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The space-group distribution of molecular organic structures
International Tables for Crystallography (2006). Vol. C, ch. 9.7, pp. 897-906 [ doi:10.1107/97809553602060000623 ]
... distribution of molecular organic structures is reviewed. Topics discussed include: a priori classifications of space groups; special positions of given symmetry ... space-group frequencies; the use of molecular symmetry; structural classes; a statistical model for space-group frequency; molecular packing; and a priori predictions of molecular crystal structures. 9.7.1. A priori ...
Factors determining accuracy
International Tables for Crystallography (2006). Vol. C, Section 5.2.13, pp. 501-504 [ doi:10.1107/97809553602060000596 ]
... to 0.0001% is rarely reached and each determination is virtually a research project. The more important factors are: (1) Differentiation of ... the term, the error in [Delta]d is smaller for a given angular accuracy . The gain is not as great ... and (iv) fewer problems of overlapping. In any particular case, a balance of advantage must be sought. The forward reflections ...
Instrumental line-profile-shape standards
International Tables for Crystallography (2006). Vol. C, Section 5.2.12, p. 501 [ doi:10.1107/97809553602060000596 ]
... Instrumental line-profile standards are required to determine resolution, as a check that alignment has been optimized, or to compare the ... therefore be required if samples of interest do not have a high absorption coefficient for the radiation used. In addition to ... by NIST as SRM 660 and it also serves as a line position standard. Other materials used as instrumental standards ...
Intensity standards
International Tables for Crystallography (2006). Vol. C, Section 5.2.11, p. 500 [ doi:10.1107/97809553602060000596 ]
... and CeO2. Table 5.2.11.1, taken from the NIST certificate, is a partial list of pertinent data. The lattice parameters have an ... of 3 parts in 105, which must be increased by a factor of 2 or 3 because of uncertainty in internal standards and thermal expansion. The five materials have a wide range of absorption coefficient and the crystallite size ( ...
Powder-diffraction standards
International Tables for Crystallography (2006). Vol. C, Section 5.2.10, pp. 498-499 [ doi:10.1107/97809553602060000596 ]
... and 95% of the particles are < 10µm. There is a wide range of particle sizes in SRM 640, and sieving ... to 298K. Because this wavelength was later found to have a systematic error (see Section 4.2.2 ), and a more accurate value, 1.5405929(5)Å (see Table 4.2.2.1 ), is ...
Testing for remanent systematic error
International Tables for Crystallography (2006). Vol. C, Section 5.2.9, p. 498 [ doi:10.1107/97809553602060000596 ]
... is lower. The IUCr lattice-parameter project (Parrish, 1960) showed a standard deviation of 1 in 30000 in inter-laboratory comparisons ... deviation of the sum S is expected to be approximately (Wilson, 1980), so that if the actual value of S exceeds ... remaining systematic error' based on likelihood were available; they assumed a normal distribution of errors, possibly without realizing, and certainly ...
Camera methods
International Tables for Crystallography (2006). Vol. C, Section 5.2.8, pp. 497-498 [ doi:10.1107/97809553602060000596 ]
... the apparent values of the lattice parameter were plotted against a function something like ([pi] - 2[theta])2. A function that has been found very satisfactory in practice was ... Jay arrangements. For Straumanis-Ievins', + or - and , respectively. References Langford, J. I., Pike, E. R. & Beu, K. E. (1964). ...
Energy-dispersive techniques
International Tables for Crystallography (2006). Vol. C, Section 5.2.7, pp. 496-497 [ doi:10.1107/97809553602060000596 ]
... available. In both, the specimen and detector are fixed in a selectable [theta]-2[theta] setting. The method (Giessen & Gordon, 1968) first described and most widely used requires a solid-state detector and a multichannel pulse-height analyser (Section 2.3.2 and Chapter 2.5 ) ...
Whole-pattern methods
International Tables for Crystallography (2006). Vol. C, Section 5.2.6, p. 496 [ doi:10.1107/97809553602060000596 ]
... Rietveld (1967, 1969) described in Chapter 8.6 . In outline, a profile-fitting function containing adjustable parameters to vary the width ... that is attained but the estimated standard deviations quoted in a number of papers (see, for example, Young, 1988) appear to ... are derived from profile fitting and the data used in a powder least-squares-refinement program. The reflections may be ...
Angle-dispersive diffractometer methods: synchrotron sources
International Tables for Crystallography (2006). Vol. C, Section 5.2.5, pp. 495-496 [ doi:10.1107/97809553602060000596 ]
... methods: synchrotron sources Lattice-parameter determination with synchrotron radiation has a number of advantages over focusing methods (Parrish, Hart, Huang & Bellotto ... low uniform background out to the highest [theta] values give a higher statistical counting precision, an important factor in accurate measurements. ... 2[theta]) when an analysing crystal is used instead of a receiving slit, and of the order of 0.05° when ...
International Tables for Crystallography (2006). Vol. C, ch. 9.7, pp. 897-906 [ doi:10.1107/97809553602060000623 ]
... distribution of molecular organic structures is reviewed. Topics discussed include: a priori classifications of space groups; special positions of given symmetry ... space-group frequencies; the use of molecular symmetry; structural classes; a statistical model for space-group frequency; molecular packing; and a priori predictions of molecular crystal structures. 9.7.1. A priori ...
Factors determining accuracy
International Tables for Crystallography (2006). Vol. C, Section 5.2.13, pp. 501-504 [ doi:10.1107/97809553602060000596 ]
... to 0.0001% is rarely reached and each determination is virtually a research project. The more important factors are: (1) Differentiation of ... the term, the error in [Delta]d is smaller for a given angular accuracy . The gain is not as great ... and (iv) fewer problems of overlapping. In any particular case, a balance of advantage must be sought. The forward reflections ...
Instrumental line-profile-shape standards
International Tables for Crystallography (2006). Vol. C, Section 5.2.12, p. 501 [ doi:10.1107/97809553602060000596 ]
... Instrumental line-profile standards are required to determine resolution, as a check that alignment has been optimized, or to compare the ... therefore be required if samples of interest do not have a high absorption coefficient for the radiation used. In addition to ... by NIST as SRM 660 and it also serves as a line position standard. Other materials used as instrumental standards ...
Intensity standards
International Tables for Crystallography (2006). Vol. C, Section 5.2.11, p. 500 [ doi:10.1107/97809553602060000596 ]
... and CeO2. Table 5.2.11.1, taken from the NIST certificate, is a partial list of pertinent data. The lattice parameters have an ... of 3 parts in 105, which must be increased by a factor of 2 or 3 because of uncertainty in internal standards and thermal expansion. The five materials have a wide range of absorption coefficient and the crystallite size ( ...
Powder-diffraction standards
International Tables for Crystallography (2006). Vol. C, Section 5.2.10, pp. 498-499 [ doi:10.1107/97809553602060000596 ]
... and 95% of the particles are < 10µm. There is a wide range of particle sizes in SRM 640, and sieving ... to 298K. Because this wavelength was later found to have a systematic error (see Section 4.2.2 ), and a more accurate value, 1.5405929(5)Å (see Table 4.2.2.1 ), is ...
Testing for remanent systematic error
International Tables for Crystallography (2006). Vol. C, Section 5.2.9, p. 498 [ doi:10.1107/97809553602060000596 ]
... is lower. The IUCr lattice-parameter project (Parrish, 1960) showed a standard deviation of 1 in 30000 in inter-laboratory comparisons ... deviation of the sum S is expected to be approximately (Wilson, 1980), so that if the actual value of S exceeds ... remaining systematic error' based on likelihood were available; they assumed a normal distribution of errors, possibly without realizing, and certainly ...
Camera methods
International Tables for Crystallography (2006). Vol. C, Section 5.2.8, pp. 497-498 [ doi:10.1107/97809553602060000596 ]
... the apparent values of the lattice parameter were plotted against a function something like ([pi] - 2[theta])2. A function that has been found very satisfactory in practice was ... Jay arrangements. For Straumanis-Ievins', + or - and , respectively. References Langford, J. I., Pike, E. R. & Beu, K. E. (1964). ...
Energy-dispersive techniques
International Tables for Crystallography (2006). Vol. C, Section 5.2.7, pp. 496-497 [ doi:10.1107/97809553602060000596 ]
... available. In both, the specimen and detector are fixed in a selectable [theta]-2[theta] setting. The method (Giessen & Gordon, 1968) first described and most widely used requires a solid-state detector and a multichannel pulse-height analyser (Section 2.3.2 and Chapter 2.5 ) ...
Whole-pattern methods
International Tables for Crystallography (2006). Vol. C, Section 5.2.6, p. 496 [ doi:10.1107/97809553602060000596 ]
... Rietveld (1967, 1969) described in Chapter 8.6 . In outline, a profile-fitting function containing adjustable parameters to vary the width ... that is attained but the estimated standard deviations quoted in a number of papers (see, for example, Young, 1988) appear to ... are derived from profile fitting and the data used in a powder least-squares-refinement program. The reflections may be ...
Angle-dispersive diffractometer methods: synchrotron sources
International Tables for Crystallography (2006). Vol. C, Section 5.2.5, pp. 495-496 [ doi:10.1107/97809553602060000596 ]
... methods: synchrotron sources Lattice-parameter determination with synchrotron radiation has a number of advantages over focusing methods (Parrish, Hart, Huang & Bellotto ... low uniform background out to the highest [theta] values give a higher statistical counting precision, an important factor in accurate measurements. ... 2[theta]) when an analysing crystal is used instead of a receiving slit, and of the order of 0.05° when ...
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