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Metastable Nanosized Diamond Formation from Fluid Systems S. K. Simakov^a, ^aGeological Department, St.Petersburg University, 7/9 Universitetskaya Nab., St.Petersburg, 199034, Russia

The model of nanosized diamond particles formation at metastable P-T parameters from fluid is presented. It explains the specific of CVD diamond synthesis gases mixtures and hydrothermal growth of diamond at low P-T parameters as well as it explains the geneses of metamorphic and magmatic nano- and microdiamond in the shallow depth Earth rocks and the genesis of interstellar nanodiamond formations in the space.

The optimal gases system compositions for metastable diamond formations have been long debated in many publications during the long period. Badziag et al.¹ came to the conclusion that nanometer-sized diamonds could be more stable than graphite when formed from hydrocarbons with a H/C ratio of more than 0.24. Simakov² has shown that the addition of oxygen to the hydrocarbon gases can stabilize the diamond nucleus formation in the P-T field of graphite stability. The question of whether diamond could be grown under hydrothermal conditions mimicking those under which it is formed in the Earth has been also long debated^3,4. Roy et al.⁵ have made the detailed study of the hydrothermal growth of diamond in the C-H-O and C-H-O-halogen systems. Shimansky et al.⁶ have claimed hydrothermal growth of diamond but no details were given on the composition of the liquid and the characterization of the phases. Zhao et al.⁷ provided the diamond hydrothermal synthesis from the mixture of the glassy carbon, powdered nickel, diamond seeds and water at 800^o C and 1.4 kbar. From another hand, Bachmann et al.⁸ have analysed gaseous compositions of the different 78 CVD diamond syntheses and shown that their compositions lie in the corridor extended range from H to CO compositions of the C-O-H system. The triangularly shaped “diamond domain” is adjusted along the CO line of the diagram and is limited by the lines X_CO2 ≈ 0.57 on its carbon-rich side and X_CO2 ≈ 0.45 on its oxygen-rich side (see Fig. 1 in ref. 8). The main part of the synthesis compositions lies in the middle part of the domain between methane and acetylene lines meanwhile only the lesser part corresponds to hydrogen.

For diamond, it has been argued, that crystallization under P-T conditions, where diamond is actually thermodynamically unstable with respect to graphite, is possible due to kinetic factors ^9,10. Nanosize diamond particles have energetic preference upon graphitic particles of the same size and could be more stable at low P-T parameters (ref.1)^11-13. Fedoseev et al.¹⁴ have shown that critical radii of graphite and diamond nuclei depends upon the surface energy (s), atomic volume of carbon (V) and chemical potential of the resaturation (Dm):

r_g/r_d = V_gs_g Dm_d / V_ds_d Dm_g (1)

s of nanosized diamond (d) and graphite (g) particles depends upon temperature and size of the particles¹⁵. From s_g/s_d relation given in¹⁶ and from (ref.12) it follows that for nanoparticles V_gs_g/V_ds_d ≈ 1. Than r_g/r_d ratio could be expressed as:

r_g/r_d = Dm_d / Dm_g (2)

On the other hand the chemical potentials of the resaturation for diamond and graphite could be expressed as follows:

Dm_g =RTln(Pi/Pi_g) (3)

Dm_d =RTln(Pi/Pi_d) (4)

where Pi and Pi_g,d are the real and equilibrium pressures of carbonaceous gases

As it follows from equations (2-4), (r_g/r_d) depends on the ratio between real and calculated equilibrium pressures of carbonaceous gases. Within the range of graphite stability Pi_g <>d, which corresponds to preferable graphite formation from fluid phase. The condition of preferable diamond formation corresponds to Pi_g > Pi_d. The difference between Dm_g and Dm_d depends upon the difference of Pi/Pi_g and Pi/Pi_d , and at lower Pi_car it tends to zero, which corresponds to optimal condition of diamond formation from gaseous mixture within the range of graphite stability.

In the hydrocarbon-hydrogen mixture the gas-solid reaction of hydrocarbon destruction could be proposed for carbon formation in a fluid:

CH₄ ® C + 2H₂ (I)

At high temperatures equilibrated pressure of hydrogen would be greater than equilibrated pressure of methane and in vacuum P_CH4(d) tends to P_CH4(g) (Fig.1,A). The predomination of hydrogen under hydrocarbon in the gaseous mixture has also suppressed the growth rate of graphite more than it suppressed the growth rate of diamond (ref.10). As a result, it could stabilize the diamond growth at these conditions. Based on this effect, Deryagin and Fedoseev (ref.9) have grown diamond on the diamond seeds at vacuum conditions.

Subsequent work has shown that the addition of oxygen to the hydrocarbon gases can stabilize the diamond nucleus formation in the P-T range of graphite stability (ref.2). This conclusion coincides with the established fact that diamond is more stable in the oxygen environment than graphite, because oxygen reduces graphite to a greater degree than diamond¹⁷. Calculations done for the C-O-H system show that P_CH4(car) is very low within the ranges of the system, close to the upper limit of carbon stability by oxygen (CCO buffer)¹⁸. Within the ranges at lower pressure and temperature, P_CH4(g) ≈ P_CH4(d), which corresponds to diamond nucleus stabilization.

The presented model explains the extended Bachmann’s “diamond domain” along the CO line from H to CO compositions in the C-O-H system (ref. 8). The fluid calculations performed at 1000^o C and 10^-3 bar within the wide range of oxygen fugacity show that the diamond stability range corresponds in more degree to CO composition and in less degree to H₂ composition of the gases mixture (Fig. 1,A).

From the calculations it follows that this model provides a common basis for low-pressure diamond CVD methods. It comprises and connects data for more than 30 years of diamond CVD. By means of this model, special relations between very different source gasses and gas mixtures become clear. On the other hand, the model explains the possibility of metastable hydrothermal growth of the diamond too (Fig. 1, C). Our experiments at 500°C and total pressure of nearly 1000 bar from water liquid of organic matter proved the possibility of nanodiamond formation from C-O-H fluids at low temperatures and pressures without seeds ¹⁹. The determined relations may help to develop new models of the surface processes and growth species needed for diamond deposition.

It is known that the bulk of Earth diamonds is formed due to the deep upper mantle rocks - kimberlites formed at P and T corresponding to diamond thermodynamic stability. Meanwhile for the last 40 years micro- and nanodiamonds have also been found in shallow metamorphic earth rocks formed at P-T parameters corresponding to graphite thermodynamic stability ^20-22 as well as in the basalts ^23,24. The highest grade is observed in hydrothermal metasomatic zones of Kokchetave metamorphic massive situated in Northern Kazakhstan ²⁵. The fluid calculations performed at P-T parameters corresponded to Hawaiian basalt formation show that the diamond stability range here corresponds to CO₂ and H₂O compositions of the fluid (Fig. 1,B). It explains the relationship of Hawaiian nanodiamonds with carbon dioxide fluids (ref.24). The calculations performed at lower P-T parameters corresponded to hydrothermal metasomatic zones of Kokchetave metamorphic massive formation show that the diamond stability range also corresponds to CO₂ and H₂O compositions of the fluid (Fig. 1,C). It explains the relationship of the Kokchetave diamonds with water and carbon dioxide²⁶.

The origin of diamonds in the interstellar space has been a topic of intense discussion since the discovery of presolar nanodiamonds in chondrites ²⁷. Meteoritic nanodiamonds provide information on the nucleosynthesis of evolved stars and the evolution of the astrophysical environment, which formed the solar system. Sellgren ²⁸ identified the relationship between the interstellar diamond and water ice. Nakano et al.²⁹ related interstellar diamond formation with organic matter. Based on these relationships Kouch et al.³⁰ identified new formation routes of diamond in the interstellar clouds and parent bodies of carbonaceous chondrites during laboratory experiments. It’s the ice mixture of H₂O, CO, NH₃ and CH ₄ (4 : 2 : 2 : 1). The questions of when and how does nanodiamonds originate in the Cosmos remain open, although comparative microstructural analysis of nanodiamonds extracted from meteorites, indicates that the majority of cosmic nanodiamonds are formed by low-pressure vapor condensation³¹. The fluid calculations performed at 250^o C and 10^-3 bar show that the diamond stability range here corresponds to CO₂ and H₂O compositions of the fluid (Fig. 1,D). It explains the relationship of interstellar diamonds with water (ref. 28).

The presented in the paper model explains the specificity of the CVD diamond synthesis gas compositions and the hydrothermal growth of diamond at low P-T parameters as well as the geneses of metamorphic and magmatic nano- and microdiamond in the shallow depth Earth rocks and of interstellar nanodiamonds in the space at P-T parameters corresponding to graphite stability. Nanosized diamond particles could be formed from carbon-bearing fluids at low temperatures and pressures without seeds in the range of the upper limit of carbon stability by oxygen.

References:

1. Badziag, P., Verwoerd, W.S., Ellis, W.P., Greimer N.R. Nanometer-sized diamonds are more stable than graphite. Nature. 343, 244-245. (1990)

2. Simakov, S.K. Thermodynamic estimation of oxygen-hydrogen conditions influence on diamond and graphite critical nucleus formation at processes of methane destruction at low pressures. Rus. J. Phys.-Chem. 69, 3460-347. (1995)

3. Shatsky, V. S., Sobolev, N. V. Origin of diamonds in metamorphic rocks. Dokl. Akad. Nauk. 331, 217-219. (1993)

4. DeVries, R. C., Roy, R., Somiya, S., Yamada, S. A review of liquid phase systems pertinent to diamond synthesis. Trans. Mat. Res. Soc. Jap. 14B, 1421-1445. (1994)

5. Roy, R., Ravichandran, D., Ravindranathan, P., Badzian, A. Evidence for hydrothermal growth of diamond in the C-H-O and C-H-O halogen system. J. Materi. Res., 11, 1164-1168. (1996)

6. Szymanski, A., Abgarowicz, E., Bakon, A., Niedbalska, A., Salacinski, R., Sentek, J. Diamond formed at low pressures and temperatures through liquid-phase hydrothermal synthesis. Diam. Relat. Mater., 4, 234-235. (1995)

7. Xing-Zhong Zhao, Rustum, R., Kuruvilla A. C., A. Badzian. Hydrothermal growth of diamond in metal–C–H₂O systems. Nature 385, 513 – 515. (1996)

8. Bachmann, P.K., Leers, D., Lydtin, H. Towards a general concept of diamond chemical vapour deposition. Diam. Relat. Mater., 1, 1-12. (1991)

9. Deryagin, B.V. & Fedoseev, D.V. Growth of diamond and graphite from the gas phase. Nauka, Moscow. 115 p. (1977)

10. Chauhan, S.P., Angus, J.C. & Gardner, N.C. Kinetics of carbon deposition on diamond powder. J.Appl. Phys. 47, 4746-4754 (1976)

11. Chaikovskii, E.F., Rosenberg, G.H. Phase diagram of carbon and possibility of diamond formation at low pressures. Dokl. Akad. Nauk SSSR 279, 1372-1375. (1984)

12. Gamarnik, M.Y. Energetical preference of diamond nanoparticles. Physical Rev. B. 54, 2150-2156. (1996)

13. Tawson, V.L., Abramovich, M.G. Polymorphism of crystals and phases size effect: transformation diamond to graphite. Dokl. Akad. Nauk SSSR 287, 291-295. (1986)

14. Fedoseev, D.V., Deryagin, B.V., Varshavskaya, I.G., Semenova-Tyan-Shanskaya, A.S. Diamond crystallization. Nauka, Moscow. 134 p. (1984)

15. Magomedov, M.N. About the relationship of surface energy with size and form of nanocrystals. Phys. Tverd. Tela. 46, 924-937. (2004)

16. Nuth, J. A. Small-particle physics and interstellar diamonds. Nature. 329, 589. (1987)

17. Rudenko, A.P., Kulakova, I.I., Skvortsova, V.I. Chemical diamond synthesis. Aspects of general theory. Usp. Him. (Rus. Chem. Rev.) 62, 99-117. (1993)

18. Simakov, S.K. Redox state of Earth's upper mantle peridotites under the ancient cratons and its connection with diamond genesis. Geoch. Cosm. Acta. 62, 1811-1820. (1998)

19. Simakov, S.K., Dubinchuk, V.T., Baidakova, M.V. Synthesis of nanosize diamond and diamondlike phases at lower temperatures and pressures. NDNC2007 Abstract Book. 279. (2007)

20. Rozen, O.M., Zorin, U.M. & Zayachkovsky, A.A. Diamond foundation in connection of precambrian eclogites of Kokchetave massive. Dokl. Akad. Nauk SSSR. 203, 674-676. (1972)

21. Dobrzhinetskaya, L.F., Eide, E.A., Larsen, R.B., Sturt, B.A., Tronnes, R.G., Smith, D.C., Taylor, W.R., Posukhova, T.V. Microdiamonds in high-grade metamorphic rocks of the Western Gneiss region, Norway. Geology. 23, 597-600. (1995)

22. Sobolev, N.V., Shatsky, V.S. Diamond inclusions in garnets from metamorphic rocks; a new environment for diamond formation. Nature. 343, 742-746. (1990)

23. Novgorodova, M.I., Rasskazov, A.V. High-pressure carbon mineral phase formation as a result of heat explosion at shift transformation of graphite. Dokl. Akad. Nauk SSSR. 322, 379-381. (1992)

24. Wirth, R., Rocholl, A. Nanocrystalline diamonds from the Earth’s mantle underneath Hawaii. Earth Plan. Scie. Lett. 211, 357-362. (2003)

25. Pechnikov, V.A., Kaminsky, F.V. Diamond potential of metamorphic rocks in the Kokchetav Massif, northern Kazakhstan. Eur. J. Mineral. 20, 395–413. (2008)

26. De Corte, K., Cartigny, P., Shatsky, V.S., De Paepe, P., Sobolev, M.V., Jovay, M. Characteristics of microdiamond from UHPM rocks of the Kokchetav massif (Kazakhstan). Proc. VII^th Int. Kimb. Conf. 2, 174-182. (1999)

27. Bernatowicz, T., Zinner, E.. Astrophysical Implications of the Laboratory Study of Presolar Materials, AIP Conference Proceedings 402, New York. (1997)

28. Sellgren, K. Aromatic hydrocarbons, diamonds, and fullerence in interstellar space: puzzles to be solved by laboratory and theoretical astrochemistry. Spectrochimica Acta P.A. 57, 627-642. (2001)

29. Nakano, H., Kouchi, A., Arakawa, M., Kimura, Y., Kaito, C., Ohno, H., Hondoh, T. Alteration of interstellar organic materials in meteorites’ parent bodies: a novel route in diamond formation. Proc. Japan Acad. Ser. B. 78, 277-281. (2002)

30. Kouchi, A., Nakano, H., Kimura1, Y., Kaito, C. Novel routes for diamond formation in interstellar ices and meteoritic parent bodies. The Astrophysical Journal. 626, L129–L132. (2005)

31.Daulton, T.L. Extraterrestrial nanodiamonds in the cosmos. In: Ultrananocrystalline diamond. William-Andrew. Norwich. UK., 23-79 (2006)

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A loan is a type of debt. Like all debt instruments, a loan entails the redistribution of financial assets over time, between the lender and the borrowerIn a loan, the borrower initially receives or borrows an amount of money, called the principal, from the lender, and is obligated to pay back or repay an equal amount of money to the lender at a later time. Typically, the money is paid back in regular installments, or partial repayments; in an annuity, each installment is the same amount. The loan is generally provided at a cost, referred to as interest on the debt, which provides an incentive for the lender to engage in the loan. In a legal loan, each of these obligations and restrictions is enforced by contract, which can also place the borrower under additional restrictions known as loan covenants. Although this article focuses on monetary loans, in practice any material object might be lent.Acting as a provider of loans is one of the principal tasks for financial institutions. 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However, it carries a credit-card brand (Visa, MasterCard, American Express or Discover) and can be used in similar ways just as though it were a regular credit card.[8][9]After purchasing the card, the cardholder loads the account with any amount of money, up to the predetermined card limit [10] and then uses the card to make purchases the same way as a typical credit card. Prepaid cards can be issued to minors (above 13) since there is no credit line involved. The main advantage over secured credit cards (see above section) is that you are not required to come up with $500 or more to open an account. [11] With prepaid credit cards you are not charged any interest but you are often charged a purchasing fee plus monthly fees after an arbitrary time period. Many other fees also usually apply to a prepaid card.[8]Prepaid credit cards are sometimes marketed to teenagers[8] for shopping online without having their parents complete thection.[12][13][14][15]Because of the many fees that apply to obtaining and using credit-card-branded prepaid cards, the Financial Consumer Agency of Canada describes them as "an expensive way to spend your own money".[16] The agency publishes a booklet, "Pre-paid cards",[17] which explains the advantages and disadvantages of this type of prepaid card.[edit] FeaturesAs well as convenient, accessible credit, credit cards offer consumers an easy way to track expenses, which is necessary for both monitoring personal expenditures and the tracking of work-related expenses for taxation and reimbursement purposes. Credit cards are accepted worldwide, and are available with a large variety of credit limits, repayment arrangement, and other perks (such as rewards schemes in which points earned by purchasing goods with the card can be redeemed for further goods and services or credit card cashback).Some countries, such as the United States, the United Kingdom, and France, limit the amount for which a consumer can be held liable due to fraudulent transactions as a result of a consumer's credit card being lost or stolen.[edit] Security problems and solutionsMain article: Credit card fraudCredit card security relies on the physical security of the plastic card as well as the privacy of the credit card number. Therefore, whenever a person other than the card owner has access to the card or its number, security is potentially compromised. Once, merchants would often accept credit card numbers without additional verification for mail order purchases. It's now common practice to only ship to confirmed addresses as a security measure to minimise fraudulent purchases. Some merchants will accept a credit card number for in-store purchases, whereupon access to the number allows easy fraud, but many require the card itself to be present, and require a signature. A lost or stolen card can be cancelled, and if this is done quickly, will greatly limit the fraud that can take place in this way. For internet purchases, there is sometimes the same level of security as for mail order (number only) hence requiring only that the fraudster take care about collecting the goods, but often there are additional measures. <--The main one is to require a security PIN with the card, which requires that the thief have access to the card, as well as the PIN. Commented out: Doesn't quite make sense in this section as PINs are not used for "card not present" transactions. Comment following is nonsense: PINs are for ATM and debit cards, not credit cards.-->The PCI DSS is the security standard issued by The PCI SSC (Payment Card Industry Security Standards Council). This data security standard is used by acquiring banks to impose cardholder data security measures upon their merchants.The low security of the credit card system presents countless opportunities for fraud. This opportunity has created a huge black market in stolen credit card numbers, which are generally used quickly before the cards are reported stolen.The goal of the credit card companies is not to eliminate fraud, but to "reduce it to manageable levels".[18] This implies that high-cost low-return fraud prevention measures will not be used if their cost exceeds the potential gains from fraud reduction - as would be expected from organisations whose goal is profit maximisation.Most internet fraud is done through the use of stolen credit card information which is obtained in many ways, the simplest being copying information from retailers, either online or offline. Despite efforts to improve security for remote purchases using credit cards, systems with security holes are usually the result of poor implementations of card acquisition by merchants. For example, a website that uses SSL to encrypt card numbers from a client may simply email the number from the webserver to someone who manually processes the card details at a card terminal. Naturally, anywhere card details become human-readable before being processed at the acquiring bank, a security risk is created. However, many banks offer systems where encrypted card details captured on a merchant's web server can be sent directly to the payment processor.Controlled Payment Numbers which are used by various banks such as Citibank (Virtual Account Numbers), Discover (Secure Online Account Numbers, Bank of America (Shop Safe), 5 banks using eCarte Bleue and CMB's Virtualis in France, and Swedbank of Sweden's eKort product are another option for protecting one's credit card number. These are generally one-time use numbers that front one's actual account (debit/credit) number, and are generated as one shops on-line. They can be valid for a relatively short time, for the actual amount of the purchase, or for a price limit set by the user.