|
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. 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 composed of i molecules with a surface and a similar configuration of i molecules located inside an infinitely large crystal. This quantity is therefore the energy associated with the surface. The equilibrium shape of the crystal will then be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thermodynamic Equilibrium
Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is 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 matter nor of energy within a system or between systems. In a system that is in its own state of internal thermodynamic equilibrium, no macroscopic change occurs. 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, until disturbed by a thermodynamic operation. In a macroscopic equilibrium, perfectly or almost perfectly balanced microscopic exchanges occur; this is the physical explanation of the notion of macroscopic equilibrium. A thermodynamic sys ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Droplet
A drop or droplet is a small column of liquid, bounded completely or almost completely by free surfaces. A drop may form when liquid accumulates at the lower end of a tube or other surface boundary, producing a hanging drop called a pendant drop. Drops may also be formed by the condensation of a vapor or by atomization of a larger mass of solid. Water vapor will condense into droplets depending on the temperature. The temperature at which droplets form is called the dew point. Surface tension Liquid forms drops because it exhibits surface tension. A simple way to form a drop is to allow liquid to flow slowly from the lower end of a vertical tube of small diameter. The surface tension of the liquid causes the liquid to hang from the tube, forming a pendant. When the drop exceeds a certain size it is no longer stable and detaches itself. The falling liquid is also a drop held together by surface tension. Viscosity and pitch drop experiments Some substances that appear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Crystal
A crystal or crystalline solid is a solid material whose constituents (such as atoms, molecules, or ions) are arranged in a highly ordered microscopic structure, forming a crystal lattice that extends in all directions. In addition, macroscopic single crystals are usually identifiable by their geometrical shape, consisting of flat faces with specific, characteristic orientations. The scientific study of crystals and crystal formation is known as crystallography. The process of crystal formation via mechanisms of crystal growth is called crystallization or solidification. The word ''crystal'' derives from the Ancient Greek word (), meaning both "ice" and "rock crystal", from (), "icy cold, frost". Examples of large crystals include snowflakes, diamonds, and table salt. Most inorganic solids are not crystals but polycrystals, i.e. many microscopic crystals fused together into a single solid. Polycrystals include most metals, rocks, ceramics, and ice. A third category of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Energy Minimization
In the field of computational chemistry, energy minimization (also called energy optimization, geometry minimization, or geometry optimization) is the process of finding an arrangement in space of a collection of atoms where, according to some computational model of chemical bonding, the net inter-atomic force on each atom is acceptably close to zero and the position on the potential energy surface (PES) is a stationary point (described later). The collection of atoms might be a single molecule, an ion, a condensed phase, a transition state or even a collection of any of these. The computational model of chemical bonding might, for example, be quantum mechanics. As an example, when optimizing the geometry of a water molecule, one aims to obtain the hydrogen-oxygen bond lengths and the hydrogen-oxygen-hydrogen bond angle which minimize the forces that would otherwise be pulling atoms together or pushing them apart. The motivation for performing a geometry optimization is the physic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Josiah Willard Gibbs
Josiah Willard Gibbs (; February 11, 1839 – April 28, 1903) was an American scientist who made significant theoretical contributions to physics, chemistry, and mathematics. His work on the applications of thermodynamics was instrumental in transforming physical chemistry into a rigorous inductive science. Together with James Clerk Maxwell and Ludwig Boltzmann, he created statistical mechanics (a term that he coined), explaining the laws of thermodynamics as consequences of the statistical properties of Statistical ensemble (mathematical physics), ensembles of the possible states of a physical system composed of many particles. Gibbs also worked on the application of Maxwell's equations to problems in physical optics. As a mathematician, he invented modern vector calculus (independently of the British scientist Oliver Heaviside, who carried out similar work during the same period). In 1863, Yale University, Yale awarded Gibbs the first American Doctor of Philosophy, doctorate ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gibbs Free Energy
In thermodynamics, the Gibbs free energy (or Gibbs energy; symbol G) is a thermodynamic potential that can be used to calculate the maximum amount of work that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy change , measured in joules in SI) is the ''maximum'' amount of non-expansion work that can be extracted from a closed system (one that can exchange heat and work with its surroundings, but not matter) at fixed temperature and pressure. This maximum can be attained only in a completely reversible process. When a system transforms reversibly from an initial state to a final state under these conditions, the decrease in Gibbs free energy equals the work done by the system to its surroundings, minus the work of the pressure forces. The Gibbs energy is the thermodynamic potential that is minim ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Surface Energy
In surface science, surface free energy (also interfacial free energy or surface 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 (the atoms on the surface have more energy compared with the atoms in the bulk), otherwise there would be a driving force for surfaces to be created, removing the bulk of the material (see 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 at the two surfaces. Cutting a solid body into pieces disrupts its bonds and increases the surface area, and th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
George Wulff
George (Georgy/Yuri Viktorovich) Wulff (russian: Георгий (Юрий) Викторович Вульф) (22 June 1863, Nizhyn (Russian Empire, nowadays Ukraine) – 25 December 1925, Moscow) was a Russian crystallographer. The Wulff construction,G Wulff, '' Zeitschrift fur Krystallographie und Mineralogie'', 34, 5/6, pp 449-530, 1901. Wulff net, Wulff-Bragg's condition and the mineral wulffite are named after him. Wulff was one of the first to experiment with X-ray crystallography X-ray crystallography is the experimental science determining the atomic and molecular structure of a crystal, in which the crystalline structure causes a beam of incident X-rays to diffract into many specific directions. By measuring the angles .... References 1863 births 1925 deaths Physicists from the Russian Empire 19th-century Ukrainian physicists Crystallographers {{physicist-stub ... [...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 from ... [...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 diffraction of X-rays by crystals. In addition to his scientific endeavors with contributions in optics, crystallography, quantum theory, superconductivity, and the theory of relativity, Laue had a number of administrative positions which advanced and guided 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 Strassburg, he began his compulsory year of military service, after which in 1899 he started to study mathematics, physics, and chemistry at the University of Strassburg, the University of Göttingen, and the Ludwig Maximilian Uni ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intensive And Extensive Properties
Physical 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. According to IUPAC, an intensive quantity is one whose magnitude is independent of the size of the system, whereas an extensive quantity is one whose magnitude is additive for subsystems. The terms ''intensive and extensive quantities'' were introduced into physics by German writer Georg Helm in 1898, and by American physicist and chemist Richard C. Tolman in 1917. An intensive property does not depend on the system size or the amount of material in the system. It 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, extensive properties such as the mass, volume and entropy of syst ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
