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Gram–Charlier approach for anharmonic atomic displacements in inorganic solids: A review

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Pages 151-194 | Received 02 Jun 2023, Accepted 25 Sep 2023, Published online: 16 Oct 2023

References

  • Morse PM. Diatomic molecules according to the wave mechanics. II. Vibrational levels. Phys Rev. 1929;34:57–64. doi:10.1103/PhysRev.34.57
  • Kuhs WF. Statistical description of multimodal atomic probability densities. Acta Crystallogr A. 1983;39:148–158. doi:10.1107/S0108767383000240
  • Kuhs WF. Generalized atomic displacements in crystallographic structure analysis. Acta Cryst. 1992;A48:80–98. doi:10.1107/S0108767391009510
  • Kuhs WF. The anharmonic temperature factor in crystallographic structure analysis. Aust J Phys. 1988;41:369. doi:10.1071/PH880369
  • Kuhs WF. Atomic displacement parameters. In: International tables for crystallography. Ed. A. Authier. Chester: International Union of Crystallography; 2013. p. 231–245.
  • Johnson CK. Addition of higher cumulants to the crystallographic structure-factor equation: a generalized treatment for thermal-motion effects. Acta Crystallogr A. 1969;25:187–194. doi:10.1107/S0567739469000325
  • Kendall MG. The advanced theory of statistics. London: Griffin; 1958.
  • Johnson CK. Series expansion models for thermal motion. 1970 Winter Meeting. Tulane University; 1970. p. 60.
  • Scheringer C. A general expression for the anharmonic temperature factor in the isolated-atom-potential approach. Acta Crystallogr A. 1985;41:73–79. doi:10.1107/S0108767385000125
  • Coppens P. Thermal smearing and chemical bonding. In: PJ Becker, editor. Electron and magnetization densities in molecules and solids. New York: Plenum; 1980. p. 521–544.
  • Krivoglaz MA, Tikhonova EA. Sov Phys-Cryst. 1961: 6: 399–403.
  • Maradudin AA, Flinn PA. Anharmonic contributions to the Debye–Waller factor. Phys Rev. 1963;129:2529–2547. doi:10.1103/PhysRev.129.2529
  • Burns JH, Agron PA, Levy HA. Noble-gas compounds. Ed. H. H. Hyman, p. 211. Chicago: University of Chicago Press; 1963.
  • Johnson CK, Levy HA. Thermal motion analysis using Bragg diffraction data. Ed. W.C. Hamilton. In: International tables for X-ray crystallography. Dordrecht: Kluwer Academic Publishers; 1974. p. 311–336.
  • Coppens P. Relative merits of the three expansions. In: U. Shmueli, editor. International tables for crystallography. 2010. p. 22.
  • Zucker UH, Schulz H. Statistical approaches for the treatment of anharmonic motion in crystals. I. A comparison of the most frequently used formalisms of anharmonic thermal vibrations. Acta Crystallogr Sect A. 1982;38:563–568. doi:10.1107/S0567739482001211
  • Trueblood KN, Bürgi HB, Burzlaff H, et al. Atomic displacement parameter nomenclature. report of a subcommittee on atomic displacement parameter nomenclature. Acta Crystallogr A. 1996;52:770–781. doi:10.1107/S0108767396005697
  • Petříček V, Palatinus L, Plášil J, et al. Jana2020– a new version of the crystallographic computing system Jana. Z Kristallogr Cryst Mater. 2023;229:345-352.
  • Petříček V, Dušek M, Palatinus L. Crystallographic computing system JANA2006: general features. Z Kristallogr Cryst Mater. 2014;229:345–352. doi:10.1515/zkri-2014-1737
  • Petříček V, Dušek M, Plášil J. Crystallographic computing system Jana2006: solution and refinement of twinned structures. Z Kristallogr Cryst Mater. 2016;231:583–599. doi:10.1515/zkri-2016-1956
  • Reilly AM, Morrison CA, Rankin DWH, et al. Using molecular-dynamics simulations to understand and improve the treatment of anharmonic vibrations. II. Developing and assessing new Debye–Waller factors. Acta Crystallogr A. 2011;67:346–356. doi:10.1107/S010876731101395X
  • Reilly AM, Morrison CA, Rankin DWH. Using molecular-dynamics simulations to understand and improve the treatment of anharmonic vibrations. I. Study of positional parameters. Acta Crystallogr A. 2011;67:336–345. doi:10.1107/S0108767311013948
  • Muradyan LA, Sirota MA, Makarova IP, Simonov V.I. Kristallografiya. 1985;30: 258-266.
  • Rabadanov MH, Ataev MC. Vliyaniye teplovykh kolebaniy atomov na intensivnosti breggovskikh otrazheniy (Influence of thermal vibrations of atoms on the intensities of Bragg reflections). DGU. 1998. p. 100.
  • Tsarkov AG, Tsirelson VG. Anharmonic effects in the thermal diffuse scattering of X-rays. Physica Status Solidi (b). 1991;167:417–428. doi:10.1002/pssb.2221670204
  • Tsirelson VG, Ozerov RP. Electron density and bonding in crystals. Boca Raton: CRC Press; 2020.
  • Mallinson PR, Koritsanszky T, Elkaim E, et al. The Gram–Charlier and multipole expansions in accurate X-ray diffraction studies: can they be distinguished? Acta Crystallogr A. 1988;44:336–343. doi:10.1107/S0108767387012558
  • Coppens P. X-Ray charge densities and chemical bonding. New York: Oxford University Press; 1997.
  • Momma K, Izumi F. VESTA: a three-dimensional visualization system for electronic and structural analysis. J Appl Crystallogr. 2008;41:653–658. doi:10.1107/S0021889808012016
  • Rohlíček J, Hušák M. MCE2005 – a new version of a program for fast interactive visualization of electron and similar density maps optimized for small molecules. J Appl Crystallogr. 2007;40:600–601. doi:10.1107/S0021889807018894
  • Spek AL. checkCIF validation ALERTS: what they mean and how to respond. Acta Crystallogr E Crystallogr Commun. 2020;76:1–11. doi:10.1107/S2056989019016244
  • Spek AL. Single-crystal structure validation with the program PLATON. J Appl Crystallogr. 2003;36:7–13. doi:10.1107/S0021889802022112
  • Boysen H. Anharmonic Thermal motion refinement software.
  • Zucker UH, Perenthaler E, Kuhs WF, et al. PROMETHEUS. A program system for investigation of anharmonic thermal vibrations in crystals. J Appl Crystallogr. 1983;16:358–358. doi:10.1107/S0021889883010560
  • Berar J-F, Baldinozzi G. Xnd code: from X-ray laboratory data to incommensurately modulated phases. Rietveld modelling of complex materials. IUCr CPD Newsletter. 1998;20:3–5.
  • Andrianov VI. AREN-85 — system of crystallographical programs rentgen for EVM NORD. Crystallogr Rep. 1987;32:228–232.
  • Kuhs WF. Atomic displacement parameters. In: International tables for crystallography. Ed. A. Authier. Chester: International Union of Crystallography; 2006. p. 228–242.
  • Tsirelson VG. Chemical bond and atomic motion in crystals. Moscow: VINITI Publ.; 1993.
  • Hansen NK, Coppens P. Testing aspherical atom refinements on small-molecule data sets. Acta Crystallogr Sect A. 1978;34:909–921. doi:10.1107/S0567739478001886
  • Coppens P, Guru Row TN, Leung P, et al. Net atomic charges and molecular dipole moments from spherical-atom X-ray refinements, and the relation between atomic charge and shape. Acta Crystallogr Sect A. 1979;35:63–72. doi:10.1107/S0567739479000127
  • Gianopoulos CG, Zhurov V V, Minasian SG, et al. Bonding in uranium(V) hexafluoride based on the experimental electron density distribution measured at 20 K. Inorg Chem. 2017;56:1775–1778. doi:10.1021/acs.inorgchem.6b02971
  • Volkov A, Macchi P, Farrugia LJ, et al. (2006). XD2006 – A Computer Program Package for Multipole Refinement, Topological Analysis of Charge Densities and Evaluation of Intermolecular Interaction Energies from Experimental and Theoretical Structure Factors, University at Buffalo, State University of New York, NY, USA; University of Milano, Italy; University of Glasgow, UK; CNRISTM, Milano, Italy; Middle Tennessee State University, TN USA.
  • Stewart RF, Spackman MA, Flensburg C. VALRAY User’s Manual (Version 2.1): Carnegie-Mellon University, Pittsburgh, and University of Copenhagen; 2000.
  • Guillot B, Viry L, Guillot R, et al. Refinement of proteins at subatomic resolution with MOPRO. J Appl Crystallogr. 2001;34:214–223. doi:10.1107/S0021889801001753
  • Hübschle CB, Dittrich B. Molecoolqt – a molecule viewer for charge-density research. J Appl Crystallogr. 2011;44:238–240. doi:10.1107/S0021889810042482
  • Hübschle CB, Ruhmlieb C, Burkhardt A, et al. On avoiding negative electron density in Gram-Charlier refinements of anharmonic motion: the example of glutathione. Z Kristallogr Cryst Mater. 2018;233:695–706. doi:10.1515/zkri-2018-2060
  • Li N, Su Z, Coppens P, et al. X-ray diffraction study of the electronic ground state of (meso-tetraphenylporphinato)iron(II). J Am Chem Soc. 1990;112:7294–7298. doi:10.1021/ja00176a032
  • Scheins S, Zheng S-L, Benedict JB, et al. Charge-density analysis of the ground state of a photochromic 1,10-phenanthroline zinc(II) bis(thiolate) complex. Acta Crystallogr B. 2010;66:366–372. doi:10.1107/S0108768110009687
  • Coppens P, Iversen B, Larsen FK. The use of synchrotron radiation in X-ray charge density analysis of coordination complexes. Coord Chem Rev. 2005;249:179–195. doi:10.1016/j.ccr.2004.02.019
  • Flensburg C, Larsen S, Stewart RF. Experimental charge density study of methylammonium hydrogen succinate monohydrate. A salt with a very short O-H-O hydrogen bond. J Phys Chem. 1995;99:10130–10141. doi:10.1021/j100025a013
  • Birkedal H, Madsen D, Mathiesen RH, et al. The charge density of urea from synchrotron diffraction data. Acta Crystallogr A. 2004;60:371–381. doi:10.1107/S0108767304015120
  • Krause L, Niepötter B, Schürmann CJ, et al. Validation of experimental charge-density refinement strategies: when do we overfit? IUCrJ. 2017;4:420–430. doi:10.1107/S2052252517005103
  • Capelli SC, Bürgi H-B, Dittrich B, et al. Hirshfeld atom refinement. IUCrJ. 2014;1:361–379. doi:10.1107/S2052252514014845
  • Jayatilaka D, Dittrich B. X-ray structure refinement using aspherical atomic density functions obtained from quantum-mechanical calculations. Acta Crystallogr A. 2008;64:383–393. doi:10.1107/S0108767308005709
  • Herbst-Irmer R, Henn J, Holstein JJ, et al. Anharmonic motion in experimental charge density investigations. J Phys Chem A. 2013;117:633–641. doi:10.1021/jp309985e
  • Volkov SN, Charkin DO, Manelis LS, et al. A new salt-inclusion compound, |Ag4Br|@[B7O12], with a novel type of the porous double-layered borate anion and strong anharmonicity of the “guest” sublattice. Solid State Sci. 2022;125. doi:10.1016/j.solidstatesciences.2022.106831
  • Volkov SN, Charkin DO, Arsent’ev M, et al. Bridging the salt-inclusion and open-framework structures: the case of acentric Ag4B4O7X2(X = Br. I) borate halides. Inorg Chem. 2020;59:2655–2658. doi:10.1021/acs.inorgchem.0c00306
  • Zubkova NV, Pushcharovsky D, Atencio D, et al. The crystal structure of lewisite, (Ca,Sb3+,Fe3+,Al,Na,Mn,□)2(Sb5+,Ti)2O6(OH). J Alloys Compd. 2000;296:75–79. doi:10.1016/S0925-8388(99)00513-7
  • Dudka AP, Nesterenko SN, Tursina AI. Refinement of the crystal structure of a new intermetallic Ce2Rh2Ga. J Surf Investig: X-ray. Synchrotron and Neutron Techn. 2020;14:1121–1125. doi:10.1134/S1027451020040047
  • Delarue P, Lecomte C, Jannin M, et al. Evolution towards centrosymmetry of the nonlinear-optical material RbTiOPO4 in the temperature range 293–973 K: alkaline displacements and titanyl deformations. Phys Rev B. 1998;58:5287–5295. doi:10.1103/PhysRevB.58.5287
  • Kiat J-M, Baldinozzi G, Dunlop M, et al. Anharmonicity and disorder in simple and complex perovskites: a high energy synchrotron and hot neutron diffraction study. J Phys: Condens Matter. 2000;12:8411–8425. doi:10.1088/0953-8984/12/39/305
  • Nakatsuka A, Shimokawa M, Nakayama N, et al. Static disorders of atoms and experimental determination of Debye temperature in pyrope: low- and high-temperature single-crystal X-ray diffraction study. Am Mineral. 2011;96:1593–1605. doi:10.2138/am.2011.3714
  • Rabadanov M, Verin IA, Ivanov Y, et al. Refinement of the atomic structure of CdTe single crystals. Crystallogr Rep. 2001;46:636–641. doi:10.1134/1.1387130
  • Destro R, Ruffo R, Roversi P, et al. Anharmonic motions versus dynamic disorder at the Mg ion from the charge densities in pyrope (Mg3Al2Si3O12) crystals at 30 K: six of one, half a dozen of the other. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2017;73:722–736. doi:10.1107/S2052520617006102
  • Dudka AP, Bolotina NB, Khrykina ON. Debyefit: a simple tool to obtain an appropriate model of atomic vibrations in solids from atomic displacement parameters obtained at different temperatures. J Appl Crystallogr. 2019;52:690–692. doi:10.1107/S1600576719005818
  • Dudka A, Nesterenko S, Tursina A. Multi-temperature X-ray diffraction study of a reversible structural phase transition in the high-temperature polymorph of Ce2Rh2Ga compound. J Alloys Compd. 2022;890:161759. doi:10.1016/j.jallcom.2021.161759
  • Krogh-Moe J. The crystal structure of silver tetraborate Ag2O.4B2O3. Acta Crystallogr 1965;18:77–81. doi:10.1107/S0365110X65000142
  • Penin N, Touboul M, Nowogrocki G. Crystal structure of the second form of silver octoborate β-Ag2B8O13. Solid State Sci. 2003;5:559–564. doi:10.1016/S1293-2558(03)00036-0
  • Volkov SN, Charkin DO, Arsentev MY, et al. Where the extraordinaries meet: a cascade of isosymmetrical superionic phase transitions and negative thermal expansion in a novel silver salt-inclusion borate halide. CrystEngComm. 2022;24:4174–4179. doi:10.1039/D2CE00307D
  • Shepelev Y, Bubnova RS, Filatov SK, et al. Lib3O5 crystal structure at 20, 227 and 377°C. J Solid State Chem. 2005;178:2987–2997. doi:10.1016/j.jssc.2005.06.017
  • Marsh P, Siegrist T, Fleming RM, et al. Anharmonic thermal motion in the 93-K superconductor Ba2YCu3O7 using multiple-wavelength x-ray diffraction. Phys Rev B. 1988;38:874–877. doi:10.1103/PhysRevB.38.874
  • Sennova N, Bubnova RS, Cordier G, et al. Temperature-dependent changes of the crystal structure of Li2B4O7. Z Anorg Allg Chem. 2008;634:2601–2607. doi:10.1002/zaac.200800295
  • Lander GH, Brown PJ, Faber J. Neutron diffraction study of anharmonicity in AuCu3 in the ordered phase. J Phys C Solid State Phys. 1982;15:6699–6708. doi:10.1088/0022-3719/15/33/008
  • Senyshyn A, Boysen H, Niewa R, et al. High-temperature properties of lithium tetraborate Li2B4O7. J Phys D Appl Phys. 2012;45:175305. doi:10.1088/0022-3727/45/17/175305
  • Pfitzner A. Disorder of Cu+ in Cu3SbS3: structural investigations of the high- and low-temperature modification. Z Kristallogr Cryst Mater. 1998;213:228–236. doi:10.1524/zkri.1998.213.4.228
  • Laumann A, Boysen H, Bremholm M, et al. Lithium migration at high temperatures in Li4Ti5O12 studied by neutron diffraction. Chem Mater. 2011;23:2753–2759. doi:10.1021/cm103332y
  • Gaudin E, Boucher F, Petricek V, et al. Structures and phase transitions of the A7PSe6 (A = Ag, Cu) argyrodite-type ionic conductors. II. β- and γ-Cu7PSe6. Acta Crystallogr B. 2000;56:402–408. doi:10.1107/S0108768199016614
  • Boukamp BA, Huggins RA. Lithium ion conductivity in lithium nitride. Phys Lett A. 1976;58:231–233. doi:10.1016/0375-9601(76)90082-7
  • Bachmann R, Kreuer KD, Rabenau A, et al. Relationship between crystal structure and ionic conductivity in CuTeBr. Acta Crystallogr B. 1982;38:2361–2364. doi:10.1107/S0567740882008796
  • Etschmann B, Ishizawa N, Streltsov V, et al. A synchrotron X-ray diffraction analysis of near-stoichiometric LiNbO3. Z Kristallogr Cryst Mater. 2001;216:455–461. doi:10.1524/zkri.216.8.455.20357
  • Gągor A, Pietraszko A, Kaynts D. Diffusion paths formation for Cu+ ions in superionic Cu6PS5I single crystals studied in terms of structural phase transition. J Solid State Chem. 2005;178:3366–3375. doi:10.1016/j.jssc.2005.08.015
  • Schneider J, Schröder T, Hoelzel M, et al. Phase transitions to superionic Li2Te and Li2Se – A high-temperature neutron powder diffraction study, atom displacements, probability density functions and atom potentials. Solid State Ion. 2018;325:90–101. doi:10.1016/j.ssi.2018.07.024
  • Maisonneuve V, Evain M, Payen C, et al. Room-temperature crystal structure of the layered phase CuIInIIIP2S6. J Alloys Compd. 1995;218:157–164. doi:10.1016/0925-8388(94)01416-7
  • Freiheit HKH-GKAK H-C. High temperature X-ray synchrotron study on LiNaSO4: Anharmonic thermal vibrations and effective atomic potentials. Hamburg. 1999.
  • Roth N, Brummerstedt Iversen B. Dynamic correlations and possible diffusion pathway in the superionic conductor Cu2−xSe. IUCrJ. 2023;10:199–209. doi:10.1107/S2052252523001318
  • Schwarzmüller S, Hoelzel M, Fritsch K, et al. Lithium atom mobility in lithium germanium antimony tellurides elucidated by neutron diffraction and quasielastic neutron scattering. J Alloys Compd. 2020;827:154346. doi:10.1016/j.jallcom.2020.154346
  • Danilkin SA. An investigation of the structural dynamics in the fast ionic conductor Cu2−δSe using neutron scattering. J Alloys Compd. 2009;467:509–513. doi:10.1016/j.jallcom.2007.12.064
  • Iyi N, Kitamura K, Izumi F, et al. Comparative study of defect structures in lithium niobate with different compositions. J Solid State Chem. 1992;101:340–352. doi:10.1016/0022-4596(92)90189-3
  • Gagor A, Gnida D, Pietraszko A. Order–disorder phenomena in layered CuCrSe2 crystals. Mater Chem Phys. 2014;146:283–288. doi:10.1016/j.matchemphys.2014.03.024
  • Wiedemann D, Meutzner F, Fabelo O, et al. The inverse perovskite BaLiF3: single-crystal neutron diffraction and analyses of potential ion pathways. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2018;74:643–650. doi:10.1107/S2052520618014579
  • Malcherek T, Mihailova B, Welch MD. Structural phase transitions of clinoatacamite and the dynamic Jahn–Teller effect. Phys Chem Miner. 2017;44:307–321. doi:10.1007/s00269-016-0859-9
  • Tadin M, Schneider J, Boysen H, et al. Neutron- and X-Ray powder investigation of the zintl phases NaTl and LiAl at temperatures up to 900 K. Mater Sci Forum. 1991;79–82:635–642. doi:10.4028/www.scientific.net/MSF.79-82.635
  • Dalgaard KJ, Eikeland EZ, Sist M, et al. Maximum entropy method visualization of disorder and ion migration in thermoelectric Cu2-δSe. Adv Theory Simul. 2018;1:1800068. doi:10.1002/adts.201800068
  • Wiedemann D, Islam MM, Nakhal S, et al. Lithium diffusion pathways in 3R-LixTiS2: a combined neutron diffraction and computational study. J Phys Chem C. 2015;119:11370–11381. doi:10.1021/acs.jpcc.5b01166
  • Golovenchits EI, Sanina VA, Levin AA, et al. Jahn–Teller effect and the orbital ground state of Cu2+ ions in Eu2CuO4 and La2CuO4 crystals. Phys Solid State. 1997;39:1425–1432. doi:10.1134/1.1130151
  • Wiedemann D, Nakhal S, Rahn J, et al. Unravelling ultraslow lithium-ion diffusion in γ-LiAlO2: experiments with tracers, neutrons, and charge carriers. Chem Mater. 2016;28:915–924. doi:10.1021/acs.chemmater.5b04608
  • Pfitzner A, Evain M, Petricek V. Cu12Sb4S13: a temperature-dependent structure investigation. Acta Crystallogr B. 1997;53:337–345. doi:10.1107/S0108768196014024
  • Malcherek T. Structure and phase transitions of LiTaOGeO4. Acta Crystallogr B. 2002;58:607–612. doi:10.1107/S010876810200825X
  • Oliveria M. Single crystal neutron diffraction analysis of the cation distribution in the high-temperature phases α-Cu2−xS, α-Cu2−xSe, and α-Ag2Se. Solid State Ion 1988;28–30:1332–1337. doi:10.1016/0167-2738(88)90382-7
  • Ohgaki M, Tanaka K, Marumo F. Structure refinement of lithium (I) niobium (V) trioxide,: LiNbO3, with anharmonic thermal vibration model. Mineralogical J. 1992;16:150–160. doi:10.2465/minerj.16.150
  • Makarova IP, Verin IA, Aleksandrov KS. Structure and twinning of RbLiCrO4 crystals. Acta Crystallogr B. 1993;49:19–28. doi:10.1107/S0108768192006141
  • Yaroslavzev AA, Kuznetsov AN, Dudka AP, et al. Laves polyhedra in synthetic tennantite, Cu12As4S13, and its lattice dynamics. J Solid State Chem. 2021;297:122061. doi:10.1016/j.jssc.2021.122061
  • Schulz H, Zucker U, Frech R. Crystal structure of KLiSO4 as a function of temperature. Acta Crystallogr B. 1985;41:21–26. doi:10.1107/S0108768185001525
  • Sakakura T, Wang J, Ishizawa N, et al. Structural phase transitions in KNbO3 and Na0.5K0.5NbO3. IOP Conf Ser Mater Sci Eng. 2011;18:022006. doi:10.1088/1757-899X/18/2/022006
  • Laufek F, Sejkora J, Dušek M. The role of silver in the crystal structure of pyrargyrite: single crystal X-ray diffraction study. J Geosci. 2012: 161–167. doi:10.3190/jgeosci.067
  • Yahia HB, Nilges T, Rodewald U, et al. New arsenates (V) NaKAl2O[AsO4]2 and Na2KAl3[AsO4]4. Mater Res Bull. 2010;45:2017–2023. doi:10.1016/j.materresbull.2010.07.009
  • Bindi L, Evain M. Gram–Charlier development of the atomic displacement factors into mineral structures: the case of samsonite,: Ag4MnSb2S6. Am Mineralogist. 2007;92:886–891. doi:10.2138/am.2007.2364
  • Weber H, Schulz H. Ionic conduction in one dimension: a structural study of the hollandite K1.54Mg0.77Ti7.23O16 over the range 133≤ T ≤919 K. J Chem Phys. 1986;85:475–484. doi:10.1063/1.451820
  • Belin R, Aldon L, Zerouale A, et al. Crystal structure of the non-stoichiometric argyrodite compound Ag7–xGeSe5I1–x (x = 0.31). A highly disordered silver superionic conducting material. Solid State Sci. 2001;3:251–265. doi:10.1016/S1293-2558(00)01108-0
  • Hansen NK, Protas J, Marnier G. The electron-density distribution in KTiOPO4. Acta Crystallogr B. 1991;47:660–672. doi:10.1107/S0108768191004135
  • Scheringer C. A deficiency of the cumulant expansion of the anharmonic temperature factor. Acta Crystallogr A. 1985;41:79–81. doi:10.1107/S0108767385000137
  • Michiue Y, Yoshikado S. X-ray diffraction study for one-dimensional ionic conductors Kx(Ga1−yAly)2+xTi2−xO7 (x ≃ 0.14, y ≃ 0.10, 0.23, 0.39). Acta Crystallogr B. 2005;61:608–615. doi:10.1107/S0108768105031034
  • Leitl M, Pfitzner A, Bindi L. Preferred ion diffusion pathways and activation energies for Ag in the crystal structure of stephanite,: Ag5SbS4. Mineral Mag. 2009;73:17–26. doi:10.1180/minmag.2009.073.1.17
  • Gougeon P, Gall P, Al Rahal Al Orabi R, et al. Synthesis, crystal and electronic structures, and thermoelectric properties of the novel cluster compound Ag3In2Mo15Se19. Chem Mater. 2012;24:2899–2908. doi:10.1021/cm3009557
  • Dahaoui S, Hansen NK, Protas J, et al. Electric properties of KTiOPO4 and NaTiOPO4 from temperature-dependent X-ray diffraction. J Appl Crystallogr. 1999;32:1–10. doi:10.1107/S002188989800497X
  • Cava RJ, Reidinger F, Wuensch BJ. Single-crystal neutron-diffraction study of AgI between 23° and 300°C. Solid State Commun. 1977;24:411–416. doi:10.1016/0038-1098(77)91306-0
  • Michiue Y. Probability density analyses of guest ions in hollandite AxMgx/2Ti8−x/2O16 (A = K. Rb). Acta Crystallogr B. 2007;63:577–583. doi:10.1107/S0108768107023531
  • Lee A VD, Wiegers GA. Anharmonic thermal motion of Ag in AgCrSe2: a high-temperature single-crystal X-ray diffraction study. J Solid State Chem. 1989;82:216–224. doi:10.1016/0022-4596(89)90285-5
  • Delarue P, Lecomte C, Jannin M, et al. Behaviour of the non-linear optical material KTiOPO4 in the temperature range 293–973 K studied by x-ray diffractometry at high resolution: alkaline displacements. J Phys: Condens Matter. 1999;11:4123–4134. doi:10.1088/0953-8984/11/21/301
  • Perenthaler E, Schulz H, Beyeler HU. Structure investigations, atomic potentials, and phase transitions of the fast ionic conductor Ag3SI. Solid State Ion. 1981;5:493–496. doi:10.1016/0167-2738(81)90300-3
  • Kopnin E, Coste S, Jobic S, et al. Synthesis and crystal structure determination of three layered-type thiophosphate compounds KMP2S7 (M = Cr, V. In). Mater Res Bull. 2000;35:1401–1410. doi:10.1016/S0025-5408(00)00352-4
  • Didisheim J, Mcmullan R, Wuensch B. A single-crystal neutron diffraction study of the distribution and thermal motion of silver ions in alpha- and beta- Ag3SI. Solid State Ion. 1986;18–19:1150–1162. doi:10.1016/0167-2738(86)90325-5
  • Alekseeva OA, Blomberg MK, Molchanov VN, et al. Refinement of the K0.96Ti0.96Nb0.04OPO4 structure. Crystallogr Rep. 2001;46:642–646. doi:10.1134/1.1387131
  • H. Boysen. Anharmonic thermal parameters, disorder and phase transitions. In: E. Prince JKS, editor. Accuracy in powder diffraction II. Gaithersburg: NIST; 1992. p. 165–174.
  • Bindi L, Evain M, Menchetti S. Temperature dependence of the silver distribution in the crystal structure of natural pearceite,: (Ag,Cu)16(As,Sb)2S11. Acta Crystallogr B. 2006;62:212–219. doi:10.1107/S010876810600108X
  • Boucher F, Evain M, Brec R. Distribution and ionic diffusion path of silver in γ-Ag8GeTe6: a temperature dependent anharmonic single crystal structure study. J Solid State Chem. 1993;107:332–346. doi:10.1006/jssc.1993.1356
  • Zaiss T, Deiseroth H-J. Crystal structure of nonasilver hexathioaluminate,: Ag9AlS6, the ϒ phase. Z KristallogrNew Cryst Struct. 2006;221:119–120.
  • Li L, Wölfel A, Schönleber A, et al. Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb2ZnCl4. Acta Crystallogr B. 2011;67:205–217. doi:10.1107/S0108768111013814
  • Gaudin E, Deiseroth HJ, Zaiß T. The argyrodite γ-Ag9AlSe6: a non-metallic filled laves phase. Z Kristallogr Cryst Mater. 2001;216:39–44. doi:10.1524/zkri.216.1.39.19001
  • Durand E, Evain M, Brec R. Synthesis and structure of RbVP2S7: a new thiophosphate in the MI-V-P-S family. J Solid State Chem. 1993;102:146–155. doi:10.1006/jssc.1993.1017
  • Delarue P, Lecomte C, Jannin M, et al. Order-disorder evolution in solid solutions of the NLO material KTiOPO: KRbTiOPO and KRbTiOPO in the temperature range 293–973 K. Eur Phys J B. 2000;14:227–238. doi:10.1007/s100510050124
  • Volkov SN, Charkin DO, Firsova VA, et al. Ag4B7O12X (X = Cl, Br, I) heptaborate family: comprehensive crystal chemistry, thermal stability trends, topology, and vibrational anharmonicity. Inorg Chem. 2023;62:30–34. doi:10.1021/acs.inorgchem.2c03680
  • Alekseeva OA, Dudka AP, Novikova NE, et al. Structure of the RbTi0.98Zr0.02OPO4 single crystal at temperatures of 293 and 105 K. Crystallogr Rep. 2008;53:557–564. doi:10.1134/S1063774508040056
  • Streltsov VA, Nordborg J, Albertsson J. Synchrotron X-ray analysis of RbTiOAsO4. Acta Crystallogr B. 2000;56:785–792. doi:10.1107/S0108768100006285
  • Kasper JS, Browall KW. Single crystal structure study of α-Ag2HgI4: evidence for anharmonic vibration. J Solid State Chem. 1975;13:49–56. doi:10.1016/0022-4596(75)90080-8
  • Bagautdinov B, Luedecke J, Schneider M, et al. Disorder in the crystal structure of Cs2HgCl4 studied by the maximum entropy method. Acta Crystallogr B. 1998;54:626–634. doi:10.1107/S010876819800233X
  • Bindi L, Cooper MA, McDonald AM. Twinning and disorder in the crystal structure of kurilite,: Ag8Te3Se: toward a new fast ionic conductor? The Canadian Mineralogist. 2015;53:159–168. doi:10.3749/canmin.1500009
  • Meyerheim HL, Moritz W, Schulz H, et al. Anharmonic thermal vibrations observed by surface X-ray diffraction for. Surf Sci. 1995;331–333:1422–1429. doi:10.1016/0039-6028(95)00199-9
  • Bindi L, Voudouris P, Spry PG. Structural role of tellurium in the minerals of the pearceite-polybasite group. Mineral Mag. 2013;77:419–428. doi:10.1180/minmag.2013.077.4.02
  • Sjövall R. Structure of dicaesium tetraiodocadmate(II). Acta Crystallogr C. 1989;45:667–669. doi:10.1107/S0108270188012624
  • Lee Avd, Boucher F, Evain Μ, et al. Temperature dependence of the silver distribution in Ag2MnP2S6 by single crystal X-ray diffraction. Z Kristallogr Cryst Mater. 1993;203:247–264. doi:10.1524/zkri.1993.203.12.247
  • Sist M, Fischer KFF, Kasai H, et al. Low-temperature anharmonicity in cesium chloride (CsCl). Angew Chem, Int Ed. 2017;56:3625–3629. doi:10.1002/anie.201700638
  • Arakcheeva A V, Chapuis G, Meyer M. The LT phase of Cs3Bi2I9. Z Kristallogr Cryst Mater. 2001;216:199–205. doi:10.1524/zkri.216.4.199.23261
  • Bindi L, Keutsch FN. Old defined minerals with complex: still unresolved structures: the case of stützite, Ag5−xTe3. Z Kristallogr Cryst Mater. 2018;233:247–253. doi:10.1515/zkri-2017-2120
  • Novikova MS, Makarova IP, Blomberg MK, et al. Structure and phase transitions in trigonal Cs3Sb2I9 crystals. Crystallogr Rep. 2001;46:26–29. doi:10.1134/1.1343121
  • Kihara K, Matsumoto T. Refinements of Ag3AsSe3 based on high-order thermal-motion tensors. Z Kristallogr Cryst Mater. 1986;177:211–218. doi:10.1524/zkri.1986.177.14.211
  • Ishizawa N, Setoguchi H, Yanagisawa K. Structural evolution of calcite at high temperatures: phase V unveiled. Sci Rep. 2013;3:2832. doi:10.1038/srep02832
  • Gaudin E, Fischer L, Boucher F, et al. Ag2Ti2P2S11: a new layered thiophosphate. synthesis, structure determination and temperature dependence of the silver distribution. Acta Crystallogr B. 1997;53:67–75. doi:10.1107/S010876819601097X
  • Bindi L, Stanley CJ, Spry PG. New structural data reveal benleonardite to be a member of the pearceite-polybasite group. Mineral Mag. 2015;79:1213–1221. doi:10.1180/minmag.2015.079.5.15
  • Nakae H, Kihara K, Okuno M, et al. The crystal structure of the quartz-type form of GaPO4 and its temperature dependence. Z Kristallogr Cryst Mater. 1995;210:746–753. doi:10.1524/zkri.1995.210.10.746
  • Sarp H, Pushcharovsky Du, MacLean EJ, et al. Tillmannsite, (Ag3Hg)(V,As)O4, a new mineral: its description and crystal structure. Eur J Mineral. 2003;15:177–180. doi:10.1127/0935-1221/2003/0015-0177
  • Karine SaG. Structural Investigation of Quaternary Copper Oxides with Low Dimensional Magnetic Properties. Von der Fakult¨at f¨ur Bergbau, H¨uttenwesen und Geowissenschaften der Rheinisch-Westf¨alischen Technischen Hochschule Aachen; 2003.
  • Sciau P, Kania A, Dkhil B, et al. Structural investigation of AgNbO3 phases using x-ray and neutron diffraction. J Phys: Condens Matter. 2004;16:2795–2810. doi:10.1088/0953-8984/16/16/004
  • Gonschorek G, Weitzel H, Miehe G, et al. The crystal structures of NaNO3 at 100, 120 and 563 K. Z Kristallogr Cryst Mater. 2000;215:752–756. doi:10.1524/zkri.2000.215.12.752
  • Daszkiewicz M, Gulay LD, Pietraszko A, et al. Crystal structures of the La3AgSnSe7 and R3Ag1−δSnS7 (R = La, Ce; δ = 0.18−0.19) compounds. J Solid State Chem. 2007;180:2053–2060. doi:10.1016/j.jssc.2007.05.007
  • Kihara K, Matsumoto T, Imamura M. High-order thermal-motion tensor analyses of tridymite. Zeitschr Kristallograph. 1986;177:39–52.
  • McMullan RK, Klooster WT, Weber H-P. Deuterated γ-malonic acid: its neutron crystal structure in relationship to other polymorphs of aliphatic dicarboxylic acids. Acta Crystallogr B. 2008;64:230–239. doi:10.1107/S0108768108000268
  • Quarez E, Mentré O, Oumellal Y, et al. Crystal structures of new silver ion conductors Ag7Fe3(X2O7)4 (X = P. As). New J Chem. 2009;33:998. doi:10.1039/b819846b
  • Kvick Å, Smith J V. A neutron diffraction study of the zeolite edingtonite. J Chem Phys. 1983;79:2356–2362. doi:10.1063/1.446041
  • Schneider J, Schulz H. X-ray powder diffraction of Ag2Te at temperatures up to 1123 Κ. Z Kristallogr Cryst Mater. 1993;203:1–16.
  • Zhurova EA, Zavodnik VE, Ivanov SA, et al. Electron density and anharmonic thermal atomic vibrations in K1-xLixTaO3 (x = 0, 0.05, 0.15) perovskites. Zeitschr Naturforsch A. 1993;48:25–28. doi:10.1515/zna-1993-1-208
  • van der Lee A. Disorder and thermal motion of Ag in Ag0.6NbS2. Solid State Ion. 1991;44:287–292. doi:10.1016/0167-2738(91)90020-C
  • Gao Q, Clancy L, Weber H-P, et al. Structure of the adipate complex [Na2(C6H9O4)2(C6H10O4)].2H2O from neutron diffraction at 220 and 295 K. Acta Crystallogr B. 1991;47:368–375. doi:10.1107/S0108768190014021
  • Brummerstedt Iversen B, Krebs Larsen F, Reynolds PA, et al. Single-crystal neutron diffraction study of diammonium hexaaquacopper disulfate at 15 and 293 K. investigation of anharmonic motion. Acta Chem Scand. 1994;48:800–809. doi:10.3891/acta.chem.scand.48-0800
  • Vanderlee A, Wiegers G, Haas C. Probability density and effective one-particle potential of octahedral Ag in the fast ion conductor Ag0.39TiS2. Solid State Ion. 1992;50:147–158. doi:10.1016/0167-2738(92)90047-S
  • B N, Bolotina TID& NAB. Atomic structure of boron suboxycarbide B(C,O)0.155. Crystallogr Rep. 2001;46:734–740. doi:10.1134/1.1405858
  • Bindi L, Evain M, Pradel A, et al. Fast ion conduction character and ionic phase-transitions in disordered crystals: the complex case of the minerals of the pearceite–polybasite group. Phys Chem Miner. 2006;33:677–690. doi:10.1007/s00269-006-0117-7
  • Sawada H. An electron density residual study of α-ferric oxide. Mater Res Bull. 1996;31:141–146. doi:10.1016/0025-5408(95)00183-2
  • Muraoka Y, Kihara K. The temperature dependence of the crystal structure of berlinite, a quartz-type form of AlPO4. Phys Chem Miner. 1997;24:243–253. doi:10.1007/s002690050036
  • Števko M, Mikuš T, Sejkora J, et al. Argentopolybasite, Ag16Sb2S11, a new member of the polybasite group. Mineral Mag. 2023: 87:1–42.
  • Jarzembska KN, Kamiński R, Durka K, et al. Ground-state charge-density distribution in a crystal of the luminescent ortho -phenylenediboronic acid complex with 8-hydroxyquinoline. J Phys Chem A. 2018;122:4508–4520. doi:10.1021/acs.jpca.8b00832
  • Zubkova NV, Pushcharovsky Du, Ivaldi G, et al. Crystal structure of natrite, gamma-Na2CO3. Neues Jahrbuch Mineral Monatshef. 2002;2002:85–96. doi:10.1127/0028-3649/2002/2002-0085
  • Ghose S, McMullan RK, Weber H-P. Neutron diffraction studies of the P1− → 1− transition in anorthite,: CaAl2Si2O8, and the crystal structure of the body-centered phase at 514 Κ. Z Kristallogr Cryst Mater. 1993;204:215–238.
  • Gougeon P, Gall P, Al Rahal Al Orabi R, et al. Electronic band structure and transport properties of the cluster compound Ag3Tl2Mo15Se19. Inorg Chem. 2019;58:5533–5542. doi:10.1021/acs.inorgchem.8b03452
  • Martin U, Boysen H, Frey F. Neutron powder investigation of tetragonal and cubic stabilized zirconia,: TZP and CSZ, at temperatures up to 1400 K. Acta Crystallogr B. 1993;49:403–413. doi:10.1107/S0108768192011297
  • Sasaki S, Kawaguchi K, Nakao M. Site occupancy and anharmonic thermal vibration in superconductor Tl2CaBa2Cu2O8. Jpn J Appl Phys. 1992;31:L467. doi:10.1143/JJAP.31.L467
  • Kuhs WF, Sänger AT. Structural disorder in hydroxyapatite. Z Kristallogr Cryst Mater. 1992;199:123–148. doi:10.1524/zkri.1992.199.14.123
  • Jannin M, Kolinsky C, Godefroy G, Jannot B, Sorokina NI, Lee DY, Simonov VI, Vronkova VI, Yanoviskii VK, Crystal structures and dielectric properties of compounds in the KTiOPO4-TlTiOPO4 and RbTiOPO4-TlTiOPO4 systems. Eur. J. Solid State Inorg. Chem. 1996. doi:.
  • Boysen H, Frey F, Lerch M, et al. A neutron powder investigation of the high-temperature phase transition in NiTiO3. Z Kristallogr Cryst Mater. 1995;210:328–337. doi:10.1524/zkri.1995.210.5.328
  • Bindi L, Petříček V, Withers RL, et al. A novel high-temperature commensurate superstructure in a natural bariopyrochlore: a structural study by means of a multiphase crystal structure refinement. J Solid State Chem. 2006;179:729–738. doi:10.1016/j.jssc.2005.11.031
  • Radaev SF, Joswig W, Baur WH. Synthesis and precise characterization of large single crystals of as-synthesized CrAPO-5, H2.1[Cr0.08Al11.62P12O48]F1.2 ·1.6TEA. J Mater Chem. 1996;6:1413–1418. doi:10.1039/JM9960601413
  • Retuerto M, Emge T, Hadermann J, et al. Synthesis and properties of charge-ordered thallium halide perovskites, CsTl+0.5Tl3+0.5X3 (X = F or Cl): theoretical precursors for superconductivity? Chemistry of Materials. 2013;25:4071–4079. doi:10.1021/cm402423x
  • Kahlert H, Frey F, Boysen H, et al. Structural investigations of the ionic conductivity in zirconia single crystals by neutron diffraction at high temperatures and simultaneously applied electric field. Ionics (Kiel). 1996;2:88–96. doi:10.1007/BF02375800
  • Salloum D, Gougeon P, Roisnel T, et al. Syntheses and crystal structures of the compounds In3.7Mo15S19, In1.6Rb2Mo15S19, In2.2CsMo15S19 and ScTl2Mo15S19 containing Mo6 and Mo9 clusters. J Alloys Compd. 2004;383:57–62. doi:10.1016/j.jallcom.2004.04.008
  • Rolle A, Giridharan N V, Roussel P, et al. Oxide ion conduction in oxygen rich doped Ba2In2O5+δ brownmillerite. MRS Proc. 2004;835:K2.4. doi:10.1557/PROC-835-K2.4
  • Artioli G, Smith J V, Kvick Å. Multiple hydrogen positions in the zeolite brewsterite,: (Sr0.95,Ba0.05)Al2Si6O16.5H2O. Acta Crystallogr C. 1985;41:492–497. doi:10.1107/S0108270185004401
  • Gougeon P, Gall P, Misra S, et al. Synthesis, crystal structure and transport properties of the cluster compounds Tl2Mo15S19 and Ag3Tl2Mo15S19. Mater Res Bull. 2021;136:111152. doi:10.1016/j.materresbull.2020.111152
  • Henke H, Kuhs WF. The protonated water complex H14O62+. Z Kristallogr Cryst Mater. 1987;181:113–126. doi:10.1524/zkri.1987.181.14.113
  • Desgranges L, Baldinozzi G, Fischer HE, et al. Temperature-dependent anisotropy in the bond lengths of UO2 as a result of phonon-induced atomic correlations. J Phys: Condens Matter. 2023;35:10LT01. doi:10.1088/1361-648X/acaf1d
  • Gougeon P, Salloum D, Potel M. Cr1.45Tl1.87Mo15Se19, a monoclinic variant of the hexagonal In3Mo15Se19 type. Acta Crystallogr C. 2009;65:i87–i90. doi:10.1107/S0108270109047301
  • Rolle A, Roussel P, Giridharan N, et al. A neutron diffraction study of the oxygen diffusion in molybdenum doped Ba2In2O5. Solid State Ion. 2008;179:1986–1995. doi:10.1016/j.ssi.2008.06.021
  • Yude Y, Boysen H, Schulz H. Neutron powder investigation of CuI*. Z Kristallogr. 1990;191:79–91. doi:10.1524/zkri.1990.191.1-2.79
  • Ishizawa N, Tateishi K, Oishi S, et al. Bond-length fluctuation in the orthorhombic 3(3(1 superstructure of LiMn2O4 spinel. Am Mineral. 2014;99:1528–1536. doi:10.2138/am.2014.4840
  • Yaroslavzev AA, Mironov A V, Kuznetsov AN, et al. Tennantite: multi-temperature crystal structure, phase transition and electronic structure of synthetic Cu12As4S13. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2019;75:634–642. doi:10.1107/S2052520619007595
  • Kahlert H, Boysen H, Frey F. Neutron powder investigations of Zr0.85Ca0.15O1.85 sinter material at temperatures up to 1100 K and with a simultaneously applied electric field. J Appl Crystallogr. 1997;30:893–899. doi:10.1107/S0021889896015853
  • Altorfer F, Graneli B, Fischer P, et al. An investigation of anharmonic atomic vibrations of gamma -CuCl and gamma -CuBr by powder neutron diffraction. J Phys: Condens Matter. 1994;6:9949–9962. doi:10.1088/0953-8984/6/46/013
  • Zhang N, Paściak M, Glazer AM, et al. A neutron diffuse scattering study of PbZrO3 and Zr-rich PbZr1–xTixO3. J Appl Crystallogr. 2015;48:1637–1644. doi:10.1107/S1600576715017069
  • Schwarzmüller S, Souchay D, Günther D, et al. Argyrodite-type Cu8GeSe6-xTex (0 ≤ x ≤ 2): temperature-dependent crystal structure and thermoelectric properties. Z Anorg Allg Chem. 2018;644:1915–1922. doi:10.1002/zaac.201800453
  • Schulz H, Perenthaler E, Zucker UH. Anharmonic thermal vibrations and atomic potentials in lead fluoride (β-PbF2) as a function of temperature. Acta Crystallogr Sect A. 1982;38:729–733. doi:10.1107/S0567739482001466
  • Safarik DJ, Klimczuk T, Llobet A, et al. Localized anharmonic rattling of Al atoms in VAl10.1. Phys Rev B. 2012;85:014103. doi:10.1103/PhysRevB.85.014103
  • Grigor’eva NB, Maksimov BA, Sobolev BP. X-ray diffraction study of Ca0.88Gd0.12F2.12 single crystals with a modified fluorite structure. Crystallogr Rep. 2000;45:718–720. doi:10.1134/1.1312907
  • Bessas D, Rushchanskii KZ, Kachlik M, et al. Lattice instabilities in bulk EuTiO3. Phys Rev B. 2013;88:144308. doi:10.1103/PhysRevB.88.144308
  • Brach I, Schulz H. Determination of the diffusion path in the ionic conductor LaF3. Solid State Ion. 1985;15:135–138. doi:10.1016/0167-2738(85)90091-8
  • Takeda S, Zhang Z-G, Moriyoshi C, et al. Structure fluctuation in Gd- and Mg-substituted BaTiO3 with cubic structure. Jpn J Appl Phys. 2017;56:10PB10. doi:10.7567/JJAP.56.10PB10
  • Sulyanova EA, Karimov DN, Sobolev BP. Nanostructured crystals of fluorite phases Sr1−xRxF2+x and their ordering: VIII. imperfect crystal structure of Sr0.71Ce0.29F2.29. Crystallography Reports. 2013;58:678–681. doi:10.1134/S1063774513040202
  • Claiser N, Souhassou M, Lecomte C. Problems in experimental charge density modelling of rare earth atom complexes: the case of gadolinium. J Phys Chem Solids. 2004;65:1927–1933. doi:10.1016/j.jpcs.2004.08.002
  • Jauch W, McIntyre GJ, Schultz AJ. Single-crystal neutron diffraction studies of MnF2 as a function of temperature: the effect of magnetostriction. Acta Crystallogr B. 1990;46:739–742. doi:10.1107/S0108768190008370
  • Fukuda K, Asaka T, Ishizawa N, et al. Combined effect of germanium doping and grain alignment on oxide-ion conductivity of apatite-type lanthanum silicate polycrystal. Chem Mater. 2012;24:2611–2618. doi:10.1021/cm301484q
  • Arakcheeva A V, Grinevich V V, Mitin A V, et al. Crystal structure and resistivity characteristics of new tantalum bronze K6Ta6.5O15+xF6+y. Crystallogr Rep. 2001;46:182–189. doi:10.1134/1.1358390
  • Fukuda K, Asaka T, Hara S, et al. Crystal structure and oxide-ion conductivity of highly grain-aligned polycrystalline lanthanum germanate oxyapatite grown by reactive diffusion between solid La2GeO5 and gases [GeO + 1/2O2 ]. Cryst Growth Des. 2015;15:3435–3441. doi:10.1021/acs.cgd.5b00509
  • Sulyanova EA, Karimov DN, Sobolev BP. Nanostructured crystals of fluorite phases Sr1–xRxF2+x (R are rare-earth elements) and their ordering. 16: defect structure of the nonstoichiometric phases Sr1–xRxF2+x (R = Pr, Tb–Yb) as grown. Crystallograph Report. 2020;65:560–565. doi:10.1134/S1063774520040215
  • Gout D, Gourdon O, Bauer ED, et al. An experimental and theoretical study of the variation of 4f hybridization across the La1−xCexIn3 series. Inorg Chem. 2008;47:2569–2575. doi:10.1021/ic701930j
  • Gout D, Gourdon O, Bauer ED, et al. An experimental and theoretical study of the variation of 4f hybridization across the La1−xCexIn3 series. Inorg Chem. 2008;47:2569–2575. doi:10.1021/ic701930j
  • Bolotina NB, Kalyukanov AI, Chernaya TS, et al. Ordering of tysonite structure in an as-grown Er0.715Ca0.285F2.715 crystal and in a component of annealed two-phase crystal of the Er0.67Ca0.33F2.67 composition. Crystallogr Rep. 2014;59:504–512. doi:10.1134/S1063774514030055
  • Dudka AP, Khrykina ON, Bolotina NB, et al. An exceptionally-high diffraction quality dodecaboride LuB12: growth and single-crystal structure. J Alloys Compd. 2017;692:535–544. doi:10.1016/j.jallcom.2016.09.059
  • van Reeuwijk SJ, van Beek KG, Feil D. Hydrogen bonds in NH4F and NH4HF2 crystals. comparison of electron density distribution obtained by X-ray diffraction and by quantum chemistry. J Phys Chem A. 2000;104:10901–10912. doi:10.1021/jp001747e
  • Sulyanova EA, Molchanov VN, Verin IA, et al. Nanostructured crystals of the fluorite phases Sr1−xRxF2+x (R—rare-earth elements) and their ordering: II. crystal structure of the ordered Sr4Lu3F17 phase. Crystallography Reports. 2009;54:516–525. doi:10.1134/S1063774509030249
  • Belzner A, Schulz H, Heger G. The thermal vibrations and the fluorine ionic conductivity in LaF3. Z Kristallogr Cryst Mater. 1994;209:239–248. doi:10.1524/zkri.1994.209.3.239
  • Blomberg MK, Merisalo MJ, Korsukova MM, et al. Single-crystal X-ray diffraction study of NdB6, EuB6 and YbB6. J Alloys Compd. 1995;217:123–127. doi:10.1016/0925-8388(94)01313-7
  • Sulyanova EA, Karimov DN, Sulyanov SN, et al. Nanostructured crystals of fluorite phases Sr1−xRxF2+x and their ordering: 9. The defect crystal and real structure of quenched fluorite phases Sr1−xCexF2+x (x = 0–0.5). Crystallography Reports. 2014;59:14–21. doi:10.1134/S1063774514010179
  • Makarova IP, Simonov VI, Blomberg MK, et al. X-ray diffraction study of Nd2CuO4 single crystals at 20 K. Acta Crystallogr B. 1996;52:93–99. doi:10.1107/S0108768195009967
  • Palmer A, Jauch W. Charge-density analyses of the antiferromagnets NiF2 and FeF2 by means of γ-ray diffraction. Phys Rev B. 1993;48:10304–10310. doi:10.1103/PhysRevB.48.10304
  • Makarova IP, Bram A, Markl J, et al. Influence of Ce doping on the distribution of the electron density in Nd2−xCexCuO4−δ. Physica C Supercond. 1994;223:1–13. doi:10.1016/0921-4534(94)00040-9
  • Chernaya TS, Bolotina NB, Verin IA, et al. X-ray diffraction study of an as-grown crystal of a two-phase sample of Lu0.65Ca0.35F2.65. Crystallogr Rep. 2014;59:874–877. doi:10.1134/S1063774514060066
  • Bram A, Markl J, Makarova IP, et al. Changes in the distribution of electron density in Nd2−xCexCuO4−y, x = 0.13 during cooldown. Physica C Supercond. 1996;272:209–219. doi:10.1016/S0921-4534(96)00614-4
  • Ivanov Y, Nimura T, Tanaka K. Electron density and electrostatic potential of KMnF3: a phase-transition study. Acta Crystallogr B. 2004;60:359–368. doi:10.1107/S0108768104009437
  • Vasylechko L, Akselrud L, Morgenroth W, et al. The crystal structure of NdGaO3 at 100 and 293 K based on synchrotron data. J Alloys Compd. 2000;297:46–52. doi:10.1016/S0925-8388(99)00603-9
  • Sul’yanova EA, Verin IA, Sobolev BP. Nanostructured crystals of fluorite phases Sr1−xRxF2+x and their ordering: 7. A procedure for cluster modeling of Sr1−xRxF2+x based on the structure of an ordered phase (R = Lu). Crystallograph Report. 2012;57:73–84. doi:10.1134/S1063774512010130
  • Trounov VA, Malyshev AL, Chernyshov DY, et al. Temperature dependences of the parameters of atoms in the crystal structure of the intermediate-valence semiconductor SmB6: investigation by high-resolution powder neutron diffraction. J Phys: Condens Matter. 1993;5:2479–2488. doi:10.1088/0953-8984/5/16/007
  • Bolotina N, Khrykina O, Azarevich A, et al. Fine details of crystal structure and atomic vibrations in YbB12 with a metal–insulator transition. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2020;76:1117–1127. doi:10.1107/S2052520620013566
  • Restori R, Schwarzenbach D. X-Ray diffraction study of the electron density and anharmonicity in K2PtCl6. Z Naturforsch A. 1993;48:12–20. doi:10.1515/zna-1993-1-206
  • Voufack AB, Kibalin I, Yan Z, et al. Spin resolved electron density study of YTiO3 in its ferromagnetic phase: signature of orbital ordering. IUCrJ. 2019;6:884–894. doi:10.1107/S2052252519009230
  • McMullan RK, Ghose S, Haga N, et al. Sodalite, Na4Si3Al3O12Cl: structure and ionic mobility at high temperatures by neutron diffraction. Acta Crystallogr B. 1996;52:616–627. doi:10.1107/S0108768196004132
  • Bolotina NB, Molchanov VN, Dyuzheva TI, et al. Single-crystal structures of high-pressure phases FeOOH, FeOOD, and GaOOH. Crystallogr Rep. 2008;53:960–965. doi:10.1134/S1063774508060084
  • Milašinović V, Vuković V, Krawczuk A, et al. The nature of π-hole interactions between iodide anions and quinoid rings in the crystalline state. IUCrJ. 2023;10:156–163. doi:10.1107/S2052252523000052
  • Farrugia LJ, Evans C. Experimental X-ray charge density studies on the binary carbonyls Cr(CO)6, Fe(CO)5, and Ni(CO)4. J Phys Chem A. 2005;109:8834–8848. doi:10.1021/jp053107n
  • Quilichini M, Bernede P, Lefebvre J, et al. Neutron study of the normal-incommensurate phase transition in K2ZnCl4. J Phys: Condens Matter. 1990;2:4543–4558. doi:10.1088/0953-8984/2/20/001
  • Rabadanov M, Ataev MB. Refinement of the structure of nickel monosilicide crystals. Inorg Mater. 2002;38:120–123. doi:10.1023/A:1014056825562
  • Sparkes HA, Chaplin AB, Weller AS, et al. Bond catastrophes in rhodium complexes: experimental charge-density studies of [Rh(C7H8)(Pt Bu3)Cl] and [Rh(C7H8)(PCy3)Cl]. Acta Crystallogr B. 2010;66:503–514. doi:10.1107/S0108768110031496
  • Pan F, Wang R, Englert U. Competing protonation sites in sulfadiazine: answers from chemistry and electron density. CrystEngComm. 2013;15:1164–1172. doi:10.1039/C2CE26633D
  • Abrahams SC, Ihringer J, Marsh P. Structural and thermal dependence of normal-mode condensations in K2TeBr6. Acta Crystallogr B. 1989;45:26–34. doi:10.1107/S0108768188010493
  • Eklöf D, Fischer A, Ektarawong A, et al. Mysterious SiB3: identifying the relation between α- and ββ-SiB3. ACS Omega. 2019;4:18741–18759. doi:10.1021/acsomega.9b02727
  • Thornley FR, Kennedy NSJ, Nelmes RJ. Structural studies of boracites. IV. Thermal motion in cubic Ni3B7O13 I at 77 K. J Phys C Solid State Phys. 1976;9:681–692. doi:10.1088/0022-3719/9/5/010
  • Gourdon O, Petricek V, Dusek M, et al. Determination of the modulated structure of Sr14/11CoO3 through a (3 + 1)-dimensional space description and using non-harmonic ADPs. Acta Crystallogr B. 1999;55:841–848. doi:10.1107/S0108768199006485
  • Sawada H. The crystal structure of garnets (I): the residual electron density distribution in pyrope. Z Kristallogr Cryst Mater. 1993;203:41–48. doi:10.1524/zkri.1993.203.Part-1.41
  • Podberezskaya N V, Bolotina NB, Komarov V, et al. Orthorhombic YBaCo4O8.4 crystals as a result of saturation of hexagonal YBaCo4O7 crystals with oxygen. Crystallogr Rep. 2015;60:484–492. doi:10.1134/S1063774515040161
  • Artioli G, Pavese A, Stahl K, et al. Single-crystal neutron-diffraction study of pyrope in the temperature range 30-1173 K. Canadian Mineral. 1997;35:1009–1997.
  • Alekseeva OA, Verin IA, Dudka AP, et al. Single-crystal structure of Nd5Mo3O16 at T = 30 K. Crystallogr Rep. 2013;58:568–574. doi:10.1134/S1063774513040032
  • Bell DR, Ihinger PD, Rossman GR. Quantitative analysis of trace OH in garnet and pyroxenes. Am Mineral. 1995;80:465–474. doi:10.2138/am-1995-5-607
  • Antipin AM, Alekseeva OA, Sorokina NI, et al. Single-crystal structure of vanadium-doped Nd5Mo3O16. Crystallogr Rep. 2014;59:141–145. doi:10.1134/S1063774514020047
  • Antipin AM, Sorokina NI, Alekseeva OA, et al. Structure of fluorite-like compound based on Nd5Mo3O16 with lead partly substituting for neodymium. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2015;71:186–193. doi:10.1107/S2052520615003315
  • Arakcheeva A V, Grinevich V V, Chapuis G, et al. Structure studies of solid solutions of oxygen in electrolytic niobium. Crystallogr Rep. 2002;47:237–244. doi:10.1134/1.1466499
  • Sawada H. An electron density residual study of magnesium aluminum oxide spinel. Mater Res Bull. 1995;30:341–345. doi:10.1016/0025-5408(95)00010-0
  • Terlan B, Akselrud L, Baranov AI, et al. Experimental QTAIM analysis of the electron density in TiB2. Z Anorg Allg Chem. 2013;639:2065–2070. doi:10.1002/zaac.201200524
  • Sawada H. Electron density study of spinels: magnesium gallium oxide. Mater Res Bull. 1996;31:367–371. doi:10.1016/0025-5408(96)00009-8
  • Alekseeva OA, Sorokina NI, Verin IA, et al. Synthesis and X-ray diffraction study of K2.92Nb2.58Ti1.42P2.5O17 single crystals. Crystallogr Rep. 2001;46:741–747. doi:10.1134/1.1405859
  • Takazawa H, Ohba S, Saito Y, et al. Electron-density distribution in crystals of K2[MCl6](M = Re, Os, Pt) and K2[PtCl4] at 120 K. Acta Crystallogr B. 1990;46:166–174. doi:10.1107/S0108768189012693
  • Sawada H, Marumo F, Kodama N. Crystal structure study of (Ca,Gd)2(Al, Ti)O4. J Solid State Chem. 1998;139:204–206. doi:10.1006/jssc.1998.7830
  • Seidel S, Schubert L, Hoffmann R-D, et al. Centrosymmetric LaRh2Ga2. Z Kristallogr Cryst Mater. 2020;235:41–46. doi:10.1515/zkri-2019-0074
  • Dudka AP, Mill B V. Crystal structure refinement of Sr3TaGa3Si2O14. Crystallogr Rep. 2011;56:443–450. doi:10.1134/S1063774511020064
  • Farrugia LJ, Senn HM. On the unusual weak intramolecular C … C interactions in Ru3(CO)12: a case of bond path artifacts introduced by the multipole model? J Phys Chem A. 2012;116:738–746. doi:10.1021/jp2100039
  • Dudka AP, Mill B V. Crystal-structure refinement of Sr3Ga2Ge4O14. Crystallogr Rep. 2012;57:49–56. doi:10.1134/S1063774511030084
  • Arakcheeva A, Chapuis G, Grinevitch V. The self-hosting structure of ββ-Ta. Acta Crystallogr B. 2002;58:1–7. doi:10.1107/S0108768101017918
  • Deniard P, Caldes MT, Zou XD, et al. Structural modulation in Sr1.4Ta0.6O2.9: non-harmonicity on ADPs during Rietveld refinement. Int J Inorg Mater. 2001;3:1121–1123. doi:10.1016/S1466-6049(01)00111-8
  • Terlan B, Akselrud L, Baranov AI, et al. On the transferability of electron density in binary vanadium borides VB, V3B4 and VB2. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2015;71:777–787. doi:10.1107/S2052520615018363
  • Evain M, Boucher F, Gourdon O, et al. Incommensurate versus commensurate description of the AxBX3 hexagonal perovskite-type structure. Sr1.2872NiO3 incommensurate composite compound example. Chem Mater. 1998;10:3068–3076. doi:10.1021/cm9801800
  • Abrahams SC, Marsh P, Ravez J. Coupling of ferroelasticity to ferroelectricity in Na5W3O9F5 and the structure at 295 K. Acta Crystallogr B. 1989;45:364–370. doi:10.1107/S0108768189004805
  • Jauch W, Reehuis M. Electron-density distribution in cubic SrTiO3: a comparative γ-ray diffraction study. Acta Crystallogr A. 2005;61:411–417. doi:10.1107/S0108767305013231
  • Sawada H. Residual electron density study of α-aluminum oxide through refinement of experimental atomic scattering factors. Mater Res Bull. 1994;29:127–133. doi:10.1016/0025-5408(94)90132-5
  • Baldinozzi G, Dutheil M, Simeone D, et al. Charge density in disordered boron carbide: B12C3. An experimental and ab-initio study. MRS Proc. 2002;730:V7.4. doi:10.1557/PROC-730-V7.4
  • Bubnova R, Volkov S, Albert B, et al. Borates—crystal structures of prospective nonlinear optical materials: high anisotropy of the thermal expansion caused by anharmonic atomic vibrations. Crystals (Basel). 2017;7:93. doi:10.3390/cryst7030093
  • Tsirelson V, Stash A, Kohout M, et al. Features of the electron density in magnesium diboride: reconstruction from X-ray diffraction data and comparison with TB-LMTO and FPLO calculations. Acta Crystallogr B. 2003;59:575–583. doi:10.1107/S0108768103012072
  • Laval J-P, Mayet R, Mikou A. Cationic ordering in tysonite type structures: II: Crystal structure of α-, β- and γ-baryum hexafluoridouranates (IV). J Fluor Chem. 2017;193:126–135. doi:10.1016/j.jfluchem.2016.11.002
  • Kasai H, Nishibori E. Spatial distribution of electrons near the Fermi level in the metallic LaB6 through accurate X-ray charge density study. Sci Rep. 2017;7:41375. doi:10.1038/srep41375
  • Friese K, Morgenroth W, Posse JM, et al. Disorder in BaThF6 – refinement of anharmonic displacement parameters from high-pressure single-crystal X-ray diffraction data. Dalton Trans. 2011;40:1902. doi:10.1039/c0dt00924e
  • Larsen FK, Lehmann MS, Merisalo M. Mean-square atomic displacement and antisymmetric atomic vibrations in beryllium at room temperature determined from short-wavelength neutron data. Acta Crystallograph Sect A. 1980;36:159–163. doi:10.1107/S0567739480000356
  • Iversen BB, Larsen FK, Souhassou M, et al. Experimental evidence for the existence of non-nuclear maxima in the electron-density distribution of metallic beryllium. A comparative study of the maximum entropy method and the multipole refinement method. Acta Crystallogr B. 1995;51:580–591. doi:10.1107/S0108768194010360
  • Bentien A, Iversen BB, Bryan JD, et al. Maximum entropy method analysis of thermal motion and disorder in thermoelectric clathrate Ba8Ga16Si. J Appl Phys. 2002;91:5694–5699. doi:10.1063/1.1466531
  • Sovago I, Gutmann MJ, Hill JG, et al. Experimental electron density and neutron diffraction studies on the polymorphs of sulfathiazole. Cryst Growth Des. 2014;14:1227–1239. doi:10.1021/cg401757z
  • Chernaya TS, Verin IA, Khrykina ON, et al. Defect structures of La1–ySryF3–y, La1–yBayF3–y, and Nd1–yCayF3–y (y = 0.05, 0.10) nonstoichiometric tysonite phases. Crystallogr Report. 2018;63:45–51. doi:10.1134/S1063774518010042
  • Sist M, Zhang J, Brummerstedt Iversen B. Crystal structure and phase transition of thermoelectric SnSe. Acta Crystallogr B Struct Sci Cryst Eng Mater. 2016;72:310–316. doi:10.1107/S2052520616003334
  • Sasaki S, Inoue Z, Iyi N, et al. Electron density study of YBa2Cu3O6+δ. Acta Crystallogr B. 1992;48:393–400. doi:10.1107/S0108768192000405
  • Sist M, Jensen Hedegaard EM, Christensen S, et al. Carrier concentration dependence of structural disorder in thermoelectric Sn1−xTe. IUCrJ. 2016;3:377–388. doi:10.1107/S2052252516012707
  • Yamanaka T, Ahart M, Nakamoto Y, et al. Anharmonic atomic vibrations in the relaxor ferroelectric Pb(Mg1/3Nb2/3)O3 under pressure. Phys Rev B. 2012;86:174108. doi:10.1103/PhysRevB.86.174108
  • Dudka AP, Golovina TG, Konstantinova AF. Search for helices of atomic electron density as a structural basis of optical activity in α-TeO2 crystal. Crystallogr Rep. 2019;64:937–941. doi:10.1134/S106377451906004X
  • Zubkova NV, Pushcharovsky D, Giester G, et al. The crystal structure of arsentsumebite, Pb2Cu[(As,S)O4]2(OH). Mineral Petrol. 2002;75:79–88. doi:10.1007/s007100200016
  • Yamanaka T, Morimoto S. Isotope effect on anharmonic thermal atomic vibration and κ refinement of 12C and 3C diamond. Acta Crystallogr B. 1996;52:232–238. doi:10.1107/S0108768195010810
  • Noda S, Yokoi Y, Nakahira Y, et al. Structural fluctuation of Pb(Mg1/3Nb2/3)O3 in the cubic phase. Jpn J Appl Phys. 2019;58:SLLA06. doi:10.7567/1347-4065/ab0784
  • Baldinozzi G, Raulot J-M, Seshadri R. Lead stereochemistry in incommensurate ferroelectric perovskites and in incommensurate lead monoxide. MRS Proceedings. 2002;718:D12.7. doi:10.1557/PROC-718-D12.7
  • Saravanan R, Mohanlal SK, Chandrasekaran KS. Anharmonic temperature factors, anomalous-dispersion effects and bonding charges in gallium arsenide. Acta Crystallogr A. 1992;48:4–9. doi:10.1107/S0108767391005512
  • Abrahams SC, Albertsson J, Svensson C, et al. Structure of Pb5Cr3F19 at 295 K, polarization reversal and the 555 K phase transition. Acta Crystallogr B. 1990;46:497–502. doi:10.1107/S0108768190004256
  • Dudka AP, Simonov VI. Structural conditionality of the piezoelectric properties of langasite family crystals. Crystallogr Rep. 2011;56:980–985. doi:10.1134/S1063774511060058
  • Kastbjerg S, Bindzus N, Søndergaard M, et al. Direct evidence of cation disorder in thermoelectric lead chalcogenides PbTe and PbS. Adv Funct Mater. 2013;23:5477–5483. doi:10.1002/adfm.201300722
  • Haarmann F, Jacobs H, Reehuis M, et al. Anharmonicity of potentials of atoms in potassium hydrogensulfide (KDS) determined by neutron single-crystal diffraction. Acta Crystallogr B. 2000;56:988–992. doi:10.1107/S0108768100011952
  • Grey IE, Mumme WG, Bordet P, et al. A new crystal-chemical variation of the alunite-type structure in monoclinic PbZn0.5Fe3(AsO4)2(OH)6. Canadian Mineral. 2008;46:1355–1364. doi:10.3749/canmin.46.5.1355
  • Desgranges L, Calvarin G, Chevrier G. Interlayer interactions in M(OH)2: a neutron diffraction study of Mg(OH)2. Acta Crystallogr B. 1996;52:82–86. doi:10.1107/S0108768195008275
  • Desgranges L, Grebille D, Calvarin G, et al. Hydrogen thermal motion in calcium hydroxide: Ca(OH)2. Acta Crystallogr B. 1993;49:812–817. doi:10.1107/S0108768193003556
  • Robl C, Kuhs WF. Alkaline-earth squarates. J Solid State Chem. 1988;73:172–178. doi:10.1016/0022-4596(88)90066-7
  • Abrahams SC, Marsh P, Bridenbaugh PM. Atomic substitution in Cd1−xMnxTe for 0.1 < x < 0.4. Acta Crystallogr C. 1989;45:545–548. doi:10.1107/S010827018801296X
  • Hasegawa R, Okabe M, Asaka T, et al. Structure and ionic conductivity of well-aligned polycrystalline sodium titanogallate grown by reactive diffusion. J Solid State Chem. 2015;229:252–259. doi:10.1016/j.jssc.2015.06.005
  • Belik AA, Mironov AV, Shpanchenko RV, et al. The high-pressure form of cadmium vanadate, CdV2O6. Acta Crystallogr C. 2007;63:i37–i39. doi:10.1107/S0108270107017623
  • Carrillocabrera W, Thomas J, Farrington G. The ionic distribution in trivalent Gd3+ ββ″-alumina. Solid State Ion 1983;9–10:245–248. doi:10.1016/0167-2738(83)90241-2
  • Boucher F, Evain M, Brec R. Second-order Jahn—Teller effect in CdPS3 and ZnPS3 demonstrated by a non-harmonic behaviour of Cd2+ and Zn2+ d10 ions. J Alloys Compd. 1994;215:63–70. doi:10.1016/0925-8388(94)90819-2
  • Fischer A, Scheidt E-W, Scherer W, et al. Thermal and vibrational properties of thermoelectric ZnSb: exploring the origin of low thermal conductivity. Phys Rev B. 2015;91:224309. doi:10.1103/PhysRevB.91.224309
  • Yamanaka T, Tokonami M. The anharmonic thermal vibration in ZnX (X = S, Se, Te) and its dependence on the chemical-bond characters. Acta Crystallogr B. 1985;41:298–304. doi:10.1107/S010876818500218X
  • Volkov SN, Charkin DO, Bubnova RS. Structural changes of AgBi2B5O11 in the range of 100 to 400 K. Glass Phys Chem. 2021;47:70–73. doi:10.1134/S1087659621010144
  • Aksenov SM, Yamnova NA, Borovikova E, et al. Bi3(PO4)O3, the simplest bismuth(III) oxophosphate: synthesis, IR spectroscopy, crystal structure, and structural complexity. Inorg Chem. 2018;57:6799–6802. doi:10.1021/acs.inorgchem.8b01195
  • YuA A, Reznik IM, Tsirelson VG, et al. Chemical bonding and Bi atom anharmonicity in Ba0.87K0.13BiO3 crystal. Physica C Supercond. 1995;254:189–192. doi:10.1016/0921-4534(95)00548-X
  • Aurivillius B, Glaum R, Gruehn R, et al. Crystal structure of [Bi13 1/3[]2/3 Cu2O16](SO4)6. Acta Chem Scand. 1991;45:769–774. doi:10.3891/acta.chem.scand.45-0769
  • Dudka AP, Mill’ B V. Accurate crystal-structure refinement of Ca3Ga2Ge4O14 at 295 and 100 K and analysis of the disorder in the atomic positions. Crystallogr Rep. 2013;58:594–603. doi:10.1134/S1063774513040081
  • Schulz H. Relations between crystal structures and ionic conductivity. The physics of superionic conductors and electrode materials. Boston (MA): Springer US; 1983. p. 5–26.
  • Bachmann R, Schulz H. Anharmonic potentials and pseudo potentials in ordered and disordered crystals. Acta Crystallogr A. 1984;40:668–675. doi:10.1107/S0108767384001379
  • Nelmes RJ, Tun Z. Determining skewness in atomic probability density functions for non-centrosymmetric structures. Acta Crystallogr A. 1987;43:635–638. doi:10.1107/S0108767387098805
  • Bürgi HB, Capelli SC, Birkedal H. Anharmonicity in anisotropic displacement parameters. Acta Crystallogr A. 2000;56:425–435. doi:10.1107/S0108767300008734
  • Shu-Ping H, Dong-Sheng W, Xiao-Dong L, et al. Band structures, chemical bonding and frequency-dependent optical properties of nonlinear optical crystals HgGa2S4 and Hg0.5Cd0.5Ga2S4. Chin Phys. 2005;14:1631–1638. doi:10.1088/1009-1963/14/8/030

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