Hence, William Hallowes Miller in 1839 was able to give each face a unique label of three small integers, the Miller indices which are still used today for identifying crystal faces.

The orientation of a particular set of sheets is identified by its three Miller indices ( h, k, l ), and let their spacing be noted by d. William Lawrence Bragg proposed a model in which the incoming X-rays are scattered specularly ( mirror-like ) from each plane ; from that assumption, X-rays scattered from adjacent planes will combine constructively ( constructive interference ) when the angle θ between the plane and the X-ray results in a path-length difference that is an integer multiple n of the X-ray wavelength λ.

A reflection is said to be indexed when its Miller indices ( or, more correctly, its reciprocal lattice vector components ) have been identified from the known wavelength and the scattering angle 2θ.

Planes with different Miller indices in cubic crystals

That is, the Miller indices are proportional to the inverses of the intercepts of the plane with the unit cell ( in the basis of the lattice vectors ).

A plane containing a co-ordinate axis is translated so that it no longer contains that axis before its Miller indices are determined.

The Miller indices for a plane are integers with no common factors.

In an orthogonal co-ordinate system, the Miller indices of a plane are the Cartesian components of a vector normal to the plane.

So, in this common case, the Miller indices ( ℓmn ) and both simply denote normals / directions in Cartesian coordinates.

John Miller in Dollars & Sense has stated that the indices are " a poor barometer of either freedom more broadly construed or of prosperity.

John Miller further observes that Hong Kong and Singapore, both only " partially free " according to Freedom House, are leading countries on both economic freedom indices and casts doubt on the claim that measured economic freedom is associated with political freedom.

Miller indices are named after William Hallowes Miller, the method having been described in his Treatise on Crystallography ( 1839 ).

Planes with different Miller indices in cubic crystals

Miller indices form a notation system in crystallography for planes in crystal ( Bravais ) lattices.

In particular, a family of lattice planes is determined by three integers h, k, and ℓ, the Miller indices.

Each band can be indexed individually by the Miller indices of the diffracting plane which formed it.

On the other hand, ED patterns of inorganic crystals have often a high resolution (= interplanar spacings with high Miller indices ) much below 1 Ångström.

More specialist uses include Miller indices in crystallography, strike and dip in geology and grade on maps and signs.

Planes with different Miller indices in cubic crystals

The attitude of a lattice plane is the orientation of the line normal to the plane, and is described by the plane's Miller indices.

In three-space a family of planes ( a series of parallel planes ) can be denoted by its Miller indices ( hkl ), so the family of planes has an attitude common to all its constituent planes.

Then, the poles of the other planes are placed on the figure, with the Miller indices for each pole.

Regional chefs are emerging as localized celebrity chefs with growing broader appeal, such as Peter Merriman ( Hawaii Regional Cuisine ), Jerry Traunfeld, Alan Wong ( Pacific Rim cuisine ), Norman Van Aken ( New World Cuisine-fusion Latin, Caribbean, Asian, African and American ), and Mark Miller ( American Southwest cuisine ).

" The divine call for massacre at Jericho and elsewhere can be explained in terms of cultural norms ( Israel wasn't the only Iron Age state to practice herem ) and theology ( a measure to ensure Israel's purity as well as the fulfillment of God's promise ), but Patrick D. Miller in his commentary on Deuteronomy remarks, " there is no real way to make such reports palatable to the hearts and minds of contemporary readers and believers.

While in Fort Worth, Wills added the " rowdy city blues " of Bessie Smith and Emmett Miller to a repertoire of mainly waltzes and breakdowns he had learned from his father, and patterned his vocal style after that of Miller and other performers such as Al Bernard.

Despite such concerns from critics, legislators, and publishers, Scott Miller later recounted that 3D Realms saw very little negative feedback to the game's controversial elements from actual gamers or their parents.

Loren Miller proposed his Maximum Game Fun principle as a basis for gaming, which soon became a game system in its own right, David Dunham proposed his PenDragon Pass system, a nearly freeform game system, and several ambitious freeform games were played at conventions, such as Home of the Bold with up to 80 participants.

The hypothesis that Japanese might be related to Korean has had some supporters due to some apparent overlap in vocabulary and similar grammatical features that have been elaborated upon by such researchers as Samuel E. Martin and Roy Andrew Miller.

In The Dharma at Big Sur, Adam's draws from literary texts such as Jack Kerouac, Gary Snyder and Henry Miller to illustrate the California landscape.

In the 1980s, American and European dancers from California, New York, London and Sweden ( such as Sylvia Sykes, Erin Stevens, Steven Mitchell, Terry Monaghan and Warren Heyes who formed London's Jiving Lindy Hoppers performance troupe, and Stockholm's Rhythm Hot Shots / Harlem Hot Shots ) went about ' reviving ' Lindy Hop using archival films such as Hellzapoppin ' and A Day at the Races and by contacting dancers such as Frankie Manning, Al Minns, Norma Miller, Jewel McGowan and Dean Collins.

Mersenne primes are used in pseudorandom number generators such as the Mersenne twister, Park – Miller random number generator, Generalized Shift Register and Fibonacci RNG.

More than once, the magazine has enlisted popular comic book artists such as Frank Miller or Jim Lee to design and illustrate a series of " Rejected Superheroes.

The two main kinds of theory of physical probability are frequentist accounts ( such as those of Venn, Reichenbach and von Mises ) and propensity accounts ( such as those of Popper, Miller, Giere and Fetzer ).

Geoffrey Miller proposes that sexual selection might have contributed by creating evolutionary modules such as Archaeopteryx feathers as sexual ornaments, at first.

Geoffrey Miller, drawing on some of Darwin's largely neglected ideas about human behavior, has hypothesized that many human behaviors not clearly tied to survival benefits, such as humor, music, visual art, verbal creativity, and some forms of altruism, are courtship adaptations that have been favored through sexual selection.

Libertarians such as Dennis Miller ( based in Los Angeles ), Jon Arthur, Host Of Jon Arthur Live!

Traditionally, politically driven talk radio from the United States does not air on Canadian stations, with a few scattered exceptions ( e. g. the now-defunct CFBN, which carried political programming such as the Glenn Beck Program and Dennis Miller, and the also-discontinued talk format of CHAM, which carried Miller ).

Described as a place of unending Springtime and a paradise of green plants, Tlalocan was the destination in the afterlife for those who died violently from phenomena associated with water, such as by lightning, drowning and water-borne diseases ( Miller and Taube, 1993 ).

The tempera medium was used by American artists such as the Regionalists Andrew Wyeth, Thomas Hart Benton and his student Roger Medearis ; expressionists Ben Shahn, Mitchell Siporin and John Langley Howard, magic realists George Tooker, Paul Cadmus, Jared French, Julia Thecla and Louise E. Marianetti ; Art Students League of New York instructors Kenneth Hayes Miller and William C. Palmer, Social Realists Isabel Bishop, Reginald Marsh, and Noel Rockmore, Edward Laning, Anton Refregier, Jacob Lawrence, Rudolph F. Zallinger, Robert Vickrey, Peter Hurd, and science fiction artist John Schoenherr, notable as the cover artist of Dune.

Other UU ministers, such as the Reverend David Miller, are atheists.

The Advent Movement emerged in the 1830s and 1840s in North America, and was preached by ministers such as William Miller, whose followers became known as Millerites.