the annihilation γ -rays (E1 + E2 ) is 2m0 c2 − EB , where the first part is the sum of the rest mass energy of electron–positron pair and second part is electron binding energy. The energy difference of the γ -rays E = E1 − E2 = cPL /2. PL is the longitudinal component of the electron–positron pair momentum along the direction of the γ -ray emission. The Doppler broadening spectra were obtained from vertical cuts of the spectra with more than 5 × 106 counts along the energy conservation line E1 + E2 = 1022 keV. CDBS of Mg, B, unirradiated and Ne ion irradiated MgB2 and Si samples were carried out. The Doppler broadening spectra of all the samples were normalised with respect to a spectrum of high purity Si sample. 3. Results and discussion 3.1. XRD Figs. 1(a) and (b) show the XRD patterns of the unirradiated and irradiated MgB2 samples. There has not been any significant development of other phases due to irradiation. The lattice parameters extracted from Rietveld refinement programme LS1 [12] are listed in Table 1. There is an increase in the lattice parameter due to irradiation. Increase in both c and a are around 0.29%. In the irradiated sample, intensities corresponding to 001 and 100 reflection planes are enhanced. The pattern of the irradiated sample shows line broadening corresponding to characteristic reflection plane 110. This may be due to the damage caused in the boron layer due to irradiation. From the parameters, it is observed that there is an increase in cell volume after irradiation, which may be due to the implantation of Ne ions in the interstitials. The occupancy of Mg in the unirradiated sample as obtained from fitting is 93.2%. In case of the irradiated sample, the occupancies of both Mg and B atoms decrease. The Ne ion irradiation causes displacement of both the atoms from lattice site. 3.2. Heat capacity Fig. 2 shows the specific heat versus T of the sample A at H = 0 T from 2.5 K to 300 K. Inset of Fig. 2 shows the

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Fig. 1. The X-ray diffraction patterns of (a) unirradiated sample A and (b) irradiated sample B.

Fig. 2. The specific heat versus temperature curve of sample A in zero magnetic field from 2.5 K to 300 K. Inset: the normal state specific heat versus temperature for samples A and B plotted in log–log scale.

log–log plot of normal state Cp versus T of irradiated and unirradiated samples. The heat capacity measurement gives the transition temperature of the bulk material. Fig. 3 shows Cp (Cp (0 T) − Cp (14 T)) versus temperature of both the samples. The temperature corresponding to the peak of the λ-transition of sample A is 36.8 K and that of sample B is 35.8 K. The transition peak of the irradiated sample is at smaller height and the transition width is larger than that of the unirradiated sample. This is due to the fact that the irradiated sample is more disordered than the unirradiated one. At low temperature, there is a difference between the specific heats of the two samples. To find out the effect of irradiation on electronic and lattice parts of the specific heat, we have fitted the normal state specific heat curves from 22.7 K to 40 K with the formula C(T ) = γn T + βT 3 + δT 5 . The normal state Sommerfeld constants γn were obtained as 3.0 and 3.3 mJ/mol K2 for A and B, respectively. The values of the coefficients are listed in Table 2. The normal state electronic contribution to the specific

Table 2 The parameters of normal state specific heat Sample A B

γ (mJ/mol K2 )

β (mJ/mol K4 )

δ (mJ/mol K6 )

3.0 3.3

5.99 × 10−3

3.23 × 10−7 2.33 × 10−6

5.59 × 10−3

heat is Cel = γn T with: γn =

π 2 kB2 N (0)(1 + λ) . 3

(1)

Here, N (0) is the electronic density of states at Fermi surface, and λ is the electron–phonon coupling constant. With irradiation, there is slight decrease in Tc . Hence change in EDOS at this irradiation dose is negligible. The displacement per atom (dpa) with 160 MeV Ne ions at a moderate dose of 2 × 1015 cm−2 is around 10−2 . In conventional superconductors, there is negligible change in EDOS at this dpa. MgB2 is

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Fig. 3. The specific heat Cp versus T of samples A and B near the superconducting transition temperature.

Fig. 4. Coincidence Doppler Broadening Spectra of Mg, B, unirradiated MgB2 (sample A) and irradiated MgB2 (sample B)—normalised and divided by the spectrum of a pure Si sample.

similar to the conventional superconductors and at the same time it is structurally stable. Hence its response towards particle irradiation bears resemblance to conventional superconductors. Taking N (0) = 0.71 states eV−1 unit cell−1 [13], we get λ = 0.79 for sample A which is near to the theoretical value of 0.7 [2], and 0.97 for the sample B. λ can be expressed as: λ = λσ + λπ

(2)

where λ σ = λ σ σ + λσ π ;

λπ = λππ + λπσ .

(3)

Due to irradiation, there are changes in λσ π and λπσ . At the dose of 2 × 1015 cm−2 (corresponding to dpa of 10−2 ), inter band scattering is expected to rise [14] leading to increase in resistivity (both ρ0 , dρ/dT ) [8] and normal state Sommerfeld constant. On the other hand, the intra-band scattering rate is greater than inter-band scattering and is not affected much by the irradiation up to this dose as evident from the inappreciable change in Tc .

3.3. PALS and CDBS For the analysis of the chemical environment of the vacancies, the CDBS of samples A, B, pure boron and magnesium were studied. For qualitative analysis, the ratios of each spectrum to that of defect free pure Si are plotted in Fig. 4. The similarity between the nature of the spectra of boron and sample A shows that the positrons in MgB2 annihilate mainly with the electrons of boron atoms. There are Mg vacancies in the unirradiated MgB2 as can be seen from XRD. At the same time, magnesium ions are positively charged and boron ions are negatively charged. The spectrum of sample B is not similar to the spectrum of sample A. This shows that the chemical environment of the positron annihilation site has changed due to neon ion irradiation. The electron momentum distribution of sample B is close to that of Mg though not exactly similar to it. Due to irradiation, both boron and magnesium are displaced from the lattice site. At the same time, the neon ions are implanted in MgB2 matrix. This gives rise to additional annihilation of positrons with core

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Fig. 5. The positron annihilation spectra of (a) unirradiated sample A and (b) irradiated sample B. Table 3 The positron annihilation lifetimes and intensities of unirradiated (A) and irradiated (B) MgB2 samples Sample τ1 (ps) A B

τ2 (ps)

τ3 (ps)

I1 (%)

I2 (%)

I3 (%)

171 ± 3 324 ± 7 2320 ± 173 65.9 ± 2.4 33.6 ± 2.4 0.5 ± 0.04 163 ± 2 304 ± 8 2171 ± 130 70.2 ± 2.5 29.2 ± 2.5 0.6 ± 0.04

electrons of neon atoms. The electron core of Ne atom is similar to that of Mg. Hence the CDBS of irradiated sample B is more similar to that of Mg than sample A. The positrons predominantly annihilate with the valence electrons of the atom [15]. In a defect-free solid, the free positron lifetime decreases with increasing valence electron density. PALS of both the samples are shown in Figs. 5(a) and (b). We have extracted three lifetime components for both the samples, which are listed in Table 3. Of these three components, first component (τ1 ) is the free positron lifetime, shortened by the Bloch-state residence time and the second component (τ2 ) is due to the annihilation of the trapped positrons. The third component (τ3 ) with longer lifetime and intensity less than 1% is due to positronium (Ps). It can be observed that there is a small decrease in lifetimes (both τ1 and τ2 ) of positron with insignificant change in intensities due to irradiation. The decrease in positron lifetime is due to two reasons. Vacancy-interstitial recombination is one of them. At lower dose of irradiation, the vacancy type defects are annealed due to irradiation. This causes a decrease in resistivity. In the case of irradiated MgB2 at a dose of 2 × 1015 cm−2 , there is an increase in resistivity. Both ρ0 and dρ/dT increased due to irradiation. At the same time, the specific heat measurement showed that there is increase in inter-band scattering. These imply that there is

an increase in vacancy concentration. The second possibility is that the positrons are annihilated with electrons of the neon atoms implanted in MgB2 lattice as we have seen in CDBS studies. 4. Conclusion We have studied specific heat and positron annihilation spectroscopy of 160 MeV Neon ion irradiated polycrystalline MgB2 . Both Mg and B are displaced from lattice sites due to irradiation. There is some decrease in lifetime (τ1 and τ2 ) due to neon ion implantation. τ1 has decreased from 171 to 163 ps and τ2 has decreased from 324 to 304 ps. CDBS studies reflect the irradiated sample behaving similar to magnesium, whereas the unirradiated sample shows similarity to boron. There is a small enhancement of Sommerfeld parameter γn (from 3.0 to 3.3 mJ/mole K2 ) as obtained from the specific heat measurements. As there is insignificant change in EDOS at this dpa for MgB2 (behaving like conventional superconductors), the enhancement of γn can be related to the increase in electron– phonon coupling constant. This increases resistivity and dρ/dT without appreciable decrease in Tc . Acknowledgements The authors thank the staff of UGC-DAE Consortium for Scientific Research, Indore, for helping in measurements of specific heat. One of the authors, A.T., acknowledges Council for Scientific and Industrial Research (CSIR), New Delhi for financial support.

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