Nucleating heterogeneities and glass formation

The kinetic treatment of glass formation is extended by the introduction of continuous cooling (CT) curves to estimate the cooling rates required to form glasses of various materials. The CT curves may be constructed from isothermal time-temperature-transformation curves following the approach originally suggested by Grange and Kiefer. The modified analysis is used to evaluate the effects of nucleating heterogeneities on glass formation. It is found that for the concentrations of such heterogeneities found in most liquids, those characterized by contact angles greater than about 100° have a negligible effect on the cooling rate required to form glasses. Heterogeneities with smaller contact angles, can, however, have a significant effect on glass formation, with the critical cooling rate increasing with decreasing contact angle. The effects on glass formation of changes in the contact angle of nucleating heterogeneities are also compared with the effects of changes in the thermodynamic barrier to nucleation (in the crystal-liquid surface energy).     

Pressure dependence of the elastic moduli of glasses in the K2OSiO2 system

The elastic moduli and their variation with pressure have been determined for three glass compositions in the K₂OSiO₂ glass system. The results may be summarized:

     

33.

Gensynthese     

Joachim W. Engels  Eugen Uhlmann 《Angewandte Chemie (Weinheim an der Bergstrasse, Germany)》1989,101(6):733-752

     

34.

A kinetic treatment of glass formation. VIII: Critical cooling rates for Na₂OSiO₂ and K₂OSiO₂ glasses     

Chih-Yao Fang  H. Yinnon  D.R. Uhlmann 《Journal of Non》1983,57(3):465-471

The critical cooling rates required to form glass have been measured for Na₂OSiO₂ compositions containing 15.4, 20.6, 29.9 and 34.0 wt% Na₂O and for K₂OSiO₂ compositions containing 15.3, 21.7, 34.3, 41.8 and 43.9 wt% K₂O. Pronounced minima in critical cooling rate are observed in the ranges about 25 wt% Na₂O and 33 wt% K₂O. The locations of these minima correlate with regions of low liquidus temperatures (near eutectics) in the phase diagrams.Calculations of critical cooling rates have been carried out using the analysis of crystallization statistics and the simplified model of glass formation. In both cases, the models predict well the measured critical cooling rates and their variation with composition.     

35.

Light intensity distribution in conical refraction     

G. A. Uhlmann 《纯数学与应用数学通讯》1982,35(1):69-80

     

36.

Lagrangian Intersection and the Cauchy Problem     

R. B. Melrose  G. A. Uhlmann 《纯数学与应用数学通讯》1979,32(4):483-519

     

37.

Structure of glassy polymers. VII. Small-angle X-ray scattering from epoxy resins     

R. J. Matyi  D. R. Uhlmann  J. A. Koutsky 《Journal of Polymer Science.Polymer Physics》1980,18(5):1053-1063

The small-angle x-ray scattering (SAXS) from an Epon 812 and two Epon 828 (one amine-cured and one anhydride-cured) epoxy resins has been measured using a Bonse-Hart system. The data cover the angular range (2θ) between 20 sec and 60 min. After correction for absorption, background and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a previously studied polycarbonate sample. The corrected absolute intensity decreases strongly with increasing angle between 20 sec and 2 min, decreases more gradually between 2 and 20–30 min, and reaches a nearly constant asymptotic value at larger angles. The magnitude of the intensity in the constant-intensity region is close to the value predicted by thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at angles smaller than 20–30 min is associated with heterogeneities in the cured resins. These heterogeneities cover a range of sizes in all samples, from less than 100 Å to more than 1000 Å, with the most frequently occurring size in the range 100–200 Å.     

38.

A problem relating to positive linear maps on matrix algebras     

P.M. Alberti  A. Uhlmann 《Reports on Mathematical Physics》1980,18(2):163-176

In this paper we investigate conditions under which two finite-dimensional density matrices can be transformed simultaneously into two other ones by means of a positive linear map which maps density matrices into density matrices. The result of this paper provides a complete answer in case of the matrix algebra of two-by-two matrices.     

39.

Contribution à l'étude d'un produit de β-hydroxyéthylation du rutoside. Partie 1. Isolement et identification des constituants majeurs par chromatographie sur papier     

P. Courbat  J. Favre  R. Guerne  G. Uhlmann 《Helvetica chimica acta》1966,49(3):1203-1211

     

40.

Inverting the local geodesic X-ray transform on tensors     

Plamen Stefanov  Gunther Uhlmann  András Vasy 《Journal d'Analyse Mathématique》2018,136(1):151-208

We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n ≥ 3. We also present an inversion formula. Under the condition that the manifold can be foliated with a continuous family of strictly convex surfaces, we prove a global result which also implies a lens rigidity result near such a metric. The class of manifolds satisfying the foliation condition includes manifolds with no focal points, and does not exclude existence of conjugate points.     

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Property/Composition	0.15K2O–0.85SiO2	0.25K2O–0.75SiO2	0.33K2O–0.67SiO2
Shear modulus $\text{G(}\text{kb}\text{)}$	266	241	231
Bulk modulus $\text{K}{}_{\mathrm{<mtext>s</mtext>}}\text{(}\text{kb}\text{)}$	310	283	273
Young's modulus $\text{E(}\text{kb}\text{)}$	620	564	540
($\text{?K}{}_{\mathrm{<mtext>s</mtext>}}\text{/?P)}{}_{\mathrm{<mtext>500\; </mtext><mtext>K</mtext>}}$	?5.1	?4.4	?3.9
($\text{?G/?P)}{}_{\mathrm{<mtext>500\; </mtext><mtext>K</mtext>}}$	?2.8	?2.6	?2.5
Poisson's ratio σ	0.167	0.168	0.170
($\text{?σ/?P) (}\text{x}\text{10}{}^{\mathrm{?3}}$)
(kb?1)	?1.5	?1.2	?0.95

A kinetic treatment of glass formation. VIII: Critical cooling rates for Na2OSiO2 and K2OSiO2 glasses

The critical cooling rates required to form glass have been measured for Na₂OSiO₂ compositions containing 15.4, 20.6, 29.9 and 34.0 wt% Na₂O and for K₂OSiO₂ compositions containing 15.3, 21.7, 34.3, 41.8 and 43.9 wt% K₂O. Pronounced minima in critical cooling rate are observed in the ranges about 25 wt% Na₂O and 33 wt% K₂O. The locations of these minima correlate with regions of low liquidus temperatures (near eutectics) in the phase diagrams.Calculations of critical cooling rates have been carried out using the analysis of crystallization statistics and the simplified model of glass formation. In both cases, the models predict well the measured critical cooling rates and their variation with composition.     

Structure of glassy polymers. VII. Small-angle X-ray scattering from epoxy resins

The small-angle x-ray scattering (SAXS) from an Epon 812 and two Epon 828 (one amine-cured and one anhydride-cured) epoxy resins has been measured using a Bonse-Hart system. The data cover the angular range (2θ) between 20 sec and 60 min. After correction for absorption, background and vertical beam divergence, they have been placed on an absolute basis by comparison with the scattering from a previously studied polycarbonate sample. The corrected absolute intensity decreases strongly with increasing angle between 20 sec and 2 min, decreases more gradually between 2 and 20–30 min, and reaches a nearly constant asymptotic value at larger angles. The magnitude of the intensity in the constant-intensity region is close to the value predicted by thermodynamic fluctuation theory for fluids applied at the glass transition temperature. The increase in intensity at angles smaller than 20–30 min is associated with heterogeneities in the cured resins. These heterogeneities cover a range of sizes in all samples, from less than 100 Å to more than 1000 Å, with the most frequently occurring size in the range 100–200 Å.     

A problem relating to positive linear maps on matrix algebras

In this paper we investigate conditions under which two finite-dimensional density matrices can be transformed simultaneously into two other ones by means of a positive linear map which maps density matrices into density matrices. The result of this paper provides a complete answer in case of the matrix algebra of two-by-two matrices.     

Inverting the local geodesic X-ray transform on tensors

We prove the local invertibility, up to potential fields, and stability of the geodesic X-ray transform on tensor fields of order 1 and 2 near a strictly convex boundary point, on manifolds with boundary of dimension n ≥ 3. We also present an inversion formula. Under the condition that the manifold can be foliated with a continuous family of strictly convex surfaces, we prove a global result which also implies a lens rigidity result near such a metric. The class of manifolds satisfying the foliation condition includes manifolds with no focal points, and does not exclude existence of conjugate points.