Amorphous materials have an internal structure of molecular-scale structural blocks that can be similar to the basic structural units in the crystalline phase of the same compound.[4] Unlike in crystalline materials, however, no long-range regularity exists: amorphous materials cannot be described by the repetition of a finite unit cell. Statistical measures, such as the atomic density function andradial distribution function, are more useful in describing the structure of amorphous solids.[1][3]
Glass is a commonly encountered example of amorphous solids.
Although amorphous materials lack long range order, they exhibit localized order on small length scales.[1] By convention,short range order extends only to the nearest neighbor shell, typically only 1-2 atomic spacings.[5]Medium range order may extend beyond the short range order by 1-2 nm.[5]
At very low temperatures (below 1-10 K), a large family of amorphous solids have various similar low-temperature properties.Although there are various theoretical models, neitherglass transition nor low-temperature properties ofglassy solids are well understood on thefundamental physics level.
Amorphous solids is an important area ofcondensed matter physics aiming to understand these substances at high temperatures ofglass transition and at lowtemperatures towardsabsolute zero. From the 1970s, low-temperature properties of amorphous solids were studied experimentally in great detail.[6][7] For all of these substances,specific heat has a (nearly) linear dependence as a function of temperature, andthermal conductivity has nearly quadratic temperature dependence. These properties are conventionally calledanomalous being very different from properties ofcrystalline solids.
On the phenomenological level, many of these properties were described by a collection of tunnelling two-level systems.[8][9] Nevertheless, the microscopic theory of these properties is still missing after more than 50 years of the research.[10]
Remarkably, adimensionless quantity of internal friction is nearly universal in these materials.[11] This quantity is a dimensionless ratio (up to a numerical constant) of the phononwavelength to the phononmean free path. Since the theory of tunnelling two-level states (TLSs) does not address the origin of the density of TLSs, this theory cannot explain the universality of internal friction, which in turn is proportional to the density of scattering TLSs. The theoretical significance of this important and unsolved problem was highlighted byAnthony Leggett.[12]
Amorphous materials will have some degree ofshort-range order at the atomic-length scale due to the nature of intermolecularchemical bonding.[a] Furthermore, in very smallcrystals, short-range order encompasses a large fraction of theatoms; 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 asX-ray diffraction andtransmission electron microscopy, can have difficulty distinguishing amorphous and crystalline structures at short-size scales.[13]
Due to the lack of long-range order, standard crystallographic techniques are often inadequate in determining the structure of amorphous solids.[14] 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.[citation needed]
Unlike crystalline materials, which exhibit strongBragg diffraction, the diffraction patterns of amorphous materials are characterized by broad and diffuse peaks.[15] 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.[16]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.[15] 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.[17] From these techniques, the local order of an amorphous material can be elucidated.
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 theoxidation state,coordination number, and species surrounding the atom in question as well as the distances at which they are found.[18]
The atomic electrontomography 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.[19] After image acquisition, a significant amount of processing must be done to correct for issues such as drift, noise, and scan distortion.[19] 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 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.[20] Fluctuation electron microscopy experiments can be done in conventional orscanning transmission electron microscope mode.[20]
Amorphous phases are important constituents ofthin films. Thin films are solid layers of a fewnanometres to tens ofmicrometres 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 thehomologous temperature (Th), which is the ratio of deposition temperature to melting temperature.[21][22] 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]
Regarding their applications, amorphous metallic layers played an important role in the discovery ofsuperconductivity inamorphous metals made by Buckel and Hilsch.[23][24] The superconductivity of amorphous metals, including amorphous metallic thin films, is now understood to be due tophonon-mediatedCooper pairing. The role ofstructural disorder can be rationalized based on the strong-couplingEliashberg theory of superconductivity.[25]
Amorphous solids typically exhibit higher localization of heat carriers compared to crystalline, giving rise to low thermal conductivity.[26] Products for thermal protection, such asthermal barrier coatings and insulation, rely on materials with ultralow thermal conductivity.[26]
In thepharmaceutical industry, some amorphous drugs have been shown to offer higherbioavailability than their crystalline counterparts as a result of the highersolubility of the amorphous phase. However, certain compounds can undergo precipitation in their amorphous formin vivo and can then decrease mutual bioavailability if administered together.[28][29] Studies of GDC-0810 ASDs show a strong interrelationship between microstructure, physical properties and dissolution performance.[30]
Amorphous phases were a phenomenon of particular interest for the study of thin-film growth.[32] 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][33] Wedge-shaped polycrystals were identified bytransmission 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 ofOstwald's rule of stages[34] that predicts the formation of phases to proceed with increasing condensation time towards increasing stability.[24][33][e]
^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 hydrogenated amorphous silicon, the missing long-range order between silicon atoms is partly induced by the presence of hydrogen in the per cent 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.
^abCheng, Y.Q.; Ma, E. (May 2011). "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.
^Stephens, Robert B.; Liu, Xiao (2021).Low-Energy Excitations in Disordered Solids. A Story of the 'Universal' Phenomena of Structural Tunneling.doi:10.1142/11746.ISBN978-981-12-1724-1.[page needed]
^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.ISBN978-1-4939-6674-5.{{cite book}}: CS1 maint: location missing publisher (link)
^abYang, 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 (April 2021). "Determining the three-dimensional atomic structure of an amorphous solid".Nature.592 (7852):60–64.arXiv:2004.02266.Bibcode:2021Natur.592...60Y.doi:10.1038/s41586-021-03354-0.PMID33790443.
^abZhou, Jihan; Yang, Yongsoo; Ercius, Peter; Miao, Jianwei (April 2020). "Atomic electron tomography in three and four dimensions".MRS Bulletin.45 (4):290–297.Bibcode:2020MRSBu..45..290Z.doi:10.1557/mrs.2020.88.
^Buckel, W.; Hilsch, R. (February 1956). "Supraleitung und elektrischer Widerstand neuartiger Zinn-Wismut-Legierungen".Zeitschrift für Physik.146 (1):27–38.Bibcode:1956ZPhy..146...27B.doi:10.1007/BF01326000.
^abBuckel, W. (1961). "The influence of crystal bonds on film growth".Elektrische en Magnetische Eigenschappen van dunne Metallaagies. Leuven, Belgium.
^Hsieh, Yi-Ling; Ilevbare, Grace A.; Van Eerdenbrugh, Bernard; Box, Karl J.; Sanchez-Felix, Manuel Vincente; Taylor, Lynne S. (October 2012). "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.PMID22580905.
^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.PMID26805787.
^Jia, Wei; Yawman, Phillip D.; Pandya, Keyur M.; Sluga, Kellie; Ng, Tania; Kou, Dawen; Nagapudi, Karthik; Luner, Paul E.; Zhu, Aiden; Zhang, Shawn; Hou, Hao Helen (December 2022). "Assessing the Interrelationship of Microstructure, Properties, Drug Release Performance, and Preparation Process for Amorphous Solid Dispersions Via Noninvasive Imaging Analytics and Material Characterization".Pharmaceutical Research.39 (12):3137–3154.doi:10.1007/s11095-022-03308-9.PMID35661085.
^Encyclopedia of Soil Science. Marcel Dekker. pp. 93–94.
^abBirkholz, 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".Physical Review B.64 (8) 085402.Bibcode:2001PhRvB..64h5402B.doi:10.1103/PhysRevB.64.085402.
^Ostwald, W. (1897). "Studien über die Bildung und Umwandlung fester Körper".Zeitschrift für Physikalische Chemie.22U:289–330.doi:10.1515/zpch-1897-2233.
