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Electron diffraction

Electron diffraction is a generic term for phenomena associated with changes in the direction of electron beams due to elastic interactions with atoms. It occurs due to elastic scattering, when there is no change in the energy of the electrons. The negatively charged electrons are scattered due to Coulomb forces when they interact with both the positively charged atomic core and the negatively charged electrons around the atoms. The resulting map of the directions of the electrons far from the sample is called a diffraction pattern, see for instance Figure 1. Beyond patterns showing the directions of electrons, electron diffraction also plays a major role in the contrast of images in electron microscopes.

This article provides an overview of electron diffraction and electron diffraction patterns, collective referred to by the generic name electron diffraction. This includes aspects of how in a general way electrons can act as waves, and diffract and interact with matter. It also involves the extensive history behind modern electron diffraction, how the combination of developments in the 19th century in understanding and controlling electrons in vacuum and the early 20th century developments with electron waves were combined with early instruments, giving birth to electron microscopy and diffraction in 1920–1935. While this was the birth, there have been a large number of further developments since then.

There are many types and techniques of electron diffraction. The most common approach is where the electrons transmit through a thin sample, from 1 nm to 100 nm (10 atoms to 1000 thick), where the results depending upon how the atoms are arranged in the material, for instance a single crystal, many crystals or different types of solids. Other cases such as larger repeats, no periodicity or disorder have their own characteristic patterns. There are many different ways of collecting diffraction information, from parallel illumination to a converging beam of electrons or where the beam is rotated or scanned across the sample which produce information that is often easier to interpret. There are also many other types of instruments. For instance, in a scanning electron microscope (SEM), electron backscatter diffraction can be used to determine crystal orientation across the sample. Electron diffraction patterns can also be used to characterize molecules using gas electron diffraction, liquids, surfaces using lower energy electrons, a technique called LEED, and by reflecting electrons off surfaces, a technique called RHEED.

There are also many levels of analysis of electron diffraction, including:

 * 1) The simplest approximation using the de Broglie wavelength  for electrons, where only the geometry is considered and often Bragg's law  is invoked. This approach only considers the electrons far from the sample, a far-field or Fraunhofer  approach.
 * 2) The first level of more accuracy where it is approximated that the electrons are only scattered once, which is called kinematical diffraction   and is also a far-field or Fraunhofer  approach.
 * 3) More complete and accurate explanations where multiple scattering is included, what is called dynamical diffraction (e.g. refs     ). These involve more general analyses using relativistically corrected Schrödinger equation methods, and track the electrons through the sample, being accurate both near and far from the sample (both Fresnel and Fraunhofer diffraction).

Electron diffraction is similar to x-ray and neutron diffraction. However, unlike x-ray and neutron diffraction where the simplest approximations are quite accurate, with electron diffraction this is not the case. Simple models give the geometry of the intensities in a diffraction pattern, but dynamical diffraction approaches are needed for accurate intensities and the positions of diffraction spots.

A primer on electron diffraction
All matter can be thought of as matter waves, from small particles such as electrons up to macroscopic objects – although it is impossible to measure any of the "wave-like" behavior of macroscopic objects. Waves can move around objects and create interference patterns, and a classic example is the Young's two-slit experiment shown in Figure 2, where a wave impinges upon two slits in the first of the two images (blue waves). After going through the slits there are directions where the wave is stronger, ones where it is weaker – the wave has been diffracted. If instead of two slits there are a number of small points then similar phenomena can occur as shown in the second image where the wave (red and blue) is coming in from the bottom right corner. This is comparable to diffraction of an electron wave where the small dots would be atoms in a small crystal, see also note. Note the strong dependence on the relative orientation of the crystal and the incoming wave.

Close to an aperture or atoms, often called the "sample", the electron wave would be described in terms of near field or Fresnel diffraction. This has relevance for imaging within electron microscopes,  whereas electron diffraction patterns are measured far from the sample, which is described as far-field or Fraunhofer diffraction. A map of the directions of the electron waves leaving the sample will show high intensity (white) for favored directions, such as the three prominent ones in the Young's two-slit experiment of Figure 2, while the other directions will be low intensity (dark). Often there will be an array of spots (preferred directions) as in Figure 1 and the other figures shown later.

History
The historical background is divided into several subsections. The first is the general background to electrons in vacuum and the technological developments that led to cathode-ray tubes as well as vacuum tubes that dominated early television and electronics; the second is how these led to the development of electron microscopes; the last is work on the nature of electron beams and the fundamentals of how electrons behave, a key component of quantum mechanics and the explanation of electron diffraction.

Electrons in vacuum
Experiments involving electron beams occurred long before the discovery of the electron; ēlektron (ἤλεκτρον) is the Greek word for amber, which is connected to the recording of electrostatic charging by Thales of Miletus around 585 BCE, and possibly others even earlier.

In 1650, Otto von Guericke invented the vacuum pump allowing for the study of the effects of high voltage electricity passing through rarefied air. In 1838, Michael Faraday applied a high voltage between two metal electrodes at either end of a glass tube that had been partially evacuated of air, and noticed a strange light arc with its beginning at the cathode (negative electrode) and its end at the anode (positive electrode). Building on this, in the 1850s, Heinrich Geissler was able to achieve a pressure of around 10−3 atmospheres, inventing what became known as Geissler tubes. Using these tubes, while studying electrical conductivity in rarefied gases in 1859, Julius Plücker observed that the radiation emitted from the negatively charged cathode caused phosphorescent light to appear on the tube wall near it, and the region of the phosphorescent light could be moved by application of a magnetic field.

In 1869, Plücker's student Johann Wilhelm Hittorf found that a solid body placed between the cathode and the phosphorescence would cast a shadow on the tube wall, e.g. Figure 3. Hittorf inferred that there are straight rays emitted from the cathode and that the phosphorescence was caused by the rays striking the tube walls. In 1876 Eugen Goldstein showed that the rays were emitted perpendicular to the cathode surface, which differentiated them from the incandescent light. Eugen Goldstein dubbed them cathode rays. By the 1870s William Crookes and others were able to evacuate glass tubes below 10−6 atmospheres, and observed that the glow in the tube disappeared when the pressure was reduced but the glass behind the anode began to glow. Crookes was also able to show that the particles in the cathode rays were negatively charged and could be deflected by an electromagnetic field.

In 1897, Joseph Thomson measured the mass of these cathode rays, proving they were made of particles. These particles, however, were 1800 times lighter than the lightest particle known at that time – a hydrogen atom. These were originally called corpuscles and later named electrons by George Johnstone Stoney.

The control of electron beams that this work led to resulted in significant technology advances in electronic amplifiers and television displays.

Waves, diffraction and quantum mechanics
Independent of the developments for electrons in vacuum, at about the same time the components of quantum mechanics were being assembled. In 1924 Louis de Broglie in his PhD thesis Recherches sur la théorie des quanta introduced his theory of electron waves. He suggested that an electron around a nucleus could be thought of as standing waves, and that electrons and all matter could be considered as waves. He merged the idea of thinking about them as particles (or corpuscles), and of thinking of them as waves. He proposed that particles are bundles of waves (wave packets) that move with a group velocity and have an effective mass, see for instance Figure 4. Both of these depend upon the energy, which in turn connects to the wavevector and the relativistic formulation of Albert Einstein a few years before.

This rapidly became part of what was called by Erwin Schrödinger undulatory mechanics, now called the Schrödinger equation or wave mechanics. As stated by Louis de Broglie on September 8, 1927, in the preface to the German translation of his theses (in turn translated into English): "M. Einstein from the beginning has supported my thesis, but it was M. E. Schrödinger who developed the propagation equations of a new theory and who in searching for its solutions has established what has become known as “Wave Mechanics”." The Schrödinger equation combines the kinetic energy of waves and the potential energy due to, for electrons, the Coulomb potential. He was able to explain earlier work such as the quantization of the energy of electrons around atoms in the Bohr model, as well as many other phenomena. Electron waves as hypothesized by de Broglie were automatically part of the solutions to his equation, see also introduction to quantum mechanics and matter waves.

Both the wave nature and the undulatory mechanics approach were experimentally confirmed for electron beams by experiments from two groups performed independently, the first the Davisson–Germer experiment,   the other by George Paget Thomson and Alexander Reid; see note for more discussion. Alexander Reid, who was Thomson's graduate student, performed the first experiments, but he died soon after in a motorcycle accident and is rarely mentioned. These experiments were rapidly followed by the first non-relativistic diffraction model for electrons by Hans Bethe based upon the Schrödinger equation, which is very close to how electron diffraction is now described. Significantly, Clinton Davisson and Lester Germer noticed that their results could not be interpreted using a Bragg's law approach as the positions were systematically different; the approach of Hans Bethe which includes the refraction due to the average potential yielded more accurate results. These advances in understanding of electron wave mechanics were important for many developments of electron-based analytical techniques such as Seishi Kikuchi's observations of lines due to combined elastic and inelastic scattering, gas electron diffraction developed by Herman Mark and Raymond Weil, diffraction in liquids by Louis Maxwell, and the first electron microscopes developed by Max Knoll and Ernst Ruska.

Electron microscopes and early electron diffraction
In order to have a practical microscope or diffractometer, just having an electron beam was not enough, it needed to be controlled. Many developments laid the groundwork of electron optics; see the paper by Chester J. Calbick for an overview of the early work. One significant step was the work of Heinrich Hertz in 1883 who made a cathode-ray tube with electrostatic and magnetic deflection, demonstrating manipulation of the direction of an electron beam. Others were focusing of electrons by an axial magnetic field by Emil Wiechert in 1899, improved oxide-coated cathodes which produced more electrons by Arthur Wehnelt in 1905 and the development of the electromagnetic lens in 1926 by Hans Busch.

Building an electron microscope involves combining these elements, similar to an optical microscope but with magnetic or electrostatic lenses instead of glass ones. To this day the issue of who invented the transmission electron microscope is controversial, as discussed by Thomas Mulvey and more recently by Yaping Tao. Extensive additional information can be found in the articles by Martin Freundlich, Reinhold Rüdenberg and Mulvey.

One effort was university based. In 1928, at the Technical University of Berlin, Adolf Matthias (Professor of High Voltage Technology and Electrical Installations) appointed Max Knoll to lead a team of researchers to advance research on electron beams and cathode-ray oscilloscopes. The team consisted of several PhD students including Ernst Ruska. In 1931, Max Knoll and Ernst Ruska successfully generated magnified images of mesh grids placed over an anode aperture. The device, a replicate of which is shown in Figure 5, used two magnetic lenses to achieve higher magnifications, the first electron microscope. (Max Knoll died in 1969, so did not receive a share of the Nobel Prize in Physics in 1986.)

Apparently independent of this effort was work at Siemens-Schuckert by Reinhold Rudenberg. According to patent law (U.S. Patent No. 2058914 and 2070318, both filed in 1932), he is the inventor of the electron microscope, but it is not clear when he had a working instrument. He stated in a very brief article in 1932 that Siemens had been working on this for some years before the patents were filed in 1932, so his effort was parallel to the university effort. He died in 1961, so similar to Max Knoll, was not eligible for a share of the Nobel Prize.

These instruments could produce magnified images, but were not particularly useful for electron diffraction; indeed, the wave nature of electrons was not exploited during the development. Key for electron diffraction in microscopes was the advance in 1936 where Hans Boersch showed that they could be used as micro-diffraction cameras with an aperture —the birth of selected area electron diffraction.

Less controversial was the development of LEED—the early experiments of Davisson and Germer used this approach. As early as 1929 Germer investigated gas adsorption, and in 1932 Harrison E. Farnsworth probed single crystals of copper and silver. However, the vacuum systems available at that time were not good enough to properly control the surfaces, and it took almost forty years before these became available. Similarly, it was not until about 1965 that Peter B. Sewell and M. Cohen demonstrated the power of RHEED in a system with a very well controlled vacuum.

Subsequent developments in methods and modelling
Despite early successes such as the determination of the positions of hydrogen atoms in NH4Cl crystals by W. E. Laschkarew and I. D. Usykin in 1933, boric acid by John M. Cowley in 1953 and orthoboric acid by William Houlder Zachariasen in 1954, electron diffraction for many years was a qualitative technique used to check samples within electron microscopes. John M Cowley explains in a 1968 paper: "Thus was founded the belief, amounting in some cases almost to an article of faith, and persisting even to the present day, that it is impossible to interpret the intensities of electron diffraction patterns to gain structural information."This has changed, in transmission, reflection and for low energies. Some of the key developments (some of which are also described later) from the early days to 2023 have been:

 * Fast numerical methods based upon the Cowley-Moodie multislice algorithm, which only became possible once the fast Fourier transform (FFT) method was developed. With these and other numerical methods Fourier transforms are fast, and it became possible to calculate accurate, dynamical diffraction in seconds to minutes with laptops using widely available multislice programs.
 * Developments in the convergent-beam electron diffraction approach. Building on the original work of Walther Kossel and Gottfried Möllenstedt in 1939, it was extended by Peter Goodman and Gunter Lehmpfuhl, then mainly by the groups of John Steeds  and Michiyoshi Tanaka who showed how to determine point groups and space groups. It can also be used for higher-level refinements of the electron density;  for a brief history see CBED history. In many cases this is the best method to determine symmetry.
 * The development of new approaches to reduce dynamical effects such as precession electron diffraction and three-dimensional diffraction methods. Averaging over different directions has, empirically, been found to significantly reduce dynamical diffraction effects, e.g., see PED history for further details. Not only is it easier to identify known structures with this approach, it can also be used to solve unknown structures in some cases  – see precession electron diffraction for further information.
 * The development of experimental methods exploiting ultra-high vacuum technologies (e.g. the approach described by Daniel J. Alpert in 1953 ) to better control surfaces, making LEED and RHEED more reliable and reproducible techniques. In the early days the surfaces were not well controlled; with these technologies they can both be cleaned and remain clean for hours to days, a key component of surface science.
 * Fast and accurate methods to calculate intensities for LEED so it could be used to determine atomic positions, for instance references. These have been extensively exploited to determine the structure of many surfaces, and the arrangement of foreign atoms on surfaces.
 * Methods to simulate the intensities in RHEED, so it can be used semi-quantitatively to understand surfaces during growth and thereby to control the resulting materials.
 * The development of advanced detectors for transmission electron microscopy such as charge-coupled device and direct electron detectors, which improve the accuracy and reliability of intensity measurements. These have efficiencies and accuracies that can be a thousand or more times that of the photographic film used in the earliest experiments, with the information available in real time rather than requiring photographic processing after the experiment.

Plane waves, wavevectors and reciprocal lattice
What is seen in an electron diffraction pattern depends upon the sample and also the energy of the electrons. The electrons need to be considered as waves, which involves describing the electron via a wavefunction, written in crystallographic notation (see notes and) as: $$\psi (\mathbf r) = \exp(2\pi i \mathbf k \cdot \mathbf r)$$for a position $$\mathbf r$$. This is a quantum mechanics description; one cannot use a classical approach. The vector $$\mathbf k$$ is called the wavevector, has units of inverse nanometers, and the form above is called a plane wave as the term inside the exponential is constant on the surface of a plane. The vector $$\mathbf k$$ is what is used when drawing ray diagrams, and in vacuum is parallel to the direction or, better, group velocity   or probability current  of the plane wave. For most cases the electrons are travelling at a respectable fraction of the speed of light, so rigorously need to be considered using relativistic quantum mechanics via the Dirac equation, which as spin does not normally matter can be reduced to the Klein–Gordon equation. Fortunately one can side-step many complications and use a non-relativistic approach based around the Schrödinger equation. Following Kunio Fujiwara and Archibald Howie, the relationship between the total energy of the electrons and the wavevector is written as:$$E = \frac{h^2 k^2}{2m^*}$$with$$m^* = m_0 + \frac{E}{2c^2}$$where $$h$$ is Planck's constant, $$m^*$$ is a relativistic effective mass used to cancel out the relativistic terms for electrons of energy $$E$$ with $$c$$ the speed of light and $$m_0$$ the rest mass of the electron. The concept of effective mass occurs throughout physics (see for instance Ashcroft and Mermin), and comes up in the behavior of quasiparticles. A common one is the electron hole, which acts as if it is a particle with a positive charge and a mass similar to that of an electron, although it can be several times lighter or heavier. For electron diffraction the electrons behave as if they are non-relativistic particles of mass $$m^*$$ in terms of how they interact with the atoms.

The wavelength of the electrons $$\lambda$$ in vacuum is from the above equations$$ \lambda = \frac 1 k = \frac{h}{\sqrt{2m^* E}} = \frac{h c}{\sqrt{E(2 m_0 c^2 + E)}},$$and can range from about 0.1 nanometers, roughly the size of an atom, down to a thousandth of that. Typically the energy of the electrons is written in electronvolts (eV), the voltage used to accelerate the electrons; the actual energy of each electron is this voltage times the electron charge. For context, the typical energy of a chemical bond is a few eV; electron diffraction involves electrons up to 5,000,000 eV.

The magnitude of the interaction of the electrons with a material scales as $$2 \pi \frac{m^*}{h^2 k} = 2\pi\frac{ m^* \lambda} {h^2} = \frac \pi {hc} \sqrt{\frac{2m_0 c^2}{E} + 1}.$$While the wavevector increases as the energy increases, the change in the effective mass compensates this so even at the very high energies used in electron diffraction there are still significant interactions.

The high-energy electrons interact with the Coulomb potential, which for a crystal can be considered in terms of a Fourier series (see for instance Ashcroft and Mermin), that is$$V(\mathbf r) = \sum V_g \exp(2 \pi i \mathbf g \cdot \mathbf r)$$with $$\mathbf g$$ a reciprocal lattice vector and $$V_g$$ the corresponding Fourier coefficient of the potential. The reciprocal lattice vector is often referred to in terms of Miller indices $$(h k l)$$, a sum of the individual reciprocal lattice vectors $$\mathbf A,\mathbf B,\mathbf C$$ with integers $$h, k, l$$ in the form: $$\mathbf g = h \mathbf A + k \mathbf B + l \mathbf C$$(Sometimes reciprocal lattice vectors are written as $$\mathbf a^*$$, $$\mathbf b^*$$, $$\mathbf c^*$$ and see note.) The contribution from the $$V_g$$ needs to be combined with what is called the shape function (e.g.  ), which is the Fourier transform of the shape of the object. If, for instance, the object is small in one dimension then the shape function extends far in that direction in the Fourier transform—a reciprocal relationship.

Around each reciprocal lattice point one has this shape function. How much intensity there will be in the diffraction pattern depends upon the intersection of the Ewald sphere, that is energy conservation, and the shape function around each reciprocal lattice point—see Figure 6, 20 and 22. The vector from a reciprocal lattice point to the Ewald sphere is called the excitation error $$\mathbf s_g$$.

For transmission electron diffraction the samples used are thin, so most of the shape function is along the direction of the electron beam. For both LEED and RHEED the shape function is mainly normal to the surface of the sample. In LEED this results in (a simplification) back-reflection of the electrons leading to spots, see Figure 20 and 21 later, whereas in RHEED the electrons reflect off the surface at a small angle and typically yield diffraction patterns with streaks, see Figure 22 and 23 later. By comparison, with both x-ray and neutron diffraction the scattering is significantly weaker, so typically requires much larger crystals, in which case the shape function shrinks to just around the reciprocal lattice points, leading to simpler Bragg's law diffraction.

For all cases, when the reciprocal lattice points are close to the Ewald sphere (the excitation error is small) the intensity tends to be higher; when they are far away it tends to be smaller. The set of diffraction spots at right angles to the direction of the incident beam are called the zero-order Laue zone (ZOLZ) spots, as shown in Figure 6. One can also have intensities further out from reciprocal lattice points which are in a higher layer. The first of these is called the first order Laue zone (FOLZ); the series is called by the generic name higher order Laue zone (HOLZ).

The result is that the electron wave after it has been diffracted can be written as an integral over different plane waves: $$ \psi (\mathbf r) = \int \phi (\mathbf k) \exp(2 \pi i \mathbf k \cdot \mathbf r) d^3\mathbf k ,$$that is a sum of plane waves going in different directions, each with a complex amplitude $$\phi (\mathbf k)$$. (This is a three dimensional integral, which is often written as $$d\mathbf k$$ rather than $$d^3\mathbf k$$.) For a crystalline sample these wavevectors have to be of the same magnitude for elastic scattering (no change in energy), and are related to the incident direction $$\mathbf k_0$$ by (see Figure 6)

$$\mathbf k = \mathbf k_0 + \mathbf g + \mathbf s_g.$$A diffraction pattern detects the intensities$$ I(\mathbf k) = \left| \phi(\mathbf k) \right| ^2 .$$For a crystal these will be near the reciprocal lattice points typically forming a two dimensional grid. Different samples and modes of diffraction give different results, as do different approximations for the amplitudes $$\phi (\mathbf k)$$.

A typical electron diffraction pattern in TEM and LEED is a grid of high intensity spots (white) on a dark background, approximating a projection of the reciprocal lattice vectors, see Figure 1, 9, 10, 11, 14 and 21 later. There are also cases which will be mentioned later where diffraction patterns are not periodic, see Figure 15, have additional diffuse structure as in Figure 16, or have rings as in Figure 12, 13 and 24. With conical illumination as in CBED they can also be a grid of discs, see Figure 7, 9 and 18. RHEED is slightly different, see Figure 22, 23. If the excitation errors $$s_g$$ were zero for every reciprocal lattice vector, this grid would be at exactly the spacings of the reciprocal lattice vectors. This would be equivalent to a Bragg's law condition for all of them. In TEM the wavelength is small and this is close to correct, but not exact. In practice the deviation of the positions from a simple Bragg's law interpretation is often neglected, particularly if a column approximation is made (see below).

Kinematical diffraction
In Kinematical theory an approximation is made that the electrons are only scattered once. For transmission electron diffraction it is common to assume a constant thickness $$t$$, and also what is called the Column Approximation (e.g. references and further reading). For a perfect crystal the intensity for each diffraction spot $$\mathbf g$$ is then:$$I_{g} = \left|\phi(\mathbf k)\right|^2 \propto \left|F_{g}\frac{\sin(\pi t s_z)}{\pi s_z}\right|^2 $$where $$s_z$$ is the magnitude of the excitation error $$|\mathbf s_z|$$ along z, the distance along the beam direction (z-axis by convention) from the diffraction spot to the Ewald sphere, and $$F_{g}$$ is the structure factor: $$F_{g} = \sum_{j=1}^N f_j \exp{(2 \pi i \mathbf g \cdot \mathbf r_j -T_j g^2)} $$the sum being over all the atoms in the unit cell with $$f_j$$ the form factors, $$\mathbf g$$ the reciprocal lattice vector, $$T_j$$ is a simplified form of the Debye–Waller factor, and $$\mathbf k$$ is the wavevector for the diffraction beam which is:$$\mathbf k = \mathbf k_0 + \mathbf g + \mathbf s_z$$for an incident wavevector of $$\mathbf k_0$$, as in Figure 6 and above. The excitation error comes in as the outgoing wavevector $$\mathbf k$$ has to have the same modulus (i.e. energy) as the incoming wavevector $$\mathbf k_0$$. The intensity in transmission electron diffraction oscillates as a function of thickness, which can be confusing; there can similarly be intensity changes due to variations in orientation and also structural defects such as dislocations. If a diffraction spot is strong it could be because it has a larger structure factor, or it could be because the combination of thickness and excitation error is "right". Similarly the observed intensity can be small, even though the structure factor is large. This can complicate interpretation of the intensities. By comparison, these effects are much smaller in x-ray diffraction or neutron diffraction because they interact with matter far less and often Bragg's law is adequate.

This form is a reasonable first approximation which is qualitatively correct in many cases, but more accurate forms including multiple scattering (dynamical diffraction) of the electrons are needed to properly understand the intensities.

Dynamical diffraction
While kinematical diffraction is adequate to understand the geometry of the diffraction spots, it does not correctly give the intensities and has a number of other limitations. For a more complete approach one has to include multiple scattering of the electrons using methods that date back to the early work of Hans Bethe in 1928. These are based around solutions of the Schrödinger equation using the relativistic effective mass $$m^*$$ described earlier. Even at very high energies dynamical diffraction is needed as the relativistic mass and wavelength partially cancel, so the role of the potential is larger than might be thought. The main components of current dynamical diffraction of electrons include:
 * Taking into account the scattering back into the incident beam both from diffracted beams and between all others, not just single scattering from the incident beam to diffracted beams. This is important even for samples which are only a few atoms thick.
 * Modelling at least semi-empirically the role of inelastic scattering by an imaginary component of the potential,  also called an "optical potential".  There is always inelastic scattering, and often it can have a major effect on both the background and sometimes the details, see Figure 7 and 18.
 * Higher-order numerical approaches to calculate the intensities such as multislice, matrix methods which are called Bloch-wave approaches or muffin-tin approaches. With these diffraction spots which are not present in kinematical theory can be present, e.g.
 * Contributions to the diffraction from elastic strain and crystallographic defects, and also what Jens Lindhard called the string potential.
 * For transmission electron microscopes effects due to variations in the thickness of the sample and the normal to the surface.
 * Both in the geometry of scattering and calculations, for both LEED and RHEED, effects due to the presence of surface steps, surface reconstructions and other atoms at the surface. Often these change the diffraction details significantly.
 * For LEED, use more careful analyses of the potential because contributions from exchange terms can be important. Without these the calculations may not be accurate enough.

Kikuchi lines
Kikuchi lines, first observed by Seishi Kikuchi in 1928, are linear features created by electrons scattered both inelastically and elastically. As the electron beam interacts with matter, the electrons are diffracted via elastic scattering, and also scattered inelastically losing part of their energy. These occur simultaneously, and cannot be separated – according to the Copenhagen interpretation of quantum mechanics, only the probabilities of electrons at detectors can be measured. These electrons form Kikuchi lines which provide information on the orientation.

Kikuchi lines come in pairs forming Kikuchi bands, and are indexed in terms of the crystallographic planes they are connected to, with the angular width of the band equal to the magnitude of the corresponding diffraction vector $$|\mathbf g|$$. The position of Kikuchi bands is fixed with respect to each other and the orientation of the sample, but not against the diffraction spots or the direction of the incident electron beam. As the crystal is tilted, the bands move on the diffraction pattern. Since the position of Kikuchi bands is quite sensitive to crystal orientation, they can be used to fine-tune a zone-axis orientation or determine crystal orientation. They can also be used for navigation when changing the orientation between zone axes connected by some band, an example of such a map produced by combining many local sets of experimental Kikuchi patterns is in Figure 8; Kikuchi maps are available for many materials.

In a transmission electron microscope

Electron diffraction in a TEM exploits controlled electron beams using electron optics. Different types of diffraction experiments, for instance Figure 9, provide information such as lattice constants, symmetries, and sometimes to solve an unknown crystal structure.

It is common to combine it with other methods, for instance images using selected diffraction beams, high-resolution images showing the atomic structure, chemical analysis through energy-dispersive x-ray spectroscopy, investigations of electronic structure and bonding through electron energy loss spectroscopy, and studies of the electrostatic potential through electron holography; this list is not exhaustive. Compared to x-ray crystallography, TEM analysis is significantly more localized and can be used to obtain information from tens of thousands of atoms to just a few or even single atoms.

Formation of a diffraction pattern

In TEM, the electron beam passes through a thin film of the material as illustrated in Figure 10. Before and after the sample the beam is manipulated by the electron optics including magnetic lenses, deflectors and apertures; these act on the electrons similar to how glass lenses focus and control light. Optical elements above the sample are used to control the incident beam which can range from a wide and parallel beam to one which is a converging cone and can be smaller than an atom, 0.1 nm. As it interacts with the sample, part of the beam is diffracted and part is transmitted without changing its direction. This occurs simultaneously as electrons are everywhere until they are detected (wavefunction collapse) according to the Copenhagen interpretation.

Below the sample, the beam is controlled by another set of magnetic lneses and apertures. Each set of initially parallel rays (a plane wave) is focused by the first lens (objective) to a point in the back focal plane of this lens, forming a spot on a detector; a map of these directions, often an array of spots, is the diffraction pattern. Alternatively the lenses can form a magnified image of the sample. Herein the focus is on collecting a diffraction pattern; for other information see the pages on TEM and scanning transmission electron microscopy.

Selected area electron diffraction
The simplest diffraction technique in TEM is selected area electron diffraction (SAED) where the incident beam is wide and close to parallel. An aperture is used to select a particular region of interest from which the diffraction is collected. These apertures are part of a thin foil of a heavy metal such as tungsten which has a number of small holes in it. This way diffraction information can be limited to, for instance, individual crystallites. Unfortunately the method is limited by the spherical aberration of the objective lens, so is only accurate for large grains with tens of thousands of atoms or more; for smaller regions a focused probe is needed.

If a parallel beam is used to acquire a diffraction pattern from a single-crystal, the result is similar to a two-dimensional projection of the crystal reciprocal lattice. From this one can determine interplanar distances and angles and in some cases crystal symmetry, particularly when the electron beam is down a major zone axis, see for instance the database by Jean-Paul Morniroli. However, projector lens aberrations such as barrel distortion as well as dynamical diffraction effects (e.g. ) cannot be ignored. For instance, certain diffraction spots which are not present in x-ray diffraction can appear, for instance those due to Gjønnes-Moodie extinction conditions.

If the sample is tilted relative to the electron beam, different sets of crystallographic planes contribute to the pattern yielding different types of diffraction patterns, approximately different projections of the reciprocal lattice, see Figure 11. This can be used to determine the crystal orientation, which in turn can be used to set the orientation needed for a particular experiment. Furthermore, a series of diffraction patterns varying in tilt can be acquired and processed using a diffraction tomography approach. There are ways to combine this with direct methods algorithms using electrons and other methods such as charge flipping, or automated diffraction tomography  to solve crystal structures.

Polycrystalline pattern

Diffraction patterns depend on whether the beam is diffracted by one single crystal or by a number of differently oriented crystallites, for instance in a polycrystalline material. If there are many contributing crystallites, the diffraction image is a superposition of individual crystal patterns, see Figure 12. With a large number of grains this superposition yields diffraction spots of all possible reciprocal lattice vectors. This results in a pattern of concentric rings as shown in Figure 12 and 13.

Textured materials yield a non-uniform distribution of intensity around the ring, which can be used to discriminate between nanocrystalline and amorphous phases. However, diffraction often cannot differentiate between very small grain polycrystalline materials and truly random order amorphous. Here high-resolution transmission electron microscopy and fluctuation electron microscopy can be more powerful, although this is still a topic of continuing development.

Multiple materials and double diffraction
In simple cases there is only one grain or one type of material in the area used for collecting a diffraction pattern. However, often there is more than one. If they are in different areas then the diffraction pattern will be a combination. In addition there can be one grain on top of another, in which case the electrons that go through the first are diffracted by the second. Electrons have no memory (like many of us), so after they have gone through the first grain and been diffracted, they traverse the second as if their current direction was that of the incident beam. This leads to diffraction spots which are the vector sum of those of the two (or even more) reciprocal lattices of the crystals, and can lead to complicated results. It can be difficult to know if this is real and due to some novel material, or just a case where multiple crystals and diffraction is leading to odd results.

Bulk and surface superstructures
Many materials have relatively simple structures based upon small unit cell vectors $$\mathbf a,\mathbf b,\mathbf c$$ (see also note). There are many others where the repeat is some larger multiple of the smaller unit cell (subcell) along one or more direction, for instance $$N\mathbf a, M\mathbf b, \mathbf c$$. which has larger dimensions in two directions. These superstructures can arise from many reasons:

 * 1) Larger unit cells due to electronic ordering which leads to small displacements of the atoms in the subcell. One example is antiferroelectricity ordering.
 * 2) Chemical ordering, that is different atom types at different locations of the subcell.
 * 3) Magnetic order of the spins. These may be in opposite directions on some atoms, leading to what is called antiferromagnetism.

In addition to those which occur in the bulk, superstructures can also occur at surfaces. When half the material is (nominally) removed to create a surface, some of the atoms will be under coordinated. To reduce their energy they can rearrange. Sometimes these rearrangements are relatively small; sometimes they are quite large. Similar to a bulk superstructure there will be additional, weaker diffraction spots. One example is for the silicon (111) surface, where there is a supercell which is seven times larger than the simple bulk cell in two directions. This leads to diffraction patterns with additional spots some of which are marked in Figure 14. Here the (220) are stronger bulk diffraction spots, and the weaker ones due to the surface reconstruction are marked 7x7—see note for convention comments.

Aperiodic materials
In an aperiodic crystal the structure can no longer be simply described by three different vectors in real or reciprocal space. In general there is a substructure describable by three (e.g. $$\mathbf a, \mathbf b, \mathbf c$$), similar to supercells above, but in addition there is some additional periodicity (one to three) which cannot be described as a multiple of the three; it is a genuine additional periodicity which is an irrational number relative to the subcell lattice. The diffraction pattern can then only be described by more than three indices.

An extreme example of this is for quasicrystals, which can be described similarly by a higher number of Miller indices in reciprocal space—but not by any translational symmetry in real space. An example of this is shown in Figure 15 for an Al-Cu-Fe-Cr decagonal quasicrystal grown by magnetron sputtering on a sodium chloride substrate and then lifted off by dissolving the substrate with water. In the pattern there are pentagons which are a characteristic of the aperiodic nature of these materials.

Diffuse scattering
A further step beyond superstructures and aperiodic materials is what is called diffuse scattering in electron diffraction patterns due to disorder, which is also known for x-ray or neutron scattering. This can occur from inelastic processes, for instance, in bulk silicon the atomic vibrations (phonons) are more prevalent along specific directions, which leads to streaks in diffraction patterns. Sometimes it is due to arrangements of point defects. Completely disordered substitutional point defects lead to a general background which is called Laue monotonic scattering. Often there is a probability distribution for the distances between point defects or what type of substitutional atom there is, which leads to distinct three-dimensional intensity features in diffraction patterns. An example of this is for a Nb0.83CoSb sample, with the diffraction pattern shown in Figure 16. Because of the vacancies at the niobium sites, there is diffuse intensity with snake-like structure due to correlations of the distances between vacancies and also the relaxation of Co and Sb atoms around these vacancies.

Convergent beam electron diffraction
In convergent beam electron diffraction (CBED),  the incident electrons are normally focused in a converging cone-shaped beam with a crossover located at the sample, e.g. Figure 17, although other methods exist. Unlike the parallel beam, the convergent beam is able to carry information from the sample volume, not just a two-dimensional projection available in SAED. With convergent beam there is also no need for the selected area aperture, as it is inherently site-selective since the beam crossover is positioned at the object plane where the sample is located.

A CBED pattern consists of disks arranged similar to the spots in SAED. Intensity within the disks represents dynamical diffraction effects and symmetries of the sample structure, see Figure 7 and 18. Even though the zone axis and lattice parameter analysis based on disk positions does not significantly differ from SAED, the analysis of disks content is more complex and simulations based on dynamical diffraction theory is often required. As illustrated in Figure 18, the details within the disk change with sample thickness, as does the inelastic background. With appropriate analysis CBED patterns can be used for indexation of the crystal point group, space group identification, measurement of lattice parameters, thickness or strain.

The disk diameter can be controlled using the microscope optics and apertures. The larger is the angle, the broader the disks are with more features. If the angle is increased to significantly, the disks begin to overlap. This is avoided in large angle convergent electron beam diffraction (LACBED) where the sample is moved upwards or downwards. There are applications, however, where the overlapping disks are beneficial, for instance with a ronchigram. It is a CBED pattern, often but not always of an amorphous material, with many intentionally overlapping disks providing information about the optical aberrations of the electron optical system.

Precession electron diffraction
Precession electron diffraction (PED), invented by Roger Vincent and Paul Midgley in 1994, is a method to collect electron diffraction patterns in a transmission electron microscope (TEM). The technique involves rotating (precessing) a tilted incident electron beam around the central axis of the microscope, compensating for the tilt after the sample so a spot diffraction pattern is formed, similar to a SAED pattern. However, a PED pattern is an integration over a collection of diffraction conditions, see Figure 19. This integration produces a quasi-kinematical diffraction pattern that is more suitable as input into direct methods algorithms using electrons to determine the crystal structure of the sample. Because it avoids many dynamical effects it can also be used to better identify crystallographic phases.

4D STEM
4D scanning transmission electron microscopy (4D STEM) is a subset of scanning transmission electron microscopy (STEM) methods which uses a pixelated electron detector to capture a convergent beam electron diffraction (CBED) pattern at each scan location; see the main page for further information. This technique captures a 2 dimensional reciprocal space image associated with each scan point as the beam rasters across a 2 dimensional region in real space, hence the name 4D STEM. Its development was enabled by better STEM detectors and improvements in computational power. The technique has applications in diffraction contrast imaging, phase orientation and identification, strain mapping, and atomic resolution imaging among others; it has become very popular and rapidly evolving from about 2020 onwards.

The name 4D STEM is common in literature, however it is known by other names: 4D STEM EELS, ND STEM (N- since the number of dimensions could be higher than 4), position resolved diffraction (PRD), spatial resolved diffractometry, momentum-resolved STEM, "nanobeam precision electron diffraction", scanning electron nano diffraction, nanobeam electron diffraction, or pixelated STEM. Most of these are the same, although there are instances such as momentum-resolved STEM where the emphasis can be very different.

Low-energy electron diffraction (LEED)
Low-energy electron diffraction (LEED) is a technique for the determination of the surface structure of single-crystalline materials by bombardment with a collimated beam of low-energy electrons (30–200 eV). In this case the Ewald sphere leads to approximately back-reflection, as illustrated in Figure 20, and diffracted electrons as spots on a fluorescent screen as shown in Figure 21; see the main page for more information and references. It has been used to solve a very large number of relatively simple surface structures of metals and semiconductors, plus cases with simple chemisorbants. For more complex cases transmission electron diffraction or surface x-ray diffraction have been used, often combined with scanning tunneling microscopy and density functional theory calculations.

LEED may be used in one of two ways:

 * 1) Qualitatively, where the diffraction pattern is recorded and analysis of the spot positions gives information on the symmetry of the surface structure. In the presence of an adsorbate the qualitative analysis may reveal information about the size and rotational alignment of the adsorbate unit cell with respect to the substrate unit cell.
 * 2) Quantitatively, where the intensities of diffracted beams are recorded as a function of incident electron beam energy to generate the so-called I–V curves. By comparison with theoretical curves, these may provide accurate information on atomic positions on the surface.

Reflection high-energy electron diffraction (RHEED)
Reflection high energy electron diffraction (RHEED), is a technique used to characterize the surface of crystalline materials by reflecting electrons off a surface. As illustrated for the Ewald sphere construction in Figure 22, it uses mainly the higher-order Laue zones which have a reflection component. An experimental diffraction pattern is shown in Figure 23 and shows both rings from the higher-order Laue zones and streaky spots. RHEED systems gather information only from the surface layers of the sample, which distinguishes RHEED from other materials characterization methods that also rely on diffraction of electrons. Transmission electron microscopy samples mainly the bulk of the sample, although in special cases it can provide surface information. Low-energy electron diffraction (LEED) is also surface sensitive, and achieves surface sensitivity through the use of low energy electrons. The main uses of RHEED to date have been during thin film growth, as the geometry is amenable to simultaneous collection of the diffraction data and deposition. It can, for instance, be used to monitor surface roughness during growth by looking at both the shapes of the streaks in the diffraction pattern as well as variations in the intensities.

Gas electron diffraction

Gas electron diffraction (GED) can be used to determine the geometry of molecules in gases. A gas carrying the molecules is exposed to the electron beam, which is diffracted by the molecules. Since the molecules are randomly oriented, the resulting diffraction pattern consists of broad concentric rings, see Figure 24. The diffraction intensity is a sum of several components such as background, atomic intensity or molecular intensity.

In GED the diffraction intensities at a particular diffraction angle $$\theta$$ is described via a scattering variable defined as $$ |s| = \frac{4\pi}{\lambda} \sin \left(\frac\theta 2\right).$$The total intensity is then given as a sum of partial contributions: $$ I_\text{tot}(s) = I_a(s) + I_m(s) + I_t(s) + I_b(s) ,$$where $$I_a(s)$$ results from scattering by individual atoms, $$I_m(s)$$ by pairs of atoms and $$I_t(s)$$ by atom triplets. Intensity $$I_b(s)$$ corresponds to the background which, unlike the previous contributions, must be determined experimentally. The intensity of atomic scattering $$I_a(s)$$ is defined as $$ I_a(s) = \frac{K^2}{R^2} I_0 \sum_{i=1}^N |f_i(s)|^2 ,$$where $$K = (8 \pi ^2 me^2)/h^2$$, $$R$$ is the distance between the scattering object detector, $$I_0$$ is the intensity of the primary electron beam and $$f_i(s)$$ is the scattering amplitude of the atom $$i$$ of the molecular structure in the experiment. $$I_a(s)$$ is the main contribution and easily obtained for known gas composition. Note that the vector $$s$$ used here is not the same as the excitation error used in other areas of diffraction, see earlier.

The most valuable information is carried by the intensity of molecular scattering $$I_a(s)$$, as it contains information about the distance between all pairs of atoms in the molecule. It is given by $$ I_m(s) = \frac{K^2}{R^2} I_0 \sum_{i=1}^N \sum_{\stackrel{j=1}{i\neq j}}^N \left| f_i(s) \right| \left| f_j(s)\right| \frac{\sin [s(r_{ij}-\kappa s^2)]}{sr_{ij}} e^{-(1/2 l_{ij} s^2)} \cos [\eta _i (s) - \eta _i (s)] ,$$where $$r_{ij}$$ is the distance between two atoms, $$l_{ij}$$ is the mean square amplitude of vibration between the two atoms, similar to a Debye–Waller factor, $$\kappa$$ is the anharmonicity constant and $$\eta$$ a phase factor which is important for atomic pairs with very different nuclear charges. The summation is performed over all atom pairs. Atomic triplet intensity $$I_t(s)$$ is negligible in most cases. If the molecular intensity is extracted from an experimental pattern by subtracting other contributions, it can be used to match and refine a structural model against the experimental data.

Similar methods of analysis have also been applied to analyze electron diffraction data from liquids.

In a scanning electron microscope

In a scanning electron microscope the region near the surface can be mapped using an electron beam that is scanned in a grid across the sample. A diffraction pattern can be recorded using electron backscatter diffraction (EBSD), as illustrated in Figure 25, captured with a camera inside the microscope. A depth from a few nanometers to a few microns, depending upon the electron energy used, is penetrated by the electrons, some of which are diffracted backwards and out of the sample. As result of combined inelastic and elastic scattering, typical features in an EBSD image are Kikuchi lines. Since the position of Kikuchi bands is highly sensitive to the crystal orientation, EBSD data can be used to determine the crystal orientation at particular locations of the sample. The data are processed by software yielding two-dimensional orientation maps. As the Kikuchi lines carry information about the interplanar angles and distances and, therefore, about the crystal structure, they can also be used for phase identification or strain analysis.

title: Electron diffraction


text:
N. Chandrababu Naidu

Nara Chandrababu Naidu (born 20 April 1950), commonly known as CBN, is an Indian politician who is currently serving as the 13th Chief Minister of Andhra Pradesh and currently holds the record of longest serving Chief Minister in the political history of telugu states. He is the national president of the Telugu Desam Party (TDP).

In 1978, he was elected to the Andhra Pradesh Legislative Assembly from the Indian National Congress party, and from 1980 to 1982, he served as a minister in the state cabinet. Afterwards, he switched party allegiance and joined TDP, which had been founded by his father-in-law N. T. Rama Rao. Naidu served as a TDP Member of the Legislative Assembly (MLA) from 1989 to 1995. In 1995, he became the Chief Minister of Andhra Pradesh.

During his two previous terms as Chief Minister, Naidu's public image was that of an economic reformer and proponent of information technology-based economic growth. His policies brought modernisation and investments particularly to Hyderabad, where he directed the founding of HITEC City. He also had a role in national politics, first as the convener of the United Front in 1996. He supported the Bharatiya Janata Party (BJP)-led National Democratic Alliance (NDA) after the 1999 Lok Sabha elections, in which TDP won 29 seats, enhancing Naidu's reputation as a nationally prominent politician. In 2014, Naidu returned as Chief Minister, winning in the now-residuary (due to bifurcation) Andhra Pradesh.

In the 2019 Andhra Pradesh Legislative Assembly election, Naidu's party faced an electoral setback, with TDP winning only 23 out of 175 seats. In September 2023, Naidu was arrested by the Crime Investigation Department (CID) police in Andhra Pradesh due to alleged involvement in the skills development case and was granted bail by Andhra Pradesh High Court in November 2023. In the 2024 Andhra Pradesh Legislative Assembly election, the TDP returned to power once again and Naidu became Chief Minister for the fourth time.

Early life and education
Naidu was born on 20 April 1950 in a Telugu agrarian family to Nara Kharjura Naidu and his wife Amanamma in Naravaripalle, Tirupati district, in present-day Andhra Pradesh. He has a younger brother Nara Ramamurthy Naidu and two younger sisters. Naidu has vitiligo, an autoimmune disease that causes white patches on the skin.

Since his village had no school, Naidu attended primary school in Seshapuram up to class five and the Chandragiri Government High School up to class 10. He completed his B.A. degree in 1972 from Sri Venkateswara Arts College, Tirupati. Later, he got his master's degree in economics from Sri Venkateswara University. In 1974, under the guidance of professor Dr. D. L. Narayana he started work on his Ph.D. on the topic of Economic ideas of Professor N. G. Ranga, but did not complete his Ph.D.

Indian National Congress
Naidu started his political activities as a student union leader in Sri Venkateswara University while pursuing his master's degree. In 1975, he joined Indian Youth Congress and became the president of its local chapter in Pulicherla. After the emergency was imposed on the country in 1975, he became a supporter of Sanjay Gandhi.

With the help of N. G. Ranga, Naidu secured a candidacy from the Congress party, under its 20% quota for the youth, and became a member of the Legislative Assembly (MLA) for the Chandragiri constituency in the 1978 assembly elections. He initially served as a director of Andhra Pradesh Small Scale Industries Development Corporation. Later, he was appointed as a minister in T. Anjaiah's government. Between 1980 and 1983, Naidu held various portfolios, including archives, cinematography, technical education, and minor irrigation in the state government. He became the youngest MLA at the age of 28 and a minister at the age of 30 in Andhra Pradesh at that time.

As the cinematography minister, Naidu came in contact with N. T. Rama Rao, a popular film star in Telugu cinema. In September 1981, he married Bhuvaneswari, Rao's second daughter.

Telugu Desam Party
In 1982, N. T. Rama Rao, also known as NTR, formed the Telugu Desam Party (TDP) and swept the Andhra Pradesh assembly polls held in 1983. Chandrababu Naidu, who was his son-in-law, remained in the Congress Party and even dared to contest against his father-in-law. Naidu, however, was defeated by a TDP candidate in the elections from Chandragiri assembly constituency. Soon after, he joined the Telugu Desam Party. Initially, Naidu involved himself in the party work, organising training camps and computerising membership records. He played an active role during the 1984 August crisis in the government triggered by Nadendla Bhaskara Rao's coup. NTR appointed Naidu as general secretary of the TDP in 1986.

Legislative career (1989–1995)
In the 1989 assembly election, Naidu contested from Kuppam constituency as a TDP candidate and won by 5,000 votes. INC, however, had regained power in the election, so Naidu had to sit in the opposition. Rama Rao appointed him as a coordinator of the TDP, in which capacity he handled the party's role of the main opposition in the assembly which won him wide appreciation from both the party and the public. His role during this phase, both inside the Legislative Assembly and outside, was a critical factor for the subsequent success of the party.

Naidu won the 1994 elections from Kuppam constituency. He became the Finance and Revenue Minister in N. T. Rama Rao's ministry.

First term as Chief Minister of Andhra Pradesh (1995–1999)
On 1 September 1995, Naidu, at the age of 45, was sworn in as the Chief Minister following a successful coup against the leadership of N.T. Rama Rao. The internal rebellion was triggered by the controversial role of Lakshmi Parvathi, NTR's second wife, in the party and the government. Naidu was able to secure the support of the majority of the legislators. Naidu however, already in the saddle, firmly entrenched himself as the leader of the TDP and as Chief Minister. Naidu has carried TDP as NTR legacy and helped it to survive.

Second term as Chief Minister of Andhra Pradesh (1999–2004)
In the 1999 state legislature elections, Chandrababu Naidu led his party to victory, securing 180 out of 294 seats in the state assembly. Additionally, the TDP won 29 out of 42 seats in the Parliament elections.The TDP's tally in the Lok Sabha made it not only the biggest of the BJP's allies, but also the fourth largest party in the Lok Sabha. These elections marked a critical juncture for Naidu, as they served as a significant test of his legitimacy both as the Chief Minister of the state and as the President of the TDP. Upon his return to power, the media hailed him as the first economic reformer to secure a strong electoral mandate.

Assassination attempt
On 1 October 2003, Naidu survived a land mine blast by the People's War Group (PWG) near Alipiri tollgate in Tirupati. The Chief Minister's convoy was attacked on his way to Tirumala to participate in the annual ritual of Brahmotsavam of Lord Venkateswara atop the seven hills. A total of 17 Claymore mines were planted, of which 9 exploded. Naidu was the first Chief Minister in the country to have been targeted by the ultra-left-wing Naxalites for assassination. Naidu's escape with minor injuries was considered miraculous given the severity of the blast. The PWG claimed it attacked him for being a "World Bank agent."

Role in National Politics
Chandrababu Naidu's involvement in national politics during this period (1996–2004) dominated by non-Congress coalition politics in Delhi is notable. In the aftermath of the 1996 parliamentary elections, he assumed the role of convenor for the United Front, a coalition comprising 13 political parties that secured power at the centre. The coalition government was headed by H.D. Deve Gowda and later I.K. Gujral between 1996 and 1998. The United Front had its headquarters at Andhra Pradesh Bhavan in New Delhi.

Subsequently, Chandrababu Naidu's significance in national affairs got amplified after the 1999 Lok Sabha elections.The TDP and the BJP, which had a pre-poll understanding in the state, together won 36 MPs out of 42. The BJP emerged as the largest single party in the Lok Sabha. The TDP extended the support of 29 of its MPs to the National Democratic Alliance (NDA) government headed by A.B.Vajpayee. TDP did not join the government, extending only 'issue-based support'. Naidu claimed that though Vajpayee had offered eight cabinet berths to his party, the TDP stayed away from the union cabinet and offered external support to the NDA government.

Leader of the Opposition (2004–2014)
Naidu, soon after the assassination attempt on him, dissolved the state assembly. Elections to the state were held along with the parliamentary polls in April 2004. The TDP government faced anti-incumbency fuelled by high power tariffs and the absence of support to the agricultural sector. Besides, the newly formed Congress(I)-TRS alliance posed a major challenge to the TDP popularity in Telangana. The Telugu Desam Party was defeated in both the state and Lok Sabha elections. The Congress Party won 185 seats while the TDP ended up with 47 seats in the assembly, the lowest in the party's electoral history. The TDP won only 5 seats out of 42 in Parliament. Naidu felt that the severe drought that gripped Andhra Pradesh the previous year as well as advancing the timing of the election were the major reasons for his 'shock' defeat.

In the 2009 assembly and parliamentary elections, Naidu faced another challenge as popular actor Chiranjeevi formed Praja Rajyam party and turned the election into a three-cornered contest. The TDP, which formed an alliance with TRS this time, once again lost to the incumbent Congress Party. The TDP secured 92 seats in the assembly, whereas the Congress got 156 seats, a thin majority in the assembly. Chiranjeevi's Praja Rajyam won in 18 seats. Naidu blamed Chiranjeevi's entry into the political arena for his party's debacle.

Chief Minister of Andhra Pradesh (2014–2019)
After the bifurcation, elections were held in 2014 in the newly formed states of Andhra Pradesh and Telangana. Naidu formed an alliance again with the BJP and Jana Sena Party and returned to power in the bifurcated, residual Andhra Pradesh state, winning 102 seats out of 175 seats. The TDP also won 16 Lok Sabha seats. Naidu took oath as the first Chief Minister of the residuary state of Andhra Pradesh at Mangalagiri on the grounds of Acharya Nagarjuna University near Guntur. His party joined the NDA government at the centre and held two portfolios in the union cabinet. Two cabinet berths in the state were allocated to the BJP.

The Chief Minister faced a host of challenges in the new state. The newly born state of Andhra Pradesh was left without a capital city and was deprived of a major economic hub. Naidu took up the construction of a new capital city, named Amaravati, on the southern side of river Krishna near Vijayawada. During Naidu's term, the state achieved top ranking in the World Bank's Ease of Business rankings in the country since 2015. The state attracted mega companies like Kia Motors, Isuzu Motors, Pepsi, Mondelez and Foxconn.

2015 cash-for-vote scam
Naidu's name figured in the cash-for-vote scandal which pertains to the alleged role of the TDP to buy votes in the 2015 Telangana Legislative Council elections. It started off when the TDP leaders of Telangana state were caught on video footage, aired in the media, allegedly offering bribes to a nominated MLA, Elvis Stephenson, for his vote in the 2015 Council elections. Telangana Anti-Corruption Bureau (ACB) claimed that it was in possession of a recorded telephonic conversation that purportedly took place between Elvis Stephenson and TDP president N Chandrababu Naidu, who was the then Andhra Pradesh Chief Minister. Both the TRS (now BRS) and YSR Congress Party demanded that Naidu should be named in the case. However, the ACB and later the Enforcement Directorate (ED), in their charge sheets, did not name Naidu as an accused in the case, as they did not find evidence to prove that the money was sent to Stevenson at the behest of Naidu.

Special status dispute and break with BJP
In March 2018, the TDP withdrew its two ministers from Prime Minister Narendra Modi's government over the issue of Andhra special category status (SCS). The SCS had been promised by the previous Congress government on the floor of the Parliament during the passage of the AP Reorganisation Bill. Subsequently, Naidu announced the TDP's departure from the National Democratic Alliance (NDA) due to the "injustice" inflicted upon Andhra Pradesh by the denial of SCS.

In 2016, Naidu had previously agreed to the announcement made by the then Union Finance Minister Arun Jaitley regarding a financial package for Andhra Pradesh instead of granting it special status. In this backdrop, the decision of the ruling TDP to withdraw from the NDA was perceived as a political response to the mounting criticism from the Opposition regarding the non-fulfilment of the special category status. Naidu further criticised the central government on the issue by staging a hunger strike, known as 'Dharma Porata Deeksha' (a day-long 'protest for justice'), in Delhi. This event marked a significant deterioration in the relationship between the TDP and the BJP.

Alliance with the Congress Party
In an unexpected turn of events, the TDP forged an alliance with the Congress Party for the 2018 Telangana assembly elections. The alliance, consisting of the Congress, the TDP, and the Communist Party of India (CPI), formed the "Maha Kootami" (grand alliance) with the primary objective of defeating the TRS (now BRS) in the elections. This marked the first time that the TDP, which had been founded on an anti-Congress platform in 1982, joined hands with the Congress party. During this period, Naidu was advocating for a non-BJP coalition comprising regional parties with the support of Congress to make a significant impact in the upcoming parliamentary elections. This experiment faced a failure in the Telangana elections with K.Chandrashekar Rao's TRS winning by a big margin. As a result, the TDP and the Congress subsequently parted ways for the 2019 Andhra Pradesh assembly elections. The alliance with the Congress and its aftermath left a bitter outcome for Naidu, leading to a considerable erosion of his credibility due to the perceived flip-flop in alliances.

2019 elections
In the 2019 assembly and parliamentary elections, the ruling TDP was decisively defeated by the YSR Congress Party led by Y. S. Jagan Mohan Reddy. The YSRCP achieved a landslide victory by securing 151 seats in the assembly out of 175, while the TDP could manage 23 seats. In the Lok Sabha, the TDP won three seats, while the YSRCP secured the remaining 22 seats.

Corruption allegations and arrest
On 9 September 2023, Naidu was arrested by the Andhra Pradesh Crime Investigation Department (AP-CID), accused of misappropriation of public funds amounting to 371 crore INR. He was listed as accused number 37 in the case. On 10 September 2023, he appeared at the ACB court and the court remanded him in custody for 14 days, for which he was moved to the Central Jail in Rajamahendravaram. After being in judicial custody for 52 days, he was released on bail on 31 October 2023.

Fourth term as chief minister (2024–present)
Pawan Kalyan in June 2022, hinted of an alliance between his Jana Sena Party (JSP) and the TDP for the elections in 2024. There was also speculation suggesting that Naidu was attempting to regain the confidence of the BJP.

Naidu was sworn in as the chief minister of Andhra Pradesh for a record fourth term, surpassing N. T. Rama Rao who had served as the chief minister of the state for three terms, on 12 June 2024 after the TDP in alliance with the BJP and the JSP won the 2024 state legislative assembly election in a landslide, garnering 164 out of 175 seats and defeating the YSR Congress Party led by Y. S. Jagan Mohan Reddy. Pawan Kalyan was sworn in as his deputy.

He has vowed to revive Amaravati as the sole capital of Andhra Pradesh and said that he will rebuild the capital as soon as possible. Mr. Naidu said he would seek the Central government’s cooperation to rebuild Amaravati and exuded confidence that the expected support would come. The Centre had provided capital gains exemption for all sales of land and released ₹1,500 crore of the approved ₹2,500 crore for Amaravati.

Business career
Heritage Foods Limited (HFL), a dairy enterprise, was incorporated by Naidu in 1992. The company went public in 1994. The annual turnover of Heritage Foods stood at INR 26,429 million in the financial year 2021–22. Currently, Nara Bhuvaneswari, Naidu's wife, holds the position of vice-chairperson & managing director, while Nara Brahmani, Naidu's daughter-in-law, serves as the executive director. Heritage has hundreds of outlets throughout Andhra Pradesh and Telangana and a significant presence across many states in the country. Heritage has also a renewable energy vertical which runs captive solar & wind power plants at 11 different locations. HFL comprises a solid portion of Naidu's current assets.

Global Forum for Sustainable Transformation
Chandrababu Naidu serves as the chairman and director of the Global Forum for Sustainable Transformation (GFST), an organisation he established in March 2020 in Hyderabad. It is positioned as a global not-for-profit and apolitical think tank, with the aim of promoting sustainability in economies and communities. In June 2023, GFST hosted a seminar on 'Deep Technologies' in Hyderabad. Among its projects is the development of Vision India@2047, aligning with India's 100th year of Independence. Naidu unveiled a vision document titled India@2047, authored by GFST, on 15 August 2023, in Visakhapatnam.

NTR Trust
The NTR Memorial Trust was founded in 1997 by Chandrababu Naidu as a non-profit organisation. The Trust is involved in a variety of activities including initiatives like providing free education, offering blood transfusion facilities, conducting health camps, and supporting empowerment and livelihood programs. The Trust manages a blood bank and Thalassemia center in Hyderabad, as well as blood banks in Visakhapatnam and Tirupati. Additionally, it operates schools in Hyderabad and Challapalli (Krishna district), along with NTR Junior & Degree College for Women in Hyderabad. The Trust's day-to-day operations are overseen by Naidu's wife, Nara Bhuvaneswari, who serves as the managing trustee.

Criticism
Naidu faced severe criticism from various quarters for his policies. Both the Congress and left parties vehemently opposed his privatisation initiatives, labelling him as a symbol of World Bank policies. The power sector reforms implemented by him encountered strong resistance throughout the state. Naidu attracted criticism for allegedly prioritising information technology over the agriculture sector, which was a vital source of livelihood for a significant portion of the state's workforce. While the corporate industry hailed him as the "CEO of Andhra Pradesh Inc.," a substantial portion of the state's population perceived him as "anti-poor", which reflected in the loss of the 2004 elections. Amaravati, the new capital city that he set out to build in his latest term, ran into rough weather over various controversies.

Public image
Chandrababu Naidu was one of the most recognised Chief Ministers in the country during his nine-and-a-half-year tenure from 1995 to 2004. He was a strong supporter of liberalisation policies at the state level. The western media hailed him as "one of the most promising local leaders not just in India but in the developing world." Andhra Pradesh was the first state in India to receive a direct World Bank loan for economic restructuring. Naidu was a regular participant at World Economic Forum meetings in Davos, Switzerland.

He is credited with commissioning HITEC City, and Genome Valley in 1998 by the erstwhile combined Government of Andhra Pradesh, adjoining Cyberabad to the west of Hyderabad, propelling the information technology industry and enhancing modern infrastructure in Hyderabad, including the Rajiv Gandhi International Airport and the Indian School of Business (ISB). Naidu's meetings with Bill Gates, the chairman of Microsoft, in New Delhi in 1997, followed by Gates' visit to Hyderabad in 2002, and the visit of US President Bill Clinton in 2000, played a significant role in enhancing his reputation.

During his third term between 2014 and 2019, Naidu took up the ambitious project of building a capital city Amaravati for the bifurcated state. Andhra Pradesh also became the number one state in Ease of Doing Business (EoDB) Rankings during this period.

Awards
Naidu has won a number of awards, including IT Indian of the Millennium from India Today, Business Person of the Year by The Economic Times, South Asian of the Year from Time Asia, Golden Peacock Award for leadership in Public Service & Economic Transformation, and membership in the World Economic Forum's Dream Cabinet. Naidu chaired the National IT Panel under the National Democratic Alliance (India) (NDA) government and was described as one of the "hidden seven" working wonders of the world by Profit (Oracle Corporation's monthly magazine). Naidu was offered an honorary professorship by US business school, the Kellogg School of Management in 2000. He was the Chairman of National Task Force on Micro-irrigation from Government of India, Ministry of Agriculture in 2003. He was the head of 13-member Committee of Chief Ministers to promote digital payment systems and financial inclusion in India which was constituted by federal government in 2016.
 * The then Governor of Illinois, Jim Edgar, created a Naidu day on 24 September 1998 in his honour.
 * Voted IT Indian of the Millennium in a poll by India Today and 20:20 Media.
 * He was named South Asian of the Year in 1999 by Time magazine, US
 * In 2001, he was described as one of the hidden "Seven working wonders around the world", by Profit, a monthly magazine published by Oracle Corporation, US.
 * Business Person of the Year by Economic Times.
 * Golden Peacock Award for Leadership in Public Service & Economic Transformation - 2017
 * Global Agriculture Policy Leadership Award by Indian Council of Food and Agriculture (ICFA).
 * The Pune-based organisation, Bharatiya Chatra Sansad, in partnership with MIT School of Governance, honoured him with Aadarsh Mukhyamantri Puraskar (Model CM Award) in its 6th annual session on 30 January 2016.
 * Transformative Chief Minister Award in May 2017 by US-India Business Council (USIBC) at West Coast Summit in the Silicon Valley.

In popular culture

 * Portrayed by Rana Daggubati in NTR:Kathanayakudu(2019) and its sequel NTR:Mahanayakudu(2020).
 * Portrayed by Sritej in the 2019 RGV's film Lakshmi's NTR.

Books

 * India's Glocal Leader, Tejaswini Pagadala
 * Manasulo Maata, Sevanthi Nenon, An Autobiography of Chandrababu Naidu
 * Nirantar Pragathi Ke Path Par Chandrababu Naidu (in Hindi, Telugu), Dr. Inagati Lavanya

Case studies

 * New Modern Economy Management in Andhra Pradesh: A Case Study of Sri Honorable Chief Minister N Chandra Babu Naidu by authors N. Sree Ramulu and Morusu Siva Sankar

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: N. Chandrababu Naidu


text:
Vitellaria

Vitellaria paradoxa (formerly Butyrospermum parkii), commonly known as shea tree, shi tree, or vitellaria, is a tree of the family Sapotaceae. It is the only species in the genus Vitellaria, and is indigenous to Africa.

The shea fruit consists of a thin, tart, nutritious pulp that surrounds a relatively large, oil-rich seed from which shea butter is extracted. It is a deciduous tree usually 7 – tall, but has reached 25 m and a trunk diameter of 2 m.

The shea tree is a traditional African food plant. It has been claimed to have potential to improve nutrition, boost food supply in the "annual hungry season", foster rural development, and support sustainable land care.

Description
The tree starts bearing its first fruit when it is 10 to 15 years old; full production is attained when the tree is about 20 to 30 years old. It then produces nuts for up to 200 years.

The fruits resemble large plums 4 to 8 centimetres long weighing between 10 and 57 grams each. These fruits take 4 to 6 months to ripen; the average yield is 15 to 20 kg of fresh fruit per tree, with optimum yields up to 45 kg. Each kilogram of fruit gives approximately 400 g of dry seeds. The fruit is edible.

Nomenclature and taxonomy
Vitellaria is a monotypic genus, i.e., it comprises only one species. The species has variously been known botanically as Vitellaria paradoxa, Butyrospermum parkii, and Butyrospermum paradoxum. Many botanical works from the late 19th and much of the 20th centuries used the name Butyrospermum parkii, which is still commonly found in the cosmetics trade. However, Vitellaria paradoxa is the oldest name (published in 1807) and has been generally used in recent decades, as necessitated by the rules of botanical nomenclature; efforts in 1962 to make Butyrospermum the official scientific name for the genus (i.e., to "conserve" the name) were unsuccessful.

The species comprises two subspecies:

Vitellaria paradoxa subsp. paradoxa  (roughly from the Nigeria-Cameroon border westward).

Vitellaria paradoxa subsp. nilotica (Kotschy) A.N. Henry & Chithra & N.C. Nair (roughly from the Nigeria-Cameroon border eastward).

Distribution and habitat

The shea tree grows naturally in the wild in the dry savannah belt of West and South from Senegal in the west to Sudan and South Sudan in the east, and onto the foothills of the Ethiopian highlands. It occurs in 19 countries across the African continent, namely Benin, Burkina Faso, Cameroon, Central African Republic, Chad, Ethiopia, Ghana, Guinea Bissau, Ivory Coast, Mali, Niger, Nigeria, Senegal, Sierra Leone, South Sudan, Sudan, Togo, Uganda, Democratic Republic of the Congo, and Guinea. The habitat area extends over more than 5000 km.

A testa found at the site of the medieval village of Saouga is evidence of shea butter production by the 14th century.

Uses
Shea butter has many uses and may or may not be refined. In the West it is most commonly used as an emollient in cosmetics and is less commonly used in food. Throughout Africa it is used extensively for food, is a major source of dietary fat, and for medicinal purposes. In Ghana and Nigeria, shea butter is a major ingredient for making the African black soap.

The edible protein-rich caterpillars of the moth Cirina butyrospermi which feed solely on its leaves are widely collected and eaten raw, dried or fried.

Composition of shea butter
Shea butter extract is a complex fat that in addition to many nonsaponifiable components (substances that cannot be fully converted into soap by treatment with alkali) contains the following fatty acids: oleic acid (40–60%), stearic acid (20–50%), linoleic acid (3–11%), palmitic acid (2–9%), linolenic acid (<1%) and arachidic acid (<1%). It also contains the vitamins A, E and F.

Etymology
The common name is shíyiri (in N'Ko: ߛ߭ߌ߭ߦߌߙߌ) or shísu (ߛ߭ߌ߭ߛߎ, lit. "shea tree") in the Bambara language of Mali. This is the origin of the English word, whose primary pronunciation is (rhyming with "tea"), although the pronunciation  (rhyming with "day") is common and is listed second in major dictionaries. The tree is called ghariti in the Wolof language of Senegal, which is the origin of the French name of the tree and the butter, karité.

In Hausa language the tree is called Kaɗe or Kaɗanya. Indeed, the shea tree is so indispensable in Mole-Dagbang culinary and ethno-botanical practices that the Northern Ghanaian city of Tamale etymologically derives its name from the more traditional Dagomba name 'Tama-yile' (meaning 'Home of Shea nuts').

The tree was formerly classified in the genus Butyrospermum, meaning "butter seed". The species name parkii honors Scottish explorer Mungo Park, who learned of the tree while exploring Senegal. Park's Scottish origin is reflected in the English word shea, with a final -ea.

title: Vitellaria


text:
Heartbreakers (2001 film)

Heartbreakers is a 2001 American romantic crime comedy film directed by David Mirkin and written by Robert Dunn, Paul Guay, and Stephen Mazur. The film stars Sigourney Weaver, Jennifer Love Hewitt, Ray Liotta, Jason Lee, and Gene Hackman. It marks the last onscreen film appearance of Anne Bancroft before her death in June 2005.

Heartbreakers received mixed reviews from critics, and grossed over $57 million. Weaver was nominated for a Satellite Award for her performance in the film.

Plot
Max and Page Conners are a mother-daughter con artist team. When the film opens, the Conners are finishing a con on Dean Cumanno, an auto-body shop owner and small-time crook. The con, which the Conners have played many times before on other men, involves Max marrying Dean, passing out on their wedding night to avoid consummating the marriage, and then Page (posing as Dean's secretary) luring Dean into a compromising position to justify Max's immediate divorce and hefty settlement. The con is a success.

Page declares that she wants to go solo. Max initially relents, but when they go to the bank to split their earnings, they're confronted by an IRS agent who declares that they owe the government a considerable sum on top of the rest of their savings, which have already been seized. Page reluctantly agrees to work one last con with Max in Palm Beach, to get enough money to pay off the IRS and set Page up to work on her own. For their target, they choose widower William B. Tensy, a tobacco tycoon who is addicted to his own product.

While working the main con with Tensy, Page attempts a side con without her mother's knowledge. Page targets beachfront bartender Jack, who is worth $3 million; she tells him that her name is Jane, but develops genuine feelings for him. Max learns of the side con and tells Page to break the relationship off, which Page does reluctantly.

Tensy proposes to Max ahead of schedule, but before they can get married, he accidentally chokes and dies while trying to initiate sex with Max. While Max and Page are deciding what to do with the body, Dean arrives, having tracked Max down to apologize and propose to her again. Dean figures out that Max and Page conned him, and threatens to call the authorities. Max offers to return Dean's divorce settlement money if he'll help them make Tensy's death look like an accident. Max tells Page that their money wasn't really taken by the IRS; the agent was Max's mentor, Barbara, who agreed to help prevent Page from leaving. However, when Max, Page and Dean go to the bank, the money really was gone, having been liquidated in an act of betrayal by Barbara.

In order to help Max, Page returns to Jack and accepts his proposal, planning to work it as a regular con. Page insists that Jack will not cheat on her, but is heartbroken when, on their wedding night, she breaks into her mother's room and finds him in a compromising position with Max. After the divorce settlement is paid, Dean confronts Max about the ethics of their con, pointing out that even a "goody-goody" like Jack is only human. Max reveals that Jack actually turned her down and that she had to drug him, but she defends her actions by saying that Jack would hurt Page eventually. Dean counters that Max has no right to keep Page from the man she loves because of what "might" happen.

Chastened, Max tells Page the truth, admitting that her efforts to protect her daughter have only hurt her in other ways. Page returns to Jack and both reconcile, giving him back the bar he'd had to sell to pay the settlement, and tells him her real name. Max and Dean also get together, Dean having admitted that he still loves Max despite what she put him through. The final shot of the film is of Dean — using the name 'Stanley' — romancing Barbara, with Max watching them via binoculars, implying that Max and Dean are now working together to get Max's money back from Barbara.

Cast

 * Sigourney Weaver as Max Conners / Angela Nardino / Ulga Yevanova, a con artist and Page's mother.
 * Jennifer Love Hewitt as Page Conners / Jane Helstorm / Wendy, Max's daughter, also a con artist.
 * Ray Liotta as Dean Cumanno / Vinny Staggliano / Stanley. Max's love interest.
 * Jason Lee as Jack Withrowe, Page's love interest.
 * Anne Bancroft as Gloria Vogal / Barbara, Max's longtime friend and mentor in the con game.
 * Jeffrey Jones as Mr. Appel, a hotel manager in Palm Beach.
 * Gene Hackman as William B. Tensy
 * Nora Dunn as Miss Madress, Tensy's housekeeper.
 * Julio Oscar Mechoso as Leo, Dean's friend and a security guard.
 * Ricky Jay as Dawson's Auctioneer
 * Sarah Silverman as Linda, Jack's friend and a waitress.
 * Zach Galifianakis as Bill, Jack's friend and a fry cook.
 * Michael Hitchcock as Dr. Arnold Davis
 * Carrie Fisher as Ms. Surpin, Max's divorce attorney.
 * Elya Baskin as Vladimir, Kremlin Waiter
 * Kevin Nealon as Man at the bar
 * David Mirkin as Jack's Lawyer
 * Patricia Belcher as hotel housekeeping maid

Production
The film was set in Palm Beach, Florida. Filming started in and around Los Angeles in late April 2000. By June 2000, filming moved to South Florida for sequences shot in Palm Beach, Miami and Florida Keys. Locations included The Breakers, The Glades, and Worth Avenue. According to the DVD commentary by director David Mirkin, only a few external shots were actually shot in Palm Beach, with the rest utilizing Los Angeles area locations as stand-ins. The film contains several references to The Beatles, including Sigourney Weaver singing a Russian folk version of "Back in the U.S.S.R." and the use of John Lennon's "Oh My Love" in several key scenes.

Music
John Debney composed the score, while Danny Elfman composed the Heartbreakers theme.

Release
The film opened at #1 in the U.S. box-office, earning $12.3 million on its opening weekend. It went on to gross a total of $57,756,408 worldwide.

Reception
Heartbreakers received mixed reviews from critics upon release. Roger Ebert gave the film three stars out of four and said that, "it does what a comedy must: It makes us laugh." A.O. Scott of the New York Times gave a glowing review of the film, stating that: "At a time when most comedies go for your wallet with a kick in the groin and a blackjack to the back of the head, this one, though it has some blunt instruments in its bag of tricks, has the class and professionalism to perpetrate an honest and sophisticated con."

On Rotten Tomatoes, 54% of 123 critic reviews are positive. The "critics consensus" on the website states, "Though the actors pour a lot of energy into their roles, Heartbreakers is too drawn out, and the romantic subplot doesn't blend well. Also, the con women aren't particularly sympathetic." On Metacritic, the film has a score of 47 out of 100, based on reviews from 32 critics, indicating "mixed or average reviews". Audiences surveyed by CinemaScore gave the film a grade of B− on scale of A to F.

Accolades
In 2002, Weaver received a nomination for a Satellite Award for Best Actress – Musical or Comedy. Hewitt was nominated in the Choice Movie: Actress category of the 2001 Teen Choice Awards.

Home media
The film was released on VHS and DVD on October 2, 2001. The film was released on Blu-ray on November 24, 2015.

title: Heartbreakers (2001 film)


text:
Talk:GSM localization

How does it work?
Somebody needs to explain how these methods work. AxelBoldt 11:33 26 Jul 2003 (UTC)

 * Also what, if any, systems are used on what networks in what countries. --jmb 00:36, 4 September 2007 (UTC)

updated article; request for merger
I have updated the article with the necessary details. However, reading the other one on mobile position, the two articles are basically related. I have requested for a merger. Koxinga CDF 03:12, 30 September 2007 (UTC)

 * You should merge it with Cell phone tracking as well. Slacker99 (talk) 07:48, 11 December 2007 (UTC)

 * I agree. All three articles should be merged. --Gronky (talk) 08:44, 18 February 2008 (UTC)

 * Go for it. --Matt Lewis (talk) 12:40, 29 May 2008 (UTC)

Advertising in External links
I've removed a lot of what I consider adverts from the External links. I've left one or two I'm not sure about. Perhaps we could be harder here? External links are rarely needed and easily exploited - any ambiguity and the link should go really. Can someone look through it again?--Matt Lewis (talk) 12:12, 29 May 2008 (UTC)

title: Talk:GSM localization


text:
The Tuxedo

The Tuxedo is a 2002 American science fiction action comedy film directed by Kevin Donovan and starring Jackie Chan and Jennifer Love Hewitt. It is a spy parody that involves a special tuxedo that grants its wearer special abilities. It also involves a corporate terrorist, threatening to poison the United States' fresh water supply with bacteria that spills electrolytes into the blood and totally dehydrates the host.

The film received negative reviews from critics upon release and earned a total worldwide box office gross of $104.4 million.

Plot
James "Jimmy" Tong is a taxi driver notorious for his speed and ability to get his customers anywhere in the least amount of time, with no accidents whatsoever. His reputation lands him a job as the personal chauffeur of the mysterious but wealthy Clark Devlin. Jimmy does not really know what his new boss' job is, but Devlin's friendly nature, imperturbable demeanor, and willingness to offer Jimmy advice wins Jimmy over and the two become friends. What Jimmy does not realize is that Devlin is a secret spy and undercover government agent, for an agency called the CSA. When an attempt to kill Devlin with a car bombing sends him into a coma, Jimmy ends up with Devlin's recent case notes and a special watch that controls Devlin's rather unusual tuxedo.

The tuxedo is a gadget capable of granting its wearer special abilities (including martial arts, speed, the ability to dance, sing, cling to walls, and various acrobatics) which Jimmy must use to stop the criminal organization responsible for Devlin's attempted murder. The group is a terrorist organization disguised as a corporation named Banning Corporation and is headed by the notorious and ruthless Dietrich Banning. Its goal is to take over the global drinking water supply, starting with the poisoning of major US reservoirs by means of genetically modified water strider insects. These water striders have bacteria that can spread from person to person, causing severe dehydration. By pure chance, Jimmy is joined by a genius scientist with aspirations of field work, Delilah "Del" Blaine. Blaine is completely new to field work and is delighted to be on assignment with Devlin, only to be very confused by Jimmy as he impersonates Devlin, relying on the tuxedo's special abilities to compensate for his lack of skill and training.

At first, Blaine thinks Jimmy is weird and annoying, and then a fraud when Jimmy's impersonation is finally exposed. She confiscates his borrowed tuxedo and attempts to stop the evil Dietrich Banning on her own by feigning a desire to become a turncoat for Banning Corporation. Meanwhile, Jimmy is ready to give up and go back to his life as a taxi driver, but while packing his belongings he discovers that Devlin had ordered a second suit for Jimmy himself, believing that Jimmy could also be a great agent. Using his new suit, Jimmy defeats the villain, Banning, by putting a cigarette in Blaine's mouth. Banning's tuxedo automatically forces him to pull out a lighter and light her cigarette. While Blaine is (comically) puffing on the lit cigarette, Jimmy begins to punch Banning. During the fight, Jimmy throws a glass containing the queen of the water striders into Banning's mouth. He is then infected with bacteria from the water strider. The other remaining water striders attack Banning and he then dies instantaneously from terminal dehydration.

As compensation for his role in bringing down Banning, the organization uses its resources to orchestrate an operation so that Jimmy can finally meet his dream girl. However, confused by Blaine's and the now-recovered Devlin's conflicting instructions on how to act Jimmy succeeds only in alarming the girl into threatening to mace him, resulting in the operation being aborted. Counseling Jimmy afterwards, Blaine admits feeling sad that no one had ever tried to do for her what Jimmy had just done, and Jimmy tells Blaine that she has to change her shrewish personality and be more accommodating if she ever wants to have a boyfriend. Feeling a tentative attraction for each other, they walk away to buy coffee together.

Cast

 * Jackie Chan as Jimmy Tong / Clark Devlin
 * Jennifer Love Hewitt as CSA Agent Delilah "Del" Blaine
 * Jason Isaacs as CSA Agent Clark Devlin / Brad Dillford (Inspired by Ian Fleming's James Bond)
 * Debi Mazar as CSA Agent Steena
 * Ritchie Coster as Dietrich Banning
 * Peter Stormare as Dr. Simms
 * Mia Cottet as Cheryl
 * Romany Malco as Mitch
 * Daniel Kash as Rogers
 * Jody Racicot as Kells
 * Boyd Banks as Vic
 * Bob Balaban as CSA Director Winton Chalmers (uncredited)
 * Christian Potenza as CSA Agent Joel
 * Scott Wickware as CSA Agent Wallace
 * Karen Glave as CSA Agent Randa
 * Scott Yaphe as CSA Agent Gabe
 * Jordan Madley as Holly
 * James Brown as himself
 * Colin Mochrie as Gallery Owner
 * Noah Danby as Bike Messenger
 * Kim Roberts as ER Nurse

Production
Jackie Chan was unsure about the project adding special effects together with stunts, but was interested to work with DreamWorks for the chance to meet Steven Spielberg. Chan found the American approach to stunts and safety restrictive and wanted to repeat a jump but was not allowed. "American films are different -- it drives me crazy," said Chan. On her first day of stunts, Jennifer Love Hewitt suffered a broken finger after being struck by one of the stunt men.

Principal photography began in September 2001 and ended in January 2002. During filming in Toronto, Chan and Love Hewitt appeared on an on-set webcam and interacted with fans.

Chan worked on The Tuxedo in between shooting The Medallion, which started before, and completed shooting later.

Soundtrack
After an initial score by Christophe Beck, John Debney was brought in to rescore the film (incorporating Beck's thematic material). Both composers ultimately had cues included in the final version.

Varèse Sarabande released a soundtrack album on October 1, 2002, including different cues written by the composers for the same scenes. Cues by Debney are in italics, cues by Beck in bold.

 * 1) Jimmy's Tux (2:50)
 * 2) Skateboard Chase (2:00)
 * 3) Mad Bike Messenger (1:04)
 * 4) Jimmy's Dream (:48)
 * 5) Main Title - "The Tuxedo" (3:01)
 * 6) First Mission (2:54)
 * 7) Swallow The Queen (2:25)
 * 8) Demolition (1:20)
 * 9) Putting on Tux (1:59)
 * 10) Demolition Program (1:02)
 * 11) Rope Fight (2:58)
 * 12) Rope Fight (2:14)
 * 13) Superhuman (1:39)
 * 14) Walter Strider (1:21)
 * 15) High Noon (:49)
 * 16) Banning Opens The Pods (2:29)
 * 17) Banning Swallows Queen (:49)
 * 18) Jimmy Saves Blaine (1:50)
 * 19) Get Up (I Feel Like Being a Sex Machine) - James Brown (3:19)

Box office
On a reported budget of $60 million, the film grossed $50.5 million in the United States. In its opening weekend, the film grossed $15 million from 3,022 theaters, ranking in second place behind Sweet Home Alabama. The film's total worldwide gross is $104.4 million.

Critical response
On Rotten Tomatoes, the film has an approval rating of 21% based on 140 reviews and an average rating of 4.33/10. The site's critical consensus reads, "Chan is as charming as ever, but his talents are squandered by special effects and bad writing." On Metacritic, the film has a score of 30 out of 100 based on 27 critics, indicating "generally unfavorable reviews". Audiences polled by CinemaScore gave the film an average grade of "B" on an A+ to F scale.

Roger Ebert of the Chicago Sun-Times commented that "The movie is silly beyond comprehension, and even if it weren't silly, it would still be beyond comprehension" but does comment that the film has its good moments. He gave the film one and a half stars out of four. Robert Koehler of Variety magazine says that the film's central problem is the mix of Chan's actual stunts and effects, which plays against Chan's whole career and hard-core commitment to doing all of his own body-defying stunts. He notes that Hewitt "has displayed a Chan-like sweetness herself in past roles" and is disappointed that her character is "a haggling, high-strung shrew who’s instantly repellent" rather than an amusing sidekick as Chan has had in other Hollywood films. Koehler also criticizes the "pallid direction", and "virtually incomprehensible plot line". American film critic Wheeler Winston Dixon described the trademark action comedy as having an "unlikely pairing" of Jennifer Love Hewitt with Chan, and noted that Chan's doing his own stunts, even in his middle age, added a "welcome touch of verisimilitude to the endless succession of doubles who normally populate such films."

Novelization
A novelization of the film was released by publisher Price Stern Sloan adapted by Ellen Weiss.

title: The Tuxedo