**10. References**


46 Will-be-set-by-IN-TECH

• *ψ*ˆ*α*: field annihilation operator at the state *α*

*<sup>α</sup>*: field creation operator at the state *α*

• *ρ*ˆ: statistical distribution function operator of unperturbed system

: statistical distribution function operator by perturbation

• *χμν*: *μ*-direction magnetic susceptibility with respect to *ν*-direction external field

• *ζ*: index for microstates of the system; zeta function (depending on context)

Abrikosov, A. A. & Khalatnikov, I. M. (1959). The theory of a Fermi liquid (the properties of

Aharonov, Y. & Bohm, D. (1949). Significance of electromagnetic potentials in the quantum

Almbladh, C. O. & von Barth, U. (1985). Exact results for the charge and spin densities,

Alsayed, A. M., Islam, M. F., Zhang, J., Collins, P. J. & Yodh, A. G. (2005). Premelting at defects

Altmann, S. L. (1995). *Band Theory of Solids: An Introduction from the Point of View of Symmetry*,

Anderson, P. A. & Toulouse, G. (1977). Phase slippage without vortex cores: Vortex textures

Argaman, N. & Makov, G. (2000). Density functional theory: An introduction, *Am. J. Phys.*

Aschcroft, N. W. & Mermin, N. D. (1976). *Solid State Physics*, Thomson Learning, Singapore.

Anderson, P. W. (1963). Plasmons, gauge invariance, and mass, *Phys. Rev.* 130(1): 439–442. Anderson, P. W. (1997). *Basic Notions of Condensed Matter Physics*, Westview Press, Reading. Andreev, A. F. & Lifshitz, I. M. (1969). Quantum theory of defects in crystals, *Soviet Phys. JETP*

exchange-correlation potentials, and density-functional eigenvalues, *Phys. Rev. B*

liquid 3He at low temperatures), *Rep. Prog. Phys.* 22(1): 329–367.

within bulk colloidal crystals, *Science* 309(5738): 1207–1210.

in superfluid 3he, *Phys. Rev. Lett.* 38(9): 508–511.

• *χ<sup>T</sup>* (*H*): isothermal magnetic susceptibility as function of *H*

• *τ*: imaginary time; time difference (depending on context)

• *πn* (*R*, *x*): *n*th homotopy group of *R* at base point *x*

: Poisson bracket of operators *A*ˆ and *B*ˆ

theory, *Phys. Rev.* 115(3): 485–491.

Oxford University Press, Oxford.

*<sup>i</sup>* : *i*th Kohn-Sham orbital • *φn*: *n*th eigenfunction of *H*ˆ

• *ρ*: statistical distribution function

• *χ*∗: final state wavefunction • *σ*: Stefan-Boltzmann constant

• *ω*: frequency of a single-particle

• *ωn*: Matsubara frequency

• 4 − *�*: near four dimension

31(6): 3231–3244.

29: 1107–.

68(1): 69–79.

**10. References**

• *ξ*: correlation length

• *ψ*ˆ†

• *ψ*KS

• *ρ*ˆ�

• *A*ˆ, *B*ˆ 

• *θ*: step function


Galitskii, V. M. & Migdal, A. B. (1958). Application of quantum field theory methods to the

Towards the Authentic *Ab Intio* Thermodynamics 591

Gammaitoni, L., Häggi, P., Jung, P. & Marchesoni, F. (1998). Stochastic resonance, *Rev. Mod.*

Gaudin, M. (1960). Une Démonstration Simplifiée du Théoème de Wick en Mécanique

Ghosh, G. & Olson, G. B. (2002). Precipitation of paraequilibrium cementite: Experiments, and thermodynamic and kinetic modeling, *Acta Mater.* 50(8): 2099–2119. Giuliani, G. F. & Vignale, G. (2005). *Quantum Theory of the Electron Liquid*, Cambridge

Goldenfeld, N. (1992). *Lectures on Phase Transitions and the Renormalization Group*, Perseus,

Goldstone, J. (1957). Derivation of Brueckner many-body theory, *Proc. R. Soc. (London)*

Goldstone, J. (1961). Field theories with «superconductor» solutions., *Nuovo Cim.*

Goldstone, J., Salam, A. & Weinberg, S. (1962). Broken symmetries, *Phys. Rev.* 127(3): 965–970. Gordon, W. (1926). Der Comptoneffekt der Schrödingerschen Theorie, *Z. Physik*

Gross, F. (1999). *Relativistic Quantum Mechanics and Field Theory*, John Wiley & Sons, New York. Hartree, D. R. (1928). The wave mechanics of an atom with a non-Coulomb central field. Part II. Some results and discussion, *Proc. Cambridge Phil. Soc.* 24(1): 111–132. Heisenberg, W. & Pauli, W. (1929). Zur quantendynamik der Wellenfelder, *Z. Physik*

Hillert, M. & Jarl, M. (1978). A model for alloying effects in ferromagnetic metals, *CALPHAD*

Hohenberg, P. & Kohn, W. (1964). Inhomogeneous electron gas, *Phys. Rev.* 136(3B): B864–B871.

Jang, J. H., Kim, I. G. & Bhadeshia, H. K. D. H. (2009). Substitutional solution of silicon in cementite: A first-principles study, *Comp. Mater. Sci.* 44(4): 1319–1326. Jones, W. & March, N. H. (1973a). *Theoretical Solid State Physics Volume 1*, John Wiley & Sons,

Jones, W. & March, N. H. (1973b). *Theoretical Solid State Physics Volume 2*, John Wiley & Sons,

Kim, D. J. (1974). Free energy of the interacting electron gas including higher-order exchange

Kim, D. J. (1982). Electron-phonon interactions and itinerant-electron ferromagnetism, *Phys.*

Kim, D. J. (1988). The electron-phonon interaction and itinerant electron magnetism, *Phys.*

Kim, D. J. (1989). Electron-phonon interaction mechanism of magnetovolume and

Kim, D. J. (1999). *New Perspectives in Magnetism of Metals*, Kluwer Academic/Plenum, New

magnetoelaticity effects in itinerant electron ferromagnets, *Phys. Rev. B*

Jordan, P. & Pauli, W. (1928). Über Paulische Äquivalenzverbot, *Z. Physik* 47(3-4): 151–173. Kaufman, L. (2001). Computational thermodynamics and materials design, *CALPHAD*

Itzykson, C. & Zuber, J. B. (1980). *Quantum Field Theory*, McGraw-Hill, New York.

Goldstein, H. (1980). *Classical Mechanics (2nd Ed.)*, Addison-Wesley, Reading.

many body problem, *Soviet Phys. JETP* 7: 96–104.

*Phys.* 70(1): 223–287.

239(1217): 267–279.

19(1): 154–164.

40(1-2): 117–133.

56(1-2): 1–61.

2(3): 227–238.

London.

London.

25(2): 141–161.

effects, *Phys. Rev. B* 9(8): 3307–3312.

*Rev. B* 25(11): 6919–6938.

*Rep.* 171(4): 129–229.

39(10): 6844–6856.

York.

Reading.

Statistique, *Nucl. Phys.* 15(1): 89–91.

University Press, Cambridge.

Cotterill, R. M. J. (1980). The physics of melting, *J. Cryst. Growth* 48(4): 582–588.


48 Will-be-set-by-IN-TECH

de Oliveira, N. A. & von Ranke, P. J. (2010). Theoretical aspects of the magnetocaloric effect,

Dietel, J. & Kleinert, H. (2006). Triangular lattice model of two-dimensional defect melting,

Dirac, P. A. M. (1926). On the theory of quantum mechanics, *Proc. R. Soc. (London)*

Dirac, P. A. M. (1928a). The quantum theory of the electron, *Proc. R. Soc. (London)*

Dirac, P. A. M. (1928b). The quantum theory of the electron. Part II, *Proc. R. Soc. (London)*

Dirac, P. A. M. (1998). *The Principles of Quantum Mechanics (4th Ed.)*, Clarendon Press/Oxford,

Doniach, S. & Sondheimer, E. H. (1982). *Green's Functions for Solid State Physicists*,

Dyson, F. J. (1949a). The radiation theories of Tomonaga, Schwinger, and Feynman, *Phys. Rev.*

Dyson, F. J. (1949b). The *S* matrix in quantum electrodynamics, *Phys. Rev.* 75(11): 1736–1755. Einstein, A. (1905). Zur Elektrodynamik bewegter Körper, *Ann. Phys.* 322(10): 891–921. Einstein, A. (1907). Die Plancksche Theorie der Strahlung unde die Theorie der spezifischen

Einstein, A. (1911). Eine Beziehung Zwishcen dem elastischen Verhalten und der spezifischen Wärme bei festen Körpern mit einatomigen Molekül, *Ann. Phys.* 34: 170–174. Einstein, A. (1924). Quantentheorie des einatomigen idealen Gases, *Sitzungsber. K. Preuss.*

Einstein, A. (1925). Quantentheorie des einatomigen idealen Gases. 2. Abhandlung,

Fermi, E. (1926). Zur quantelung des idealen einatomigen Gases, *Z. Physik* 36(11-12): 902–912. Fermi, E. (1927). Eine statistische Methode zur Bestimmung einiger Eigenschaften des Atoms

Fetter, A. L. & Walecka, J. D. (2003). *Quantum Theory of Many-Particle Systems*, Dover, Mineola. Feynman, R. P. (1949a). Space-time approach to quantum electrodynamics, *Phys. Rev.*

Fock, V. (1930). Näherungsmethode zur Lösung des quamtenmechanischen

Fowler, R. H. & Jones, H. (1938). The properties of a perfect Einstein-Bose gas at low

Fradkin, E. (1991). *Field Theories of Condensed Matter Systems*, Addison-Wesley, Redwood City. Gabrielse, G., Hanneke, D., Kinoshita, T., Nio, M. & Odom, B. (2006). New determination

Gabrielse, G., Hanneke, D., Kinoshita, T., Nio, M. & Odom, B. (2007). Erratum: New

of the fine structure constant from the electron *g* value and QED, *Phys. Rev. Lett.*

determination of the fine structure constant from the electron *g* value and QED, *Phys.*

und ihre Anwendung auf die Theorie des periodischen Systems der Elemente., *Z.*

Drude, P. (1900). Zur electronentheorie der Metalle, *Ann. Phys.* 306(3): 566–613.

*Sitzungsber. K. Preuss. Akad. Wiss., Phys. Math. Kl.* pp. 3–14.

Feynman, R. P. (1949b). The theory of positrons, *Phys. Rev.* 76(6): 749–759.

temperatures, *Proc. Cambridge Phil. Soc.* 34(4): 573–576.

Mehrkörperproblems, *Z. Physik* 61(1-2): 126–148.

Cotterill, R. M. J. (1980). The physics of melting, *J. Cryst. Growth* 48(4): 582–588.

Debye, P. (1912). Zur Théorie der spezifischen Wärmen, *Ann. Phys.* 344(14): 789–839. DeHoff, R. T. (1993). *Thermodynamics in Materials Science*, McGraw-Hill, New York.

*Phys. Rep.* 489(4-5): 89–159.

*Phys. Rev. B* 73(2): 024113.

A112(112): 281–305.

A117(778): 610–624.

A118(779): 351–361.

Addison-Wesley, Redwood City.

Wärme, *Ann. Phys.* 327(1): 180–190.

*Akad. Wiss., Phys. Math. Kl.* pp. 261–267.

Oxford.

75(3): 486–502.

*Physik* 48(1-2): 73–79.

76(6): 769–789.

97(3): 030802.

*Rev. Lett.* 99(3): 039902.


Matsubara, T. (1955). A new approach to quantum-statistical mechanics, *Prog. Theor. Phys.*

Towards the Authentic *Ab Intio* Thermodynamics 593

Melrose, D. B. (2008). *Quantum Plasmadynamics: Unmagnetized Plasmas*, Springer, New York. Mermin, N. D. (1965). Thermal properties of the inhomogeneous electron gas, *Phys. Rev.*

Mermin, N. D. (1979). The topological theory of defects in ordered media, *Rev. Mod. Phys.*

Midownik, A. P. (1977). The calculation of magnetic contributions to phase stability,

Negele, J. W. & Orland, H. (1988). *Quantum Many-Particle Systems*, Addison-Wesley, Redwood

Nozières, P. & Luttinger, J. M. (1962). Derivation of the Landau theory of Fermi liquids. I.

Nyquist, H. (1928). Thermal agitation of electric charge in conductors, *Phys. Rev.*

Odom, B., Hanneke, D., D'Urso, B. & Gabrielse, G. (2006). New measurement of the

Onsager, L. (1931a). Reciprocal relations in irreversible processes. I., *Phys. Rev.* 37(4): 405–426. Onsager, L. (1931b). Reciprocal relations in irreversible processes. II., *Phys. Rev.*

Peskin, M. E. & Schroeder, D. V. (1995). *An Introduction to Quantum Field Theory*,

Planck, M. (1901). Ueber das Gesetz der Energieverteilung im Normalspectrum, *Ann. Phys.*

Poénaru, V. & Toulouse, G. (1977). The crossing of defects in ordered media and the topology

Ruban, A. V. & Abrikosov, I. A. (2008). Configurational thermodynamics of alloys from first principles: effective cluster interactions, *Rep. Prog. Phys.* 71(4): 046501. Sakurai, J. J. (1994). *Modern Quantum Mechanics (Revised Ed.)*, Addison-Wesley, Reading. Sawada, K. (1957). Correlation energy of an electron gas at high density, *Phys. Rev.*

Sawada, K., Brueckner, K. A., Fukada, N. & Brout, R. (1957). Correlation energy of an electron

Schneider, T. (1971). Theory of the liquid-solid phase transition, *Phys. Rev. A* 3(6): 2145–2148.

Schwinger, J. (1949a). Quantum electrodynamics. II. Vacuum polarization and self-energy,

Schrödinger, E. (1926a). Quantisierung als Eigenwertproblem, *Ann. Phys.* 384(4): 361–376. Schrödinger, E. (1926b). Quantisierung als Eigenwertproblem, *Ann. Phys.* 384(6): 489–527. Schrödinger, E. (1926c). Quantisierung als Eigenwertproblem, *Ann. Phys.* 385(13): 437–490. Schrödinger, E. (1926d). Quantisierung als Eigenwertproblem, *Ann. Phys.* 386(18): 109–139. Schwinger, J. (1948). Quantum electrodynamics. I. A covariant formulation, *Phys. Rev.*

gas at high density: Plasma oscillations, *Phys. Rev.* 108(3): 507–514.

Schrieffer, J. R. (1988). *Theory of Superconductivity*, Addison-Wesley, Reading.

Olson, G. B. (2000). Designing a new material world, *Science* 288(5468): 993–998.

Parisi, G. (1988). *Statistical Field Theory*, Addison-Wesley, Redwood City.

Pines, D. (1962). *The Many-Body Problem*, Benjamin/Cummings, Reading. Pines, D. (1999). *Elementary excitations in Solids*, Perseus Books, Reading.

of 3-manifolds, *J. Phys. France* 8(8): 887–895.

electron magnetic moment using a one-electron quantum cyclotron, *Phys. Rev. Lett.*

Formal preliminaries, *Phys. Rev.* 127(5): 1423–1431.

14(4): 351–378.

51(3): 591–648.

32(1): 110–113.

97(3): 030801.

38(12): 2265–2279.

309(3): 553–563.

106(2): 372–383.

74(10): 1439–1461.

*Phys. Rev.* 75(4): 651–679.

Addison-Wesley, Reading.

City.

137(5A): A1441–A1443.

*CALPHAD* 1(2): 133–158.


Mahan, G. (2000). *Many-Particle Physics (3rd Ed.)*, Kluwer Academic/Plenum, New York.

50 Will-be-set-by-IN-TECH

Kim, D. J., Schwartz, B. B. & Praddaude, H. C. (1973). Spin and charge susceptibility of a

Klein, O. (1927). Elektrodynamik und Wellenmechanik von Standpunkt des

Kleinert, H. & Jiang, Y. (2003). Defect melting models for cubic lattices and universal laws for

Kleman, M. & Friedel, J. (2008). Disclinations, dislocations, and continuous defects: A

Kohn, W. & Sham, L. J. (1965). Self-consistent equations including exchange and correlation

Koopmans, T. (1934). Über die Zuordnung von Wellenfunktionen und Wigenwerten zu den

Kosterlitz, J. M. & Thouless, D. J. (1973). Ordering, metastability and phase transitions in

Kozeschnik, E. & Bhadeshia, H. K. D. H. (2008). Influence of silicon on cementite precipitation

Kubo, R. (1957). Statistical-mechanical theory of irreversible process. I. General theory

Kubo, R., Yokota, M. & Nakajima, S. (1957). Statistical-mechanical theory of irreversible process. I. Response to thermal disturbance, *J. Phys. Soc. Japan* 12(11): 1203–1211. Kümmel, S. & Kronik, L. (2008). Orbital dependent density functionals: Theory and

Landau, L. D. (1958). The properties of the Green function for particles in statistics, *Soviet*

Larzar, M. (2010). The gauge theory of dislocations: A nonuniformly moving screw

Lee, J. H., Hsue, Y. C. & Freeman, A. J. (2006). Free energy of the interacting electron gas

Lee, J. I., Zhang, H. I. & Choe, A. S. (1989). Self-consistent derivation of electric and

Lehmann, H. (1954). Über Eigenschaften von Ausbreitungsfunktïonen und Renormierungskonstanten quantisierter Felder, *Nuovo Cim.* 11(11): 342–357. Levy, M., Perdew, J. P. & Sahni, V. (1984). Exact differential equation for the density and ionization energy of a many-particle system, *Phys. Rev. A* 30(5): 2745–2748. Lines, M. E. (1979). Elastic properties of magnetic materials, *Phys. Rep.* 55(2): 133–181.

Luttinger, J. M. & Nozières, P. (1962). Derivation of the Landau theory of Fermi liquids. I. Equilibrium properties and transport equation, *Phys. Rev.* 127(5): 1431–1440.

Mahan, G. (2000). *Many-Particle Physics (3rd Ed.)*, Kluwer Academic/Plenum, New York.

magnetic susceptibilities of spin-polarized metallic electron system, *J. Korean Phys.*

including higher-order exchange effects, *Phys. Rev. B* 73(17): 172405.

Leggett, A. J. (1970). Broken symmetries, *Phys. Rev. Lett.* 25(22): 1543–1546.

Madelung, O. (1978). *Introduction to Statistical Physics*, Springer, Berlin.

and simple application to magnetic and conduction problems, *J. Phys. Soc. Japan*

ferromagnetic electrons gas, *Phys. Rev. B* 7(1): 205–214. Kittel, C. (2005). *Introduction to Solid State Physics*, John Wiley & Sons, Danvers.

Korrespondenzprinzips, *Z. Physik* 41(10): 407–442.

reappraisal, *Rev. Mod. Phys.* 80(1): 61–115.

effects, *Phys. Rev.* 140(4A): A1133–A1138.

in steels, *Mater. Sci. Technol.* 24(3): 343–347.

applications, *Rev. Mod. Phys.* 80(1): 3–60.

dislocations, *Phys. Lett. A* 374: 3092–3098.

12(6): 570–586.

*Phys. JETP* 7: 182–.

*Soc* 22(1): 38–42.

melting temperatures, *Phys. Lett. A* 313(1-2): 152–157.

Einzelnen Elektronen Eines Atoms, *Physica* 1(1-6): 104–113.

two-dimensional systems, *J. Phys. C: Solid State Phys.* 6: 1181–1203.

Kubo, R. (1966). The fluctuation-dissipation theorem, *Rep. Prog. Phys.* 29(1): 255–284.

Landau, L. D. (1957a). Oscillations in a Fermi liquid, *Soviet Phys. JETP* 7: 101–108. Landau, L. D. (1957b). The theory of a Fermi liquid, *Soviet Phys. JETP* 3: 920–925.

Landau, L. D. (1959). On the theory of the Fermi liquid, *Soviet Phys. JETP* 8: 70–74. Landau, L. D. & Lifshitz, E. M. (1978). *Mechanics*, Pergamon Press, Oxford. Landau, L. D. & Lifshitz, E. M. (1980). *Statistical Physics*, Elsevier, Amsterdam.


**22** 

*Russia* 

**Thermodynamics of the Phase Equilibriums of** 

A comprehensive investigation of the phase equilibriums and determination of thermodynamic properties of pure substances is a significant object of the chemical thermodynamics. Data on the phase transitions, heat capacities, and saturation vapor pressure over the solid and liquid phases are used in many fields of science and technology, including calculations on the basis of the third law of thermodynamics. Theoretical and practical applications of thermodynamic data require verification of their reliability. The Clapeyron equation combines different properties of coexisting phases: temperature, vapor pressure, volume, enthalpy of the phase transitions, and caloric values*Cp* and*Cv* . Using this equation allows one to verify numerical data for thermodynamic concordance, to reveal unreliable quantities, and to predict failing thermodynamic properties. Mutual concordance and reliability of the calorimetric data on the heat capacity, the saturated vapor pressures, and the properties of phase transition can be verified by comparison of the absolute entropies determined from the experimental data by the third thermodynamic law,

with those ones calculated by statistical thermodynamics, ( ) *<sup>o</sup> S stat <sup>m</sup>* . A

congruence of these values within errors limits justifies their reliability. Critical analyses of the recent data on thermodynamic properties of some organic compounds are published by the National Institute of the Standards and Technology [NIST], USA. Literature data on the vapor pressures and the enthalpies of vaporization for *n*-alkanes C5 – C20 were reviewed and critically analyzed in the reference (Ruzicka & Majer, 1994). Thermodynamic properties of many classes of organic compounds were considered in monograph (Domalski & Hearing, 1993; Poling et al., 2001) that favoured the development of the Benson's calculation method. This chapter deals with reviewing and summarizing the data on the phase equilibriums carried out for some functional organic compounds by the low temperature adiabatic calorimetry, comparative ebulliometry, and vaporization calorimetry in the Luginin's Laboratory of Thermochemistry [LLT] of the Moscow State University [MSU] and other research centres. The numerous data on the heat capacity, the vapor pressure, enthalpies of the phase transitions, and derived thermodynamic functions were obtained for series of freons, cyclic hydrocarbons and fluorocarbons, and derivatives of ferrocene. A sufficient attention was given to the critical analyses of the thermodynamic data, their reliability, and to interconnections between the properties and some structural parameters of the

**1. Introduction** 

( )( ) *<sup>o</sup> S g <sup>m</sup>* e x p t

**Some Organic Compounds** 

Raisa Varushchenko and Anna Druzhinina

*Lomonosov Moscow State University* 

