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For a galvanic cell, subtract the standard anode reduction potential from the standard cathode reduction potential:A reduction potential is not multiplied by the number of transferred electrons.

Iron is the negative anode and tin is the positive cathode of this spontaneous galvanic cell. electrons travel through the external circuit from iron to tin. An intact tin coating protects iron mainly by physically excluding the corrosive medium. If a defect exposes iron while the metals remain electrically connected, tin is not a sacrificial coating: the exposed iron can become the anodic corrosion site. A small exposed iron area coupled to a large cathodic tin area can be especially damaging; this distinction follows from the electrode-potential order rather than the appearance of the coating.

In a galvanic cell, a spontaneous oxidation-reduction reaction supplies electrical work: ${\Delta }_{r}G<0$ for discharge, the anode is negative, and the cathode positive. A discharging electric battery and a hydrogen–oxygen fuel cell are two practical examples. The first stores its reactants internally; the second is supplied continuously with fuel and oxidant.

An electrolytic cell consumes externally supplied electrical work to drive electrode reactions or material transfer under an applied potential. Its anode is positive and cathode negative. water electrolysis for hydrogen production and metal electroplating are two practical examples. oxidation always occurs at the anode and reduction at the cathode in both cell types; the electrode signs change. The electrolyte conducts ions, while electrons flow through the external circuit. A rechargeable battery can operate in either regime depending on whether it is discharging or being charged.

This is a conventional transmitted-beam bright-field transmission electron microscopy image containing high-resolution electron phase contrast and visible lattice fringes, rather than an element-specific chemical map. Relative to the scale bar, the smaller particle has an outer projected diameter of roughly $40\mathrm{nm}$. It is approximately rounded and contains a denser outer rim with several lighter internal regions separated by material. A porous or internally hollow particle is a plausible morphological interpretation; the image is not a simple featureless solid sphere.

Greater projected thickness generally removes more intensity from the transmitted beam, producing darker mass–thickness contrast. Different crystallite orientations also scatter intensity differently and give diffraction contrast. Local lattice fringes reveal crystalline material and changes of fringe orientation indicate more than one coherent domain. Bright/dark edge fringes also contain defocus-dependent Fresnel contrast; their width is not a direct shell-thickness measurement. Neither an exact alumina polymorph nor three-dimensional closed porosity can be uniquely established from this projection alone. Use calibrated fringe spacings and electron diffraction for phase identification, tilt-series imaging for void geometry, and a through-focus or dose series to test contrast artefacts.

From the illuminated side downward, the p-type gallium arsenide cap provides a low-resistance route to the front metal contact. It should remain beneath the contact grid but be removed from the optical aperture to reduce parasitic absorption. The wider-band gap p-type aluminium gallium arsenide window transmits much of the useful light and reduces front-surface recombination of carriers in the adjacent absorber. The optical-window and reduced-recombination rationale has a primary experimental basis in early heteroface devices.^[ref]

The p-type gallium arsenide emitter and n-type gallium arsenide base form the p-n junction. Absorbed photons generate electrons and electron holes; diffusion and the junction's electric field direct them toward the appropriate contacts. The n-type aluminium gallium arsenide back-surface-field layer provides a barrier to minority holes moving toward the substrate and reduces rear recombination. The n-type gallium arsenide substrate supports the epitaxial layers and conducts majority carriers to the rear contact.

The front metal must collect current with limited shading and the back metal provides the return contact. Interpreting the patterned hatched region as the optical antireflection coating, it reduces reflected light over the exposed window. Carrier selectivity, low recombination, low series resistance and low shading must work together; the equilibrium junction field alone is not a source of electrical energy.

The emission energies are approximatelyDraw the Al-rich interface as a wider-gap barrier between these two emitting regions: a raised conduction-band edge impedes electron transfer, and a lowered valence-band edge impedes hole transfer. The following is a consistent straddling-barrier schematic, with the shell having the smaller optical gap.

The two emission wavelengths determine optical transition energies, not unique conduction- and valence-band offsets. Exciton binding, confinement and strain can shift emission relative to the bulk band gap. The stated barrier supports inhibited charge exchange; its separate electron and hole barrier heights need additional band-alignment data.

A larger-gap AlGaAs barrier has a higher conduction-band edge than GaAs. Donors in AlGaAs supply electrons that transfer into lower-energy GaAs states, leaving a positively charged donor region. The resulting electrostatic field bends the GaAs conduction band into a triangular interface well. Motion normal to the interface is quantized, while motion parallel to it remains approximately free, producing a two-dimensional electron gas.

The confined envelope peaks just inside GaAs and decays into the AlGaAs barrier; a triangular-well treatment gives an Airy-function-like envelope with boundary matching. An undoped spacer separates the electrons from the donors, strongly reducing ionized-impurity scattering compared with uniformly doped 3D material and enabling high mobility. Band offsets, donor supply, interface roughness and electrostatics jointly determine whether a single occupied subband is obtained.

n-type doping adds donor impurities with weakly bound electrons near the conduction-band edge; ionization supplies conduction electrons and leaves positive donor ions. p-type doping introduces acceptors near the valence-band edge, producing holes and negatively charged ionized acceptors. Silicon and germanium commonly use group-V donors and group-III acceptors; dopant behaviour in a compound semiconductor depends on its lattice site.

Doping sets carrier concentration, Fermi level and resistivity. Spatially patterned donor and acceptor regions form p-n junctions, transistor source/drain regions and electrical contacts; remote doping can supply carriers to a cleaner conducting layer. Compensation and incomplete ionization mean carrier density need not equal the total impurity concentration.

For longitudinal motion in transverse subband $i$,For a completely free particle take $E_i=0$ and use the full wave vector. In a semiconductor the parabolic-band mass is the appropriate effective mass rather than necessarily the bare electron mass.

Use the one-way density per unit length $g_{+}/L=2/(h|v|)$. The electron-flux magnitude in an interval is charge times velocity times line density:If $g$ is instead defined for a finite length $L$, the traversal frequency is $|v|/L$; the same cancellation follows. The printed $I=Nev$ therefore requires $N$ to be a line density, not an unscaled total particle number.

Subtract the opposite reservoir's incoming flux. With the stated electron electrochemical potentials, conventional positive current is opposite to electron-number flux, soAt low temperature and small bias, each fully transmitted occupied spin-degenerate subband contributes $2e^2/h$. Hence $\boxed{G=N_{b}2e^2/h}$. More generally, the Landauer formula weights each mode by its transmission probability; imperfect transmission removes exact integer plateaux.

The resolved graphitic fringes indicate high-resolution phase contrast in a multi-walled carbon nanotube. Interference of transmitted and diffracted electron waves produces lattice fringes; their darkness is controlled by defocus, thickness and the contrast transfer function, so a dark fringe is not an unqualified map of individual carbon atoms. The weakly scattering central channel is lighter than the multilayer walls. Curved, roughly parallel fringes at its sides identify concentric graphitic shells; the dense fringes at the lower edge arise from overlapping graphitic material or another tube, not necessarily the wall count of the central tube.

Using the printed $5\mathrm{nm}$ scale bar, the central tube has an outer diameter of roughly $9$–$10\mathrm{nm}$ and an inner channel of roughly $6$–$7\mathrm{nm}$, depending on the cross-section selected away from the overlap. Several wall fringes are resolved on each side, with separations of order $0.34\mathrm{nm}$, consistent with graphitic interlayer spacing. These are approximate image measurements, not a determination of chirality, chemical purity or an exact shell count. The image alone cannot establish those quantities.

For bright-field transmission electron microscopy, place the objective aperture in the back focal plane around the transmitted beam, excluding most diffracted beams. Adjust the intermediate lens to image the objective's real-space image plane; projector lenses enlarge that image onto the screen or camera. Regions removing electrons from the admitted beam tend to be darker, although phase contrast can also contribute.

For selected-area electron diffraction, put the selected-area aperture in the objective image plane to choose a specimen region. Remove or open the objective aperture and change the intermediate-lens excitation to image the objective's back focal plane onto the camera. The projector then magnifies the diffraction pattern, rather than the specimen image. Thus the two apertures act in different conjugate planes.

Projection lithography images a mask through reduction optics; its resolution scales approximately as $k_1\lambda /\mathrm{NA}$. It offers parallel exposure, high throughput and accurate repeat patterning, but small features demand short wavelengths, large numerical aperture, costly optics and high-quality masks, with a shrinking depth of focus.

Electron beam lithography directly writes a programmable pattern using a focused electron beam. Its much shorter wavelength and small probe permit nanometre-scale features without an optical mask, making it attractive for research prototypes, low-volume devices and mask fabrication. Its limitations are serial writing time, charging of insulating substrates, beam drift, field stitching and forward/backscattering proximity effects in electron-beam lithography. Electron wavelength alone does not set the resist resolution. E-beam is often preferable for a few very small custom structures; projection remains preferable for high-volume repeated manufacture.

The discharge reaction is $2\mathrm{Li}+{\mathrm{I}}_2\to 2\mathrm{LiI}$. It transfers two electrons and has $\Delta G^{\circ }=-539.4\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ per reaction as written. The reversible open-circuit voltage isThe supplied free energy is already at approximately the requested temperature, so an additional temperature factor is unnecessary. Actual activities or discharge polarization could alter the terminal voltage.

An alkaline zinc-air battery combines a porous Zn negative electrode, aqueous KOH, an ion-permeable separator and a gas-diffusion positive electrode. At discharge, oxygen is reduced at the air electrode:Zinc oxidation can be written $\mathrm{Zn}+4{\mathrm{OH}}^{-}\to {\mathrm{Zn}(\mathrm{OH})}_4^{2-}+2e^{-}$, followed by ZnO precipitation and hydroxide regeneration. The net reaction is $2\mathrm{Zn}+{\mathrm{O}}_2\to 2\mathrm{ZnO}$.

High energy requires high accessible Zn loading and low inactive mass; high power requires short ion paths, good electronic conduction and a large catalytically active gas/electrolyte/electron interface. A porous hydrophobic gas-diffusion layer admits oxygen while controlling electrolyte flooding and drying. Zn morphology and electrolyte composition must avoid premature passivation, excessive corrosion and hydrogen evolution; atmospheric CO2 can carbonate the alkaline electrolyte. A very high loading can impair transport, so energy and power must be optimized together.

Electrical recharge is possible, but is not guaranteed by a primary Zn-air design. It requires reversible Zn deposition with controlled morphology and an oxygen electrode that can evolve oxygen efficiently without rapid catalyst or support corrosion. Dendrites, shape change, ZnO redistribution, gas evolution and large oxygen-reaction overpotentials limit cycling. Bifunctional oxygen catalysts, or separate oxygen-reduction and oxygen-evolution electrodes, help. Mechanical replacement of spent Zn is a different form of refuelling.^[ref]

Two electrons are transferred per formula unit of Li2O2. Its theoretical specific capacity isAt $3\mathrm{V}$, the corresponding theoretical specific energy is $3q=3.50\mathrm{Wh}{\mathrm{g}}^{-1}$, or $3500\mathrm{Wh}\mathrm{k}{\mathrm{g}}^{-1}$. The mass basis is Li2O2, equivalently the combined stoichiometric masses of consumed Li and O2; a value normalized to Li metal alone would be different.

A real lithium-air battery also includes electrolyte, porous positive-electrode support, separator, current collectors, excess reactants, packaging and possibly oxygen treatment. Insulating Li2O2 can block pores and electron transport, limiting utilization; polarization, electrolyte decomposition, moisture/CO2 contamination and parasitic reactions lower useful voltage and reversible capacity. A lithium-ion battery instead shuttles Li ions between pre-existing host electrodes, generally in a closed cell without consuming atmospheric oxygen; the oxygen/peroxide reaction and its mass/transport requirements make the Li-air mechanism distinct.

Use a lithium-metal negative electrode and a carbon-monofluoride composite positive electrode, separated by a porous, electrically insulating battery separator wetted by a lithium-salt electrolyte in a suitable nonaqueous solvent. Conducting carbon and a binder provide electronic contact through the fluorinated-carbon electrode to its electric current collector; the lithium electrode has its own electric current collector. A sealed stacked or wound assembly supplies useful area and contains the electrolyte.

During discharge lithium is the anode and the carbon-monofluoride composite is the cathode. lithium ions move through the electrolyte while electrons flow through the external load. The battery separator prevents electronic shorting while permitting ionic transport. An aqueous electrolyte is unsuitable because metallic lithium reacts with water. The requested very long operating time requires enough active material and low self-discharge, not merely a high nominal voltage.

For the specified $x=1$, the discharge half-reactions and their sum areEach mole of CF formula units consumes one mole of lithium and transfers one mole of electrons. For general $x$, the corresponding formula-unit reaction would be ${\mathrm{CF}}_x+x\mathrm{Li}⟶\mathrm{C}+x\mathrm{LiF}$.

Using $365$ days per year, the required time is $2\times 365\times 24=17520\mathrm{h}$. Hencelithium transfers one electron per atom, soThis is the stoichiometric minimum for one cell, or one cell-equivalent parallel assembly, with complete utilization and no self-discharge. Practical loading must be larger. If a pack uses several cells in series, each series cell must carry the full delivered charge and the total lithium mass increases accordingly; no required pack voltage or series count is supplied.

The reaction consumes one mole of CF for each mole of electrons. Using $M_{\mathrm{CF}}=12.01+19.00=31.01\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$,This is active CF alone for the same single-cell-equivalent assumption, not the full positive-electrode or pack mass. Conductive additive, binder, electrolyte, battery separator, collectors and casing add mass, and incomplete utilization increases the required CF.