A reexamination of the crystal structures of α and β nitrogen

Bolz, L. H.; Boyd, Molly; Mauer, F. A.; Peiser, H. S.

doi:10.1107/s0365110x59000688

Cited by 84 publications

(22 citation statements)

References 1 publication

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“…After all, for strictly positive quantities, such as V 0 or T m , an invariable shift seems counterintuitive. The impact of such an error is much larger when the investigated prop- for the cohesive energy [46,75], equilibrium volume [43,[76][77][78][79][80][81][82][83], bulk modulus [46,62,[84][85][86][87][88][89][90][91], pressure derivative of the bulk modulus [92][93][94][95][96][97][98], and elastic constants [40,99,100]. The full, black line stands for xexp = x th .…”

Section: Eliminating Outliersmentioning

confidence: 99%

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

Lejaeghere

Speybroeck

Oost

et al. 2013

Critical Reviews in Solid State and Materials Sciences

491

390

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Predictions of observable properties by density-functional theory calculations (DFT) are used increasingly often by experimental condensed-matter physicists and materials engineers as data.These predictions are used to analyze recent measurements, or to plan future experiments in a rational way. Increasingly more experimental scientists in these fields therefore face the natural question: what is the expected error for such a first-principles prediction? Information and experience about this question is implicitly available in the computational community, scattered over two decades of literature. The present review aims to summarize and quantify this implicit knowledge. This eventually leads to a practical protocol that allows any scientist-experimental or theoretical-to determine justifiable error estimates for many basic property predictions, without having to perform additional DFT calculations.A central role is played by a large and diverse test set of crystalline solids, containing all ground-state elemental crystals (except most lanthanides). For several properties of each crystal, the difference between DFT results and experimental values is assessed. We discuss trends in these deviations and review explanations suggested in the literature.A prerequisite for such an error analysis is that different implementations of the same firstprinciples formalism provide the same predictions. Therefore, the reproducibility of predictions across several mainstream methods and codes is discussed too. A quality factor expresses the spread in predictions from two distinct DFT implementations by a single number. To compare the PAW method to the highly accurate APW+lo approach, a code assessment of VASP and GPAW (PAW) with respect to WIEN2k (APW+lo) yields -values of 1.9 and 3.3 meV/atom, respectively. In both cases the PAW potentials recommended by the respective codes have been used. These differences are an order of magnitude smaller than the typical difference with experiment, and therefore predictions by APW+lo and PAW are for practical purposes identical.

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Section: Eliminating Outliersmentioning

confidence: 99%

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

Lejaeghere

Speybroeck

Oost

et al. 2013

Critical Reviews in Solid State and Materials Sciences

491

390

View full text Add to dashboard Cite

show abstract

“…To mimic the application of pressure, lattice constants of aϭ5.6, 5.4, 5.2, and 5.0 Å were chosen ͑experimentally, aϭ5.644 Å͒. 35 A lattice constant of aϭ5.4 Å corresponds to a pressure of approximately 0.4 GPa. 36 However, since our calculations do not allow relaxation of the N 2 molecules, a direct correspondence between a and pressure cannot be made.…”

Section: E Ab Initio Calculationsmentioning

confidence: 99%

N 2 and CO2 vibrational modes in solid nitrogen under pressure

McCluskey

Zhuravlev

2002

The Journal of Chemical Physics

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Nitrogen has a complex phase diagram that has presented a formidable challenge to theoretical models. In this study, infrared (IR) spectroscopy has been performed on solid nitrogen at low temperatures and pressures up to 6 GPa. In the ε phase, two IR absorption peaks were observed that correspond to N–N stretch modes. The presence of two IR-active N2 vibrons is consistent with a tetragonal structure (P43212) and is inconsistent with an earlier proposed rhombohedral (R3̄C) structure. The matrix isolation of CO2 molecules in solid N2 led to the observation of transverse (ν2) vibrational modes, which showed a splitting consistent with the structures of the different N2 phases. The ν3 mode of CO212 and CO213 molecules was measured as a function of pressure, as well as combination modes. All the vibrational-mode frequencies shifted discontinuously at the critical pressures for N2 phase transitions. For CO2 concentrations of 0.1%, phase separation is present at low pressures, but is suppressed for pressures greater than 1 GPa. In summary, these studies have contributed to the knowledge of the N2 phase diagram and the nature of guest-host interactions in molecular systems.

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“…Nitrogen and oxygen both have several solid phases [25][26][27][28][29][30][31][32][33][34] and [35][36][37][38][39][40][41][42][43][44][45][46]. Recent X-ray, electron and neutron diffraction experiments have provided information on the structure of these solids which is summarized in table 3.…”

Section: Comparison With Other Phases Of Nitrogen and Oxygenmentioning

confidence: 99%

Neutron scattering by liquid nitrogen and liquid oxygen

1975

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Measurements have been made of the neutron scattering structure factors of liquid nitrogen and liquid oxygen at 77 K and 84 K respectively in the Q-value range of 3 to 36 A -1. 'White' incident thermal neutrons were produced in the wavelength range of 0"3 to 3"0 )k by a pulsed electron linac and detected in a total-scattering time-of-flight spectrometer. Qualitative agreement has been obtained between these present data and a simple molecular form factor in the Q-value range of 12-36 A a.Using reactor data [1], structure factors over a total Q-value range of 0"3 to 36 A-1 were obtained. Fourier transforms of the structure factor curves yield pair distribution functions which show a distinct separation of the inter and intra-molecular distances in the liquid. A comparison is made with results for the solid phase.

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A reexamination of the crystal structures of α and β nitrogen

Cited by 84 publications

References 1 publication

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

Error Estimates for Solid-State Density-Functional Theory Predictions: An Overview by Means of the Ground-State Elemental Crystals

N 2 and CO2 vibrational modes in solid nitrogen under pressure

Neutron scattering by liquid nitrogen and liquid oxygen

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