scholarly journals Crystal flex bases and the RUM spectrum

2021 ◽  
pp. 1-27
Author(s):  
G. Badri ◽  
D. Kitson ◽  
S. C. Power
Keyword(s):  
Spectral Analysis ◽  
Space Group ◽  
First Order ◽  
2D And 3D

A theory of infinite spanning sets and bases is developed for the first-order flex space of an infinite bar-joint framework, together with space group symmetric versions for a crystallographic bar-joint framework ${{\mathcal {C}}}$ . The existence of a crystal flex basis for ${{\mathcal {C}}}$ is shown to be closely related to the spectral analysis of the rigid unit mode (RUM) spectrum of ${{\mathcal {C}}}$ and an associated geometric flex spectrum. Additionally, infinite spanning sets and bases are computed for a range of fundamental crystallographic bar-joint frameworks, including the honeycomb (graphene) framework, the octahedron (perovskite) framework and the 2D and 3D kagome frameworks.

Incommensurately modulated phase of Rb2CoBr4 at 295 and 200 K

2000 ◽  
Vol 56 (1) ◽  
pp. 17-21 ◽  
Author(s):  
K. Friese ◽  
G. Madariaga ◽  
T. Breczewski
Keyword(s):  
Crystal Structure ◽  
Close Relationships ◽  
Room Temperature ◽  
Lattice Parameters ◽  
Modulated Structure ◽  
Space Group ◽  
Average Structure ◽  
First Order ◽  
Modulation Function ◽  
Modulated Phase

The crystal structure of Rb_2CoBr_4 at 295 and 200 K has been determined. At these temperatures Rb_2CoBr_4 exhibits an incommensurately modulated structure with wavevector {\bf q} = (1/3+\delta){\bf a}^*. At room temperature only the average structure was refined. Lattice parameters are a = 9.732 (3), b = 13.328 (4), c = 7.654 (3) Å, space group Pnam. The R(F) value was 0.0414 for 286 observed reflections (0.0778 for all 477 reflections). At 200 K the lattice parameters are a = 9.691 (4), b = 13.278 (5), c = 7.630 (6) Å, superspace group P:Pnam:\overline{1}ss. Main reflections and satellite reflections of first order were measured. The refinement converged at R(F) = 0.052 for 309 observed reflections (255 main reflections and 54 satellites) and 0.2971 for all reflections (1849; 695 main reflections and 1154 satellites). Amplitudes and phases of the modulation function as well as bond distances show close relationships to those observed in the incommensurately modulated phase of Rb_2ZnBr_4.

Time Series Analysis of Ultrasonic Observations of Gross Fetal Body Movements during the Last 10 Weeks of Pregnancy

1981 ◽  
Vol 3 (4) ◽  
pp. 330-341 ◽  
Author(s):  
Karen Campbell ◽  
Ian MacNeill ◽  
John Patrick
Keyword(s):  
Time Series ◽  
Spectral Analysis ◽  
Time Series Analysis ◽  
Regression Model ◽  
Body Movement ◽  
Frequency Range ◽  
Body Movements ◽  
Significant Power ◽  
First Order ◽  
Auto Regression

Thirty fetuses were observed for 24 hours and one fetus was observed for 20 hours during the last 10 weeks of gestation. Observations were made of the amount of gross fetal body movement in each successive 5 minute observation epoch, thus resulting in 30 time series of 288 observations and one time series of 240 observations. Spectral analysis of these time series demonstrated the presence of significant power in the frequency range of 0.002 to 0.0175 cpm. Application of Box-Jenkins techniques to the time series resulted in the choice of a first-order auto-regression model to fit the data. It was concluded that the incidence of episodes of gross fetal body movements were non-random and were, in fact, pseudoperiodic.

scholarly journals Structure determination and phase transition behaviour of dimethyl sulfate

2006 ◽  
Vol 62 (2) ◽  
pp. 280-286 ◽  
Author(s):  
Richard M. Ibberson ◽  
Mark T. F. Telling ◽  
Simon Parsons
Keyword(s):  
Phase Transition ◽  
Dimethyl Sulfate ◽  
Monoclinic Structure ◽  
Orthorhombic Structure ◽  
X Ray Diffraction ◽  
Coordination Environment ◽  
Space Group ◽  
X Ray ◽  
First Order ◽  
Transition Behaviour

The crystal structures of phase I and phase II of dimethyl sulfate, (CH3O)2SO2, have been determined using complementary high-resolution neutron powder and single-crystal X-ray diffraction techniques. Below its melting point of 241 K dimethyl sulfate crystallizes in an orthorhombic structure (I) in the space group Fdd2. On cooling below ∼175 K the crystal transforms to a monoclinic structure (II) in the space group I2/a. The molecule is located on a twofold axis (Z′ = 1/2) in both structures. The phase transition is of first order with strong hysteresis. The phase transition results in changes to both the intra- and the intermolecular coordination environment.

A temperature-induced order–disorder phase transition in a 4-substituted 4,2′:6′,4′′-terpyridine

2015 ◽  
Vol 71 (6) ◽  
pp. 805-813 ◽  
Author(s):  
Juan Granifo ◽  
Marleen Westermeyer ◽  
Maricel Riquelme ◽  
Rubén Gaviño ◽  
Sebastián Suárez ◽  
...  
Keyword(s):  
Phase Transition ◽  
Single Crystal ◽  
Single Molecule ◽  
Temperature Phase ◽  
Asymmetric Unit ◽  
Phase Form ◽  
Space Group ◽  
Cell Parameters ◽  
Disorder Phase Transition ◽  
First Order

Crystals of 4′-(isoquinolin-4-yl)-4,2′:6′,4′′-terpyridine (iqtp), C24H16N4, grown from an ethanol solution, undergo a reversible first-order single-crystal to single-crystal phase transition at T c in the range 273–275 K, from a disordered higher-temperature phase [form (I)] in the space group P21/c, with one single molecule in the asymmetric unit, to an ordered lower-temperature one [form (II)] in the space group P21/n, with two independent molecules in the asymmetric unit. There is a group–subgroup relationship linking (I)–(II), due to cell doubling and the disappearance of a number of symmetry operations. In addition to X-ray diffraction, the transition has been monitored by Raman spectroscopy and differential scanning calorimetry, the latter disclosing an enthalpy change of 0.72 (6) kJ mol−1. Variations of the unit-cell parameters with temperature between 170 and 293 K are presented. The evolution of diffraction spots in the vicinity of the transition temperature shows the coexistence of both phases, confirming the first-order character of the transition. Structural details of both phases are analyzed and intermolecular interactions compared in order to investigate the mechanism of the phase transition. A three-dimensional Hirshfeld surface analysis was performed to corroborate the significant changes in the intermolecular features.

scholarly journals ANALYSIS OF HIGH RESOLUTION AEROMAGNETIC DATA OF SOME PARTS OF BENUE TROUGH, NIGERIA

2020 ◽  
Vol 4 (2) ◽  
pp. 76-85
Author(s):  
Nuraddeen Usman ◽  
Ibrahim Jibril
Keyword(s):  
Spectral Analysis ◽  
Magnetic Anomalies ◽  
Aeromagnetic Data ◽  
Benue Trough ◽  
First Order ◽  
Qualitative Interpretation ◽  
Maximum Value ◽  
Magnetic Source ◽  
Analysis Technique ◽  
Basement Depth

This work is aimed to determine the depth to basement of some magnetic sources in the study area. Four aeromagnetic sheets were acquired from the Nigerian Geological Survey Agency which includes (Bajoga, 131, Gulani, 132, Gombe, 152 and Wuyo, 153). The study area covers an estimated area of about 12100km2 between latitude 90N-110N and longitude 110E-130E. The total magnetic field of the study area have been evaluated. In order to determine the basement depth, spectral analysis technique was applied. Detailed analysis of the aeromagnetic data for the study area was performed. The procedure involved in the analysis include reduction to equator to remove the effect of inclination, contouring of the total magnetic intensity, separation of the regional and residual anomalies using polynomial fitting of first order, qualitative interpretation and quantitative interpretation. The residual field of the study area composes of low magnetic anomalies reaching a minimum value of -158.6nT as observed in the northern and southern parts and high magnetic anomalies reaching a maximum value of 178.1nT as observed in the western part of the study area. The result from the spectral analysis for each block shows that the depths to the magnetic source are 5.20Km for block 1, 5.74Km for block 2, 7.59Km for block 3 and 3.56Km for block 4. The average depth to magnetic source in the study area was found to be 5.52Km. Based on the computed average sedimentary thickness obtained in this study area, hydrocarbon accumulation in the study area is feasible.

scholarly journals Evidence for differentiation in the iron-helicoidal chain in GdFe3(BO3)4

2005 ◽  
Vol 61 (5) ◽  
pp. 481-485 ◽  
Author(s):  
S. A. Klimin ◽  
D. Fausti ◽  
A. Meetsma ◽  
L. N. Bezmaternykh ◽  
P. H. M. van Loosdrecht ◽  
...  
Keyword(s):  
Low Temperature ◽  
Room Temperature ◽  
Structural Phase ◽  
Structure Study ◽  
Temperature Structure ◽  
Space Group ◽  
X Ray ◽  
First Order ◽  
New Perspective ◽  
Insight Into

A single-crystal X-ray structure study of gadolinium triiron tetraborate, GdFe_3(BO_3)_4, at room temperature and at 90 K is reported. At room temperature GdFe_3(BO_3)_4 crystallizes in a trigonal space group, R32 (No. 155), the same as found for other members of the iron borate family RFe_3(BO_3)_4. At 90 K the structure of GdFe_3(BO_3)_4 transforms to the space group P3_{1}21 (No. 152). The low-temperature structure determination gives new insight into the weakly first-order structural phase transition at 156 K and into the related Raman phonon anomalies. The presence of two inequivalent iron chains in the low-temperature structure provides a new perspective on the interpretation of the low-temperature magnetic properties.

New polymorphism for BaTi(IO3)6 with two polymorphs crystallizing in the same space group

2020 ◽  
Vol 49 (25) ◽  
pp. 8443-8447 ◽  
Author(s):  
Zhen Qian ◽  
Hongping Wu ◽  
Hongwei Yu ◽  
Zhanggui Hu ◽  
Jiyang Wang ◽  
...  
Keyword(s):  
Phase Transition ◽  
Order Phase Transition ◽  
Powder Xrd ◽  
Space Group ◽  
First Order ◽  
First Order Phase Transition ◽  
First Order Phase

New polymorphic α- and β-BaTi(IO3)6 have been synthesized. They crystallize in the same space group and exhibit similar structures, but the powder XRD and crystal morphologies show their phase transition belongs to the first-order phase transition.

Group-theoretical analysis of octahedral tilting in ferroelectric perovskites

2002 ◽  
Vol 58 (6) ◽  
pp. 934-938 ◽  
Author(s):  
Harold T. Stokes ◽  
Erich H. Kisi ◽  
Dorian M. Hatch ◽  
Christopher J. Howard
Keyword(s):  
Phase Transitions ◽  
Theoretical Analysis ◽  
Landau Theory ◽  
Group Symmetry ◽  
Theoretical Methods ◽  
Space Group Symmetry ◽  
Space Group ◽  
First Order ◽  
Octahedral Tilting ◽  
Group Theoretical Analysis

Group-theoretical methods are used to analyze perovskite structures where both ferroelectric cation displacements and simple tilting of octahedral units are present. This results in a list of 40 different structures, each with a unique space-group symmetry. The list is compared with that of Aleksandrov & Bartolomé [Phase Transit. (2001), 74, 255–335] and a number of differences are found. The group–subgroup relationships between the structures are also determined, along with an indication of those phase transitions that must be first order by Landau theory.

scholarly journals Spectral analysis of discrete dirac equation with generalized eigenparameter in boundary condition

Filomat ◽  
2019 ◽  
Vol 33 (18) ◽  
pp. 6039-6054 ◽  
Author(s):  
Turhan Koprubasi ◽  
Ram Mohapatra
Keyword(s):  
Boundary Condition ◽  
Spectral Analysis ◽  
Dirac Equation ◽  
Dirac Operator ◽  
Spectral Properties ◽  
Difference Operators ◽  
Spectral Singularities ◽  
First Order ◽  
Complex Sequences

Let L denote the discrete Dirac operator generated in ?2 (N,C2) by the non-selfadjoint difference operators of first order (an+1y(2)n+1 + bny(2)n + pny(1)n = ?y(1)n, an-1y(1)n-1 + bny(1)n + qny(2)n = ?y(2)n, n ? N, (0.1) with boundary condition Xp k=0 (y(2)1?k + y(1)0 ?k)?k=0, (0.2) where (an), (bn), (pn) and (qn), n ? N are complex sequences, ?i; ?i ? C, i = 0, 1, 2,..., p and ? is a eigenparameter. We discuss the spectral properties of L and we investigate the properties of the spectrum and the principal vectors corresponding to the spectral singularities of L, if ?? n=1 |n|(|1-an| + |1+bn| + |pn| + |qn|) < ? holds.

General Representations of Polynomial Elastic Fields

2012 ◽  
Vol 79 (2) ◽  
Author(s):  
Min-Zhong Wang ◽  
Bai-Xiang Xu ◽  
Ying-Tao Zhao
Keyword(s):  
Homogeneous Polynomial ◽  
Energy Functional ◽  
Stress Fields ◽  
Complementary Energy ◽  
Third Order ◽  
Elastic Fields ◽  
First Order ◽  
Stress Functions ◽  
3D Elasticity ◽  
2D And 3D

For hybrid finite elements based, for example, on complementary energy functional, polynomial trial functions of stress fields are required. Systematic schemes are given for the 2D and 3D elasticity, respectively. For 2D problems, the paper shows that there are maximal four independent polynomials for the nth order homogeneous polynomial Airy stress functions: two for the first order, three for the second order, and four for the nth order (n not less than 3). For 3D problems, there are 3(2n + 1) independent polynomials for the nth order homogeneous polynomial displacement. The corresponding stress field can be given directly. As examples, explicit expressions of the corresponding independent polynomials are listed: up to the tenth order for the 2D case and up to the third order for the 3D case.

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