In materials science, Ostwald's rule or Ostwald's step rule, conceived by Wilhelm Ostwald, [1] describes the formation of polymorphs. The rule states that usually the less stable polymorph crystallizes first. [2] Ostwald's rule is not a universal law but a common tendency observed in nature. [3]
This can be explained on the basis of irreversible thermodynamics, structural relationships, or a combined consideration of statistical thermodynamics and structural variation with temperature. Unstable polymorphs more closely resemble the state in solution, and thus are kinetically advantaged.
For example, out of hot water, metastable, fibrous crystals of benzamide appear first, only later to spontaneously convert to the more stable rhombic polymorph. A dramatic example is phosphorus, which upon sublimation first forms the less stable white phosphorus, which only slowly polymerizes to the red allotrope. This is notably the case for the anatase polymorph of titanium dioxide, which having a lower surface energy is commonly the first phase to form by crystallisation from amorphous precursors or solutions despite being metastable, with rutile being the equilibrium phase at all temperatures and pressures. [4]
Allotropy or allotropism is the property of some chemical elements to exist in two or more different forms, in the same physical state, known as allotropes of the elements. Allotropes are different structural modifications of an element: the atoms of the element are bonded together in different manners. For example, the allotropes of carbon include diamond, graphite, graphene, and fullerenes.
In chemistry and physics, metastability denotes an intermediate energetic state within a dynamical system other than the system's state of least energy. A ball resting in a hollow on a slope is a simple example of metastability. If the ball is only slightly pushed, it will settle back into its hollow, but a stronger push may start the ball rolling down the slope. Bowling pins show similar metastability by either merely wobbling for a moment or tipping over completely. A common example of metastability in science is isomerisation. Higher energy isomers are long lived because they are prevented from rearranging to their preferred ground state by barriers in the potential energy.
Rutile is an oxide mineral composed of titanium dioxide (TiO2), the most common natural form of TiO2. Rarer polymorphs of TiO2 are known, including anatase, akaogiite, and brookite.
In chemistry, thermodynamics, and other related fields like physics and biology, a phase transition is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure. This can be a discontinuous change; for example, a liquid may become gas upon heating to its boiling point, resulting in an abrupt change in volume. The identification of the external conditions at which a transformation occurs defines the phase transition point.
Anatase is a metastable mineral form of titanium dioxide (TiO2) with a tetragonal crystal structure. Although colorless or white when pure, anatase in nature is usually a black solid due to impurities. Three other polymorphs (or mineral forms) of titanium dioxide are known to occur naturally: brookite, akaogiite, and rutile, with rutile being the most common and most stable of the bunch. Anatase is formed at relatively low temperatures and found in minor concentrations in igneous and metamorphic rocks. Glass coated with a thin film of TiO2 shows antifogging and self-cleaning properties under ultraviolet radiation.
Aragonite is a carbonate mineral and one of the three most common naturally occurring crystal forms of calcium carbonate, the others being calcite and vaterite. It is formed by biological and physical processes, including precipitation from marine and freshwater environments.
Titanium dioxide, also known as titanium(IV) oxide or titania, is the inorganic compound with the chemical formula TiO
2. When used as a pigment, it is called titanium white, Pigment White 6 (PW6), or CI 77891. It is a white solid that is insoluble in water, although mineral forms can appear black. As a pigment, it has a wide range of applications, including paint, sunscreen, and food coloring. When used as a food coloring, it has E number E171. World production in 2014 exceeded 9 million tonnes. It has been estimated that titanium dioxide is used in two-thirds of all pigments, and pigments based on the oxide have been valued at a price of $13.2 billion.
In chemistry, the standard state of a material is a reference point used to calculate its properties under different conditions. A degree sign (°) or a superscript Plimsoll symbol (⦵) is used to designate a thermodynamic quantity in the standard state, such as change in enthalpy (ΔH°), change in entropy (ΔS°), or change in Gibbs free energy (ΔG°). The degree symbol has become widespread, although the Plimsoll is recommended in standards, see discussion about typesetting below.
Vaterite is a mineral, a polymorph of calcium carbonate (CaCO3). It was named after the German mineralogist Heinrich Vater. It is also known as mu-calcium carbonate (μ-CaCO3). Vaterite belongs to the hexagonal crystal system, whereas calcite is trigonal and aragonite is orthorhombic.
Crystallization is the process by which solids form, where the atoms or molecules are highly organized into a structure known as a crystal. Some ways by which crystals form are precipitating from a solution, freezing, or more rarely deposition directly from a gas. Attributes of the resulting crystal depend largely on factors such as temperature, air pressure, cooling rate, and in the case of liquid crystals, time of fluid evaporation.
Phosphorus pentoxide is a chemical compound with molecular formula P4O10 (with its common name derived from its empirical formula, P2O5). This white crystalline solid is the anhydride of phosphoric acid. It is a powerful desiccant and dehydrating agent.
In crystallography, polymorphism describes the phenomenon where a compound or element can crystallize into more than one crystal structure. The preceding definition has evolved over many years and is still under discussion today. Discussion of the defining characteristics of polymorphism involves distinguishing among types of transitions and structural changes occurring in polymorphism versus those in other phenomena.
Silver selenide (Ag2Se) is the reaction product formed when selenium toning analog silver gelatine photo papers in photographic print toning. The selenium toner contains sodium selenite (Na2SeO3) as one of its active ingredients, which is the source of the selenide (Se2−) anion combining with the silver in the toning process.
Nanogeoscience is the study of nanoscale phenomena related to geological systems. Predominantly, this is investigated by studying environmental nanoparticles between 1–100 nanometers in size. Other applicable fields of study include studying materials with at least one dimension restricted to the nanoscale and the transfer of energy, electrons, protons, and matter across environmental interfaces.
Elemental phosphorus can exist in several allotropes, the most common of which are white and red solids. Solid violet and black allotropes are also known. Gaseous phosphorus exists as diphosphorus and atomic phosphorus.
In thermodynamics, the limit of local stability with respect to small fluctuations is clearly defined by the condition that the second derivative of Gibbs free energy is zero.
Amorphous calcium carbonate (ACC) is the amorphous and least stable polymorph of calcium carbonate. ACC is extremely unstable under normal conditions and is found naturally in taxa as wide-ranging as sea urchins, corals, mollusks, and foraminifera. It is usually found as a monohydrate, holding the chemical formula CaCO3·H2O; however, it can also exist in a dehydrated state, CaCO3. ACC has been known to science for over 100 years when a non-diffraction pattern of calcium carbonate was discovered by Sturcke Herman, exhibiting its poorly-ordered nature.
Nickel sulfide is any inorganic compound with the formula NiSx. These compounds range in color from bronze (Ni3S2) to black (NiS2). The nickel sulfide with simplest stoichiometry is NiS, also known as the mineral millerite. From the economic perspective, Ni9S8, the mineral pentlandite, is the chief source of mined nickel. Other minerals include heazlewoodite (Ni3S2) and polydymite (Ni3S4), and the mineral Vaesite (NiS2). Some nickel sulfides are used commercially as catalysts.
Titanium dioxide nanoparticles, also called ultrafine titanium dioxide or nanocrystalline titanium dioxide or microcrystalline titanium dioxide, are particles of titanium dioxide with diameters less than 100 nm. Ultrafine TiO2 is used in sunscreens due to its ability to block ultraviolet radiation while remaining transparent on the skin. It is in rutile crystal structure and coated with silica or/and alumina to prevent photocatalytic phenomena. The health risks of ultrafine TiO2 from dermal exposure on intact skin are considered extremely low, and it is considered safer than other substances used for ultraviolet protection.
In materials science, disappearing polymorphs describes a phenomenon in which a seemingly stable crystal structure is suddenly unable to be produced, instead transforming into a polymorph, or differing crystal structure with the same chemical composition, during nucleation. Sometimes the resulting transformation is extremely hard or impractical to reverse, because the new polymorph may be more stable. It is hypothesized that contact with a single microscopic seed crystal of the new polymorph can be enough to start a chain reaction causing the transformation of a much larger mass of material. Widespread contamination with such microscopic seed crystals may lead to the impression that the original polymorph has "disappeared."