Final Report Summary - PRESS (Precipitate Elastic Stress States)
Stressed or relaxed?
A fundamental study of chemical change under mechanical stress.
Final summary report for the EU Research Executive Agency, Marie Curie Actions Project No: 254334
"Precipitate Elastic Stress States"
The simultaneous action of mechanical stresses and chemical reactions is ubiquitous. While plate tectonics force mountains to build and ocean floors to subduct the minerals in the rocks are deforming mechanically and changing chemically. When steel and aluminium alloys are extruded, rolled and pressed to structural shapes for cars, buildings and watches etc. the grains of the alloys undergo the same processes as the rock minerals. When semiconductor microchips for our computers, mobile phones etc. are built, atomic layer by layer, the mechanical stresses induced are comparable to stresses causing earthquakes and those applied to forming of metals. Mountains, concrete and steel structures are slowly broken down to soil by chemical reactions causing mechanical stresses that cause fractures that enhance the rate of chemical reactions.
The fundamental formulation of equilibrium was laid out and its consequences were discussed 150 years ago by pioneers like J.W. Gibbs, J. Thomson and his younger brother Lord Kelvin. They recognised that there remained an ambiguity in the criterion of chemical equilibrium for solids under mechanical stress: the atoms precipitating on a stressed solid during a chemical reaction may choose either to be stressed like the parent solid or it may choose to relax the stress. The theory could not predict which choice the precipitating atoms would make.
The background for this project was a discrepancy between experimental results and simulation predictions. The main question of the project was formulated as:
Can the stress state of the precipitate be taken into account explicitly in macroscopic/thermodynamic modeling of non-hydrostatically stressed crystals in contact with their solution?
In order to translate the main question into meaningful research a small set of testable hypotheses were formulated:
1. The stress state of the precipitate can be described by a single parameter, dc: the length scale of a smooth relaxation profile or the critical thickness.
2. The stress relaxation length scale dc is always small compared to the ATG critical length scale λ for stresses smaller than the yield stress of the material.
3. Subcritical crack growth by dissolution will always be stopped at some maximum depth by the precipitation of a stress free skin. (A constant stress intensity factor at the crack tip is assumed.)
4. The maximum depth of dissolution grooves/cracks is controlled by the ratio between the diffusion time scale and the dissolution/precipitation time scale.
5. In the presence as well as in the absence of unstressed crystals a (sufficiently large) non-hydrostatically stressed crystal will always end up with a smooth stress free interface with the solution.
During the course of this project hypotheses 1,2 and 5 have been confirmed by new experiments and by microscopic theory and the results are about to be published[1]. The study performed on subcritical crack growth[2] could not verify or falsify hypothesis 3. Instead of focusing on the transient stages of the transformations we have focused on transformations on length scales larger than dc. Here we have proposed[3] a diffuse interface model using Gibbs energy and concentrations for chemical equilibrium and Helmholtz energy and momentum for mechanical equilibrium, the two being coupled by the pertinent Maxwell relations. This model is used to cast light on three recent experimental observations that have contended usual theoretical treatment. This method of calculating local equilibrium during irreversible, coupled mechanical and chemical interface propagation in liquids and solids goes far beyond the main question set out in the project description. In addition we have also published an experimental study.
A fundamental study of chemical change under mechanical stress.
Final summary report for the EU Research Executive Agency, Marie Curie Actions Project No: 254334
"Precipitate Elastic Stress States"
The simultaneous action of mechanical stresses and chemical reactions is ubiquitous. While plate tectonics force mountains to build and ocean floors to subduct the minerals in the rocks are deforming mechanically and changing chemically. When steel and aluminium alloys are extruded, rolled and pressed to structural shapes for cars, buildings and watches etc. the grains of the alloys undergo the same processes as the rock minerals. When semiconductor microchips for our computers, mobile phones etc. are built, atomic layer by layer, the mechanical stresses induced are comparable to stresses causing earthquakes and those applied to forming of metals. Mountains, concrete and steel structures are slowly broken down to soil by chemical reactions causing mechanical stresses that cause fractures that enhance the rate of chemical reactions.
The fundamental formulation of equilibrium was laid out and its consequences were discussed 150 years ago by pioneers like J.W. Gibbs, J. Thomson and his younger brother Lord Kelvin. They recognised that there remained an ambiguity in the criterion of chemical equilibrium for solids under mechanical stress: the atoms precipitating on a stressed solid during a chemical reaction may choose either to be stressed like the parent solid or it may choose to relax the stress. The theory could not predict which choice the precipitating atoms would make.
The background for this project was a discrepancy between experimental results and simulation predictions. The main question of the project was formulated as:
Can the stress state of the precipitate be taken into account explicitly in macroscopic/thermodynamic modeling of non-hydrostatically stressed crystals in contact with their solution?
In order to translate the main question into meaningful research a small set of testable hypotheses were formulated:
1. The stress state of the precipitate can be described by a single parameter, dc: the length scale of a smooth relaxation profile or the critical thickness.
2. The stress relaxation length scale dc is always small compared to the ATG critical length scale λ for stresses smaller than the yield stress of the material.
3. Subcritical crack growth by dissolution will always be stopped at some maximum depth by the precipitation of a stress free skin. (A constant stress intensity factor at the crack tip is assumed.)
4. The maximum depth of dissolution grooves/cracks is controlled by the ratio between the diffusion time scale and the dissolution/precipitation time scale.
5. In the presence as well as in the absence of unstressed crystals a (sufficiently large) non-hydrostatically stressed crystal will always end up with a smooth stress free interface with the solution.
During the course of this project hypotheses 1,2 and 5 have been confirmed by new experiments and by microscopic theory and the results are about to be published[1]. The study performed on subcritical crack growth[2] could not verify or falsify hypothesis 3. Instead of focusing on the transient stages of the transformations we have focused on transformations on length scales larger than dc. Here we have proposed[3] a diffuse interface model using Gibbs energy and concentrations for chemical equilibrium and Helmholtz energy and momentum for mechanical equilibrium, the two being coupled by the pertinent Maxwell relations. This model is used to cast light on three recent experimental observations that have contended usual theoretical treatment. This method of calculating local equilibrium during irreversible, coupled mechanical and chemical interface propagation in liquids and solids goes far beyond the main question set out in the project description. In addition we have also published an experimental study.
