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65-544: Solid materials are formed from densely packed atoms, which interact intensely. These interactions produce the mechanical (e.g. hardness and elasticity ), thermal , electrical , magnetic and optical properties of solids. Depending on the material involved and the conditions in which it was formed, the atoms may be arranged in a regular, geometric pattern ( crystalline solids , which include metals and ordinary water ice ) or irregularly (an amorphous solid such as common window glass ). The bulk of solid-state physics, as

130-437: A crystal disrupt periodicity, this use of Bloch's theorem is only an approximation, but it has proven to be a tremendously valuable approximation, without which most solid-state physics analysis would be intractable. Deviations from periodicity are treated by quantum mechanical perturbation theory . Modern research topics in solid-state physics include: Hardness In materials science , hardness (antonym: softness )

195-452: A crystal of sodium chloride (common salt), the crystal is made up of ionic sodium and chlorine , and held together with ionic bonds . In others, the atoms share electrons and form covalent bonds . In metals, electrons are shared amongst the whole crystal in metallic bonding . Finally, the noble gases do not undergo any of these types of bonding. In solid form, the noble gases are held together with van der Waals forces resulting from

260-484: A decrease in the material's hardness. The way to inhibit the movement of planes of atoms, and thus make them harder, involves the interaction of dislocations with each other and interstitial atoms. When a dislocation intersects with a second dislocation, it can no longer traverse through the crystal lattice. The intersection of dislocations creates an anchor point and does not allow the planes of atoms to continue to slip over one another A dislocation can also be anchored by

325-424: A different type of atom at the lattice site that should normally be occupied by a metal atom, a substitutional defect is formed. If there exists an atom in a site where there should normally not be, an interstitial defect is formed. This is possible because space exists between atoms in a crystal lattice. While point defects are irregularities at a single site in the crystal lattice, line defects are irregularities on

390-451: A few crystals per meter of length. Another application of single-crystal solids is in materials science in the production of high strength materials with low thermal creep , such as turbine blades . Here, the absence of grain boundaries actually gives a decrease in yield strength, but more importantly decreases the amount of creep which is critical for high temperature, close tolerance part applications. Researcher Barry Piearcey found that

455-423: A general theory, is focused on crystals . Primarily, this is because the periodicity of atoms in a crystal — its defining characteristic — facilitates mathematical modeling. Likewise, crystalline materials often have electrical , magnetic , optical , or mechanical properties that can be exploited for engineering purposes. The forces between the atoms in a crystal can take a variety of forms. For example, in

520-450: A means to understand the ultimate performance of metallic conductors. It is vital for understanding the basic science such as catalytic chemistry, surface physics, electrons, and monochromators . Production of metallic single crystals have the highest quality requirements and are grown, or pulled, in the form of rods. Certain companies can produce specific geometries, grooves, holes, and reference faces along with varying diameters. Of all

585-409: A modified Kyropoulos method can be used to grow high quality 300 kg sapphire single crystals. The Verneuil method , also called the flame-fusion method, was used in the early 1900s to make rubies before CZ. The diagram on the right illustrates most of the conventional methods. There have been new breakthroughs such as chemical vapor depositions (CVD) along with different variations and tweaks to

650-413: A plane of atoms. Dislocations are a type of line defect involving the misalignment of these planes. In the case of an edge dislocation, a half plane of atoms is wedged between two planes of atoms. In the case of a screw dislocation two planes of atoms are offset with a helical array running between them. In glasses, hardness seems to depend linearly on the number of topological constraints acting between

715-463: A right-angle bend at the casting mold would decrease the number of columnar crystals and later, scientist Giamei used this to start the single-crystal structure of the turbine blade. Single crystals are essential in research especially condensed-matter physics and all aspects of materials science such as surface science . The detailed study of the crystal structure of a material by techniques such as Bragg diffraction and helium atom scattering

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780-637: A single crystal is an amorphous structure where the atomic position is limited to short-range order only. In between the two extremes exist polycrystalline , which is made up of a number of smaller crystals known as crystallites , and paracrystalline phases. Single crystals will usually have distinctive plane faces and some symmetry, where the angles between the faces will dictate its ideal shape. Gemstones are often single crystals artificially cut along crystallographic planes to take advantage of refractive and reflective properties. Although current methods are extremely sophisticated with modern technology,

845-464: A tensile test. This relationship can be used to describe how the material will respond to almost any loading situation, often by using the Finite Element Method (FEM). This applies to the outcome of an indentation test (with a given size and shape of indenter, and a given applied load). However, while a hardness number thus depends on the stress-strain relationship, inferring the latter from

910-486: A topic of fervent research. One of the main challenges has been growing uniform single crystals of bilayer or multilayer graphene over large areas; epitaxial growth and the new CVD (mentioned above) are among the new promising methods under investigation. Organic semiconducting single crystals are different from the inorganic crystals. The weak intermolecular bonds mean lower melting temperatures, and higher vapor pressures and greater solubility. For single crystals to grow,

975-424: Is a measure of the resistance to localized plastic deformation , such as an indentation (over an area) or a scratch (linear), induced mechanically either by pressing or abrasion . In general, different materials differ in their hardness; for example hard metals such as titanium and beryllium are harder than soft metals such as sodium and metallic tin , or wood and common plastics . Macroscopic hardness

1040-406: Is also used as optical windows because of its transparency at specific infrared (IR) wavelengths , making it very useful for some instruments. Sapphires : Also known as the alpha phase of aluminum oxide (Al 2 O 3 ) to scientists, sapphire single crystals are widely used in hi-tech engineering. It can be grown from gaseous, solid, or solution phases. The diameter of the crystals resulting from

1105-442: Is broadly considered to be the subfield of condensed matter physics, often referred to as hard condensed matter, that focuses on the properties of solids with regular crystal lattices. Many properties of materials are affected by their crystal structure . This structure can be investigated using a range of crystallographic techniques, including X-ray crystallography , neutron diffraction and electron diffraction . The sizes of

1170-437: Is easier with single crystals because it is possible to study directional dependence of various properties and compare with theoretical predictions. Furthermore, macroscopically averaging techniques such as angle-resolved photoemission spectroscopy or low-energy electron diffraction are only possible or meaningful on surfaces of single crystals. In superconductivity there have been cases of materials where superconductivity

1235-527: Is extremely difficult to grow single crystals of the polymers. It is mainly because that the polymer chains are of different length and due to the various entropy reasons. However, topochemical reactions are one of the easy methods to get single crystals of the polymer. [1] One of the most used single crystals is that of Silicon in the semiconductor industry. The four main production methods for semiconductor single crystals are from metallic solutions: liquid phase epitaxy (LPE), liquid phase electroepitaxy (LPEE),

1300-831: Is generally characterized by strong intermolecular bonds , but the behavior of solid materials under force is complex; therefore, hardness can be measured in different ways, such as scratch hardness , indentation hardness , and rebound hardness. Hardness is dependent on ductility , elastic stiffness , plasticity , strain , strength , toughness , viscoelasticity , and viscosity . Common examples of hard matter are ceramics , concrete , certain metals , and superhard materials , which can be contrasted with soft matter . There are three main types of hardness measurements: scratch, indentation, and rebound. Within each of these classes of measurement there are individual measurement scales. For practical reasons conversion tables are used to convert between one scale and another. Scratch hardness

1365-665: Is known as a scleroscope . Two scales that measures rebound hardness are the Leeb rebound hardness test and Bennett hardness scale. Ultrasonic Contact Impedance (UCI) method determines hardness by measuring the frequency of an oscillating rod. The rod consists of a metal shaft with vibrating element and a pyramid-shaped diamond mounted on one end. There are five hardening processes: Hall-Petch strengthening , work hardening , solid solution strengthening , precipitation hardening , and martensitic transformation . In solid mechanics , solids generally have three responses to force , depending on

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1430-459: Is known as the Hall-Petch relationship . However, below a critical grain-size, hardness decreases with decreasing grain size. This is known as the inverse Hall-Petch effect. Hardness of a material to deformation is dependent on its microdurability or small-scale shear modulus in any direction, not to any rigidity or stiffness properties such as its bulk modulus or Young's modulus . Stiffness

1495-407: Is often confused for hardness. Some materials are stiffer than diamond (e.g. osmium) but are not harder, and are prone to spalling and flaking in squamose or acicular habits. The key to understanding the mechanism behind hardness is understanding the metallic microstructure , or the structure and arrangement of the atoms at the atomic level. In fact, most important metallic properties critical to

1560-413: Is the sclerometer . Another tool used to make these tests is the pocket hardness tester . This tool consists of a scale arm with graduated markings attached to a four-wheeled carriage. A scratch tool with a sharp rim is mounted at a predetermined angle to the testing surface. In order to use it a weight of known mass is added to the scale arm at one of the graduated markings, the tool is then drawn across

1625-453: Is the measure of how resistant a sample is to fracture or permanent plastic deformation due to friction from a sharp object. The principle is that an object made of a harder material will scratch an object made of a softer material. When testing coatings, scratch hardness refers to the force necessary to cut through the film to the substrate. The most common test is Mohs scale , which is used in mineralogy . One tool to make this measurement

1690-436: Is the tendency of a material to fracture with very little or no detectable plastic deformation beforehand. Thus in technical terms, a material can be both brittle and strong. In everyday usage "brittleness" usually refers to the tendency to fracture under a small amount of force, which exhibits both brittleness and a lack of strength (in the technical sense). For perfectly brittle materials, yield strength and ultimate strength are

1755-693: The American Physical Society . The DSSP catered to industrial physicists, and solid-state physics became associated with the technological applications made possible by research on solids. By the early 1960s, the DSSP was the largest division of the American Physical Society. Large communities of solid state physicists also emerged in Europe after World War II , in particular in England , Germany , and

1820-601: The Czochralski process (CZ) , Floating zone (or Zone Movement), and the Bridgman technique . Dr. Teal and Dr. Little of Bell Telephone Laboratories were the first to use the Czochralski method to create Ge and Si single crystals. Other methods of crystallization may be used, depending on the physical properties of the substance, including hydrothermal synthesis , sublimation , or simply solvent-based crystallization . For example,

1885-663: The Soviet Union . In the United States and Europe, solid state became a prominent field through its investigations into semiconductors , superconductivity , nuclear magnetic resonance , and diverse other phenomena. During the early Cold War, research in solid state physics was often not restricted to solids, which led some physicists in the 1970s and 1980s to found the field of condensed matter physics , which organized around common techniques used to investigate solids, liquids, plasmas, and other complex matter. Today, solid-state physics

1950-412: The defects associated with grain boundaries can give monocrystals unique properties, particularly mechanical, optical and electrical, which can also be anisotropic , depending on the type of crystallographic structure. These properties, in addition to making some gems precious, are industrially used in technological applications, especially in optics and electronics. Because entropic effects favor

2015-451: The amount of force and the type of material: Strength is a measure of the extent of a material's elastic range, or elastic and plastic ranges together. This is quantified as compressive strength , shear strength , tensile strength depending on the direction of the forces involved. Ultimate strength is an engineering measure of the maximum load a part of a specific material and geometry can withstand. Brittleness , in technical usage,

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2080-475: The atoms of the network. Hence, the rigidity theory has allowed predicting hardness values with respect to composition. Dislocations provide a mechanism for planes of atoms to slip and thus a method for plastic or permanent deformation. Planes of atoms can flip from one side of the dislocation to the other effectively allowing the dislocation to traverse through the material and the material to deform permanently. The movement allowed by these dislocations causes

2145-458: The critical dimensions of an indentation left by a specifically dimensioned and loaded indenter. Common indentation hardness scales are Rockwell , Vickers , Shore , and Brinell , amongst others. Rebound hardness , also known as dynamic hardness , measures the height of the "bounce" of a diamond-tipped hammer dropped from a fixed height onto a material. This type of hardness is related to elasticity . The device used to take this measurement

2210-433: The density of dislocations increases, there are more intersections created and consequently more anchor points. Similarly, as more interstitial atoms are added, more pinning points that impede the movements of dislocations are formed. As a result, the more anchor points added, the harder the material will become. Careful note should be taken of the relationship between a hardness number and the stress-strain curve exhibited by

2275-405: The dislocations and other crystal defects which are sources of resistance. But the resulting wires are still polycrystalline. The grain boundaries and remaining crystal defects are responsible for some residual resistance. This can be quantified and better understood by examining single crystals. Single-crystal copper did prove to have better conductivity than polycrystalline copper. However,

2340-412: The electrons are modelled as a Fermi gas , a gas of particles which obey the quantum mechanical Fermi–Dirac statistics . The free electron model gave improved predictions for the heat capacity of metals, however, it was unable to explain the existence of insulators . The nearly free electron model is a modification of the free electron model which includes a weak periodic perturbation meant to model

2405-491: The existing methods. These are not shown in the diagram. In the case of metal single crystals, fabrication techniques also include epitaxy and abnormal grain growth in solids. Epitaxy is used to deposit very thin (micrometer to nanometer scale) layers of the same or different materials on the surface of an existing single crystal. Applications of this technique lie in the areas of semiconductor production, with potential uses in other nanotechnological fields and catalysis. It

2470-565: The focus of ultrafast electronic devices for its intrinsic carrier mobility. Arsenide : Arsenide III can be combined with various elements such as B, Al, Ga, and In, with the GaAs compound being in high demand for wafers. Cadmium Telluride : CdTe crystals have several applications as substrates for IR imaging, electrooptic devices, and solar cells . By alloying CdTe and ZnTe together room-temperature X-ray and gamma-ray detectors can be made. Metals can be produced in single-crystal form and provide

2535-447: The form of optical fiber with its large-diameter substrates. Other photonic devices include lasers, photodetectors, avalanche photo diodes, optical modulators and amplifiers, signal processing, and both optoelectronic and photonic integrated circuits. Germanium : This was the material in the first transistor invented by Bardeen, Brattain, and Shockley in 1947. It is used in some gamma-ray detectors and infrared optics. Now it has become

2600-478: The former is far from simple and is not attempted in any rigorous way during conventional hardness testing. (In fact, the Indentation Plastometry technique, which involves iterative FEM modelling of an indentation test, does allow a stress-strain curve to be obtained via indentation, but this is outside the scope of conventional hardness testing.) A hardness number is just a semi-quantitative indicator of

2665-400: The grain level of the microstructure that are responsible for the hardness of the material. These irregularities are point defects and line defects. A point defect is an irregularity located at a single lattice site inside of the overall three-dimensional lattice of the grain. There are three main point defects. If there is an atom missing from the array, a vacancy defect is formed. If there is

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2730-399: The growth method are important when considering electronic uses after. They are used for lasers and nonlinear optics . Some notable uses are as in the window of a biometric fingerprint reader, optical disks for long-term data storage, and X-ray interferometer. Indium Phosphide : These single crystals are particularly appropriate for combining optoelectronics with high-speed electronics in

2795-424: The growth of Silicon crystals. Other inorganic semiconducting single crystals include GaAs, GaP, GaSb, Ge, InAs, InP, InSb, CdS, CdSe, CdTe, ZnS, ZnSe, and ZnTe. Most of these can also be tuned with various doping for desired properties. Single-crystal graphene is also highly desired for applications in electronics and optoelectronics with its large carrier mobility and high thermal conductivity, and remains

2860-445: The highest light-to-electricity conversion. On the quantum scale that microprocessors operate on, the presence of grain boundaries would have a significant impact on the functionality of field effect transistors by altering local electrical properties. Therefore, microprocessor fabricators have invested heavily in facilities to produce large single crystals of silicon. The Czochralski method and floating zone are popular methods for

2925-449: The ideal arrangements, and it is these defects that critically determine many of the electrical and mechanical properties of real materials. Properties of materials such as electrical conduction and heat capacity are investigated by solid state physics. An early model of electrical conduction was the Drude model , which applied kinetic theory to the electrons in a solid. By assuming that

2990-427: The individual crystals in a crystalline solid material vary depending on the material involved and the conditions when it was formed. Most crystalline materials encountered in everyday life are polycrystalline , with the individual crystals being microscopic in scale, but macroscopic single crystals can be produced either naturally (e.g. diamonds ) or artificially. Real crystals feature defects or irregularities in

3055-546: The interaction between the conduction electrons and the ions in a crystalline solid. By introducing the idea of electronic bands , the theory explains the existence of conductors , semiconductors and insulators . The nearly free electron model rewrites the Schrödinger equation for the case of a periodic potential . The solutions in this case are known as Bloch states . Since Bloch's theorem applies only to periodic potentials, and since unceasing random movements of atoms in

3120-443: The interaction with interstitial atoms. If a dislocation comes in contact with two or more interstitial atoms, the slip of the planes will again be disrupted. The interstitial atoms create anchor points, or pinning points, in the same manner as intersecting dislocations. By varying the presence of interstitial atoms and the density of dislocations, a particular metal's hardness can be controlled. Although seemingly counter-intuitive, as

3185-529: The manufacturing of today’s goods are determined by the microstructure of a material. At the atomic level, the atoms in a metal are arranged in an orderly three-dimensional array called a crystal lattice . In reality, however, a given specimen of a metal likely never contains a consistent single crystal lattice. A given sample of metal will contain many grains, with each grain having a fairly consistent array pattern. At an even smaller scale, each grain contains irregularities. There are two types of irregularities at

3250-518: The material contains immobile positive ions and an "electron gas" of classical, non-interacting electrons, the Drude model was able to explain electrical and thermal conductivity and the Hall effect in metals, although it greatly overestimated the electronic heat capacity. Arnold Sommerfeld combined the classical Drude model with quantum mechanics in the free electron model (or Drude-Sommerfeld model). Here,

3315-412: The material. The latter, which is conventionally obtained via tensile testing , captures the full plasticity response of the material (which is in most cases a metal). It is in fact a dependence of the (true) von Mises plastic strain on the (true) von Mises stress , but this is readily obtained from a nominal stress – nominal strain curve (in the pre- necking regime), which is the immediate outcome of

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3380-513: The metallic elements, silver and copper have the best conductivity at room temperature, setting the bar for performance. The size of the market, and vagaries in supply and cost, have provided strong incentives to seek alternatives or find ways to use less of them by improving performance. The conductivity of commercial conductors is often expressed relative to the International Annealed Copper Standard , according to which

3445-457: The origins of crystal growth can be traced back to salt purification by crystallization in 2500 BCE. A more advanced method using an aqueous solution was started in 1600 CE while the melt and vapor methods began around 1850 CE. Basic crystal growth methods can be separated into four categories based on what they are artificially grown from: melt, solid, vapor, and solution. Specific techniques to produce large single crystals (aka boules ) include

3510-491: The polarisation of the electronic charge cloud on each atom. The differences between the types of solid result from the differences between their bonding. The physical properties of solids have been common subjects of scientific inquiry for centuries, but a separate field going by the name of solid-state physics did not emerge until the 1940s , in particular with the establishment of the Division of Solid State Physics (DSSP) within

3575-541: The presence of some imperfections in the microstructure of solids , such as impurities , inhomogeneous strain and crystallographic defects such as dislocations , perfect single crystals of meaningful size are exceedingly rare in nature. The necessary laboratory conditions often add to the cost of production. On the other hand, imperfect single crystals can reach enormous sizes in nature: several mineral species such as beryl , gypsum and feldspars are known to have produced crystals several meters across. The opposite of

3640-420: The purest copper wire available in 1914 measured around 100%. The purest modern copper wire is a better conductor, measuring over 103% on this scale. The gains are from two sources. First, modern copper is more pure. However, this avenue for improvement seems at an end. Making the copper purer still makes no significant improvement. Second, annealing and other processes have been improved. Annealing reduces

3705-405: The purity of the material is crucial and the production of organic materials usually require many steps to reach the necessary purity. Extensive research is being done to look for materials that are thermally stable with high charge-carrier mobility. Past discoveries include naphthalene, tetracene, and 9,10-diphenylanthacene (DPA). Triphenylamine derivatives have shown promise, and recently in 2021,

3770-406: The resistance to plastic deformation. Although hardness is defined in a similar way for most types of test – usually as the load divided by the contact area – the numbers obtained for a particular material are different for different types of test, and even for the same test with different applied loads. Attempts are sometimes made to identify simple analytical expressions that allow features of

3835-446: The same hardness number. The use of hardness numbers for any quantitative purpose should, at best, be approached with considerable caution. Single crystal In materials science , a single crystal (or single-crystal solid or monocrystalline solid ) is a material in which the crystal lattice of the entire sample is continuous and unbroken to the edges of the sample, with no grain boundaries . The absence of

3900-484: The same, because they do not experience detectable plastic deformation. The opposite of brittleness is ductility . The toughness of a material is the maximum amount of energy it can absorb before fracturing, which is different from the amount of force that can be applied. Toughness tends to be small for brittle materials, because elastic and plastic deformations allow materials to absorb large amounts of energy. Hardness increases with decreasing particle size . This

3965-620: The single-crystal copper not only became a better conductor than high purity polycrystalline silver, but with prescribed heat and pressure treatment could surpass even single-crystal silver. Although impurities are usually bad for conductivity, a silver single crystal with a small amount of copper substitutions proved to be the best. As of 2009, no single-crystal copper is manufactured on a large scale industrially, but methods of producing very large individual crystal sizes for copper conductors are exploited for high performance electrical applications. These can be considered meta-single crystals with only

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4030-409: The single-crystal structure of α-phenyl-4′-(diphenylamino)stilbene (TPA) grown using the solution method exhibited even greater potential for semiconductor use with its anisotropic hole transport property. Single crystals have unique physical properties due to being a single grain with molecules in a strict order and no grain boundaries. This includes optical properties, and single crystals of silicon

4095-464: The stress-strain curve, particularly the yield stress and Ultimate Tensile Stress (UTS), to be obtained from a particular type of hardness number. However, these are all based on empirical correlations, often specific to particular types of alloy: even with such a limitation, the values obtained are often quite unreliable. The underlying problem is that metals with a range of combinations of yield stress and work hardening characteristics can exhibit

4160-412: The test surface. The use of the weight and markings allows a known pressure to be applied without the need for complicated machinery. Indentation hardness measures the resistance of a sample to material deformation due to a constant compression load from a sharp object. Tests for indentation hardness are primarily used in engineering and metallurgy . The tests work on the basic premise of measuring

4225-441: The traveling heater method (THM), and liquid phase diffusion (LPD). However, there are many other single crystals besides inorganic single crystals capable semiconducting, including single-crystal organic semiconductors . Monocrystalline silicon used in the fabrication of semiconductors and photovoltaics is the greatest use of single-crystal technology today. In photovoltaics, the most efficient crystal structure will yield

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