The following topics related to the treatment of cuttings, cavings and spallings releases to the surface environment in the 1996 performance assessment for the Waste Isolation Pilot Plant (WIPP) are presented: (1) mathematical description of models. (2) uncertainty and sensitivity analysis results arising from subjective (i.e., epistemic) uncertainty for individual releases, (3) construction of complementary cumulative distribution functions (CCDFs) arising from stochastic (i.e., aleatory) uncertainty, and (4) uncertainty and sensitivity analysis results for CCDFs. The presented results indicate that direct releases due to cuttings, cavings and spallings do not constitute a serious threat to the effectiveness of the WIPP as a disposal facility for transuranic waste. Even when the effects of uncertain analysis inputs are taken into account, the CCDFs for cuttings, cavings and spallings releases fall substantially to the left of the boundary line specified in the US Environmental Protection Agency standard for the geologic disposal of radioactive waste (40 CFR 191, 40 CFR 194).
The Waste Isolation Pilot Plant (WIPP) is the first operational repository designed for the safe disposal of transuranic (TRU) radioactive waste from the defense programs of the US Department of Energy (DOE). The US Environmental Protection Agency (EPA) is responsible for certifications and regulation of the WIPP facility for the radioactive components of the waste. The EPA has promulgated general radioactive waste disposal standards at 40 CFR Part 191. and WIPP-specific criteria to implement and interpret the generic disposal standards at 40 CFR Part 194. In October 1996. the DOE submitted its Compliance Certification Application (CCA) to the EPA to demonstrate compliance with the disposal standards at Subparts B and C of 40 CFR Part 191. This paper summarizes the development of the overall legal framework for radioactive waste disposal at the WIPP, the parallel development of the WIPP performance assessment (PA), and how the EPA disposal standards and implementing criteria formed the basis for the CCA WIPP PA. The CCA resulted in a certification in May 1998 by the EPA of the WIPP'S compliance with the EPA's disposal standard, thus enabling the WIPP to begin radioactive waste disposal.
Most algorithms used in preconditioned iterative methods are generally applicable to complex valued linear systems, with real valued linear systems simply being a special case. However, most iterative solver packages available today focus exclusively on real valued systems, or deal with complex valued systems as an afterthought. One obvious approach to addressing this problem is to recast the complex problem into one of a several equivalent real forms and then use a real valued solver to solve the related system. However, well-known theoretical results showing unfavorable spectral properties for the equivalent real forms have diminished enthusiasm for this approach. At the same time, experience has shown that there are situations where using an equivalent real form can be very effective. In this paper, the authors explore this approach, giving both theoretical and experimental evidence that an equivalent real form can be useful for a number of practical situations. Furthermore, they show that by making good use of some of the advance features of modem solver packages, they can easily generate equivalent real form preconditioners that are computationally efficient and mathematically identical to their complex counterparts. Using their techniques, they are able to solve very ill-conditioned complex valued linear systems for a variety of large scale applications. However, more importantly, they shed more light on the effectiveness of equivalent real forms and more clearly delineate how and when they should be used.
An astonishing variety of inorganic networks templated by organic species have been reported over the last 10 years. A great deal of attention has been paid to the structure-directing role of the organic species, and the structural effect of variously coordinated cations, for example distorted octahedral vanadium and pyramidal tin. Less exploratory work has been carried out on the anionic part of the inorganic network, and most groups reported so far (phosphate, germanate, etc.) invariably adopt tetrahedral coordination. The possibilities of incorporating the pyramidal [HP0{sub 3}]{sup 2{minus}} hydrogen phosphite group into extended structures templated by inorganic, alkaline earth cations was explored a few years ago. In this paper the authors report the synthesis, crystal structure, and some properties of (CN{sub 3}H{sub 6}){sub 4}{center_dot}Zn{sub 3}(SeO{sub 3}){sub 5}, the first organically-templated phase to contain the pyramidal selenite [SeO{sub 3}]{sup 2{minus}} anion.
The fracture of highly-crosslinked networks is investigated by molecular dynamics simulations. The network is modeled as a bead-spring polymer network between two solid surfaces. The network is dynamically formed by crosslinking an equilibrated liquid mixture. Tensile pull fracture is simulated as a function of the number of interracial bonds. The sequence of molecular structural deformations that lead to failure are determined, and the connectivity is found to strongly control the stress-strain response and failure modes. The failure strain is related to the minimal paths in the network that connect the two solid surfaces. The failure stress is a fraction of the ideal stress required to fracture all the interracial bonds, and is linearly proportional to the number of interracial bonds. By allowing only a single bond between a crosslinker and the surface, interracial failure always occurs. Allowing up to half of the crosslinker's bonds to occur with the surface, cohesive failure can occur.
The relationship between beam focus position and penetration depth in CW laser welding was studied numerically and experimentally for different welding conditions. Calculations were performed using a transient hydrodynamic model that incorporates the effect of evaporation recoil pressure and the associated melt expulsion. The simulation results are compared with measurements made on a series of test welds obtained using a 1650 W CO2 laser. The simulations predict, and the experiments confirm, that maximum penetration occurs with a specific location of the beam focus, with respect to the original sample surface, and that this relationship depends on the processing conditions. In particular, beam absorption in the plasma has a significant effect on the relationship between penetration and focus position. When the process parameters result in strong beam absorption in the keyhole plasma, the maximum penetration will occur when the laser focus is at or above the sample surface. In a case of weak absorption however, the penetration depth reaches its maximum value when the beam focus is located below the sample surface. In all cases, the numerical results are in good agreement with the experimental measurements.
The 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) maintains a separation between stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty, with stochastic uncertainty arising from the possible disruptions that could occur at the WIPP over the 10,000 yr regulatory period specified by the US Environmental Protection Agency (40 CFR 191, 40 CFR 194) and subjective uncertainty arising from an inability to uniquely characterize many of the inputs required in the 1996 WIPP PA. The characterization of stochastic uncertainty is discussed including drilling intrusion time, drilling location penetration of excavated/nonexcavated areas of the repository, penetration of pressurized brine beneath the repository, borehole plugging patterns, activity level of waste, and occurrence of potash mining. Additional topics discussed include sampling procedures, generation of individual 10,000 yr futures for the WIPP, construction of complementary cumulative distribution functions (CCDFs), mechanistic calculations carried out to support CCDF construction the Kaplan/Garrick ordered triple representation for risk and determination of scenarios and scenario probabilities.
Uncertainty and sensitivity analysis results obtained in the 1996 performance assessment for the Waste Isolation Pilot Plant are presented for two-phase flow the vicinity of the repository under undisturbed conditions. Techniques based on Latin hypercube sampling, examination of scatterplots, stepwise regression analysis, partial correlation analysis and rank transformation are used to investigate brine inflow, gas generation repository pressure, brine saturation and brine and gas outflow. Of the variables under study, repository pressure is potentially the most important due to its influence on spallings and direct brine releases, with the uncertainty in its value being dominated by the extent to which the microbial degradation of cellulose takes place, the rate at which the corrosion of steel takes place, and the amount of brine that drains from the surrounding disturbed rock zone into the repository.
The following topics related to the treatment of direct brine releases to the surface environment in the 1996 performance assessment for the Waste Isolation Pilot Plant (WIPP) are presented (1) mathematical description of models, (2) uncertainty and sensitivity analysis results arising from subjective (i.e., epistemic) uncertainty for individual releases, (3) construction of complementary cumulative distribution functions (CCDFs) arising from stochastic (i.e., aleatory) uncertainty, and (4) uncertainty and sensitivity analysis results for CCDFs. The presented analyses indicate that direct brine releases do not constitute a serious threat to the effectiveness of the WIPP as a disposal facility for transuranic waste. Even when the effects of uncertain analysis inputs are taken into account, the CCDFs for direct brine releases fall substantially to the left of the boundary line specified in the US Environmental Protection Agency's standard for the geologic disposal of radioactive waste (4O CFR 191.40 CFR 194).
Transuranic (TRU) waste generated by the handling of plutonium in research on or production of US nuclear weapons will be disposed of in the Waste Isolation Pilot Plant (WIPP). This paper describes the physical and radiological properties of the TRU waste that will be deposited in the WIPP. This geologic repository will accommodate up to 175,564 m{sup 3} of TRU waste, corresponding to 168,485 m{sup 3} of contact-handled (CH-) TRU waste and 7,079 m{sup 3} of remote-handled (RH-) TRU waste. Approximately 35% of the TRU waste is currently packaged and stored (i.e., legacy) waste, with the remainder of the waste to be packaged or generated and packaged in activities before the year 2033, the closure time for the repository. These wastes were produced at 27 US Department of Energy (DOE) sites in the course of generating defense nuclear materials. The radionuclide and nonradionuclide inventories for the TRU wastes described in this paper were used in the 1996 WIPP Compliance Certification Application (CCA) performance assessment calculations by Sandia National Laboratories/New Mexico (SNL/NM).
The Waste Isolation Pilot Plant (WIPP) is under development by the US Department of Energy (DOE) for the geologic disposal of transuranic waste. The construction of complementary cumulative distribution functions (CCDFs) for total radionuclide release from the WIPP to the accessible environment is described. The resultant CCDFs (1) combine releases due to cuttings and cavings, spallings, direct brine release, and long-term transport in flowing groundwater, (2) fall substantially to the left of the boundary line specified by the U.S. Environmental Protection Agency's (EPA's) standard 40 CFR 191 for the geologic disposal of radioactive waste, and (3) constitute an important component of the DOE's successful Compliance Certification Application to the EPA for the WIPP. Insights and perspectives gained in the performance assessment (PA) that led to these CCDFs are described, including the importance of (1) an iterative approach to PA, (2) uncertainty and sensitivity analysis, (3) a clear conceptual model for the analysis, (4) the separation of stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty, (5) quality assurance procedures, (6) early involvement of peer reviewers, regulators, and stake holders, (7) avoidance of conservative assumptions, and (8) adequate documentation.
The appropriate disposal of radioactive waste is a problem of great importance, wide-spread interest, and some controversy. As part of the solution to this problem the Waste Isolation Pilot Plant (WIPP) is under development by the US Department of Energy (DOE) for the deep geologic disposal of transuranic (TRU) waste generated by defense programs in the United States. The DOE submitted a Compliance Certification Application (CCA){sup 17} for the WIPP to the US Environmental Protection Agency (EPA) in October 1996, and a positive certification decision for the WIPP was issued by the EPA in May 1998. The first disposal of TRU waste in the WIPP took place in March 1999. The 1996 CCA for the WIPP was supported by an extensive performance assessment (PA) carried out by Sandia National Laboratories (SNL), with this PA often designated the 1996 WIPP PA, the 1996 CCA PA, or simply the 1996 PA. In turn, the 1996 PA was supported by site characterization activities, experimental programs, model development programs, data development programs, uncertainty and sensitivity analyses, a dedicated computational environment, a rigorous quality assurance (QA) program and a sequence of earlier PAs. Further, this PA was carried out in a regulatory environment defined by the following EPA regulations: Environmental Radiation Protection Standards for the Management and Disposal of Spent Nuclear Fuel, High-Level and Transuranic Radioactive Wastes (40 CFR Part 191) and Criteria for the Certification and Re-Certification of the Waste Isolation Pilot Plant's Compliance with the 40 CFR Part 191 Disposal Regulations (40 CFR Part 194) The WIPP is the first licensed facility in the United States for the deep geologic disposal of radioactive waste. As a result, there is extensive interest in both the WIPP and the analyses that led to its certification by the EPA for the disposal of TRU waste. The WIPP program has produced large amounts of documentation both as part of the CCA itself and in large numbers of technical reports and supporting analysis documents. Although this information is publicly available, in practice its great quantity and availability at only specific locations (e.g., EPA Docket locations, the WIPP Records Centers in Albuquerque and Carlsbad) make obtaining a detailed understanding of the 1996 WIPP PA an arduous undertaking.
The interlayer structure and the dynamics of Cl{sup {minus}} ions and H{sub 2}O molecules in the interlayer space of two typical LDH [Layered Double Hydroxide] phases were investigated by molecular dynamics computer simulations. The simulations of hydrocalumite, [Ca{sub 2}Al(OH){sub 6}]Cl{center_dot}2H{sub 2}O reveal significant dynamic disorder in the orientations of interlayer water molecules. The hydration energy of hydrotalcite, [Mg{sub 2}Al(0H){sub 6}]Cl{center_dot}nH{sub 2}O, is found to have a minimum at approximately n = 2, in good agreement with experiment. The calculated diffusion coefficient of Cl{sup {minus}} as an outer-sphere surface complex is almost three times that of inner-sphere Cl{sup {minus}}, but is still about an order of magnitude less than that of Cl{sup {minus}} in bulk solution. The simulations demonstrate unique capabilities of combined NMR and molecular dynamics studies to understand the structure and dynamics of surface and interlayer species in mineral/water systems.
Decommissioning high level nuclear waste tanks will leave small amounts of residual sludge clinging to the walls and floor of the structures. The permissible amount of material left in the tanks depends on the radionuclide release characteristics of the sludge. At present, no systematic process exists for assessing how much of the remaining inventory will migrate, and which radioisotopes will remain relatively fixed. Working with actual sludges is both dangerous and prohibitively expensive. Consequently, methods were developed for preparing sludge simulants and doping them with nonradioactive surrogates for several radionuclides and RCRA metals of concern in actual sludges. The phase chemistry of these mixes was found to be a reasonable match for the main phases in actual sludges. Preliminary surrogate release characteristics for these sludges were assessed by lowering the ionic strength and pH of the sludges in the manner that would occur if normal groundwater gained access to a decommissioned tank. Most of the Se, Cs and Tc in the sludges will be released into the first pulse of groundwater passing through the sludge. A significant fraction of the other surrogates will be retained indefinitely by the sludges. This prolonged sequestration results from a combination coprecipitated and sorbed into or onto relatively insoluble phases such as apatite, hydrous oxides of Fe, Al, Bi and rare earth oxides and phosphates. The coprecipitated fraction cannot be released until the host phase dissolves or recrystallizes. The sorbed fraction can be released by ion exchange processes as the pore fluid chemistry changes. However, these releases can be predicted based on a knowledge of the fluid composition and the surface chemistry of the solids. In this regard, the behavior of the hydrous iron oxide component of most sludges will probably play a dominant role for many cationic radionuclides while the hydrous aluminum oxides may be more important in governing anion releases.
Conventional performance assessments assume that radioactive {sup 99}Tc travels as a non-sorbing component with an effective K{sub d} (distribution coefficient) of 0. This is because soil mineral surfaces commonly develop net negative surface charges and pertechnetate (TcO{sub 4}), with large ionic size and low electrical density, is not sorbed onto them. However, a variety of materials have been identified that retain Tc and may eventually lead to promising Tc getters. In assessing Tc getter performance it is important to evaluate the environment in which the getter is to function. In many contaminant plumes Tc will only leach slowly from the source of the contamination and significant dilution is likely. Thus, sub-ppb Tc concentrations are expected and normal groundwater constituents will dominate the aquifer chemistry. In this setting a variety of constituents were found to retard TcO{sub 4}: imogolite, boehmite, hydrotalcite, goethite, copper sulfide and oxide and coal. Near leaking tanks of high level nuclear waste, Tc may be present in mg/L level concentrations and groundwater chemistry will be dominated by constituents from the waste. Both bone char, and to a lesser degree, freshly precipitated Al hydroxides may be effective Tc scavengers in this environment. Thus, the search for Tc getters is far from hopeless, although much remains to be learned about the mechanisms by which these materials retain Tc.
The US Department of Energy (DOE) has millions of gallons of high level nuclear waste stored in underground tanks at Hanford, Washington and Savannah River, South Carolina. These tanks will eventually be emptied and decommissioned. This will leave a residue of sludge adhering to the interior tank surfaces that may contaminate groundwaters with radionuclides and RCRA metals. Experimentation on such sludges is both dangerous and prohibitively expensive so there is a great advantage to developing artificial sludges. The US DOE Environmental Management Science Program (EMSP) has funded a program to investigate the feasibility of developing such materials. The following text reports on the success of this program, and suggests that much of the radioisotope inventory left in a tank will not move out into the surrounding environment. Ultimately, such studies may play a significant role in developing safe and cost effective tank closure strategies.
A number of Hanford tanks have leaked high level radioactive wastes (HLW) into the surrounding unconsolidated sediments. The disequilibrium between atmospheric C0{sub 2} or silica-rich soils and the highly caustic (pH > 13) fluids is a driving force for numerous reactions. Hazardous dissolved components such as {sup 133}Cs, {sup 79}Se, {sup 99}Tc may be adsorbed or sequestered by alteration phases, or released in the vadose zone for further transport by surface water. Additionally, it is likely that precipitation and alteration reactions will change the soil permeability and consequently the fluid flow path in the sediments. In order to ascertain the location and mobility/immobility of the radionuclides from leaked solutions within the vadose zone, the authors are currently studying the chemical reactions between: (1) tank simulant solutions and Hanford soil fill minerals; and (2) tank simulant solutions and C0{sub 2}. The authors are investigating soil-solution reactions at: (1) elevated temperatures (60--200 C) to simulate reactions which occur immediately adjacent a radiogenically heated tank; and (2) ambient temperature (25 C) to simulate reactions which take place further from the tanks. The authors studies show that reactions at elevated temperature result in dissolution of silicate minerals and precipitation of zeolitic phases. At 25 C, silicate dissolution is not significant except where smectite clays are involved. However, at this temperature CO{sub 2} uptake by the solution results in precipitation of Al(OH){sub 3} (bayerite). In these studies, radionuclide analogues (Cs, Se and Re--for Tc) were partially removed from the test solutions both during high-temperature fluid-soil interactions and during room temperature bayerite precipitation. Altered soils would permanently retain a fraction of the Cs but essentially all of the Se and Re would be released once the plume was past and normal groundwater came in contact with the contaminated soil. Bayerite, however, will retain significant amounts of all three radionuclides.
{sup 137}Cs was dispersed globally by cold war activities and, more recently, by the Chernobyl accident. Engineered extraction of {sup 137}Cs from soils and groundwaters is exceedingly difficult. Because the half life of {sup 137}Cs is only 30.2 years, remediation might be more effective (and less costly) if {sup 137}Cs bioavailability could be demonstrably limited for even a few decades by use of a reactive barrier. Essentially permanent isolation must be demonstrated in those few settings where high nuclear level wastes contaminated the environment with {sup 135}Cs (half life 2.3x10{sup 6} years) in addition to {sup 137}Cs. Clays are potentially a low-cost barrier to Cs movement, though their long-term effectiveness remains untested. To identify optimal clays for Cs retention Cs resorption was measured for five common clays: Wyoming Montmorillonite (SWy-1), Georgia Kaolinites (KGa-1 and KGa-2), Fithian Illite (F-Ill), and K-Metabentonite (K-Mbt). Exchange sites were pre-saturated with 0.16 M CsCl for 14 days and readily exchangeable Cs was removed by a series of LiNO{sub 3} and LiCl washes. Washed clay were then placed into dialysis bags and the Cs release to the deionized water outside the bags measured. Release rates from 75 to 139 days for SWy-1, K-Mbt and F- 111 were similar; 0.017 to 0.021% sorbed Cs released per day. Both kaolinites released Cs more rapidly (0.12 to 0.05% of the sorbed Cs per day). In a second set of experiments, clays were doped for 110 days and subjected to an extreme and prolonged rinsing process. All the clays exhibited some capacity for irreversible Cs uptake so most soils have some limited ability to act as a natural barrier to Cs migration. However, the residual loading was greatest on K-Mbt ({approximately} 0.33 wt% Cs). Thus, this clay would be the optimal material for constructing artificial reactive barriers.
The conceptual structure of the 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) is described. This structure involves three basic entities (EN1, EN2, EN3): (1) EN1, a probabilistic characterization of the likelihood of different futures occurring at the WIPP site over the next 10,000 yr, (2) EN2, a procedure for estimating the radionuclide releases to the accessible environment associated with each of the possible futures that could occur at the WIPP site over the next 10,000 yr, and (3) EN3, a probabilistic characterization of the uncertainty in the parameters used in the definition of EN1 and EN2. In the formal development of the 1996 WIPP PA, EN1 is characterized by a probability space (S{sub st}, P{sub st}, p{sub st}) for stochastic (i.e., aleatory) uncertainly; EN2 is characterized by a function {line_integral} that corresponds to the models and associated computer programs used to estimate radionuclide releases; and EN3 is characterized by a probability space (S{sub su}, P{sub su}, p{sub su}) for subjective (i.e., epistemic) uncertainty. A high-level overview of the 1996 WIPP PA and references to additional sources of information are given in the context of (S{sub st}, P{sub st}, p{sub st}), {line_integral} and (S{sub su}, P{sub su}, p{sub su}).
The 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) maintains a separation between stochastic (i.e., aleatory) and subjective (i.e., epistemic) uncertainty, with stochastic uncertainty arising from the possible disruptions that could occur at the WIPP over the 10,000 yr regulatory period specified by the US Environmental Protection Agency (40 CFR 191,40 CFR 194) and subjective uncertainty arising from an inability to uniquely characterize many of the inputs required in the 1996 WIPP PA. The characterization of subjective uncertainty is discussed, including assignment of distributions, uncertain variables selected for inclusion in analysis, correlation control, sample size, statistical confidence on mean complementary cumulative distribution functions, generation of Latin hypercube samples, sensitivity analysis techniques, and scenarios involving stochastic and subjective uncertainty.
The following topics related to the representation of two-phase (gas and brine) flow in the vicinity of the repository in the 1996 performance assessment (PA) for the Waste Isolation Pilot Plant (WIPP) are discussed: (1) system of nonlinear partial differential equations used to model two-phase flow, (2) incorporation of repository shafts into model (3) creep closure of repository. (4) interbed fracturing, (5) gas generation (6) capillary action in waste, (7) borebole model (8) numerical solution and (9) gas and brine flow across specified boundaries. Two-phase flow calculations are a central part of the 1996 WIPP PA and supply results that are subsequently used in the calculation of releases to the surface at the time of a drilling intrusion (i.e., spallings, direct brine releases) and long-term releases due to radionuclide transport by flowing groundwater.
Laser Engineered Net Shaping (LENS) is a novel manufacturing process for fabricating metal parts directly from Computer Aided Design (CAD) solid models. The process is similar to rapid prototyping technologies in its approach to fabricate a solid component by layer additive methods. However, the LENS technology is unique in that fully dense metal components with material properties that are similar to that of wrought materials can be fabricated. The LENS process has the potential to dramatically reduce the time and cost required realizing functional metal parts. In addition, the process can fabricate complex internal features not possible using existing manufacturing processes. The real promise of the technology is the potential to manipulate the material fabrication and properties through precision deposition of the material, which includes thermal behavior control, layered or graded deposition of multi-materials, and process parameter selection. This paper describes the authors' research to understand solidification aspects, thermal behavior, and material properties for laser metal deposition technologies.
What possesses someone to volunteer and go through hoops and red tape to make a presentation at a conference? For that matter, why does anyone ever present anything to anyone? Actually, presentations are a fact of life and there are many reasons for doing a presentation and doing it well. New and existing staff need training and orientation to the way things are done here. Handing all of them a manual and hoping they read it is pretty much a waste of paper. On the other hand, an effective, entertaining and upbeat presentation on the relevant topics is more likely to stick with those people. They will even have a name and face to remember and seek out when they have an issue on or with that topic. This can be a very effective beginning for networking with new peers. The presenter is seen as knowledgeable, as a source of information on company topics and possibly evaluated as a potential mentor or future manager. Project staff and/or peers benefit from clear, concise, presentations of topical knowledge. This is one way that a group working on various aspects of the same project or program can stay in touch and in step with each other. Most importantly, presentations may be the best or only door into the minds (and budgets) of management and customers. These presentations are a wonderful opportunity to address legal and compliance issues, budget, staffing, and services. Here is a chance, maybe the only one, to demonstrate and explain the wonderfulness of a program and the benefit they get by using the services offered most effectively. An interactive presentation on legal and compliance issues can be an effective tool in helping customers and/or management make good risk management decisions.
The structural properties, energetics, and dynamics of Ca{sup 2+} and Mn{sup 2+} substituents in KTaO{sub 3} are investigated from first principles. It is found that Ca substitutes for both K and Ta ions. Oxygen vacancies bind to isolated Ca ions residing at Ta-sites, causing off-center Ca displacement and forming large dipoles. There is also evidence that oppositely charged defects may cluster together. The calculations predict that the activation energy for dipole reorientation via oxygen vacancy hopping within the first neighbor shell of Ta-substituting Ca or Mn exceeds 2 eV. On the other hand, Mn{sup 2+} substituting at the K-site displaces off center along the (100) direction, also forming a dipole. This dipole can reorient via Mn hopping motion with an activation energy of {approximately} 0.18 eV, in reasonable agreement with experiments. The authors argue that, in general, metal ion hopping at the A-site, not oxygen vacancy hopping, is responsible for the small activation energies found in experiments.