El etiquetado social y su aplicación documental: estudios previos

Two main theories have been proposed as mechanisms of bubble growth: the single bubble induced pressure model and the interbubble fracture generated crack model. These two models agree that bubbles nucleate due to a collection of hydrogen-vacancy complexes. This hydrogen vacancy clustering (i.e. H2− v clusters) can occur at temperatures higher than

Tm/4 (with Tmbeing the melting temperature) given that vacancies have enough energy to

be mobile and agglomerate into clusters (Post and Behrisch, 1986). At lower temperatures vacancies can agglomerate into clusters in the presence of high concentrations of hydrogen in the material.

Hydrogen trapped as interstitials induce strains and changes in the electronic structure leading to an increase in the energy of the system. To compensate for this energy increase, the formation energy of vacancies decreases, which in turn leads to the creation of more vacancies. This effect is known as hydrogen induced superabundant vacancy concentration. If further vacancies are created, there is an additional energy increase in the system. To counteract this energy increase vacancies tend to organize into clusters, as shown in Fig. 1.24 (Condon and Schober, 1993; Ren et al., 2008).

Fig. 1.24 Schematic representation of the vacancy clustering model: a) Superabundant vacancies or thermal vacancies accumulate in a cluster. b) Hydrogen atoms form molecules. c) The void continues to grow by collecting additional vacancies. d) As the pressure inside the bubble reaches a certain value, cracks may form

in the wall (Ren et al., 2008)

The energy decrease by the aggregation of interstitial hydrogen atoms into spherical hydrogen clusters without any external stresses may be estimated by taking the energy decrease due to the aggregation of hydrogen in the bubbles minus the increase in energy of

1.6 Bubble formation and material modifications 41 the system due to the creation of a dislocation loop (i.e. punching of dislocation loops out of a bubble due to excess pressure). The energy decrease may be expressed as follows (Fujita, 1976; Ren et al., 2008): ∆E = −πr 3_ε Ω − Gb2rln(r/r0) 2(1 − ν) (1.15)

where r is the radius of the vacancy cluster in cm, ε is the binding energy of a solute hydrogen atom to a cluster in eV, Ω is the atomic volume of hydrogen in the cluster in cm3, that is the volume one mole of an element occupies at room temperature, G is the modulus of rigidity in dynes/cm2, b is the Burgers vector in cm, ν is the Poisson’s ratio and r0is the

dislocation core radius in cm.

Once the H2− v cluster is formed it is able to grow if the work done by the hydrogen

pressure does not exceed the total binding energy of a newly created vacancy to an existing cluster. The pressure at which this occurs is the critical pressure under which bubbles can grow in the material. The critical pressure is given by (Ren et al., 2008):

P= Et

∆V (1.16)

where Et is that total energy of binding an existing cluster to a newly created vacancy (i.e

the formation energy of a vacancy plus the binding energy of a vacancy to a cluster) and ∆V is the change in volume which in this case corresponds to the volume of a vacancy.

Once clusters are formed, hydrogen atoms combine into molecules inside the H2−

vcluster (Fig. 1.24 b) and c)),releasing energy into the system (Ren et al., 2008):

H_{+ H → H}2 (1.17)

This chemical reaction has a dissociation energy of −4.5 eV at 300 K. Once hydrogen molecules are formed, it is very difficult for them to dissociate.

Once the bubble is formed and exposure to hydrogen flux continues, the pressure contin- ues to increase. For increasing pressures, cracks may form on the bubble wall and propagate as shown in Fig. 1.24 d) (Ren et al., 2008).

Bubble growth

Single bubble induced pressure model

This models proposes that vacancies (inherent to the material or produced by the incident ion beam) act as trap for hydrogen during implantation (Fig. 1.25 a)). Above a certain concentration of hydrogen, there is an increase in size and density. This increase is due to the internal gas pressure, in the order of GPa, which punches the interstitial loops out of one side of the bubble in a process known as interstitial loop punching. The interstitial will then rapidly glide away from the bubble along the direction of its Burgers vector (Fig. 1.25 b)). Once the elastic limit is reached the wall of the cavity is deformed (Behrish, 1983; Condon and Schober, 1993; Jacques, 1983).

At the high pressures required to generate dislocation loops, intermolecular repulsions becomes more important and the values of pressure and fugacity deviate from each other. The stresses, due to high fugacity in the bubbles, are able to deform the material around the bubble. Depending on the material’s ability to deform plastically, bubbles can have spherical shape (Jacques, 1983) or a terraced structure (Kolasinski et al., 2011)

Fig. 1.25 Schematic representation of the loop punching process due to an excessive pressure: a) Hydrogen accumulates at vacancies b) After a certain pressure is achieved, interstitial loops are punched out of one side

1.6 Bubble formation and material modifications 43 Interbubble fracture generated crack model

Another proposed mechanism of bubble formation is the interbubble fracture generated crack model. This model assumes that small bubbles with a high pressure nucleate in the implanted layer of the material (Fig 1.26 a)). Due to the high pressure of the bubbles, there are tensile stresses in the material. As the pressure increases, cracks are produced along the bubbles (Fig 1.26 b)). These cracks are large when compared to the initial bubble size. As more bubbles break into the cavity, a flat cavity is formed (Fig 1.26 d)). This flat cavity develops in a bubble (Fig 1.26 f)). Afterwards, two bubble growth mechanisms are proposed: loop punching due to the high pressure inside the bubble, and acquisition of vacancy clusters(Behrish, 1983; Evans, 1977; Jacques, 1983).

Fig. 1.26 Schematic representation of the interbubble or crack fracture model. a) Bubbles form in the lattice. b) Tensile stresses due to the high pressures inside the bubble results in the formation of cracks. c-d) The cracks

continues to grow. e-f) a flat cavity forms which then develops in a bubble (Evans, 1977)

These theories provide two different mechanisms for bubble growth. However, both of them agree on the fact that at high pressures bubbles grow by dislocation loop punching. This section provided a brief introduction of the different mechanisms involved in bubble nucleation and growth. This information, along with the other described topics (i.e. plasma sheath, PWI, structure of crystalline solids and hydrogen in metals) provide the basic tools to study bubble and blister formation. The main concepts described in the previous section are summarized in Fig. 1.27.

Incoming H

flux

a)

Hydrogen molecules dissociate into atoms Hydrogen may reside in solute sites occupying either tetrahedral or octahedral

positions. The behavior of hydrogen depends on the nature of the material. Exothermic materials usually have a high

solubility and form hydrides whereas endothermic materials

have a low hydrogen solubility. Atoms may jump from

one solution site to the next one. During this diffusion process they

may be trapped in defects such as vacancies.

Incoming H

flux

b)

As hydrogen flux continues, concentrations far above the solubility limit are reached. At this limit, endothermic materials undergo a phase change and bubble

nucleation may take place

c)

temperature, incident ion energy and flux.

Two models are used to describe bubble growth: single bubble induced pressure model and the inter bubble fracture generated

crack model.

These models agree that at high pressures bubbles grow by dislocation loop punching. This mechanism is determined by the

slip system of the sample which depends on its crystal system

l

1.7 Aluminum as a possible proxy for Beryllium 45