title: A Hard Rain's a-Gonna Fall

text: One month later, on October 22, U.S. President John F. Kennedy appeared on national television to announce the discovery of Soviet missiles on the island of Cuba, initiating the Cuban Missile Crisis. In the sleeve notes on the "Freewheelin"' album, Nat Hentoff would quote Dylan as saying that he wrote "A Hard Rain" in response to the Cuban Missile Crisis: "Every line in it is actually the start of a whole new song. But when I wrote it, I thought I wouldn't have enough time alive to write all those songs so I put all I could into this one." In actuality, Dylan had written the song more than a month before the crisis broke.


title: A Hard Rain's a-Gonna Fall

text: Folk singer Pete Seeger interpreted the line "Where the home in the valley meets the damp dirty prison" as referring to when a young person suddenly wants to leave his home but then qualified that by saying, "People are wrong when they say 'I know what he means.'"


title: A Hard Rain's a-Gonna Fall

text: While some have suggested that the refrain of the song refers to nuclear fallout, Dylan disputed that this was a specific reference. In a radio interview with Studs Terkel in 1963, Dylan said: No, it's not atomic rain, it's just a hard rain. It isn't the fallout rain. I mean some sort of end that's just gotta happen ... In the last verse, when I say, "the pellets of poison are flooding the waters," that means all the lies that people get told on their radios and in their newspapers.In "No Direction Home", Martin Scorsese's documentary on Dylan, the Beat poet Allen Ginsberg talked about the first time he heard Dylan's music: When I got back from India, and got to the West Coast, there's a poet, Charlie Plymell - at a party in Bolinas — played me a record of this new young folk singer. And I heard "Hard Rain," I think. And wept. 'Cause it seemed that the torch had been passed to another generation. From earlier bohemian, or Beat illumination. And self-empowerment.


title: A Hard Rain's a-Gonna Fall

text: Although Dylan may have first played the song to friends, "A Hard Rain's a-Gonna Fall" was formally premiered at Carnegie Hall on September 22, 1962, as part of a hootenanny organized by Pete Seeger. Seeger recalled: "I had to announce to all the singers, 'Folks, you're gonna be limited to three songs. No more. 'Cause we each have ten minutes apiece.' And Bob raised his hand and said, 'What am I supposed to do? One of my songs is ten minutes long.'"


title: A Hard Rain's a-Gonna Fall

text: Dylan featured the song regularly in concerts in the years since he premiered it, and there have been several dramatic performances. An October 1963 performance at Carnegie Hall was released on "", while another New York City performance, recorded one year later, appeared on "". Dylan performed the song in August 1971 at The Concert for Bangla Desh, organized by George Harrison and Ravi Shankar, for East Pakistan refugee relief (now independent Bangladesh) after the 1970 Bhola cyclone and during the 1971 Bangladesh Liberation War. On December 4, 1975, at the Forum de Montréal, Canada, Dylan recorded an upbeat version of the song, which appeared on "". That rendition was featured in the 2019 Netflix documentary "", and it also appears on the box set "", along with a November 21, 1975 performance and a still earlier rehearsal. On May 23, 1994, Dylan performed the song at "The Great Music Experience" festival in Japan, backed by a 90-piece symphony orchestra conducted by Michael Kamen. At the end of 2007, Dylan recorded a new version of "A Hard Rain's a-Gonna Fall" exclusively for the Expo 2008 Zaragoza world fair, scheduled to open on June 8, 2008, to highlight the Expo theme of "water and sustainable development". As well as choosing local-band Amaral to record a version of the song in Spanish, Dylan's new version ended with a few spoken words about his "being proud to be a part of the mission to make water safe and clean for every human being living in this world."


title: A Hard Rain's a-Gonna Fall

text: Patti Smith performed the song with orchestral accompaniment at the Nobel Prize Award Ceremony on December 10, 2016, to commemorate Dylan receiving the Nobel Prize in Literature.


title: A Hard Rain's a-Gonna Fall

text: Photographer Mark Edwards took a series of photographs illustrating the lyrics of the song which were exhibited in many locations such as the United Nations headquarters. These were published in a book in 2006.


title: Jahn–Teller effect

text: The Jahn–Teller effect (JT effect or JTE) is an important mechanism of spontaneous symmetry breaking in molecular and solid-state systems which has far-reaching consequences in different fields, and is responsible for a variety of phenomena in spectroscopy, stereochemistry, crystal chemistry, molecular and solid-state physics, and materials science. The effect is named for Hermann Arthur Jahn and Edward Teller, who first reported studies about it in 1937.


title: Jahn–Teller effect

text: The Jahn–Teller effect, sometimes also referred to as Jahn–Teller distortion, describes the geometrical distortion of molecules and ions that result from certain electron configurations. The Jahn–Teller theorem essentially states that any non-linear molecule with a spatially degenerate electronic ground state will undergo a geometrical distortion that removes that degeneracy, because the distortion lowers the overall energy of the species. For a description of another type of geometrical distortion that occurs in crystals with substitutional impurities see article off-center ions.


title: Jahn–Teller effect

text: The Jahn–Teller effect is most often encountered in octahedral complexes of the transition metals. The phenomenon is very common in six-coordinate copper(II) complexes. The "d" electronic configuration of this ion gives three electrons in the two degenerate "e" orbitals, leading to a doubly degenerate electronic ground state. Such complexes distort along one of the molecular fourfold axes (always labelled the "z" axis), which has the effect of removing the orbital and electronic degeneracies and lowering the overall energy. The distortion normally takes the form of elongating the bonds to the ligands lying along the "z" axis, but occasionally occurs as a shortening of these bonds instead (the Jahn–Teller theorem does not predict the direction of the distortion, only the presence of an unstable geometry). When such an elongation occurs, the effect is to lower the electrostatic repulsion between the electron-pair on the Lewis basic ligand and any electrons in orbitals with a "z" component, thus lowering the energy of the complex. The inversion centre is preserved after the distortion.


title: Jahn–Teller effect

text: In octahedral complexes, the Jahn–Teller effect is most pronounced when an odd number of electrons occupy the "e" orbitals. This situation arises in complexes with the configurations "d", low-spin "d" or high-spin "d" complexes, all of which have doubly degenerate ground states. In such compounds the "e" orbitals involved in the degeneracy point directly at the ligands, so distortion can result in a large energetic stabilisation. Strictly speaking, the effect also occurs when there is a degeneracy due to the electrons in the "t" orbitals ("i.e." configurations such as "d" or "d", both of which are triply degenerate). In such cases, however, the effect is much less noticeable, because there is a much smaller lowering of repulsion on taking ligands further away from the "t" orbitals, which do not point "directly" at the ligands (see the table below). The same is true in tetrahedral complexes (e.g. manganate: distortion is very subtle because there is less stabilisation to be gained because the ligands are not pointing directly at the orbitals.


title: Jahn–Teller effect

text: The Jahn–Teller effect is manifested in the UV-VIS absorbance spectra of some compounds, where it often causes splitting of bands. It is readily apparent in the structures of many copper(II) complexes. Additional, detailed information about the anisotropy of such complexes and the nature of the ligand binding can be however obtained from the fine structure of the low-temperature electron spin resonance spectra.


title: Jahn–Teller effect

text: The underlying cause of the Jahn–Teller effect is the presence of molecular orbitals that are both degenerate and open shell (i.e., incompletely occupied). This situation is not unique to coordination complexes and can be encountered in other areas of chemistry. In organic chemistry the phenomenon of antiaromaticity has the same cause and also often sees molecules distorting; as in the case of cyclobutadiene and cyclooctatetraene (COT).


title: Jahn–Teller effect

text: The formal mathematical proof of the Jahn–Teller theorem rests heavily on symmetry arguments, more specifically the theory of molecular point groups. The argument of Jahn and Teller assumes no details about the electronic structure of the system. Jahn and Teller made no statement about the strength of the effect, which may be so small that it is immeasurable. Indeed, for electrons in non-bonding or weakly bonding molecular orbitals, the effect is expected to be weak. However, in many situations the JT effect is important.


title: Jahn–Teller effect

text: Interest in the JTE increased after its first experimental verification. Various model systems were developed probing the degree of degeneracy and the type of symmetry. These were solved partly analytically and partly numerically to obtain the shape of the pertinent potential energy surfaces (PES) and the energy levels for the nuclear motion on the JT-split PES. These energy levels are not vibrational energy levels in the traditional sense because of the intricate coupling to the electronic motion that occurs, and are better termed vibronic energy levels. The new field of ‘vibronic coupling’ or ‘vibronic coupling theory’ was born.


title: Jahn–Teller effect

text: A further breakthrough occurred upon the advent of modern ("ab initio") electronic structure calculations whereby the relevant parameters characterising JT systems can be reliably determined from first principles. Thus one could go beyond studies of model systems that explore the effect of parameter variations on the PES and vibronic energy levels; one could also go on beyond fitting these parameters to experimental data without clear knowledge about the significance of the fit. Instead, well-founded theoretical investigations became possible which greatly improved the insight into the phenomena at hand and into the details of the underlying mechanisms.


title: Jahn–Teller effect

text: While recognizing the JTE distortion as a concrete example of the general spontaneous symmetry breaking mechanism, the exact degeneracy of the involved electronic state was identified as a non-essential ingredient for this symmetry breaking in polyatomic systems. Even systems that in the undistorted symmetric configuration present electronic states which are near in energy but not precisely degenerate, can show a similar tendency to distort. The distortions of these systems can be treated within the related theory of the pseudo Jahn–Teller effect (in the literature often referred to as "second-order JTE"). This mechanism is associated to the vibronic couplings between adiabatic PES separated by nonzero energy gaps across the configuration space: its inclusion extends the applicability of JT-related models to symmetry breaking in a far broader range of molecular and solid-state systems.


title: Jahn–Teller effect

text: A given JT problem will have a particular point group symmetry, such as T symmetry for magnetic impurity ions in semiconductors or I symmetry for the fullerene C. JT problems are conventionally classified using labels for the irreducible representations (irreps) that apply to the symmetry of the electronic and vibrational states. For example, E ⊗ e would refer to an electronic doublet state transforming as E coupled to a vibrational doublet state transforming as e.


title: Jahn–Teller effect

text: In general, a vibrational mode transforming as Λ will couple to an electronic state transforming as Γ if the symmetric part of the Kronecker product [Γ ⊗ Γ] contains Λ, unless Γ is a double group representation when the antisymmetric part {Γ ⊗ Γ} is considered instead. Modes which do couple are said to be JT-active.


title: Jahn–Teller effect

text: As an example, consider a doublet electronic state E in cubic symmetry. The symmetric part of E ⊗ E is A + E. Therefore, the state E will couple to vibrational modes formula_1 transforming as a and e. However, the a modes will result in the same energy shift to all states and therefore do not contribute to any JT splitting. They can therefore be neglected. The result is an E ⊗ e JT effect. This JT effect is experienced by triangular molecules X, tetrahedral molecules ML, and octahedral molecules ML when their electronic state has E symmetry.


title: Jahn–Teller effect

text: Components of a given vibrational mode are also labelled according to their transformation properties. For example, the two components of an e mode are usually labelled formula_2 and formula_3, which in octahedral symmetry transform as formula_4 and formula_5 respectively.


title: Jahn–Teller effect

text: Eigenvalues of the Hamiltonian of a polyatomic system define PESs as functions of normal modes formula_1 of the system (i.e. linear combinations of the nuclear displacements with specific symmetry properties). At the reference point of high symmetry, where the symmetry-induced degeneracy occurs, several of the eigenvalues coincide. By a detailed and laborious analysis, Jahn and Teller showed that – excepting linear molecules – there are always first-order terms in an expansion of the matrix elements of the Hamiltonian in terms of symmetry-lowering (in the language of group theory: non-totally symmetric) normal modes. These linear terms represent forces that distort the system along these coordinates and lift the degeneracy. The point of degeneracy can thus not be stationary, and the system distorts toward a stationary point of lower symmetry where stability can be attained.


title: Jahn–Teller effect

text: Proof of the JT theorem follows from the theory of molecular symmetry (point group theory). A less rigorous but more intuitive explanation is given in section .


title: Jahn–Teller effect

text: To arrive at a quantitative description of the JT effect, the forces appearing between the component wave functions are described by expanding the Hamiltonian in a power series in the formula_1. Owing to the very nature of the degeneracy, the Hamiltonian takes the form of a matrix referring to the degenerate wave function components. A matrix element between states formula_8 and formula_9 generally reads as:


title: Jahn–Teller effect

text: The expansion can be truncated after terms linear in the formula_1, or extended to include terms quadratic (or higher) in the formula_1.


title: Jahn–Teller effect

text: The adiabatic potential energy surfaces (APES) are then obtained as the eigenvalues of this matrix. In the original paper it is proven that there are always linear terms in the expansion. It follows that the degeneracy of the wave function cannot correspond to a stable structure.


title: Jahn–Teller effect

text: In mathematical terms, the APESs characterising the JT distortion arise as the eigenvalues of the potential energy matrix. Generally, the APESs take the characteristic appearance of a double cone, circular or elliptic, where the point of contact, i.e. degeneracy, denotes the high-symmetry configuration for which the JT theorem applies. For the above case of the linear E ⊗ e JT effect the situation is illustrated by the APES


title: Jahn–Teller effect

text: displayed in the figure, with part cut away to reveal its shape, which is known as a Mexican Hat potential. Here, formula_14 is the frequency of the vibrational e mode, formula_15 is its mass and formula_16 is a measure of the strength of the JT coupling.


title: Jahn–Teller effect

text: The conical shape near the degeneracy at the origin makes it immediately clear that this point cannot be stationary, that is, the system is unstable against asymmetric distortions, which leads to a symmetry lowering. In this particular case there are infinitely many isoenergetic JT distortions. The formula_1 giving these distortions are arranged in a circle, as shown by the red curve in the figure. Quadratic coupling or cubic elastic terms lead to a warping along this "minimum energy path", replacing this infinite manifold by three equivalent potential minima and three equivalent saddle points. In other JT systems, linear coupling results in discrete minima.


title: Jahn–Teller effect

text: The high symmetry of the double-cone topology of the linear E ⊗ e JT system directly reflects the high underlying symmetry. It is one of the earliest (if not the earliest) examples in the literature of a conical intersection of potential energy surfaces. Conical intersections have received wide attention in the literature starting in the 1990s and are now considered paradigms of nonadiabatic excited-state dynamics, with far-reaching consequences in molecular spectroscopy, photochemistry and photophysics. Some of these will be commented upon further below. In general, conical intersections are far less symmetric than depicted in the figure. They can be tilted and elliptical in shape etc., and also peaked and sloped intersections have been distinguished in the literature. Furthermore, for more than two degrees of freedom, they are not point-like structures but instead they are seams and complicated, curved hypersurfaces, also known as intersection space. The coordinate sub-space displayed in the figure is also known as a branching plane.


title: Jahn–Teller effect

text: The characteristic shape of the JT-split APES has specific consequences for the nuclear dynamics, here considered in the fully quantum sense. For sufficiently strong JT coupling, the minimum points are sufficiently far (at least by a few vibrational energy quanta) below the JT intersection. Two different energy regimes are then to be distinguished, those of low and high energy.


title: Jahn–Teller effect

text: As already stated above, the distinction of low and high energy regimes is valid only for sufficiently strong JT couplings, that is, when several or many vibrational energy quanta fit into the energy window between the conical intersection and the minimum of the lower JT-split APES. For the many cases of small to intermediate JT couplings this energy window and the corresponding adiabatic low-energy regime does not exist. Rather, the levels on both JT-split APES are intricately mixed for all energies and the nuclear motion always proceeds on both JT split APES simultaneously.


title: Jahn–Teller effect

text: In 1965, Frank Ham proposed that the dynamic JTE could reduce the expected values of observables associated with the orbital wavefunctions due to the superposition of several electronic states in the total vibronic wavefunction. This effect leads, for example, to a partial quenching of the spin–orbit interaction and allowed the results of previous Electron Paramagnetic Resonance (EPR) experiments to be explained.


title: Jahn–Teller effect

text: In general, the result of an orbital operator acting on vibronic states can be replaced by an effective orbital operator acting on purely electronic states. In first order, the effective orbital operator equals the actual orbital operator multiplied by a constant, whose value is less than one, known as a first-order (Ham) reduction factor. For example, within a triplet T electronic state, the spin–orbit coupling operator formula_18 can be replaced by formula_19, where formula_20 is a function of the strength of the JT coupling which varies from 1 in zero coupling to 0 in very strong coupling. Furthermore, when second-order perturbation corrections are included, additional terms are introduced involving additional numerical factors, known as second-order (Ham) reduction factors. These factors are zero when there is no JT coupling but can dominate over first-order terms in strong coupling, when the first-order effects have been significantly reduced.


title: Jahn–Teller effect

text: Reduction factors are particularly useful for describing experimental results, such as EPR and optical spectra, of paramagnetic impurities in semiconducting, dielectric, diamagnetic and ferrimagnetic hosts.


title: Jahn–Teller effect

text: For a long time, applications of JT theory consisted mainly in parameter studies (model studies) where the APES and dynamical properties of JT systems have been investigated as functions on the system parameters such as coupling constants etc. Fits of these parameters to experimental data were often doubtful and inconclusive. The situation changed in the 1980s when efficient ab initio methods were developed and computational resources became powerful enough to allow for a reliable determination of these parameters from first principles. Apart from wave function-based


title: Jahn–Teller effect

text: techniques (which are sometimes considered genuinely ab initio in the literature) the advent of density functional theory (DFT) opened up new avenues to treat larger systems including solids. This allowed details of JT systems to be characterised and experimental findings to be reliably interpreted. It lies at the heart of most developments addressed in section .


title: Jahn–Teller effect

text: Naturally, the more accurate approach (2) may be limited to smaller systems, while the simpler approach (1) lends itself to studies of larger systems.


title: Jahn–Teller effect

text: The JT distortion of small molecules (or molecular ions) is directly deduced from electronic structure calculations of their APES (through DFT and/or ab initio computations). These molecules / ions are often radicals, such as trimers of alkali atoms (Li and Na), that have unpaired spins and in particular in (but not restricted to) doublet states. Besides the JTE in E′ and E″ states, also the pseudo JTE between an E state and a nearby A state may play a role. The JT distortion reduces the symmetry from D to C (see figure), and it depends on the details of the interactions whether the isosceles triangle has an acute or an obtuse-angled (such as Na) minimum energy structure. Natural extensions are systems like NO and NH where a JT distortion has been documented in the literature for ground or excited electronic states.


title: Jahn–Teller effect

text: A somewhat special role is played by tetrahedral systems like CH and P. Here threefold degenerate electronic states and vibrational modes come into play. Nevertheless, also twofold degeneracies continue to be important.


title: Jahn–Teller effect

text: Among larger systems, a focus in the literature has been on benzene and its radical cation, as well as on their halo (especially fluoro) derivatives. Already in the early 1980s, a wealth of information emerged from the detailed analysis of experimental emission spectra of 1,3,5- trifluoro- and hexafluoro (and chloro) benzene radical cations. The Jahn–Teller effect in the 1,3,5-trifluoro benzene radical cation is discussed in Section 13.4.2 of the textbook by Bunker and


title: Jahn–Teller effect

text: Jensen. For the parent benzene cation one has to rely on photoelectron spectra with comparatively lower resolution because this species does not fluoresce (see also section ). Rather detailed ab initio calculations have been carried out which


title: Jahn–Teller effect

text: document the JT stabilization energies for the various (four) JT active modes and also quantify the moderate barriers for the JT pseudorotation.


title: Jahn–Teller effect

text: Finally, a somewhat special role is played by systems with a fivefold symmetry axis like the cyclopentadienyl radical. Careful laser spectroscopic investigations have shed useful light on the JT interactions. In particular they reveal that the barrier to pseudorotation almost vanishes (the system is highly "fluxional") which can be attributed to the fact that the 2nd-order coupling terms vanish by symmetry and the leading higher-order terms are of 4th order.


title: Jahn–Teller effect

text: The JTE is usually stronger where the electron density associated with the degenerate orbitals is more concentrated. This effect therefore plays a large role in determining the structure of transition metal complexes with active internal 3d orbitals.


title: Jahn–Teller effect

text: The most iconic and prominent of the JT systems in coordination chemistry is probably the case of Cu(II) octahedral complexes. While in perfectly equivalent coordination, like a CuF complex associated to a Cu(II) impurity in a cubic crystal like KMgF, perfect octahedral (O) symmetry is expected. In fact a lower tetragonal symmetry is usually found experimentally. The origin of this JTE distortion it revealed by examining the electronic configuration of the undistorted complex. For an octahedral geometry, the five 3d orbitals partition into t and e orbitals (see diagram). These orbitals are occupied by nine electrons corresponding to the formula_21 electronic configuration of Cu(II). Thus, the t shell is filled, and the e shell contains 3 electrons. Overall the unpaired electron produces a E state, which is Jahn–Teller active. The third electron can occupy either of the orbitals comprising the e shell: the mainly formula_4 orbital or the mainly formula_5 orbital. If the electron occupies the mainly formula_4 level, which antibonding orbital the final geometry of the complex would be elongated as the axial ligands will be pushed away to reduce the global energy of the system. On the other hand, if the electron went into the mainly formula_5 antibonding orbital the complex would distort into a compressed geometry. Experimentally elongated geometries are overwhelmingly observed and this fact has been attributed both to metal-ligand anharmonic interactions and 3d-4s hybridisations. Given that all the directions containing a fourfold axis are equivalent the distortion is equally likely to happen in any of these orientations. From the electronic point of view this means that the formula_4 and formula_5 orbitals, that are degenerate and free to hybridise in the octahedral geometry, will mix to produce appropriate equivalent orbitals in each direction like formula_28 or formula_29.


title: Jahn–Teller effect

text: The JTE is not just restricted to Cu(II) octahedral complexes. There are many other configurations, involving changes both in the initial structure and electronic configuration of the metal that yield degenerate states and, thus, JTE. However, the amount of distortion and stabilisation energy of the effect is strongly dependent on the particular case. In octahedral Cu(II), the JTE is particularly strong because


title: Jahn–Teller effect

text: In other configurations involving π or δ bonding, like for example when the degenerate state is associated to the t orbitals of an octahedral configuration, the distortion and stabilisation energies are usually much smaller and the possibility of not observing the distortion due to dynamic JT effects is much higher. Similarly for rare-earth ions where covalency is very small, the distortions associated to the JTE are usually very weak.


title: Jahn–Teller effect

text: Importantly, the JTE is associated with strict degeneracy in the electronic subsystem and so it cannot appear in systems without this property. For example, the JTE is often associated to cases like quasi-octahedral CuXY complexes where the distances to X and Y ligands are clearly different. However, the intrinsic symmetry of these complexes is already tetragonal and no degenerate e orbital exists, having split into a (mainly formula_4) and b (mainly formula_5) orbitals due to the different electronic interactions with axial X ligands and equatorial Y ligands. In this and other similar cases some remaining vibronic effects related to the JTE are still present but are quenched with respect to the case with degeneracy due to the splitting of the orbitals.


title: Jahn–Teller effect

text: From spectra with rotational resolution, moments of inertia and hence bond lengths and angles can be determined "directly" (at least in principle). From less well-resolved spectra one can still determine important quantities like JT stabilization energies and energy barriers (e.g. to pseudorotation). However, in the whole spectral intensity distribution formula_32 of an electronic transition more information is encoded. It has been used to decide on the presence (or absence) of the geometric phase which is accumulated during the pseudorotational motion around the JT (or other type of) conical intersection. Prominent examples of either type are the ground (X) or an excited (B) state of Na. The Fourier transform of formula_32, the so-called autocorrelation function formula_34 reflects the motion of the wavepacket after an optical (= vertical) transition to the APES of the final electronic state. Typically it will move on the timescale of a vibrational period which is (for small molecules) of the order of 5–50 fs, i.e. ultrafast. Besides a nearly periodic motion, mode–mode interactions with very irregular (also chaotic) behaviour and spreading of the wavepacket may also occur. Near a conical intersection this will be accompanied/complemented by nonradiative transitions (termed internal conversion) to other APESs occurring on the same ultrafast time scale.


title: Jahn–Teller effect

text: For the JT case the situation is somewhat special, as compared to a general conical intersection, because the different JT potential sheets are symmetry-related to each other and have (exactly or nearly) the same energy minimum. The "transition" between them is thus more oscillatory than one would normally expect, and their time-averaged populations are close to 1/2. For a more typical scenario a more general conical intersection is "required".


title: Jahn–Teller effect

text: The JT effect still comes into play, namely in combination with a different nearby, in general non-degenerate electronic state. The result is a pseudo Jahn–Teller effect, for example, of an E state interacting with an A state. This situation is common in JT systems, just as interactions between two nondegenerate electronic states are common for non-JT systems. Examples are excited electronic states of NH and the benzene radical cation. Here, crossings between the E and A state APESs amount to triple intersections, which are associated with very complex spectral features (dense line structures and diffuse spectral envelopes under low resolution). The population transfer between the states is also ultrafast, so fast that fluorescence (proceeding on a nanosecond time scale) cannot compete. This helps to understand why the benzene cation, like many other organic radical cation, does not fluoresce.


title: Jahn–Teller effect

text: To be sure, photochemical reactivity emerges when the internal conversion makes the system explore the nuclear configuration space such that new chemical species are formed. There is a plethora of femtosecond pump-probe spectroscopic techniques to reveal details of these processes occurring, for example, in the process of vision.


title: Jahn–Teller effect

text: free electrons in a solid, introduced for example by doping or irradiation, can interact with the vibrations of the lattice to form a localized quasi-particle known as a polaron. Strongly localized polarons (also called Holstein polarons) can condensate around high-symmetry sites of the lattice with electrons or holes occupying local degenerate orbitals that experience the JTE. These Jahn–Teller polarons break both translational and point group symmetries of the lattice where they are found and have been attributed important roles in effects like colossal magnetoresistance and superconductivity.


title: Jahn–Teller effect

text: Paramagnetic impurities in semiconducting, dielectric, diamagnetic and ferrimagnetic hosts can all be described using a JT model. For example, these models were used extensively in the 1980s and 1990s to describe ions of Cr, V and Ti substituting for Ga in GaAs and GaP.


title: Jahn–Teller effect

text: The fullerene C can form solid compounds with alkali metals known as fullerides. CsC can be superconducting at temperatures up to 38K under applied pressure, whereas compounds of the form AC are insulating (as reviewed by Gunnarsson). JT effects both within the C molecules (intramolecular) and between C molecules (intermolecular) play a part in the mechanisms behind various observed properties in these systems. For example, they could mean that the Migdal–Eliashberg treatment of superconductivity breaks down. Also, the fullerides can form a so-called new state of matter known as a Jahn–Teller metal, where localised electrons coexist with metallicity and JT distortions on the C molecules persist.


title: Jahn–Teller effect

text: The JTE is usually associated with degeneracies that are well localised in space, like those occurring in a small molecule or associated to an isolated transition metal complex. However, in many periodic high-symmetry solid-state systems, like perovskites, some crystalline sites allow for electronic degeneracy giving rise under adequate compositions to lattices of JT-active centers. This can produce a cooperative JTE, where global distortions of the crystal occur due to local degeneracies.


title: Jahn–Teller effect

text: In order to determine the final electronic and geometric structure of a cooperative JT system, it is necessary to take into account both the local distortions and the interaction between the different sites, which will take such form necessary to minimise the global energy of the crystal.


title: Jahn–Teller effect

text: While works on the cooperative JTE started in the late fifties, it was in 1960 that Kanamori published the first work on the cooperative JTE where many important elements present in the modern theory for this effect were introduced. This included the use of pseudospin notation to discuss orbital ordering, and discussions of the importance of the JTE to discuss magnetism, the competition of this effect with the spin–orbit coupling and the coupling of the distortions with the strain of the lattice. This point was later stressed in the review by Gehring and Gehring as being the key element to establish long-range order between the distortions in the lattice. An important part of the modern theory of the cooperative JTE, can lead to structural phase transitions.


title: Jahn–Teller effect

text: It is important to note that many cooperative JT systems would be expected to be metals from band theory as, to produce them, a degenerate orbital has to be partially filled and the associated band would be metallic. However, under the perturbation of the symmetry-breaking distortion associated to the cooperative JTE, the degeneracies in the electronic structure are destroyed and the ground state of these systems is often found to be insulating (see e.g.). In many important cases like the parent compound for colossal magnetoresistance perovskites, LaMnO, an increase of temperature leads to disorder in the distortions which lowers the band splitting due to the cooperative JTE, thus triggering a metal–insulator transition.


title: Jahn–Teller effect

text: In modern solid-state physics, it is common to classify systems according to the kind of degrees of freedom they have available, like electron (metals) or spin (magnetism). In crystals that can display the JTE, and before this effect is realised by symmetry-breaking distortions, it is found that there exists an orbital degree of freedom consisting of how electrons occupy the local degenerate orbitals. As initially discussed by Kugel and Khomskii, not all configurations are equivalent. The key is the relative orientation of these occupied orbital, in the same way that spin orientation is important in magnetic systems, and the ground state can only be realised for some particular orbital pattern. Both this pattern and the effect giving rise to this phenomenon is usually denominated orbital-ordering.


title: Jahn–Teller effect

text: In order to predict the orbital-ordering pattern, Kugel and Khomskii used a particularisation of the Hubbard model. In particular they established how superexchange interactions, usually described by the Anderson–Kanamori–Goodenough rules, change in the presence of degenerate orbitals. Their model, using a pseudospin representation for the local orbitals, leads to a Heisenberg-like model in which the ground state is a combination of orbital and spin patterns. Using this model it can be shown, for example, that the origin of the unusual ground insulating ferromagnetic state of a solid like KCuF can be traced to its orbital ordering.


title: Jahn–Teller effect

text: Even when starting from a relatively high-symmetry structure the combined effect of exchange interactions, spin–orbit coupling, orbital-ordering and crystal deformations activated by the JTE can lead to very low symmetry magnetic patterns with specific properties. For example, in CsCuCl an incommensurable helicoidal pattern appears both for the orbitals and the distortions along the formula_35-axis. Moreover, many of these compounds show complex phase diagrams when varying temperature or pressure.


title: L'Occitane en Provence

text: L'Occitane en Provence, "the Occitan woman (in Provence)," commonly known as L'Occitane, is a French luxury retailer of body, face, hair, fragrances, and home products based in Manosque, France. Founded in 1976 by Olivier Baussan, with the purpose to create a company that celebrates and preserves the traditions of his native Provence. In 2010, the company became listed on the Hong Kong Stock Exchange.


title: L'Occitane en Provence

text: In 1976, 23-year-old Olivier Baussan used steam distillation to produce essential oil from wild rosemary and lavender which he sold at open-air markets in his native Provence. "L'Occitane" was named for the women of Occitania. This area existed during the Middle Ages, spanning southern France, north-eastern Spain and northern Italy. Occitan was the native language and is still spoken as a second language in some areas of this region.


title: L'Occitane en Provence

text: In 1976, using an old soap factory that was donated to him, Olivier Baussan revived the traditional art of Marseille soap-making in Manosque, another Provençal village. He manufactured vegetable-based soaps. The first L'Occitane factory and boutique opened in 1981 in Volx, a village in Provence.


title: L'Occitane en Provence

text: In the 1990s, Baussan sold a majority stake in the business to venture capitalists to finance expansion. As their approaches were incompatible, Baussan found himself excluded from daily management and strategic decision-making.


title: L'Occitane en Provence

text: In 1994, Austrian businessman Reinold Geiger bought a 33% stake in the group. Through a series of capital increases, Geiger became majority shareholder in 1996. Geiger, as the new chairman, asked Baussan to return as creative director and lead product development. The company's new focus on marketing strategy paved the way for international expansion. In the late 1990s the company changed its name to 'L'Occitane en Provence', to strengthen the connection with the company's roots and because the term 'Provence' had more meaning to an international audience. On 20 April 2001, Clarins became a financial investor in the company through subscription to approximately 5.18% of the company's shares and €11,433,750 convertible debenture loan. On 22 February 2005, Clarins further invested €16,525,580 in convertible debentures. When the debentures were converted, Clarins held 23.33% of the shares. The management executed a leveraged buyout in May 2007 following which Reinold Geiger's stake rose from 31.9% to 48.7%, and Clarins' stake was diluted to 10.0%.


title: L'Occitane en Provence

text: L'Occitane has shops in over 90 countries, in North America, South America, Europe, Asia, Australia and Africa; with 170 shops in the United States. At the launch of its IPO in 2010, the company announced that its products were sold in over 80 countries through over 1,500 retail locations; it had 753 L'Occitane Stores. In the year ended 31 March 2009, it generated sales of €537.3 million. It planned over 650 store openings with the capital raised.


title: L'Occitane en Provence

text: In 2013, the company employed 6,600 people worldwide and created a new brand "L'Occitane au Brésil", focused on products from Brazil.


title: L'Occitane en Provence

text: In March 2022, L’Occitane acquired a majority stake in the Australian skincare brand, Grown Alchemist.


title: L'Occitane en Provence

text: Following 2022 Russian invasion of Ukraine, L'Occitane announced it would continue to keep its Russian stores open on the grounds that it wanted to protect its staff from potential retaliation. Several days later L'Occitane reversed their decision announcing that it would be closing its Russian shops and website. Nevertheless, Russian stores are still supplied with products, only as a separate legal entity with a new name (Л'Окситан).


title: L'Occitane en Provence

text: In March 2010, the listing committee of the Hong Kong Stock Exchange approved its plan for a $400–$600 million initial public offering of L'Occitane International S.A., underwritten by CLSA, HSBC and UBS which the company had originally planned in 2008, but postponed because of the 2008 financial crisis. The company stated that two-thirds of the proceeds would be used to finance store openings. China Investment Corporation invested US$50 million in the company's IPO as the cornerstone investor (for approximately 1.9% of the shares). Following the listing of shares in L'Occitane International SA, L'Occitane Groupe SA retains 75% of the shareholding of the company; shares owned by Geiger, Clarins and other shareholders are indirect.


title: L'Occitane en Provence

text: All of L'Occitane's products are developed and produced from its base in Manosque, where 1,000 employees work. The company sources the majority of its production from Provence and one of their main product l'Immortelle plants (Helichrysum italicum) from Corsica from producers who rely on traditional production methods.


title: L'Occitane en Provence

text: In addition to products sourced from Provence, shea butter is purchased directly from women's groups in Burkina Faso as Fair Trade with the ECOCERT certification. The shea tree is considered sacred, and its butter is known as "women's gold" because it is how the women make their money. Shea butter traditions are still used, such as only fallen fruit may be collected by women, and only women know the secret to making shea butter.


title: L'Occitane en Provence

text: According to the company, it does not conduct animal testing, and no animal product or by-product, except for beehive products are used in the manufacturing process. L'Occitane develops most of its products and ingredients in line with the organic cosmetics specifications of the ECOCERT.


title: L'Occitane en Provence

text: L'Occitane bought Groupe M&A Development and its subsidiary, M&A Santé Beauté, which includes the organic cosmetic brand Melvita, in 2008. The company, which was founded in the Ardèche in 1983 by French biologist Bernard Chevilliat, commercialises ecological and organic cosmetics principally in France. In 1990, Melvita launched its first organic cosmetics range and its manufacturing obtained the ECOCERT certification. They now have stores in thirteen countries.


title: L'Occitane en Provence

text: "La Fondation d'Entreprise L'Occitane" is a private organisation founded in 2006 by the company, with a budget of 4 million euros for 6 years, to support visually impaired people and help the economic emancipation of women. It supports associations for the visually impaired particularly in Burkina Faso with NGOs that are specialised in training professionals to reduce blindness. The L'Occitane Foundation has formed a partnership with Orbis, an organisation that fights against avoidable blindness in developing countries. To support economic emancipation of women, the L'Occitane Foundation partnered with the association Faa-I-tuora to improve the way of living of people in Dissin, in the South West region of Burkina Faso.


title: L'Occitane en Provence

text: In 2013, the United Nations Development Programme (UNDP) decided to recognise L'Occitane en Provence as an exemplary company within the framework of its 2013 "Growing Inclusive Markets" initiative. Since 2013, L'Occitane Foundation has rewarded an ophthalmologist every two years for his work in the fight against blindness. In 2013 Professor Volker Klaus received the first l'Occitane Sight Award with a €50,000 grant for his action in Africa.


title: Hazard Pay

text: "Hazard Pay" is the third episode of the fifth season of the American television drama series "Breaking Bad", and the 49th overall episode of the series. Written by Peter Gould and directed by Adam Bernstein, it originally aired on AMC in the United States on July 29, 2012.


title: Hazard Pay

text: Mike Ehrmantraut and his attorney spend an entire day visiting his former subordinates in jail who are under heavy scrutiny from the police due to their association with Gus Fring. Mike reassures them they will get their compensation.


title: Hazard Pay

text: While scouting for a new location for a meth laboratory, Walter White proposes using a pest removal company to secretly make meth in their clients' homes. Vamonos Pest, a local pest removal company, is perfect for this as the owner and his employees are already criminals. They agree to facilitate Walt and Jesse Pinkman cooking in their clients' homes. The first cook at the mobile site is a success, and afterward, Walt feigns enthusiasm for Jesse's relationship with Andrea Cantillo, but hints that Jesse should break up with her after mentioning the problems it would cause if she discovered his secret life.


title: Hazard Pay

text: While discussing Walt's upcoming 51st birthday with Marie Schrader at the car wash, Skyler White begins to light a cigarette. As Marie begins to confront her about smoking, Skyler suffers a nervous breakdown. Marie confronts Walt at home about Skyler's breakdown and demands to know the truth. Walt tells her about Skyler's affair with Ted Beneke and that her breakdown was due to stress over his recent accident.


title: Hazard Pay

text: Mike allocates the money earned from the first cook, but Walt becomes upset when so much of it is given to dealers, mules, Saul Goodman, and Vamonos Pest. Walt becomes further angered when he learns of the hazard pay to Mike's old henchmen but eventually relents. Walt deduces that the final amount taken home by the partners was less than what he was making when he was working for Gus. Jesse, who reveals that he broke off the relationship with Andrea, tells Walt that he was "looking at it wrong." Jesse explains to Walt that under Gus, they were employees, but as owners, they were actually making more considering the volume of the output. Walt, however, hints that they may need to get rid of some of the other members of the team.


title: Hazard Pay

text: Charles Baker's ability to play the piano was noticed by the writers of the show and in the episode, his character Skinny Pete plays an intricate piano melody (CPE Bach - Solfeggietto) on a keyboard.


title: Hazard Pay

text: The episode was watched by approximately 2.20 million American viewers in its original broadcast, a slight drop from the previous episode.


title: Hazard Pay

text: The episode received positive reviews. Allison Keene of Collider was originally going to rate the episode with a C, but gave it a B for the "Skinny Pete scene and the cook montage", adding: "Introducing Skinny Pete in 'Hazard Pay' with him artfully and flawlessly dancing through a piano melody on a keyboard in the music store was funny, but also deeply sad." She added about the cook: "Every season Walt and Jesse seem to find some foolproof place to cook in peace, and I always get a weird sense of calm. The RV, the lab, and now a mobile meth lab in bug-bombed houses. It's a stroke of genius, and one that can nearly be 'ripped from the headlines'." "Entertainment Weekly"s Ken Tucker called "Hazard Pay" "a marvelous episode, full of problem-solving and execution, along with a few wild-card emotional moments." Tucker particularly liked Mike's money-division scene at the end of the episode, calling it "a beautifully simple lesson in economics, laid out clearly for both Walter and Jesse, and for us."


title: Hazard Pay

text: In 2019 The Ringer ranked "Hazard Pay" 62nd out of 62 total "Breaking Bad" episodes. Claire McClear wrote of Walt meeting Brock for the first time as displaying that Walt was "a monster now, make no mistake," considering the former had just tried to kill the boy.


title: Hideaki Itsuno

text: Hideaki Itsuno was a fighting game fan who was hired by Capcom in 1994; his entrance exam happened the same day as the "Super Street Fighter II Turbo" location test. He went for it over other companies because it would be an easy commute. There, he was assigned work as a designer on their arcade division (which by 1997 had been reorganized as Production Studio 1), starting with two quiz games. In that first year at the company, a project for a "Street Fighter" prequel was brewing; Itsuno's superior Noritaka Funamizu saw there was no designer attached, and asked him to take that role in December. Other members of that team came from the same background, all gathered so "Street Fighter Alpha" had a broader appeal and captured the audience drawn to SNK fighters.


title: Hideaki Itsuno

text: His first director job was on another fighter, "Star Gladiator", a project he entered halfway through to fulfill a desire: "at the time I wanted to make that kind of game with a large scale cabinet, because Capcom had never done anything like that before. That's why I joined the company". Due to visual effects and hardware constraints, that game runs at 30 frames per second, to Itsuno's chagrin: "At 30fps, I feel you can't have a real competitive fighting game, so I wanted to make a linear fighting game with 60fps in mind". Driven to make a 60fps polygon-based fighting game, he conceived an original project with wide appeal—driven so partly by a more story-heavy approach and the inclusion of role-playing elements—which became "".


title: Hideaki Itsuno

text: Most of Itsuno's output for the first nine years of his career was fighting games, both in 2D and 3D, as either director or designer. As the genre and the arcade market declined, he worked on console games of various genres, within both positions he'd been in before: "One Piece Mansion", "GioGio's Bizarre Adventure" and "Auto Modellista".


title: Hideaki Itsuno

text: After Itsuno had finished work on "Capcom vs. SNK 2", he started conceiving a role-playing video game. Since he appeared to be "idle", his boss ordered him to work on "Devil May Cry 2". Itsuno was asked to "reorganize the project" in a supplementary role, which effectively meant taking over leadership, as upper management saw it as director-less. In exchange, he would go uncredited, but ended up the only director listed in the final version of the game. Most of Team Devil (the staff on that title) hadn't worked on "Devil May Cry" and lacked experience in 3D action-adventure games, which resulted in a production severely behind schedule with six months left on the deadline. Itsuno accomplished the request, but was dissatisfied with his level of involvement and the final product's quality.


title: Hideaki Itsuno

text: He didn't want "Devil May Cry 2" to be his legacy within the series, so before development had wrapped, Itsuno asked his higher-ups for "", with himself as director from the start of the project. He rallied Team Devil to stay for it; some members shared his sentiment, with many wanting to work with what they learned making "Devil May Cry 2". Gameplay elements such as the size of environments and the game's battle engine were reconsidered, and common criticisms such as decreases to Dante's cockiness and the game's difficulty were brought back in line with the first game. These changes were met with praise and the game was very well-received.


title: Hideaki Itsuno

text: Itsuno returned to direct "Devil May Cry 4". He stated that the visual design sought to deliver a satisfying sensation of floating in the air, and that the actions of Nero's Devil Bringer could not be done on contemporary generation consoles, necessitating a new generation of consoles such as the PlayStation 3. Devil May Cry 4 (2008) was met with both commercial and critical success.


title: Hideaki Itsuno

text: The next game in the series, "," was developed by British developer Ninja Theory; Itsuno was the supervising director on that project. When discussing this decision, Itsuno said: "With "DmC" this time, we wanted to avoid the problem that befalls some series where you keep making it with the same team, same hardware, and it tends to decrease and fans move away from it... We don’t want the series to die." The development team included over ninety members, several of whom were from Capcom. Alex Jones and Motohide Eshiro acted as producers, aiming to help Ninja Theory make "DmC" play like the previous "Devil May Cry" games. Itsuno's latest work, "Devil May Cry 5", was released in 2019.


title: Hideaki Itsuno

text: Itsuno later directed "Dragon's Dogma." During the press conference at Capcom's Captivate event in 2011, he called it a game he had been dreaming of making since his school days, which could be finally realized due to technological advancements. At the time of the press conference, he had been directing a staff of 150 people at Capcom Japan for three years of concept and project development. In the process, the team developed techniques that allow the feel of playing in 60fps on a 30fps game.


title: Hideaki Itsuno

text: Itsuno stated that his team had "come up to this point through our experience of action games. We're trying to make a new genre: We're using our action heritage and putting that into an action RPG." He cited the influence of Capcom's previous works (such as "Breath of Fire", "Resident Evil", "Devil May Cry", and "Monster Hunter"), other Eastern RPGs such as "Dragon Quest," and Western RPGs such as "Fable" and "". Itsuno later explained that they had "seen a great deal of open-world action RPGs over the years, [but never] one that really put everything together in the action parts. We figured that if there hasn't been a game made by people who understand how action works, then we ought to do it ourselves. We wanted a game where the player is thrown into the world and needs to figure out how to stay alive via nothing but his own controller".


title: Hideaki Itsuno

text: However, the game was designed to allow players to take a less action-oriented approach, with Itsuno stating that they "[made] this game such that you can beat the monsters even if you build up EXP, collect good companions and/or pawns, and sit back and watch the battle unfold." He elaborated that while it is an action game, "that's not all that it is. You can fully configure your party and put as much thought as you like into battle, which is something we're doing for people who really want to get into this world".


title: Hideaki Itsuno

text: Initially, "Dragon's Dogma" was intended to be a Western fantasy game. In March 2012, Itsuno said he hoped the game would sell 10 million copies worldwide and one million in Japan. It was successful upon release, prompting Capcom to begin development on a sequel. Itsuno reports that the team was only able to accomplish 60-70% of what they had wanted to in the first game, and hope to include those ideas in the sequel.


title: Hideaki Itsuno

text: In 2012, Itsuno hinted that the "Rival Schools" and "Capcom vs. SNK" series may see a revival. The former series was once again hinted in the next year alongside the possibility of a new "Devil May Cry" entry. Itsuno has also expressed interest in developing a fighting game that would recreate the influence "Street Fighter II" had on the genre.


title: Jay Osmond

text: Jay Wesley Osmond (born March 2, 1955) is an American musician. He is best known for being a member of the Osmond family of performers. He was the drummer for the group although has now retired from performing continues to work in other areas, such as support for the 2022 musical "The Osmonds.


title: Jay Osmond

text: Jay Wesley Osmond was born in Ogden, Utah, the sixth son of Olive May (née Davis; 1925–2004) and George Virl Osmond (1917–2007). Four of the Osmonds were cast over a seven-year period on NBC's "The Andy Williams Show". They also appeared in nine episodes of the 1963-1964 ABC western television series, "The Travels of Jaimie McPheeters", with Jay in the role of young Lamentations Kissel. The series starred then 12-year-old Kurt Russell on a wagon train headed to the American West.


title: Jay Osmond

text: In addition to drums, he shared lead vocals on the group's hit "Crazy Horses," a hard rock song that fit Jay's more guttural voice better than usual lead singers Merrill or Donny; he occasionally contributed lead vocals to other tracks, usually ones with a harder-driving sound, such as "One Way Ticket to Anywhere" and "Having a Party." Jay continued with Merrill and Wayne (later joined by Jimmy) as a member of the Osmond Brothers when the group shifted to country music in the 1980s.


title: Jay Osmond

text: Osmond wrote the story to the 2022 musical "The Osmonds." It is based on the life and music of The Osmonds musical group and family.


title: Jay Osmond

text: Jay married Kandilyn Harris on August 25, 1987. They were divorced in 2011. Together, they have three sons: Jason George (born on September 23, 1988), Eric Clinton (born on January 2, 1991) and Marcus Jay (born on January 8, 1996). Jay's oldest son Jason married Lauren Merrill on March 11, 2011, and they have one son, Grayson George, born 2013, and two daughters, Roslyn Renee born 2015 and Charlotte Dee born 2018. Jay married Karen Randall in May 2014. Karen was a fellow divorcee who had never heard of The Osmonds before meeting Jay and eventually became involved in the Osmonds' business enterprises, including the Osmonds musical. His step-granddaughter London Brise Mortensen (born on October 14, 2006) was accidentally killed on September 18, 2014, at age 7.


title: Jay Osmond

text: Like the rest of his family, Jay Osmond is a member of the Church of Jesus Christ of Latter-day Saints.


title: Standard hydrogen electrode

text: The standard hydrogen electrode (abbreviated SHE), is a redox electrode which forms the basis of the thermodynamic scale of oxidation-reduction potentials. Its absolute electrode potential is estimated to be at 25 °C, but to form a basis for comparison with all other electrochemical reactions, hydrogen's standard electrode potential ("E"°) is declared to be zero volts at any temperature. Potentials of all other electrodes are compared with that of the standard hydrogen electrode at the same temperature.


title: Standard hydrogen electrode

text: The hydrogen electrode is based on the redox half cell corresponding to the reduction of two hydrated protons, 2 H(aq), into one gaseous hydrogen molecule, H(g).


title: Standard hydrogen electrode

text: The reaction quotient ("") of the half-reaction is the ratio between the chemical activities ("a") of the reduced form (the reductant, ) and the oxidized form (the oxidant, ).


title: Standard hydrogen electrode

text: at chemical equilibrium, the ratio ' of the reaction products by the reagents is equal to the equilibrium constant ' of the half-reaction:


title: Standard hydrogen electrode

text: Where, formula_5 and formula_6 correspond to the chemical activity of the reduced and oxidized species involved in the redox reaction while formula_7 and formula_8 respectively denote the chemical activity and the partial pressure of hydrogen () and formula_9 represents the activity of . The term "p" is the standard pressure (1 bar = 10 pascal) introduced here simply to overcome the pressure unit and to obtain an equilibrium constant without unit. The hydrogen activity in the gas phase (more commonly named hydrogen fugacity) is thus approximated here by its partial pressure formula_10 expressed without unit (formula_11, with formula_12 and formula_13 representing here respectively the mole fraction and the total gas pressure in the system). More details on managing gas fugacity to get rid of pressure unit in thermodynamic calculations can be found at thermodynamic activity#Gases. The followed approach is the same as for chemical activity and molar concentration of solutes in solution. In the SHE, pure hydrogen gas (formula_14) at the standard pressure formula_13 of is engaged in the system. Meanwhile the general SHE equation can also be applied to other thermodynamic systems with different mole fraction or total pressure of hydrogen.


title: Standard hydrogen electrode

text: The electrode is dipped in an acidic solution and pure hydrogen gas is bubbled through it. The concentration of both the reduced form and oxidised form is maintained at unity. That implies that the pressure of hydrogen gas is 1 bar (100 kPa) and the activity coefficient of hydrogen ions in the solution is unity. The activity of hydrogen ions is their effective concentration, which is equal to the formal concentration times the activity coefficient. These unit-less activity coefficients are close to 1.00 for very dilute water solutions, but usually lower for more concentrated solutions.


title: Standard hydrogen electrode

text: Simply neglecting the pressure unit present in formula_8, this last equation can often be directly written as:


title: Standard hydrogen electrode

text: And by solving the numerical values for the term formula_22, the practical formula commonly used in the calculations of this Nernst equation is:


title: Standard hydrogen electrode

text: This last equation describes the straight line with a negative slope of -0.0591 volt/ pH unit delimiting the lower stability region of water in a Pourbaix diagram where gaseous hydrogen is evolving because of water decomposition.


title: Standard hydrogen electrode

text: During the early development of electrochemistry, researchers used the normal hydrogen electrode as their standard for zero potential. This was convenient because it could "actually be constructed" by "[immersing] a platinum electrode into a solution of 1 N strong acid and [bubbling] hydrogen gas through the solution at about 1 atm pressure". However, this electrode/solution interface was later changed. What replaced it was a theoretical electrode/solution interface, where the concentration of H was 1 M, but the H ions were assumed to have no interaction with other ions (a condition not physically attainable at those concentrations). To differentiate this new standard from the previous one it was given the name 'Standard Hydrogen Electrode'.


title: Standard hydrogen electrode

text: The surface of platinum is platinized (i.e., covered with a layer of fine powdered platinum also known as platinum black) to:


title: Standard hydrogen electrode

text: Other metals can be used for fabricating electrodes with a similar function such as the palladium-hydrogen electrode.


title: Standard hydrogen electrode

text: Because of the high adsorption activity of the platinized platinum electrode, it's very important to protect electrode surface and solution from the presence of organic substances as well as from atmospheric oxygen. Inorganic ions that can be reduced to a lower valency state at the electrode also have to be avoided (e.g., , ). A number of organic substances are also reduced by hydrogen on a platinum surface, and these also have to be avoided.


title: Standard hydrogen electrode

text: Cations that can be reduced and deposited on the platinum can be source of interference: silver, mercury, copper, lead, cadmium and thallium.


title: Standard hydrogen electrode

text: Substances that can inactivate ("poison") the catalytic sites include arsenic, sulfides and other sulfur compounds, colloidal substances, alkaloids, and material found in biological systems.


title: Standard hydrogen electrode

text: The standard redox potential of the deuterium couple is slightly different from that of the proton couple (ca. −0.0044 V vs SHE). Various values in this range have been obtained: −0.0061 V, −0.00431 V, −0.0074 V.


title: Standard hydrogen electrode

text: Also difference occurs when hydrogen deuteride (HD, or deuterated hydrogen, DH) is used instead of hydrogen in the electrode.


title: Noel Neill

text: Noel Darleen Neill (November 25, 1920 – July 3, 2016) was an American actress. She played Lois Lane in the film serials "Superman" (1948) and "Atom Man vs. Superman" (1950), as well as the 1950s television series "Adventures of Superman". She appeared in 80 films and television series in her career.


title: Noel Neill

text: Following high school graduation in Minneapolis, Minnesota, Neill took up professional acting and modeling in the early 1940s before taking the role of Lois Lane. She later appeared in various productions of the Superman franchise. She was cast as the parent or another relative of the main character: Neill briefly appeared in the 1978 "Superman" feature film, the 1980s TV series "Superboy" and a featured cameo in the 2006 film "Superman Returns".


title: Noel Neill

text: Noel Darleen Neill was born in Minneapolis, Minnesota, the daughter of journalist David Holland Neill, news editor of the Minneapolis Star Journal newspaper, and stage dancer Lavere Gorsboth. When she was 4 years old, her parents enrolled her at "a school for aspiring performers." During her teen years, Neill "danced, sang and even played the banjo at county fairs throughout the midwest." She attended Central High School in Minneapolis. When she graduated from high school in 1938, her first job was writing articles for "Women's Wear Daily".


title: Noel Neill

text: In her teens, Neill was a popular photographic model. While Betty Grable's pin-up was number one among GIs during World War II, Neill's was ranked number two. After she signed a contract with Paramount Pictures, it led to appearances in many of the studio's feature films and short subjects. In the mid-1940s, Noel had a leading role in one of Monogram Pictures' wayward-youth melodramas, and she became a familiar face in Monogram features for the next several years called "Teen Agers", especially in the recurring role of Betty Rogers. She appeared in the last of the original Charlie Chan movies, "Sky Dragon" (1949), and also played damsels in distress in Monogram Westerns and Republic Pictures serials. Neill also appeared in a 1950 episode of "The Lone Ranger".


title: Noel Neill

text: Neill sang with Bob Crosby and his orchestra. She also sang at the Del Mar Turf Club, which was owned by Bing Crosby.


title: Noel Neill

text: In 1945, producer Sam Katzman gave Neill the recurring role of Betty Rogers, an aggressive reporter for a high-school newspaper, in his series of "Teen Agers" musical comedies, beginning with "Junior Prom" in 1946. When Katzman was casting his "Superman" serial for Columbia Pictures, he remembered Noel Neill's news-hawk portrayals and signed her to play Lois Lane. She played the role in the film serials "Superman" (1948) and "Atom Man vs. Superman" (1950), with Kirk Alyn portraying Superman/Clark Kent.


title: Noel Neill

text: When "Adventures of Superman" came to television in 1951, veteran movie actors George Reeves and Phyllis Coates took the leading roles for the first season. By the time the series found a sponsor and a network time slot, Coates had committed herself to another production, so the producers called on Neill to reprise her role as Lois. She continued on the series for five seasons until it left the air in 1958. In 1954 she also appeared in "Stamp Day for Superman" which was produced by Superman Inc. for the United States Department of the Treasury to promote the purchase of U.S.Savings Bonds. It was only distributed in schools to educate children about the bond program. She was scheduled to appear in the seventh season with co-star Jack Larson in 1960, but after Reeves's tragic and sudden death, the seventh season was canceled, officially ending the show. While Phyllis Coates generally distanced herself from the role, Neill embraced her association with Lois Lane, giving frequent talks on college campuses during the 1970s, when interest in the series was revived, endearing herself to audiences with her warmth and humor.


title: Noel Neill

text: Neill continued to appear in "Superman"-related productions. She originated the role of Lois Lane's mother, Ellen (alternatively, Ella) Lane, in a cameo for the 1978 film "Superman", with Kirk Alyn as Lois's father, Sam Lane – as was the case in reverse with the role of Lois in 1951, Phyllis Coates would later succeed Neill in the role of Ella in ""; "Lois & Clark" star Teri Hatcher continued the tradition when she made a guest appearance on "Smallville" as Ella Lane. In an episode of the TV series "Superboy", Neill appeared alongside her former castmate Jack Larson, who had played Jimmy Olsen on TV. Her personal appearance at the Metropolis, Illinois, "Superman Festival" was featured on "The Tonight Show with Jay Leno". As "Aunt Lois", she made a guest appearance in the independent superhero film "", and she played Gertrude Vanderworth (the dying elderly wife of Lex Luthor) in the 2006 film "Superman Returns".


title: Noel Neill

text: Neill and "Superman" actor Jack Larson donated their time to record commentaries for the DVD releases of the "Superman" TV episodes. On the documentary "", Neill remarked that a frequent question she would get from children was, "Why didn't you know that Clark Kent was Superman, just wearing a pair of those darn eyeglasses?" She replied to the children (and later to college audiences), "I don't want to lose my job!"


title: Noel Neill

text: On June 15, 2010, the southern Illinois city of Metropolis unveiled a statue of Lois Lane. The Lois Lane statue is modeled on Noel Neill. Neill stated that she was honored to be memorialized with the statue.


title: Noel Neill

text: In 2003, writer Larry Ward wrote an authorized biography of Neill, "Truth, Justice, & The American Way: The Life And Times Of Noel Neill, The Original Lois Lane". A limited-edition, expanded version of the book was released in 2006. In 2007, Ward wrote another book on Neill, "Beyond Lois Lane", which focused on the actress' other acting and modeling work.


title: Noel Neill

text: In 1943, Neill married makeup artist Harold Lierley in Hollywood, California. The marriage was annulled shortly afterward. Neill then married William Behrens in 1953 in Santa Monica, California; the marriage ended in divorce in 1962. While still married to Behrens, the "Superman" television program was cancelled. It was then that her acting career diminished and Neill became a homemaker, later working in the television department at United Artists. Following her divorce from Behrens, Neill married Joel Taylor. The marriage lasted seven years and ended with the couple divorcing in 1971.


title: Noel Neill

text: A fall at her Tucson, Arizona, home in 2010 resulted in Neill suffering from a hip fracture. She was hospitalized following surgery to repair the fracture at Tucson Medical Center.


title: Noel Neill

text: Following an extended illness, Neill died in Tucson on July 3, 2016, at age 95. Her publicist and biographer, Larry Ward, paid tribute to her role as Lois Lane, as did actor Mark Hamill. Neill had no immediate surviving family members.


title: Noel Neill

text: In November 2017, the TV show "Supergirl" paid tribute by naming a character Noel Neill in the 3rd season episode "Midvale", portrayed by Erica Durance (who also played Lois Lane in "Smallville" before replacing Laura Benanti as Alura Zor-El post-season three of "Supergirl").


title: National Ignition Facility

text: The National Ignition Facility (NIF) is a laser-based inertial confinement fusion (ICF) research device, located at Lawrence Livermore National Laboratory in Livermore, California, United States. NIF's mission is to achieve fusion ignition with high energy gain. It achieved the first scientific breakeven controlled fusion experiment on December 5, 2022, with an energy gain of 1.5 megajoules. It supports nuclear weapon maintenance and design by studying the behavior of matter under the conditions found within nuclear explosions.


title: National Ignition Facility

text: NIF is the largest and most powerful ICF device built to date. The basic ICF concept is to squeeze a small amount of fuel to reach pressure and temperature necessary for fusion. NIF hosts the world's most energetic laser. The laser heats the outer layer of a small sphere. The energy is so intense that it causes the sphere to implode, squeezing the fuel inside. The implosion reaches a peak speed of , raising the fuel density from about that of water to about 100 times that of lead. The delivery of energy and the adiabatic process during implosion raises the temperature of the fuel to hundreds of millions of degrees. At these temperatures, fusion processes occur in the tiny interval before the fuel explodes outward.


title: National Ignition Facility

text: Construction on the NIF began in 1997. NIF was completed five years behind schedule and cost almost four times its original budget. Construction was certified complete on March 31, 2009, by the U.S. Department of Energy. The first large-scale experiments were performed in June 2009 and the first "integrated ignition experiments" (which tested the laser's power) were declared completed in October 2010.


title: National Ignition Facility

text: From 2009 to 2012 experiments were conducted under the National Ignition Campaign, with the goal of reaching ignition just after the laser reached full power, some time in the second half of 2012. The campaign officially ended in September 2012, at about the conditions needed for ignition. Thereafter NIF has been used primarily for materials science and weapons research. In 2021, after improvements in fuel target design, NIF produced 70% of the energy of the laser, beating the record set in 1997 by the JET reactor at 67% and achieving a burning plasma. On December 5, 2022, after further technical improvements, NIF reached "ignition", or scientific breakeven, for the first time, achieving a 154% energy yield.


title: National Ignition Facility

text: Inertial confinement fusion (ICF) devices use intense energy to rapidly heat the outer layers of a target in order to compress it. In an H-bomb, this is provided by a nuclear fission explosive. In non-fission devices, energy sources include laser and particle beams.


title: National Ignition Facility

text: The target is a small spherical pellet containing a few milligrams of fusion fuel, typically a mix of deuterium (D) and tritium (T), as this composition has the lowest ignition temperature.


title: National Ignition Facility

text: Multiple laser beams heat the surface of the pellet into a plasma, which explodes away from the surface. The rest of the pellet is driven inward on all sides, into a small volume of extremely high density. The surface explosion creates shock waves that travel inward. At the center of the fuel, a small volume is further heated and compressed. When the temperature and density are high enough, fusion reactions occur. The energy must be delivered quickly and spread extremely evenly across the target's outer surface in order to compress the fuel symmetrically.


title: National Ignition Facility

text: The reactions release high-energy particles, some of which, primarily alpha particles, collide with unfused fuel and heat it further, potentially triggering additional fusion. At the same time, the fuel is also losing heat through x-ray losses and hot electrons leaving the fuel area. Thus the rate of alpha heating must be greater than the loss rate, termed "bootstrapping". Given the right conditions—high enough density, temperature, and duration—bootstrapping results in a chain reaction, burning outward from the center. This is known as "ignition", which fuses a significant portion of the fuel and releases large amounts of energy.


title: National Ignition Facility

text: As of 1998, most ICF experiments had used laser drivers. Other drivers have been examined, such as heavy ions driven by particle accelerators.


title: National Ignition Facility

text: As of 2004, NIF used the indirect drive method of operation, in which the laser heats a small metal cylinder surrounding the capsule inside it. The heat causes the cylinder, known as a hohlraum (German for "hollow room", or cavity), to re-emit the energy as even higher frequency X-rays, which are still more evenly distributed and symmetrical. Experimental systems, including the OMEGA and Nova lasers, validated this approach. The NIF's high power supports a much larger target; the baseline pellet design is about 2 mm in diameter. It is chilled to about 18 kelvin (−255 °C) and lined with a layer of frozen deuterium–tritium (DT) fuel. The hollow interior contains a small amount of DT gas.


title: National Ignition Facility

text: In a typical experiment, the laser generates 3 MJ of infrared laser energy of a possible 4. About 1.5 MJ remains after conversion to UV, and another 15 percent is lost in the hohlraum. About 15 percent of the resulting x-rays, about 150 kJ, are absorbed by the target's outer layers. The coupling between the capsule and the x-rays is lossy, and ultimately only about 10 to 14 kJ of energy is deposited in the fuel.


title: National Ignition Facility

text: The fuels in the center of the target is compressed to a density of about 1,000 g/cm For comparison, lead has a density of about 11 g/cm). The pressure is the equivalent of 300 billion atmospheres.


title: National Ignition Facility

text: Based on simulations, it was expected that about 20 MJ of fusion energy would be released, resulting in a net fusion energy gain, denoted "Q", of about 15 (fusion energy out/UV laser energy in). Improvements in both the laser system and hohlraum design are expected to improve the energy absorbed by the capsule to about 420 kJ (and thus perhaps 40 to 50 in the fuel itself), which, in turn, could generate up to 100–150 MJ of fusion energy. The baseline design allows for a maximum of about 45 MJ of fusion energy release, due to the design of the target chamber. This is the equivalent of about 11 kg of TNT exploding.


title: National Ignition Facility

text: As of 1996, these output energies were less than the 400 MJ of energy in the system's capacitors that power the laser amplifiers. The net wall-plug efficiency of NIF (UV laser energy out divided by the energy required to pump the lasers from an external source) would be less than one percent, and the total wall-to-fusion efficiency is under 10% at best. To be useful for energy production, the fusion output must be at least an order of magnitude more than this input. Commercial laser fusion systems would use much more efficient diode-pumped solid state lasers, where wall-plug efficiencies of 10 percent have been demonstrated, and efficiencies 16–18 percent were expected with advanced concepts under development in 1996.


title: National Ignition Facility

text: As of 2010 NIF aimed to create a single 500 terawatt (TW) peak flash of light that reaches the target from numerous directions within a few picoseconds. The design uses 192 beamlines in a parallel system of flashlamp-pumped, neodymium-doped phosphate glass lasers.


title: National Ignition Facility

text: To ensure that the output of the beamlines is uniform, the laser is amplified from a single source in the Injection Laser System (ILS). This starts with a low-power flash of 1053-nanometer (nm) infrared light generated in an ytterbium-doped optical fiber laser termed Master Oscillator. Its light is split and directed into 48 Preamplifier Modules (PAMs). Each PAM conducts a two-stage amplification process via xenon flash lamps. The first stage is a regenerative amplifier in which the pulse circulates 30 to 60 times, increasing its energy from nanojoules to tens of millijoules. The second stage sends the light four times through a circuit containing a neodymium glass amplifier similar to (but much smaller than) the ones used in the main beamlines, boosting the millijoules to about 6 joules. According to LLNL, designing the PAMs was one of the major challenges. Subsequent improvements allowed them to surpass their initial design goals.


title: National Ignition Facility

text: The main amplification takes place in a series of glass amplifiers located at one end of the beamlines. Before firing, the amplifiers are first optically pumped by a total of 7,680 flash lamps. The lamps are powered by a capacitor bank that stores 400 MJ (110 kWh). When the wavefront passes through them, the amplifiers release some of the energy stored in them into the beam. The beams are sent through the main amplifier four times, using an optical switch located in a mirrored cavity. These amplifiers boost the original 6 J to a nominal 4 MJ. Given the time scale of a few nanoseconds, the peak UV power delivered to the target reaches 500 TW.


title: National Ignition Facility

text: Near the center of each beamline, and taking up the majority of the total length, are "spatial filters". These consist of long tubes with small telescopes at the end that focus the beam to a tiny point in the center of the tube, where a mask cuts off any stray light outside the focal point. The filters ensure that the beam image is extremely uniform. Spatial filters were a major step forward. They were introduced in the Cyclops laser, an earlier LLNL experiment.


title: National Ignition Facility

text: The end-to-end length of the path the laser beam travels, including switches, is about . The various optical elements in the beamlines are generally packaged into Line Replaceable Units (LRUs), standardized boxes about the size of a vending machine that can be dropped out of the beamline for replacement from below.


title: National Ignition Facility

text: After amplification is complete the light is switched back into the beamline, where it runs to the far end of the building to the target chamber. The target chamber is a multi-piece steel sphere weighing . Just before reaching the target chamber, the light is reflected off mirrors in the switchyard and target area in order to hit the target from different directions. Since the path length from the Master Oscillator to the target is different for each beamline, optics are used to delay the light in order to ensure that they all reach the center within a few picoseconds of each other.


title: National Ignition Facility

text: One of the last steps before reaching the target chamber is to convert the infrared (IR) light at 1053 nm into the ultraviolet (UV) at 351 nm in a device known as a frequency converter. These are made of thin sheets (about 1 cm thick) cut from a single crystal of potassium dihydrogen phosphate. When the 1053 nm (IR) light passes through the first of two of these sheets, frequency addition converts a large fraction of the light into 527 nm light (green). On passing through the second sheet, frequency combination converts much of the 527 nm light and the remaining 1053 nm light into 351 nm (UV) light. Infrared (IR) light is much less effective than UV at heating the targets, because IR couples more strongly with hot electrons that absorb a considerable amount of energy and interfere with compression. The conversion process can reach peak efficiencies of about 80 percent for a laser pulse that has a flat temporal shape, but the temporal shape needed for ignition varies significantly over the duration of the pulse. The actual conversion process is about 50 percent efficient, reducing delivered energy to a nominal 1.8 MJ.


title: National Ignition Facility

text: As of 2010, one important aspect of any ICF research project was ensuring that experiments could be carried out on a timely basis. Previous devices generally had to cool down for many hours to allow the flashlamps and laser glass to regain their shapes after firing (due to thermal expansion), limiting their use to one or fewer firings per day. One of the goals for NIF has been to reduce this time to less than four hours, in order to allow 700 firings a year.


title: National Ignition Facility

text: NIF is also exploring new types of targets. Previous experiments generally used plastic ablators, typically polystyrene (CH). NIF targets are constructed by coating a plastic form with a layer of sputtered beryllium or beryllium–copper alloy, and then oxidizing the plastic out of the center. Beryllium targets offer higher implosion efficiencies from x-ray inputs.


title: National Ignition Facility

text: Although NIF was primarily designed as an indirect drive device, the energy in the laser as of 2008 was high enough to be used as a direct drive system, where the laser shines directly on the target without conversion to x-rays. The power delivered by NIF UV rays was estimated to be more than enough to cause ignition, allowing fusion energy gains of about 40x, somewhat higher than the indirect drive system.


title: National Ignition Facility

text: As of 2005, scaled implosions on the OMEGA laser and computer simulations showed NIF to be capable of ignition using a polar direct drive (PDD) configuration where the target was irradiated directly by the laser only from the top and bottom, without changes to the NIF beamline layout.


title: National Ignition Facility

text: As of 2005, other targets, called saturn targets, were specifically designed to reduce the anisotropy and improve the implosion. They feature a small plastic ring around the "equator" of the target, which becomes a plasma when hit by the laser. Some of the laser light is refracted through this plasma back towards the equator of the target, evening out the heating. NIF ignition with gains of just over thirty-five times are thought to be possible, producing results almost as good as the fully symmetric direct drive approach.


title: National Ignition Facility

text: The history of ICF at Lawrence Livermore National Laboratory in Livermore, California, started with physicist John Nuckolls, who started considering the problem after a 1957 meeting arranged by Edward Teller there. During these meetings, the idea later known as PACER emerged. PACER envisioned the explosion of small hydrogen bombs in large caverns to generate steam that would be converted into electrical power. After identifying problems with this approach, Nuckolls wondered how small a bomb could be made that would still generate net positive power.


title: National Ignition Facility

text: A typical hydrogen bomb has two parts: a plutonium-based fission bomb known as the "primary", and a cylindrical arrangement of fusion fuels known as the "secondary". The primary releases x-rays, which are trapped within the bomb casing. They heat and compress the secondary until it ignites. The secondary consists of lithium deuteride (LiD) fuel, which requires an external neutron source. This is normally in the form of a small plutonium "spark plug" in the center of the fuel. Nuckolls's idea was to explore how small the secondary could be made, and what effects this would have on the energy needed from the primary to cause ignition. The simplest change is to replace the LiD fuel with DT gas, removing the need for the spark plug. This allows secondaries of any size – as the secondary shrinks, so does the amount of energy needed for ignition. At the milligram level, the energy levels started to approach those available through several known devices.


title: National Ignition Facility

text: By the early 1960s, Nuckolls and several other weapons designers had developed ICF's outlines. The DT fuel would be placed in a small capsule, designed to rapidly ablate when heated and thereby maximize compression and shock wave formation. This capsule would be placed within an engineered shell, the hohlraum, which acts like the bomb casing. The hohlraum did not have to be heated by x-rays; any source of energy could be used as long as it delivered enough energy to heat the hohlraum and produce x-rays. Ideally the energy source would be located some distance away, to mechanically isolate both ends of the reaction. A small atomic bomb could be used as the energy source, as in a hydrogen bomb, but ideally smaller energy sources would be used. Using computer simulations, the teams estimated that about 5 MJ of energy would be needed from the primary, generating a 1 MJ beam. To put this in perspective, a small (0.5 kt ) fission primary releases 2 TJ.


title: National Ignition Facility

text: While Nuckolls and LLNL were working on hohlraum-based concepts, UCSD physicist Keith Brueckner was independently working on direct drive. In the early 1970s, Brueckner formed KMS Fusion to commercialize this concept. This sparked an intense rivalry between KMS and the weapons labs. Formerly ignored, ICF became a hot topic and most of the labs started ICF work. LLNL decided to concentrate on glass lasers, while other facilities studied gas lasers using carbon dioxide (e.g. ANTARES, Los Alamos National Laboratory) or KrF (e.g. Nike laser, Naval Research Laboratory).


title: National Ignition Facility

text: Throughout these early stages, much of the understanding of the fusion process was the result of computer simulations, primarily LASNEX. LASNEX simplified the reaction to a 2-dimensional approximation, which was all that was possible with the available computing power. LASNEX estimated that laser drivers in the kJ range could reach low gain, which was just within the state of the art. This led to the Shiva laser project which was completed in 1977. Shiva fell far short of its goals. The densities reached were thousands of times smaller than predicted. This was traced to issues with the way the laser delivered heat to the target. Most of its energy energized electrons rather than the entire fuel mass. Further experiments and simulations demonstrated that this process could be dramatically improved by using shorter wavelengths.


title: National Ignition Facility

text: Further upgrades to the simulation programs, accounting for these effects, predicted that a different design would reach ignition. This system took the form of the 20-beam 200 kJ Nova laser. During the construction phase, Nuckolls found an error in his calculations, and an October 1979 review chaired by former LLNL director John S. Foster Jr. confirmed that Nova would not reach ignition. It was modified into a smaller 10-beam design that converted the light to 351 nm and increase coupling efficiency. Nova was able to deliver about 30 kJ of UV laser energy, about half of what was expected, primarily due to optical damage to the final focusing optics. Even at those levels, it was clear that the predictions for fusion production were wrong; even at the limited powers available, fusion yields were far below predictions.


title: National Ignition Facility

text: Each experiment showed that the energy needed to reach ignition continued to be underestimated. The Department of Energy (DOE) decided that direct experimentation was the best way to settle the issue, and in 1978 they started a series of underground experiments at the Nevada Test Site that used small nuclear bombs to illuminate ICF targets. The tests were known as Halite (LLNL) and Centurion (LANL).


title: National Ignition Facility

text: The basic concept behind the tests had been developed in the 1960s as a way to develop anti-ballistic missile warheads. It was found that bombs that exploded outside the atmosphere gave off bursts of X-rays that could damage an enemy warhead at long range. To test the effectiveness of this system, and to develop countermeasures to protect US warheads, the Defense Atomic Support Agency developed a system using fast-shutting doors that allowed the X-ray burst from a bomb to travel down long tunnels and then close the doors before the nuclear blast arrived. This saved the reentry vehicle (RV) from damage and allowed them to be inspected.


title: National Ignition Facility

text: ICF tests used the same system, replacing the RVs by hohlraums. Each test simultaneously illuminated many targets, each at a different distance from the bomb. Another question was how large the fuel assembly had to be in order for the fuel to self-heat from the fusion reactions and thus reach ignition. Initial data were available by mid-1984, and the testing ceased in 1988. Ignition was achieved for the first time during these tests. The amount of energy and the size of the fuel targets needed to reach ignition was far higher than predicted. During this same period, experiments began on Nova using similar targets to understand their behavior under laser illumination, allowing direct comparison against the bomb tests.


title: National Ignition Facility

text: Data suggested that about 10 MJ of X-ray energy would be needed to reach ignition. Beaming an IR laser to a hohlraum, as in Nova or NIF, required laser energy on the order of 100 MJ.


title: National Ignition Facility

text: This triggered a debate in the ICF community. One group suggested an attempt to build a laser of this power; Leonardo Mascheroni and Claude Phipps designed a new type of hydrogen fluoride laser pumped by high-energy electrons and reach the 100 MJ threshold. Others used the same data and new versions of their computer simulations to suggest that careful shaping of the laser pulse and more beams spread more evenly could achieve ignition with a laser powered between 5 and 10 MJ.


title: National Ignition Facility

text: These results prompted the DOE to request a custom military ICF facility named the "Laboratory Microfusion Facility" (LMF). LMF would use a driver on the order of 10 MJ, delivering fusion yields of between 100 and 1,000 MJ. A 1989–1990 review of this concept by the National Academy of Sciences suggested that LMF was too ambitious, and that fundamental physics needed to be further explored. They recommended further experiments before attempting to move to a 10 MJ system. Nevertheless, the authors noted, "Indeed, if it did turn out that a 100 MJ driver were required for ignition and gain, one would have to rethink the entire approach to, and rationale for, ICF".


title: National Ignition Facility

text: As of 1992, the Laboratory Microfusion Facility was estimated to cost about $1 billion. LLNL initially submitted a design with a 5 MJ 350 nm (UV) driver that would be able to reach about 200 MJ yield, which was enough to attain the majority of the LMF goals.That program was estimated to cost about $600 million FY 1989 dollars. An additional $250 million would pay to upgrade it to a full 1,000 MJ. The total would surpass $1 billion to meet all of the goals requested by the DOE.


title: National Ignition Facility

text: The NAS review led to a reevaluation of these plans, and in July 1990, LLNL responded with the Nova Upgrade, which would reuse most of Nova, along with the adjacent Shiva facility. The resulting system would be much lower power than the LMF concept, with a driver of about 1 MJ. The new design included features that advanced the state of the art in the driver section, including multi-pass in the main amplifiers, and 18 beamlines (up from 10) that were split into 288 "beamlets" as they entered the target area. The plans called for the installation of two main banks of beamlines, one in the existing Nova beamline room, and the other in the older Shiva building next door, extending through its laser bay and target area into an upgraded Nova target area. The lasers would deliver about 500 TW in a 4 ns pulse. The upgrades were expected to produce fusion yields of between 2 and 10 MJ. The initial estimates from 1992 estimated construction costs around $400 million, with construction taking place from 1995 to 1999.


title: National Ignition Facility

text: Throughout this period, the ending of the Cold War led to dramatic changes in defense funding and priorities. The political support for nuclear weapons declined and arms agreements led to a reduction in warhead count, and the US was faced with the prospect of losing a generation of nuclear weapon designers able to maintain existing stockpiles, or design new weapons. At the same time, the Comprehensive Nuclear-Test-Ban Treaty (CNTB) was signed in 1996, which would ban all criticality testing and made the development of newer generations of nuclear weapons more difficult.


title: National Ignition Facility

text: Out of these changes came the Stockpile Stewardship and Management Program (SSMP), which, among other things, included funds for the development of methods to design and build nuclear weapons without having to test them explosively. In a series of meetings that started in 1995, an agreement formed between the labs to divide up SSMP efforts. An important part of this would be confirmation of computer models using low-yield ICF experiments. The Nova Upgrade was too small to use for these experiments. A redesign matured into NIF in 1994. The estimated cost of the project remained almost $1 billion, with completion in 2002.


title: National Ignition Facility

text: In spite of the agreement, the large project cost combined with the ending of similar projects at other labs resulted in critical comments by scientists at other labs, Sandia National Laboratories in particular. In May 1997, Sandia fusion scientist Rick Spielman publicly stated that NIF had "virtually no internal peer review on the technical issues" and that "Livermore essentially picked the panel to review themselves". A retired Sandia manager, Bob Puerifoy, was even more blunt than Spielman: "NIF is worthless ... it can't be used to maintain the stockpile, period". Ray Kidder, one of the original developers of the ICF concept at LLNL, was also highly critical. He stated in 1997 that its primary purpose was to "recruit and maintain a staff of theorists and experimentalists" and that while some of the experimental data would prove useful for weapons design, differences in the experimental setup limit their relevance. "Some of the physics is the same; but the details, 'wherein the devil lies,' are quite different. It would therefore also be wrong to assume that NIF will be able to support for the long term a staff of weapons designers and engineers with detailed design competence comparable to that of those now working at the weapons design laboratories."