Void Migration Research Articles

A comparison of critical heat flux in tubes and annuli

This paper examines the differences in critical heat flux (CHF) between internally heated annuli and tubes, cooled by water, based on an 8 mm tube CHF look-up table as the reference. The quality, gap size and pressure were identified as the most important parameters to account for differences in CHF between concentric annuli and tubes. Eccentricity, void migration parameter γ and quality caused the main differences in CHF between eccentric and concentric annuli. These parameters were used to develop CHF correlations for both types of annuli. The proposed correlations predict the CHF with an r.m.s. error of 9.26% for concentric annuli (based on 1547 CHF data points), and 11.6% for eccentric annuli (based on 331 CHF data points). These correlations predict the correct parametric and asymptotic trends, and are more accurate than other CHF prediction methods for annuli.

Recent underground investigations of abandoned chalk mine workings beneath Norwich City, Norfolk

The city of Norwich is underlain at shallow depth by abandoned mineworkings made for the extraction of chalk and flints. Early workings took the form of surface pits and quarries, with later working of underground mines. The latter, often several hundred years old, are liable to collapse, and may reach the ground surface. Most of the mines are now inaccessible, although the recent investigation of two such mines has included the use of direct mining techniques to gain access to the old workings. Stability at Harford mine has been found to be adequate, due to adequate rock cover, moderate age and a rural setting. Collapses at Earlham Road mine have been found to be well developed, due to inadequate rock cover, great age, poor rock quality and disturbance due to the urban location. The principal collapse mechanism is identified as localised void migration, following roof collapse, with a possible secondary contribution from pillar over-stressing.

Two-fluid modeling versus mechanistic approach and lift effects in bubbly sheared flows

The behavior of bubbles in a shear flow is experimentally studied. The lift force experienced by a single bubble in constant shear is determined. It proves to be roughly equal to a half of the virtual mass coefficient up to Reynolds numbers of the order of 2000. Besides, the void—migration taking place inside a bubbly boundary layer on a flat plate is studied and shown to be associated with an actual lateral deflection of the bubbles only under certain conditions. Finally, the link between the lagrangian description of the motion and the two-fluid model is qualitatively discussed.

Stress and current induced voiding in passivated metal lines

Thermal stress and current induced damage processes may well determine the ultimate limit for the achievable line widths in microelectronic circuits. According to our current understanding, thermal stresses cause void nucleation during cool-down from high temperature process steps. The voids may continue to grow during subsequent storage. The application of an electrical current may lead to further void growth, as well as migration and coalescence of voids. A recently developed model provides the framework for improved reliability assessments, including the effects of statistics, as well as for the development of remedies.

On void nucleation and growth in metal interconnect lines under electromigration conditions

Electromigration failure in rigidly passivated metal interconnect lines is studied with particular reference to the vacancy supersaturations and hydrostatic stresses that can be developed at blocking grain boundaries under electromigration conditions. It is shown that the high stresses needed for homogeneous void nucleation to occur are probably too high to be developed by electromigration and that failure is more likely to involve the growth of pre-existing voids. We also show that the amount of void growth that can occur at a blocking grain boundary by electromigration of vacancies down the adjoining grain boundaries is small relative to the dimensions of the line unless the adjoining grain boundaries are continuous in a very long section of the line. This suggests that other mechanisms of void growth are responsible for electromigration failure. An analysis of the electromigration of small pre-existing voids shows that above a critical size, large voids migrate faster than smaller ones. This leads to a catastrophic process in which large voids can catch up with and coalesce with smaller ones, growing in size and migrating more rapidly as they do so. We conclude that the migration and coalescence of preexisting voids is a more likely mechanism of electromigration failure.

Thermal expansion of high-modulus fibers

A resistance-heating technique was used to measure the axial thermal expansion of high-modulus boron and silicon carbide (SiC) fibers from room temperature to 700 and 1500°C, respectively. Both types of fibers investigated in this study were manufactured by a chemical vapor deposition (CVD) process. The boron fibers examined here are composed of boron and a tungsten boride core arising from reaction of deposited boron with a tungsten wire substrate. The composition of the SiC fibers consists of a SiC sheath with a carbon-rich outer coating surrounding an unreacted pyrolytic graphite coated carbon core. The thermal expansion of boron fibers was found to increase parabolically with temperature up to 700°C. Above this temperature the fiber contracted due to void migration and subsequent residual stress relaxation. For SiC fibers, a relatively small initial expansion from room temperature to 450°C was observed. Above 450°C the expansion was found to increase linearly with temperature up to 1300°C, where a hysteresis effect was observed involving a 50% reduction in expansion. Possible explanations for this hysteresis effect were considered and different theories presented. Volume percentage of carbon core was varied and found to have negligible effect on expansion. The conclusion was reached that expansion of these SiC fibers is controlled by the SiC sheath.

Homogeneous Turbulence in Bubbly Flows

The present study is devoted to the interaction between a swarm of bubbles and a turbulent field in a linear shear flow. The transversal and longitudinal evolutions of the void fraction and of the Reynolds stress tensor have been measured. When the air bubbles are blown uniformly into the shear, the void fraction profiles exhibit a strong gradient which can be explained by kinematical effects. No void migration has been observed. The behavior of the Reynolds tensor indicates that the nonisotropy induced by the mean velocity gradient decreases when the void fraction increases. A simple mechanism is proposed to interpret this fact, and a turbulence model based on one-point closures is compared to the experimental data.

Mining subsidence in Lethbridge, Alberta

Coal mining in Lethbridge began in 1872 and continued until 1965. Workings were by underground room and pillar techniques on a single near-horizontal seam. Parts of the city, and particularly the recently developed or soon to be developed areas, to the north and west of the city, are underlain by mine workings. This has necessitated comprehensive geotechnical investigations to evaluate potential subsidence hazards and to enable guidelines for construction precautions to be developed. Because of the relatively uniform conditions throughout the area, the borehole data accumulated during these investigations illustrate well some aspects of the process of mining subsidence above abandoned workings. Another interesting aspect of the Lethbridge case history is the phenomenon of soil cracking that occurs around the edge of worked seams. Even though calculated potential tensile strains are small, it appears that they can be concentrated to form thin cracks in the very stiff, unsaturated overburden soils. These cracks can subsequently be exploited by surface erosion processes and result in voids or soft zones, which are a potential hazard to construction. Key words: mining subsidence, void migration, soil cracking, development guidelines.

A case study on past shortwall mining methods and the risk of ground subsidence in the Lanarkshire Coalfield, Scotland

Abstract A site investigation involving archival research and a borehole drilling programme was carried out in order to assess the risk to surface stability from abandoned shallow shortwall mineworkings at a proposed housing development site located on the Lanarkshire Coalfield. Of the exploitable coal seams present below the site, the Ell coals were confirmed to be at shallow depth and were mined into the mid-1950’s from the adjacent Thankerton Colliery. The Ell coal in this part of the coalfield occurs in three distinct leaves, the uppermost of which crops through the site and was not mined. The investigation confirmed the extent of mining in the Mid and Lower Ell seams which were proved to be no more than 0.5 m apart with a combined unworked thickness of 1.5 to 1.9 m. The mine records indicate that the Mid and Lower Ell seams were mined by shortwall methods, individual panels having been worked from a network of main roadways or headings with subsidiary side or haulage roadways. Due to the thin partings between the seams, a method of mining each seam from common roadways extending to the full height of combined seams was used in addition to single seam workings of the thicker Mid Ell. From the abandonment information it has been deduced that mining involved the total extraction of the Mid Ell whilst maintaining the integrity of the roadways. Subsequently, the same roadways allowed access to the Lower Ell for extraction below the collapsed Mid Ell workings. The investigations recorded the shortwall panels to be largely consolidated but also noted that several panels had been undeveloped with respect to the lower seam and that some roadways were confined to the Mid Ell seam. The borehole investigation together with the use of down-the-hole closed circuit television (CCTV) also confirmed the presence of broken ground and open voids of 0.3 to 2.0 m height along former roadway alignments. A risk to surface stability was identified from these open voids and development constraints zones are discussed in relation to the likely mining methods. Seam depths, void heights, condition of roof strata and thickness of superficial cover are considered in the assessment of void migration mechanisms arising from such a past mining situation.

The geology of Castlefields Mine, Dudley, and its effect on the stability of the mine roof

Abstract The mining of the Wenlock Limestone, which has taken place in the West Midlands during the last two hundred years, has resulted in a long and continuing history of subsidence and crownhole formation in a mainly urban area. In 1983, as part of a major study of the abandoned limestone mines, a programme of micro-seismic emission monitoring of rock falls and of rock paste infilling trials was started at the Castlefields Mine near Dudley. The mine is in Upper Wenlock Limestone with an overburden of approximately 22 m comprising about 1.5 m Passage Beds overlain by Lower Ludlow Shale. A number of stages of instability were observed, ranging from initial slabbing failure of the Passage Beds to extensive upward void migration through the Lower Ludlow Shale to within a few metres of the surface. The pattern of joints, and their condition, plays an important role in controlling the instabilities in a mine. Five joint sets, with varying degrees of dilation, movement and infilling, were identified in a survey of structural discontinuities in Castlefields Mine. One master joint set, characterized by uneven dilation and clay infilling, was found to exert a major influence on the position and development of roof instabilities within the mine. In this paper, the lithology, geological and mining history and structure of Castlefields Mine are described and their influence on mine stability discussed.

Application of lithic and structural geological data to the assessment of ground stability above shallow abandoned coal mines

Abstract Borehole log data gathered during a subsidence investigation in 1978–79 are used to derive a classification scheme for Coal Measure rocks. The results of height of void migration above workings are compared to those arising from use of Piggott & Eynon’s (1977) geometrical collapse zone method and Bienawski’s (1980) Rock Mass Rating scheme. It is concluded that the analysis helps to assess areas of greatest instability, which thus aids land-use planning and also the planning of ground investigations, ground stabilization, and re-development.

A computer model for postdeposition annealing of porous thin films

The changes that a porous thin film undergoes during annealing are studied by means of a two-dimensional computer simulation. The model allows a detailed investigation of thermally activated hopping processes, which result in the migration of excess vacancies and smaller voids quenched-in during film formation. To simulate fluctuations in vibrational energy, Boltzmann-ordered statistics are used. For thin gold film the coalescence of vacancies, their merging with preexisting voids, and the deterioration in adhesion due to the potential diffusion of vacancies to the film–substrate interface are predicted.

Void coarsening during the annealing of neutron irradiated molybdenum

The annealing effect on the void swelling of neutron irradiated molybdenum is investigated in the present work. The behavior of voids during post-irradiation annealing is analyzed using a reaction rate equation. The best agreement of experimental results with the reaction rate equation is found when the reaction order is 2. This fact indicates that there is an interaction between voids during the post-irradiation annealing of molybdenum. Activation energy for void annealing is about 2.0 eV. From these results void migration or void coarsening by pipe diffusion of vacancies is discussed as the mechanism of void annealing.

Stochastic Theory of Particle Flow under Gravity

A discrete theory of cohesionless particle (radius a) flow under gravity is developed, which assumes particle positions are restricted to the sites of a (random) lattice. Downward particle flow toward and through an orifice is represented in terms of an equivalent upward-biased random flight of voids (unoccupied lattice sites) originating at the orifice. The void migration rate is assumed limited by the time required for a particle above a void to fall freely through a distance of 2a into the void. Because of the strong + z (upward) void-jump bias, the theory of random flight yields for the steady-state concentration c of voids the equation ∂2c∂x2+∂2c∂y2=1α∂c∂z ,from which the usual term ∂2c/∂z2 is absent. Since this equation is formally identical to the two-dimensional diffusion or heat flow equation under the substitution (time) → z, steady-state problems in gravitational particle flow, termed stochastic flow on our model, may be converted to boundary value problems in ordinary diffusion theory. Solutions representing a point orifice and a finite orifice (radius R) in the floor of a semi-infinite bed and a point orifice in the bottom of a pipe are given. Particle flux lines and marker motion and exit times are defined and calculated. Time-dependent flow is discussed briefly. Finally, an idealized theory of flow in the immediate vicinity of the orifice is given, which pictures the transition between stochastic flow in the particle bed and bulk free fall in the orifice vicinity as occurring abruptly on a dome-shaped interface surmounting the orifice. Calculated values of the total rate of particle flow through the orifice show the observed particle size effects and agree well with measured values in the literature for 5<R/a ≲ 25. All main results are given in both two and three dimensions; the former may apply to certain traffic problems.

Void Migration in Sodium Chloride Crystal under Temperature Gradient

A simulation experiment on columnar grain formation in UO2 was performed using NaCl single crystals, to examine the progress of void formation and migration. When two single crystals of NaCl were held together under a temperature gradient, plate-like or lenticular voids were observed to generate and migrate towards the hot side, forming columnar grains in the NaCl crystal. The crystallographic orientation of the colder crystal was found to affect the void shapes observed in the hotter crystal. This void behavior is explained by calculations concerning the evaporation and condensation of the NaCl molecule.

Void Migration in Sodium Chloride Crystal under Temperature Gradient

A simulation experiment on columnar grain formation in UO2 was performed using NaCl single crystals, to examine the progress of void formation and migration. When two single crystals of NaCl were held together under a temperature gradient, plate-like or lenticular voids were observed to generate and migrate towards the hot side, forming columnar grains in the NaCl crystal. The crystallographic orientation of the colder crystal was found to affect the void shapes observed in the hotter crystal. This void behavior is explained by calculations concerning the evaporation and condensation of the NaCl molecule.

Influence des caractéristiques d'un agrégat polycristallin sur la croissanceàl'état solide d'un monocristal de ferrite hexagonal

We give a method of single crystal growth for BaFe 12O 19 entirely in the solid state, in a cylindrical polycrystalline aggregate of very small grains. This method is based on the control of discontinuous or exaggerated grain growth. We use neither crucible nor flux. Single crystal growth occurs at relatively low temperatures, therefore the thermal defect concentration is reduced. A single crystal growth rate of 25 mm/h normal to the c axis was attained. Single crystals ≅ 10 mm in diameter and several centimeters in length have been obtained. We draw attention to the effect of the main parameters of the polycrystalline aggregate, i.e. crystal diameter and its standard deviation. It is shown that decrease of the standard deviation makes solid state crystal growth possible without any thermal gradient. We point out that the effect of the thermal gradient on the crystal growth rate may originate from the migration of residual voids.

Microstructures of Columnar Grains in Uranium Dioxide

Microstructures of columnar grains of uranium dioxide grown under the temperature gradient —sintered pellets, swaged compacts and vibratory compacts— below the melting point have been studied by optical and electron micrography.The main results obtained are as follows:1. The dominant mechanism in columnar grain growth varies with porosity. The columnar grains in high density sintered pellets of 97% theoretical density are considered to be grown by the migration of grain boundary. As the porosity increases, the migration of large voids plays a dominant role in the columnar grain growth.2. In addition to lenticular voids, voids or gaps along the grain boundary of columnar grains are observed in porous specimens.3. As for the powder compacts of the same composition and different compact densities, the size and number of lenticular voids increase with decreasing density.

Grain Growth in Sintered Uranium Dioxide: II, Columnar Grain Growth

Evidence is presented which shows that columnar grains can be induced to grow in high-density sintered uranium dioxide specimens by applying a steep temperature gradient at temperatures above 1700°C but below the melting point of 2800°C. Columnar growth apparently is a result of the migration of large transverse voids, whose individual widths define the cross sections of the grains, up a temperature gradient by a sublimation process. The grains grown by this process have a (111) preferred orientation along their columnar axis. A consequence of such void migration in operating fuel elements containing solid UO2 pellets is the formation of a central void bounded by a region of oxide exhibiting columnar growth.