Amorpheus: a Python-based software for the treatment of X-ray scattering data of amorphous and liquid systems

References

• Scherrer P, Debye P. Interferenzen an regellos orientierten teilchen im röntgenlicht. i, Nachrichten von der Gesellschaft der Wissenschaften zu Göttingen. Math Phys Klasse. 1916;1916:1–15.
   Google Scholar
• Danielson GC. X-ray diffraction in liquids. Vancouver: University of British Columbia; 1935.
   Google Scholar
• Rahman A. Normalization of diffraction data from liquids. J Chem Phys. 1965;42(10):3540–3542.
   Web of Science ®Google Scholar
• Warren BE. X-Ray diffraction. Reading (MA): Addison-Wesley; 1969.
   Google Scholar
• Kaplow R, Strong SL, Averbach BL. Radial density functions for liquid mercury and lead. Phys Rev. 1965 May;138:A1336–A1345.
   Web of Science ®Google Scholar
• Sanloup C, Guyot F, Gillet P, et al. Structural changes in liquid Fe at high pressures and high temperatures from synchrotron X-ray diffraction. Europhys Lett. 2000;52(2):151–157.
   Google Scholar
• Eggert JH, Weck G, Loubeyre P, et al. Quantitative structure factor and density measurements of high-pressure fluids in diamond anvil cells by x-ray diffraction: argon and water. Phys Rev B. 2002 Apr;65(17):174105.
   Google Scholar
• Funamori N, Tsuji K. Structural transformation of liquid tellurium at high pressures and temperatures. Phys Rev B. 2001 Dec;65:014105.
   Google Scholar
• Funamori N, Tsuji K. Pressure-induced structural change of liquid silicon. Phys Rev Lett. 2002 Jun;88:255508.
   Google Scholar
• Wang Y, Uchida T, Von Dreele R, et al. A new technique for angle-dispersive powder diffraction using an energy-dispersive setup and synchrotron radiation. J Appl Crystallogr. 2004 Dec;37(6):947–956.
   Google Scholar
• Xu F, Morard G, Guignot N, et al. Thermal expansion of liquid fe-s alloy at high pressure. Earth Planet Sci Lett. 2021;563:116884.
   Google Scholar
• King A, Guignot N, Henry L, Morard G, Clark A, Le Godec Y, Itié J-P. J. Appl. Cryst. 2022: 55. https://doi.org/https://doi.org/10.1107/S1600576722000322
   Google Scholar
• Shen G, Rivers ML, Sutton SR, et al. The structure of amorphous iron at high pressures to 67 GPa measured in a diamond anvil cell. Phys Earth Planet Inter. 2004;143(1–2):481–495.
   Google Scholar
• Morard G, Garbarino G, Antonangeli D, et al. Density measurements and structural properties of liquid and amorphous metals under high pressure. High Press Res. 2014;34(1):9–21.
   Web of Science ®Google Scholar
• Prescher C, Prakapenka VB, Stefanski J, et al. Beyond sixfold coordinated Si in SiO2 glass at ultrahigh pressures. Proc Natl Acad Sci USA. 2017;114(38):10041–10046.
   PubMed Web of Science ®Google Scholar
• Morard G, Nakajima Y, Andrault D, et al. Structure and density of fe-c liquid alloys under high pressure. J Geophys Res Solid Earth. 2017;122(10):7813–7823.
   Web of Science ®Google Scholar
• Morard G, Boccato S, Rosa A, et al. Solving controversies on the iron phase diagram under high pressure. Geophys Res Lett. 2018;45(20):11–074. 082
   Web of Science ®Google Scholar
• Briggs R, Gorman MG, Zhang S, et al. Coordination changes in liquid tin under shock compression determined using in situ femtosecond x-ray diffraction. Appl Phys Lett. 2019;115(26):264101–0.
   Google Scholar
• Morard G, Hernandez J-A, Guarguaglini M, et al. In situ x-ray diffraction of silicate liquids and glasses under dynamic and static compression to megabar pressures. Proc Nat Acad Sci. 2020;117(22):11981–11986.
   PubMed Web of Science ®Google Scholar
• Kuwayama Y, Morard G, Nakajima Y, et al. Equation of state of liquid iron under extreme conditions. Phys Rev Lett. 2020;124(16):165701.
   Google Scholar
• Henry L, Mezouar M, Garbarino G, et al. Liquid-liquid transition and critical point in sulfur. Nature. 2020;584:382–386.
   PubMed Web of Science ®Google Scholar
• Morard G, Siebert J, Andrault D, et al. The earth's core composition from high pressure density measurements of liquid iron alloys. Earth Planet Sci Lett. 2013;373:169–178.
   Web of Science ®Google Scholar
• Sastry S, Austen Angell C. Liquid liquid phase transition in supercooled silicon. Nat Mater. 2003;2:739–743.
   PubMed Web of Science ®Google Scholar
• Bhat MH, Molinero V, Soignard E, et al. Vitrification of a monatomic metallic liquid. Nature. 2007;448(7155):787–790.
   PubMed Web of Science ®Google Scholar
• Cadien A, Hu QY, Meng Y, et al. First-order liquid-liquid phase transition in cerium. Phys Rev Lett. 2013 Mar;110:125503.
   Google Scholar
• Billinge SJL. The rise of the x-ray atomic pair distribution function method: a series of fortunate events. Philos Trans R Soc A Math Phys Eng Sci. 2019;377(2147):20180413.
   Google Scholar
• Louvel M, Drewitt JWE, Ross A, et al. The HXD95: a modified Bassett-type hydrothermal diamond-anvil cell for in situ XRD experiments up to 5 GPa and 1300 K. J Synchrotron Radiat. 2020 Mar;27(2):529–537.
   PubMedGoogle Scholar
• Prescher C. Glassure: an API and GUI program for analyzing angular dispersive total X-ray diffraction data, Sept 2017. doi:https://doi.org/10.5281/zenodo.880836.
   Google Scholar
• Heinen BJ. Liquiddiffract v1.0.0, Dec 2019.
   Google Scholar
• Devoto F. Available from: https://github.com/cicciodevoto/lasdia.
   Google Scholar
• Juhás P, Davis T, Farrow CL, et al. PDFgetX3: a rapid and highly automatable program for processing powder diffraction data into total scattering pair distribution functions. J Appl Crystallogr. 2013 Apr;46(2):560–566.
   Google Scholar
• Soper AK. Gudrunn and gudrunx: programs for correcting raw neutron and x-ray diffraction data to differential scattering cross section. Rutherford Appleton Laboratory Technical Reports. 2011.
   Google Scholar
• Shen G, Prakapenka VB, Rivers ML, et al. Structure of liquid iron at pressures up to 58 GPa. Phys Rev Lett. 2004;92(18):185701–1.
   Google Scholar
• Krogh-Moe J. A method for converting experimental X-ray intensities to an absolute scale. Acta Crystallogr. 1956 Nov;9(11):951–953.
   Google Scholar
• Pickup D, Moss R, Newport R. NXFit: a program for simultaneously fitting X-ray and neutron diffraction pair-distribution functions to provide optimized structural parameters. J Appl Crystallogr. 2014 Oct;47(5):1790–1796.
   Google Scholar
• Waser J, Schomaker V. The Fourier inversion of diffraction data. Rev Mod Phys. 1953 Jul;25(3):671–690.
   Web of Science ®Google Scholar
• Lorch E. Neutron diffraction by germania, silica and radiation-damaged silica glasses. J Phys C Solid State Phys. 1969 Feb;2(2):305.
   Google Scholar
• Skinner LB, Huang C, Schlesinger D, et al. Benchmark oxygen-oxygen pair-distribution function of ambient water from x-ray diffraction measurements with a wide Q -range. J Chem Phys. 2013 Feb;138(7):074506.
   Google Scholar
• Faber TE, Ziman JM. A theory of the electrical properties of liquid metals. Philos Mag A J Theor Exp Appl Phys. 1965;11(109):153–173.
   Google Scholar
• Harris CR, Millman KJ, van der Walt SJ, et al. Array programming with NumPy. Nature. 2020 Sep;585(7825):357–362.
   PubMed Web of Science ®Google Scholar
• Morard G, Mezouar M, Bauchau S, et al. High efficiency multichannel collimator for structural studies of liquids and low-z materials at high pressures and temperatures. Rev Sci Instrum. 2011;82(2):023904.
   Google Scholar
• Weck G, Garbarino G, Ninet S, et al. Use of a multichannel collimator for structural investigation of low-z dense liquids in a diamond anvil cell: validation on fluid h2 up to 5 Gpa. Rev Sci Instrum. 2013;84(6):063901.
   Google Scholar
• Virtanen P, Gommers R, Oliphant TE, et al. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat Methods. 2020;17:261–272.
   PubMed Web of Science ®Google Scholar
• Hunter JD. Matplotlib: A 2d graphics environment. Comput Sci Eng. 2007;9(3):90–95.
   Web of Science ®Google Scholar
• Schoonjans T, Brunetti A, Golosio B, et al. The xraylib library for x-ray matter interactions. recent developments. Spectrochim Acta B Atomic Spectrosc. 2011;66(11):776–784.
   Web of Science ®Google Scholar
• Newville M, Otten R, Nelson A, et al. lmfit/lmfit-py: 1.0.3. Version 1.0.3. Zenodo; 2021 Oct.
   Google Scholar
• Lundh F. An introduction to tkinter. 1999. Available from: http://jgaltier.free.fr/Terminale_S/ISN/TclTk_Introduction_To_Tkinter.pdf.
   Google Scholar
• Boulard E, King A, Guignot N, et al. High-speed tomography under extreme conditions at the psiche beamline of the soleil synchrotron. J Synchrotron Radiat. 2018;25(3):818–825.
   PubMedGoogle Scholar
• Guignot N, King A, Boulard E. Synchrotron x-ray computed microtomography for high pressure science. J Appl Phys. 2020;127(24):240901–00.
   Google Scholar
• Decremps F, Morard G, Garbarino G, et al. Polyamorphism of a ce-based bulk metallic glass by high-pressure and high-temperature density measurements. Phys Rev B. 2016 Feb;93:054209.
   Web of Science ®Google Scholar
• Zhang Bo, Wang RJ, Zhao DQ, et al. Properties of Ce-based bulk metallic glass-forming alloys. Phys Rev B. 2004 Dec;70:224208.
   Google Scholar
• Zhang B, Pan MX, Zhao DQ, Soft bulk metallic glasses based on cerium. Appl Phys Lett. 2004;85(1):61–63.
   Web of Science ®Google Scholar
• Morard G, Andrault D, Antonangeli D, et al. Properties of iron alloys under the earth's core conditions. Comp Rendus Geosci. 2014;346(5-6):130–139.
   Web of Science ®Google Scholar
• Dewaele A, Belonoshko AB, Garbarino G, et al. High-pressure-high-temperature equation of state of KCl and KBr. Phys Rev B Condensed Matter Mater Phys. 2012;85(21):1–7.
   Web of Science ®Google Scholar
• Campbell AJ, Danielson L, Righter K, et al. High pressure effects on the iron — iron oxide and nickel — nickel oxide oxygen fugacity buffers. Earth Planet Sci Lett. 2009;286(3-4):556–564.
   Web of Science ®Google Scholar
• Prescher C, Prakapenka VB. DIOPTAS: a program for reduction of two-dimensional X-ray diffraction data and data exploration. High Press Res. 2015 Jul;35(3):223–230.
   Web of Science ®Google Scholar
• Kuwayama Y, Hirose K. Phase relations in the system FeFeSi at 21 GPa. Amer Mineralog. 2004;89:273–276.
   Web of Science ®Google Scholar
• Petitgirard S, Malfait WJ, Sinmyo R, et al. Fate of mgsio3 melts at core–mantle boundary conditions. Proc Nat Acad Sci. 2015;112(46):14186–14190.
   PubMed Web of Science ®Google Scholar
• Kono Y, Shibazaki Y, Kenney-Benson C, et al. Pressure-induced structural change in MgSiO3 glass at pressures near the earth's core–mantle boundary. Proc Nat Acad Sci. 2018;115(8):1742–1747.
   PubMed Web of Science ®Google Scholar
• Salmon PS, Moody GS, Ishii Y, et al. Pressure induced structural transformations in amorphous MgSiO3 and CaSiO3. J Non-Crystalline Solids X. 2019;3:100024.
   Google Scholar
• Yin CD, Okuno M, Morikawa H, et al. Structure analysis of MgSiO3 glass. J Non Cryst Solids. 1983;55(1):131–141.
   Web of Science ®Google Scholar
• Yamada A, Wang Y, Inoue T, et al. High-pressure x-ray diffraction studies on the structure of liquid silicate using a paris-edinburgh type large volume press. Rev Sci Instrum. 2011;82(1):015103.
   Google Scholar
• Petitgirard S, Malfait WJ, Journaux B, et al. SiO2 glass density to lower-mantle pressures. Phys Rev Lett. 2017 Nov;119(21):215701.
   Google Scholar
• Funamori N, Yamamoto S, Yagi T, et al. Exploratory studies of silicate melt structure at high pressures and temperatures by in situ x-ray diffraction. J Geophys Res Solid Earth. 2004;109(B3). doi:https://doi.org/10.1029/2003JB002650
   Google Scholar
• Kono Y, Shu Y, Kenney-Benson C, Structural evolution of SiO2 glass with Si coordination number greater than 6. Phys Rev Lett. 2020 Nov;125:205701.
   PubMed Web of Science ®Google Scholar
• Zhao Y, Von Dreele RB, Weidner DJ, et al. P- v- t data of hexagonal boron nitride h bn and determination of pressure and temperature using thermoelastic equations of state of multiple phases. High Press Res. 1997;15(6):369–386.
   Web of Science ®Google Scholar
• Matsui M, Parker SC, Leslie M. The MD simulation of the equation of state of MgO: application as a pressure calibration standard at high temperature and high pressure. Amer Mineralog. 2000 Feb;85(2):312–316.
   Web of Science ®Google Scholar
• Matsui M, Ito E, Katsura T, et al. The temperature-pressure-volume equation of state of platinum. J Appl Phys. 2009;105(1):013505.
   Google Scholar
• Ikuta D, Kono Y, Shen G. Structural analysis of liquid aluminum at high pressure and high temperature using the hard sphere model. J Appl Phys. 2016;120(13):135901.
   Google Scholar
• Jakse N, Pasturel A. Liquid aluminum: atomic diffusion and viscosity from ab initio molecular dynamics. Sci Rep. 2013;3(1):2045–2322.
   PubMedGoogle Scholar
• González DJ, González LE, López JM, et al. Dynamical properties of liquid al near melting: an orbital-free molecular dynamics study. Phys. Rev. B. 2002;65:184201–00.
   Google Scholar
• Shibazaki Y, Kono Y. Effect of silicon, carbon, and sulfur on structure of liquid iron and implications for structure-property relations in liquid iron-light element alloys. J Geophys Res Solid Earth. 2018;123(6):4697–4706.
   Web of Science ®Google Scholar
• Sanloup C, Fiquet G, Gregoryanz E, et al. Effect of Si on liquid Fe compressibility: implications for sound velocity in core materials. Geophys Res Lett. 2004;31(L07604):1–4.
   Google Scholar
• Tateyama R, Ohtani E, Terasaki H, et al. Density measurements of liquid Fe–Si alloys at high pressure using the sink-float method. Phys Chem Miner. 2011;38(10):801–807.
   Web of Science ®Google Scholar
• Ashcroft NW, Langreth DC. Structure of binary liquid mixtures. i. Phys Rev. 1967 Apr;156:685–692.
   Web of Science ®Google Scholar
• Sanloup C, Jwe D, Crépisson C, et al. Structure et la densité de fayalite fondu à haute pression. Geochim Cosmochim Acta. 2013;118:118–128.
   Google Scholar