Bragg's equation

(noun)

Gives the angles for coherent and incoherent scattering from a crystal lattice.

Related Terms

Examples of Bragg's equation in the following topics:

  • X-Ray Diffraction Analysis

    • At certain angles of the sensor, populations of crystals have the correct angle so that Bragg's equation is satisfied for one of the crystal planes, resulting in a spike in X-rays.

  • X-Ray Diffraction

    • In x-ray crystallography, the term for diffraction is Bragg diffraction, which is the scattering of waves from a crystalline structure.
    • William Lawrence Bragg formulated the equation for Bragg's law, which relates wavelength to the angle of incidence and lattice spacing.
    • Refer to for a diagram of the following equation: $n\lambda = 2d sin(\theta)$

  • The Battle of Chattanooga

    • The flanking option was deemed to be impracticable because Bragg's army was short on ammunition, they had no pontoon for river crossing, and Longstreet's corps from Virginia had arrived at Chickamauga without wagons.
    • Bragg's army besieged the city, threatening to starve the Union forces into surrender.
    • Sherman's attack on Bragg's right flank made little progress.
    • Hoping to distract Bragg's attention, Grant authorized Thomas's army to advance in the center of his line to the base of Missionary Ridge.
    • Bragg's defeat eliminated the last Confederate stronghold in Tennessee and opened the door to an invasion of the Deep South, leading to Sherman's Atlanta Campaign of 1864.

  • The de Broglie Wavelength

    • In 1926, Erwin Schrödinger published an equation describing how a matter wave should evolve—the matter wave equivalent of Maxwell's equations—and used it to derive the energy spectrum of hydrogen.
    • The two equations can be equivalently written as
    • He related this to the principal quantum number n through the equation:
    • The angular dependence of the reflected electron intensity was measured and was determined to have the same diffraction pattern as those predicted by Bragg for X-rays.
    • Use the de Broglie equations to determine the wavelength, momentum, frequency, or kinetic energy of particles

  • X-Ray Spectra: Origins, Diffraction by Crystals, and Importance

    • Shown below, Bragg's Law gives the angles for coherent and incoherent scattering of light from a crystal lattice, which happens during x-ray diffraction.
    • This is called the Braggs diffraction, and is the basis for x-ray diffraction.
    • Bragg's Law of diffraction: illustration of how x-rays interact with crystal lattice.

  • Union Victories in the Western Theater

    • Braxton Bragg took command of 56,000 troops of the Army of Tennessee.
    • Bragg's general plan was to invade Kentucky, cut Union lines of communications, and then turn back to defeat Grant.
    • However, after some small successes, Bragg realized that he was outnumbered and retreated through the Cumberland Gap, returning to Murfreesboro by way of Chattanooga.
    • Bragg was relieved of duty and replaced by General Joseph E.
    • Identify the battles fought by Generals Johnston, Bragg, Hood, Sherman, Rosecrans, and Grant in the Western Theater of the Civil War.

  • Photon Energies of the EM Spectrum

    • Maxwell's equations predicted an infinite number of frequencies of electromagnetic waves, all traveling at the speed of light.
    • In 1886, the physicist Hertz built an apparatus to generate and detect what are now called radio waves, in an attempt to prove Maxwell's equations and detect such low-frequency electromagnetic radiation.
    • However, in 1910, British physicist William Henry Bragg demonstrated that gamma rays are electromagnetic radiation, not particles.
    • The relationship between photon energy and the radiation's frequency and wavelength is illustrated as the following equilavent equation: $\nu = \frac{c}{\lambda}$, or $\nu = \frac{E}{h}$ or $E = \frac{hc}{\lambda}$, where $\nu$ is the frequency, $\lambda$ is the wavelength, E is photon energy, c is the speed of light, and h is the Planck constant.

  • The Battles: 1863–1865

    • General Braxton Bragg defeated Union troops, who retreated to Chattanooga, which Bragg then besieged.
    • Grant marched to the relief of troops in Chattanooga and defeated Bragg at the Third Battle of Chattanooga, driving Confederate forces out of Tennessee and opening a route to Atlanta and the heart of the Confederacy.

  • Inconsistent and Dependent Systems

    • In mathematics, a system of linear equations (or linear system) is a collection of linear equations involving the same set of variables.
    • The equations of a linear system are independent if none of the equations can be derived algebraically from the others.
    • When the equations are independent, each equation contains new information about the variables, and removing any of the equations increases the size of the solution set.
    • For example, the equations
    • Adding the first two equations together gives 3x + 2y = 2, which can be subtracted from the third equation to yield 0 = 1.

  • Solving Systems Graphically

    • A simple way to solve a system of equations is to look for the intersecting point or points of the equations.
    • A system of equations (also known as simultaneous equations) is a set of equations with multiple variables, solved when the values of all variables simultaneously satisfy all of the equations.
    • Once you have converted the equations into slope-intercept form, you can graph the equations.
    • To determine the solutions of the set of equations, identify the points of intersection between the graphed equations.
    • This graph shows a system of equations with two variables and only one set of answers that satisfies both equations.