Euhedral and anhedral
Euhedral crystals are those that are well-formed, with sharp recognised faces. The opposite is anhedral: a rock with an anhedral texture is composed of mineral grains that have no well-formed crystal faces or cross-section shape in thin section. Anhedral crystal growth occurs in a competitive environment with no free space for the formation of crystal faces. An intermediate texture with some crystal face-formation is termed subhedral. Crystals that grow from cooling liquid magma do not form smooth faces or sharp crystal outlines; as magma cools, the crystals grow and touch each other, preventing crystal faces from forming properly or at all. When snowflakes crystallize, they do not touch each other. Thus, snowflakes form six-sided twinned crystals. In rocks, the presence of euhedral crystals may signify that they formed early in the crystallization of magma or crystallized in a cavity or vug, without hindrance from other crystals. "Euhedral" is derived from the Greek eu meaning well and hedron meaning shape.
Euhedral crystals have flat faces with sharp angles. The flat faces are oriented in a specific way relative to the underlying atomic arrangement of the crystal: They are planes of low Miller index; this occurs. As a crystal grows, new atoms attach to the rougher and less stable parts of the surface, but less to the flat, stable surfaces. Therefore, the flat surfaces tend to grow larger and smoother, until the whole crystal surface consists of these plane surfaces. Xenomorph Idiomorph Crystal habit Rock microstructure List of rock textures
Chromium is a chemical element with symbol Cr and atomic number 24. It is the first element in group 6, it is a steely-grey, lustrous and brittle transition metal. Chromium boasts a high usage rate as a metal, able to be polished while resisting tarnishing. Chromium is the main additive in stainless steel, a popular steel alloy due to its uncommonly high specular reflection. Simple polished chromium reflects 70% of the visible spectrum, with 90% of infrared light being reflected; the name of the element is derived from the Greek word χρῶμα, chrōma, meaning color, because many chromium compounds are intensely colored. Ferrochromium alloy is commercially produced from chromite by silicothermic or aluminothermic reactions and chromium metal by roasting and leaching processes followed by reduction with carbon and aluminium. Chromium metal is of high value for hardness. A major development in steel production was the discovery that steel could be made resistant to corrosion and discoloration by adding metallic chromium to form stainless steel.
Stainless steel and chrome plating together comprise 85% of the commercial use. In the United States, trivalent chromium ion is considered an essential nutrient in humans for insulin and lipid metabolism. However, in 2014, the European Food Safety Authority, acting for the European Union, concluded that there was not sufficient evidence for chromium to be recognized as essential. While chromium metal and Cr ions are not considered toxic, hexavalent chromium is both toxic and carcinogenic. Abandoned chromium production sites require environmental cleanup. Chromium is the fourth transition metal found on the periodic table, has an electron configuration of 3d5 4s1, it is the first element in the periodic table whose ground-state electron configuration violates the Aufbau principle. This occurs again in the periodic table with other elements and their electron configurations, such as copper and molybdenum; this occurs. In the previous elements, the energetic cost of promoting an electron to the next higher energy level is too great to compensate for that released by lessening inter-electronic repulsion.
However, in the 3d transition metals, the energy gap between the 3d and the next-higher 4s subshell is small, because the 3d subshell is more compact than the 4s subshell, inter-electron repulsion is smaller between 4s electrons than between 3d electrons. This lowers the energetic cost of promotion and increases the energy released by it, so that the promotion becomes energetically feasible and one or two electrons are always promoted to the 4s subshell. Chromium is the first element in the 3d series where the 3d electrons start to sink into the inert core. Chromium is a strong oxidising agent in contrast to the tungsten oxides. Chromium is hard, is the third hardest element behind carbon and boron, its Mohs hardness is 8.5, which means that it can scratch samples of quartz and topaz, but can be scratched by corundum. Chromium is resistant to tarnishing, which makes it useful as a metal that preserves its outermost layer from corroding, unlike other metals such as copper and aluminium. Chromium has a melting point of 1907 °C, low compared to the majority of transition metals.
However, it still has the second highest melting point out of all the Period 4 elements, being topped by vanadium by 3 °C at 1910 °C. The boiling point of 2671 °C, however, is comparatively lower, having the third lowest boiling point out of the Period 4 transition metals alone behind manganese and zinc. Chromium has an unusually high specular reflection in comparison to that of other transition metals. At 425 μm, chromium was found to have a relative maximum reflection of about 72% reflectance, before entering a depression in reflectivity, reaching a minimum of 62% reflectance at 750 μm before rising again to reflecting 90% of 4000 μm of infrared waves.. When chromium is formed into a stainless steel alloy and polished, the specular reflection decreases with the inclusion of additional metals, yet is still rather high in comparison with other alloys. Between 40% and 60% of the visible spectrum is reflected from polished stainless steel; the explanation on why chromium displays such a high turnout of reflected photon waves in general the 90% of infrared waves that were reflected, can be attributed to chromium's magnetic properties.
Chromium has unique magnetic properties in the sense that chromium is the only elemental solid which shows antiferromagnetic ordering at room temperature. Above 38 °C, its magnetic ordering changes to paramagnetic.. The antiferromagnetic properties, which cause the chromium atoms to temporarily ionize and bond with themselves, are present because the body-centric cubic's magnetic properties are disproportionate to the lattice periodicity; this is due to the fact that the magnetic moments at the cube's corners and the cube centers are not equal, but are still antiparallel. From here, the frequency-dependent relative permittivity of chromium, deriving from Maxwell's equations in conjunction with chromium's antiferromagnetivity, leaves chromium with a high infrared and visible light reflectance. Chromium metal left standing in air is passivated by oxidation, forming a th
The pyroxenes are a group of important rock-forming inosilicate minerals found in many igneous and metamorphic rocks. Pyroxenes have the general formula XY2O6 where X represents calcium, iron or magnesium and more zinc, manganese or lithium and Y represents ions of smaller size, such as chromium, iron, cobalt, scandium, vanadium or iron. Although aluminium substitutes extensively for silicon in silicates such as feldspars and amphiboles, the substitution occurs only to a limited extent in most pyroxenes, they share a common structure consisting of single chains of silica tetrahedra. Pyroxenes that crystallize in the monoclinic system are known as clinopyroxenes and those that cystallize in the orthorhombic system are known as orthopyroxenes; the name pyroxene is derived from the Ancient Greek words for stranger. Pyroxenes were so named because of their presence in volcanic lavas, where they are sometimes seen as crystals embedded in volcanic glass. However, they are early-forming minerals that crystallized before the lava erupted.
The upper mantle of Earth is composed of olivine and pyroxene. Pyroxene and feldspar are the major minerals in gabbro; the chain silicate structure of the pyroxenes offers much flexibility in the incorporation of various cations and the names of the pyroxene minerals are defined by their chemical composition. Pyroxene minerals are named according to the chemical species occupying the X site, the Y site, the tetrahedral T site. Cations in Y site are bound to 6 oxygens in octahedral coordination. Cations in the X site can be coordinated depending on the cation size. Twenty mineral names are recognised by the International Mineralogical Association's Commission on New Minerals and Mineral Names and 105 used names have been discarded. A typical pyroxene has silicon in the tetrahedral site and predominately ions with a charge of +2 in both the X and Y sites, giving the approximate formula XYT2O6; the names of the common calcium–iron–magnesium pyroxenes are defined in the'pyroxene quadrilateral' shown in Figure 2.
The enstatite-ferrosilite series contain up to 5 mol.% calcium and exists in three polymorphs, orthorhombic orthoenstatite and protoenstatite and monoclinic clinoenstatite. Increasing the calcium content prevents the formation of the orthorhombic phases and pigeonite only crystallises in the monoclinic system. There is not complete solid solution in calcium content and Mg-Fe-Ca pyroxenes with calcium contents between about 15 and 25 mol.% are not stable with respect to a pair of exolved crystals. This leads to a miscibility gap between augite compositions. There is an arbitrary separation between the diopside-hedenbergite solid solution; the divide is taken at >45 mol.% Ca. As the calcium ion cannot occupy the Y site, pyroxenes with more than 50 mol.% calcium are not possible. A related mineral wollastonite has the formula of the hypothetical calcium end member but important structural differences mean that it is not grouped with the pyroxenes. Magnesium and iron are by no means the only cations that can occupy the X and Y sites in the pyroxene structure.
A second important series of pyroxene minerals are the sodium-rich pyroxenes, corresponding to nomenclature shown in Figure 3. The inclusion of sodium, which has a charge of +1, into the pyroxene implies the need for a mechanism to make up the "missing" positive charge. In jadeite and aegirine this is added by the inclusion of a +3 cation on the Y site. Sodium pyroxenes with more than 20 mol.% calcium, magnesium or iron components are known as omphacite and aegirine-augite, with 80% or more of these components the pyroxene falls in the quadrilateral shown in Figure 2. Table 1 shows the wide range of other cations that can be accommodated in the pyroxene structure, indicates the sites that they occupy. In assigning ions to sites, the basic rule is to work from left to right in this table, first assigning all silicon to the T site and filling the site with the remaining aluminium and iron. Not all the resulting mechanisms to achieve charge neutrality follow the sodium example above, there are several alternative schemes: Coupled substitutions of 1+ and 3+ ions on the X and Y sites respectively.
For example, Na and Al give the jadeite composition. Coupled substitution of a 1+ ion on the X site and a mixture of equal numbers of 2+ and 4+ ions on the Y site; this leads to e.g. NaFe2+0.5Ti4+0.5Si2O6. The Tschermak substitution where a 3+ ion occupies the Y site and a T site leading to e.g. CaAlAlSiO6. In nature, more than one substitution may be found in the same mineral. Clinopyroxenes Aegirine, NaFe3+Si2O6 Augite, 2O6 Clinoenstatite, MgSiO3 Diopside, CaMgSi2O6 Esseneite, CaFe3+ Hedenbergite, CaFe2+Si2O6 Jadeite, NaSi2O6 Jervisite, Si2O6 Johannsenite, CaMn2+Si2O6 Kanoite, Mn2+Si2O6 Kosmochlor, NaCrSi2O6 Namansilite, NaMn3+Si2O6 Natalyite, NaV3+Si2O6 Omphacite, Si2O6 Petedunnite, CaSi2O6 Pigeonite, Si2O6 Spodumene, LiAl2 Orthopyroxenes Hypersthene, SiO3 Donpeacorite, MgSi2O6 Enstatite, Mg2Si2O6 Ferrosilite, Fe2Si2O6 Nchwaningite, Mn2+2SiO32•(H
The mineral olivine is a magnesium iron silicate with the formula 2SiO4. Thus it is a type of orthosilicate, it is a common mineral in Earth's subsurface but weathers on the surface. The ratio of magnesium to iron varies between the two endmembers of the solid solution series: forsterite and fayalite. Compositions of olivine are expressed as molar percentages of forsterite and fayalite. Forsterite's melting temperature is unusually high at atmospheric pressure 1,900 °C, while fayalite's is much lower. Melting temperature varies smoothly between the two endmembers. Olivine incorporates only minor amounts of elements other than oxygen, silicon and iron. Manganese and nickel are the additional elements present in highest concentrations. Olivine gives its name to the group of minerals with a related structure —which includes tephroite and kirschsteinite. Olivine's crystal structure incorporates aspects of the orthorhombic P Bravais lattice, which arise from each silica unit being joined by metal divalent cations with each oxygen in SiO4 bound to 3 metal ions.
It has a spinel-like structure similar to magnetite but uses one quadrivalent and two divalent cations M22+ M4+O4 instead of two trivalent and one divalent cations. Olivine gemstones are called chrysolite. Olivine rock is harder than surrounding rock and stands out as distinct ridges in the terrain; these ridges are dry with little soil. Drought resistant scots pine is one of few trees. Olivine pine forest is unique to Norway, it found on dry olivine ridges in the fjord districts of Sunnmøre and Nordfjord. Olivine rock is base-rich; the habitat is endangered by road construction. Olivine is named for its olive-green color, though it may alter to a reddish color from the oxidation of iron. Translucent olivine is sometimes used as a gemstone called peridot, it is called chrysolite. Some of the finest gem-quality olivine has been obtained from a body of mantle rocks on Zabargad Island in the Red Sea. Olivine occurs in both mafic and ultramafic igneous rocks and as a primary mineral in certain metamorphic rocks.
Mg-rich olivine crystallizes from magma, rich in magnesium and low in silica. That magma crystallizes to mafic rocks such as basalt. Ultramafic rocks such as peridotite and dunite can be residues left after extraction of magmas, they are more enriched in olivine after extraction of partial melts. Olivine and high pressure structural variants constitute over 50% of the Earth's upper mantle, olivine is one of the Earth's most common minerals by volume; the metamorphism of impure dolomite or other sedimentary rocks with high magnesium and low silica content produces Mg-rich olivine, or forsterite. Fe-rich olivine is much less common, but it occurs in igneous rocks in small amounts in rare granites and rhyolites, Fe-rich olivine can exist stably with quartz and tridymite. In contrast, Mg-rich olivine does not occur stably with silica minerals, as it would react with them to form orthopyroxene. Mg-rich olivine is stable to pressures equivalent to a depth of about 410 km within Earth; because it is thought to be the most abundant mineral in Earth’s mantle at shallower depths, the properties of olivine have a dominant influence upon the rheology of that part of Earth and hence upon the solid flow that drives plate tectonics.
Experiments have documented that olivine at high pressures can contain at least as much as about 8900 parts per million of water, that such water content drastically reduces the resistance of olivine to solid flow. Moreover, because olivine is so abundant, more water may be dissolved in olivine of the mantle than is contained in Earth's oceans. Mg-rich olivine has been discovered in meteorites, on the Moon and Mars, falling into infant stars, as well as on asteroid 25143 Itokawa; such meteorites include collections of debris from the early Solar System. The spectral signature of olivine has been seen in the dust disks around young stars; the tails of comets have the spectral signature of olivine, the presence of olivine was verified in samples of a comet from the Stardust spacecraft in 2006. Comet-like olivine has been detected in the planetesimal belt around the star Beta Pictoris. Minerals in the olivine group crystallize in the orthorhombic system with isolated silicate tetrahedra, meaning that olivine is a nesosilicate.
In an alternative view, the atomic structure can be described as a hexagonal, close-packed array of oxygen ions with half of the octahedral sites occupied with magnesium or iron ions and one-eighth of the tetrahedral sites occupied by silicon ions. There are two distinct metal sites and only one distinct silicon site. O1, O2, M2 and Si all lie on mirror planes. O3 lies in a general position. At the high temperatures and pressures found at depth within the Earth the olivine structure is no longer stable. Below depths of about 410 km olivine undergoes an exothermic phase transition to the sorosilicate, wadsleyite and, at a
Almandine known incorrectly as almandite, is a species of mineral belonging to the garnet group. The name is a corruption of alabandicus, the name applied by Pliny the Elder to a stone found or worked at Alabanda, a town in Caria in Asia Minor. Almandine is an iron alumina garnet, of deep red color, inclining to purple, it is cut with a convex face, or en cabochon, is known as carbuncle. Viewed through the spectroscope in a strong light, it shows three characteristic absorption bands. Almandine is one end-member of a mineral solid solution series, with the other end member being the garnet pyrope; the almandine crystal formula is: Fe3Al23. Magnesium substitutes for the iron with pyrope-rich composition. Almandine, Fe2+3Al2Si3O12, is the ferrous iron end member of the class of garnet minerals representing an important group of rock-forming silicates, which are the main constituents of the Earth's crust, upper mantle and transition zone. Almandine crystallizes in the cubic space group Ia3d, with unit-cell parameter a ≈ 11.512 Å at 100 K.
Almandine is antiferromagnetic with the Néel temperature of 7.5 K. It contains two equivalent magnetic sublattices. Almandine occurs rather abundantly in the gem-gravels of Sri Lanka, whence it has sometimes been called Ceylon-ruby; when the color inclines to a violet tint, the stone is called Syriam garnet, a name said to be taken from Syriam, an ancient town of Pegu. Large deposits of fine almandine-garnets were found, some years ago, in the Northern Territory of Australia, were at first taken for rubies and thus they were known in trade for some time afterwards as Australian rubies. Almandine is distributed. Fine rhombic dodecahedra occur in the schistose rocks of the Zillertal, in Tyrol, are sometimes cut and polished. An almandine in which the ferrous oxide is replaced by magnesia is found at Luisenfeld in German East Africa. In the United States there are many localities. Fine crystals of almandine embedded in mica-schist occur near Wrangell in Alaska; the coarse varieties of almandine are crushed for use as an abrasive agent.
Connecticut has almandine garnet as its state gemstone
Manganese is a chemical element with symbol Mn and atomic number 25. It is not found as a free element in nature. Manganese is a metal with important industrial metal alloy uses in stainless steels. Manganese is named for pyrolusite and other black minerals from the region of Magnesia in Greece, which gave its name to magnesium and the iron ore magnetite. By the mid-18th century, Swedish-German chemist Carl Wilhelm Scheele had used pyrolusite to produce chlorine. Scheele and others were aware that pyrolusite contained a new element, but they were unable to isolate it. Johan Gottlieb Gahn was the first to isolate an impure sample of manganese metal in 1774, which he did by reducing the dioxide with carbon. Manganese phosphating is used for corrosion prevention on steel. Ionized manganese is used industrially as pigments of various colors, which depend on the oxidation state of the ions; the permanganates of alkali and alkaline earth metals are powerful oxidizers. Manganese dioxide is used as the cathode material in alkaline batteries.
In biology, manganese ions function as cofactors for a large variety of enzymes with many functions. Manganese enzymes are essential in detoxification of superoxide free radicals in organisms that must deal with elemental oxygen. Manganese functions in the oxygen-evolving complex of photosynthetic plants. While the element is a required trace mineral for all known living organisms, it acts as a neurotoxin in larger amounts. Through inhalation, it can cause manganism, a condition in mammals leading to neurological damage, sometimes irreversible. Manganese is a silvery-gray metal, it is hard and brittle, difficult to fuse, but easy to oxidize. Manganese metal and its common ions are paramagnetic. Manganese tarnishes in air and oxidizes like iron in water containing dissolved oxygen. Occurring manganese is composed of one stable isotope, 55Mn. Eighteen radioisotopes have been isolated and described, ranging in atomic weight from 46 u to 65 u; the most stable are 53Mn with a half-life of 3.7 million years, 54Mn with a half-life of 312.3 days, 52Mn with a half-life of 5.591 days.
All of the remaining radioactive isotopes have half-lives of less than three hours, the majority of less than one minute. The primary decay mode before the most abundant stable isotope, 55Mn, is electron capture and the primary mode after is beta decay. Manganese has three meta states. Manganese is part of the iron group of elements, which are thought to be synthesized in large stars shortly before the supernova explosion. 53Mn decays to 53Cr with a half-life of 3.7 million years. Because of its short half-life, 53Mn is rare, produced by cosmic rays impact on iron. Manganese isotopic contents are combined with chromium isotopic contents and have found application in isotope geology and radiometric dating. Mn–Cr isotopic ratios reinforce the evidence from 26Al and 107Pd for the early history of the solar system. Variations in 53Cr/52Cr and Mn/Cr ratios from several meteorites suggest an initial 53Mn/55Mn ratio, which indicates that Mn–Cr isotopic composition must result from in situ decay of 53Mn in differentiated planetary bodies.
Hence, 53Mn provides additional evidence for nucleosynthetic processes before coalescence of the solar system. The most common oxidation states of manganese are +2, +3, +4, +6, +7, though all oxidation states from −3 to +7 have been observed. Mn2+ competes with Mg2+ in biological systems. Manganese compounds where manganese is in oxidation state +7, which are restricted to the unstable oxide Mn2O7, compounds of the intensely purple permanganate anion MnO4−, a few oxyhalides, are powerful oxidizing agents. Compounds with oxidation states +5 and +6 are strong oxidizing agents and are vulnerable to disproportionation; the most stable oxidation state for manganese is +2, which has a pale pink color, many manganese compounds are known, such as manganese sulfate and manganese chloride. This oxidation state is seen in the mineral rhodochrosite. Manganese most exists with a high spin, S = 5/2 ground state because of the high pairing energy for manganese. However, there are a few examples of S = 1/2 manganese.
There are no spin-allowed d–d transitions in manganese, explaining why manganese compounds are pale to colorless. The +3 oxidation state is known in compounds like manganese acetate, but these are quite powerful oxidizing agents and prone to disproportionation in solution, forming manganese and manganese. Solid compounds of manganese are characterized by its strong purple-red color and a preference for distorted octahedral coordination resulting from the Jahn-Teller effect; the oxidation state +5 can be produced by dissolving manganese dioxide in molten sodium nitrite. Manganate salts can be produced by dissolving Mn compounds, such as manganese dioxide, in molten alkali while exposed to air. Permanganate compounds are purple, can give glass a violet color. Potassium permanganate, sodium permanganate, barium permanganate are all potent oxidizers. Potassium permanganate called Condy's crystals, is a used laboratory reagent because of its oxidizing properties. Solutions of potassium permanganate were among the first stains and fixatives to be used in the preparation of biological cells and tissues for electron microscopy
Absorption spectroscopy refers to spectroscopic techniques that measure the absorption of radiation, as a function of frequency or wavelength, due to its interaction with a sample. The sample absorbs i.e. photons, from the radiating field. The intensity of the absorption varies as a function of frequency, this variation is the absorption spectrum. Absorption spectroscopy is performed across the electromagnetic spectrum. Absorption spectroscopy is employed as an analytical chemistry tool to determine the presence of a particular substance in a sample and, in many cases, to quantify the amount of the substance present. Infrared and ultraviolet-visible spectroscopy are common in analytical applications. Absorption spectroscopy is employed in studies of molecular and atomic physics, astronomical spectroscopy and remote sensing. There are a wide range of experimental approaches for measuring absorption spectra; the most common arrangement is to direct a generated beam of radiation at a sample and detect the intensity of the radiation that passes through it.
The transmitted energy can be used to calculate the absorption. The source, sample arrangement and detection technique vary depending on the frequency range and the purpose of the experiment. A material's absorption spectrum is the fraction of incident radiation absorbed by the material over a range of frequencies; the absorption spectrum is determined by the atomic and molecular composition of the material. Radiation is more to be absorbed at frequencies that match the energy difference between two quantum mechanical states of the molecules; the absorption that occurs due to a transition between two states is referred to as an absorption line and a spectrum is composed of many lines. The frequencies where absorption lines occur, as well as their relative intensities depend on the electronic and molecular structure of the sample; the frequencies will depend on the interactions between molecules in the sample, the crystal structure in solids, on several environmental factors. The lines will have a width and shape that are determined by the spectral density or the density of states of the system.
Absorption lines are classified by the nature of the quantum mechanical change induced in the molecule or atom. Rotational lines, for instance, occur. Rotational lines are found in the microwave spectral region. Vibrational lines correspond to changes in the vibrational state of the molecule and are found in the infrared region. Electronic lines correspond to a change in the electronic state of an atom or molecule and are found in the visible and ultraviolet region. X-ray absorptions are associated with the excitation of inner shell electrons in atoms; these changes can be combined, leading to new absorption lines at the combined energy of the two changes. The energy associated with the quantum mechanical change determines the frequency of the absorption line but the frequency can be shifted by several types of interactions. Electric and magnetic fields can cause a shift. Interactions with neighboring molecules can cause shifts. For instance, absorption lines of the gas phase molecule can shift when that molecule is in a liquid or solid phase and interacting more with neighboring molecules.
The width and shape of absorption lines are determined by the instrument used for the observation, the material absorbing the radiation and the physical environment of that material. It is common for lines to have the shape of a Lorentzian distribution, it is common for a line to be described by its intensity and width instead of the entire shape being characterized. The integrated intensity—obtained by integrating the area under the absorption line—is proportional to the amount of the absorbing substance present; the intensity is related to the temperature of the substance and the quantum mechanical interaction between the radiation and the absorber. This interaction is quantified by the transition moment and depends on the particular lower state the transition starts from, the upper state it is connected to; the width of absorption lines may be determined by the spectrometer used to record it. A spectrometer has an inherent limit on how narrow a line it can resolve and so the observed width may be at this limit.
If the width is larger than the resolution limit it is determined by the environment of the absorber. A liquid or solid absorber, in which neighboring molecules interact with one another, tends to have broader absorption lines than a gas. Increasing the temperature or pressure of the absorbing material will tend to increase the line width, it is common for several neighboring transitions to be close enough to one another that their lines overlap and the resulting overall line is therefore broader yet. Absorption and transmission spectra represent equivalent information and one can be calculated from the other through a mathematical transformation. A transmission spectrum will have its maximum intensities at wavelengths where the absorption is weakest because more light is transmitted through the sample. An absorption spectrum will have its maximum intensities at wavelengths where the absorption is strongest. Emission is a process. Emission can occur at any frequency at which absorption can occur, this allows the absorption lines to be determined from an emission spectrum.
The emission spectrum will have a quite different intensity pattern from the absorption spectrum, though