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Small-angle X-ray scattering in type Ia diamonds
Diamond and Related Materials 9 Ž2000. 1494᎐1499
Small-angle X-ray scattering in type Ia diamonds U
A.A. Shiryaeva, , Yu A. Klyuevb, A.M. Naletovb, A.T. Demboc, B.N. Feigelsond a
Vernadsky Institute of Geochemistry and Analytical Chemistry RAS, Kosygin St. 19, Moscow B-334, Russia b VNIIAlmaz, Gilyaro¨ skii St. 65, Moscow, Russia c Shubniko¨ Institute of Crystallography RAS, Leninskii prospekt 59, Moscow, Russia d Research Center ‘Basis’, Moscow, Russia Received 20 January 2000; accepted 19 April 2000
Abstract The results of a small-angle X-ray scattering ŽSAXS. investigation of natural and synthetic diamonds, with different types of nitrogen-related defects, are presented. They reveal a presence of impurity-rich spherical clusters with a diameter of approxi˚ in an IaB diamond. SAXS scattering in an IaA diamond has a much lower intensity, and originates from larger mately 90 A clusters with a considerable variation in size. It is likely that the dominant impurity in these clusters is nitrogen. Present data suggest the possibility that some of the nitrogen-related point defects ŽA- and B-centers . are not randomly distributed in the diamond lattice, but instead are concentrated in clusters. It is suggested that, although optical manifestations of the A-nitrogen are similar in different diamonds, IaA diamonds can be divided into two sub-groups. The IaA1 group includes annealed, synthetic, and some natural diamonds. They contain randomly distributed nitrogen pairs, which do not influence mechanical properties and do not produce X-ray scattering. In the IaA2 group, the diamond aggregation process went further and the formation of nitrogen-containing clusters began. The process of nitrogen aggregation is described in terms of the decay of a supersaturated solid solution of nitrogen in diamond. The driving force for the creation of impurity clusters is the lowering of the free energy of nitrogen dissolution in the diamond lattice, and the decrease of strain. 䊚 2000 Elsevier Science S.A. All rights reserved. Keywords: Nitrogen defects; Small-angle X-ray scattering; Defects annealing; Impurity clusters
1. Introduction Nitrogen is the main elemental impurity in diamond. It substitutes carbon in the lattice and forms different defect centers. In the type Ib diamond, nitrogen is dominantly present as a single substitutional atom, referred to as the C center in IR absorption, and the P1 center in ESR studies. Almost all synthetic diamonds belong to this type. The rarity of natural Ib
U
Corresponding author. Tel.: q7095-1378638; fax: q7095-9382054. E-mail address: a ᎏ [email protected] ŽA.A. Shiryaev..
diamonds is usually explained by the high-pressure high-temperature ŽHPHT. aggregation of single substitutional nitrogen atoms to the so-called A- and B-complexes, via the process C ª Aª B w1᎐3x. Diamonds with these defects are referred to as type IaA and IaB, respectively. Following the pioneering work by Sobolev et al. w4x, ESR w5x and optical studies w6x showed that the A-center is a pair of nearest-neighbor substitutional nitrogen atoms. The microscopic structure of the B-defect has not been definitely established. The results obtained by ESR w7x and electron nuclear double resonance Žvan Wyk and Loubser, 1984, unpublished. suggest a complex of four nitrogen atoms in a tetra-
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A.A. Shiryae¨ et al. r Diamond and Related Materials 9 (2000) 1494᎐1499
hedral coordination around a vacancy. Although, on an atomic scale these models are probably correct, the evidence for them is indirect. Numerous data exist revealing the presence of larger impurity-containing aggregates. One of the best-known examples is the so-called ‘platelets’-planar Žin 1004 plane. defects of uncertain composition. X-Ray diffuse scattering shows that Ia diamonds also contain planar 1114 precipitations w8᎐10x, which are probably dislocation loops stabilized by nitrogen. The existence of sphere-like Žisometric. clusters with a diameter of ˚ and a high nitrogen content was reported ; 80᎐90 A by Klyuev et al. w11x and Naletov et al. w12x. The presence of such clusters is also consistent with the results on hardness w13,14x and low-temperature thermal conductivity w15,16x. Larger clusters were observed by Ramanan et al. w17x. The correlation of IR absorption from the A- and B-defects, and the intensity of X-ray diffuse scattering from sphere-like clusters were found in Klyuev et al. w11x and Naletov et al. w12x, respectively. It was proposed that the A- and B-defects are sphere-like Žisometric. regions of the diamond lattice with a nitrogen concentration of ; 25 at.%, and a ˚ Žfor review, see w14x.. It should diameter of ; 80᎐90 A be noted that in the latter model, the atomic arrangement of the nitrogen atoms was not specified and the existence of point nitrogen-related centers inside those clusters is possible. Additional evidence in favor of the presence of clusters can be found in the data on the aggregation of the single substitutional nitrogen atoms. Following Chrenko et al. w1x, the kinetics of aggregation is usually described by the second order process kts 1rct y 1rco , where co and ct are the concentrations of nitrogen atoms, respectively, before and after annealing, t is the duration of annealing and k is a rate constant. This process implies the reaction Nq Nª wN᎐Nx. However, the second-order kinetics often fail to satisfy experimental results w18x. For example, the estimation of the age of many natural diamonds from second-order kinetics leads to the time exceeding the age of the Earth Žsee discussion in w19x, w20x.. Many of experimental results on nitrogen aggregation can be better fitted by the Avraami equation corct s expŽyktn . w3,21x, which describes the formation of impurity clusters on a diffusion-limited stage. Such impurity clusters are indeed present in materials with diamond-like structures, such as Si and Ge Že.g. w22x.. It is worth noting that the presence of nitrogen-containing clusters does not imply the existence of pure nitrogen precipitations in diamond Žlike voidites.. The inobservance w23x of such clusters in the electron microscope Žsee, however, w24x. could be due to the poor image contrast. In this paper, we present experimental results on small-angle X-ray scattering ŽSAXS. in natural IaB and natural and synthetic IaA diamonds. They reveal the
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presence of spherical clusters of defects, approximately ˚ in diameter in the IaB diamond. In type IaA 90 A diamonds, clusters are also observed; however, the scattering contrast is much weaker and the scatter in the clusters size is significant. It is likely that the clusters are nitrogen-related.
2. Experimental Four natural type IaB diamonds, and four natural and two synthetic IaA diamonds have been studied. Synthetic diamonds were grown by the HTHP method, and then annealed under stabilizing pressure in order to aggregate dispersed nitrogen to the A-form. All diamonds were polished prior to analyses. The thickness of the samples was 1᎐1.5 mm. High quality natural nitrogenless Žtype IIa. crystal was used as a reference sample. Several IaB diamonds from this set were previously studied by X-ray diffuse scattering w12,25,26x and they showed the existence of scattering objects with a ˚ In the studied IaB samples, only diameter of ; 80 A. IR absorption due to the B-centers was observed, with no lines related to platelets or A-defects detectable Žexcept sample 4.. Natural IaA diamonds contained a small amount of platelets and negligible absorption from the B-defects. For a description of the samples see Table 1. For an introduction to the SAXS, see, for example, Feigin and Svergun w29x. In our experiments, the angular region from 15⬘ to 1.2⬚ was investigated. A small-angle X-ray diffractometer AMUR-K w30x with a Kratkicollimator and a linear position-sensitive detector were used. A Cu-anode fine focus tube was employed as the source of X-ray radiation. The monochromatization was achieved with Ni-filtration. Since the size of the Table 1 Description of samples a Sample
␣A cmy1
␣B cmy1
␣C cmy1
Platelets
Type
1 Žnatural . 2 Žnatural . 3 Žnatural . 4 Žnatural . 5 Žnatural . 6 Žsynthetic . 7 Žsynthetic . 8 Žnatural . 9 Žnatural . 10 Žnatural . 11 Žnatural .
n.d. n.d. n.d. 2.3 n.d. 10.6 8.4 42.1 40.5 45.3 20.6
n.d. 25.3 6.7 15.5 12 n.d. n.d. 0.2 n.d. 0.4 0.3
n.d. n.d. n.d. n.d. n.d. 1 n.d. n.d. n.d. n.d. n.d.
n.d. n.d. n.d. n.d. n.d. n.d. n.d. 1.3; 1369.7 n.d. 1.6; 1369.4 n.d.
IIa IaB IaB IaB IaB IaA IaA IaA IaA IaA IaA
a
␣ i- absorption by corresponding defect. To calculate amount of nitrogen in each defect one can use empirical relations from the literature w14,27,28x. For platelets, the absorption and position of line Žin cmy1 . are indicated. N.d. is ‘not detected’ Žabsorption - 0.1 cmy1 ..
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probing X-ray beam was relatively large Ž2 = 0.2 mm., an overlapping of signals from different growth sectors could be present. However, the IR mapping of diamonds shows that the nitrogen concentration and aggregation state were relatively uniform Žexcept sample 4. and inhomogeneities did not significantly influence the conclusions of this work. The experimental curves were normalized to the primary beam intensity, and the sample absorption coefficient; the holder scattering was subtracted. The calculation of the size distribution of scattering objects was performed with the computer code GNOM w31x. All of the distributions presented in this study are stable solutions against the variations of maximal size of the scattering centers. During the search for a solution, no limits on the relative abundance of defects with small sizes were imposed.
3. Results and discussion
The small-angle scattering in the defect-free IIa diamond was negligible, and almost coincided with the background. This fact indicated the insignificance of thermal contribution to SAXS at room temperature, which could be attributed to the high Debye temperature of diamond Ž1800 K.. Therefore, we assumed that scattering in the IIa diamond was caused by the diamond matrix itself, and subtracted it from curves for other crystals. Normalized SAXS curves from several IaB and IaA diamonds are presented in Fig. 1. It revealed that scattering in IaA and IaB diamonds is markedly higher than in the IIa sample. We assumed that the scattering centers could be represented by a polydisperse system, and fitted the observed curves by scattering on disk-like objects w8,9x and on hard spheres. The best agreement was achieved using a hard sphere approximation. The volume distribution of hard spheres vs. scattering cluster diameter is shown in Fig. 2a,b.
Fig. 1. Normalized small-angle X-ray scattering curves for investigated diamonds.
Fig. 2. Volume distribution of defects in IaB ŽFig. 2a. and in IaA ŽFig. 2b. diamonds. Hard spheres approximation.
3.1. IaB diamonds
As seen from Fig. 2a, the results from IaB diamonds can be best explained in terms of scattering on spheri˚ The cal defects with a diameter of approximately 90 A. deviation of the curve for diamond no. 5 from the others can probably be explained by internal zonation. The small scatter in cluster size is remarkable. Besides some physical reasons, such as different time orrand temperature of growth, this scatter could be partially ascribed to the contributions from different growth sectors. It is worth noting that the size of clusters obtained from the diffuse w12,25x and small-angle scattering is identical. A positive correlation between the size of the defects and nitrogen concentration in the B-form was observed for several samples Žnos. 2, 3, 5.. This correlation fits well to the model of formation of B-defects Žsee below., but the statistics are poor, and it is not clear yet if this trend is general. In this work we were unable to establish a reliable correlation between the intensity of the SAXS and optical data. The scattering contrast in SAXS is determined by the difference in the electronic density of the impurity cluster and that of the matrix. The electronic density of clusters in different diamonds can
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alter due to variations in the nitrogen content. As frequently observed in metallic and semiconducting alloys Že.g. w22,32x., the structure of the impurity clusters could be heterogeneous: a heavily impurity-doped core and a depleted outer part. From the X-ray diffuse scattering, Naletov w25x concluded that the same could be valid for diamond as well. Our preliminary comparative results on X-ray and neutron small-angle scattering show that these defect clusters could indeed have some internal structure. This heterogeneity, together with possible variations in the contrast of electron density, makes the existence of a direct correlation between X-ray and IR data difficult. Reliable confirmation of such a correlation will only be possible after absolute measurements of SAS, which will give information about the difference of electronic densities of cluster and matrix. This work is in progress. Since point defects do not produce small-angle scattering Že.g. w29x., the presence of scattering indicates the presence of extended defects. Dislocation loops and other planar formations should be ruled out due to the failure of approximation of SAXS data by scattering on disk-shape objects, and due to the small contrast in electron density with the perfect lattice, which makes their detection by SAXS possible only at very high concentrations Ž) 1011 rcm2 .. Voidites, in principle, could contribute to SAXS. Estimations of nitrogen amount in them Žtherefore, scattering contrast. gives figures, similar to proposed for sphere-like clusters Ž; 25 at.%. w33x. However, voidites demonstrate con˚ w33x. even inside siderable scatter in sizes Ž20᎐100 A one diamond, while observed defects Ž‘clusters’. have a well-defined diameter. Another reason to believe that voidites do not contribute to the presented results is that ‘clusters’ are observed in diamonds of different types, while voidites are limited to certain types of stones. At present we cannot make an unambiguous conclusion about the composition of the defects clusters. In Ramanan et al. w17x it was suggested that observed clusters are related to vacancies andror interstitials. This is a reasonable explanation, but to the best of our knowledge no clusters have yet been reported for IIa. As a working model, until more studies on nitrogenless diamonds are performed, we consider the clusters as being nitrogen-related Žfollowing w11,12x.. SAXS data for IaB diamonds, together with the results of X-ray diffuse scattering w12,26x, suggest a presence of sphere-like regions Ž‘clusters’. with a high concentration of impurity Žnitrogen?. and a diameter of ˚ in the diamond lattice. The slight scatter in 80᎐100 A the size of the ‘clusters’ from sample-to-sample could be explained by a different degree of aggregation andror different growth temperature. The structure of nitrogen inside these clusters is currently uncertain. It is possible that nitrogen inside the clusters is present in
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the B-form. A high concentration of nitrogen, and a relatively large diameter of the ‘clusters’ suggest that they could be formed as a result of decay of nitrogen solid solution in the diamond matrix. If the clusters are N-related, an important question arises: a high density of neighboring point defects should produce strain and a broadening of corresponding optical lines. A combination of optical, thermal conductivity and X-ray data gives a preliminary estimate of 25 at.% of nitrogen in these regions w14x. The above-mentioned broadening is indeed observed in electron-irradiated diamonds w34x. At present we do not have an unambiguous explanation as to why the majority of nitrogen-related optical lines in non-treated diamonds are so sharp. We could speculate that the estimation of 25 at.% of nitrogen is too high, and the actual amount of nitrogen inside clusters is much lower. Another explanation is that the driving force for the decay of the nitrogen solid solution has at least two components: the decrease of the free energy of impurity dissolution, and the lowering of strain. Some ordering of point defects inside clusters may also lead to these sharp optical lines. 3.2. IaA diamonds SAXS results from IaA samples are much less systematic, than from IaB crystals. From the six IaA diamonds studied here, only three Ž7, 8 and 10. show scattering different from the background. Even in these cases, the scattering is much weaker than in IaB diamonds. This can be seen in Fig. 2a, where the volume distribution for IaA diamond no. 8 is plotted together with the results for IaB samples. Note that the volume of scattering defects in IaA diamonds is two orders of magnitude smaller than in IaB crystals. The size distribution of defects in IaA diamonds is shown in Fig. 2b. A large scatter in cluster size is observed; only two ˚ and at samples have pronounced maxima Žat ; 120 A ˚ .. Similar results were reported by Ramanan 380᎐500 A et al. w17x. The larger maximum can not be explained by platelets since no platelets exist in synthetic diamonds Žcurve 7.. Moreover, in diamond 10, with the highest IR absorption from platelets, no such maximum is observed. Current studies suggest that while diamonds with B-defects possess a relatively well-defined structure ˚ ., the Žisometric clusters with a diameter of ; 80᎐100 A IaA crystals are very inhomogeneous from the X-ray scattering viewpoint. Based on the industrial mechanical testing of a large number of natural and synthetic diamonds, Klyuev et al. w15x suggested that though optical manifestations of the A-defect are identical, two groups of type IaA diamonds can be recognized. Present X-ray investigations support this division. In the group IaA1 , the nitrogen impurity of the stones was
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present as point defects Žpairs.. X-Ray scattering Žboth diffuse and small-angle., as well as hardening by dispersed impurity, was negligible. In the group IaA2 , the nitrogen in the diamonds formed clusters, which were responsible for small-angle and diffuse X-ray scattering, and for the hardening of diamonds. Inside these clusters, nitrogen atoms could be arranged in pairs. In the next section we discuss the possible origin of these groups. 3.3. Discussion of the nitrogen aggregation process in diamonds The existence of nitrogen clusters, and their possible relation to A- and B-defects, suggests that the process of nitrogen aggregation in diamonds is the decay of a supersaturated solid solution, with the formation of impurity clusters on a diffusion-limited stage. The process of aging of metallic and semiconducting solid solutions leads to the precipitation of impurity aggregates. Their shape, structure and size depend on the initial degree of supersaturation, temperature and the duration of annealing. The driving force for the clusterization of defects is a lowering of the free energy of impurity dissolution and decrease of strain. Currently it is not clear in which form nitrogen atoms incorporate into natural diamonds. In synthetic diamonds, grown with metallic catalysts, the predominant form of nitrogen is a single atom. This fact is easy to explain, since nitrogen is dissolved in metal under the P-T conditions of synthesis. However, nitrogen speciation in the growth medium of natural diamonds is not clear, and depends on the chemical composition of the medium and on redox conditions. Nitrogen can be present as chemical compounds Že.g. N2 , NH4 , nitrides. or as dissolved atoms. Inclusions of N2 were found in diamondiferous xenoliths and in natural diamonds w35,36x. However, gas-chromatographic studies of HPHT diamonds and of growth Fe᎐Ni alloys w37x show that N2 is present in very small amounts Žat degassing temperatures structural nitrogen was not released.. Thus, it is possible that in some natural diamonds, nitrogen could be incorporated as a pair. This could happen, for example, in fibrous diamonds, the majority of which belong to IaA type. Many researchers Že.g. w38x. suggest that their formation could be directly related to the kimberlite event; therefore, their mantle residence time could be very short Žseveral days.. This makes aggregation process of C ª A, with a high kinetic barrier Žespecially in cubic sectors., almost improbable at inferred temperatures. The proposed difference in nitrogen incorporation in synthetic and some natural diamonds agrees with the fact that the nitrogen content in natural diamonds is usually much higher than in HPHT diamonds. The method of nitrogen incorporation into the dia-
mond lattice should affect only the first aggregation stage, because if nitrogen was introduced in the lattice as a single atom, annealing would lead to the formation of nitrogen pairs. Annealing of synthetic and some natural diamonds usually stops at this stage Žgroup IaA1 diamonds.. Calculations w39x suggest that the kinetic barrier for vacancy-mediated aggregation is much lower than in case of a direct atom exchange. Indeed, experiments show that presence of even 5 ppm of vacancies markedly increases the aggregation rate w40x. The concentration of vacancies in diamonds is unknown. Positron annihilation studies Žw41x and references therein . indicate that the concentration of nitrogen-vacancy complexes in natural diamonds is in the 0.2᎐20 ppm range. Since the formation of vacancies and other lattice defects is energetically favored in stressed regions, e.g. strain fields around dislocations, the aggregation rate can be slightly higher there. These stressed regions could serve as a sink for migrating nitrogen atoms. Therefore, further annealing can lead ˚ in diameto the formation of large regions Ž400᎐500 A . ter , characterized by an increased nitrogen concentration Žgroup IaA2 diamonds, low-temperature stage, formation of Guinier᎐Preston zones.. In these zones, the concentration of lattice defects is high and that can explain the results of studies of vacancy formation and migration w34,42x. According to Ramanan et al. w17x, large impurity clusters observed in diamonds have a considerable number of interstitials and vacancies. With the progression of annealing, the nitrogen content in these regions increases and stops at some optimal concentration. Inside the formed clusters, nitrogen atoms can be arranged as point defects, e.g. 4Nq V complexes. Possible clusterization of point nitrogen defects can have a profound influence on nitrogen aggregation kinetics. It is possible that in the early aggregation stages Žcreation of the IaA1 groups. nitrogen aggregation is limited by interatomic interactions, thus yielding second order kinetics w1x, while in the later stages, aggregation is diffusion-limited and is better described by the Avraami equation: c 0rct s expŽyktn . w3,21x. 4. Conclusions The results of small-angle X-ray scattering ŽSAXS. in natural and synthetic diamonds with different types of nitrogen-related defects are presented. They reveal the presence of nitrogen-containing spherical clusters with ˚ in the IaB diamond. a diameter of approximately 90 A Scattering from IaA diamonds has much lower intensity and originates from clusters with a large variation in size. It is suggested that, although the optical manifestations of the A-defect are similar in different diamonds, IaA diamonds can be divided into two sub-
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groups. The group IaA1 includes annealed synthetic and some natural diamonds. They contain randomly distributed nitrogen pairs, which do not significantly affect mechanical properties and do not produce reasonable X-ray scattering. In the diamonds of the IaA2 group, nitrogen underwent a further aggregation stage and the formation of nitrogen-containing clusters began. It is possible that inside these clusters, nitrogen is arranged in pairs. Further annealing leads to the for˚ . nitrogen-rich mation of smaller Ždiameter of ; 90 A clusters. They are not precipitations of pure nitrogen, however, as they can contain nitrogen in the B-form. It is possible that in the early aggregation stages Žstage I. nitrogen aggregation is limited by interatomic interactions resulting in second order kinetics w1x; on the later stages aggregation is diffusion-limited and is better described by the Avraami equation c0rct s expŽyktn ..
Acknowledgements We acknowledge the comments made by K. Iakoubovskii and by three anonymous reviewers, whose remarks helped us to clarify some of our statements. References w1x R.M. Chrenko, R.E. Tuft, H.M. Strong, Nature 270 Ž1977. 141. w2x T. Evans, Z. Qi, Proc. R. Soc. Lond A381 Ž1982. 159. w3x Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha et al., Zhurnal Fizicheskoi Khimii wEnglish translation: Russ. J. Phys. Chem. 56 Ž1982. 323x 56 Ž1982. 524. w4x E.V. Sobolev, V.I. Lisoivan, S.V. Lenskaya, Sov. Phys. Dokl. 12 Ž1968. 665. w5x M. Ya Shcherbakova, E.V. Sobolev, V.A. Nadolinnyi, Doklady AN SSSR Žin Russian. 204 Ž1972. 851. w6x G. Davies, J. Phys. C9 Ž1976. L537. w7x J.A. van Wyk, G. Woods, J. Phys. Condens. Matter 7 Ž1995. 5901. w8x V.I. Lisoivan, Doklady AN SSSR Žin Russian. 230 Ž1976. 88. w9x V.I. Lisoivan, Fiz. Tverdogo. Tela. Žin Russian. 21 Ž1979. 240. w10x G.M. Rylov, E.V. Sobolev, Ext. abstracts 6th int. Kimberlite conf, in: N.V. Sobolev et al. ŽEd.., Novosibirsk, 1995, p. 479. w11x Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha et al., Fiz. Tverdogo Tela wEnglish translation: Sov. Phys. Solid State 19 Ž1977. 7x 19 Ž1977. 14. w12x A.M. Naletov, Y.A. Klyuev, V.I. Nepsha, Fiz. Tverdogo Tela Žin Russian. 19 Ž1977. 1529. w13x Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha, Proceedings of the
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International Conference on New Diamond Science and Technology, Materials Research Society, Washington, 1990, p. 149. G.B. Bokii, G.N. Bezrukov, Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha, Prirodnye i sinteticheskie almazy Žin Russian., Natural and Synthetic Diamonds, Nauka Publishers, Moscow, 1986, p. 220. R. Berman, M. Martinez, Diamond Res., Suppl. Ind. Diam. Rev, Ž1976. 7. J.W. Vandersande, J. Phys. C13 Ž1980. 759.q R.R. Ramanan, S.N.N. Goswami, K. Lal, Acta Cryst. A54 Ž1998. 163. D. Fisher, S.C. Lawson, Diamond Rel. Mater. 7 Ž1998. 299. J. Harris, A.T. Collins, Ind. Diamond Rev. 3r85 Ž1986. 128. S.R. Boyd, C.T. Pillinger, H.J. Milledge, M.J. Seal, Earth Planet. Sci. Lett. 108 Ž1992. 139. L.D. Belimenko, Yu. A., Klyuev, V.A. Laptev et al., Doklady AN SSSR wEnglish translation: Sov. Phys. Dokl., 259 Ž1981. 722x 26 Ž1981. 1360. V.I. Fistul’, Raspad Peresyshennih Poluprovodnikovyh Tverdyh Rastvorov ŽDecay of Supersaturated Semiconducting Solid Solutions. Žin Russian., Ž1977. 240. T. Evans, in: J. Field ŽEd.., The Properties of Natural and Synthetic Diamond, Academic Press, 1992, p. 710. P.R.W. Hudson, P.P. Phakey, Nature 269 Ž1977. 227. A.M. Naletov, Unpublished PhD thesis, Kiev, 1978. A.A. Shiryaev, Yu. A., Klyuev, AM Naletov et al., 17th General Conf of Condensed Matter Div, in: G. Thomas et al. ŽEd.., EPS Book of Abstracts Grenoble: European Physical Society, 22E Ž1998. 146. S.R. Boyd, I. Kiflawi, G.S. Woods, Phil. Mag. B69 Ž1992. 1149. S.R. Boyd, I. Kiflawi, G.S. Woods, Phil. Mag. B72 Ž1995. 351. L.A. Feigin, D.I. Svergun, Structure Analysis by Small-Angle X-Ray and Neutron Scattering, Plenum Press, NY, 1987. L. Yu Mogilevsky, A.T. Dembo, D.I. Svergun, L.A. Feigin, Kristallografiya Žin Russian. 29 Ž1984. 581. D.I. Svergun, J. Appl. Cryst. 24 Ž1991. 485. C.B. Walker, A. Guinier, Acta Metallurgica 1 Ž1953. 568. P.B. Hirsch, P. Pirouz, J.C. Barry, Proc. R. Soc. London A407 Ž1986. 239. G. Davies, S.C. Lawson, A.T. Collins, Phys. Rev. B46 Ž1992. 13157. A.A. Tomilenko, A.I. Chepurov, Yu N. Pal’yanov et al., Russ. Geol. Geophys. 38 Ž1998. 1. K. De Corte, P. Cartigny, V.S. Shatsky et al., Geochim. Cosmochim. Acta 62 Ž1998. 3765. I.I. Fedorov, D.G. Bagryantsev, A.A. Chepurov et al., Geokhimiya 4 Ž1998. 416. S.R. Boyd, F. Pineau, M. Javoy, Chem. Geol. 116 Ž1994. 29. A. Mainwood, Phys. Rev. B49 Ž1994. 7934. A.T. Collins, J. Phys. C11 Ž1978. L417. A.A. Shiryaev, A. van Veen, H. Schut, A.C. Kruseman, O.D. Zakharchenko, Rad. Phys. Chem. Ž2000. in press. S.C. Lawson, G. Davies, A.T. Collins, A. Mainwood, J. Phys. Condens. Matter 4 Ž1992. L125.
Small-angle X-ray scattering in type Ia diamonds U
A.A. Shiryaeva, , Yu A. Klyuevb, A.M. Naletovb, A.T. Demboc, B.N. Feigelsond a
Vernadsky Institute of Geochemistry and Analytical Chemistry RAS, Kosygin St. 19, Moscow B-334, Russia b VNIIAlmaz, Gilyaro¨ skii St. 65, Moscow, Russia c Shubniko¨ Institute of Crystallography RAS, Leninskii prospekt 59, Moscow, Russia d Research Center ‘Basis’, Moscow, Russia Received 20 January 2000; accepted 19 April 2000
Abstract The results of a small-angle X-ray scattering ŽSAXS. investigation of natural and synthetic diamonds, with different types of nitrogen-related defects, are presented. They reveal a presence of impurity-rich spherical clusters with a diameter of approxi˚ in an IaB diamond. SAXS scattering in an IaA diamond has a much lower intensity, and originates from larger mately 90 A clusters with a considerable variation in size. It is likely that the dominant impurity in these clusters is nitrogen. Present data suggest the possibility that some of the nitrogen-related point defects ŽA- and B-centers . are not randomly distributed in the diamond lattice, but instead are concentrated in clusters. It is suggested that, although optical manifestations of the A-nitrogen are similar in different diamonds, IaA diamonds can be divided into two sub-groups. The IaA1 group includes annealed, synthetic, and some natural diamonds. They contain randomly distributed nitrogen pairs, which do not influence mechanical properties and do not produce X-ray scattering. In the IaA2 group, the diamond aggregation process went further and the formation of nitrogen-containing clusters began. The process of nitrogen aggregation is described in terms of the decay of a supersaturated solid solution of nitrogen in diamond. The driving force for the creation of impurity clusters is the lowering of the free energy of nitrogen dissolution in the diamond lattice, and the decrease of strain. 䊚 2000 Elsevier Science S.A. All rights reserved. Keywords: Nitrogen defects; Small-angle X-ray scattering; Defects annealing; Impurity clusters
1. Introduction Nitrogen is the main elemental impurity in diamond. It substitutes carbon in the lattice and forms different defect centers. In the type Ib diamond, nitrogen is dominantly present as a single substitutional atom, referred to as the C center in IR absorption, and the P1 center in ESR studies. Almost all synthetic diamonds belong to this type. The rarity of natural Ib
U
Corresponding author. Tel.: q7095-1378638; fax: q7095-9382054. E-mail address: a ᎏ [email protected] ŽA.A. Shiryaev..
diamonds is usually explained by the high-pressure high-temperature ŽHPHT. aggregation of single substitutional nitrogen atoms to the so-called A- and B-complexes, via the process C ª Aª B w1᎐3x. Diamonds with these defects are referred to as type IaA and IaB, respectively. Following the pioneering work by Sobolev et al. w4x, ESR w5x and optical studies w6x showed that the A-center is a pair of nearest-neighbor substitutional nitrogen atoms. The microscopic structure of the B-defect has not been definitely established. The results obtained by ESR w7x and electron nuclear double resonance Žvan Wyk and Loubser, 1984, unpublished. suggest a complex of four nitrogen atoms in a tetra-
0925-9635r00r$ - see front matter 䊚 2000 Elsevier Science S.A. All rights reserved. PII: S 0 9 2 5 - 9 6 3 5 Ž 0 0 . 0 0 2 7 5 - 2
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hedral coordination around a vacancy. Although, on an atomic scale these models are probably correct, the evidence for them is indirect. Numerous data exist revealing the presence of larger impurity-containing aggregates. One of the best-known examples is the so-called ‘platelets’-planar Žin 1004 plane. defects of uncertain composition. X-Ray diffuse scattering shows that Ia diamonds also contain planar 1114 precipitations w8᎐10x, which are probably dislocation loops stabilized by nitrogen. The existence of sphere-like Žisometric. clusters with a diameter of ˚ and a high nitrogen content was reported ; 80᎐90 A by Klyuev et al. w11x and Naletov et al. w12x. The presence of such clusters is also consistent with the results on hardness w13,14x and low-temperature thermal conductivity w15,16x. Larger clusters were observed by Ramanan et al. w17x. The correlation of IR absorption from the A- and B-defects, and the intensity of X-ray diffuse scattering from sphere-like clusters were found in Klyuev et al. w11x and Naletov et al. w12x, respectively. It was proposed that the A- and B-defects are sphere-like Žisometric. regions of the diamond lattice with a nitrogen concentration of ; 25 at.%, and a ˚ Žfor review, see w14x.. It should diameter of ; 80᎐90 A be noted that in the latter model, the atomic arrangement of the nitrogen atoms was not specified and the existence of point nitrogen-related centers inside those clusters is possible. Additional evidence in favor of the presence of clusters can be found in the data on the aggregation of the single substitutional nitrogen atoms. Following Chrenko et al. w1x, the kinetics of aggregation is usually described by the second order process kts 1rct y 1rco , where co and ct are the concentrations of nitrogen atoms, respectively, before and after annealing, t is the duration of annealing and k is a rate constant. This process implies the reaction Nq Nª wN᎐Nx. However, the second-order kinetics often fail to satisfy experimental results w18x. For example, the estimation of the age of many natural diamonds from second-order kinetics leads to the time exceeding the age of the Earth Žsee discussion in w19x, w20x.. Many of experimental results on nitrogen aggregation can be better fitted by the Avraami equation corct s expŽyktn . w3,21x, which describes the formation of impurity clusters on a diffusion-limited stage. Such impurity clusters are indeed present in materials with diamond-like structures, such as Si and Ge Že.g. w22x.. It is worth noting that the presence of nitrogen-containing clusters does not imply the existence of pure nitrogen precipitations in diamond Žlike voidites.. The inobservance w23x of such clusters in the electron microscope Žsee, however, w24x. could be due to the poor image contrast. In this paper, we present experimental results on small-angle X-ray scattering ŽSAXS. in natural IaB and natural and synthetic IaA diamonds. They reveal the
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presence of spherical clusters of defects, approximately ˚ in diameter in the IaB diamond. In type IaA 90 A diamonds, clusters are also observed; however, the scattering contrast is much weaker and the scatter in the clusters size is significant. It is likely that the clusters are nitrogen-related.
2. Experimental Four natural type IaB diamonds, and four natural and two synthetic IaA diamonds have been studied. Synthetic diamonds were grown by the HTHP method, and then annealed under stabilizing pressure in order to aggregate dispersed nitrogen to the A-form. All diamonds were polished prior to analyses. The thickness of the samples was 1᎐1.5 mm. High quality natural nitrogenless Žtype IIa. crystal was used as a reference sample. Several IaB diamonds from this set were previously studied by X-ray diffuse scattering w12,25,26x and they showed the existence of scattering objects with a ˚ In the studied IaB samples, only diameter of ; 80 A. IR absorption due to the B-centers was observed, with no lines related to platelets or A-defects detectable Žexcept sample 4.. Natural IaA diamonds contained a small amount of platelets and negligible absorption from the B-defects. For a description of the samples see Table 1. For an introduction to the SAXS, see, for example, Feigin and Svergun w29x. In our experiments, the angular region from 15⬘ to 1.2⬚ was investigated. A small-angle X-ray diffractometer AMUR-K w30x with a Kratkicollimator and a linear position-sensitive detector were used. A Cu-anode fine focus tube was employed as the source of X-ray radiation. The monochromatization was achieved with Ni-filtration. Since the size of the Table 1 Description of samples a Sample
␣A cmy1
␣B cmy1
␣C cmy1
Platelets
Type
1 Žnatural . 2 Žnatural . 3 Žnatural . 4 Žnatural . 5 Žnatural . 6 Žsynthetic . 7 Žsynthetic . 8 Žnatural . 9 Žnatural . 10 Žnatural . 11 Žnatural .
n.d. n.d. n.d. 2.3 n.d. 10.6 8.4 42.1 40.5 45.3 20.6
n.d. 25.3 6.7 15.5 12 n.d. n.d. 0.2 n.d. 0.4 0.3
n.d. n.d. n.d. n.d. n.d. 1 n.d. n.d. n.d. n.d. n.d.
n.d. n.d. n.d. n.d. n.d. n.d. n.d. 1.3; 1369.7 n.d. 1.6; 1369.4 n.d.
IIa IaB IaB IaB IaB IaA IaA IaA IaA IaA IaA
a
␣ i- absorption by corresponding defect. To calculate amount of nitrogen in each defect one can use empirical relations from the literature w14,27,28x. For platelets, the absorption and position of line Žin cmy1 . are indicated. N.d. is ‘not detected’ Žabsorption - 0.1 cmy1 ..
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probing X-ray beam was relatively large Ž2 = 0.2 mm., an overlapping of signals from different growth sectors could be present. However, the IR mapping of diamonds shows that the nitrogen concentration and aggregation state were relatively uniform Žexcept sample 4. and inhomogeneities did not significantly influence the conclusions of this work. The experimental curves were normalized to the primary beam intensity, and the sample absorption coefficient; the holder scattering was subtracted. The calculation of the size distribution of scattering objects was performed with the computer code GNOM w31x. All of the distributions presented in this study are stable solutions against the variations of maximal size of the scattering centers. During the search for a solution, no limits on the relative abundance of defects with small sizes were imposed.
3. Results and discussion
The small-angle scattering in the defect-free IIa diamond was negligible, and almost coincided with the background. This fact indicated the insignificance of thermal contribution to SAXS at room temperature, which could be attributed to the high Debye temperature of diamond Ž1800 K.. Therefore, we assumed that scattering in the IIa diamond was caused by the diamond matrix itself, and subtracted it from curves for other crystals. Normalized SAXS curves from several IaB and IaA diamonds are presented in Fig. 1. It revealed that scattering in IaA and IaB diamonds is markedly higher than in the IIa sample. We assumed that the scattering centers could be represented by a polydisperse system, and fitted the observed curves by scattering on disk-like objects w8,9x and on hard spheres. The best agreement was achieved using a hard sphere approximation. The volume distribution of hard spheres vs. scattering cluster diameter is shown in Fig. 2a,b.
Fig. 1. Normalized small-angle X-ray scattering curves for investigated diamonds.
Fig. 2. Volume distribution of defects in IaB ŽFig. 2a. and in IaA ŽFig. 2b. diamonds. Hard spheres approximation.
3.1. IaB diamonds
As seen from Fig. 2a, the results from IaB diamonds can be best explained in terms of scattering on spheri˚ The cal defects with a diameter of approximately 90 A. deviation of the curve for diamond no. 5 from the others can probably be explained by internal zonation. The small scatter in cluster size is remarkable. Besides some physical reasons, such as different time orrand temperature of growth, this scatter could be partially ascribed to the contributions from different growth sectors. It is worth noting that the size of clusters obtained from the diffuse w12,25x and small-angle scattering is identical. A positive correlation between the size of the defects and nitrogen concentration in the B-form was observed for several samples Žnos. 2, 3, 5.. This correlation fits well to the model of formation of B-defects Žsee below., but the statistics are poor, and it is not clear yet if this trend is general. In this work we were unable to establish a reliable correlation between the intensity of the SAXS and optical data. The scattering contrast in SAXS is determined by the difference in the electronic density of the impurity cluster and that of the matrix. The electronic density of clusters in different diamonds can
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alter due to variations in the nitrogen content. As frequently observed in metallic and semiconducting alloys Že.g. w22,32x., the structure of the impurity clusters could be heterogeneous: a heavily impurity-doped core and a depleted outer part. From the X-ray diffuse scattering, Naletov w25x concluded that the same could be valid for diamond as well. Our preliminary comparative results on X-ray and neutron small-angle scattering show that these defect clusters could indeed have some internal structure. This heterogeneity, together with possible variations in the contrast of electron density, makes the existence of a direct correlation between X-ray and IR data difficult. Reliable confirmation of such a correlation will only be possible after absolute measurements of SAS, which will give information about the difference of electronic densities of cluster and matrix. This work is in progress. Since point defects do not produce small-angle scattering Že.g. w29x., the presence of scattering indicates the presence of extended defects. Dislocation loops and other planar formations should be ruled out due to the failure of approximation of SAXS data by scattering on disk-shape objects, and due to the small contrast in electron density with the perfect lattice, which makes their detection by SAXS possible only at very high concentrations Ž) 1011 rcm2 .. Voidites, in principle, could contribute to SAXS. Estimations of nitrogen amount in them Žtherefore, scattering contrast. gives figures, similar to proposed for sphere-like clusters Ž; 25 at.%. w33x. However, voidites demonstrate con˚ w33x. even inside siderable scatter in sizes Ž20᎐100 A one diamond, while observed defects Ž‘clusters’. have a well-defined diameter. Another reason to believe that voidites do not contribute to the presented results is that ‘clusters’ are observed in diamonds of different types, while voidites are limited to certain types of stones. At present we cannot make an unambiguous conclusion about the composition of the defects clusters. In Ramanan et al. w17x it was suggested that observed clusters are related to vacancies andror interstitials. This is a reasonable explanation, but to the best of our knowledge no clusters have yet been reported for IIa. As a working model, until more studies on nitrogenless diamonds are performed, we consider the clusters as being nitrogen-related Žfollowing w11,12x.. SAXS data for IaB diamonds, together with the results of X-ray diffuse scattering w12,26x, suggest a presence of sphere-like regions Ž‘clusters’. with a high concentration of impurity Žnitrogen?. and a diameter of ˚ in the diamond lattice. The slight scatter in 80᎐100 A the size of the ‘clusters’ from sample-to-sample could be explained by a different degree of aggregation andror different growth temperature. The structure of nitrogen inside these clusters is currently uncertain. It is possible that nitrogen inside the clusters is present in
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the B-form. A high concentration of nitrogen, and a relatively large diameter of the ‘clusters’ suggest that they could be formed as a result of decay of nitrogen solid solution in the diamond matrix. If the clusters are N-related, an important question arises: a high density of neighboring point defects should produce strain and a broadening of corresponding optical lines. A combination of optical, thermal conductivity and X-ray data gives a preliminary estimate of 25 at.% of nitrogen in these regions w14x. The above-mentioned broadening is indeed observed in electron-irradiated diamonds w34x. At present we do not have an unambiguous explanation as to why the majority of nitrogen-related optical lines in non-treated diamonds are so sharp. We could speculate that the estimation of 25 at.% of nitrogen is too high, and the actual amount of nitrogen inside clusters is much lower. Another explanation is that the driving force for the decay of the nitrogen solid solution has at least two components: the decrease of the free energy of impurity dissolution, and the lowering of strain. Some ordering of point defects inside clusters may also lead to these sharp optical lines. 3.2. IaA diamonds SAXS results from IaA samples are much less systematic, than from IaB crystals. From the six IaA diamonds studied here, only three Ž7, 8 and 10. show scattering different from the background. Even in these cases, the scattering is much weaker than in IaB diamonds. This can be seen in Fig. 2a, where the volume distribution for IaA diamond no. 8 is plotted together with the results for IaB samples. Note that the volume of scattering defects in IaA diamonds is two orders of magnitude smaller than in IaB crystals. The size distribution of defects in IaA diamonds is shown in Fig. 2b. A large scatter in cluster size is observed; only two ˚ and at samples have pronounced maxima Žat ; 120 A ˚ .. Similar results were reported by Ramanan 380᎐500 A et al. w17x. The larger maximum can not be explained by platelets since no platelets exist in synthetic diamonds Žcurve 7.. Moreover, in diamond 10, with the highest IR absorption from platelets, no such maximum is observed. Current studies suggest that while diamonds with B-defects possess a relatively well-defined structure ˚ ., the Žisometric clusters with a diameter of ; 80᎐100 A IaA crystals are very inhomogeneous from the X-ray scattering viewpoint. Based on the industrial mechanical testing of a large number of natural and synthetic diamonds, Klyuev et al. w15x suggested that though optical manifestations of the A-defect are identical, two groups of type IaA diamonds can be recognized. Present X-ray investigations support this division. In the group IaA1 , the nitrogen impurity of the stones was
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present as point defects Žpairs.. X-Ray scattering Žboth diffuse and small-angle., as well as hardening by dispersed impurity, was negligible. In the group IaA2 , the nitrogen in the diamonds formed clusters, which were responsible for small-angle and diffuse X-ray scattering, and for the hardening of diamonds. Inside these clusters, nitrogen atoms could be arranged in pairs. In the next section we discuss the possible origin of these groups. 3.3. Discussion of the nitrogen aggregation process in diamonds The existence of nitrogen clusters, and their possible relation to A- and B-defects, suggests that the process of nitrogen aggregation in diamonds is the decay of a supersaturated solid solution, with the formation of impurity clusters on a diffusion-limited stage. The process of aging of metallic and semiconducting solid solutions leads to the precipitation of impurity aggregates. Their shape, structure and size depend on the initial degree of supersaturation, temperature and the duration of annealing. The driving force for the clusterization of defects is a lowering of the free energy of impurity dissolution and decrease of strain. Currently it is not clear in which form nitrogen atoms incorporate into natural diamonds. In synthetic diamonds, grown with metallic catalysts, the predominant form of nitrogen is a single atom. This fact is easy to explain, since nitrogen is dissolved in metal under the P-T conditions of synthesis. However, nitrogen speciation in the growth medium of natural diamonds is not clear, and depends on the chemical composition of the medium and on redox conditions. Nitrogen can be present as chemical compounds Že.g. N2 , NH4 , nitrides. or as dissolved atoms. Inclusions of N2 were found in diamondiferous xenoliths and in natural diamonds w35,36x. However, gas-chromatographic studies of HPHT diamonds and of growth Fe᎐Ni alloys w37x show that N2 is present in very small amounts Žat degassing temperatures structural nitrogen was not released.. Thus, it is possible that in some natural diamonds, nitrogen could be incorporated as a pair. This could happen, for example, in fibrous diamonds, the majority of which belong to IaA type. Many researchers Že.g. w38x. suggest that their formation could be directly related to the kimberlite event; therefore, their mantle residence time could be very short Žseveral days.. This makes aggregation process of C ª A, with a high kinetic barrier Žespecially in cubic sectors., almost improbable at inferred temperatures. The proposed difference in nitrogen incorporation in synthetic and some natural diamonds agrees with the fact that the nitrogen content in natural diamonds is usually much higher than in HPHT diamonds. The method of nitrogen incorporation into the dia-
mond lattice should affect only the first aggregation stage, because if nitrogen was introduced in the lattice as a single atom, annealing would lead to the formation of nitrogen pairs. Annealing of synthetic and some natural diamonds usually stops at this stage Žgroup IaA1 diamonds.. Calculations w39x suggest that the kinetic barrier for vacancy-mediated aggregation is much lower than in case of a direct atom exchange. Indeed, experiments show that presence of even 5 ppm of vacancies markedly increases the aggregation rate w40x. The concentration of vacancies in diamonds is unknown. Positron annihilation studies Žw41x and references therein . indicate that the concentration of nitrogen-vacancy complexes in natural diamonds is in the 0.2᎐20 ppm range. Since the formation of vacancies and other lattice defects is energetically favored in stressed regions, e.g. strain fields around dislocations, the aggregation rate can be slightly higher there. These stressed regions could serve as a sink for migrating nitrogen atoms. Therefore, further annealing can lead ˚ in diameto the formation of large regions Ž400᎐500 A . ter , characterized by an increased nitrogen concentration Žgroup IaA2 diamonds, low-temperature stage, formation of Guinier᎐Preston zones.. In these zones, the concentration of lattice defects is high and that can explain the results of studies of vacancy formation and migration w34,42x. According to Ramanan et al. w17x, large impurity clusters observed in diamonds have a considerable number of interstitials and vacancies. With the progression of annealing, the nitrogen content in these regions increases and stops at some optimal concentration. Inside the formed clusters, nitrogen atoms can be arranged as point defects, e.g. 4Nq V complexes. Possible clusterization of point nitrogen defects can have a profound influence on nitrogen aggregation kinetics. It is possible that in the early aggregation stages Žcreation of the IaA1 groups. nitrogen aggregation is limited by interatomic interactions, thus yielding second order kinetics w1x, while in the later stages, aggregation is diffusion-limited and is better described by the Avraami equation: c 0rct s expŽyktn . w3,21x. 4. Conclusions The results of small-angle X-ray scattering ŽSAXS. in natural and synthetic diamonds with different types of nitrogen-related defects are presented. They reveal the presence of nitrogen-containing spherical clusters with ˚ in the IaB diamond. a diameter of approximately 90 A Scattering from IaA diamonds has much lower intensity and originates from clusters with a large variation in size. It is suggested that, although the optical manifestations of the A-defect are similar in different diamonds, IaA diamonds can be divided into two sub-
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groups. The group IaA1 includes annealed synthetic and some natural diamonds. They contain randomly distributed nitrogen pairs, which do not significantly affect mechanical properties and do not produce reasonable X-ray scattering. In the diamonds of the IaA2 group, nitrogen underwent a further aggregation stage and the formation of nitrogen-containing clusters began. It is possible that inside these clusters, nitrogen is arranged in pairs. Further annealing leads to the for˚ . nitrogen-rich mation of smaller Ždiameter of ; 90 A clusters. They are not precipitations of pure nitrogen, however, as they can contain nitrogen in the B-form. It is possible that in the early aggregation stages Žstage I. nitrogen aggregation is limited by interatomic interactions resulting in second order kinetics w1x; on the later stages aggregation is diffusion-limited and is better described by the Avraami equation c0rct s expŽyktn ..
Acknowledgements We acknowledge the comments made by K. Iakoubovskii and by three anonymous reviewers, whose remarks helped us to clarify some of our statements. References w1x R.M. Chrenko, R.E. Tuft, H.M. Strong, Nature 270 Ž1977. 141. w2x T. Evans, Z. Qi, Proc. R. Soc. Lond A381 Ž1982. 159. w3x Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha et al., Zhurnal Fizicheskoi Khimii wEnglish translation: Russ. J. Phys. Chem. 56 Ž1982. 323x 56 Ž1982. 524. w4x E.V. Sobolev, V.I. Lisoivan, S.V. Lenskaya, Sov. Phys. Dokl. 12 Ž1968. 665. w5x M. Ya Shcherbakova, E.V. Sobolev, V.A. Nadolinnyi, Doklady AN SSSR Žin Russian. 204 Ž1972. 851. w6x G. Davies, J. Phys. C9 Ž1976. L537. w7x J.A. van Wyk, G. Woods, J. Phys. Condens. Matter 7 Ž1995. 5901. w8x V.I. Lisoivan, Doklady AN SSSR Žin Russian. 230 Ž1976. 88. w9x V.I. Lisoivan, Fiz. Tverdogo. Tela. Žin Russian. 21 Ž1979. 240. w10x G.M. Rylov, E.V. Sobolev, Ext. abstracts 6th int. Kimberlite conf, in: N.V. Sobolev et al. ŽEd.., Novosibirsk, 1995, p. 479. w11x Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha et al., Fiz. Tverdogo Tela wEnglish translation: Sov. Phys. Solid State 19 Ž1977. 7x 19 Ž1977. 14. w12x A.M. Naletov, Y.A. Klyuev, V.I. Nepsha, Fiz. Tverdogo Tela Žin Russian. 19 Ž1977. 1529. w13x Yu. A. Klyuev, A.M. Naletov, V.I. Nepsha, Proceedings of the
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