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Structure and superconductivity of isotope-enriched boron-doped diamond

Evgeny A Ekimov1,✉,Vladimir A Sidorov1,Andrey V Zoteev2,Julia B Lebed3,Joe D Thompson4,Sergey M Stishov1
1Institute for High Pressure Physics, Russian Academy of Sciences, 142190 Troitsk, Russia
2Physics Department, Moscow State University, 119992 Moscow, Russia
3Institute for Nuclear Research, Russian Academy of Sciences, 142190 Troitsk, Russia
4Los Alamos National Laboratory, 87545 Los Alamos, NM, USA
✉

Email:ekimov@hppi.troitsk.ru

Received 2008 Oct 19; Accepted 2008 Dec 10; Revised 2009 Jan 28; Collection date 2008 Dec.

© 2008 National Institute for Materials Science
PMCID: PMC5099641  PMID:27878027

Abstract

Superconducting boron-doped diamond samples were synthesized with isotopes of10B,11B,13C and12C. We claim the presence of a carbon isotope effect on the superconducting transition temperature, which supports the ‘diamond-carbon’-related nature of superconductivity and the importance of the electron–phonon interaction as the mechanism of superconductivity in diamond. Isotope substitution permits us to relate almost all bands in the Raman spectra of heavily boron-doped diamond to the vibrations of carbon atoms. The 500 cm−1 Raman band shifts with either carbon or boron isotope substitution and may be associated with vibrations of paired or clustered boron. The absence of a superconducting transition (down to 1.6 K) in diamonds synthesized in the Co–C–B system at 1900 K correlates with the small boron concentration deduced from lattice parameters.

Keywords: boron-doped diamond, superconductivity, Raman spectroscopy, isotope effect

Introduction

Diamond heavily doped with boron is a promising structural material thanks to its high electrical conductivity, chemical stability and excellent mechanical properties. The discovery of superconductivity in polycrystalline boron-doped diamond (BDD) [1] synthesized at high pressures and high temperatures (HPHT) stimulated studies of the mechanisms of boron incorporation in diamond and of the BDD properties at low temperatures [2–7]. Physical properties and the structure of BDD strongly depend on the method of diamond production. In this context, it is pertinent to compare here some methods for the synthesis of BDD using the HPHT technique. In the initial work [1], polycrystalline BDD was obtained in the boron–carbon (B4C–C) system at pressures 8–9 GPa and temperatures about 2500–2800 K. In this system, B4C reacts with graphite to form the eutectic melt; graphite dissolves in the melt and diamond crystallizes from it [8]. Boron is incorporated into the diamond lattice directly in the course of diamond crystallization. In accordance with current views on phase diagrams of partial solid solutions, the amount of boron incorporated into the diamond lattice during the synthesis must correspond to the boron solubility limit at the synthesis temperature. It was reported in [9] that an increase of pressure for the synthesis of BDD from 8–9 GPa [1] to 20 GPa [9] reduced the cubic lattice parameter of diamond from 3.5755±0.0005 Å [1] to 3.5724–3.5739 Å [9] and decreased the superconducting transition temperatures from 4–2.3 K [1] to 2.3–1.4 K [9]. We believe that this effect is related to a change in the mechanism of the graphite-to-diamond transformation at higher pressure. Graphite directly transforms into diamond at pressures of 12–25 GPa and temperatures exceeding 1900 K [10], and one cannot exclude that the synthesis of BDD in the B4C-graphite system at 20 GPa [9] begins from the direct conversion of graphite to diamond, which finally leads to a BDD formation scenario very different from that in [1]. In [11,12], the BDD synthesis was carried out using a temperature gradient method at a pressure of 5.5 GPa and temperatures of about 1700–1800 K. A metallic alloy was used as a crystal growth medium for the BDD synthesis. It was reported that the concentration of boron in the crystals did not reach the critical value 7×1020 cm−3, at which a metal-to-insulator transition takes place in the bulk HPHT single crystals of BDD synthesized with a metal melt [13] and in single-crystalline superconducting films grown by chemical vapor deposition (CVD) [14]. Note that crystals in [13] were cooled down to 2–4 K, probably a little above any possible superconducting transition. Unfortunately, the conditions for diamond crystal synthesis were not reported in [13]. Undoubtedly, the problem of the BDD synthesis in the form of single crystals is rather difficult because incorporation of boron in diamond strains the diamond lattice and thus might interfere with the crystal growth. On the other hand, it is necessary to consider the effect of kinetic factors on the doping and the effect of the synthesis temperature on the solubility of boron in diamond. For example, solubility of boron (substitutional impurity) in graphite increases from 1% at 2100 K to 2.35% at 2600 K (temperature of the B4C-graphite eutectic) [15].

Little is known about the properties of the solid solution of boron in diamond at high boron doping levels. With increasing boron concentration in diamond, the zone-centre optical phonon peak in Raman spectra of diamond broadens and shifts from 1332 cm−1 towards lower wavenumbers [16,17]. Also, new strong bands appear at 1225 and 500 cm−1; the origin of these bands is yet uncertain. The observation of an isotope effect would be very important for identification of the vibrational modes as well as for understanding the nature of superconductivity in BDD. Recent work [7] on isotopic substitution of12C by13C in BDD (C+7% B) has reported a large carbon-isotope effect on the superconducting transition temperatureTc. If this result is correct then it indicates a diamond-related nature of superconductivity in BDD even with boron-rich (95% B+C) inclusions [18]. Considering the sensitivity of the physical properties of BDD to the sample preparation procedures, it is necessary to reveal the isotope effect on superconductivity of BDD using another HPHT route.

The purpose of this work is to study the carbon and boron isotope effects on vibrational properties and superconducting transition temperature of heavily boron-doped diamond. Assuming that Co has no substantial effect on the solubility of boron in diamond, the effect of temperature during diamond synthesis on properties of BDD was tested using the Co–B–C system.

Materials and methods

Polycrystalline samples of BDD were synthesized in the B–C system at pressure of 8–9 GPa and a temperature of about 2500 K for 6–10 s. Under pressure, an HPHT cell was heated by passing electric current through a graphite bar with a piece of boron in the centre of the bar. As soon as the temperature inside the bar reaches the temperature of the eutectic melting in the B–C system, diamond formation takes place at the boron-graphite boundary. In principle, the mechanism of BDD synthesis is similar to that [1] briefly described above. A polycrystalline aggregate (30–35 mg) of BDD with grain size up to 10 μm is produced at the boundary of the graphite bar and the piece of boron (0.8–1.5 mg). Parts of a high-pressure cell with a sample of BDD are shown in figure1. The overall amount of boron in a sample of BDD (with unreacted boron in the centre of a sample) was calculated as about 4 at.%. All samples in the B–C system were produced under the same synthesis conditions. For the synthesis of BDD from13C carbon, an amorphous carbon (13C 99 at.%, Fe 0.001%, Isotec) pellet with a piece of boron was placed inside a graphite bar. Samples of BDD were produced from graphite (12C 99%, C 99.999%) and amorphous carbon (13C) using boron with the natural isotope composition (10B 20 at.%+11B 80 at.%, crystalline, B 99.7%, Aldrich Chem. Co.),10B (10B 96 at.%, B 99.9% crystalline, Alfa Aesar) and11B (11B 96 at.%, B 99.9%, crystalline, Alfa Aesar). The samples synthesized from carbon and natural boron are labelled as B-13C and B-12C. The samples obtained with10B and11B are denoted as10B-12C(13C) and11B-12C(13C), respectively. Electron probe microanalysis (INCA ENERGY, JSM-6390LV) did not detect metallic impurities (<0.2%) in diamond samples synthesized in the B–C systems. Synthesis of BDD using metallic growth medium was carried out in two ways: by placing a piece of the B (15 mass%)–Co alloy in the centre of a graphite bar and by placing a piece of Co in the centre of the graphite-boron (10%) mixture. Note that the presence of Co in the diamond growth system decreases the BDD synthesis temperature to about 1700–1900 K. After the synthesis, diamond samples were boiled in HClO4 and a mixture of H2SO4 with HNO3 acids to remove the growth medium. A LabRam HR-800 spectrometer with He-Ne and Ar lasers emitting at 632.8 and 488 nm, respectively, were used for micro-Raman analysis of BDD samples. Laser radiation was focused to a spot of about 1–2 (objective ×100), 5 (×50) and 10 μm (×10) in diameter. X-ray diffraction patterns were recorded with a powder diffractometer STADI MP (Stoe) using monochromatic Cu Kα1 radiation. Magnetic ac susceptibility measurements were performed with a home-built coil system and SR830 lock-in amplifier.

Figure 1.

Figure 1

Parts of a high pressure cell after experiment: (1) two parts of a graphite bar (heater), (2) a ball-like sample of BDD recovered from the hole in the bar.

Results and discussion

Raman study

Micro-Raman spectroscopy (488 nm excitation) revealed inhomogeneous incorporation of boron in our BDD samples when the measuring spot size on the sample surface was decreased from 10 (objective×10) to 1–2 μm (×100). Analysis of the spectra in figure2 suggests that microstructure of our BDD samples can be envisioned as a polycrystalline BDD matrix with tiny inclusions of slightly B-doped diamond. These inclusions can be accidently detected in the samples with the laser spot of 1–2 μm. The formation of slightly doped diamond is believed to be due to the formation of diamond growth sectors which accept less boron [19].

Figure 2.

Figure 2

Raman spectra of the B-12C BDD excited at 488 nm using different objectives: ×100, ×50, ×10. Spectra were collected from different parts of the same sample and shifted for presentation purposes. Inhomogeneous incorporation of boron in BDD was revealed when the measuring spot size on the sample surface was decreased from 10 (objective ×10) to 1–2(×100) μm: tiny inclusions of slightly B-doped diamond (one-phonon diamond Raman line at 1329 cm−1) were detected in the polycrystalline heavily boron-doped diamond matrix.

Because the intensities of the bands at 1225 and 500 cm−1 in the Raman spectra of our samples increased with excitation wavelength (from 488 to 632.8 nm), we used the 632.8 nm excitation for the investigation of an isotope effect in the Raman scattering spectra. Note that inhomogeneous incorporation of boron in BDD complicates evaluation of an isotope effect in these experiments. We compared Raman spectra from the most heavily boron-doped regions of our samples, assuming that these regions belong to {111} sectors of diamond grains [19]. A signature of the most heavily doped regions is an extreme low-frequency shift of all the BDD Raman bands. Thus, spectra of B-13C and B-12C,11B-12C and10B-12C in figures3 and4 correspond to such most heavily boron-doped regions which are typical of the polycrystalline BDD matrix. Figures3 and4 plot representative spectra for each sample. They show the extreme band positions (largest shift) among numerous measurements on the same sample. Except for the 500 cm−1 band, the carbon isotope substitution shifts the Raman bands in the corresponding spectra in good agreement with the relationshipM1/2(12C)ν(12C)=M1/2(13C)ν(13C), where ν is the corresponding Raman frequency andM is the atomic mass. The situation with the 500 cm−1 band is more complicated. An average carbon isotope shift of the 500 cm−1 band ν(12C)/ν(13C)∼1.02, is less than 1.04 expected for a carbon-only vibration. The 500 cm−1 band in Raman spectra of BDD was previously assigned to a local vibrational mode of boron pairs [17,21]. Consistent with this assignment, the isotope shift ν(10B)/ν(11B)∼1.04 of the 500 cm−1 band was observed by changing the boron isotope in BDD prepared with12C. The observation of a strong boron isotope shift of the 500 cm−1 Raman band along with a less pronounced carbon isotope shift suggests that boron dimers or clustered boron atoms contribute to this band. No changes caused by boron isotopic substitution were detected in the frequencies of other bands in the Raman spectra of BDD. This result suggests that 1225 and 1000 cm−1 Raman bands of BDD originate from the phonon density of states of diamond.

Figure 3.

Figure 3

Raman spectra of isotope-enriched BDD excited at 632.8 nm: B-13C (1, 2) and B-12C (3, 4); objective ×100. Each couple of spectra along with wavenumbers (cm−1) of Raman band position demonstrates local variation of Raman spectra characteristic of the samples. Spectra are shifted for presentation purposes.

Figure 4.

Figure 4

Raman spectra of isotope-enriched BDD excited at 632.8 nm:11B-12C (1, 2) and10B-12C (3, 4); objective ×50. Each couple of spectra along with wavenumbers (cm−1) of Raman band position demonstrates local variation of Raman spectra characteristic of the samples. Spectra are shifted for presentation purposes.

The effect of temperature of the diamond synthesis on properties of BDD

Introduction of Co into the B–C system decreases the BDD synthesis temperature to about 1700–1900 K, at which the eutectic melting takes place in the Co–B–C system. Assuming that Co has no substantial effect on solubility of boron in diamond, the effect of the temperature of the diamond synthesis on properties of BDD was tested using the Co–B–C system. Diamond samples obtained in the Co–C–B growth system at temperatures of about 1700–1900 K did not show a superconducting transition down to 1.6 K. At temperatures ranging from 1.6 to 300 K, all the samples demonstrated semiconducting behaviour of their resistivity. X-ray diffraction patterns of these samples reveal substantially smaller expansion of the diamond lattice compared to BDD synthesized in the B–C system (figure5, table1). A Vegard's model, in the case of substitutional incorporation of boron in diamond, estimates boron concentration in the samples produced in the Co–C–B system as ∼1020 cm−3, which is critical for observation of superconductivity in BDD. A decrease in efficiency of boron doping in Co–C–B (∼1700–1900 K) as compared with doping in the B–C (∼2500 K) system can be explained in terms of a temperature-dependent solubility of boron in diamond, boron carbide formation and solubility of boron carbide in the Co–C melt.

Figure 5.

Figure 5

Characteristic x-ray diffraction patterns of diamond samples synthesized in the B–C–Co (a) and B–C (b) systems (after removing a growth medium): non-diamond peaks were not detected. Inset: x-ray diffraction patterns of diamond samples near the (331) diamond (D) reflection: (1)13C-10B, (2)13C-11B, (3)12C-11B, (4)12C-10B, (5)12C-B, synthesized in the Co–C–B system, (6)12C, undoped diamond sample. The (533) peak of a Si standard was used to calculate the lattice parameter of diamond. Si powder was placed on the surface of a small diamond sample. X-ray diffraction patterns are shifted for presentation purposes.

Table 1.

Lattice parameters of BDD samples used for magnetic ac susceptibility measurements.

Sample12C-10B12C-11B13C-10B13C-11B12C12C-B(Co–B–C)
Lattice parameter3.57493.57483.57433.57443.56673.569
(±0.0001 Å)(±0.001 Å)

Isotope effect onTc

The observation of an isotope effect on superconductivity of BDD is a very difficult task. The shift of the critical temperatureTc due to isotopic substitution is expected to be small ∼(12/13)0.5=0.96 and can be easily masked by a shift ofTc due to different boron doping level; that is, the doping level of two samples composed of different isotopes should be equal. The inherent inhomogeneity of boron distribution in diamond samples broadens the superconducting transition thereby masking the isotope effects. Doping levels of two samples can be compared via, for example, their Hall concentrations or lattice parameters. The comparison of the critical temperatures is possible via electrical resistivity or magnetic susceptibility measurements. We used susceptibility measurements to study the isotope effect onTc, because resistivity measurements on different samples may be affected by different percolation paths in the samples compared. The macroscopic inhomogeneity of BDD sample properties can be reduced by choosing as small a sample as possible. First, we determined lattice parameters of the selected samples using x-ray diffraction, with Si as a standard. And finally, ac susceptibility measurements were made on these samples (having approximately equal masses, ∼0.5 mg) in the same coil system. Even when synthesizing samples at the same P-T parameters, it is difficult to obtain samples of BDD with exactly the same lattice parameters because of the different initial structures of12C (graphite) and13C (amorphous) materials. However, we were able to prepare a series of samples with sufficiently close values of the lattice parameters of12C and13C BDD.

The x-ray diffraction patterns near the (331) peak are shown in figure5 for selected samples of this series. The (533) peak of a Si standard was used to calculate the lattice parameter of diamond (table1). Si powder was placed on the surface of a small diamond piece. The (331) peak of BDD samples is broad and slightly asymmetric, which may be related to the presence of grains with different growth directions in these polycrystalline samples. The results of ac susceptibility measurements χ′ on these samples are shown in figure6. All samples of the series exhibit one broad superconducting transition. The transitions in two13C diamonds are shifted by about 500 mK to lower temperatures compared to two12C samples. To extract an isotope effect from this shift ofTc, one should take into account the difference in boron doping, which can be calculated from experimentally determined values of the lattice parameters (table1), and the dependence ofTc on the lattice parameter [22]. We estimated ΔTc due to a difference in boron doping as 0.25 K for samples12C-10B and13C-10B and 0.16 K for samples12C-11B and13C-11B. The value of the isotope effect coefficient is β0=−dlnTc/dlnM. The value β0=0.5 is expected for phonon-mediated superconductivity. After correction of measuredTc for different boron doping, we obtained a large carbon isotope effect (β0C) in our samples. For diamond samples doped with10B, the value is β0C=1.1±0.4. For diamond samples doped with11B, the value is β0C=1.4±0.4. Recently Dubrovinskaiaet al [7] reported a large carbon isotope effect on superconductivity in B-doped diamond. They found a 0.2 K difference inTc of two samples of12C and13C BDD, withTc∼2.4 K (zero resistance at 1.4 K), synthesized at 20 GPa. The calculated isotope effect coefficient β0C∼1.8 is even larger than we found for our samples. Experimental values of β0C are well above β0=0.5, which is expected for ‘pure’ electron–phonon mechanism of superconductivity. In most superconductors with the electron–phonon mechanism of superconductivity, β0 deviates to lower values relative to 0.5. This is explained by accounting for the Coulomb repulsion. When the Coulomb pseudopotential μ∗ is significant compared to the electron–phonon interaction, the value of β0 may be reduced below 0.5. In some rare cases, enhanced values of β0 were observed. One model (Carbotteet al [23]) of this β0 enhancement looks relevant to the case of BDD. This model describes the pair-breaking effect of paramagnetic impurities (in the manner of Abrikosov–Gor'kov theory) on the isotope effect in superconductivity. The pair-breaking effect in this model is isolated in the sense that all other mechanisms of changing β0 are ignored and β0=0.5 without pair-breaking. Pair-breaking is introduced via a parameter τp, which is equal to infinity in the absence of pair-breaking (infinite life-time of Cooper pairs) but becomes finite and small in the case of strong pair-breaking. Calculations [23] show that an increase of pair-breaking (decrease of τp) results in suppression ofTc and an increase of β0 well above β0=0.5. The role of the τp parameter for diamond may affect the real life-time of Cooper pairs which is short in BDD due to strong disorder [24]. A high degree of disorder in BDD manifests itself in broad superconducting transitions and a very short mean free path of doped holes. Calculations [24] showed that ordering of boron atoms incorporated into the diamond lattice will substantially enhance the superconducting transition temperature of BDD. In the case of highly disordered boron atoms in BDD with broad transitions, it is natural to expect an enhanced isotope effect in the spirit of the model of Carbotteet al [23]. More experimental and theoretical work is needed on the isotope effect in boron-doped diamond.

Figure 6.

Figure 6

The dispersive part χ′ of the magnetic ac susceptibility of four boron-doped diamond samples (1–4 in figure5).

Conclusions

Polycrystalline samples of BDD were synthesized at high pressure (8 GPa) and high temperatures (1700–2500 K) in the Co–C–B and B–C systems. The effects of carbon and boron isotopic substitutions and of the synthesis temperature were studied. We observed a carbon isotope effect on the superconducting transition temperatureTc that supports the importance of the electron–phonon interaction as the mechanism of superconductivity in diamond. Isotopic substitution permits us to relate almost all bands in the Raman spectra of BDD with vibrations of carbon atoms. The 500 cm−1 Raman band shifts either with carbon or boron isotope substitution and may be associated with vibrations of paired or clustered boron. The absence of a superconducting transition (down to 1.6 K) in BDD synthesized in the Co–C–B system at 1700–1900 K was explained by the reduced solubility of boron in diamond with decrease in temperature of the BDD synthesis.

Acknowledgments

This work was supported by the Russian Foundation for Basic Research (Grant 06-02-17480). Work at Los Alamos was performed under the auspices of the US DOE/Office of Science.

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