Residual entropy is the difference in entropy between a non-equilibrium state and crystal state of a substance close to absolute zero. This term is used in condensed matter physics to describe the entropy at zero kelvin of a glass or plastic crystal referred to the crystal state, whose entropy is zero according to the third law of thermodynamics. It occurs if a material can exist in many different states when cooled. The most common non-equilibrium state is vitreous state, glass.
A common example is the case of carbon monoxide, which has a very small dipole moment. As the carbon monoxide crystal is cooled to absolute zero, few of the carbon monoxide molecules have enough time to align themselves into a perfect crystal (with all of the carbon monoxide molecules oriented in the same direction). Because of this, the crystal is locked into a state with different corresponding microstates, giving a residual entropy of , rather than zero.
Another example is any amorphous solid (glass). These have residual entropy, because the atom-by-atom microscopic structure can be arranged in a huge number of different ways across a macroscopic system.
One of the first examples of residual entropy was pointed out by Pauling to describe water ice. In water, each oxygen atom is bonded to two hydrogen atoms. However, when water freezes it forms a tetragonal structure where each oxygen atom has four hydrogen neighbors (due to neighboring water molecules). The hydrogen atoms sitting between the oxygen atoms have some degree of freedom as long as each oxygen atom has two hydrogen atoms that are 'nearby', thus forming the traditional H2O water molecule. However, it turns out that for a large number of water molecules in this configuration, the hydrogen atoms have a large number of possible configurations that meet the 2-in 2-out rule (each oxygen atom must have two 'near' (or 'in') hydrogen atoms, and two far (or 'out') hydrogen atoms). This freedom exists down to absolute zero, which was previously seen as an absolute one-of-a-kind configuration. The existence of these multiple configurations (choices for each H of orientation along O--O axis) that meet the rules of absolute zero (2-in 2-out for each O) amounts to randomness, or in other words, entropy. Thus systems that can take multiple configurations at or near absolute zero are said to have residual entropy.[2]
Although water ice was the first material for which residual entropy was proposed, it is generally very difficult to prepare pure defect-free crystals of water ice for studying. A great deal of research has thus been undertaken into finding other systems that exhibit residual entropy. Geometrically frustrated systems in particular often exhibit residual entropy. An important example is spin ice, which is a geometrically frustrated magnetic material where the magnetic moments of the magnetic atoms have Ising-like magnetic spins and lie on the corners of network of corner-sharing tetrahedra. This material is thus analogous to water ice, with the exception that the spins on the corners of the tetrahedra can point into or out of the tetrahedra, thereby producing the same 2-in, 2-out rule as in water ice, and therefore the same residual entropy. One of the interesting properties of geometrically frustrated magnetic materials such as spin ice is that the level of residual entropy can be controlled by the application of an external magnetic field. This property can be used to create one-shot refrigeration systems.
Absolute zero is the lowest limit of the thermodynamic temperature scale; a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibrational motion, retaining only quantum mechanical, zero-point energy-induced particle motion. The theoretical temperature is determined by extrapolating the ideal gas law; by international agreement, absolute zero is taken as −273.15 degrees on the Celsius scale, which equals −459.67 degrees on the Fahrenheit scale. The corresponding Kelvin and Rankine temperature scales set their zero points at absolute zero by definition.
Combustion, or burning, is a high-temperature exothermic redox chemical reaction between a fuel and an oxidant, usually atmospheric oxygen, that produces oxidized, often gaseous products, in a mixture termed as smoke. Combustion does not always result in fire, because a flame is only visible when substances undergoing combustion vaporize, but when it does, a flame is a characteristic indicator of the reaction. While activation energy must be supplied to initiate combustion, the heat from a flame may provide enough energy to make the reaction self-sustaining.
A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical reactions encompass changes that only involve the positions of electrons in the forming and breaking of chemical bonds between atoms, with no change to the nuclei, and can often be described by a chemical equation. Nuclear chemistry is a sub-discipline of chemistry that involves the chemical reactions of unstable and radioactive elements where both electronic and nuclear changes can occur.
In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and plasma. Many intermediate states are known to exist, such as liquid crystal, and some states only exist under extreme conditions, such as Bose–Einstein condensates and Fermionic condensates, neutron-degenerate matter, and quark–gluon plasma. For a list of exotic states of matter, see the article List of states of matter.
In organic chemistry, an acetal is a functional group with the connectivity R2C(OR')2. Here, the R groups can be organic fragments or hydrogen, while the R' groups must be organic fragments not hydrogen. The two R' groups can be equivalent to each other or not. Acetals are formed from and convertible to aldehydes or ketones and have the same oxidation state at the central carbon, but have substantially different chemical stability and reactivity as compared to the analogous carbonyl compounds. The central carbon atom has four bonds to it, and is therefore saturated and has tetrahedral geometry.
In materials that exhibit antiferromagnetism, the magnetic moments of atoms or molecules, usually related to the spins of electrons, align in a regular pattern with neighboring spins pointing in opposite directions. This is, like ferromagnetism and ferrimagnetism, a manifestation of ordered magnetism. The phenomenon of antiferromagnetism was first introduced by Lev Landau in 1933.
The third law of thermodynamics states that the entropy of a closed system at thermodynamic equilibrium approaches a constant value when its temperature approaches absolute zero. This constant value cannot depend on any other parameters characterizing the system, such as pressure or applied magnetic field. At absolute zero the system must be in a state with the minimum possible energy.
Molecular hydrogen occurs in two isomeric forms, one with its two proton nuclear spins aligned parallel (orthohydrogen), the other with its two proton spins aligned antiparallel (parahydrogen). These two forms are often referred to as spin isomers or as nuclear spin isomers.
Ice Ih is the hexagonal crystal form of ordinary ice, or frozen water. Virtually all ice in the biosphere is ice Ih, with the exception only of a small amount of ice Ic that is occasionally present in the upper atmosphere. Ice Ih exhibits many peculiar properties that are relevant to the existence of life and regulation of global climate. For a description of these properties, see Ice, which deals primarily with ice Ih.
In condensed matter physics, the term geometrical frustration refers to a phenomenon where atoms tend to stick to non-trivial positions or where, on a regular crystal lattice, conflicting inter-atomic forces lead to quite complex structures. As a consequence of the frustration in the geometry or in the forces, a plenitude of distinct ground states may result at zero temperature, and usual thermal ordering may be suppressed at higher temperatures. Much studied examples are amorphous materials, glasses, or dilute magnets.
In chemistry, a non-covalent interaction differs from a covalent bond in that it does not involve the sharing of electrons, but rather involves more dispersed variations of electromagnetic interactions between molecules or within a molecule. The chemical energy released in the formation of non-covalent interactions is typically on the order of 1–5 kcal/mol. Non-covalent interactions can be classified into different categories, such as electrostatic, π-effects, van der Waals forces, and hydrophobic effects.
In a tetrahedral molecular geometry, a central atom is located at the center with four substituents that are located at the corners of a tetrahedron. The bond angles are cos−1(−1⁄3) = 109.4712206...° ≈ 109.5° when all four substituents are the same, as in methane as well as its heavier analogues. Methane and other perfectly symmetrical tetrahedral molecules belong to point group Td, but most tetrahedral molecules have lower symmetry. Tetrahedral molecules can be chiral.
A spin ice is a magnetic substance that does not have a single minimal-energy state. It has magnetic moments (i.e. "spin") as elementary degrees of freedom which are subject to frustrated interactions. By their nature, these interactions prevent the moments from exhibiting a periodic pattern in their orientation down to a temperature much below the energy scale set by the said interactions. Spin ices show low-temperature properties, residual entropy in particular, closely related to those of common crystalline water ice. The most prominent compounds with such properties are dysprosium titanate (Dy2Ti2O7) and holmium titanate (Ho2Ti2O7). The orientation of the magnetic moments in spin ice resembles the positional organization of hydrogen atoms (more accurately, ionized hydrogen, or protons) in conventional water ice (see figure 1).
The concept entropy was first developed by German physicist Rudolf Clausius in the mid-nineteenth century as a thermodynamic property that predicts that certain spontaneous processes are irreversible or impossible. In statistical mechanics, entropy is formulated as a statistical property using probability theory. The statistical entropy perspective was introduced in 1870 by Austrian physicist Ludwig Boltzmann, who established a new field of physics that provided the descriptive linkage between the macroscopic observation of nature and the microscopic view based on the rigorous treatment of large ensembles of microstates that constitute thermodynamic systems.
In thermodynamics, entropy is a numerical quantity that shows that many physical processes can go in only one direction in time. For example, cream and coffee can be mixed together, but cannot be "unmixed"; a piece of wood can be burned, but cannot be "unburned". The word 'entropy' has entered popular usage to refer a lack of order or predictability, or of a gradual decline into disorder. A more physical interpretation of thermodynamic entropy refers to spread of energy or matter, or to extent and diversity of microscopic motion.
In thermodynamics, entropy is often associated with the amount of order or disorder in a thermodynamic system. This stems from Rudolf Clausius' 1862 assertion that any thermodynamic process always "admits to being reduced [reduction] to the alteration in some way or another of the arrangement of the constituent parts of the working body" and that internal work associated with these alterations is quantified energetically by a measure of "entropy" change, according to the following differential expression:
In statistical mechanics, the ice-type models or six-vertex models are a family of vertex models for crystal lattices with hydrogen bonds. The first such model was introduced by Linus Pauling in 1935 to account for the residual entropy of water ice. Variants have been proposed as models of certain ferroelectric and antiferroelectric crystals.
Temperature is a physical quantity that expresses quantitatively the attribute of hotness or coldness. Temperature is measured with a thermometer. It reflects the kinetic energy of the vibrating and colliding atoms making up a substance.
Water is a polar inorganic compound that is at room temperature a tasteless and odorless liquid, which is nearly colorless apart from an inherent hint of blue. It is by far the most studied chemical compound and is described as the "universal solvent" and the "solvent of life". It is the most abundant substance on the surface of Earth and the only common substance to exist as a solid, liquid, and gas on Earth's surface. It is also the third most abundant molecule in the universe.
In chemistry, ice rules are basic principles that govern arrangement of atoms in water ice. They are also known as Bernal–Fowler rules, after British physicists John Desmond Bernal and Ralph H. Fowler who first described them in 1933.
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