Crystallographic point and space group symmetries in the one- and two-body density of crystals and generalized Patterson functions: Fourier path integral Monte Carlo case studies of novel high-temperature/high-pressure 4He quantum crystals

Zeitschrift fur Kristallographie

Volumn 218, Issue 10, 2003, Pages 651-674

  Gernoth, Klaus A ^a  

^a UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

HELIUM;

ARTICLE; CRYSTAL; CRYSTAL STRUCTURE; CRYSTALLIZATION; CRYSTALLOGRAPHY; DENSITY; FOURIER ANALYSIS; FOURIER TRANSFORMATION; HIGH TEMPERATURE; HYPERBARISM; MATHEMATICAL ANALYSIS; MONTE CARLO METHOD; QUANTUM MECHANICS;

EID: 0142058765     PISSN: 00442968     EISSN: None     Source Type: Journal    
DOI: 10.1524/zkri.218.10.651.20765     Document Type: Article

References (29)

1. Ashcroft, N. W.; Mermin, N. D.: Solid State Physics. Holt, Rinehart Winston, New York (1976).
2. Aziz, R. A.; Slaman, M. J.; Koide, A.; Allnat, A. R.; Meath, W. J.: Exchange-Coulomb Potential Energy Curves for He-He and Related Properties. Mol. Phys. 77 (1992) 321-337.
3. Balescu, R.: Equilibrium and Nonequilibrium Statistical Mechanics. Wiley, New York (1975).
4. Boninsegni, M.; Pierleoni, C.; Ceperley, D. M.: Isotopic Shift of Helium Melting Pressure: Path Integral Monte Carlo Study. Phys. Rev. Lett. 72 (1994) 1854-1857.
5. Burns, G.; Glazer, A. M.: Space Groups for Solid State Scientists. 2nd Ed., Academic Press, Boston (1990).
6. Ceperley, M.: Path Integrals in the Theory of Condensed Helium. Rev. Mod. Phys. 67 (1995) 279-355.
7. Cornwell, J. F.: Group Theory in Physics. Vol. I, 5th Ed., Academic Press, London (1994).
8. Doll, J. D.; Coalson, R. D.; Freeman, D. L.: Fourier Path-Integral Monte Carlo Methods: Partial Averaging. Phys. Rev. Lett. 55 (1985) 1-4.
9. Doll, J. D.; Freeman, D. L.; Beck, T. L.: Equilibrium and Dynamical Fourier Path Integral Methods. Adv. Chem. Phys. LXXVIII (1990) 61-127.
10. 4He. Phys. Rev. B61 (2000) 12094-12100.
11. Elliot, S.: The Physics and Chemistry of Solids. John Wiley & Sons, Chichester (1998).
12. Feynman, R. P.; Hibbs, A. R.: Quantum Mechanics and Path Integrals. McGraw-Hill, New York (1965).
13. Gernoth, K. A.: Crystallographic Point and Space Group Symmetries in Correlated Many-Body Wave Functions. In: Proceedings of the 165. WE-Heraeus-Seminar, Theory of Spin Lattices and Lattice Gauge Models, Lecture Notes in Physics, Vol. 494 (Eds.: Clark, J. W.; Ristig, M. L.), Springer-Verlag, Berlin (1997a), pp. 84-109.
14. Gernoth, K. A.: Crystalline Symmetries in Correlated Quantum Systems. In: Condensed Matter Theories, Vol. 12 (Eds.: Clark, J. W.; Panat, P. V.), Nova Science Publishers, Commack, NY (1997b), pp. 331-343.
15. Gernoth, K. A.: Explorations of the Microstructure of Crystalline Quantum Many-Body Systems. Ann. Phys. (N.Y.) 285 (2000) 61-137.
16. Gernoth, K. A.: Analytical and Numerical (Monte Carlo) Studies of Point and Space Group Symmetry-Breaking in the Liquid-Solid Phase Transition. Ann. Phys. (N.Y.) 291 (2001a) 202-266.
17. Gernoth, K. A.: Path Integral Monte Carlo Calculations of Symmetry-Breaking in Structural Phase Transitions. In: 150 Years of Quantum Many-Body Theory, Series on Advances in Quantum Many-Body Theory, Vol. 5 (Eds.: Bishop, R. F.; Gernoth, K. A.; Walet, N. R.), World Scientific, Singapore (2001b), pp. 249-256.
18. Gernoth, K. A.: Spatial Microstructure of Quantum Crystals. J. Low Temp. Phys. 126 (2002) 725-730.
19. Gradshteyn, I. S.; Ryzhik, I. M.: Table of Integrals, Series, and Products. Academic Press, New York (1980), pp. 951-952.
20. Hahn, T. (Ed.): International Tables for Crystallography. Vol. A, 4th Ed., Kluwer Academic Publishers, Dordrecht (1996).
21. Kalos, M. H.; Whitlock, P. A.: Monte Carlo Methods. Vol. 1, Wiley, New York (1986).
22. Kittel, C.: Introduction to Solid State Physics. 5th Ed., John Wiley Sons, New York (1976).
23. 4He from Single-Crystal X-Ray Diffraction over a Large P-T Domain. Phys. Rev. Lett. 71 (1993) 2272-2275.
24. Mao, H. K.; Hemley, R. J.; Wu, Y.; Jephcoat, A. P.; Finger, L. W.; Zha, C. S.; Basset, W. A.: High-Pressure Phase Diagram and Equation of State of Solid Helium from Single-Crystal X-Ray Diffraction to 23.3 GPa. Phys. Rev. Lett. 60 (1988) 2649-2652.
25. Patterson, A. L.: A Fourier Series Representation of the Average Distribution of Scattering Power in Crystals. Phys. Rev. 45 (1934a) 763.
26. Patterson, A. L.: A Fourier Series Method for the Determination of the Components of Interatomic Distances in Crystals. Phys. Rev. 46 (1934b) 372-376.
27. Patterson, A. L.: A Direct Method for the Determination of the Components of Interatomic Distances in Crystals. Z. Kristallogr. 90 (1935) 517-542.
28. Shmueli, U. (Ed.): International Tables for Crystallography. Vol. B, Kluwer Academic Publishers, Dordrecht (1996).
29. Wilson, A. J. C. (Ed.): International Tables for Crystallography. Vol. C, Kluwer Academic Publishers, Dordrecht (1995).