Materials science is aninterdisciplinary field of researching and discoveringmaterials.Materials engineering is anengineering field of finding uses for materials in other fields and industries.
The intellectual origins of materials science stem from theAge of Enlightenment, when researchers began to use analytical thinking fromchemistry,physics, andengineering to understand ancient,phenomenological observations inmetallurgy andmineralogy.[1][2] Materials science still incorporates elements of physics, chemistry, and engineering. As such, the field was long considered by academic institutions as a sub-field of these related fields. Beginning in the 1940s, materials science began to be more widely recognized as a specific and distinct field of science and engineering, and major technical universities around the world created dedicated schools for its study.
Materials scientists emphasize understanding how the history of a material (processing) influences its structure, and thus thematerial's properties and performance. The understanding of processing -structure-properties relationships is called the materials paradigm. Thisparadigm is used to advance understanding in a variety of research areas, includingnanotechnology,biomaterials, andmetallurgy.
Materials science is also an important part offorensic engineering andfailure analysis – investigating materials, products, structures or components, which fail or do not function as intended, causing personal injury or damage to property. Such investigations are key to understanding, for example, the causes of variousaviation accidents and incidents.
The material of choice of a given era is often a defining point. Phases such asStone Age,Bronze Age,Iron Age, andSteel Age are historic, if arbitrary examples. Originally deriving from the manufacture ofceramics and its putative derivative metallurgy, materials science is one of the oldest forms of engineering and applied science.[3] Modern materials science evolved directly frommetallurgy, which itself evolved from the use of fire. A major breakthrough in the understanding of materials occurred in the late 19th century, when the American scientistJosiah Willard Gibbs demonstrated that thethermodynamic properties related toatomic structure in variousphases are related to the physical properties of a material.[4] Important elements of modern materials science were products of theSpace Race; the understanding andengineering of the metallicalloys, andsilica andcarbon materials, used in building space vehicles enabling the exploration of space. Materials science has driven, and been driven by, the development of revolutionary technologies such asrubbers,plastics,semiconductors, andbiomaterials.
Before the 1960s (and in some cases decades after), many eventualmaterials science departments weremetallurgy orceramics engineering departments, reflecting the 19th and early 20th-century emphasis on metals and ceramics. The growth of material science in the United States was catalyzed in part by theAdvanced Research Projects Agency, which funded a series of university-hosted laboratories in the early 1960s, "to expand the national program of basic research and training in the materials sciences."[5] In comparison with mechanical engineering, thenascent material science field focused on addressing materials from the macro-level and on the approach that materials are designed on the basis of knowledge of behavior at the microscopic level.[6] Due to the expanded knowledge of the link between atomic and molecular processes as well as the overall properties of materials, the design of materials came to be based on specific desired properties.[6] The materials science field has since broadened to include every class of materials, including ceramics,polymers, semiconductors,magnetic materials, biomaterials, andnanomaterials, generally classified into three distinct groups: ceramics, metals, and polymers. The prominent change in materials science during the recent decades is active usage of computer simulations to find new materials, predict properties and understand phenomena.
The materials paradigm represented in the form of a tetrahedron
A material is defined as a substance (most often a solid, but other condensed phases can be included) that is intended to be used for certain applications.[7] There are a myriad of materials around us; they can be found in anything from[8] new and advanced materials that are being developed includenanomaterials,biomaterials,[9] andenergy materials to name a few.[10]
The basis of materials science is studying the interplay between the structure of materials, the processing methods to make that material, and the resulting material properties. The complex combination of these produce the performance of a material in a specific application. Many features across many length scales impact material performance, from the constituent chemical elements, itsmicrostructure, and macroscopic features from processing. Together with the laws ofthermodynamics andkinetics materials scientists aim to understand and improve materials.
Structure is one of the most important components of the field of materials science. The very definition of the field holds that it is concerned with the investigation of "the relationships that exist between the structures and properties of materials".[11] Materials science examines the structure of materials from the atomic scale, all the way up to the macro scale.[3]Characterization is the way materials scientists examine the structure of a material. This involves methods such as diffraction withX-rays,electrons orneutrons, and various forms ofspectroscopy andchemical analysis such asRaman spectroscopy,energy-dispersive spectroscopy,chromatography,thermal analysis,electron microscope analysis, etc.
Atomic structure deals with the atoms of the materials, and how they are arranged to give rise to molecules, crystals, etc. Much of the electrical, magnetic and chemical properties of materials arise from this level of structure. The length scales involved are in angstroms (Å). The chemical bonding and atomic arrangement (crystallography) are fundamental to studying the properties and behavior of any material.
To obtain a full understanding of the material structure and how it relates to its properties, the materials scientist must study how the different atoms, ions and molecules are arranged and bonded to each other. This involves the study and use ofquantum chemistry orquantum physics.Solid-state physics,solid-state chemistry andphysical chemistry are also involved in the study of bonding and structure.
Crystal structure of a perovskite with a chemical formula ABX3[12]
Crystallography is the science that examines the arrangement of atoms in crystalline solids. Crystallography is a useful tool for materials scientists. One of the fundamental concepts regarding the crystal structure of a material includes theunit cell, which is the smallest unit of a crystal lattice (space lattice) that repeats to make up the macroscopic crystal structure. Most common structural materials includeparallelpiped and hexagonal lattice types.[13] Insingle crystals, the effects of the crystalline arrangement of atoms is often easy to see macroscopically, because the natural shapes of crystals reflect the atomic structure. Further, physical properties are often controlled by crystalline defects. The understanding of crystal structures is an important prerequisite for understandingcrystallographic defects. Examples of crystal defects consist of dislocations including edges, screws, vacancies, self inter-stitials, and more that are linear, planar, and three dimensional types of defects.[14] New and advanced materials that are being developed includenanomaterials,biomaterials.[15] Mostly, materials do not occur as a single crystal, but in polycrystalline form, as an aggregate of small crystals or grains with different orientations. Because of this, thepowder diffraction method, which uses diffraction patterns of polycrystalline samples with a large number of crystals, plays an important role in structural determination. Most materials have a crystalline structure, but some important materials do not exhibit regular crystal structure.[16]Polymers display varying degrees of crystallinity, and many are completely non-crystalline.Glass, some ceramics, and many natural materials areamorphous, not possessing any long-range order in their atomic arrangements. The study of polymers combines elements of chemical and statistical thermodynamics to give thermodynamic and mechanical descriptions of physical properties.
Materials, which atoms and molecules form constituents in the nanoscale (i.e., they form nanostructures) are called nanomaterials. Nanomaterials are the subject of intense research in the materials science community due to the unique properties that they exhibit.
Nanostructure deals with objects and structures that are in the 1 – 100 nm range.[17] In many materials, atoms or molecules agglomerate to form objects at the nanoscale. This causes many interesting electrical, magnetic, optical, and mechanical properties.
In describing nanostructures, it is necessary to differentiate between the number of dimensions on thenanoscale.
Nanotextured surfaces haveone dimension on the nanoscale, i.e., only the thickness of the surface of an object is between 0.1 and 100 nm.
Nanotubes havetwo dimensions on the nanoscale, i.e., the diameter of the tube is between 0.1 and 100 nm; its length could be much greater.
Finally, sphericalnanoparticles havethree dimensions on the nanoscale, i.e., the particle is between 0.1 and 100 nm in each spatial dimension. The terms nanoparticles andultrafine particles (UFP) often are used synonymously although UFP can reach into the micrometre range. The term 'nanostructure' is often used, when referring to magnetic technology. Nanoscale structure in biology is often calledultrastructure.
Microstructure is defined as the structure of a prepared surface or thin foil of material as revealed by a microscope above 25× magnification. It deals with objects from 100 nm to a few cm. The microstructure of a material (which can be broadly classified into metallic, polymeric, ceramic and composite) can strongly influence physical properties such as strength, toughness, ductility, hardness, corrosion resistance, high/low temperature behavior, wear resistance, and so on.[18] Most of the traditional materials (such as metals and ceramics) are microstructured.
The manufacture of a perfectcrystal of a material is physically impossible. For example, any crystalline material will containdefects such asprecipitates, grain boundaries (Hall–Petch relationship), vacancies, interstitial atoms or substitutional atoms.[19] The microstructure of materials reveals these larger defects and advances in simulation have allowed an increased understanding of how defects can be used to enhance material properties.
Synthesis and processing involves the creation of a material with the desired micro-nanostructure. A material cannot be used in industry if no economically viable production method for it has been developed. Therefore, developing processing methods for materials that are reasonably effective and cost-efficient is vital to the field of materials science. Different materials require different processing or synthesis methods. For example, the processing of metals has historically defined eras such as theBronze Age andIron Age and is studied under the branch of materials science namedphysicalmetallurgy. Chemical and physical methods are also used to synthesize other materials such aspolymers,ceramics,semiconductors, andthin films. As of the early 21st century, new methods are being developed to synthesize nanomaterials such asgraphene.[20]
A phase diagram for a binary system displaying a eutectic point
Thermodynamics is concerned withheat andtemperature and their relation toenergy andwork. It definesmacroscopic variables, such asinternal energy,entropy, andpressure, that partly describe a body of matter or radiation. It states that the behavior of those variables is subject to general constraints common to all materials. These general constraints are expressed in the four laws of thermodynamics. Thermodynamics describes the bulk behavior of the body, not the microscopic behaviors of the very large numbers of its microscopic constituents, such as molecules. The behavior of these microscopic particles is described by, and the laws of thermodynamics are derived from,statistical mechanics.
The study of thermodynamics is fundamental to materials science. It forms the foundation to treat general phenomena in materials science and engineering, including chemical reactions, magnetism, polarizability, and elasticity.[21] It explains fundamental tools such asphase diagrams and concepts such as phaseequilibrium.
Chemical kinetics is the study of the rates at which systems that are out of equilibrium change under the influence of various forces. When applied to materials science, it deals with how a material changes with time (moves from non-equilibrium to equilibrium state) due to application of a certain field. It details the rate of various processes evolving in materials including shape, size, composition and structure.Diffusion is important in the study of kinetics as this is the most common mechanism by which materials undergo change.[22] Kinetics is essential in processing of materials because, among other things, it details how the microstructure changes with application of heat.
Materials science is a highly active area of research. Together with materials science departments,physics,chemistry, and manyengineering departments are involved in materials research. Materials research covers a broad range of topics; the following non-exhaustive list highlights a few important research areas.
Nanomaterials describe, in principle, materials of which a single unit is sized (in at least one dimension) between 1 and 1000 nanometers (10−9 meter), but is usually 1 nm – 100 nm. Nanomaterials research takes a materials science based approach tonanotechnology, using advances in materialsmetrology and synthesis, which have been developed in support ofmicrofabrication research. Materials with structure at the nanoscale often have unique optical, electronic, or mechanical properties. The field of nanomaterials is loosely organized, like the traditional field of chemistry, into organic (carbon-based) nanomaterials, such as fullerenes, and inorganic nanomaterials based on other elements, such as silicon. Examples of nanomaterials includefullerenes,carbon nanotubes, nanocrystals, etc.
A biomaterial is any matter, surface, or construct that interacts withbiological systems.[23] Biomaterials science encompasses elements of medicine, biology, chemistry, tissue engineering, and materials science.
Biomaterials can be derived either from nature or synthesized in a laboratory using a variety of chemical approaches using metallic components,polymers,bioceramics, orcomposite materials. They are often intended or adapted for medical applications, such as biomedical devices which perform, augment, or replace a natural function. Such functions may be benign, like being used for aheart valve, or may bebioactive with a more interactive functionality such ashydroxylapatite-coatedhip implants. Biomaterials are also used every day in dental applications, surgery, and drug delivery. For example, a construct with impregnated pharmaceutical products can be placed into the body, which permits the prolonged release of a drug over an extended period of time. A biomaterial may also be anautograft,allograft orxenograft used as anorgan transplant material.
Semiconductors, metals, and ceramics are used today to form highly complex systems, such as integrated electronic circuits, optoelectronic devices, and magnetic and optical mass storage media. These materials form the basis of our modern computing world, and hence research into these materials is of vital importance.
Semiconductors are a traditional example of these types of materials. They are materials that have properties that are intermediate betweenconductors andinsulators. Their electrical conductivities are very sensitive to the concentration of impurities, which allows the use ofdoping to achieve desirable electronic properties. Hence, semiconductors form the basis of the traditional computer.
With continuing increases in computing power, simulating the behavior of materials has become possible. This enables materials scientists to understand behavior and mechanisms, design new materials, and explain properties formerly poorly understood. Efforts surroundingintegrated computational materials engineering are now focusing on combining computational methods with experiments to drastically reduce the time and effort to optimize materials properties for a given application. This involves simulating materials at all length scales, using methods such asdensity functional theory,molecular dynamics,Monte Carlo, dislocation dynamics,phase field,finite element, and many more.[26]
Besides material characterization, the material scientist or engineer also deals with extracting materials and converting them into useful forms. Thusingot casting,foundry methods,blast furnace extraction, andelectrolytic extraction are all part of the required knowledge of a materials engineer. Often the presence, absence, or variation of minute quantities of secondary elements and compounds in a bulk material will greatly affect the final properties of the materials produced. For example, steels are classified based on 1/10 and 1/100 weight percentages of the carbon and other alloying elements they contain. Thus, the extracting and purifying methods used to extract iron in a blast furnace can affect the quality of steel that is produced.
Solid materials are generally grouped into three basic classifications: ceramics, metals, and polymers. This broad classification is based on the empirical makeup and atomic structure of the solid materials, and most solids fall into one of these broad categories.[27] An item that is often made from each of these materials types is the beverage container. The material types used for beverage containers accordingly provide different advantages and disadvantages, depending on the material used. Ceramic (glass) containers are optically transparent, impervious to the passage of carbon dioxide, relatively inexpensive, and are easily recycled, but are also heavy and fracture easily. Metal (aluminum alloy) is relatively strong, is a good barrier to the diffusion of carbon dioxide, and is easily recycled. However, the cans are opaque, expensive to produce, and are easily dented and punctured. Polymers (polyethylene plastic) are relatively strong, can be optically transparent, are inexpensive and lightweight, and can be recyclable, but are not as impervious to the passage of carbon dioxide as aluminum and glass.
Another application of materials science is the study ofceramics andglasses, typically the most brittle materials with industrial relevance. Many ceramics and glasses exhibit covalent or ionic-covalent bonding with SiO2 (silica) as a fundamental building block. Ceramics – not to be confused with raw, unfiredclay – are usually seen in crystalline form. The vast majority of commercial glasses contain a metal oxide fused with silica. At the high temperatures used to prepare glass, the material is a viscous liquid which solidifies into a disordered state upon cooling. Windowpanes and eyeglasses are important examples. Fibers of glass are also used for long-range telecommunication and optical transmission. Scratch resistant CorningGorilla Glass is a well-known example of the application of materials science to drastically improve the properties of common components.
Engineering ceramics are known for their stiffness and stability under high temperatures, compression and electrical stress. Alumina,silicon carbide, andtungsten carbide are made from a fine powder of their constituents in a process of sintering with a binder. Hot pressing provides higher density material. Chemical vapor deposition can place a film of a ceramic on another material. Cermets are ceramic particles containing some metals. The wear resistance of tools is derived from cemented carbides with the metal phase of cobalt and nickel typically added to modify properties.
Ceramics can be significantly strengthened for engineering applications using the principle ofcrack deflection.[28] This process involves the strategic addition of second-phase particles within a ceramic matrix, optimizing their shape, size, and distribution to direct and control crack propagation. This approach enhances fracture toughness, paving the way for the creation of advanced, high-performance ceramics in various industries.[29]
A 6 μm diameter carbon filament (running from bottom left to top right) sitting atop the much larger human hair
Another application of materials science in industry is makingcomposite materials. These are structured materials composed of two or more macroscopic phases.
Applications range from structural elements such as steel-reinforced concrete, to the thermal insulating tiles, which play a key and integral role in NASA'sSpace Shuttle thermal protection system, which is used to protect the surface of the shuttle from the heat of re-entry into the Earth's atmosphere. One example isreinforced Carbon-Carbon (RCC), the light gray material, which withstands re-entry temperatures up to 1,510 °C (2,750 °F) and protects the Space Shuttle's wing leading edges and nose cap.[30] RCC is a laminated composite material made fromgraphiterayon cloth and impregnated with aphenolic resin. Aftercuring at high temperature in anautoclave, thelaminate ispyrolized to convert the resin to carbon, impregnated withfurfuryl alcohol in a vacuum chamber, and cured-pyrolized to convert the furfuryl alcohol to carbon. To provide oxidation resistance for reusability, the outer layers of the RCC are converted tosilicon carbide.
Other examples can be seen in the "plastic" casings of television sets, cell-phones and so on. These plastic casings are usually a composite material made up of athermoplastic matrix such asacrylonitrile butadiene styrene (ABS) in whichcalcium carbonate chalk,talc,glass fibers orcarbon fibers have been added for added strength, bulk, orelectrostatic dispersion. These additions may be termed reinforcing fibers, or dispersants, depending on their purpose.
Polyvinyl chloride (PVC) is widely used, inexpensive, and annual production quantities are large. It lends itself to a vast array of applications, fromartificial leather toelectrical insulation and cabling,packaging, andcontainers. Its fabrication and processing are simple and well-established. The versatility of PVC is due to the wide range ofplasticisers and other additives that it accepts.[32] The term "additives" in polymer science refers to the chemicals and compounds added to the polymer base to modify its material properties.
Polycarbonate would be normally considered an engineering plastic (other examples includePEEK, ABS). Such plastics are valued for their superior strengths and other special material properties. They are usually not used for disposable applications, unlike commodity plastics.
Specialty plastics are materials with unique characteristics, such as ultra-high strength, electrical conductivity, electro-fluorescence, high thermal stability, etc.
The dividing lines between the various types of plastics is not based on material but rather on their properties and applications. For example,polyethylene (PE) is a cheap, low friction polymer commonly used to make disposable bags for shopping and trash, and is considered a commodity plastic, whereasmedium-density polyethylene (MDPE) is used for underground gas and water pipes, and another variety calledultra-high-molecular-weight polyethylene (UHMWPE) is an engineering plastic which is used extensively as the glide rails for industrial equipment and the low-friction socket in implantedhip joints.
Iron alloyed with various proportions of carbon giveslow, mid andhigh carbon steels. An iron-carbon alloy is only considered steel if the carbon level is between 0.01% and 2.00% by weight. For steels, thehardness and tensile strength of the steel is related to the amount of carbon present, with increasing carbon levels also leading to lower ductility and toughness.Heat treatment processes such asquenching andtempering can significantly change these properties, however. In contrast,certain metal alloys exhibit unique properties where their size and density remain unchanged across a range of temperatures.[33] Cast iron is defined as an iron–carbon alloy with more than 2.00%, but less than 6.67% carbon. Stainless steel is defined as a regular steel alloy with greater than 10% by weight alloying content ofchromium.Nickel andmolybdenum are typically also added in stainless steels.
Other significant metallic alloys are those ofaluminium,titanium,copper andmagnesium.Copper alloys have been known for a long time (since theBronze Age), while the alloys of the other three metals have been relatively recently developed. Due to the chemical reactivity of these metals, the electrolytic extraction processes required were only developed relatively recently. The alloys of aluminium, titanium and magnesium are also known and valued for their high strength to weight ratios and, in the case of magnesium, their ability to provide electromagnetic shielding.[34] These materials are ideal for situations where high strength to weight ratios are more important than bulk cost, such as in the aerospace industry and certain automotive engineering applications.
Asemiconductor is a material that has aresistivity between aconductor andinsulator. Modern day electronics run on semiconductors, and the industry had an estimated US$530 billion market in 2021.[35] Its electronic properties can be greatly altered through intentionally introducing impurities in a process referred to as doping. Semiconductor materials are used to builddiodes,transistors,light-emitting diodes (LEDs), and analog and digitalelectric circuits, among their many uses. Semiconductor devices have replacedthermionic devices like vacuum tubes in most applications. Semiconductor devices are manufactured both as single discrete devices and asintegrated circuits (ICs), which consist of a number—from a few to millions—of devices manufactured and interconnected on a single semiconductorsubstrate.[36]
Of all the semiconductors in use today,silicon makes up the largest portion both by quantity and commercial value. Monocrystalline silicon is used to produce wafers used in the semiconductor andelectronics industry.Gallium arsenide (GaAs) is the second most popular semiconductor used. Due to its higherelectron mobility andsaturation velocity compared to silicon, it is a material of choice for high-speed electronics applications. These superior properties are compelling reasons to use GaAs circuitry in mobile phones, satellite communications, microwave point-to-point links and higher frequency radar systems. Other semiconductor materials includegermanium,silicon carbide, andgallium nitride and have various applications.
The field of materials science and engineering is important both from a scientific perspective, as well as for applications field. Materials are of the utmost importance for engineers (or other applied fields) because usage of the appropriate materials is crucial when designing systems. As a result, materials science is an increasingly important part of an engineer's education.
Materials physics is the use ofphysics to describe the physical properties of materials. It is a synthesis ofphysical sciences such aschemistry,solid mechanics,solid state physics, and materials science. Materials physics is considered a subset ofcondensed matter physics and applies fundamental condensed matter concepts to complex multiphase media, including materials of technological interest. Current fields that materials physicists work in include electronic, optical, and magnetic materials, novel materials and structures, quantum phenomena in materials, nonequilibrium physics, and soft condensed matter physics. New experimental and computational tools are constantly improving how materials systems are modeled and studied and are also fields when materials physicists work in.
The field is inherentlyinterdisciplinary, and the materials scientists or engineers must be aware and make use of the methods of the physicist, chemist and engineer. Conversely, fields such as life sciences and archaeology can inspire the development of new materials and processes, inbioinspired andpaleoinspired approaches. Thus, there remain close relationships with these fields. Conversely, many physicists, chemists and engineers find themselves working in materials science due to the significant overlaps between the fields.
Components with higher strength to weight ratios, transistors that operate at higher frequency, lower cost of display screens in mobile devices, storing hydrogen for fuel cell powered cars, filtration systems, longer-lasting and faster-charging batteries, sensors to diagnose diseases[40]
Cryogenic receiver front-end (CRFE)RF and microwave filter systems for mobile phone base stations; prototypes indry ice; Hypothetical and experiments for higher temperatures[41]
Quantum dot laser, future use as programmable matter in display technologies (TV, projection), optical data communications (high-speed data transmission), medicine (laser scalpel)
^abDefonseka, Chris (2020).Polymer Fillers and Stiffening Agents: Applications and Non-traditional Alternatives. Berlin: Walter de Gruyter GmbH & Co KG. p. 31.ISBN978-3-11-066999-2.
^Psillos, Dimitris; Kariotoglou, Petros (2015).Iterative Design of Teaching-Learning Sequences: Introducing the Science of Materials in European Schools. Dordrecht: Springer. p. 79.ISBN978-94-007-7807-8.
^abChannell, David F. (2017).A History of Technoscience: Erasing the Boundaries between Science and Technology. Oxon: Routledge. p. 225.ISBN978-1-351-97740-1.
^Callister, Jr., Rethwisch. "Materials Science and Engineering – An Introduction" (8th ed.). John Wiley and Sons, 2009 pp.5–6
^Callister, Jr., Rethwisch. Materials Science and Engineering – An Introduction (8th ed.)uildings and cars to spacecraft. The main classes of materials aremetals,semiconductors,ceramics andpolymers.. John Wiley and Sons, 2009 pp.10–12
^Zagorodni, Andrei A. (2006).Ion Exchange Materials: Properties and Applications. Amsterdam: Elsevier. pp. xi.ISBN978-0-08-044552-6.
^A. Navrotsky (1998). "Energetics and Crystal Chemical Systematics among Ilmenite, Lithium Niobate, and Perovskite Structures".Chem. Mater.10 (10):2787–2793.doi:10.1021/cm9801901.
^Callister, Jr., Rethwisch. "Materials Science and Engineering – An Introduction" (8th ed.) John Wiley and Sons, 2009
^Callister, Jr., Rethwisch. "Materials Science and Engineering – An Introduction" (8th ed.). John Wiley and Sons, 2009
^Callister, Jr., Rethwisch. Materials Science and Engineering – An Introduction (8th ed.)
^Callister, William D.; Rethwish, David G. (2018).Materials Science and Engineering an Introduction (10th ed.). Hoboken, NJ: John Wiley and Sons. p. 12.ISBN9780470419977.
Gaskell, David R. (1995).Introduction to the Thermodynamics of Materials (4th ed.). Taylor and Francis Publishing.ISBN978-1-56032-992-3.
González-Viñas, W. & Mancini, H.L. (2004).An Introduction to Materials Science. Princeton University Press.ISBN978-0-691-07097-1.
Gordon, James Edward (1984).The New Science of Strong Materials or Why You Don't Fall Through the Floor (eissue ed.). Princeton University Press.ISBN978-0-691-02380-9.
Squires, G.L. (1996).Introduction to the Theory of Thermal Neutron Scattering (2nd ed.). Mineola, New York: Dover Publications Inc.ISBN978-0-486-69447-4.
Young, R.A., ed. (1993).The Rietveld Method. Oxford: Oxford University Press & International Union of Crystallography.ISBN978-0-19-855577-3.
.jpg)
