Thermodynamical Behaviour of Quartz Around the Transitions Between α, Incommensurate and β Phases

1983 ◽  
Vol 21 ◽  
Author(s):  
G. Dolino ◽  
J.P. Bachheimer
Keyword(s):  
Phase Transition ◽  
Heat Capacity ◽  
Order Parameter ◽  
Landau Theory ◽  
Microscopic Level ◽  
Incommensurate Phase ◽  
Small Temperature ◽  
Thermal Expansion Coefficients ◽  
Α Phase ◽  
Expansion Coefficients

ABSTRACTRecently an intermediate incommensurate phase has been found around 846 K in a small temperature range of 1.3 K between the usual α and β phases of quartz. In the neighborhood of these transitions most physical properties show drastic variations which has remained a puzzle. We shall present some measurements of the heat capacity Cp and of thermal expansion coefficients αi which present very large variations in the incommensurate phase. These divergences can be related by Pippard-Garland relations in the 3 phases. Furthermore in the low temperature α phase this result can be explained by the existence of a macroscopic order parameter η related to SiO4 tetrahedra, and varying as predicted by the Landau theory of 1st order phase transition. While in the high temperature phases (β and incommensurate) η vanishes, it takes a finite value in α phase, increasing continuously upon further cooling. However at the microscopic level, the discontinuity is reduced by the existence of the incommensurate phase, which corresponds probably to modulated tilting of SiO4 tetrahedra.

Influence of Magnetoelastic Anisotropy on Properties of Nanostructured Microwires

2013 ◽  
Vol 646 ◽  
pp. 59-66 ◽  
Author(s):  
Arcady Zhukov ◽  
Margarita Churyukanova ◽  
Lorena Gonzalez-Legarreta ◽  
Ahmed Talaat ◽  
Valentina Zhukova ◽  
...  
Keyword(s):  
Heat Capacity ◽  
Hysteresis Loops ◽  
Magnetic Behaviour ◽  
Soft Magnetic ◽  
Magnetoelastic Anisotropy ◽  
Thermal Expansion Coefficients ◽  
Magnetoelastic Energy ◽  
Expansion Coefficients ◽  
The Difference ◽  
Magneto Resistance

We studied the effect ofthe magnetoelastic ansitropy on properties of nanostructured glass-coated microwires with soft magnetic behaviour (Finemet-type microwires of Fe70.8Cu1Nb3.1Si14.5B10.6, Fe71.8Cu1Nb3.1Si15B9.1 and Fe73.8Cu1Nb3.1Si13B9.1 compositions) and with granular structure (Cu based Co-Cu microwires). The magnetoelastic energy originated from the difference in thermal expansion coefficients of the glass and metallic alloy during the microwires fabrication, affected the hysteresis loops, coercivity and heat capacity of Finemet-type microwires. Hysteresis loops of all as-prepared microwires showed rectangular shape, typical for Fe-rich microwires. As expected, coercivity, HC, of as-prepared microwires increases with decreasing of the ratio ρ defined as the ratio between the metallic nucleus diameter, d to total microwire diameter, D. On the other hand we observed change of heat capacity in microwires with different ratio ρ. In the case of Co-Cu microwires ρ- ratio affected the structure and the giant magneto-resistance of obtained microwires.

Test of Critical Behaviour Through the Order Parameter-Entropy Relation in the Normal-Incommensurate Phase Transition of Rb 2 ZnCl 4

2002 ◽  
Vol 270 (1) ◽  
pp. 351-356
Author(s):  
J. M. Martín-Olalla ◽  
M. C. Gallardo ◽  
S. Ramos ◽  
J. M. Perez-Mato ◽  
E. K. H. Salje
Keyword(s):  
Phase Transition ◽  
Order Parameter ◽  
Incommensurate Phase ◽  
Critical Behaviour ◽  
Entropy Relation

Static and dynamical elastic behavior of Lu5Ir4Si10 around its first-order structural phase transition

2020 ◽  
Vol 34 (12) ◽  
pp. 2050116
Author(s):  
M. Saint-Paul ◽  
C. Opagiste ◽  
C. Guttin
Keyword(s):  
Phase Transition ◽  
Theoretical Approach ◽  
Order Parameter ◽  
Landau Theory ◽  
Structural Phase ◽  
Elastic Stiffness ◽  
Elastic Behavior ◽  
Velocity Measurements ◽  
First Order ◽  
First Order Transition

Ultrasonic velocity measurements could be performed on a good quality single crystal of [Formula: see text] around its transition around 80 K. The behavior of the stiffness components demonstrates a first-order transition. The temperature dependence of the longitudinal elastic stiffness components [Formula: see text] and [Formula: see text] can be analyzed by the classical Landau theory and assuming a stricter coupling between the strain and the order parameter. A theoretical approach and experimental results are discussed.

Assessment of phase transition and thermal expansion coefficients by means of secondary multiple reflections of Renninger scans

2019 ◽  
Vol 52 (6) ◽  
pp. 1271-1279
Author(s):  
Adenilson O. dos Santos ◽  
Rossano Lang ◽  
José M. Sasaki ◽  
Lisandro P. Cardoso
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Structural Phase ◽  
Angular Position ◽  
Lattice Parameters ◽  
Rochelle Salt ◽  
Multiple Reflections ◽  
Multiple Diffraction ◽  
Thermal Expansion Coefficients ◽  
Expansion Coefficients

This paper reports the successful extension of the basis of the X-ray multiple diffraction phenomenon in the assessment of structural phase transitions and the determination of thermal expansion coefficients along three crystallographic directions, using synchrotron radiation Renninger scans. Suitable simultaneous four-beam cases have accurately resolved the lattice-parameter variation in a nearly perfect single-crystal Rochelle salt using a high-stability temperature apparatus. Secondary reflections observed in the Renninger patterns, chosen by their sensitivity to the shifts in angular position as a function of temperature, have allowed the detection of a monoclinic to orthorhombic phase transition, as well as subtle expansions of all the basic lattice parameters, i.e. without having to carry out measurements on each crystal axis. The thermal expansion coefficients have been estimated from the linear fit of the temperature dependence of the lattice parameters, and are in agreement with those reported in the literature.

Phase Transition Studies in PMBAB and PEBAB

1984 ◽  
Vol 39 (7) ◽  
pp. 696-699 ◽  
Author(s):  
V. G. K. M. Pisipati ◽  
N. V. S. Rao
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Molar Volume ◽  
Ultrasonic Velocity ◽  
Adiabatic Compressibility ◽  
First Order ◽  
Thermal Expansion Coefficients ◽  
Methylene Unit ◽  
Expansion Coefficients ◽  
Transition Studies

The variation of density and ultrasonic velocity with temperature in N-(p-methoxybenzylidene)- p-aminobenzonitrile (PMBAB) and N-(p-ethoxybenzylidene)-p-aminobenzonitrile (PEBAB) are presented. The density jumps and thermal expansion coefficients suggest the nematic-isotropic transition of both compounds to be of first order. The adiabatic compressibility βad, molar sound velocity Rn and molar compressibility Aw are computed. The contribution of a methylene unit to the molar volume is found to be higher than literature values. The anomalous ultrasonic velocity dip at the nematic-isotropic transition for both compounds is found to be high; the value is many times those found for other nematic-isotropic or nematicsmectic A transitions.

Dynamic Ginzburg-Landau Theory for the Liquid-Solid Phase Transition

1980 ◽  
Vol 35 (1) ◽  
pp. 69-74
Author(s):  
S. Hess
Keyword(s):  
Phase Transition ◽  
Entropy Production ◽  
Order Parameter ◽  
Landau Theory ◽  
Constitutive Law ◽  
Relaxation Equation ◽  
Ginzburg Landau ◽  
Specific Internal Energy ◽  
Nonlinear Relaxation ◽  
Anisotropy Tensor

Abstract The anisotropy of the probability distribution function for the unit vector joining two nearest neighbour atoms is characterized by tensorial order parameters. For cubic symmetry, the most relevant tensor is of rank 4. Starting from an ansatz for the dependence of the (specific) internal energy, volume and entropy; the entropy production is calculated which is caused by a temporial change of the 4-th rank anisotropy tensor. A constitutive law which guarantees that the entropy production is positive leads to a nonlinear relaxation equation. It shows the features typical for a dynamic Ginzburg-Landau theory. The linearized version of the relaxation equation contains an effective relaxation time and a correlation length which exhibit a temperature dependence typical for a mean field theory. For a special case where the anisotropy tensor can be characterized by a scalar order parameter, the nonlinear relaxation equation is studied in some detail. Its stationary and spatially homogeneous solutions are zero and nonzero values for the order parameter depending on whether the temperature T is larger or smaller than the transition temperature. The unordered phase corresponds to a liquid state, the ordered phase to a simple or body centered cubic crystal. The phase transition is of 1st order. There exist also metastable states.

scholarly journals Investigation of the changes in hydrogen bonding accompanying the structural reorganization at 103 K in ammonium iodate

2019 ◽  
Vol 75 (2) ◽  
pp. 152-159
Author(s):  
W. G. Marshall ◽  
R. H. Jones ◽  
K. S. Knight ◽  
C. R. Pulham ◽  
R. I. Smith
Keyword(s):  
Phase Transition ◽  
Thermal Expansion ◽  
Hydrogen Bonding ◽  
Structural Features ◽  
Neutron Powder Diffraction ◽  
Halogen Bonds ◽  
Structural Reorganization ◽  
Thermal Expansion Coefficients ◽  
Per Se ◽  
Expansion Coefficients

Neutron powder diffraction has been used to observe the changes in hydrogen bonding that occur as a function of temperature in ND4IO3 and, thus, determine the structural features that occur during the low-temperature (103 K) phase transition. It is shown that in the deuterated material the change is not a phase change per se but rather a structural reorganization in which the hydrogen bonding becomes firmly locked in at the phase transition temperature, and stays in this configuration upon further cooling to 4.2 K. In addition, both the differences and changes in the axial thermal expansion coefficients in the region 100–290 K can be explained by the changes involving both the hydrogen bonding and the secondary I...O halogen bonds.

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