Order vs. Disorder in the Solid State



According to the definition given by the International Union of Crystallographers, “by “crystal” is meant any solid having an essentially discrete diffraction diagram” [1]. A typical diffraction pattern corresponding to a “classical” periodic, perfect crystal looks like the one shown in Fig. 2.1 [2]. This pattern corresponds to the inner structure of the material, which can be represented as an array of periodically repeating fragments. The whole structure can be described by defining the repeating fragment (basis) and a set of three non-coplanar unit vectors. The three unit vectors can be used to build a parallelepiped: a unit cell. Translations are not the only symmetry elements that can be used to describe a periodic structure. Combinations of mirror reflections, rotations, inversions, glides and screw rotations form groups, that are termed space symmetry groups. [3] A periodic structure can then be described only by defining the crystallographic coordinates of an asymmetric unit and the symmetry operations of the space symmetry group.


First Sharp Diffraction Peak (SFDP) Liquid crystalsLiquid Crystals Random Close Packing (RCP) Glass transitionGlass Transition Polyamorphism 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Janssen T, Janner A, Looijenga-Vos A, de Wolff PM (2006) Incommensurate and commensurate modulated structures. Int Tables Crystallogr C:907–955. CrossRefGoogle Scholar
  2. 2.
    Wagner T, Schoenleber A (2009) A non-mathematical introduction to the superspace description of modulated structures. Acta Crystallogr B 65(3):249–268. CrossRefGoogle Scholar
  3. 3.
    Souvignier B, Wondratschek H, Aroyo MI, Chapuis G, Glazer AM (2016) Space groups and their descriptions. Int Tables Crystallogr A:42–74. Google Scholar
  4. 4.
    Smaalen SV (2007) Incommensurate crystallography. Oxford University Press, New YorkCrossRefGoogle Scholar
  5. 5.
    Arakcheeva A, Bykov M, Bykova E, Dubrovinsky L, Pattison P, Dmitriev V, Chapuis G (2017) Incommensurate atomic density waves in the high-pressure IVb phase of barium. IUCrJ 4(2):152–157. CrossRefGoogle Scholar
  6. 6.
    Shechtman D, Blech I, Gratias D, Cahn JW (1984) Metallic phase with long-range orientational order and no translational symmetry. Phys Rev Lett 53(20):1951–1953. CrossRefGoogle Scholar
  7. 7.
    Levine D, Steinhardt PJ (1984) Quasicrystals: a new class of ordered structures. Phys Rev Lett 53(26):2477–2480. CrossRefGoogle Scholar
  8. 8.
    Zong X, Ungar G, Liu Y, Percec V, Dulcey E, Hobbs JK (2004) Supramolecular dendritic liquid quasicrystals. Nature 428(11):157–160. CrossRefGoogle Scholar
  9. 9.
    Hayashida K, Dotera T, Takano A, Matsushita Y (2007) Polymeric quasicrystal: mesoscopic quasicrystalline tilling in ABC star polymers. PRL 98:195502-1–195502-4. CrossRefGoogle Scholar
  10. 10.
    Ivanov EY, Konstanchuk IG, Bokhonov BD, Boldyrev VV (1989) Mechanochemical synthesis of icosahedral phases in Mg-Zn-Al and Mg-Cu-Al alloys. React Solids 7(2):167–172. CrossRefGoogle Scholar
  11. 11.
    Bokhonov B, Konstanchuk I, Ivanov E, Boldyrev V (1992) Stage formation of quasi-crystals during mechanical treatment of the cubic Frank-Kasper phase Mg32(Zn, Al)49. J Alloys Compd 187(1):207–214. CrossRefGoogle Scholar
  12. 12.
    Janot C (1992) Quasicrystals A. Primer. Monographs on the physics and chemistry of materials. Oxford University Press, OxfordGoogle Scholar
  13. 13.
    Bokhonov B, Konstanchuk I, Boldyrev V, Ivanov E (1993) HRTEM study of milling induced phase transition and quasicrystalline formation in Mg32(Al, Zn)49 cubic Frank-Kasper phase. J Non Cryst Solids 153:606–610. CrossRefGoogle Scholar
  14. 14.
    Twarock R (2004) A tiling approach to virus capsid assembly explaining a structural puzzle in virology. J Theor Biol 226(4):477–482. CrossRefGoogle Scholar
  15. 15.
    Bokhonov BB (2008) Mechanical alloying and self-propagating high-temperature synthesis of stable icosahedral quasicrystals. J Alloys Compd 461(1):150–153. CrossRefGoogle Scholar
  16. 16.
    Steurer W, Deloudi S (2008) Fascinating quasicrystals. Acta Cryst A 64(1):1–11. CrossRefGoogle Scholar
  17. 17.
    Jaric M (2012) Introduction to quasicrystals. Elsevier, BurlingtonGoogle Scholar
  18. 18.
    Kobeko PP (1952) Amorphous compounds. USSR Academy of Sciences Publishing House, MoscowGoogle Scholar
  19. 19.
    Porai-Koshits EA (1958) The possibilities and results of x-ray methods for investigation of glassy substances. In: Lebedev AA (ed) The structure of glass. Consultants Bureau, New York, pp 25–35Google Scholar
  20. 20.
    Greaves GN, Sen S (2007) Inorganic glasses, glass-forming liquids and amorphising solids. Adv Phys 56(1):1–166. CrossRefGoogle Scholar
  21. 21.
    Henderson GS (2005) The structure of silicate melts: a glass perspective. Can Miner 43(6):1921–1958. CrossRefGoogle Scholar
  22. 22.
    Descamps M (ed) (2016) Disordered pharmaceutical materials. Wiley, WeinheimGoogle Scholar
  23. 23.
    Hancock BC, Shalaev EY, Shamblin SL (2002) Polyamorphism: a pharmaceutical science perspective. J Pharm Pharmacol 54(8):1151–1152. CrossRefGoogle Scholar
  24. 24.
    Shalaev E, Wu K, Shamblin S, Krzyzaniak JF, Descamps M (2016) Crystalline mesophases: structure, mobility, and pharmaceutical properties. Adv Drug Deliv Rev 100:194–211. CrossRefGoogle Scholar
  25. 25.
    Bates S, Zografi G, Engers D, Morris K, Crowley K, Newman A (2006) Analysis of amorphous and nanocrystalline solids from their x-ray diffraction patterns. Pharm Res 23(10):2333–2349. CrossRefGoogle Scholar
  26. 26.
    Doi K (1976) Profile analysis of amorphous haloes by means of a Fourier transformation, with special reference to the structures of amorphous Pt-C and Ni-P. J Appl Cryst 9:382–390. CrossRefGoogle Scholar
  27. 27.
    Stetsko YP, Shanahan N, Deford H, Zayed A (2017) Quantification of supplementary cementitious content in blended Portland cement using an iterative Rietveld–PONKCS technique. J Appl Cryst 50:498–507. CrossRefGoogle Scholar
  28. 28.
    Bergese P, Colombo I, Gervasoni D, Depero LE (2003) Assessment of the x-ray diffraction-absorption method for quantitative analysis of largely amorphous pharmaceutical composites. J Appl Cryst 36:74–79. CrossRefGoogle Scholar
  29. 29.
    Proffen T, Neder RB (2012) Analysis of complex materials through the application and analysis of the pair distribution function (PDF). Z Kristallogr Cryst Mater 227(5).
  30. 30.
    Wright AC, Hulme RA, Grimley D, Sinclair RN, Martin SW, Price DL, Galeener FL (1991) The structure of some simple amorphous network solids revisited. J Non Cryst Solids 129:213–232. CrossRefGoogle Scholar
  31. 31.
    Yarnell J, Katz M, Wenzel R, Koenig S (1973) Structure factor and radial distribution function for liquid argon at 85°K. Phys Rev A 7(6):2130–2144. CrossRefGoogle Scholar
  32. 32.
    Gingrich NS, Heaton L (1961) Structure of alkali metals in the liquid state. J Chem Phys 34(3):873–878. CrossRefGoogle Scholar
  33. 33.
    Sirota E, Ou-Yang H, Sinha S, Chaikin P, Axe J, Fujii Y (1989) Complete phase diagram of a charged colloidal system: a synchrotron X-ray scattering study. Phys Rev Lett 62(13):1524–1527. CrossRefGoogle Scholar
  34. 34.
    Pedersen JS (1997) Analysis of small-angle scattering data from colloids and polymer solutions: modeling and least-squares fitting. Adv Colloid Interface Sci 70:171–210. CrossRefGoogle Scholar
  35. 35.
    Toby BH, Egami T (1992) Accuracy of pair distribution function analysis applied to crystalline and non-crystalline materials. Acta Cryst A 48:336–346. CrossRefGoogle Scholar
  36. 36.
    Prill D, Juhás P, Billinge SJL, Schmidt MU (2016) Towards solution and refinement of organic crystal structures by fitting to the atomic pair distribution function. Acta Cryst A 72:62–72. CrossRefGoogle Scholar
  37. 37.
    Granlund L, Billinge SJL, Duxbury PM (2015) Algorithm for systematic peak extraction from atomic pair distribution functions. Acta Cryst A 71:392–409. CrossRefGoogle Scholar
  38. 38.
    Chapman KW, Lapidus SH, Chupas PJ (2015) Applications of principal component analysis to pair distribution function data. J Appl Cryst 48:1619–1626. CrossRefGoogle Scholar
  39. 39.
    Prill D, Juhás P, Schmidt MU, Billinge SJL (2015) Modelling pair distribution functions (PDFs) of organic compounds: describing both intra- and intermolecular correlation functions in calculated PDFs. J Appl Cryst 48:171–178. CrossRefGoogle Scholar
  40. 40.
    Peterson PF, Bozin ES, Proffen T, Billinge SJL (2003) Improved measures of quality for the atomic pair distribution function. J Appl Cryst 36:53–64. CrossRefGoogle Scholar
  41. 41.
    Mu X, Neelamraju S, Sigle W, Koch CT, Totò N, Schön JC, Bach A, Fischer D, Jansen M, van Aken PA (2013) Evolution of order in amorphous-to-crystalline phase transformation of MgF2. J Appl Cryst 46:1105–1116. CrossRefGoogle Scholar
  42. 42.
    Tran DT, Svensson G, Tai CW (2017) SUePDF: a program to obtain quantitative pair distribution functions from electron diffraction data. J Appl Cryst 50:304–312. CrossRefGoogle Scholar
  43. 43.
    Masson O, Thomas P (2013) Exact and explicit expression of the atomic pair distribution function as obtained from x-ray total scattering experiments. J Appl Cryst 46:461–465. CrossRefGoogle Scholar
  44. 44.
    Crocker JC, Grier DG (1996) Methods of digital video microscopy for colloidal studies. J Colloid Interface Sci 179:298–310. CrossRefGoogle Scholar
  45. 45.
    Nakroshis P, Amoroso M, Legere J, Smith C (2003) Measuring Boltzmann’s constant using video microscopy of Brownian motion. Am J Phys 71(6):568–573. CrossRefGoogle Scholar
  46. 46.
    Gasser U, Weeks ER, Schofield A, Pusey PN, Weitz DA (2001) Real-space imaging of nucleation and growth in colloidal crystallization. Science 292(5515):258–262. CrossRefGoogle Scholar
  47. 47.
    Weeks ER, Crocker JC, Levitt AC, Schofield A, Weitz DA (2000) Three-dimensional direct imaging of structural relaxation near the colloidal glass transition. Science 287(5453):627–631. CrossRefGoogle Scholar
  48. 48.
    Cipelletti L, Manley S, Ball RC, Weitz DA (2000) Universal aging features in the restructuring of fractal colloidal gels. Phys Rev Lett 84(10):2275–2278. CrossRefGoogle Scholar
  49. 49.
    Varadan P, Solomon MJ (2003) Direct visualization of long-range heterogeneous structure in dense colloidal gels. Langmuir 19(3):509–512. CrossRefGoogle Scholar
  50. 50.
    Peterson J, TenCate J, Proffen T, Darling T, Nakotte H, Page K (2013) Quantifying amorphous and crystalline phase content with the atomic pair distribution function. J Appl Cryst 46:332–336. CrossRefGoogle Scholar
  51. 51.
    Martin AV (2017) Orientational order of liquids and glasses via fluctuation diffraction. IUCrJ 4(1):24–36. CrossRefGoogle Scholar
  52. 52.
    Zobel M (2016) Observing structural reorientations at solvent-nanoparticle interfaces by x-ray diffraction – putting water in the spotlight. Acta Cryst A72:621–631. Google Scholar
  53. 53.
    Salmon PS (1994) Real space manifestation of the first sharp diffraction peak in the structure factor of liquid and glassy materials. Proc R Soc Lond A 445(1924):351–365. CrossRefGoogle Scholar
  54. 54.
    Elliott SR (1991) Origin of the first sharp diffraction peak in the structure factor of covalent glasses. Phys Rev Lett 67:711. CrossRefGoogle Scholar
  55. 55.
    Elliott SR (1995) Extended-range order, interstitial voids and the first sharp diffraction peak of network glasses. J Non Cryst Solids 182(1–2):40–48. CrossRefGoogle Scholar
  56. 56.
    Inamura Y, Arai M, Nakamura M, Otomo T, Kitamura N, Bennington SM, Hannon AC, Buchenau U (2001) Intermediate range structure and low-energy dynamics of densified vitreous silica. J Non Cryst Solids 283–295:389–393. CrossRefGoogle Scholar
  57. 57.
    Voronoi G (1908) Nouvelles applications des paramètres continus à la théorie des formes quadratiques. J die Reine und Angew Mathematik 133(133):97–178. Google Scholar
  58. 58.
    Brumberger H, Goodisman J (1983) Voronoi cells: an interesting and potentially useful cell model for interpreting the small-angle scattering of catalysts. J Appl Cryst 16:83–88. CrossRefGoogle Scholar
  59. 59.
    Bernal JD (1960) Geometry of the structure of monatomic liquids. Nature 185(4706):68–70. CrossRefGoogle Scholar
  60. 60.
    Bernal JD, Mason J, Knight KR (1962) Radial distribution of the random close packing of equal spheres. Nature 194(4832):957–958. CrossRefGoogle Scholar
  61. 61.
    Finney JL, Woodcock LV (2014) Renaissance of Bernal’s random close packing and hypercritical line in the theory of liquids. J Phys Condens Matter 26(46):463102(19pp). CrossRefGoogle Scholar
  62. 62.
    Li F, Liu XJ, Lu ZP (2014) Atomic structural evolution during glass formation of a Cu–Zr binary metallic glass. Comput Mater Sci 85:147–153. CrossRefGoogle Scholar
  63. 63.
    Salmon PS, Martin RA, Mason PE, Cuello GJ (2005) Topological versus chemical ordering in network glasses at intermediate and extended length scales. Nature 435(5):75–78. CrossRefGoogle Scholar
  64. 64.
    Greaves GN, Ngai KL (1995) Reconciling ionic-transport properties with atomic structure in oxide glasses. Phys Rev B52(9):6358–6380. CrossRefGoogle Scholar
  65. 65.
    Zachariasen WH (1932) The atomic arrangement in glass. J Am Chem Soc 54(10):3841–3851. CrossRefGoogle Scholar
  66. 66.
    Greaves GN (1985) EXAFS and the structure of glass. J Non Cryst Solids 71(1–3):203–217. CrossRefGoogle Scholar
  67. 67.
    Franzblau DS (1991) Computation of ring statistics for network models of solids. Phys Rev B 44(10):4925–4930. CrossRefGoogle Scholar
  68. 68.
    Gladden LF (1990) Medium-range order in v-SiO2. J Non Cryst Solids 119(3):318–330. CrossRefGoogle Scholar
  69. 69.
    Balducci R, Pearlman RS (1994) Efficient exact solution of the ring perception problem. J Chem Inf Comput Sci 34(4):822–831. CrossRefGoogle Scholar
  70. 70.
    Yuan X, Cormack AN (1997) MD simulated structures of soda-lime-silica glass and its surface. Ceram Trans 82:281–286Google Scholar
  71. 71.
    Angell CA, Kanno H (1976) Density maxima in high-pressure supercooled water and liquid silicon dioxide. Science 193(4258):1121–1122. CrossRefGoogle Scholar
  72. 72.
    Sen S, Andrus RL, Baker DE, Murtagh MT (2004) Observation of an anomalous density minimum in vitreous silica. Phys Rev Lett 93(12):125902-1–125902-4. CrossRefGoogle Scholar
  73. 73.
    Angell CA (1995) Formation of glasses from liquids and biopolymers. Science 267(5206):1924–1935. CrossRefGoogle Scholar
  74. 74.
    Andronis V, Zografi G (2000) Crystal nucleation and growth of indomethacin polymorphs from the amorphous state. J Non Cryst Solids 271(3):236–248. CrossRefGoogle Scholar
  75. 75.
    Politov AA, Kostrovskii VG, Boldyrev VV (2001) Conditions of preparation and crystallization of amorphous paracetamol. Russ J Phys Chem A 75(11):1903–1911. Google Scholar
  76. 76.
    Taylor LS, Zografi G (1997) Spectroscopic characterization of interactions between PVP and indomethacin in amorphous molecular dispersions. Pharm Res 14(12):1691–1698. CrossRefGoogle Scholar
  77. 77.
    Andronis V, Zografi G (1997) Molecular mobility of supercooled amorphous indomethacin, determined by dynamic mechanical analysis. Pharm Res 14(4):410–414. CrossRefGoogle Scholar
  78. 78.
    Turnbull D (1976) Relation of crystallization behavior to structure in amorphous systems. Ann NY Acad Sci 279:185. CrossRefGoogle Scholar
  79. 79.
    Demirjian BG, Dosseh G, Chauty A, Ferrer ML, Morineau D, Lawrence C, Takeda K, Kivelson D, Brown S (2001) Metastable solid phase at the crystalline amorphous border: the glacial phase of triphenyl phosphite. J Phys Chem B 105:2107–2116. CrossRefGoogle Scholar
  80. 80.
    Schmidt H (1989) Organic modification of glass structure. New glasses or new polymers? J Non Cryst Solids 12:419–423. CrossRefGoogle Scholar
  81. 81.
    Mishima O, Calvert LD, Whalley E (1984) Melting ice’ I at 77 K and 10 kbar: a new method of making amorphous solids. Nature 310:393–395. CrossRefGoogle Scholar
  82. 82.
    Grimsditch M (1984) Polymorhism in amorphous SiO2. Phys Rev Lett 52:2379–2381CrossRefGoogle Scholar
  83. 83.
    Mitius AC, Patashinskii AZ, Shimilo BI (1985) The liquid-liquid phase transition. Phys Lett A 113:41–44. CrossRefGoogle Scholar
  84. 84.
    Thiel MV, Ree FH (1993) High-pressure liquid-liquid phase change in carbon. Phys Rev B 48(6):3591–3599. CrossRefGoogle Scholar
  85. 85.
    Riebling EF (1970) Relationships between phase diagrams and the structure of glass-forming oxide melts. Phase diagrams. Materials science and technology, vol III. Academic, New York, pp 253–270. Google Scholar
  86. 86.
    Tsukumi I, Yamamuro O, Suga H (1994) Heat capacities and glass transitions of ground amorphous solid and liquid-quenched glass of tri-O-methyl-ß-cyclodextrin. J Non Cryst Solids 175:187–194. CrossRefGoogle Scholar
  87. 87.
    Aasland S, McMillan PF (1994) Density-driven liquid-liquid phase separation in the system Al2O3-Y2O3. Nature 369:633–636. CrossRefGoogle Scholar
  88. 88.
    Flory PJ (1973) Macromolecular chemistry-8. International symposium macromolecules held in Helsinki, Molecular configuration in bulk polymers, Finland, pp 1–15, 2–7 July 1972.
  89. 89.
    Franzese G, Malescio G, Skibinsky A, Buldyrev SV, Stanley HE (2001) Generic mechanism for generating a liquid-liquid phase transition. Nature 409(6821):692–695. CrossRefGoogle Scholar
  90. 90.
    Boyer RF (1976) General reflections on the symposium on physical structure of the amorphous state. J Macromol Sci Phys B 12(2):253–301. CrossRefGoogle Scholar
  91. 91.
    Ishii K, Nakayama H, Koyama K, Yokoyama Y, Ohashi Y (1997) Molecular conformation of butanenitrile in gas, liquid, glass, and crystalline states: in relation to the stability of the glass state. Bull Chem Soc Jpn 70(9):2085–2091. CrossRefGoogle Scholar
  92. 92.
    Jarmelo S, Maria TMR, Leitao MLP, Fausto R (2001) The low temperature crystalline and glassy states of methyl α-hydroxy-isobutyrate. Phys Chem Chem Phys 3:387–392. CrossRefGoogle Scholar
  93. 93.
    Ganguli D (2009) Polyamorphism in liquids and amorphous substances: an analogue of polymorphism in crystalline solids. Trans Indian Ceram Soc 68(2):65–80. CrossRefGoogle Scholar
  94. 94.
    Mishima O, Calvert LD, Whalley E (1985) An apparently first-order transition between two amorphous phases of ice induced by pressure. Nature 314(6006):76–78. CrossRefGoogle Scholar
  95. 95.
    Poole PH, Grande T, Angell CA, McMillan PF (1997) Polymorphic phase transitions in liquids and glasses. Science 275(5298):322–323. CrossRefGoogle Scholar
  96. 96.
    Poole PH, Sciortino F, Essmann U, Stanley HE (1992) Phase behaviour of metastable water. Nature 360(6402):324–328. CrossRefGoogle Scholar
  97. 97.
    Debenedetti PG (2003) Supercooled and glassy water. J Phys Condens Matter 15(45):R1669–R1726. CrossRefGoogle Scholar
  98. 98.
    Sciortino F, Essmann U, Stanley HE, Hemmati M, Shao J, Wolf GH, Angell CA (1995) Crystal stability limits at positive and negative pressures, and crystal-to-glass transitions. Phys Rev E 52(6):6484–6491. CrossRefGoogle Scholar
  99. 99.
    Rapoport E (1967) Model for melting-curve maxima at high pressure. J Chem Phys 46(8):2891–2896. CrossRefGoogle Scholar
  100. 100.
    Rapoport E (1967) Melting-curve maxima at high pressure. II. Liquid cesium. Resistivity, Hall Effect, and composition of molten tellurium. J Chem Phys 48(4):1433–1438. CrossRefGoogle Scholar
  101. 101.
    Sastry S, Debenedetti PG, Sciortino F, Stanley HE (1996) Singularity-free interpretation of the thermodynamics of supercooled water. Phys Rev E 53(6):6144–6154. CrossRefGoogle Scholar
  102. 102.
    Deb SK, Wilding M, Somayazulu M, McMillan PF (2001) Pressure-induced amorphization and an amorphous–amorphous transition in densified porous silicon. Nature 414(6863):528–530. CrossRefGoogle Scholar
  103. 103.
    Monahan AR, Kuder JE (1972) Spectroscopic differences between crystalline and amorphous phases of indigo. J Org Chem 37(25):4182–4184. CrossRefGoogle Scholar
  104. 104.
    Hédoux A, Paccou L, Guinet Y, Willart JF, Descamps M (2009) Using the low-frequency Raman spectroscopy to analyze the crystallization of amorphous indomethacin. Eur J Pharm Sci 38(2):156–164. CrossRefGoogle Scholar
  105. 105.
    Wang B, Pikal MJ (2010) The impact of thermal treatment on the stability of freeze dried amorphous pharmaceuticals: I. Dimer formation in sodium ethacrynate. J Pharm Sci 99(2):663–682. CrossRefGoogle Scholar
  106. 106.
    Sastry S, Angell CA (2003) Liquid–liquid phase transition in supercooled silicon. Nat Mater 2(11):739–743. CrossRefGoogle Scholar
  107. 107.
    Hedler A, Klaumunzer SL, Wesch W (2004) Amorphous silicon exhibits a glass transition. Nat Mater 3(11):804–809. CrossRefGoogle Scholar
  108. 108.
    McMillan PF (2000) Phase transitions: Jumping between liquid states. Nature 403(6667):151–152. CrossRefGoogle Scholar
  109. 109.
    Wilding MC, McMillan PF (2001) Polyamorphic transitions in yttria–alumina liquids. J Non Cryst Solids 293–295:357–365. CrossRefGoogle Scholar
  110. 110.
    Wilding MC, Wilson M, McMillan PF (2005) X–ray and neutron diffraction studies and MD simulation of atomic configurations in polyamorphic Y2O3-Al2O3 systems. Proc R Soc London, Ser A 363:589–607. Google Scholar
  111. 111.
    Katayama Y, Mizutani T, Utsumi W, Shimomura O, Yamkata M, Funakoshi K-I (2000) A first-order liquid–liquid phase transition in phosphorus. Nature 403(6766):170–173. CrossRefGoogle Scholar
  112. 112.
    Senda Y, Shimojo F, Hoshimo K (2002) The liquid–liquid phase transition of liquid phosphorus studied by ab initio molecular-dynamics simulations. J Non Cryst Solids 312–314:80–84. CrossRefGoogle Scholar
  113. 113.
    Katayama Y, Inamura Y, Mizutani T, Yamakata M, Utsumi W, Shimomura O (2004) Macroscopic separation of dense fluid phase and liquid phase of phosphorus. Science 306(5697):848–851. CrossRefGoogle Scholar
  114. 114.
    Brazhkin VV, Popova SV, Voloshin RN (1999) Pressure–temperature phase diagram of molten elements: selenium, sulfur and iodine. Phys B Condens Matter 265(1–4):64–71. CrossRefGoogle Scholar
  115. 115.
    Monaco G, Falconi S, Crichton WA, Mezouar M (2003) Nature of the first-order phase transition in fluid phosphorus at high temperature and pressure. Phys Rev Lett 90(25):255701. CrossRefGoogle Scholar
  116. 116.
    Tsybulya SV, Kryukova GN (2008) Nanocrystalline transition aluminas: nanostructure and features of x-ray powder diffraction patterns of low-temperature Al2O3 polymorphs. Phys Rev B 77(2):024112. CrossRefGoogle Scholar
  117. 117.
    Isupova LA, Alikina GM, Tsybulya SV, Boldyreva NN, Kryukova GN, Yakovleva IS, Isupov VP, Sadykov VA (2001) Real structure and catalytic activity of La1−xSrxCoO3 perovskites. Int J Inorg Mater 3(6):559–562. CrossRefGoogle Scholar
  118. 118.
    Nikulina O, Yatsenko D, Bulavchenko O, Zenkovets G, Tsybulya S (2016) Debye function analysis of nanocrystalline gallium oxide γ-Ga2O3. Z Kristallogr Cryst Mater 231(5):261–266. CrossRefGoogle Scholar
  119. 119.
    Kryukova GN, Klenov DO, Ivanova AS, Tsybulya SV (2000) Vacancy ordering in the structure of γ-Al2O3. J Eur Ceram Soc 20(8):1187–1189. CrossRefGoogle Scholar
  120. 120.
    Cherepanova SV, Tsybulya SV (2000) Simulation of X-ray powder diffraction patterns for low-ordered materials. J Mol Catal A Chem 158(1):263–266. CrossRefGoogle Scholar
  121. 121.
    Sadykov VA, Isupova LA, Tsybulya SV, Cherepanova SV, Litvak GS, Burgina EB, Kustova GN, Kolomiichuk VN, Ivanov VP, Paukshtis EA, Golovin AV, Avvakumov EG (1996) Effect of mechanical activation on the real structure and reactivity of iron (III) oxide with corundum-type structure. J Solid State Chem 123(2):191–202. CrossRefGoogle Scholar
  122. 122.
    Isupova LA, Sadykov VA, Tsybulya SV, Kryukova GN, Ivanov VP, Petrov AN, Kononchuk OF (1997) Effect of structural disorder on the catalytic activity of mixed La−Sr−Co−Fr−O perovskites. React Kinet Catal Lett 62(1):129–135. CrossRefGoogle Scholar
  123. 123.
    Cherepanova SV, Tsybulya SV (2004) Simulation of X-ray powder diffraction patterns for one-dimensionally disordered crystals. Mater Sci Forum 443:87–90. CrossRefGoogle Scholar
  124. 124.
    Cherepanova SV, Tsybulya SV (2006) Influence of coherent connection of crystalline blocks on the diffraction pattern of nanostructured materials. Z Kristallogr Suppl 23:155–160. CrossRefGoogle Scholar
  125. 125.
    Kryukova GN, Tsybulya SV, Solovyeva LP, Sadykov VA, Litvak GS, Andrianova MP (1991) Effect of heat treatment on microstructure evolution of haematite derived from synthetic goethite. Mater Sci Eng A 149(1):121–127. CrossRefGoogle Scholar
  126. 126.
    Wunderlich B (1999) A classification of molecules, phases, and transitions as recognized by thermal analysis. Thermochim Acta 340–341:37–52. CrossRefGoogle Scholar
  127. 127.
    Levine H, Shalaev E, Zografi G (2002) The concept of ‘structure’ in amorphous solids from the perspective of the pharmaceutical sxciences. In: Levine H (ed) Amorphous food and pharmaceutical systems. Royal Society of Chemistry, Cambridge, pp 11–30. CrossRefGoogle Scholar
  128. 128.
    Cui Y (2007) A material science perspective of pharmaceutical solids. Int J Pharm 339:3–18. CrossRefGoogle Scholar
  129. 129.
    Seyer JJ, Luner PE, Kemper MS (2000) Application of diffuse reflectance near-infrared spectroscopy for determination of crystallinity. J Pharm Sci 89(10):1305–1316.<1305::AID-JPS8>3.0.CO;2-Q CrossRefGoogle Scholar
  130. 130.
    Bernhard W, Wei C (1996) The difference between liquid crystals and conformationally disordered crystals. In: Isayev AI, Kyu T, Cheng SZD (eds) Liquid-crystalline polymer systems. ACS symposium series, vol 632. American Chemical Society, Washington, DC, pp 232–248. CrossRefGoogle Scholar
  131. 131.
    Singh S (2002) Liquid crystals: fundamentals. World Scientific, SingaporeCrossRefGoogle Scholar
  132. 132.
    Kumar S (2001) Liquid crystals: experimental study of physical properties and phase transitions. Cambridge University Press, CambridgeGoogle Scholar
  133. 133.
    Sherwood JN (ed) (1978) The plastically crystalline state. Wiley, Hoboken, NJGoogle Scholar
  134. 134.
    Billinge SJL, Thorpe MF (eds) (1998) Local structure from diffraction. Springer, New York. 399 pGoogle Scholar

Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Institute of PhysicsUniversity of SilesiaChorzówPoland
  2. 2.Chair of Pharmaceutical Technology and Biopharmaceutics, Faculty of PharmacyJagiellonian University - Medical CollegeKrakówPoland
  3. 3.Institute of Solid State Chemistry and Mechanochemistry, Siberian Branch of the Russian Academy of SciencesNovosibirsk State UniversityNovosibirskRussian Federation
  4. 4.AbbVieNorth ChicagoUSA

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