On the stability of crystal lattices. IV

In order to explain the phenomena of melting, tensile strength, etc., we have to investigate the stability of crystals for finite deformations, for which deviations from Hooke's law occur. Although these deviations are in most cases of an irreversible character, it is necessary, for a systematic study, to develop mathematical methods for treating the mechanical (reversible) case of a highly strained crystal lattice, where terms of higher order than the second in the deformation energy must be taken into account.

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On the stability of crystal lattices. I

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100017138 ◽

1940 ◽

Vol 36 (2) ◽

pp. 160-172 ◽

Cited By ~ 591

Author(s):

Max Born

Keyword(s):

Positive Definiteness ◽

Deformation Energy ◽

The Body ◽

Simple Explanation ◽

Crystal Lattices ◽

Simple Lattice ◽

Macroscopic Deformation ◽

The Face ◽

The Stability ◽

Central Forces

The stability of lattices is discussed from the standpoint of the method of small vibrations. It is shown that it is not necessary to determine the whole vibrational spectrum, but only its long wave part. The stability conditions are nothing but the positive definiteness of the macroscopic deformation energy, and can be expressed in the form of inequalities for the elastic constants. A new method is explained for calculating these as lattice sums, and this method is applied to the three monatomic lattice types assuming central forces. In this way one obtains a simple explanation of the fact that the face-centred lattice is stable, whereas the simple lattice is always unstable and the body-centred also except for small exponents of the attractive forces. It is indicated that this method might be used for an improvement of the, at present, rather unsatisfactory theory of strength.

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The stability of crystal lattices. III

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100017503 ◽

1940 ◽

Vol 36 (4) ◽

pp. 454-465 ◽

Cited By ~ 76

Author(s):

M. Born ◽

R. Fürth

Keyword(s):

Tensile Strength ◽

Energy Density ◽

Numerical Calculations ◽

Stability Conditions ◽

Equilibrium Conditions ◽

Crystal Lattices ◽

Cubic Lattice ◽

Special Assumption ◽

The Face ◽

The Stability

The energy density of a cubic lattice, homogeneously deformed by a force acting in the direction of one axis, is calculated, and the equilibrium conditions and the stability conditions for any arbitrary small additional deformations are derived. A special assumption is made as to the law of force between the atoms, and the numerical calculations are performed for the face-centred lattice. In this way the strain as a function of the deformation is calculated and, from the stability conditions, the tensile strength is determined. The results are not in agreement with the experimental facts, and the possible reasons for this disagreement are discussed.

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The thermodynamics of crystal lattices

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100017746 ◽

1943 ◽

Vol 39 (2) ◽

pp. 100-103 ◽

Cited By ~ 18

Author(s):

Max Born

Keyword(s):

Melting Point ◽

Crystal Lattice ◽

Temperature Dependence ◽

Elastic Constants ◽

Original Problem ◽

Lattice Stability ◽

Chemical Physics ◽

Crystal Lattices ◽

Fundamental Difficulty ◽

The Stability

In 1939 I published a paper in the American Journal of Chemical Physics (Born(1)) in which I tried to develop the thermodynamics of a crystal lattice in the domain of classical (Boltzmann) statistics. Definite formulae and numerical tables for the temperature dependence of the elastic constants up to the melting point were obtained; nevertheless the work was unsatisfactory not only because the approximations used were rough and their accuracy not known, but because a fundamental difficulty with respect to lattice stability turned up. This led to a series of investigations by my collaborators and myself, published in these Proceedings under the title ‘On the stability of crystal lattices’ (quoted here as S I to SIX), by which the difficulty mentioned has been removed. It is now possible to return to the original problem, to which the present series of papers is devoted. In this introduction I wish to recapitulate the whole situation and to explain the plan of the following papers which will be published by my collaborators.

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Preparation and Characterization of β-glucosidase Films for Stabilization and Handling in Dry Configurations

Current Pharmaceutical Biotechnology ◽

10.2174/1389201020666191202145351 ◽

2020 ◽

Vol 21 (8) ◽

pp. 741-747

Author(s):

Liguang Zhang ◽

Yanan Shen ◽

Wenjing Lu ◽

Lengqiu Guo ◽

Min Xiang ◽

...

Keyword(s):

Tensile Strength ◽

Protein Function ◽

Protein Stabilization ◽

Functional Protein ◽

Elongation At Break ◽

Gelatin Films ◽

The Stability ◽

And Function ◽

General Method

Background: Although the stability of proteins is of significance to maintain protein function for therapeutical applications, this remains a challenge. Herein, a general method of preserving protein stability and function was developed using gelatin films. Method: Enzymes immobilized onto films composed of gelatin and Ethylene Glycol (EG) were developed to study their ability to stabilize proteins. As a model functional protein, β-glucosidase was selected. The tensile properties, microstructure, and crystallization behavior of the gelatin films were assessed. Result: Our results indicated that film configurations can preserve the activity of β-glucosidase under rigorous conditions (75% relative humidity and 37°C for 47 days). In both control films and films containing 1.8 % β-glucosidase, tensile strength increased with increased EG content, whilst the elongation at break increased initially, then decreased over time. The presence of β-glucosidase had a negligible influence on tensile strength and elongation at break. Scanning electron-microscopy (SEM) revealed that with increasing EG content or decreasing enzyme concentrations, a denser microstructure was observed. Conclusion: In conclusion, the dry film is a promising candidate to maintain protein stabilization and handling. The configuration is convenient and cheap, and thus applicable to protein storage and transportation processes in the future.

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On the stability of crystal lattices IX. Covariant theory of lattice deformations and the stability of some hexagonal lattices

Mathematical Proceedings of the Cambridge Philosophical Society ◽

10.1017/s0305004100022246 ◽

1942 ◽

Vol 38 (1) ◽

pp. 82-99 ◽

Cited By ~ 25

Author(s):

M. Born

Keyword(s):

Elastic Constants ◽

Hexagonal Lattice ◽

Covariant Theory ◽

Tensor Calculus ◽

Crystal Lattices ◽

New Form ◽

The Stability ◽

Central Forces

The theory of lattice deformations is presented in a new form, using the tensor calculus. The case of central forces is worked out in detail, and the results are applied to some simple hexagonal lattices. It is shown that the Bravais hexagonal lattice is unstable but the close-packed hexagonal lattice stable. The elastic constants of this lattice are calculated.

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One-Step Quaternization/Hydroxypropylsulfonation to Improve Paste Stability, Adhesion, and Film Properties of Oxidized Starch

Polymers ◽

10.3390/polym10101110 ◽

2018 ◽

Vol 10 (10) ◽

pp. 1110 ◽

Cited By ~ 13

Author(s):

Wei Li ◽

Zhenzhen Xu ◽

Zongqian Wang ◽

Jian Xing

Keyword(s):

Tensile Strength ◽

Degree Of Crystallinity ◽

Trimethylammonium Chloride ◽

Film Properties ◽

Moisture Regain ◽

Breaking Elongation ◽

End Use ◽

Paste Viscosity ◽

The Stability ◽

Viscosity Stability

To investigate the influences of quaternization/hydroxypropylsulfonation on viscosity stability, adhesion to fibers and film properties of oxidized tapioca starch (OTS) for ameliorating its end-use ability in applications such as warp-sizing and paper-making, a series of quaternized and hydroxypropylsulfonated OTS (QHOTS) samples were synthesized by simultaneous quaternization and hydroxypropylsulfonation of OTS with N-(3-chloro-2-hydroxypropyl) trimethylammonium chloride (CHPTAC) and 3-chloro-2-hydroxy-1-propanesulfonic acid sodium salt (CHPS-Na). The QHOTS granules were characterized by Fourier transform infra-red spectroscopic and scanning electron microscope techniques. Apparent viscosity and viscosity stability were determined, and adhesion was evaluated by measuring the bonding force of starch to the fibers. Film properties were also estimated in terms of tensile strength, breaking elongation, bending endurance, degree of crystallinity, and moisture regain. It was showed that quaternization/hydroxypropylsulfonation was capable of obviously improving viscosity stability of gelatinized OTS paste, enhancing bonding forces of OTS to cotton and polylactic acid (PLA) fibers, increasing breaking elongation, bending endurance and moisture regain of film and decreasing its tensile strength and degree of crystallinity, thereby obviously stabilizing paste viscosity, improving adhesion to fibers and lessening film brittleness. Increasing the level of quaternization/hydroxypropylsulfonation favored improvement in the stability, enhancement in adhesion and decrease in brittleness. The QHOTS showed potential in the applications of cotton and PLA sizing.

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SEA-BED CONFIGURATION IN RELATION TO BREAKWATER STABILITY

Coastal Engineering Proceedings ◽

10.9753/icce.v13.81 ◽

1972 ◽

Vol 1 (13) ◽

pp. 81 ◽

Cited By ~ 1

Author(s):

J.H. Van Oarschat ◽

A. Wevers

Keyword(s):

The Netherlands ◽

Present Article ◽

Water Depth ◽

Systematic Study ◽

Public Works ◽

Irregular Waves ◽

Sea Bed ◽

Hydraulic Conditions ◽

Overall Stability ◽

The Stability

Stability tests on the Europoort breakwaters, situated on a shallow foreshore, clearly demonstrated the effect of the foreshore configuration on the overall stability. The present article gives a descriptionof the stability experiments and the interpretation leading to general conclusions regarding foreshore effects in combination with hydraulic conditions such as wave period, water depth and wave height. Both regular and irregular waves have been used. The experiments, carried out in commission of the Netherlands Government Department of Public Works (Rijkswaterstaat) were of an applied nature and were not directed primarily to the systematic study of foreshore effects.

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Concomitant polymorphs of aryl-ether amine via catemer and dimer carboxylic acid supramolecular interactions and their effect on optical properties

10.21203/rs.3.rs-264441/v1 ◽

2021 ◽

Author(s):

Mehboobali Pannipara ◽

Abdullah G Al-Sehemi

Keyword(s):

Optical Properties ◽

Carboxylic Acid ◽

Crystal Lattice ◽

Functional Groups ◽

Molecular Orbital ◽

Acid Group ◽

Supramolecular Interactions ◽

Aryl Ether ◽

Stability Calculation ◽

The Stability

Abstract Carboxylic acid supramolecular synthon exhibited dimer or catemer motifs in the crystal lattice depend on the substituent and other functional groups present in the structure. In general, presence of other competing functional groups produced catemer motifs whereas unsubstituted acids showed dimer. In this manuscript, we have synthesized a new aryl ether amine-based Schiff base with carboxylic acid functionality ( 1 ) and demonstrated polymorphic structure via catemer ( 1a ) and dimer ( 1b ) motifs in the solid state. In both the structure, carboxylic acid group adopted different orientation in the crystal lattice. The different H-bonding lead to modulation of optical properties that was further supported highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO) calculation. Further the stability calculation indicates that catemer structure was more stable by 8.54 kcal/mole relative to dimer motifs. In contrast, naphthyl group attached carboxylic acid structure did not show neither dimer nor catemer motifs in the crystal lattice as compared to diethylaminophenyl group, which confirm the presence of other substituent or competing functional groups strongly influence on the motifs of supramolecular interactions.

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Study of Mechanical Behavior and Microstructure for Low-Hardness P92 Steel

Journal of Physics Conference Series ◽

10.1088/1742-6596/2101/1/012074 ◽

2021 ◽

Vol 2101 (1) ◽

pp. 012074

Author(s):

Weixin Yu ◽

Zhen Dai ◽

Jifeng Zhao ◽

Lulu Fang ◽

Yiwen Zhang

Keyword(s):

Mechanical Properties ◽

Grain Size ◽

Tensile Strength ◽

Maximum Size ◽

Rapid Decrease ◽

Laves Phases ◽

P92 Steel ◽

A Chain ◽

The Stability ◽

Evolution Of Microstructure

Abstract The strength of P92 steel (tensile strength, specified plastic elongation strength) will decrease after its hardness is reduced, ferrite and carbides forming the structure. Carbides of grain size 5-6 are precipitated in the grains and grain boundaries. The martensite lath shape has completely disappeared. M23C6 carbide coarsened obviously, with a maximum size of about 500nm; The Laves phase is also aggregated and coarsened, connecting in a chain shape with a maximum size of more than 500nm. Evolution of microstructure, namely the obvious coarsening of M23C6 carbides and the aggregation and connection of Laves phases in a chain shape, are the main causes for rapid decrease in the stability of the material substructure and evident decline in mechanical properties and hardness. In addition, the MX phase did not change significantly, hardly affecting the hardness reduction of P92 steel.

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