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Amorphous solid

January 09, 2023

"Amorphous" redirects here. For the album by Icon For Hire, see Amorphous (album).
This article is about the solid. For amorphousness in computational systems, see amorphous computing. For amorphousness in set theory, see amorphous set.

In condensed matter physics and materials science, an amorphous solid (or non-crystalline solid) is a solid that lacks the long-range order that is characteristic of a crystal. The terms "glass" and "glassy solid" are sometimes used synonymously with amorphous solid; however, these terms refer specifically to amorphous materials that undergo a glass transition.[1] Examples of amorphous solids include glasses, metallic glasses, and certain types of plastics and polymers.[2]

Etymology

The term comes from the Greek a ("without"), and morphé ("shape, form").

Structure

 
Crystalline vs. amorphous solid

Amorphous materials have an internal structure consisting of interconnected structural blocks that can be similar to the basic structural units found in the corresponding crystalline phase of the same compound.[3] Unlike in crystalline materials, however, no long-range order exists. Amorphous materials therefore cannot be defined by a finite unit cell. Statistical methods, such as the atomic density function and radial distribution function, are more useful in describing the structure of amorphous solids.[1]

Although amorphous materials lack long range order, they exhibit localized order on small length scales. Localized order in amorphous materials can be categorized as short or medium range order.[1] By convention, short range order extends only to the nearest neighbor shell, typically only 1-2 atomic spacings.[4] Medium range order is then defined as the structural organization extending beyond the short range order, usually by 1-2 nm.[4]

 
Amorphous metals have low toughness, but high strength

Nano-structured materials

Amorphous materials will have some degree of short-range order at the atomic-length scale due to the nature of intermolecular chemical bonding.[a] Furthermore, in very small crystals, short-range order encompasses a large fraction of the atoms; nevertheless, relaxation at the surface, along with interfacial effects, distorts the atomic positions and decreases structural order. Even the most advanced structural characterization techniques, such as X-ray diffraction and transmission electron microscopy, have difficulty distinguishing amorphous and crystalline structures at short-length scales.[5]

Characterization of amorphous solids

Due to the lack of long-range order, standard crystallographic techniques are often inadequate in determining the structure of amorphous solids.[6] A variety of electron, X-ray, and computation-based techniques have been used to characterize amorphous materials. Multi-modal analysis is very common for amorphous materials.

X-ray and neutron diffraction

Unlike crystalline materials which exhibit strong Bragg diffraction, the diffraction patterns of amorphous materials are characterized by broad and diffuse peaks.[7] As a result, detailed analysis and complementary techniques are required to extract real space structural information from the diffraction patterns of amorphous materials. It is useful to obtain diffraction data from both X-ray and neutron sources as they have different scattering properties and provide complementary data.[8] Pair distribution function analysis can be performed on diffraction data to determine the probability of finding a pair of atoms separated by a certain distance.[7] Another type of analysis that is done with diffraction data of amorphous materials is radial distribution function analysis, which measures the number of atoms found at varying radial distances away from an arbitrary reference atom.[9] From these techniques, the local order of an amorphous material can be elucidated.

X-ray absorption fine-structure spectroscopy

X-ray absorption fine-structure spectroscopy is an atomic scale probe making it useful for studying materials lacking in long range order. Spectra obtained using this method provide information on the oxidation state, coordination number, and species surrounding the atom in question as well as the distances at which they are found.[10]

Atomic electron tomography

The atomic electron tomography technique is performed in transmission electron microscopes capable of reaching sub-Angstrom resolution. A collection of 2D images taken at numerous different tilt angles is acquired from the sample in question, and then used to reconstruct a 3D image.[11] After image acquisition, a significant amount of processing must be done to correct for issues such as drift, noise, and scan distortion.[11] High quality analysis and processing using atomic electron tomography results in a 3D reconstruction of an amorphous material detailing the atomic positions of the different species that are present.

Fluctuation electron microscopy

Fluctuation electron microscopy is another transmission electron microscopy based technique that is sensitive to the medium range order of amorphous materials. Structural fluctuations arising from different forms of medium range order can be detected with this method.[12] Fluctuation electron microscopy experiments can be done in conventional or scanning transmission electron microscope mode.[12]

Computational techniques

Simulation and modeling techniques are often combined with experimental methods to characterize structures of amorphous materials. Commonly used computational techniques include density functional theory, molecular dynamics, and reverse Monte Carlo.[6]

Uses and observations

Amorphous thin films

Amorphous phases are important constituents of thin films. Thin films are solid layers of a few nanometres to tens of micrometres thickness that are deposited onto a substrate. So-called structure zone models were developed to describe the microstructure of thin films as a function of the homologous temperature (Th), which is the ratio of deposition temperature to melting temperature.[13][14] According to these models, a necessary condition for the occurrence of amorphous phases is that (Th) has to be smaller than 0.3. The deposition temperature must be below 30% of the melting temperature.[b][citation needed]

Superconductivity

Regarding their applications, amorphous metallic layers played an important role in the discovery of superconductivity in amorphous metals made by Buckel and Hilsch.[15][16] The superconductivity of amorphous metals, including amorphous metallic thin films, is now understood to be due to phonon-mediated Cooper pairing. The role of structural disorder can be rationalized based on the strong-coupling Eliashberg theory of superconductivity.[17]

Thermal protection

Amorphous solids typically exhibit higher localization of heat carriers compared to crystalline, giving rise to low thermal conductivity.[18] Products for thermal protection, such as thermal barrier coatings and insulation, rely on materials with ultralow thermal conductivity.[18]

Technological uses

Today, optical coatings made from TiO2, SiO2, Ta2O5 etc. (and combinations of these) in most cases consist of amorphous phases of these compounds. Much research is carried out into thin amorphous films as a gas separating membrane layer.[19] The technologically most important thin amorphous film is probably represented by a few nm thin SiO2 layers serving as isolator above the conducting channel of a metal-oxide semiconductor field-effect transistor (MOSFET). Also, hydrogenated amorphous silicon (Si:H) is of technical significance for thin-film solar cells.[c][citation needed]

Pharmaceutical use

In the pharmaceutical industry, some amorphous drugs have been shown to offer higher bioavailability than their crystalline counterparts as a result of the higher solubility of the amorphous phase. However, certain compounds can undergo precipitation in their amorphous form in vivo, and can then decrease mutual bioavailability if administered together.[20][21]

In soils

Amorphous materials in soil strongly influence bulk density, aggregate stability, plasticity, and water holding capacity of soils. The low bulk density and high void ratios are mostly due to glass shards and other porous minerals not becoming compacted. Andisol soils contain the highest amounts of amorphous materials.[22]

Phase

The occurrence of amorphous phases turned out to be a phenomenon of particular interest for the studying of thin-film growth.[23] The growth of polycrystalline films is often used and preceded by an initial amorphous layer, the thickness of which may amount to only a few nm. The most investigated example is represented by the unoriented molecules of thin polycrystalline silicon films.[d][24] Wedge-shaped polycrystals were identified by transmission electron microscopy to grow out of the amorphous phase only after the latter has exceeded a certain thickness, the precise value of which depends on deposition temperature, background pressure, and various other process parameters. The phenomenon has been interpreted in the framework of Ostwald's rule of stages[25] that predicts the formation of phases to proceed with increasing condensation time towards increasing stability.[16][24][e]

Notes

  1. ^ See the structure of liquids and glasses for more information on non-crystalline material structure.
  2. ^ For higher values, the surface diffusion of deposited atomic species would allow for the formation of crystallites with long-range atomic order.
  3. ^ In the case of a hydrogenated amorphous silicon, the missing long-range order between silicon atoms is partly induced by the presence of hydrogen in the percent range.
  4. ^ An initial amorphous layer was observed in many studies of thin polycrystalline silicon films.
  5. ^ Experimental studies of the phenomenon require a clearly defined state of the substrate surface—and its contaminant density, etc.—upon which the thin film is deposited.

References

  1. ^ a b c Thorpe., M.F.; Tichy, L. (2001). Properties and Applications of Amorphous Materials (1st ed.). Springer Dordrecht. pp. 1–11. ISBN 978-0-7923-6811-3.
  2. ^ Ponçot, M.; Addiego, F.; Dahoun, A. (2013-01-01). "True intrinsic mechanical behaviour of semi-crystalline and amorphous polymers: Influences of volume deformation and cavities shape". International Journal of Plasticity. 40: 126–139. doi:10.1016/j.ijplas.2012.07.007. ISSN 0749-6419.
  3. ^ Mavračić, Juraj; Mocanu, Felix C.; Deringer, Volker L.; Csányi, Gábor; Elliott, Stephen R. (2018). "Similarity Between Amorphous and Crystalline Phases: The Case of TiO2". J. Phys. Chem. Lett. 9 (11): 2985–2990. doi:10.1021/acs.jpclett.8b01067. PMID 29763315.
  4. ^ a b Cheng, Y. Q.; Ma, E. (2011-05-01). "Atomic-level structure and structure–property relationship in metallic glasses". Progress in Materials Science. 56 (4): 379–473. doi:10.1016/j.pmatsci.2010.12.002. ISSN 0079-6425.
  5. ^ Goldstein, Joseph I.; Newbury, Dale E.; Michael, Joseph R.; Ritchie, Nicholas W. M.; Scott, John Henry J.; Joy, David C. (2018). Scanning Electron Microscopy and X-ray Microanalysis (Fourth ed.). New York, NY. ISBN 978-1493966745.
  6. ^ a b Yang, Yao; Zhou, Jihan; Zhu, Fan; Yuan, Yakun; Chang, Dillan J.; Kim, Dennis S.; Pham, Minh; Rana, Arjun; Tian, Xuezeng; Yao, Yonggang; Osher, Stanley J.; Schmid, Andreas K.; Hu, Liangbing; Ercius, Peter; Miao, Jianwei (March 31, 2021). "Determining the three-dimensional atomic structure of an amorphous solid". Nature. 592 (7852): 60–64. arXiv:2004.02266. doi:10.1038/s41586-021-03354-0. ISSN 1476-4687. PMID 33790443. S2CID 214802235.
  7. ^ a b Billinge, Simon J. L. (2019-06-17). "The rise of the X-ray atomic pair distribution function method: a series of fortunate events". Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences. 377 (2147): 20180413. doi:10.1098/rsta.2018.0413. PMC 6501893. PMID 31030657.
  8. ^ Ren, Yang; Zuo, Xiaobing (2018-06-13). "Synchrotron X‐Ray and Neutron Diffraction, Total Scattering, and Small‐Angle Scattering Techniques for Rechargeable Battery Research". Small Methods. 2 (8): 1800064. doi:10.1002/smtd.201800064. ISSN 2366-9608. OSTI 1558997. S2CID 139693137.
  9. ^ Senjaya, Deriyan; Supardi, Adri; Zaidan, Andi (2020-12-09). "Theoretical formulation of amorphous radial distribution function based on wavelet transformation". AIP Conference Proceedings. 2314 (1): 020001. doi:10.1063/5.0034410. ISSN 0094-243X. S2CID 234542087.
  10. ^ Newville, Matthew (July 22, 2004). "Fundamentals of XAFS" (PDF).
  11. ^ a b Zhou, Jihan; Yang, Yongsoo; Ercius, Peter; Miao, Jianwei (April 9, 2020). "Atomic electron tomography in three and four dimensions". MRS Bulletin. 45 (4): 290–297. doi:10.1557/mrs.2020.88. ISSN 0883-7694. S2CID 216408488.
  12. ^ a b Voyles, Paul; Hwang, Jinwoo (2012-10-12), Kaufmann, Elton N. (ed.), "Fluctuation Electron Microscopy", Characterization of Materials, Hoboken, NJ, USA: John Wiley & Sons, Inc., pp. com138, doi:10.1002/0471266965.com138, ISBN 978-0-471-26696-9, retrieved 2022-12-07
  13. ^ Movchan, B. A.; Demchishin, A. V. (1969). "Study of the Structure and Properties of Thick Vacuum Condensates of Nickel, Titanium, Tungsten, Aluminium Oxide and Zirconium Dioxide". Phys. Met. Metallogr. 28: 83–90.
    Russian-language version: Fiz. Metal Metalloved (1969) 28: 653-660.
  14. ^ Thornton, John A. (1974), "Influence of Apparatus Geometry and Deposition Conditions on the Structure and Topography of Thick Sputtered Coatings", Journal of Vacuum Science and Technology, 11 (4): 666–670, Bibcode:1974JVST...11..666T, doi:10.1116/1.1312732
  15. ^ Buckel, W.; Hilsch, R. (1956). "Supraleitung und elektrischer Widerstand neuartiger Zinn-Wismut-Legierungen". Z. Phys. 146: 27–38. doi:10.1007/BF01326000. S2CID 119405703.
  16. ^ a b Buckel, W. (1961). "The influence of crystal bonds on film growth". Elektrische en Magnetische Eigenschappen van dunne Metallaagies. Leuven, Belgium.
  17. ^ Baggioli, Matteo; Setty, Chandan; Zaccone, Alessio (2020). "Effective Theory of Superconductivity in Strongly Coupled Amorphous Materials" (PDF). Physical Review B. 101 (21): 214502. arXiv:2001.00404. doi:10.1103/PhysRevB.101.214502. hdl:10486/703598. S2CID 209531947. Archived (PDF) from the original on 2022-10-09.
  18. ^ a b Zhou, Wu‐Xing; Cheng, Yuan; Chen, Ke‐Qiu; Xie, Guofeng; Wang, Tian; Zhang, Gang (September 9, 2019). "Thermal Conductivity of Amorphous Materials". Advanced Functional Materials. 30 (8): 1903829. doi:10.1002/adfm.201903829. ISSN 1616-301X. S2CID 203143442.
  19. ^ de Vos, Renate M.; Verweij, Henk (1998). "High-Selectivity, High-Flux Silica Membranes for Gas Separation". Science. 279 (5357): 1710–1711. Bibcode:1998Sci...279.1710D. doi:10.1126/science.279.5357.1710. PMID 9497287.
  20. ^ Hsieh, Yi-Ling; Ilevbare, Grace A.; Van Eerdenbrugh, Bernard; Box, Karl J.; Sanchez-Felix, Manuel Vincente; Taylor, Lynne S. (2012-05-12). "pH-Induced Precipitation Behavior of Weakly Basic Compounds: Determination of Extent and Duration of Supersaturation Using Potentiometric Titration and Correlation to Solid State Properties". Pharmaceutical Research. 29 (10): 2738–2753. doi:10.1007/s11095-012-0759-8. ISSN 0724-8741. PMID 22580905. S2CID 15502736.
  21. ^ Dengale, Swapnil Jayant; Grohganz, Holger; Rades, Thomas; Löbmann, Korbinian (May 2016). "Recent Advances in Co-amorphous Drug Formulations". Advanced Drug Delivery Reviews. 100: 116–125. doi:10.1016/j.addr.2015.12.009. ISSN 0169-409X. PMID 26805787.
  22. ^ Encyclopedia of Soil Science. Marcel Dekker. pp. 93–94.
  23. ^ Magnuson, Martin; Andersson, Matilda; Lu, Jun; Hultman, Lars; Jansson, Ulf (2012). "Electronic Structure and Chemical Bonding of Amorphous Chromium Carbide Thin Films". J. Phys. Condens. Matter. 24 (22): 225004. arXiv:1205.0678. Bibcode:2012JPCM...24v5004M. doi:10.1088/0953-8984/24/22/225004. PMID 22553115. S2CID 13135386.
  24. ^ a b Birkholz, M.; Selle, B.; Fuhs, W.; Christiansen, S.; Strunk, H. P.; Reich, R. (2001). "Amorphous-crystalline phase transition during the growth of thin films: The case of microcrystalline silicon" (PDF). Phys. Rev. B. 64 (8): 085402. Bibcode:2001PhRvB..64h5402B. doi:10.1103/PhysRevB.64.085402. (PDF) from the original on 2010-03-31.
  25. ^ Ostwald, Wilhelm (1897). "Studien über die Bildung und Umwandlung fester Körper" (PDF). Z. Phys. Chem. (in German). 22: 289–330. doi:10.1515/zpch-1897-2233. S2CID 100328323. Archived (PDF) from the original on 2017-03-08.

Further reading

  • R. Zallen (1969). The Physics of Amorphous Solids. Wiley Interscience.
  • S.R. Elliot (1990). The Physics of Amorphous Materials (2nd ed.). Longman.
  • N. Cusack (1969). The Physics of Structurally Disordered Matter: An Introduction. IOP Publishing.
  • N.H. March; R.A. Street; M.P. Tosi, eds. (1969). Amorphous Solids and the Liquid State. Springer.
  • D.A. Adler; B.B. Schwartz; M.C. Steele, eds. (1969). Physical Properties of Amorphous Materials. Springer.
  • A. Inoue; K. Hasimoto, eds. (1969). Amorphous and Nanocrystalline Materials. Springer.


January 09, 2023
amorphous, solid, amorphous, redirects, here, album, icon, hire, amorphous, album, this, article, about, solid, amorphousness, computational, systems, amorphous, computing, amorphousness, theory, amorphous, condensed, matter, physics, materials, science, amorp. Amorphous redirects here For the album by Icon For Hire see Amorphous album This article is about the solid For amorphousness in computational systems see amorphous computing For amorphousness in set theory see amorphous set In condensed matter physics and materials science an amorphous solid or non crystalline solid is a solid that lacks the long range order that is characteristic of a crystal The terms glass and glassy solid are sometimes used synonymously with amorphous solid however these terms refer specifically to amorphous materials that undergo a glass transition 1 Examples of amorphous solids include glasses metallic glasses and certain types of plastics and polymers 2 Contents 1 Etymology 2 Structure 3 Nano structured materials 4 Characterization of amorphous solids 4 1 X ray and neutron diffraction 4 2 X ray absorption fine structure spectroscopy 4 3 Atomic electron tomography 4 4 Fluctuation electron microscopy 4 5 Computational techniques 5 Uses and observations 5 1 Amorphous thin films 5 2 Superconductivity 5 3 Thermal protection 5 4 Technological uses 5 5 Pharmaceutical use 5 6 In soils 6 Phase 7 Notes 8 References 9 Further readingEtymology EditThe term comes from the Greek a without and morphe shape form Structure Edit Crystalline vs amorphous solid Amorphous materials have an internal structure consisting of interconnected structural blocks that can be similar to the basic structural units found in the corresponding crystalline phase of the same compound 3 Unlike in crystalline materials however no long range order exists Amorphous materials therefore cannot be defined by a finite unit cell Statistical methods such as the atomic density function and radial distribution function are more useful in describing the structure of amorphous solids 1 Although amorphous materials lack long range order they exhibit localized order on small length scales Localized order in amorphous materials can be categorized as short or medium range order 1 By convention short range order extends only to the nearest neighbor shell typically only 1 2 atomic spacings 4 Medium range order is then defined as the structural organization extending beyond the short range order usually by 1 2 nm 4 Amorphous metals have low toughness but high strengthNano structured materials EditAmorphous materials will have some degree of short range order at the atomic length scale due to the nature of intermolecular chemical bonding a Furthermore in very small crystals short range order encompasses a large fraction of the atoms nevertheless relaxation at the surface along with interfacial effects distorts the atomic positions and decreases structural order Even the most advanced structural characterization techniques such as X ray diffraction and transmission electron microscopy have difficulty distinguishing amorphous and crystalline structures at short length scales 5 Characterization of amorphous solids EditDue to the lack of long range order standard crystallographic techniques are often inadequate in determining the structure of amorphous solids 6 A variety of electron X ray and computation based techniques have been used to characterize amorphous materials Multi modal analysis is very common for amorphous materials X ray and neutron diffraction Edit Unlike crystalline materials which exhibit strong Bragg diffraction the diffraction patterns of amorphous materials are characterized by broad and diffuse peaks 7 As a result detailed analysis and complementary techniques are required to extract real space structural information from the diffraction patterns of amorphous materials It is useful to obtain diffraction data from both X ray and neutron sources as they have different scattering properties and provide complementary data 8 Pair distribution function analysis can be performed on diffraction data to determine the probability of finding a pair of atoms separated by a certain distance 7 Another type of analysis that is done with diffraction data of amorphous materials is radial distribution function analysis which measures the number of atoms found at varying radial distances away from an arbitrary reference atom 9 From these techniques the local order of an amorphous material can be elucidated X ray absorption fine structure spectroscopy Edit X ray absorption fine structure spectroscopy is an atomic scale probe making it useful for studying materials lacking in long range order Spectra obtained using this method provide information on the oxidation state coordination number and species surrounding the atom in question as well as the distances at which they are found 10 Atomic electron tomography Edit The atomic electron tomography technique is performed in transmission electron microscopes capable of reaching sub Angstrom resolution A collection of 2D images taken at numerous different tilt angles is acquired from the sample in question and then used to reconstruct a 3D image 11 After image acquisition a significant amount of processing must be done to correct for issues such as drift noise and scan distortion 11 High quality analysis and processing using atomic electron tomography results in a 3D reconstruction of an amorphous material detailing the atomic positions of the different species that are present Fluctuation electron microscopy Edit Fluctuation electron microscopy is another transmission electron microscopy based technique that is sensitive to the medium range order of amorphous materials Structural fluctuations arising from different forms of medium range order can be detected with this method 12 Fluctuation electron microscopy experiments can be done in conventional or scanning transmission electron microscope mode 12 Computational techniques Edit Simulation and modeling techniques are often combined with experimental methods to characterize structures of amorphous materials Commonly used computational techniques include density functional theory molecular dynamics and reverse Monte Carlo 6 Uses and observations EditAmorphous thin films Edit Amorphous phases are important constituents of thin films Thin films are solid layers of a few nanometres to tens of micrometres thickness that are deposited onto a substrate So called structure zone models were developed to describe the microstructure of thin films as a function of the homologous temperature Th which is the ratio of deposition temperature to melting temperature 13 14 According to these models a necessary condition for the occurrence of amorphous phases is that Th has to be smaller than 0 3 The deposition temperature must be below 30 of the melting temperature b citation needed Superconductivity Edit Regarding their applications amorphous metallic layers played an important role in the discovery of superconductivity in amorphous metals made by Buckel and Hilsch 15 16 The superconductivity of amorphous metals including amorphous metallic thin films is now understood to be due to phonon mediated Cooper pairing The role of structural disorder can be rationalized based on the strong coupling Eliashberg theory of superconductivity 17 Thermal protection Edit Amorphous solids typically exhibit higher localization of heat carriers compared to crystalline giving rise to low thermal conductivity 18 Products for thermal protection such as thermal barrier coatings and insulation rely on materials with ultralow thermal conductivity 18 Technological uses Edit Today optical coatings made from TiO2 SiO2 Ta2O5 etc and combinations of these in most cases consist of amorphous phases of these compounds Much research is carried out into thin amorphous films as a gas separating membrane layer 19 The technologically most important thin amorphous film is probably represented by a few nm thin SiO2 layers serving as isolator above the conducting channel of a metal oxide semiconductor field effect transistor MOSFET Also hydrogenated amorphous silicon Si H is of technical significance for thin film solar cells c citation needed Pharmaceutical use Edit In the pharmaceutical industry some amorphous drugs have been shown to offer higher bioavailability than their crystalline counterparts as a result of the higher solubility of the amorphous phase However certain compounds can undergo precipitation in their amorphous form in vivo and can then decrease mutual bioavailability if administered together 20 21 In soils Edit Amorphous materials in soil strongly influence bulk density aggregate stability plasticity and water holding capacity of soils The low bulk density and high void ratios are mostly due to glass shards and other porous minerals not becoming compacted Andisol soils contain the highest amounts of amorphous materials 22 Phase EditThe occurrence of amorphous phases turned out to be a phenomenon of particular interest for the studying of thin film growth 23 The growth of polycrystalline films is often used and preceded by an initial amorphous layer the thickness of which may amount to only a few nm The most investigated example is represented by the unoriented molecules of thin polycrystalline silicon films d 24 Wedge shaped polycrystals were identified by transmission electron microscopy to grow out of the amorphous phase only after the latter has exceeded a certain thickness the precise value of which depends on deposition temperature background pressure and various other process parameters The phenomenon has been interpreted in the framework of Ostwald s rule of stages 25 that predicts the formation of phases to proceed with increasing condensation time towards increasing stability 16 24 e Notes Edit See the structure of liquids and glasses for more information on non crystalline material structure For higher values the surface diffusion of deposited atomic species would allow for the formation of crystallites with long range atomic order In the case of a hydrogenated amorphous silicon the missing long range order between silicon atoms is partly induced by the presence of hydrogen in the percent range An initial amorphous layer was observed in many studies of thin polycrystalline silicon films Experimental studies of the phenomenon require a clearly defined state of the substrate surface and its contaminant density etc upon which the thin film is deposited References Edit a b c Thorpe M F Tichy L 2001 Properties and Applications of Amorphous Materials 1st ed Springer Dordrecht pp 1 11 ISBN 978 0 7923 6811 3 Poncot M Addiego F Dahoun A 2013 01 01 True intrinsic mechanical behaviour of semi crystalline and amorphous polymers Influences of volume deformation and cavities shape International Journal of Plasticity 40 126 139 doi 10 1016 j ijplas 2012 07 007 ISSN 0749 6419 Mavracic Juraj Mocanu Felix C Deringer Volker L Csanyi Gabor Elliott Stephen R 2018 Similarity Between Amorphous and Crystalline Phases The Case of TiO2 J Phys Chem Lett 9 11 2985 2990 doi 10 1021 acs jpclett 8b01067 PMID 29763315 a b Cheng Y Q Ma E 2011 05 01 Atomic level structure and structure property relationship in metallic glasses Progress in Materials Science 56 4 379 473 doi 10 1016 j pmatsci 2010 12 002 ISSN 0079 6425 Goldstein Joseph I Newbury Dale E Michael Joseph R Ritchie Nicholas W M Scott John Henry J Joy David C 2018 Scanning Electron Microscopy and X ray Microanalysis Fourth ed New York NY ISBN 978 1493966745 a b Yang Yao Zhou Jihan Zhu Fan Yuan Yakun Chang Dillan J Kim Dennis S Pham Minh Rana Arjun Tian Xuezeng Yao Yonggang Osher Stanley J Schmid Andreas K Hu Liangbing Ercius Peter Miao Jianwei March 31 2021 Determining the three dimensional atomic structure of an amorphous solid Nature 592 7852 60 64 arXiv 2004 02266 doi 10 1038 s41586 021 03354 0 ISSN 1476 4687 PMID 33790443 S2CID 214802235 a b Billinge Simon J L 2019 06 17 The rise of the X ray atomic pair distribution function method a series of fortunate events Philosophical Transactions of the Royal Society A Mathematical Physical and Engineering Sciences 377 2147 20180413 doi 10 1098 rsta 2018 0413 PMC 6501893 PMID 31030657 Ren Yang Zuo Xiaobing 2018 06 13 Synchrotron X Ray and Neutron Diffraction Total Scattering and Small Angle Scattering Techniques for Rechargeable Battery Research Small Methods 2 8 1800064 doi 10 1002 smtd 201800064 ISSN 2366 9608 OSTI 1558997 S2CID 139693137 Senjaya Deriyan Supardi Adri Zaidan Andi 2020 12 09 Theoretical formulation of amorphous radial distribution function based on wavelet transformation AIP Conference Proceedings 2314 1 020001 doi 10 1063 5 0034410 ISSN 0094 243X S2CID 234542087 Newville Matthew July 22 2004 Fundamentals of XAFS PDF a b Zhou Jihan Yang Yongsoo Ercius Peter Miao Jianwei April 9 2020 Atomic electron tomography in three and four dimensions MRS Bulletin 45 4 290 297 doi 10 1557 mrs 2020 88 ISSN 0883 7694 S2CID 216408488 a b Voyles Paul Hwang Jinwoo 2012 10 12 Kaufmann Elton N ed Fluctuation Electron Microscopy Characterization of Materials Hoboken NJ USA John Wiley amp Sons Inc pp com138 doi 10 1002 0471266965 com138 ISBN 978 0 471 26696 9 retrieved 2022 12 07 Movchan B A Demchishin A V 1969 Study of the Structure and Properties of Thick Vacuum Condensates of Nickel Titanium Tungsten Aluminium Oxide and Zirconium Dioxide Phys Met Metallogr 28 83 90 Russian language version Fiz Metal Metalloved 1969 28 653 660 Thornton John A 1974 Influence of Apparatus Geometry and Deposition Conditions on the Structure and Topography of Thick Sputtered Coatings Journal of Vacuum Science and Technology 11 4 666 670 Bibcode 1974JVST 11 666T doi 10 1116 1 1312732 Buckel W Hilsch R 1956 Supraleitung und elektrischer Widerstand neuartiger Zinn Wismut Legierungen Z Phys 146 27 38 doi 10 1007 BF01326000 S2CID 119405703 a b Buckel W 1961 The influence of crystal bonds on film growth Elektrische en Magnetische Eigenschappen van dunne Metallaagies Leuven Belgium Baggioli Matteo Setty Chandan Zaccone Alessio 2020 Effective Theory of Superconductivity in Strongly Coupled Amorphous Materials PDF Physical Review B 101 21 214502 arXiv 2001 00404 doi 10 1103 PhysRevB 101 214502 hdl 10486 703598 S2CID 209531947 Archived PDF from the original on 2022 10 09 a b Zhou Wu Xing Cheng Yuan Chen Ke Qiu Xie Guofeng Wang Tian Zhang Gang September 9 2019 Thermal Conductivity of Amorphous Materials Advanced Functional Materials 30 8 1903829 doi 10 1002 adfm 201903829 ISSN 1616 301X S2CID 203143442 de Vos Renate M Verweij Henk 1998 High Selectivity High Flux Silica Membranes for Gas Separation Science 279 5357 1710 1711 Bibcode 1998Sci 279 1710D doi 10 1126 science 279 5357 1710 PMID 9497287 Hsieh Yi Ling Ilevbare Grace A Van Eerdenbrugh Bernard Box Karl J Sanchez Felix Manuel Vincente Taylor Lynne S 2012 05 12 pH Induced Precipitation Behavior of Weakly Basic Compounds Determination of Extent and Duration of Supersaturation Using Potentiometric Titration and Correlation to Solid State Properties Pharmaceutical Research 29 10 2738 2753 doi 10 1007 s11095 012 0759 8 ISSN 0724 8741 PMID 22580905 S2CID 15502736 Dengale Swapnil Jayant Grohganz Holger Rades Thomas Lobmann Korbinian May 2016 Recent Advances in Co amorphous Drug Formulations Advanced Drug Delivery Reviews 100 116 125 doi 10 1016 j addr 2015 12 009 ISSN 0169 409X PMID 26805787 Encyclopedia of Soil Science Marcel Dekker pp 93 94 Magnuson Martin Andersson Matilda Lu Jun Hultman Lars Jansson Ulf 2012 Electronic Structure and Chemical Bonding of Amorphous Chromium Carbide Thin Films J Phys Condens Matter 24 22 225004 arXiv 1205 0678 Bibcode 2012JPCM 24v5004M doi 10 1088 0953 8984 24 22 225004 PMID 22553115 S2CID 13135386 a b Birkholz M Selle B Fuhs W Christiansen S Strunk H P Reich R 2001 Amorphous crystalline phase transition during the growth of thin films The case of microcrystalline silicon PDF Phys Rev B 64 8 085402 Bibcode 2001PhRvB 64h5402B doi 10 1103 PhysRevB 64 085402 Archived PDF from the original on 2010 03 31 Ostwald Wilhelm 1897 Studien uber die Bildung und Umwandlung fester Korper PDF Z Phys Chem in German 22 289 330 doi 10 1515 zpch 1897 2233 S2CID 100328323 Archived PDF from the original on 2017 03 08 Further reading EditR Zallen 1969 The Physics of Amorphous Solids Wiley Interscience S R Elliot 1990 The Physics of Amorphous Materials 2nd ed Longman N Cusack 1969 The Physics of Structurally Disordered Matter An Introduction IOP Publishing N H March R A Street M P Tosi eds 1969 Amorphous Solids and the Liquid State Springer D A Adler B B Schwartz M C Steele eds 1969 Physical Properties of Amorphous Materials Springer A Inoue K Hasimoto eds 1969 Amorphous and Nanocrystalline Materials Springer Retrieved from https en wikipedia org w index php title Amorphous solid amp oldid 1131283492, wikipedia, wiki, book, books, library,

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