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Wulff Construction
The Wulff construction is a method to determine the equilibrium shape of a droplet or crystal of fixed volume inside a separate phase (usually its saturated solution or vapor). Energy minimization arguments are used to show that certain crystal planes are preferred over others, giving the crystal its shape. It is of fundamental importance in a number of areas ranging from the shape of nanoparticles and precipitates to nucleation. It also has more applied relevance in areas such as the shapes of active particles in heterogeneous catalysis. Theory In 1878 Josiah Willard Gibbs proposed that a droplet or crystal will arrange itself such that its surface Gibbs free energy is minimized by assuming a shape of low surface energy. He defined the quantity :\Delta G_i= \sum_\gamma_j O_j~ Here \gamma _j represents the surface (Gibbs free) energy per unit area of the jth crystal face and O_j is the area of said face. \Delta G_i represents the difference in energy between a real crystal c ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Wulff
Georg Wulff, Georgy Wulff or Yuri Viktorovich Vulf () (22 June 1863, Nizhyn (Russian Empire, now Ukraine) – 25 December 1925, Moscow) was a pioneer Russian crystallographer. Biography Wulff was born in Nizhyn, Chernigov province where his mother Lydia was daughter of teacher E. V. Gudim. His father Viktor Konstantinovich Vulf was a literature teacher at the 6th Warsaw Gymnasium. He grew up in Warsaw and graduated from the 6th Warsaw Gymnasium in 1880. He then went to the Imperial Warsaw University to study natural sciences. He studied under crystallographer A. E. Lagorio, and physicists N. G. Egorov and P. A. Zilov. In the third year, he studied the electrical properties of quartz for which he received a gold medal. In his fourth year he was assisting lectures of professor Zilov. He began to study the relationship of crystal structure and optical properties and in 1888 he published a paper on the "theory of rotatory polarization". He then went to St. Petersburg University wo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emilie Ringe
Emilie Ringe (born 1984) is an American chemist who is a professor of synthetic and natural nanomaterials at the University of Cambridge and a Fellow of Gonville and Caius College. She was selected by ''Chemical & Engineering News'' as one of its "Talented Twelve" young scientists in 2021. Early life and education Ringe grew up in Quebec. She was an undergraduate student at Northwestern University, where she graduated in chemistry. She remained at Northwestern for her graduate studies. Her doctoral research developed structure-function relationships of nanoparticles, and how structure and composition impacted the optoelectronic properties. During her graduate studies she started working with electron microscopy. Research and career Ringe joined the University of Cambridge as a Newton International Fellow. She held a joint position at Trinity Hall, where she served as a Gott Research Fellow. She moved to Rice University in 2014, where she established the Electron Microscopy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Extended Wulff Constructions
Extended Wulff constructions refers to a number of different ways to model the structure of nanoparticles as well as larger mineral crystals. They can be used to understand the shape of gemstones and Crystal twinning, crystals with twins, and in other areas such as understanding both the shape and how nanoparticles play a role in the commercial production of chemicals using Heterogeneous catalysis, heterogeneous catalysts. Extended Wulff constructions are variants of the Wulff construction, which is used for a solid single crystal in isolation. They include cases for solid particles on substrates, those with internal boundaries and also when growth is important. Depending upon whether there are twins or a substrate, there are different cases as indicated in the Extended Wulff constructions#Figure 1, decision tree figure. The simplest forms of these constructions yield the lowest Gibbs free energy (thermodynamic) shape, or the stable growth form for an isolated particle; it can be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aspect Ratio
The aspect ratio of a geometry, geometric shape is the ratio of its sizes in different dimensions. For example, the aspect ratio of a rectangle is the ratio of its longer side to its shorter side—the ratio of width to height, when the rectangle is oriented as a "landscape format, landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal Fraction (mathematics), fraction. The values x and y do not represent actual widths and heights but, rather, the proportion between width and height. As an example, 8:5, 16:10, 1.6:1, and 1.6 are all ways of representing the same aspect ratio. In objects of more than two dimensions, such as hyperrectangles, the aspect ratio can still be defined as the ratio of the longest side to the shortest side. Applications and uses The term is most commonly used with reference to: * Graphic / image ** Aspect ratio (image), Image aspect ratio ** Display aspect ratio ** Pape ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Product Rule
In calculus, the product rule (or Leibniz rule or Leibniz product rule) is a formula used to find the derivatives of products of two or more functions. For two functions, it may be stated in Lagrange's notation as (u \cdot v)' = u ' \cdot v + u \cdot v' or in Leibniz's notation as \frac (u\cdot v) = \frac \cdot v + u \cdot \frac. The rule may be extended or generalized to products of three or more functions, to a rule for higher-order derivatives of a product, and to other contexts. Discovery Discovery of this rule is credited to Gottfried Leibniz, who demonstrated it using "infinitesimals" (a precursor to the modern differential). (However, J. M. Child, a translator of Leibniz's papers, argues that it is due to Isaac Barrow.) Here is Leibniz's argument: Let ''u'' and ''v'' be functions. Then ''d(uv)'' is the same thing as the difference between two successive ''uvs; let one of these be ''uv'', and the other ''u+du'' times ''v+dv''; then: \begin d(u\cdot v) & = (u + d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensive And Extensive Properties
Physical or chemical properties of materials and systems can often be categorized as being either intensive or extensive, according to how the property changes when the size (or extent) of the system changes. The terms "intensive and extensive quantities" were introduced into physics by German mathematician Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. According to International Union of Pure and Applied Chemistry (IUPAC), an intensive property or intensive quantity is one whose magnitude is independent of the size of the system. An intensive property is not necessarily homogeneously distributed in space; it can vary from place to place in a body of matter and radiation. Examples of intensive properties include temperature, ''T''; refractive index, ''n''; density, ''ρ''; and hardness, ''η''. By contrast, an extensive property or extensive quantity is one whose magnitude is additive for subsystems. Examples include mass, volume and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Conyers Herring
William Conyers Herring (November 15, 1914 – July 23, 2009) was an American physicist. He was a professor of applied physics at Stanford University and the Wolf Prize in Physics recipient in 1984/5. Academic career Conyers Herring completed his Ph.D. in physics from Princeton University in 1937, submitting a dissertation entitled ''On Energy Coincidences in the Theory of Brillouin Zones'' under the direction of Eugene Wigner. In 1946, he joined the technical staff of Bell Laboratories in Murray Hill, New Jersey, where he remained until 1978. Then, he joined the faculty at Stanford University. Contributions Conyers Herring played a major role in the development of solid state physics. He laid the foundations of band structure calculations of metals and semiconductors, culminating in the discovery of the Orthogonalized Plane Wave Method (O.P.W.) in 1940. He was years ahead of his time in this contribution. A great deal of modern solid state physics as produced today stems ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Max Von Laue
Max Theodor Felix von Laue (; 9 October 1879 – 24 April 1960) was a German physicist who received the Nobel Prize in Physics in 1914 "for his discovery of the X-ray diffraction, diffraction of X-rays by crystals". In addition to his scientific endeavors with contributions in optics, crystallography, Quantum mechanics, quantum theory, superconductivity, and the theory of relativity, Laue had a number of administrative positions which advanced and guided Science and technology in Germany, German scientific research and development during four decades. A strong objector to Nazism, he was instrumental in re-establishing and organizing German science after World War II. Biography Early years Laue was born in Pfaffendorf, now part of Koblenz, Germany, to Julius Laue and Minna Zerrenner. In 1898, after passing his ''Abitur'' in Strasbourg, Strassburg, he began his compulsory year of military service, after which in 1899 he started to study mathematics, physics, and chemistry at the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Zeitschrift Für Krystallographie Und Mineralogie
A magazine is a periodical publication, print or digital, produced on a regular schedule, that contains any of a variety of subject-oriented textual and visual content forms. Magazines are generally financed by advertising, purchase price, prepaid subscriptions, or by a combination of the three. They are categorised by their frequency of publication (i.e., as weeklies, monthlies, quarterlies, etc.), their target audiences (e.g., women's and trade magazines), their subjects of focus (e.g., popular science and religious), and their tones or approach (e.g., works of satire or humor). Appearance on the cover of print magazines has historically been understood to convey a place of honor or distinction to an individual or event. Term origin and definition Origin The etymology of the word "magazine" suggests derivation from the Arabic (), the broken plural of () meaning "depot, storehouse" (originally military storehouse); that comes to English via Middle French and Italian . In ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Energy
In surface science, surface energy (also interfacial free energy or surface free energy) quantifies the disruption of intermolecular bonds that occurs when a surface is created. In solid-state physics, surfaces must be intrinsically less energetically favorable than the bulk of the material (that is, the atoms on the surface must have more energy than the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material by sublimation. The surface energy may therefore be defined as the excess energy at the surface of a material compared to the bulk, or it is the work required to build an area of a particular surface. Another way to view the surface energy is to relate it to the work required to cut a bulk sample, creating two surfaces. There is "excess energy" as a result of the now-incomplete, unrealized bonding between the two created surfaces. Cutting a solid body into pieces disrupts its bonds and increases the surfac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Equilibrium
Thermodynamic equilibrium is a notion of thermodynamics with axiomatic status referring to an internal state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable walls. In thermodynamic equilibrium, there are no net macroscopic flows of mass nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, not only is there an absence of macroscopic change, but there is an “absence of any ''tendency'' toward change on a macroscopic scale.” Systems in mutual thermodynamic equilibrium are simultaneously in mutual thermal, mechanical, chemical, and radiative equilibria. Systems can be in one kind of mutual equilibrium, while not in others. In thermodynamic equilibrium, all kinds of equilibrium hold at once and indefinitely, unless disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly ba ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
