SUMMARY / RELATED TOPICS

Miller indices form a notation system in crystallography for planes in crystal lattices. In particular, a family of lattice planes is determined by three integers h, k, ℓ, the Miller indices, they are written, denote the family of planes orthogonal to h b 1 + k b 2 + ℓ b 3, where b i are the basis of the reciprocal lattice vectors. By convention, negative integers are written with a bar, as in 3 for −3; the integers are written in lowest terms, i.e. their greatest common divisor should be 1. Miller indices are used to designate reflexions in X-ray crystallography. In this case the integers are not in lowest terms, can be thought of as corresponding to planes spaced such that the reflexions from adjacent planes would have a phase difference of one wavelength, regardless of whether there are atoms on all these planes or not. There are several related notations: the notation denotes the set of all planes that are equivalent to by the symmetry of the lattice. In the context of crystal directions, the corresponding notations are:, with square instead of round brackets, denotes a direction in the basis of the direct lattice vectors instead of the reciprocal lattice.

Miller indices were introduced in 1839 by the British mineralogist William Hallowes Miller, although an identical system had been used by German mineralogist Christian Samuel Weiss since 1817. The method was historically known as the Millerian system, the indices as Millerian, although this is now rare; the Miller indices are defined with respect to any choice of unit cell and not only with respect to primitive basis vectors, as is sometimes stated. There are two equivalent ways to define the meaning of the Miller indices: via a point in the reciprocal lattice, or as the inverse intercepts along the lattice vectors. Both definitions are given below. In either case, one needs to choose the three lattice vectors a1, a2, a3 that define the unit cell. Given these, the three primitive reciprocal lattice vectors are determined. Given the three Miller indices h, k, ℓ, denotes planes orthogonal to the reciprocal lattice vector: g h k ℓ = h b 1 + k b 2 + ℓ b 3; that is indicates a normal to the planes in the basis of the primitive reciprocal lattice vectors.

Because the coordinates are integers, this normal is itself always a reciprocal lattice vector. The requirement of lowest terms means that it is the shortest reciprocal lattice vector in the given direction. Equivalently, denotes a plane that intercepts the three points a1/h, a2/k, a3/ℓ, or some multiple thereof; that is, the Miller indices are proportional to the inverses of the intercepts of the plane, in the basis of the lattice vectors. If one of the indices is zero, it means. Considering only planes intersecting one or more lattice points, the perpendicular distance d between adjacent lattice planes is related to the reciprocal lattice vector orthogonal to the planes by the formula: d = 2 π / | g h k ℓ |; the related notation denotes the direction: h a 1 + k a 2 + ℓ a 3. That is, it uses the direct lattice basis instead of the reciprocal lattice. Note, not normal to the planes, except in a cubic lattice as described below. For the special case of simple cubic crystals, the lattice vectors are orthogonal and of equal length, as are those of the reciprocal lattice.

Thus, in this common case, the Miller indices and both denote normals/directions in Cartesian coordinates. For cubic crystals with lattice constant a, the spacing d between adjacent lattice planes is d h k ℓ = a h 2 + k 2 + ℓ 2; because of the symmetry of cubic crystals, it is possible to change the place and sign of the integers and have equivalent directions and planes: Indices in angle brackets such as ⟨100⟩

Season two of El Artista del Año premiered on July 14, 2018, on the América Televisión network. On July 11, the first ten participants of the show were presented through a press conference. Although it was predetermined that ten contestants were the same as last season, it was announced that in the second gala would enter two new participants; the first of them was Ebelin Ortiz, while John Kelvin and Mirella Paz met in a duel qualified by the judges to occupy the second pass in the competition the judges decided to give the pass to both, giving a total of thirteen contestants in place of the twelve provided. During the first five weeks, the married couple Yiddá Eslava and Julián Zucchi participated together, being the first couple participating in the show. From the sixth week they competed individually. Gisela Valcárcel and Jaime "Choca" Mandros returned as hosts, while Morella Petrozzi, Lucho Cáceres, Fiorella Rodríguez and Cecilia Bracamonte returned as judges. During the second and third week, theater director and presenter Santi Lesmes replaced Cáceres.

Red numbers indicate those sentenced for each week Green numbers indicate the highest score for each week the contestant eliminated of the week the contestant saved in the duel the contestant eliminated and saved with the lifeguard the winning contestant the runner-up contestant the third-place contestant This table only counts performances scored on a 40-point scale. This table has the highest and lowest scores of each contestants performance according to the 40-point scale. Official website

The History of East Carolina University can trace its roots to 1901 when City of Wilson citizens went to Raleigh to petition the N. C. General Assembly for an Eastern North Carolina Normal College; the delegation wanted the Normal College in Wilson. The request was denied because the politicians did not want to take money away from the State Normal College. In February 1905, Elizabeth City sent 11 citizens to persuade the General Assembly to charter a State Normal School for Eastern North Carolina; that delegation failed as well. On March 8, 1907, at the urging of State Senator James Leonidas Fleming, the General Assembly passed an act titled: "AN ACT TO STIMULATE HIGH SCHOOL INSTRUCTION IN THE PUBLIC SCHOOLS OF THE STATE AND TEACHER TRAINING". In this act it said "That there shall be established and maintained at some suitable point in eastern North Carolina a teachers' training school for the training of young white men and women under the corporate name of the East Carolina Teachers' Training School."

\$15,000 was appropriated to the fund to build the school, \$5,000 annually to fund the school. The Board of Trustees was selected on March 15, 1907 and Thomas Jordan Jarvis was chosen as the Chairman. Eight eastern North Carolina towns and cities placed bids on the location of the school; the towns and cities and what they offered is as follows: Washington - \$75,000 and the choice of two sites, 200 acres or 133 acres. When Greenville put a bond to the city and County of Pitt, Haywood Dail promised Thomas Jarvis that Greenville would pass the bond. Dail wanted the ballots to be small and have only "For Bond Issue" and "Against Bond Issue" written on them. Dail went on to chew the "Against Bond Issue" to ensure that the bond will pass; the vote passed by 352. The State Board of Education toured all eight cities in the month of June. On June 10, 1907 the SBE voted on the location of the school. On the first vote Kinston received three votes, Rocky Mount received two votes and Greenville received one vote.

On the second vote, all three locations received two votes. On the last and final vote, Greenville received four votes to Kinston two votes. One of the jobs the Board of Trustees did was to choose the President of the School. Robert Herring Wright was selected on June 11, 1907, he set out to recruit faculty. ECTTS had 10 faculty members. On October 5, 1909, Pattie Simmons Dowell was the first student to enroll to the Training School; when classes started in 1909, ECTTS has six buildings. These buildings included two dormitories: Jarvis and Wilson, Administration Building, Power Plant and Refectory. Tuition was free for all students who pledged to teach for two years, \$45.00 for all other students. In total, 104 women and 19 men accompanied the 11 faculty on the first day of classes; the School became a two-year Teacher Training School. The first vote by the students was to choose the school colors. June 11, 1911, 16 students became the first graduating class as East Carolina. In 1912, the Athletic League was formed.

The three sports played were basketball and cross-country walking. This was the beginning of the Athletic Department. A Constitution was written for the first Student Self-Government Association. After growing expediently the School decided to change its mission. Mattie Virginia Cox Thornton was the first student in line at East Carolina University in 1908, she rode a wagon pulled by a mule down dirt roads from Kinston to Greenville to be the first to enroll. Mrs. Thornton went on to become a teacher for many years. After enrollment passed 1,000 students, the Administration decided to change the School