Angle calculations for 3- and 4-circle X-ray and neutron diffractometers

The preparation and crystal structure of η2-nitrato(η4-hexadecamethylcyclooctaphosphazene (N1,N2,N4,N5))cobalt(II) nitrate

“…The significant variation in the Co-N distances (2.113(3)-2.197(3) A) reflects the trigonal bipyramidal character of the complex 2, the "equatorial" bond lengths being significantly shorter than the "axial" distances with the exception of the pair co-N(l)/N(2). (5) 47040 ( 9) 72968 ( 9) 33739( 6) P (6) 62005 ( 9) 54897 ( 8) 29246( 6) p (7) 89808 ( 9) 64455 ( 9) 31599( 6) p (8) 101019 ( 9) 64853 ( 9) 14718 ( 6) (7) 10022 ( 3) 6908 ( 3) 2495 ( 2) N(8) 9447 ( 3) 7134 ( 3) 702( 2) N (9) 4480 ( 3) 7665 ( 3) 335 ( 2) c(1) 6875 ( 4) 5848 ( 4) 335 ( 3) (32) 7993 ( 6) 7891 ( 6) -602( 3) c (3) 9848 ( 4) 9908 ( 5) 2035 ( 4) c(4) 8150 ( 6) 10641 ( 5) 728 ( 4) c(5) 8381 ( 5) 1 1004( 6) 4029( 4) C (6) 7637 ( 7) 12310 ( 5) 2593 ( 5) c (7) 3965 ( 6) 10375 ( 5) 1996( 4) c (8) 3341 ( 6) 9862 ( 6) 3752( 4) c (9) 5333 ( 6) 7869 ( 6) 4514 …”

“…The intensities of 3 check reflections, measured every 3600 s throughout the data collection, remained constant to within f 4%. After data reduction, an absorption correction was applied using the Gaussian integration method (8,9). Transmission factors ranged from 0.790 to 0.948 for 120 sampling points.…”

Instrumental aspects

“…The sample should not precess while any of the three angles , , is being adjusted while being in the center of the neutron beam. The typical experimental procedure is then to find two linearly independent (hkl) reflections which provide the ability to calculate the orientation matrix UB [4]. This matrix relates the sample lattice parameters and the diffractometer axes and allows therefore to calculate the diffractometer angles for any (hkl) reflection and hence to position the sample accordingly.…”

Angle calculations for a six-circle κ diffractometer

“…Since we deal with representations of reciprocal-lattice vectors, r P {h}, the actual coordinates have dimensions of inverse length. The orientation matrix, UB (Busing & Levy, 1967), gives the initial coordinates, indicated by the subscripts i, of the reciprocal-lattice point (hkl) in the laboratory system, i.e.…”

“…The cradle geometry is well known and has been comprehensively described by several authors (Arndt & Willis, 1966;Busing & Levy, 1967;Hamilton, 1974). In 1972, the goniostat was invented by Poot of Enraf±Nonius and protected by worldwide patents (Poot, 1972).…”