Gary E. Giles Computational Physics and Engineering Division. Jon S. Bullock Y-17npwlopment Division

Transcription

1 ORNL/CP VALIDATION OF THE BEPLATE CODE b/jf? 7/()i%T-- Gary E. Giles Computational Physics and Engineering Division Jon S. Bullock Y-17npwlopment Division Oak Ridge National Laboratory' To be published in the proceedings of The American Electroplating and Surface Finishers Electroforming Symposium October 3, 1997 San Diego, California ' RECEt \/ED JAN "The submitted manuscript has been authored by a contractor ofthe U S. Government under contract No. DEAC5-96R Accordingly. the U.S. Government retains a nonexclusive, royalty-free license to publish or reproduce the published form of this contribution. or allow others to do so, for U S. Government purposes." Managed by Lockheed Martin Energy Research Corp. for the U.S. Department of Energy under contract DE- AC5-96R [ mc PGSTECTED

2 DISCLAIMER This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency thereof, nor any of their employm, makes any warranty, express or implied. or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

3 Validation of the BEPLATE code Gary Giles, Len Gray Oak Ridge National Laboratory Jon Bullock Oak Ridge Y 12 Plant Abstract The electroforming simulation code BEPLATE (Boundary Element - PLATE) has been developed and validated for specific applications at Oak Ridge. New areas of application are opening up and more validations are being performed. This paper reports the validation experience of the BEPLATE code on two types of electroforms and describes some recent applications of the code. Introduction Electroforming is the electrochemical deposition of metal ions on a mandrel to make a free standing part. The process can be complicated and sometimes difficult to control to achieve the desired part shape and part metallurgical properties. The BEPLATE code for eiectroforming simulation was developed to improve the capabilities of the electroformer to predict the effects of changes in the electroforming cell design before actual costly and time consuming experiments are performed. The original development of the BEPLATE code is described in Ref. 1 and more current development of the user interface is reported in Ref. 2. A brief description of the basic modeling paradigm is included here. The movement of the metal plating ions through the electrolyte is controlled by diffusion, convection and migration driven by the electric field. In the BEPLATE code, the basic assumption is that this complicated process can be approximated by solving the Laplace equation for the flow of current through the electrolyte volume. The solution is modified by the nonlinear boundary conditions at the electroactive surfaces (electrodes). These boundary conditions approximate the effects of electrochemical surface reactions and of mass-transfer effects (collectively known as polarization). The paradigm used in the BEPLATE code places all the nonlinearities on the boundaries. This is equivalent to specifying constant electrical conductivity throughout the electrolyte tank. This assumption is adequate for most well-mixed situations that do not have large convective induced concentration gradients or large temperature gradients in the bulk of the electrolyte volume. These conditions are fairly typical of most electroforming processes. BEPLATE uses the Boundary Element (BE) Method to solve the linear Laplace equation for the electric field. This technique has several advantages that are uniquely suitable for the electroforming process. In this process, most of the significmt electrochemical reactions occur at the surfaces and are controlled by the local potential and current flow. Thus the parameters of interest from the solution of the Laplace Equation are a l l on the boundaries of the electrolyte (electroactive surfaces), even though some properties used are actually bulk properties, such as conductivity, diffusivity, etc. The solution is obtained only on the boundaries and thus only the surfaces need to be discretized. The discretization of the complete electrolyte volume is not required, saving considerable effort in model building. Discretization of only the surfaces allows another efficiency that is ideally suited to the simulation of electroforming. As the part surfaces grow, the shape of the cathode changes that can markedly change the solution of the basic Laplace Equation and the solution as modified by the polarization boundary conditions. This new current density distribution can significantly change the direction of subsequent part surface growth. The BE technique, as implemented in the current version of the BEPLATE code, uses a collation method where coefficients are calculated that determine the influence of each node on every other node. If one of a pair of nodes changes location, changing the shape of an element connected to it, the coefficient between these nodes 1

4 must be reevaluated. However, if both nodes are unchanged the coefficient need not be reevaluated. Recalculating only the coefficients for changed node pairs can allow significant savings in computational effort for problems in which only a small portion of the surface changes shape. This situation is typical of many electroforming setups. These advantages are especially telling when compared with the Finite Element or Finite Volume methods. In these methods, the entire volume (which can be quite complexly shaped) must be completely discretized. If one part of the surface of the electrolyte volume changes significantly these changes must be propagated throughout the volume, changing the node locations and element sizes, and all coefficients must be reevaluated. The polarization boundary condition is a set of highly nonlinear equations, and it can be extremely difficult to produce a converged solution; this appears to be especially true of the nickel electrolyte systems. We have developed improved techniques to provide more robust and efficient convergence of the nonlinear polarization boundary conditions. Even so, these solutions can require considerable computational resources, and more efficient techniques need to be developed. In addition, several important electroforming processes involve multiple simultaneous reactions. These reactions compete, and the balance between such simultaneous processes can be difficult to compute. We have begun to develop the capability to model several simultaneous reactions that will allow more accurate simulation of these complex processes. Validations- Comparison with Experiments The BEPLATE paradigm has been successfully applied in several validations (comparisons with experiments). BEPLATE was originally developed for the Y12 Plant to assist in the optimization of electroforming cell designs. The original test part for this development was the exterior of a hemisphere joined at the equator to a short cylinder. Two tests were analyzed for the original development test part. The part was rotated while suspended in the center of the top of the electrolyte surface in a square tank (Fig. 1). A thick coating of metal was deposited on the mandrel (cathode) to make the electroformed part. This test electroform used four anodes suspended in the comers of the tank. The arrangement produced a nonuniform thickness distribution from the pole to the base. The circumferential variations were averaged out by the rotation. The first two test electroforms were performed using a lead electrolyte with and without a current modification device (a nonconducting conformal shield). The electroforming calculations for the case without the shield agreed within &4% with the experiment (Fig. 2). The case with shield agreed to within +5% with the experiment (Fig. 3). A newer experiment supplied by Chris Lovette of Wendt Dunnington is quite demanding and exercises the simulator in a different direction. This part is grown on the inside of a rotating axisymrnetric mandrel with a single central cylindrical anode. The mandrel is composed of a hollow cylinder with a V-groove cut into its inner surface. The electrolyte system was nickel-cobalt with 1%of the electroform being cobalt. The electrochemical parameters were extrapolated from a nickel-only system. Since nickel and cobalt are similar electrochemically, the single-reaction form of the polarization model was used in this preliminary calculation. The comparison of the thickness distribution is shown in Fig. 4.The simulation agrees well in shape but overestimates the thickness in the bottom of the groove. The difference between the calculated and experimental thickness data is well within the variation that is possible by adjusting the electrochemical parameters for a single reaction case. Since at least two reactions are involved in this electroform, these calculations were necessarily delayed until the multi-reaction model is validated. However, the time history of the surface evolution for this case is instructive. As the two sides of the groove grow together, the current into the very bottom is restricted and the bottom node does not grow as much. A cusp forms where the two sides approach one another. In some electroforms, such a cusp can form and can be undesirable. In simulation, such a cusp may be an indication that, at the least, a finer mesh should be used. In addition, as the sides grow closer the code should adjust the mesh. This is done by merging or splitting elements to more accurately model the surface and maintain a correct topology for the surface. The present version of the code does not perform this modification to the 2

5 mesh and therefore can only provide approximate solutions for cases with large surface growth or surfaces that grow close together. Other Applications of the BEPLATE Code We have also applied the BEPLATE code to models of systems for which we do not yet have experimental data. As a demonstration of the code s capabilities, we simulated the electroforming on a frustum of a shallow angle cone (nearly a cylinder to the eye). This geometry is taker, from a NASA Mru.slitli Space Flight Ceiirel elzctrofonrling experiment to produce a grazing-angle X-Ray mirror for orbital observation of stellar objects. Figure 5 shows the thickness distribution for several shield scenarios. These shields were concentric short cylinders at the top and bottom with different heights. We plan several electroforming experiments, and characterizations of the electrochemical parameters, to produce a validation of the code in this system. We are currently investigating two electrochemical systems that are related to electroforming. The first is electrocoating, in collaboration with Ford Motor Company. The electrocoating process is similar to electroforming in that an electric field is used to deposit paint on a metal. However, the polarization-like boundary conditions are quite different; in fact, they are a little simpler. We have just started this effort and only have preliminary results. Ford wants a tool to help them in the coating of automotive parts to achieve an adequate coating that does not waste expensive paint. The second related investigation is in simulation of the electrochemical oxidation of a chemical species inside an Electrospray Mass Spectrometer (ESMS) unit. The Electrospray process is used to provide charged ions of an analyte to the mass spectrometer for purposes of quantitation. This process is depicted in Figs. 6-7, where a small diameter tube is connected to a reservoir containing an electrolyte and the analyte. One end of the tube is open and pointing at a charged plate. The voltage difference is quite large (1-1 KV) and can induce a spray from the tube. The large gradient of the electrical potential overcomes the surface tension of the meniscus at the end of the tube forming a spray of droplets. The applied voltage also causes the electrochemical oxidation of the analyte, and thus the droplet contains charged analyte ions. These droplets undergo splitting and evaporation and are transported into the Mass Spectrometer chamber to be analyzed. Our modeling concerns the electrochemical oxidation of the analyte within the small diameter (1micron) tube. The concern is the analyte oxidization distribution and completeness. If this process can be quantitatively understood, it may be controllable to produce more effective sprays. These issues influence the efficiency of the whole process, and if they can be improved then lower concentrations of analyte can be detected. In addition, in order to develop smaller ESMS units for field detection of hazardous chemicals, the details of this process must be understood. Eventually it may be possible to develop a micro-mechanical-electro-system sized ESMS unit that could exploit the very small size of the unit, in terms of the small testing volume required and potentially higher magnetic and electric fields. Conclusions The validations reported in this paper are limited and further validations are planned. Even so, the results are quite good, generally within 5% of the experimental thickness. The results also show qualitative agreement in shape of the thickness distribution for a part with shape edges. These results give confidence that future validations will be successful and, more importantly, that the application of the code in new areas will be possible. 3

6 References 1 G. E. Giles, L. J. Gray, J. S. Bullock, IV, BEPLATE - Simulation of Electrochemical Plating, WCSDlTM-89, Martin Marietta Energy Systems, Inc. Oak Ridge, TN, September 199. G. E. Giles, Electroforming Cell Design Tool Development, presented at the American Electroplaters and Surface Finishers Electroforming Symposium, Las Vegas, NV, March Cathode Fig. 1. Electroforming tank with standard test part. 4

7 u*ju.28 h E 1 I W m a, C exp ( 4% error bars) \.3 s -2? T = 37 C V = -1.69V Exchange current =. 168 Transfer coefficient =.3.2 I 2 1 Distance from base (cm) Fig. 2. Calculated and experimental plated thickness for standard test part without shield Distance from base (cm) Fig. 3. Calculated and experimental plated thickness for standard test part with conformal shield. 5

8 .35.3 e L;: o v In In ).c c.15.1 Axial distance from top (cm) Fig. 4. Experimental thickness compared with preliminary calculations Wendt Dunnington Vgroove part n E.11 i L A No shield Y v) a.1 Y E.9 t Axial distance from base (cm) 5 Fig. 5 Comparison of thickness distribution of several shields on the test electroform of a NASA X-Ray mirror. 6

9 a EI ect rospray Exterior Geometry - Taylor Cone 4, Solution inlet a* - To Mass Spectroscope Metal Fig. 6. Electrospray process used for mass spectrometer. Electrospray I nte rior Geometry v=ov Electrolyte+Analyte 4 Oxidized analyte + solution converted into a spray Fig. 7. Portion of the electrospray process modeled by BEPLATE. 7

10 M l l1l 'ubi. Date (11) 14c17 I I Sponsor Code (1 8) *DOE I '% F JC Category (19) LC- 9 9 DOE/& DOE