Amorphous solid

Incondensed matter physicsandmaterials science,anamorphous solid(ornon-crystalline solid) is asolidthat lacks thelong-range orderthat is characteristic of acrystal.The terms "glass"and" glassy solid "are sometimes used synonymously with amorphous solid; however, these terms refer specifically to amorphous materials that undergo aglass transition.^[1]Examples of amorphous solids include glasses,metallic glasses,and certain types ofplasticsandpolymers.^[2]^[3]

Etymology

The term comes from theGreeka( "without" ), andmorphé( "shape, form" ).

Structure

Crystalline vs. amorphous solid

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 mesures, such as the atomic density function andradial distribution function,are more useful in describing the structure of amorphous solids.^[1]^[3]

Glassis 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 orderextends only to the nearest neighbor shell, typically only 1-2 atomic spacings.^[5]Medium range ordermay extend beyond the short range order by 1-2 nm.^[5]

Fundamental properties of amorphous solids

Glass transitionat high temperatures

The freezing from liquid state to amorphous solid -glass transition- is considered one of the very important andunsolved problems of physics.

Universal low-temperature properties of amorphous solids

At very low temperatures (below 1-10 K), large family of amorphous solids have various similar low-temperature properties. Although there are various theoretical models, neitherglass transitionnor low-temperature properties ofglassy solidsare well understood on thefundamental physicslevel.

Amorphous solids is an important area ofcondensed matter physicsaiming to understand these substances at high temperatures ofglass transitionand at lowtemperaturestowardsabsolute zero.From 1970s, low-temperature properties of amorphous solids were studied experimentally in great detail.^[6]^[7]For all of these substances,specific heathas a (nearly) linear dependence as a function of temperature, andthermal conductivityhas nearly quadratic temperature dependence. These properties are conventionally calledanomalousbeing very different from properties ofcrystalline solids.

On the phenomenological level, many of these properties were described by a collection of tunneling 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, adimensionlessquantity of internal friction is nearly universal in these materials.^[11]This quantity is a dimensionless ratio (up to a numerical constant) of the phononwavelengthto the phononmean free path.Since the theory of tunneling 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]

Nano-structured materials

Amorphous materials will have some degree ofshort-range orderat 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 diffractionandtransmission electron microscopy,can have difficulty distinguishing amorphous and crystalline structures at short size scales.^[13]

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.^[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.

X-ray and neutron diffraction

Unlike crystalline materials which exhibit strongBraggdiffraction, 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 functionanalysis 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

X-ray absorption fine-structure spectroscopyis 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]

Atomic electron tomography

The atomic electrontomographytechnique 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

Fluctuation electron microscopyis 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 microscopemode.^[20]

Computational techniques

Simulation and modeling techniques are often combined with experimental methods to characterize structures of amorphous materials. Commonly used computational techniques includedensity functional theory,molecular dynamics,and reverseMonte Carlo.^[14]

Uses and observations

Amorphous thin films

Amorphous phases are important constituents ofthin films.Thin films are solid layers of a fewnanometresto tens ofmicrometresthickness 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(T_h), 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 (T_h) has to be smaller than 0.3. The deposition temperature must be below 30% of the melting temperature.^[b]^{[citation needed]}

Superconductivity

Amorphous metalshave lowtoughness,but high strength

Regarding their applications, amorphous metallic layers played an important role in the discovery ofsuperconductivityinamorphous metalsmade 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 disordercan be rationalized based on the strong-couplingEliashberg theoryof superconductivity.^[25]

Thermal protection

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 barriercoatings and insulation, rely on materials with ultralow thermal conductivity.^[26]

Technological uses

Today,optical coatingsmade fromTiO₂,SiO₂,Ta₂O₅etc. (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 separatingmembranelayer.^[27]The technologically most important thin amorphous film is probably represented by a few nm thin SiO₂layers serving as isolator above the conducting channel of ametal-oxide semiconductor field-effect transistor(MOSFET). Also,hydrogenated amorphous silicon(Si:H) is of technical significance forthin-film solar cells.^[c]^[28]

Pharmaceutical use

In thepharmaceutical industry,some amorphous drugs have been shown to offer higherbioavailabilitythan their crystalline counterparts as a result of the higher solubility of the amorphous phase. However, certain compounds can undergo precipitation in their amorphous formin vivo,and can then decrease mutual bioavailability if administered together.^[29]^[30]

In soils

Amorphous materials in soil strongly influencebulk density,aggregate stability,plasticity,andwater holding capacityof soils. The low bulk density and highvoid ratiosare mostly due to glass shards and other porous minerals not becomingcompacted.Andisolsoils contain the highest amounts of amorphous materials.^[31]

Phase

The occurrence of amorphous phases turned out to be a phenomenon of particular interest for the studying 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 microscopyto 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 ruleof stages^[34]that predicts the formation of phases to proceed with increasing condensation time towards increasing stability.^[24]^[33]^[e]

Notes

^See thestructure of liquids and glassesfor 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.

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