Exploring the Effect of V2O5 and Nb2O5 Content on the Structural, Thermal, and Electrical Characteristics of Sodium Phosphate Glasses and Glass-Ceramics
Language English Country Switzerland Media electronic
Document type Journal Article
Grant support
IP-2018-01-5425
Croatian Science Foundation
DOK-2021-02-9665
Croatian Science Foundation
PubMed
38474252
PubMed Central
PMC10932346
DOI
10.3390/ijms25053005
PII: ijms25053005
Knihovny.cz E-resources
- Keywords
- (micro)structure–property relationship, EPR, PXRD, SEM-EDS, electrical properties, impedance spectroscopy, phosphate glasses, phosphate glass–ceramics, vibrational spectroscopy,
- MeSH
- Electron Spin Resonance Spectroscopy MeSH
- Phosphates * chemistry MeSH
- Ions MeSH
- Ceramics chemistry MeSH
- Niobium * MeSH
- Glass chemistry MeSH
- Sodium chemistry MeSH
- Publication type
- Journal Article MeSH
- Names of Substances
- Phosphates * MeSH
- Ions MeSH
- Niobium * MeSH
- Sodium MeSH
- sodium phosphate MeSH Browser
- sodium polymetaphosphate MeSH Browser
Na-V-P-Nb-based materials have gained substantial recognition as cathode materials in high-rate sodium-ion batteries due to their unique properties and compositions, comprising both alkali and transition metal ions, which allow them to exhibit a mixed ionic-polaronic conduction mechanism. In this study, the impact of introducing two transition metal oxides, V2O5 and Nb2O5, on the thermal, (micro)structural, and electrical properties of the 35Na2O-25V2O5-(40 - x)P2O5 - xNb2O5 system is examined. The starting glass shows the highest values of DC conductivity, σDC, reaching 1.45 × 10-8 Ω-1 cm-1 at 303 K, along with a glass transition temperature, Tg, of 371 °C. The incorporation of Nb2O5 influences both σDC and Tg, resulting in non-linear trends, with the lowest values observed for the glass with x = 20 mol%. Electron paramagnetic resonance measurements and vibrational spectroscopy results suggest that the observed non-monotonic trend in σDC arises from a diminishing contribution of polaronic conductivity due to the decrease in the relative number of V4+ ions and the introduction of Nb2O5, which disrupts the predominantly mixed vanadate-phosphate network within the starting glasses, consequently impeding polaronic transport. The mechanism of electrical transport is investigated using the model-free Summerfield scaling procedure, revealing the presence of mixed ionic-polaronic conductivity in glasses where x < 10 mol%, whereas for x ≥ 10 mol%, the ionic conductivity mechanism becomes prominent. To assess the impact of the V2O5 content on the electrical transport mechanism, a comparative analysis of two analogue series with varying V2O5 content (10 and 25 mol%) is conducted to evaluate the extent of its polaronic contribution.
Department of Chemistry Faculty of Science University of Zagreb Horvatovac 102a 10000 Zagreb Croatia
Department of Physics Faculty of Science University of Zagreb Bijenička 32 10000 Zagreb Croatia
Division of Materials Chemistry Ruđer Bošković Institute Bijenička 54 10000 Zagreb Croatia
See more in PubMed
Singh: A.N., Islam M., Meena A., Faizan M., Han D., Bathula C., Hajibabaei A., Anand R., Nam K.-W. Unleashing the Potential of Sodium-Ion Batteries: Current State and Future Directions for Sustainable Energy Storage. Adv. Funct. Mater. 2023;33:2304617. doi: 10.1002/adfm.202304617. DOI
Zhao C., Liu L., Qi X., Lu Y., Wu F., Zhao J., Yu Y., Hu Y.-S., Chen L. Solid-State Sodium Batteries. Adv. Energy Mater. 2018;8:1703012. doi: 10.1002/aenm.201703012. DOI
Austin I.G., Mott N.F. Polarons in Crystalline and Non-Crystalline Materials. Adv. Phys. 1969;18:41–102. doi: 10.1080/00018736900101267. DOI
Thirupathi R., Kumari V., Chakrabarty S., Omar S. Recent Progress and Prospects of NASICON Framework Electrodes for Na-Ion Batteries. Prog. Mater. Sci. 2023;137:101128. doi: 10.1016/j.pmatsci.2023.101128. DOI
Zhou Q., Wang L., Li W., Zhao K., Liu M., Wu Q., Yang Y., He G., Parkin I.P., Shearing P.R., et al. Sodium Superionic Conductors (NASICONs) as Cathode Materials for Sodium-Ion Batteries. Electrochem. Energy Rev. 2021;4:793–823. doi: 10.1007/s41918-021-00120-8. DOI
Novikova S.A., Larkovich R.V., Chekannikov A.A., Kulova T.L., Skundin A.M., Yaroslavtsev A.B. Electrical Conductivity and Electrochemical Characteristics of Na3V2(PO4)3-Based NASICON-Type Materials. Inorg. Mater. 2018;54:794–804. doi: 10.1134/S0020168518080149. DOI
Zheng W., Gao R., Zhou T., Huang X. Enhanced Electrochemical Performance of Na3V2(PO4)3 with Ni2+ Doping by a Spray Drying-Assisted Process for Sodium Ion Batteries. Solid State Ion. 2018;324:183–190. doi: 10.1016/j.ssi.2018.07.006. DOI
Liu X., Feng G., Wu Z., Yang Z., Yang S., Guo X., Zhang S., Xu X., Zhong B., Yamauchi Y. Enhanced Sodium Storage Property of Sodium Vanadium Phosphate via Simultaneous Carbon Coating and Nb5+ Doping. Chem. Eng. J. 2020;386:123953. doi: 10.1016/j.cej.2019.123953. DOI
Bi L., Liu X., Li X., Chen B., Zheng Q., Xie F., Huo Y., Lin D. Modulation of the Crystal Structure and Ultralong Life Span of a Na3V2(PO4)3-Based Cathode for a High-Performance Sodium-Ion Battery by Niobium–Vanadium Substitution. Ind. Eng. Chem. Res. 2020;59:21039–21046. doi: 10.1021/acs.iecr.0c04187. DOI
Rao X., Wang J., Yang M.-A., Zhao H., Li Z. A Superior Na3V2(PO4)3-Based Cathode Enhanced by Nb-Doping for High-Performance Sodium-Ion Battery. APL Mater. 2022;10:010701. doi: 10.1063/5.0074325. DOI
Li X., Huang Y., Wang J., Miao L., Li Y., Liu Y., Qiu Y., Fang C., Han J., Huang Y. High Valence Mo-Doped Na3V2(PO4)3/C as a High Rate and Stable Cycle-Life Cathode for Sodium Battery. J. Mater. Chem. A. 2018;6:1390–1396. doi: 10.1039/C7TA08970H. DOI
Sun S., Chen Y., Cheng J., Tian Z., Wang C., Wu G., Liu C., Wang Y., Guo L. Constructing Dimensional Gradient Structure of Na3V2(PO4)3/C@CNTs-WC by Wolfram Substitution for Superior Sodium Storage. Chem. Eng. J. 2021;420:130453. doi: 10.1016/j.cej.2021.130453. DOI
Gandi S., Chidambara Swamy Vaddadi V.S., Sripada Panda S.S., Goona N.K., Parne S.R., Lakavat M., Bhaumik A. Recent Progress in the Development of Glass and Glass-Ceramic Cathode/Solid Electrolyte Materials for next-Generation High Capacity All-Solid-State Sodium-Ion Batteries: A Review. J. Power Sources. 2022;521:230930. doi: 10.1016/j.jpowsour.2021.230930. DOI
Wang Z., Luo S., Zhang X., Guo S., Li P., Yan S. Glass and Glass Ceramic Electrodes and Solid Electrolyte Materials for Lithium Ion Batteries: A Review. J. Non-Cryst. Solids. 2023;619:122581. doi: 10.1016/j.jnoncrysol.2023.122581. DOI
Wasiucionek M., Garbarczyk J., Kurek P., Jakubowski W. Electrical Properties of Glasses of the Na2O-V2O5-P2O5 System. Solid State Ion. 1994;70–71:346–349. doi: 10.1016/0167-2738(94)90334-4. DOI
Ungureanu M.C., Lévy M., Souquet J.L. Mixed Conductivity of Glasses in the P2O5-V2O5-Na2O System. Ionics. 1998;4:200–206. doi: 10.1007/BF02375946. DOI
Barczyński R.J., Murawski L. Mixed Electronic-Ionic Conductivity in Vanadate Oxide Glasses Containing Alkaline Ions. Mater. Sci. Pol. 2006;24:221–227.
Barczyński R.J., Król P., Murawski L. Ac and Dc Conductivities in V2O5–P2O5 Glasses Containing Alkaline Ions. J. Non-Cryst. Solids. 2010;356:1965–1967. doi: 10.1016/j.jnoncrysol.2010.07.001. DOI
Garbarczyk J.E., Wasiucionek M., Jóźwiak P., Tykarski L., Nowiński J.L. Studies of Li2O–V2O5–P2O5 Glasses by DSC, EPR and Impedance Spectroscopy. Solid State Ion. 2002;154–155:367–373. doi: 10.1016/S0167-2738(02)00574-X. DOI
Jozwiak P., Garbarczyk J.E. Mixed Electronic–Ionic Conductivity in the Glasses of the Li2O–V2O5–P2O5 System. Solid State Ion. 2005;176:2163–2166. doi: 10.1016/j.ssi.2004.06.028. DOI
Takahashi H., Karasawa T., Sakuma T., Garbarczyk J.E. Electrical Conduction in the Vitreous and Crystallized Li2O–V2O5–P2O5 System. Solid State Ion. 2010;181:27–32. doi: 10.1016/j.ssi.2009.12.001. DOI
Renka S., Pavić L., Tricot G., Mošner P., Koudelka L., Moguš-Milanković A., Šantić A. A Significant Enhancement of Sodium Ion Conductivity in Phosphate Glasses by Addition of WO3 and MoO3: The Effect of Mixed Conventional–Conditional Glass-Forming Oxides. Phys. Chem. Chem. Phys. 2021;23:9761–9772. doi: 10.1039/D1CP00498K. PubMed DOI
Kubuki S., Osouda K., Ali A.S., Khan I., Zhang B., Kitajou A., Okada S., Okabayashi J., Homonnay Z., Kuzmann E., et al. 57Fe-Mössbauer and XAFS Studies of Conductive Sodium Phospho-Vanadate Glass as a Cathode Active Material for Na-Ion Batteries with Large Capacity. J. Non-Cryst. Solids. 2021;570:120998. doi: 10.1016/j.jnoncrysol.2021.120998. DOI
Pavić L., Šantić A., Nikolić J., Mošner P., Koudelka L., Pajić D., Moguš-Milanković A. Nature of Mixed Electrical Transport in Ag2O–ZnO–P2O5 Glasses Containing WO3 and MoO3. Electrochim. Acta. 2018;276:434–445. doi: 10.1016/j.electacta.2018.04.029. DOI
Nikolić J., Pavić L., Šantić A., Mošner P., Koudelka L., Pajić D., Moguš-Milanković A. Novel Insights into Electrical Transport Mechanism in Ionic-Polaronic Glasses. J. Am. Ceram. Soc. 2018;101:1221–1235. doi: 10.1111/jace.15271. DOI
Šantić A., Nikolić J., Pavić L., Banhatti R.D., Mošner P., Koudelka L., Moguš-Milanković A. Scaling Features of Conductivity Spectra Reveal Complexities in Ionic, Polaronic and Mixed Ionic-Polaronic Conduction in Phosphate Glasses. Acta Mater. 2019;175:46–54. doi: 10.1016/j.actamat.2019.05.067. DOI
Marijan S., Razum M., Klaser T., Mošner P., Koudelka L., Skoko Ž., Pisk J., Pavić L. Tailoring Structure for Improved Sodium Mobility and Electrical Properties in V2O5–Nb2O5–P2O5 Glass(Es)-(Ceramics) J. Phys. Chem. Solids. 2023;181:111461. doi: 10.1016/j.jpcs.2023.111461. DOI
Chowdari B.V.R., Radhakrishnan K. Electrical and Electrochemical Characterization of Li2O:P2O5:Nb2O5-Based Solid Electrolytes. J. Non-Cryst. Solids. 1989;110:101–110. doi: 10.1016/0022-3093(89)90187-7. DOI
Flambard A., Videau J.J., Delevoye L., Cardinal T., Labrugère C., Rivero C.A., Couzi M., Montagne L. Structure and Nonlinear Optical Properties of Sodium–Niobium Phosphate Glasses. J. Non-Cryst. Solids. 2008;354:3540–3547. doi: 10.1016/j.jnoncrysol.2008.03.017. DOI
Honma T., Okamoto M., Togashi T., Ito N., Shinozaki K., Komatsu T. Electrical Conductivity of Na2O–Nb2O5–P2O5 Glass and Fabrication of Glass–Ceramic Composites with NASICON Type Na3Zr2Si2PO12. Solid State Ion. 2015;269:19–23. doi: 10.1016/j.ssi.2014.11.009. DOI
Benyounoussy S., Bih L., Muñoz F., Rubio-Marcos F., Naji M., El Bouari A. Structure, Dielectric, and Energy Storage Behaviors of the Lossy Glass-Ceramics Obtained from Na2O-Nb2O5-P2O5 Glassy-System. Phase Transit. 2021;94:634–650. doi: 10.1080/01411594.2021.1949458. DOI
Senapati A., Barik S.K., Venkata Krishnan R., Chakraborty S., Jena H. Studies on Synthesis, Structural and Thermal Properties of Sodium Niobium Phosphate Glasses for Nuclear Waste Immobilization Applications. J. Therm. Anal. Calorim. 2023;148:355–369. doi: 10.1007/s10973-022-11760-3. DOI
Mošner P., Hostinský T., Koudelka L. Thermal, Structural and Crystallization Study of Na2O–P2O5–Nb2O5 Glasses. J. Solid State Chem. 2022;316:123545. doi: 10.1016/j.jssc.2022.123545. DOI
Koudelka L., Kalenda P., Mošner P., Montagne L., Revel B. Potassium Niobato-Phosphate Glasses and Glass-Ceramics. J. Non-Cryst. Solids. 2021;572:121091. doi: 10.1016/j.jnoncrysol.2021.121091. DOI
Lide D.R., editor. CRC Handbook of Chemistry and Physics. CRC Press; Boca Raton, FL, USA: 2005. Bond Strengths in Diatomic Molecules. Internet Version 2005.
Bih L., Azrour M., Manoun B., Graça M.P.F., Valente M.A. Raman Spectroscopy, X-Ray, SEM, and DTA Analysis of Alkali-Phosphate Glasses Containing WO3 and Nb2O5. J. Spectrosc. 2013;2013:123519. doi: 10.1155/2013/123519. DOI
Zheng Q., Zhang Y., Montazerian M., Gulbiten O., Mauro J.C., Zanotto E.D., Yue Y. Understanding Glass through Differential Scanning Calorimetry. Chem. Rev. 2019;119:7848–7939. doi: 10.1021/acs.chemrev.8b00510. PubMed DOI
Craig D.C., Stephenson N.C. The Structure of the Bronze Na13Nb35O94 and the Geometry of Ferroelectric Domains. J. Solid State Chem. 1971;3:89–100. doi: 10.1016/0022-4596(71)90012-0. DOI
Benyounoussy S., Bih L., Muñoz F., Rubio-Marcos F., EL Bouari A. Effect of the Na2O–Nb2O5–P2O5 Glass Additive on the Structure, Dielectric and Energy Storage Performances of Sodium Niobate Ceramics. Heliyon. 2021;7:e07113. doi: 10.1016/j.heliyon.2021.e07113. PubMed DOI PMC
Razum M., Pavić L., Ghussn L., Moguš-Milanković A., Šantić A. Transport of Potassium Ions in Niobium Phosphate Glasses. J. Am. Ceram. Soc. 2021;104:4669–4678. doi: 10.1111/jace.17882. DOI
Rambo C.R., Ghussn L., Sene F.F., Martinelli J.R. Manufacturing of Porous Niobium Phosphate Glasses. J. Non-Cryst. Solids. 2006;352:3739–3743. doi: 10.1016/j.jnoncrysol.2006.03.104. DOI
Attafi Y., Liu S. Conductivity and Dielectric Properties of Na2O-K2O-Nb2O5-P2O5 Glasses with Varying Amounts of Nb2O5. J. Non-Cryst. Solids. 2016;447:74–79. doi: 10.1016/j.jnoncrysol.2016.05.038. DOI
Wang B., Greenblatt M., Yan J. Ionic Conductivities of Crystalline and Glassy Na4NbP3O12 and Crystalline Na6Nb2P6O23. Solid State Ionics. 1994;69:85–89. doi: 10.1016/0167-2738(94)90454-5. DOI
Chu C.M., Wu J.J., Yung S.W., Chin T.S., Zhang T., Wu F.B. Optical and Structural Properties of Sr–Nb–Phosphate Glasses. J. Non-Cryst. Solids. 2011;357:939–945. doi: 10.1016/j.jnoncrysol.2010.12.009. DOI
Iordanova R., Milanova M., Aleksandrov L., Shinozaki K., Komatsu T. Structural Study of WO3-La2O3-B2O3-Nb2O5 Glasses. J. Non-Cryst. Solids. 2020;543:120132. doi: 10.1016/j.jnoncrysol.2020.120132. DOI
Karam L., Adamietz F., Rodriguez V., Bondu F., Lepicard A., Cardinal T., Fargin E., Richardson K., Dussauze M. The Effect of the Sodium Content on the Structure and the Optical Properties of Thermally Poled Sodium and Niobium Borophosphate Glasses. J. Appl. Phys. 2020;128:043106. doi: 10.1063/5.0013383. DOI
Teixeira Z., Alves O.L., Mazali I.O. Structure, Thermal Behavior, Chemical Durability, and Optical Properties of the Na2O–Al2O3–TiO2–Nb2O5–P2O5 Glass System. J. Am. Ceram. Soc. 2007;90:256–263. doi: 10.1111/j.1551-2916.2006.01399.x. DOI
Chrissanthopoulos A., Pouchan C., Papatheodorou G.N. Structural Investigation of Vanadium-Sodium Metaphosphate Glasses. Zeitschrift für Naturforschung A. 2001;56:773–776. doi: 10.1515/zna-2001-1114. DOI
Hejda P., Holubová J., Černošek Z., Černošková E. The Structure and Properties of Vanadium Zinc Phosphate Glasses. J. Non-Cryst. Solids. 2017;462:65–71. doi: 10.1016/j.jnoncrysol.2017.02.012. DOI
Du M., Huang K., Guo Y., Xie Z., Jiang H., Li C., Chen Y. High Specific Capacity Lithium Ion Battery Cathode Material Prepared by Synthesizing Vanadate–Phosphate Glass in Reducing Atmosphere. J. Power Sources. 2019;424:91–99. doi: 10.1016/j.jpowsour.2019.03.106. DOI
Zhao Z., Gao X., Wachs I.E. Comparative Study of Bulk and Supported V−Mo−Te−Nb−O Mixed Metal Oxide Catalysts for Oxidative Dehydrogenation of Propane to Propylene. J. Phys. Chem. B. 2003;107:6333–6342. doi: 10.1021/jp021640m. DOI
Srikumar T., Srinvasa Rao C., Gandhi Y., Venkatramaiah N., Ravikumar V., Veeraiah N. Microstructural, Dielectric and Spectroscopic Properties of Li2O–Nb2O5–ZrO2–SiO2 Glass System Crystallized with V2O5. J. Phys. Chem. Solids. 2011;72:190–200. doi: 10.1016/j.jpcs.2010.12.009. DOI
Rao K.J., Sobha K.C., Kumar S. Infrared and Raman Spectroscopic Studies of Glasses with NASICON-Type Chemistry. J. Chem. Sci. 2001;113:497–514. doi: 10.1007/BF02708786. DOI
Ferreira B., Fargin E., Manaud J.P., Flem G.L., Rodriguez V., Buffeteau T. Second Harmonic Generation Induced by Poling in Borophosphate Bulk and Thin Film Glasses. J. Non-Cryst. Solids. 2004;343:121–130. doi: 10.1016/j.jnoncrysol.2004.07.010. DOI
Pereira R.R., Aquino F.T., Ferrier A., Goldner P., Gonçalves R.R. Nanostructured Rare Earth Doped Nb2O5: Structural, Optical Properties and Their Correlation with Photonic Applications. J. Lumin. 2016;170:707–717. doi: 10.1016/j.jlumin.2015.08.068. DOI
Ardelean I., Rusu D., Andronache C., Ciobotă V. Raman Study of xMeO·(100−x)[P2O5·Li2O] (MeO ⇒ Fe2O3 or V2O5) Glass Systems. Mater. Lett. 2007;61:3301–3304. doi: 10.1016/j.matlet.2006.11.057. DOI
Dimitrov V., Dimitriev Y. Structure of Glasses in PbO-V2O5 System. J. Non-Cryst. Solids. 1990;122:133–138. doi: 10.1016/0022-3093(90)91058-Y. DOI
Hayakawa S., Yoko T., Sakka S. IR and NMR Structural Studies on Lead Vanadate Glasses. J. Non-Cryst. Solids. 1995;183:73–84. doi: 10.1016/0022-3093(94)00652-0. DOI
Assem E.E., Elmehasseb I. Structure, Magnetic, and Electrical Studies on Vanadium Phosphate Glasses Containing Different Oxides. J. Mater. Sci. 2011;46:2071–2076. doi: 10.1007/s10853-010-5040-0. DOI
Rair D., Rochdi A., Majjane A., Jermoumi T., Chahine A., Touhami M.E. Synthesis and Study by FTIR, 31P NMR and Electrochemical Impedance Spectroscopy of Vanadium Zinc Phosphate Glasses Prepared by Sol–Gel Route. J. Non-Cryst. Solids. 2016;432:459–465. doi: 10.1016/j.jnoncrysol.2015.11.001. DOI
Komatsu T., Honma T., Tasheva T., Dimitrov V. Structural Role of Nb2O5 in Glass-Forming Ability, Electronic Polarizability and Nanocrystallization in Glasses: A Review. J. Non-Cryst. Solids. 2022;581:121414. doi: 10.1016/j.jnoncrysol.2022.121414. DOI
Moustafa Y.M., El-Egili K. Infrared Spectra of Sodium Phosphate Glasses. J. Non-Cryst. Solids. 1998;240:144–153. doi: 10.1016/S0022-3093(98)00711-X. DOI
Muñoz F., Rocherullé J., Ahmed I., Hu L. Phosphate Glasses. In: Musgraves J.D., Hu J., Calvez L., editors. Springer Handbook of Glass. Springer International Publishing; Cham, Switzerland: 2019. pp. 553–594. Springer Handbooks.
Tricot G., Montagne L., Delevoye L., Palavit G., Kostoj V. Redox and Structure of Sodium-Vanadophosphate Glasses. J. Non-Cryst. Solids. 2004;345–346:56–60. doi: 10.1016/j.jnoncrysol.2004.07.043. DOI
Tricot G., Vezin H. Description of the Intermediate Length Scale Structural Motifs in Sodium Vanado-Phosphate Glasses by Magnetic Resonance Spectroscopies. J. Phys. Chem. C. 2013;117:1421–1427. doi: 10.1021/jp307518g. DOI
Duffy J.A. Redox Equilibria in Glass. J. Non-Cryst. Solids. 1996;196:45–50. doi: 10.1016/0022-3093(95)00560-9. DOI
Murawski L., Chung C.H., Mackenzie J.D. Electrical Properties of Semiconducting Oxide Glasses. J. Non-Cryst. Solids. 1979;32:91–104. doi: 10.1016/0022-3093(79)90066-8. DOI
Saiko I.A., Saetova N.S., Raskovalov A.A., Il’ina E.A., Molchanova N.G., Kadyrova N.I. Hopping Conductivity in V2O5-P2O5 Glasses: Experiment and Non-Constant Force Field Molecular Dynamics. Solid State Ion. 2020;345:115180. doi: 10.1016/j.ssi.2019.115180. DOI
Razum M., Pavić L., Pajić D., Pisk J., Mošner P., Koudelka L., Šantić A. Casting a New Light on the Polaronic Transport in Vanadate-Phosphate Glasses. J. Am. Ceram. Soc. 2024 submitted .
Summerfield S. Universal Low-Frequency Behaviour in the a.c. Hopping Conductivity of Disordered Systems. Philos. Mag. B. 1985;52:9–22. doi: 10.1080/13642818508243162. DOI
Meyer W.V., Neldel H. Über die Beziehungen Zwischen der Energiekonstanten und der Mengenkonstanten a in der Leitwerts Temperaturformel Bei Oxydischen Halbleitern. Z. Tech. Phys. 1937;18:588–593.
De La Torre A.G., Bruque S., Aranda M.A.G. Rietveld Quantitative Amorphous Content Analysis. J. Appl. Cryst. 2001;34:196–202. doi: 10.1107/S0021889801002485. DOI