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  • 1
    Electronic Resource
    Electronic Resource
    X-ray diffraction study of the orientational order/disorder transition in NaNO3: Evidence for order parameter coupling (1989)
    Springer
    Physics and chemistry of minerals 16 (1989), S. 790-798 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The orientational ordering transition R $$R\bar 3m - R\bar 3c$$ in NaNO3 near 552 K has been investigated using x-ray diffraction techniques. NaNO3 is a model system for CaCO3 and other minerals with orientational disorder of triangular molecules in a simple NaCl-type matrix. The temperature evolution of the integrated intensities of the superlattice reflection $$\bar 1$$ 23 and the fundamental reflection 110 are discussed in terms of Landau theory of two coupled order parameters. It is shown that the known phenomenological critical exponent (Poon and Salje 1988) and the anomalous thermal expansion at T 〉 T tr (Reeder et al. 1988) can be understood as the result of a Z point instability which mainly describes the NO 3 - disorder, and a second order parameter linked with the spontaneous strain of this phase transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00209703
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  • 2
    Electronic Resource
    Electronic Resource
    Spontaneous strain at the structural phase transition in NaNO3 (1988)
    Springer
    Physics and chemistry of minerals 15 (1988), S. 605-611 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The temperature dependence of the hexagonal c unit cell parameter of high-purity NaNO3 shows an anomaly at 553 K corresponding to the orientational ordering transition. The a unit cell parameter is barely influenced by the transition. The single component spontaneous strain for this zone boundary instability is large (∼55×10−3 at 295 K), and couples quadratically with the order parameter. The critical exponent β is found to have the value 0.22 ± 0.01, which differs from that expected in the classical case. Below ca 450 K, crossover to tricritical behaviour is observed (β=1/4). The temperature evolution of the macroscopic order parameter as revealed by the temperature dependence of the spontaneous strain follows a tricritical behaviour between 70 K and 450 K. At temperatures below 70 K order parameter saturation is observed. Combined with recent data from specific heat measurements, the critical exponents suggest that the three-dimensional, three-states Potts model may describe the transition. Precursor spontaneous strain above T c is consistent with local ordering and may result from fluctuations associated with an antiordered NO3 group pair configuration.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00311033
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  • 3
    Electronic Resource
    Electronic Resource
    Thermodynamics of plagioclase III: Spontaneous strain at the $$I\overline 1 - P\overline 1$$ phase transition in Ca-rich plagioclase (1988)
    Springer
    Physics and chemistry of minerals 16 (1988), S. 157-163 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The lattice parameters of anorthites An98Ab2 and An100 have been measured from 22 to 1100 K. The spontaneous strain arising from the $$I\overline 1 - P\overline 1$$ displacive transition in An98 follows second order Landau behaviour. The spontaneous strain (ɛ s) couples quadratically to the order parameter (Q 0) with ɛ s∝Q 02∝(T c * −T) and T c * =530 K in An98. This is in contrast to the tricritical behaviour observed in pure anorthite. These observations are consistent with a Landau model for the free energy of Ca-rich plagioclases in which Al/Si order and Na content renormalize the fourth order coefficient.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00203199
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  • 4
    Electronic Resource
    Electronic Resource
    Microscopic dynamic and macroscopic thermodynamic character of the $$I\bar 1 - P\bar 1$$ phase transition in anorthite (1992)
    Springer
    Physics and chemistry of minerals 18 (1992), S. 526-533 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The dynamic character of the $$I\bar 1 - P\bar 1$$ phase transition in anorthite from Monte Somma has been studied by high-temperature hard mode infrared spectroscopy. The mean local order parameter, as revealed by the temperature evolution of the frequencies of absorption bands between 540 and 620 cm-1, follows classical second-order Landau behaviour with a critical exponent β = 1.. There is no observable first-order step. Anomalous line broadening of the 582 cm-1 band indicates that dynamic fluctuations with a relaxation time τ ≈ 10−10 s exist over a limited temperature interval of approximately 150 K about Tc, and decay rapidly as T becomes greater than Tc. Previous order-disorder models of the high-temperature $$I\bar 1$$ phase are not supported by these results. The Ca-flip motions, which we link to the line broadening, stabilize the driving soft mode of the transition. These flip motion fluctuations do not give rise to departures from the classical Landau theory because of the essential co-elastic nature of the phase transition. In the light of these results the $$I\bar 1 - P\bar 1$$ structural instability can be described as an essentially displacive transition.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00205269
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  • 5
    Electronic Resource
    Electronic Resource
    Structural phase transition in titanite, CaTiSiO5: A ramanspectroscopic study (1993)
    Springer
    Physics and chemistry of minerals 19 (1993), S. 502-506 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The structural phase transition in titanite is correlated with a strong temperature dependence of Raman scattering cross sections and, to a somewhat lesser extent, with shifts of the phonon frequencies. Their quantitative temperature evolution in the low-symmetry phase (P21/a) is compatible with a nearly 2D Ising behaviour with β≈0.12 and T c = 497 K. At temperatures above 860 K, the phonon signals agree with A 2/a symmetry but not in the temperature interval between 497 K and 860 K. In this temperature range new structural states give rise to additional phonon signals. A model based on mobile APBs between slabs of P21/a material, first proposed by van Heurck et al. (1991), is in qualitative agreement with our experimental observations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00203191
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  • 6
    Electronic Resource
    Electronic Resource
    Structural states of natural potassium feldspar: An infrared spectroscopic study (1989)
    Springer
    Physics and chemistry of minerals 16 (1989), S. 649-658 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Natural samples of K-feldspar representing various states of Al, Si order were characterised using X-ray methods, transmission electron microscopy, and Fourier transform infrared spectroscopy. Line profiles of infrared absorption bands were observed to show strong correlation with the degree of Al, Si order present. In particular, the absorption frequencies of the 540 cm−1 and 640 cm−1 bands were seen to vary by ca. 10 cm−1 between sanidine and microcline, with modulated samples respresenting intermediate behaviour. Linewidths of these modes also decrease by ca. 50% in this series. The experimental results are discussed within the framework of Hard Mode Infrared Spectroscopy (HMIS), and it is shown that the absorption frequencies vary with the short range order parameter τ = (4t1-1)2 and the symmetry breaking order parameter describing Al, Si order, Q od=(t1 0−t1 m)/Q od=(t1 0+t1 m), where t1 is the average Al occupancy on the T1 sites and t1 o and t1 m are the individual site occupancies of the T1 o and T1 m sites, respectively. The structural state of orthoclase is characterised by strain-induced modulations with large spatial variations of the modulation wavelength. No such modulations were observed in the degree of local Al, Si order. Sanidine shows mode hardening in excess of the extrapolated effect of symmetry breaking Al, Si order, which is presumably related to nonsymmetry breaking ordering between T1 and T2 sites and/or as yet unobserved short range order of the symmetry breaking ordering scheme. The possibility of an additional phase transition in K-feldspar at temperatures above 1300 K is discussed.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00223313
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  • 7
    Electronic Resource
    Electronic Resource
    Phase transitions in leucite: Order parameter behaviour and the Landau potential deduced from Raman spectroscopy and birefringence studies (1990)
    Springer
    Physics and chemistry of minerals 17 (1990), S. 259-265 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Hard mode Raman Spectroscopy and optical birefringence studies have been used to evaluate the temperature behaviour of order parameters for the cubictetragonal phase transition in leucite. There is a strong temperature-dependence of Raman line frequencies near 498 cm−1 and 529 cm−1, and the optical birefringence decreases towards zero on heating. Above the transition temperature leucite still shows slight birefringence, which correlates with the persistence of the 200 X-ray reflexion at these temperatures, and is not compatible with the ideal cubic symmetry. Quantitative observations of the temperature evolution of Raman line-frequencies and the birefringence are consistent with an order parameter showing T 1g symmetry, and a nearly-tricritical phase transition behaviour. The results of earlier X-ray and DSC studies imply the operation of an additional order parameter, with E g symmetry; this is observed, but its influence on the transition behaviour is significant only at temperatures close to T c. The two order parameters are related via linear-quadratic or biquadratic coupling. We develop the form of the Landau Potential for leucite — including both order parameters and their couplings — to discuss the present observations and previous structural data.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00201458
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  • 8
    Electronic Resource
    Electronic Resource
    Kinetic rate laws as derived from order parameter theory I: Theoretical concepts (1988)
    Springer
    Physics and chemistry of minerals 15 (1988), S. 336-348 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract A theoretical concept is outlined, which links the kinetics of structural transformations with thermodynamic theories of structural phase transitions. Starting from Landau theory and Markovian processes, the general rate laws for crystals with long correlation lengths are derived. The rate laws in Ginzburg-Landau theory are $$1{\text{n }}\Delta Q - 1{\text{n }}f\left( Q \right) \propto - \frac{t}{\tau }{\text{ for }}T \ll T_c {\text{ and }}T \gg T_c$$ and Q 2∝ for T ≈ T c . The physical meaning of the time constant τ and the correction term f(Q) are explained. Fluctuations of the order parameter lead to damping behaviour with explicit dependence on the wavelength of the fluctuation wave and modulation-dependent variations of the lattice strain. Lattice relaxations and activation processes are discussed. Typical rate laws are found to follow $$\begin{gathered} \ln \Delta Q = rln\Delta t, \hfill \\ ln\frac{Q}{Q} + \frac{{1\varepsilon }}{{2k_B T}}\left( {Q^2 - Q_0^2 } \right) = \frac{{\Delta t}}{{\tau *}} \hfill \\ \end{gathered} $$ which leads for short time intervals to a linear rate law $$\Delta Q \propto \Delta t$$ It is shown that linear terms in the Landau potential are equivalent to a logarithmic decay of the excess entropy ΔS ∝ ln Δt which is also expected to be the dominant rate law in field-induced pseudo-spin glasses: $$\Delta Q \propto 1{\text{n }}\Delta t{\text{ and }}1{\text{n}}\left( {\Delta {\text{Q}} \cdot \Delta {\text{t}}} \right) = A{\text{ }}\Delta t + B$$ Fluctuations lead to spatially heterogeneous distributions of the order parameter. A two phase field is found in this case where the nucleation energy is overcome by fluctuation processes. Random fields, arising, for example, from lattice imperfections, lead also to spacially inhomogeneous material. The dominant microstructure is the lattice modulation mostly in the form of a cross hatched pattern (tweed) but also in the form of incommensurate modulations.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00311038
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  • 9
    Electronic Resource
    Electronic Resource
    Structural states of Mg-cordierite I: Order parameters from synchrotron X-ray and NMR data (1987)
    Springer
    Physics and chemistry of minerals 14 (1987), S. 446-454 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract The hexagonal to orthorhombic phase transition in synthetic Mg-cordierite has been studied by (i) measuring the spontaneous strain associated with the transition using Synchrotron X-ray powder diffraction and (ii) measuring the degree of Al, Si order in terms of the number of Al-O-Al bonds per formula unit using solid state NMR spectroscopy. This defines the two order parametersQ andQ od respectively, and their relationship as a function of annealing temperature and time is used to define the structural states of cordierite during the ordering sequence. The formation of modulated hexagonal cordierite within which a high degree of Al, Si order can be attained, results in a strongly non-linear relationship betweenQ andQ od .The transition from modulated to orthorhombic cordierite is strongly first-order under all temperature conditions studied and involves a large step inQ, whileQ od changes continuously throughout the ordering sequence with no marked discontinuity at the phase transition. The lattice distortion, traditionally defined in cordierite by the Δ index provides no full information on the degree of Al, Si order in anhydrous Mg-cordierite, and both order parameters must be used to define its structural state. Transmission electron microscopy has been used to study the mechanism of the transformation from hexagonal to modulated to orthorhombic cordierite.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00628822
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  • 10
    Electronic Resource
    Electronic Resource
    Structural states of Mg-cordierite II: Landau theory (1987)
    Springer
    Physics and chemistry of minerals 14 (1987), S. 455-460 
    Details
    ISSN: 1432-2021
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology , Geosciences , Physics
    Notes: Abstract Mg-cordierite undergoes a ferroelestic phase transitionP6/mmc-Cccm. The order parameterQ is proportional to the spontaneous strain as reflected by changes of the lattice parametersa andb during the phase transition. The order parameter,Q od, which describes the Al, Si ordering, isnot directly involved in the phase transition and only “triggers” the structural collapse. Landau theory predicts that cordierite can exist in stable or metastable states with hexagonal, orthorhombic or monoclinic symmetry. Hexagonal cordierite can develop modulated structures which have been found by Putnis et al. (1987). The phase transition is predicted to be accompanied by singularities of the elastic constantsC 11,C 22 andC 12 leading to an elastic softening of the crystal structure.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00628823
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