Full opinion text
OPINION LONGOBARDI, Senior District Judge. I. NATURE AND STAGE OF THE PROCEEDINGS W.R. Grace & Co. — Conn. (“Grace”) is the owner of five patents relating to a composition, or the use of a composition, to reduce sulfur oxide (“SOx”) emissions from hydrocarbon conversion processes, such as fluid catalytic cracking (“FCC”) processes. The five patents-in-suit are U.S. Patents 4,469,589 (“’589 Patent”), 4,472,267 (“’267 Patent”), 4,495,305 (“’305 Patent”), 4,495,304 (“’304 Patent”), and 4,790,982 (“ ’982 Patent”). By stipulation, this case was tried on the basis of sixteen representative claims: claims 7, 21, 33, and 34 of the ’589 Patent; claims 5, 23, 31 and 39 of the ’267 patent; claims 3,15, 30, and 35 of the ’305 Patent; claims 6, 20, and 40 of the ’304 Patent; and claim 32 of the ’982 Patent. The ’304 and ’305 Patents cover compositions of spinel-containing SOx-reducing additives that are combined with hydrocarbon conversion catalysts, such as crystalline aluminosilicates (e.g., zeolites). The ’589 and ’267 Patents address the catalytic process through which the introduction of particular additives is used to reduce the level of SOx that is emitted from FCC units. The ’305 and ’267 Patents differ from the ’304 and ’589 Patents in that the ’305 and ’267 Patents require the SOx-redueing additive to contain a rare earth metal (e.g., cerium) in order to promote the oxidation of sulfur dioxide to sulfur trioxide as part of the SOx removal function of the additive. The asserted claims of the ’304, .’305, ’267, and ’589 Patents arise from two related patent applications filed simultaneously on July 29,1980. The ’982 Patent came later. Claim 32, the only claim from the ’982 Patent that is at issue in this ease, requires that the composition contain not only spinel and a rare earth metal such as cerium, but also a fourth metal component to promote (or catalyze) the sulfate reduction step of the additive’s operational cycle.- Grace alleges that Intercat, Inc. (“Inter-cat”) has contributed to and induced the direct infringement by Conoco, Inc. (“Conoco”) of the patents-in-suit. Intercat sold Conoco additives called NO-SOX and NO-SOX-PC. Conoco then introduced those additives to its FCC units, where the NO-SOX products allegedly combined with the cracking catalyst to form the claimed compositions and to perform the claimed SOx-removal process. In its defense, Intercat contends that its NO-SOx products do not infringe any of the patents-in-suit and that the patents are invalid for obviousness, for failing to distinctly claim the subject matter of the invention, and for inequitable conduct before the Patent and Trademark Office (“PTO”). At the close of Grace’s ease, Intercat and Conoco moved under Fed.R.Civ.P. 52(c) for judgment as a matter of law (“JMOL”) on the question of infringement. At the close of Defendants’ case, Grace moved under Fed. R.Civ.P. 52(c) for JMOL on each of the inequitable conduct defenses. In addition to addressing these two JMOL motions, this Court will resolve all questions relating to infringement and invalidity. This Opinion represents this Court’s findings of fact and conclusions of law. This Court has jurisdiction over the subject matter of this action under 28 U.S.C. § 1331 and § 1338. Venue is proper under 28 U.S.C. § 1391 and § 1400. II. BACKGROUND FACTS A. FCC UNITS Fluid catalytic cracking is a refinery process that converts heavy molecular weight compounds in crude oil into lighter weight compounds such as gasoline, diesel fuel, and-jet fuel. (Tr. 55). In the FCC process, the catalyst circulates through the regenerator where it comes into contact with the gas-oil feed, which is the feedstock to an FCC Unit. (UF-8; Tr. 743). This gas oil commonly contains sulfur, usually between .5% and 3% by weight and in all events between .1% and 5% by weight. (Tr. 748). The gas oil comes into contact and mixes with the FCC cracking catalyst that is circulating within the FCC unit. (UF-9). That contact occurs at a high temperature, in the range of 1,250 to 1,350 degrees Fahrenheit. (Tr. 743). In the United States, the active component of the cracking catalyst is crystalline alumi-nosilicate, also known as zeolite. (Tr. 744). The cracking catalyst looks like talcum powder and has a particle size of 20 to 120 microns in diameter. (Tr. 82). Although the catalyst is a solid, FCC units are referred to as “fluidized” because the catalysts behave like liquids when gases are passed through them. The FCC unit constantly recirculates the catalyst between the regenerator and the riser reactor sections of the FCC unit. Unwanted byproducts of this FCC process include sulfur oxides, which are considered so harmful to the environment that they are restricted by our nation’s environmental laws. (Tr. 56). There are three primary methods used to reduce the SOx emissions coming from an FCC unit. In the first, called “hydroprocessing” or “hydrotreating,” the sulfur is removed from the gas-oil feed itself. Although efficient, this method of removal is extremely expensive, requiring a capital investment of $50 million or more. A second method of SOx removal is “flue gas scrubbing” in which SOx is removed from the flue gas before it enters the atmosphere. Flue gas scrubbing also requires significant capital investment. The third method is the use of a sulfur reduction additive. (Tr. 56-57). In this third method, the SOx-reducing additive admixes with the cracking catalyst in the regenerator section of the FCC unit, is fluidized, and circulates through the FCC unit along with the catalyst. The entire process is completed in three steps. First, the SOx-reducing additive oxidizes the sulfur dioxide to sulfur trioxide. Once the sulfur trioxide is formed, the additive then captures it as a metal sulfate within the regenerator. The metal sulfate formed on the additive is stable under the conditions of the regenerator and circulates along with the cracking catalyst to the riser reactor. In the final step, the metal sulfate is reduced within the riser reactor, and the sulfur is released' from the FCC unit in the form of hydrogen sulfide. (Tr. 83-85) Then the process begins anew. Although the use of a SOx-reducing additive is not, in the long run, a cheap alternative to hydroprocessing or flue gas scrubbing, the use of an additive does not require any significant capital investment. Moreover, it offers a refiner a certain flexibility in that the refiner can adjust the amount of additive based on the sulfur content of the gas-oil feedstock. (Tr. 58-59). B. DEVELOPMENT OF THE SOx-RE-DUCING ADDITIVE INDUSTRY In the late-1970’s, Atlantic Richfield Company (“ARCO”) was operating an FCC unit near Los Angeles, California. This FCC facility was known as the Watson unit. The Watson FCC unit was subject to the regulations imposed by the South Coast Air Quality Management District (“SCAQMD”). Under those regulations, ARCO was compelled to reduce the SOx emissions of the Watson unit to a specified level by 1981 and to a much lower level by 1985. (Tr. 105-06). ARCO considered the options of a hydrotreater or a flue gas scrubber, but in order to avoid the large capital investments involved in both of those options (and in order to avoid a solid waste problem that would have resulted from the use of a flue gas scrubber), ARCO sought to develop a SOx-reducing additive as a viable way to achieve the emission standards without making a huge capital investment. In 1979, ARCO tested a SOx-reducing additive known as SOXCAT in its Watson unit and at an Amoco refinery. SOXCAT, which was jointly developed by ARCO and Engel-hard Corporation (Tr. 88), was a gamma alumina material impregnated with ceria. (UF-21). It consisted of 5% by weight cerium on alumina. The cerium in SOXCAT functioned to promote the oxidation of sulfur dioxide to sulfur trioxide, the first step in an additive’s removal of SOx. (Tr. 88). The alumina was used to capture the sulfur triox-ide to make the metal sulfate compound — the second step in the SOx removal process. (Tr. 89). SOXCAT had good initial activity, i.e., it. functioned to reduce SOx emissions from the FCC unit flue gas, but it rapidly deactivated. (UF-22). As a result, it was determined “that SOXCAT was not an economically viable SOx additive.” (Tr. 91). After the failure of the initial trial of SOX-CAT, a reorganization occurred in ARCO’s development efforts. Mr. Joseph W. Powell, who testified at trial, became a supervisor in the “process development group” which was led by Dr. Louis Magnabosco. (Tr. 94). Also formed at that time was the “process research group” headed by Dr. J. Mooi. Working for Dr. Mooi was a research chemist named Dr. John Jaeeker. (Tr. 94). Eventually, Engelhard Corporation decided not to continue participating in the joint development effort with ARCO. (Tr. 105). In the process research group, Dr. Jaecker, among others, searched for a viable additive. He recorded his progress in a laboratory notebook (DTX-13). Although Dr. Jaecker’s writing is difficult to read, the relevant substance can be extracted. On page 38563, entered on November 19, 1979, Dr. Jaeeker indicated that he and a co-worker, Marvin Johnson, discussed what they could do - to keep SOXCAT from deactivating. They “agreed that placing an ion into the alumina to prevent the possible movement of Ce into the lattice and thereby lose the activity might work.” Other possibilities were also discussed. On November 26, 1979, Dr. Jaeeker had a discussion with Dr. Mooi about SOXCAT. (DTX-13 at 38565). Dr. Mooi suggested mi-crospheres of silica as a substrate. Dr. Jaeeker also noted that Dr. Mooi “liked the spinel idea” especially with magnesium alu-mínate “which was used before.” Dr. Jaeeker wrote that Dr. Mooi “said it (magnesium alumínate spinel) prevented Co from penetrating alumina.” (DTX-13 at 38565), In a meeting held on December 3, 1979, Dr. Jaeeker suggested cerium on magnesium alumínate spinel as a potential additive. Notes from that meeting indicate that Dr. Jaeeker believed that the “spinel structure may prevent Ce from becoming buried” in the alumina. Other possibilities were also suggested. (PTX-204). Subsequent to the December 3, 1993, meeting, the process research group sent Mr. Powell a sample of cerium impregnated magnesium alumínate spinel for pilot plant testing. (Tr. 108). A pilot plant is a miniature catalytic cracking unit. (Tr. 98). ARCO had developed tests to measure both the initial activity of various compositions of SOx-re-ducing additives and their rate of deactivation. (Tr. 102-03). Mr. Powell explained the results of the testing: The cerium spinel test results were really amazing in the results that came back. We had been used to testing the SOXCAT material and whereas the baseline emission level for our little pilot plant was, maybe, 500 ppm, 5 percent concentration of SOXCAT, we would maybe take that emission level down to 250. When we first did the initial activity test of the spinel material, the engineer came back and told me that they got almost no SOx coming out of the flue gas of the little pilot plant unit. It was like eight, nine, ten ppm, almost within the scatter of the data that we had for our analysis. (Tr. 108-09). Mr. Powell was so astounded by the results that he thought there must be something wrong with the equipment. Mr. Powell instructed' his employées to recalibrate the pilot plant unit. When they did, the same results were indicated, verifying that the equipment was not faulty. (Tr. 109-10). Mr. Powell testified that he was “so amazed” he personally went to the pilot plant, which was several blocks from his office, just to look at the material. Mr. Powell recounted the real surprise of the experiment: And the shock was that we — a lot of this work was aimed at improving the stability of SOXCAT, but the surprise was that this was the initial activity test, not the stability test. We were yet to do a stability test. And so that was a complete surprise. We weren’t expecting initial activities that were much higher than SOXCAT. And that’s what I remember. That was quite an exciting time. (Tr. 110). The subsequent deactivation tests showed that not only was the cerium-impregnated magnesium alumínate spinel material more active initially in the reduction of SOx emissions, but it was also much more stable than SOXCAT. (Tr. 111). The cerium-impregnated magnesium alumínate spinel material was given the designation HRD-265. In a report dated March 17, 1980, Dr. Jaecker and some of his colleagues discussed their experiments: The major source of deactivation appears to be the transfer of cerium to the interior of the alumina lattice, probably in a reduced state, where it is unavailable for catalysis. This conclusion led to the recent preparation and Testing of MgAl204 spinel as a support for cerium, on the theory that the Mg+ + ions would occupy holes in the alumina lattice, forming a barrier to cerium diffusion. We are currently exploring other means of providing these barriers, which involve impregnating alumina with magnesium, other alkaline earths and lithium. This route should be less expensive than the spinel manufacture. (DTX-1 at 1). The researchers noted that the use of magnesium alumínate spinel reduced deactivation “markedly.” (DTX-1 at 15). ARCO contracted with a company called KATALCO to manufacture the spinel additive. (Tr. 119). The results of the first commercial trial of that material at the Watson FCC unit were disappointing. (Tr. 120). A second commercial trial was performed at Amoeo’s Whiting refinery in Whiting, Indiana. (Tr. 121). This trial also failed due primarily to mechanical problems in the unit. (Tr. 122). Having experienced apparent setbacks with their own material, ARCO tested Grace’s Additive R, which was then the only additive available commercially. (Tr. 123-24). The results of those tests showed Additive R to be no more effective than SOXCAT. (Tr. 124). KATALCO decided not to manufacture any more additive, so ARCO approached alternative suppliers. Grace’s chemical division produced a test quantity of HRD-276, a eeria-impregnated magnesium alumínate spinel, in 1983. (Tr. 125). Commercial tests of HRD-276 were “a brilliant success.” (Tr. 126). Grace’s chemical division decided not to produce more additive, so ARCO searched for other potential manufacturers. (Tr. 127-28). In 1984, ARCO' entered into an agreement with Katalistiks to manufacture commercial-sized quantities of the additive, and ARCO granted Katalistiks a license to produce HRD-276 and HRD-277. (Tr. 128-29, 136; PTX-2). The HRD-276 and HRD-277 materials were magnesium alumínate spinels having a Mg:Al atomic ratio of 0.5 and 1.0, respectively. Both materials had a surface area greater than 100 m/g and were impregnated with 9-12% wt. ceria. (PTX-2 at WRG-10282). As part of the license agreement, Katalistiks was provided with the formula for the materials. (Tr. 137). At that time, Regis Lippert, who is now the president of Intercat, was the president of Katal-istiks and signed the license agreement on behalf of Katalistiks. (Tr. 130,133). Thereafter, ARCO continued to make improvements to the additive. The introduction of vanadium into the formula doubled the effectiveness of the additive. (Tr. 131). The addition of 1% vanadium enhanced the release reaction, allowing the material to release more hydrogen sulfate in the riser reactor. (Tr. 131-32). ARCO named the vanadium-enhanced material HRD-280. (Tr. 131). Later, the HRD-280 material was sold commercially under the name DESOX. (Tr. 140). In 1985, ARCO decided to close the Harvey Technical Center and to sell its SOx-removing additive technology. (Tr. 137-38). Toward the end of 1983, Katalistiks had become part of Union Carbide Corporation (“Union Carbide”). (Tr. 868). Regis Lip-pert, who was still president of Katalistiks, advised Robert Kulperger, who was vice president of Union Carbide, that the purchase of ARCO’s SOx transfer agent teehnol-ogy would be a very good idea. (Tr. 139, 870; UF-112). In the summer of 1985, Ka-talistiks purchased the ARCO additive technology and hired some of ARCO’s personnel, including Mr. Powell. (Tr. 139-40; PTX-8). In late 1985 and early 1986, Regis Lippert left Katalistiks and started a company called Intercat USA, Inc., which was subsequently reincorporated as Intercat, Inc. (Tr. 874, 877). On April 15, 1987, Intercat obtained licenses under several Amoco patents which dealt with SOx-reducing additives. Intereat then began to manufacture an additive called LOSOX. (Tr. 886). Meanwhile Katalistiks was producing DE-SOX. Katalistiks doubled the vanadium content in DESOX in 1987, but otherwise produced the exact same composition that was originally named HRD-280. (Tr. 144, 150). In 1988, Katalistiks became a business unit ofUOP. • On .January 22, 1993, Grace .obtained UOP’s additive business, including the DE-SOX product and the patents-in-suit. (PTX-13). Grace attempted to replace the vanadium present in the DESOX product with iron and various other metals. (Tr. 643). After testing, Grace decided that replacing vanadium with iron would significantly reduce the performance of DESOX. (Tr. 648). Consequently, Grace retained the vanadium. The testimony at trial indicated that DE-SOX was far superior to any other additive on the market. As previously mentioned, DESOX was superior to SOXCAT and Grace’s Additive R. Other additives which appeared on the market were TRANSOX and LOSOX. TRANSOX, an additive developed by Chevron, showed very little SOx-removal activity. LOSOX, which was developed by Intercat, showed activity similar to SOXCAT; it was approximately one-fourth less active in reducing SOx than DESOX. (Tr. 152-53). By 1989, DESOX controlled 90% of the market, with Additive-R controlling the bulk of the remainder. (Tr. 154). Regis Lippert testified at trial that he recognized that Intercat’s LOSOX was “at best, a marginal product.” (Tr. 886). Mr. Lippert testified that although he wanted to develop a new product, he was concerned about the possibility of infringing “the ARCO patents.” (Tr. 887). He felt that Intercat needed to develop their own manufacturing process that was outside the scope of the ARCO patents. (Tr. 887). Edward Demmel and Dr. Louis Magnabosco were given the task of developing this new manufacturing process, and they succeeded in doing so. (Tr. 888). The product of that process was called NO-SOX, one of the accused products in this case. Early in 1994, Intercat introduced a new additive, NO-SOX-PC. (Tr. 902-03). NO-SOX-PC is also accused of infringing the patents-in-suit. In the period between 1993 to 1996, the NO-SOx products captured 15% of the SOx-reducing additive market. (Tr. 66). III. INFRINGEMENT A. DEFENDANTS’ MOTION FOR JMOL In their motion for JMOL, Defendants claim that Grace has not met its burden to 'prove that any of the representative claims are infringed either literally or under the doctrine of equivalents. Under Fed.R.Civ.P. 52(c), this court must weigh the evidence, resolve conflicts in the evidence, and decide where the preponderance lies. Wright & Miller, Federal Practice & Procedure: Civil 2d § 2573.1. Under Rule 52(e), this court is permitted to decline to render any judgment until the close of all evidence. This Court has chosen the latter route and will consider all of the evidence of record to determine whether Grace has proved by a preponderance of the evidence that Defendants are hable for infringement. B. CLAIM CONSTRUCTION In construing the meaning of patent claims, a court must consider three sources: the claim language, the patent specifications, and the prosecution history. Markman v. Westview Instruments, Inc., 52 F.3d 967, 979 (Fed.Cir.1995), aff'd, 517 U.S. 370, 116 S.Ct. 1384, 134 L.Ed.2d 577 (1996). A court may also hear and consider expert testimony, including evidence of how those skilled in the art would interpret the claims. Id. The initial step in claim construction is an examination of the language of the claims at issue. Stiftung v. Renishaw PLC, 945 F.2d 1173, 1177 (Fed.Cir.1991); American Standard, Inc. v. Pfizer Inc., 722 F.Supp. 86, 92 (D.Del.1989). The patent claims are what defines the right to exclude others from making the invention. Mark-man, 52 F.3d at 980. The words of a claim are normally given their ordinary and accustomed meaning, unless it appears from the specification and prosecution history that they were used differently by the inventor. In re Paulsen, 30 F.3d 1475, 1480 (Fed.Cir.1994). The patent specification contains a written description of the invention that enables one of ordinary skill in the art to make and use the invention. Markman, 52 F.3d at 979. It is “the single best guide to the meaning of a disputed term.” Vitronics Corp. v. Conceptronic, Inc., 90 F.3d 1576, 1582 (Fed.Cir.1996). The specification may act as “a sort of dictionary” which helps to explain the claims. Markman, 52 F.3d at 979. The specification cannot be used, however, to add extraneous limitations into a claim. Hoganas AB v. Dresser Indus., Inc., 9 F.3d 948, 950, (Fed.Cir.1993). Extraneous limitations are those that would be added into a claim from the specification “wholly apart from any need to interpret what the patentee meant by particular words and phrases” in the claims. Id. As stated plainly by the Federal Circuit, “claims are not to be interpreted by adding limitations appearing only in the specification.” Electro Medical Sys. S.A. v. Cooper Life Sciences, Inc., 34 F.3d 1048, 1054 (Fed.Cir.1994). On the other hand, when a particular interpretation of the terms of a claim would exclude the preferred embodiment described in the specification from the scope of the claim, such an interpretation “is rarely, if ever, correct and would require highly persuasive evidentiary support.” Vitronics, 90 F.3d at 1583. The prosecution history, which is the record of the proceedings in the Patent and Trademark Office, cannot enlarge diminish or vary the limitations in the claims but should be utilized to interpret the meaning of language used in the patent claims. Mark-man, 52 F.3d at 980. The prosecution history limits permissible claim construction to exclude any interpretation that was disclaimed during the prosecution of the patent. Southwall Technologies, Inc. v. Cardinal IG Co., 54 F.3d 1570, 1576 (Fed.Cir.1995). Extrinsic evidence such as expert testimony, dictionaries and learned treatises can be used, at the court’s discretion, “for the court’s understanding of the patent, [but] not for the purpose of varying or contradicting the terms of the claims.” Markman, 52 F.3d at 981. When intrinsic evidence alone is sufficient to resolve the ambiguity in a disputed claim term, it is improper to rely on extrinsic evidence. Vitronics, ,90 F.3d at 1583. The claims of a patent should be construed as they would have been understood by one of ordinary skill in the art at the time the invention was made. Mobil Oil Corp. v. Amoco Chems. Corp., 779 F.Supp. 1429, 1442 (D.Del.1991), aff'd, 980 F.2d 742, 1992 WL 279125 (Fed.Cir.1992) (citing Locate Corp. v. Ultraseal Ltd., 781 F.2d 861, 867 (Fed.Cir.1985)). 1. Spinel The major claim construction dispute involves the term “spinel.” Each of the representative claims is directed to a composition, or the use of a composition, which contains a bimetallic spinel within certain size and valence restrictions. {See, e.g., PTX-3, col. 20, lines 17-25). The specification describes what is meant by the term spinel: The spinel structure is based on a cubic close-packed array of oxide ions. Typically, the crystallographic unit cell of the spinel structure contains 32 oxygen atoms; one-eighth of the tetrahedral holes (of which there are two per anion) are occupied by a divalent metal ion, and one-half of the octahedral holes (of which there are two per anion) are occupied by trivalent metal ions. (PTX-8, col. 7, lines 44-50). The specification continues, “This typical spinel structure or a modification thereof is adaptable to many other mixed metal oxides” of various types. (PTX-3, col. 7, lines 51-53) (emphasis added). The specification includes magnesium alumínate spinel as one example, out of more than fifty examples, of a bimetallic spinel. (PTX-3, col. 8, lines 16, 20). The patent specification explains that alkaline earth metal spinels, “in particular magnesium alumínate spinel,” are the “preferred metal-containing spinels for use in the present invention.” (PTX-3, col. 8, lines 44^-46). The specification notes that the metal-containing spinels useful in the invention “may be derived from conventional and well known sources”’ (PTX-3, col. 8, lines 62-64). As a result, detailed descriptions of how to synthesize spinel were omitted from the specification. (PTX-3, col. 8, lines 62-64). The patentees did include, however, “a brief description of the preparation of the most preferred spinel, i.e. magnesium alumí-nate spinel.” (PTX-3. cols. 8-9, lines 67-2) Specifically, the patentees refer the reader to U.S. Patents 2,992,191 and 3,791,992, which include descriptions of how to prepare spinel. (PTX-3, col. 9, lines 5-8, 35-37). The patentees also include 25 examples which disclose how to synthesize spinel. (PTX-3, cols. 15-19). The patentees did not, however, refer to any particular method for analyzing a material to determine whether that material contains spinel. In contrast to the specification, the prosecution history is relatively unenlightening in regard to the definition of spinel. Defendants urge that the patentees relied upon the classic spinel definition included in U.S. Patent No. 4,233,186 to Duprez in order to overcome the prior art and that the scope of the claims should therefore be limited to that classic definition. It is true that the paten-tees explained to the PTO that certain materials produced in a prior art example were not spinel, relying in part on the definition of spinel in the Duprez patent. The patentees did not argue, however, that the magnesium alumínate disclosed in that prior art patent was not spinel. Rather, the patentees distinguished the magnesium alumínate disclosed in that prior art patent on the basis of surface size. (DTX 39 at 115; JSPH at 35-36, 75). This Court finds that there were no representations made in the prosecution history that would limit the scope of claim terms so as to exclude Grace’s proposed interpretation of the term' spinel. See Southwall Technologies, Inc. v. Cardinal IG Co., 54 F.3d 1570, 1576 (Fed.Cir.1995). The parties agree that in order to determine the existence of spinel in a composition a person of skill in the art at the time the invention was made would perform X-ray diffraction (“XRD”) analysis and compare the resulting pattern of peaks to a standard reference card. The parties have stipulated that XRD is the most reliable method for determining whether spinel is present in a sample. (UF-95). An organization called the International Center for Diffraction Data (“ICDD”) archives, collects, and distributes a data file of single-phase product X-ray diffraction patterns, also known as reference cards. (Tr. 184-85). The general manager and corporate secretary of the ICDD, Dr. Ronald Jenkins, testified on Grace’s behalf at trial. (Tr. 183-85). Dr. Jenkins explained that the first step in performing XRD analysis is to determine the elemental content of a sample material in order to focus the search toward reference cards for compounds that contain those elements. (Tr. 332). Then, one would perform an XRD analysis of the sample material to’ compare with the reference cards kept by the ICDD. (Tr. 184-85). A person skilled in the art would identify the three strongest peaks in the XRD pattern of the tested material and would, most likely, consult the Hanna-wait index. (Tr. 222-23). The Hannawalt index is organized so that every permutation of the three strongest peaks from each reference card appears in the index. (Tr. 222). For example, if the three strongest peaks on a reference card were at positions A, B, and C, the material would be listed in the Hanna-walt index as ABC, BCA, BAC, CBA, CAB, and ACB. (Tr. 222). The Hannawalt index would refer its user to appropriate reference cards, so that the patterns of the reference card and the XRD analysis of the material could be compared. Dr. Jenkins testified that the Hannawalt-index includes every permutation of the three strongest peaks because “the intensities [of the peaks] are unreliable.” (Tr. 1748). Dr. Jenkins explained that “[v]ery commonly one finds that the three strongest lines may be in reverse order or some other combination of orders.” (Tr. 224). In fact, even with respect to well-ordered, well-crystallized materials deviations in relative intensities of up to 40% are not uncommon. For a magnesium alumínate spinel that has a high surface area, the relative intensities could deviate by 200-300% from the reference card. (Tr. 433-34,1752). Rather than being based on the most common real world materials, reference cards are intentionally based on material that is remarkably well crystallized, so that the material gives “very good sharp peaks” which enables the ICDD to determine peak positions with greater accuracy. (Tr. 219). The dispute between the parties is whether, when comparing a composition’s XRD pattern with the magnesium alumínate spinel reference card, a person of ordinary skill in the art would require fairly strict conformity with the peak intensities on the reference card before identifying a material as spinel or whether that person would recognize a particular composition as containing spinel within the definition of the patent if there was substantial variation in the peak intensities, even though the peak positions generally matched the reference card. Grace contends that there can be substantial variation in peak intensity while Defendants assert that the peak intensities must largely match the reference card. As previously mentioned, the ’589, ’267,-’305, and ’304 Patents contain a number of examples for synthesizing spinel. Example I of those patents (“Yoo Example I”) provides one method for synthesizing magnesium alu-mínate spinel. The parties agree that the material produced by following the teaching of Yoo Example I is characterized by the patentees as magnesium alumínate spinel, yet that material does not match the applicable reference card in the relative intensities of the key peaks. Defendants contend that the patentees have therefore provided a disclosure that is in internal conflict. Grace, on the other hand, argues that a claim interpretation of spinel which would exclude the material of Yoo Example I would run counter to Federal Circuit precedent holding that a claim interpretation that would exclude from the scope of the claim the preferred embodiment described in the specification “is rarely, if ever, correct and would require highly persuasive evidentiary support.” Vitronics, 90 F.3d at 1583. This Court agrees with Grace. The paten-tees explain that “the spinel structure is based on a cubic close-packed array of oxide ions.” Then, the patentees describe the typical arrangement of the crystallographic unit cell of the spinel structure. The patentees do allow, however, for “a modification” of this typical arrangement. (PTX-3, col. 2, lines 51-53). The patentees use the term spinel in a fairly broad sense. In reading the specification as a whole, the patentees emphasize using the examples of the patent and the prior art to synthesize spinel. In particular, the patentees explain that the product created by Yoo Example I is a spinel. The claim construction urged by Defendants would exclude that preferred embodiment of the invention from the scope of the claims. This Court finds as fact that the evidence points clearly toward Grace’s interpretation of the term spinel. Each of the parties agrees that a person of ordinary skill in the art would utilize XRD analysis to determine the presence of spinel. This Court finds the testimony of Mr. Jenkins to be credible and extremely helpful in understanding XRD technology and the importance of the relative intensities of the peaks. Dr. Jenkins explained that the measurement of the intensities of the peaks in XRD analysis is “unreliable.” (Tr. 1748). Indeed, the entire Hannawalt indexing system is designed with this unreliability in mind. This certainly weighs heavily against finding that a person of ordinary skill in the art would reject a phase identification of magnesium alumínate spinel when all of the major peaks are present but differ somewhat from the reference card in their relative intensities. Defendants point to a text by Klug and Alexander which states that “[tjhere must be agreement within experimental error for all lines of the compound’s pattern both as to d spacing and relative intensity.” (DTX-727). Grace, however, points to testimony from Dr. Jenkins that the Klug and Alexander test is “way, way outdated” and reflects the state of the art in the early 1950’s when there were only 100 powder diffractometers in the entire world. (Tr. 1746-49). Indeed, the above-quoted sentence from Klug and Alexander is directly contradicted by an authoritative text, the Hannawalt search procedure guidelines, which was published only a few years before the invention at issue. (PTX-478). The Hannawalt procedure recognizes that: Because of various factors which frequently quite drastically affect intensity values, the experimental sample intensities may not agree with the File standard. But though the analyst does not know which of the three lines is strongest and which is second strongest, he can still rather quickly locate the entry by trying various combinations .... In the extreme case with enough tries, one could locate the pattern in a single entry search manual without any data on the intensities of any of the lines of the pattern. (PTX-478 at iv) (emphasis in original). Other extrinsic evidence points toward Grace’s claim interpretation of spinel. In the Bratton article admitted at trial (PTX-481), Dr. Bratton identified material as spinel when the XRD patterns matched in peak position but not in peak intensity. In contrast to Grace’s evidence of Yoo Example I and the Bratton article, Defendants have provided no evidence of a circumstance in which a person skilled in the art declined to call magnesium alumínate a spinel when the peak positions matched the reference card but the relative intensities did not. This leads the court to conclude that Defendants’ definition of spinel is litigation-inspired and not in accordance with the practice in the art. Even Dr. Wuensch, a defense witness, candidly admitted that the term spinel is used more loosely in practice than is technically precise. This Court finds that if a person of ordinary skill in the art, in comparing an XRD analysis of his or her material with the reference cards kept by the ICDD, would be led by the Hannawalt index to a reference card for spinel and would determine that such a material is spinel after comparing the XRD patterns, then that material is spinel within the meaning of the patents-in-suit. This Court finds as fact that a person of ordinary skill in the art would not demand strict compliance, or compliance within some arbitrary amount of acceptable deviation, with the relative intensities of the major peaks. This Court does not find that relative intensities are unimportant, however. They are important to an identification of the major peaks, and a greater match with relative intensities would yield greater confidence in a particular phase identification. 2. Minor Amount of Rare Earth Metal Component There is a dispute between the parties regarding whether claims 5 and 23 of the ’267 patent require a spinel that has within itself a minor amount of at least one rare earth metal component or whether the rare earth metal component is separate from the spinel and is one of the “discrete entities” within the meaning of the patent. In other words, must the rare earth metal be part of the spinel or separate from the spinel. Compare D.I. 250 at 10 with D.I. 251 at 7. The language of the claim at issue is as follows: the improvement which comprises: using in intimate admixture with said solid particles a minor amount of discrete entities having a composition different from said solid particles and comprising at least one alkaline earth metal-containing spinel including alkaline earth metal and a second metal having a valence higher than the valence of said alkaline earth metal, the atomic ratio of said alkaline earth metal to said second metal in said spinel being at least about 0.25 and said spinel having a surface area in the range of about 25 m2 /gm. to about 600 m2/gm., and a minor amount of at least one rare earth metal component, said discrete entities being present in an amount sufficient to reduce the amount of sulfur oxides in sid flue gas. (PTX-4, col. 19, line 62, to col. 10, line 8). This Court agrees with Grace that the plain meaning of the claim indicates that the “rare earth metal component” is not a component part of the spinel but of the discrete entities. Any doubt regarding the correctness of this interpretation is put to rest by the specification which states: “the discrete entities comprise (A) an effective amount of at least one alkaline earth metal containing spinel and (B) a minor amount of at least one rare earth metal component, preferably a cerium component, associated with the spinel....” (PTX-4, col. 6, 4-9). At another point in the specification, the patentees explain that the improvement involves “a particulate material comprising” the cracking catalyst and an effective amount of at least one alkaline metal-containing spinel and “a minor amount of at least one rare earth metal, preferably cerium, component associated with the spinel.” (PTX-4, col. 4, lines 31-41). Moreover, to adopt Defendants’ interpretation would be to exclude the preferred spinel, the magnesium alumínate spinel (which does not contain a rare earth metal), from the scope of the patent. The spinel and the rare earth metal are, therefore, two components of the discrete entities which are associated with each other. The ’267 patent does not require the rare earth metal to be part of the spinel. 3. Amount Sufficient to Reduce SOx in Flue Gas Claim 5 of the ’267 Patent requires the “discrete entities” to be “present in an amount sufficient to reduce the amount of sulfur oxides in said flue gas.” Defendants seem to argue that Grace was required to produce a witness to testify as to what amount of the discrete entities would be sufficient to reduce SOx emissions and whether those amounts were present in the accused processes. (D.I. 50 at 10). Grace argues that the patent does not require proof that certain numerical thresholds were met. (D.I. 251 at 8). This claim element is met so long as there is a sufficient amount of the discrete entities to reduce SOx emissions. No particular amount is mandated by the patentees. If there is a sufficient amount of the discrete entities to reduce SOx emissions in the flue gas, there is enough to satisfy this claim element. C. Application of Claims to Accused Process and Products Proof of infringement includes both the construction of the claims and the application of those claims to the products and processes at issue. Becton Dickinson & Co. v. C.R. Bard, Inc., 922 F.2d 792, 796 (Fed.Cir.1990). Having construed the claims regarding which there was a dispute, the Court will now turn to an application of those claims to the accused processes and products. 1. Does NO-SOx Contain Spinel? Grace contends that NO-SOx contains spinel, which is a claim element in all of the representative claims. More particularly, Grace alleges that NO-SOx contains the spinel most preferred by the patentees, magnesium alumínate spinel. Defendants admit that NO-SOx contains a magnesium alumínate material, but they argue that the material is not sufficiently crystallized to be in the spinel phase. Rather, Defendants argue that the magnesium alumínate of NO-SOx is in a “metastable” phase. The following evidence shows, and this Court finds as fact, that NOSOx contains “spinel” as that term is used in the patents-in-suit. a) XRD Analyses The parties agree that a person of ordinary skill in the art at the time the invention was made would perform XRD analysis and compare the resulting pattern to a standard reference card in order to determine the presence of spinel. The parties have stipulated that XRD is the most reliable method for determining whether spinel is present in a sample. If a person of ordinary skill in the art comparing an XRD analysis of NO-SOx with the reference card for magnesium alu-mínate spinel kept by the ICDD would determine that NO-SOx contains spinel, then that claim element is satisfied. Not surprisingly, the experts do not agree about whether NO-SOx contains magnesium alumínate spinel. Both Dr. Jenkins and Dr. Messing, who testified for Grace, found that the NO-SOx product contained spinel. (Tr. 332, 444). On the contrary, Dr. Uhlmann, who appeared at trial on behalf of Defendants, testified that NO-SOx does not contain spinel. (Tr. 1349). Rather, according to Dr. Uhlmann, NO-SOx contains a “quasi crystalline” magnesium alumínate material, or a metastable phase of magnesium alumí-nate. (Tr. 1351, 1354). Although the conclusions of the experts at trial diverged, the XRD patterns elicited by the various experts did not markedly differ. The basic difference between the experts, which led to their divergent conclusions, was whether to ascribe major or minor importance to the relative intensities of the peaks shown in the XRD analysis. (Tr. 1349). One challenge in the interpretation of the XRD patterns for NO-SOx is that NO-SOx contains more than just the single magnesium alumínate phase alleged by Grace to be spinel and by Defendants to be quasi-crystalline. In addition to the magnesium alumí-nate phase, Dr. Jenkins also identified magnesium oxide (periclase), and eeria. (Tr. 347-48, 352-53). Defendants agree that NO-SOx contains eeria and magnesium oxide. (D.I. 257 at OF43). Some of the peaks identified in the XRD pattern are attributable to these magnesium oxide and eeria phases. XRD analyses of the NO-SOx material can be found at PTX-250, PTX-251, PTX-252, and DTX-741. Two of those XRD charts are reproduced below. The eeria peaks can be found in the XRD patterns of NO-SOx where one would expect to find them. The three largest peaks for ceria (cerium oxide), according to its reference card, should be at 28.555 (relative intensity 100), 47.479 (relative intensity 52), and 56.335 (relative intensity 42). In addition, there should be another major peak at 33.082 (relative intensity 30). (PTX-266). The three largest-peaks in Grace’s XRD analysis of NO-SOx (PTX-252) are attributable to ceria. The very large peaks at the 28, 47, and 56 2-theta positions can .be ascribed to the presence of ceria in NO-SOx. The eeria peak at 33 2-theta is also easily identified. All of these ceria peaks are also readily identifiable in DTX-741, which is the Defendants’ XRD analysis of NO-SOx peaks. Once the ceria peaks are properly attributed, the magnesium alumínate spinel phase can be identified. The experts agree that the reference card for magnesium alumínate spinel is card -number 21-1152. (PTX-54). The XRD pattern for magnesium alumínate spinel is characterized by peaks at 19.029 degrees, 31.272 degrees, 36.853 degrees, 44.833 degrees, 59.371 degrees, and 65.243 degrees. The three highest peaks for magnesium alumínate spinel, according to its reference card (PTX-54), are at 36.853 degrees, 44.833 degrees, and 65.243 degrees. One would expect the highest peak to be at 36.853 degrees, a peak about 65% as high at 44.833 degrees, and a peak about 55% as high at 65.243 degrees. The next three highest peaks listed on the card are at 59.371 degrees with a relative intensity of 45%, at 31.272 degrees with a relative intensity of 40%, and at 19.029 degrees with a relative intensity of 35%. (PTX-54). In order to be led from the Hannawalt index to the magnesium spinel reference card, one would have to be able to identify the three highest peaks attributable to spinel at 36.853 degrees, 44.833 degrees, and 65.243 degrees. Once the ceria peaks are identified and attributed to ceria, the three largest peaks in the XRD analyses performed by both Grace and the Defendants can be found at the 36-37, 44-45, and 64-65 2-theta positions. In Grace’s analysis, the 64-65 degree peak is the largest, the 44-45 degree peak is the second largest, and the 36-37 degree peak is third in relative intensity. (PTX-252). In Defendants’ analysis, the 44-45 degree peak is the largest, followed by the 36-37 degree peak, with the 64-65 degree 2-theta peak placing third in relative intensity. (DTX-741). Importantly, both Defendants’ and Grace’s XRD analyses would lead a person of ordinary skill in the art to the reference card for magnesium alumínate spinel through use of the Hannawalt index. Furthermore, it is possible to identify each of the smaller peaks related to magnesium alumínate spinel in the analyses of NO-SOx performed by Grace (PTX-252) and by Defendants (DTX-741). There is a small bump in the pattern at the 19 2-theta position. Dr. Jenkins identified a buried peak at the 31 2-theta position, and there is clearly a peak at the 59 2-theta position. Other peaks in the XRD analyses can be attributed to the presence of magnesium oxide. The reference card for magnesium oxide indicates that there should be major peaks at the 43 and 62 2-theta positions. (PTX-265). The 43 2-theta peak appears in both PTX-252 and DTX-741 as a small peak on the slope of the incline of the 45 2-theta peak attributable to magnesium alumínate spinel. The 62 2-theta peak is a very small peak, but is also recognizable. (PTX-252, DTX-741). Dr. Uhlmann, in contrast to Dr. Jenkins, did not believe that spinel was present in NO-SOx. Although Dr. Uhlmann recognized that there are peaks in the positions where one would expect to find them for magnesium alumínate spinel, Dr. Uhlmann testified that the differences in relative intensities between the reference card and the XRD analysis of NO-SOx would preclude a phase identification of magnesium alumínate spinel. (Tr. 1343-49). Defendants do not argue, however, that a person of ordinary skill in the art who was attempting a phase identification would be led by the Hannawalt index to locate a magnesium alumínate phase other than spinel from the reference cards. Although Dr. Uhlmann argues that NO-SOx contains a metastable phase containing magnesium oxide and aluminum oxide, there is no reference card for such a material. Apparently, Defendants believe that a person skilled in the art would conclude that NO-SOx contains a material with the same peaks as magnesium alumínate spinel, but due to the variation in the relative intensities of those peaks, a person skilled in the art would not call that material spinel. This Court finds that a person of ordinary skill in the art, after performing an XRD analysis of NO-SOx, would conclude that NO-SOx does contain magnesium alumínate spinel. In both Grace’s analysis and Defendants’ analysis, one can clearly identify the three major peaks of magnesium alumínate spinel. The three minor peaks of magnesium alumínate spinel are also present. After identifying those peaks, and finding no reference card which matches the sample’s peaks better than the reference card for spinel, this Court agrees with Grace that persons of ordinary skill in the art would decide that NO-SOx contains spinel. b) XRD Arialysis By Amoco The finding that NO-SOx contains spinel is supported by Intercat’s prelitigation representations and other evidence. Perhaps the most persuasive of this other evidence is an analysis of NO-SOx performed by Amoco. Regis Lippert, as President of Intercat, wrote to Ekkehard Shoettle of Amoco to confirm that NO-SOx fell within the license agreement Intereat had éntered with Amoco. (PTX-118). Mr. Shoettle wrote back to Mr. Lippert, stating that the phases observed in the x-ray diffraction patterns of NO-SOx were ceria, magnesia,, and magnesium alumí-nate spinel. (PTX-119). Mr. Shoettle included with his letter the XRD graph of NO-SOx. The only differences between Amoco’s graph and the XRD analyses of NO-SOx produced at trial is that the magnesia peaks are somewhat more developed in the Amoco analysis. As explained earlier, in accordance with the reference card for magnesium alu-mínate spinel, one would expect the highest peak to be at 37 degrees, a peak about 65% as high at 45 degrees, and a peak about 55% as high at 65 degrees. The next three highest peaks listed on the card are at 59 degrees with a relative intensity of 45%, at 31 degrees with a relative intensity of 40%, and at 19 degrees with a relative intensity of 35%. (PTX-54). In the Amoco analysis, the 45 degree peak is the highest, followed by the 37 degree peak and the 65 degree peak which were about equal in relative intensity. Also clearly identifiable were small peaks at 19 degrees and 59 degrees. To the extent that the 31 degree peak existed in the Amoco analysis, it was buried beneath other peaks. Thus, the major peaks for magnesium alumí-nate spinel were identifiable in the Amoco analysis, but they did not match the reference card in their relative intensities. Despite the lack of a match with relative intensities, Amoco identified magnesium alu-mínate spinel as one of the phases present in NO-SOx. This evidence is especially important because Amoco had a financial incentive not to find spinel in NO-SOx. Under the license granted by Amoco to Intercat, Inter-cat was to pay less in royalties to Amoco if NO-SOx contained spinel. (PTX-71). Indeed, Intercat paid royalties to Amoco for sales of. NO-SOx under the lower rate of subparagraph 3.1(b) of the license agreement, which was only applicable to materials which contained a spinel. (Tr. 895). e) Intercat’s Papers and Patents In a paper presented to a symposium sponsored by the American Chemical Society, Louis Magnabosco and Edward Demmel, who were working for Intercat, noted that “the commercially successful SOx transfer agents are magnesium aluminum spinels that contain cerium. HRD-280 contains both cerium, and a transition metal.” (PTX-24 at 3). In their paper, Magnabosco and Demmel noted that magnesium aluminum spinel had been made by the powder method, the gel method, and the slurry peptizing method. (PTX-24 at 4). The authors then introduced a novel processing scheme, which they touted as the “quintessential extension of the Slurry-Peptizing Method to its ultimate physical limitation.” (PTX-24 at 5). The authors represented that “[t]he material made according to our processing scheme is named NO-SOx and is used successfully on a commercial scale.” (PTX-24 at 6). Magnabosco and Demmel then discuss the “magnesia-rich spinel peak” of NO-SOx. (PTX-24 at 6). In another paper written by Patrick A. Clark and Edward Demmel, who worked for Intercat, the authors unequivocally stated that “NO-SOx is a magnesia spinel made using a new, proprietary manufacturing process.” (PTX-23 at 2). A footnote to that sentence eites U.S. Patent 5,108,479 to Dem-mel and Magnabosco, which was their patent on the new manufacturing process. (PTX-23 at 4). In yet another paper, Intercat reported that “NO-SOx is a magnesia/alumina spi-nel, or crystal, made using a proprietary manufacturing process patented by Louis Magnabosco and INTERCAT’s Ed Demmel in April, 1992.” Again, Intereat cited U.S. Patent 5,108,479. (PTX-47 at 14,19). At trial, Grace introduced into evidence U.S. Patent 5,108,979 to Demmel and Magna-bosco as PTX-14. The title of that patent is “Synthetic Spinels and Processes for Making Them.” Each claim in that patent relates to a synthetic spinel or to a process for making such a spinel. (PTX-14). Regis Lippert admitted that the Demmel and Mag-nabosco manufacturing process was used in making NO-SOx. (Tr. 896). This Court finds it compelling that, prior to this litigation, Intercat consistently represented that NO-SOx contained magnesium alumínate spinel. It was not until the advent of this litigation that Intercat began claiming that NO-SOx contained not magnesium alu-mínate spinel, but a metastable phase of magnesium alumínate. d) Representations by Intercat Scientists In the context of an interoffice memorandum, Dr. Albert Vierheilig, Intercat’s resident ceramist, mentioned the 2-theta values for spinel in NO-SOx. (PTX-17). In addition, Mr. Demmel referred to NO-SOx as a magnesium rich spinel in conversations with Dr. Vierheilig. (Vierheilig Dep. at 11-12). In sum, this Court finds that Grace has proven by a preponderance of the evidence that NO-SOx contains spinel. 2. Does NO-SOx~PC Contain Spinel? In accordance with the reference card for magnesium alumínate spinel (PTX-54), the XRD pattern for magnesium alumínate spi-nel is characterized by peaks at 19.029 degrees, 31.272 degrees, 36.853 degrees, 44.833 degrees, 59.371 degrees, and 65.243 degrees. The three highest peaks for magnesium alu-mínate spinel are at 36.853 degrees, 44.833 degrees, and 65.243 degrees. One would expect the highest peak to be at 36.853 degrees, a peak about 65% as high at 44.833 degrees, and a peak about 55% as high at 65.243 degrees. The next three highest peaks listed on the card are at 59.371 degrees with a relative intensity of 45%, at 31.272 degrees with a relative intensity of 40%, and at 19.029 degrees with a relative intensity of 35%. (PTX-54). XRD analyses of the NO-SOx-PC material can be found at PTX-296, PTX-297, PTX-298, and DTX-735. Two XRD charts, PTX-296 and DTX-735, are reproduced below: In each of the analyses, there are major peaks at 28-29 degrees, 33 degrees, 36-37 degrees, 43 degrees, 44-45 degrees, 47-48 degrees, 56-57 degrees, 62-63 degrees, and 65 degrees. Those same peaks can be found in DTX-735 as the nine strongest peaks. All the experts agree that NO-SOx-PC contains eeria. The three largest peaks for eeria (cerium oxide), according to its reference card, should be at 28.555 (relative intensity 100), 47.479 (relative intensity 52), and 56.335 (relative intensity 42). In addition, there should be another major peak at 33.082 (relative intensity 30). (PTX-266). The major peaks for eeria are readily identifiable in the XRD analyses of NO-SOx-PC. The peaks located at 28-29 degrees, 33 degrees, 47-48 degrees, and 56-57 degrees can be attributed to eeria. The experts also agree that NO-SOX-PC contains magnesium oxide. The reference card for magnesium oxide reveals major peaks at the 43 and 62 2-theta positions. (PTX-265). The peaks at 43 degrees and 62-63 degrees can therefore be attributed to the magnesium oxide phase. Three 'major peaks remain unassigned, those at 36-37 degrees, 44-45 degrees, and 65 degrees. The three highest peaks for magnesium alumínate spinel, according to its reference .card (PTX-54), are at 36.853 degrees, 44.833 degrees, and 65.243 degrees. The existence of these peaks would lead one skilled in the art to the entry for magnesium alumínate spinel in the Hannawalt index. A person of ordinary skill in the art would then look for the more minor peaks of magnesium alumínate spinel; i.e., the peaks at 59 degrees, 31 degrees, and 19 degrees. A very small peak can be found at 59 degrees. The 31-degree peak is buried, as always, between the 28.555 degree and 33.082 degree ceria peaks. Although the 31-degree peak is buried, a small peak is nonetheless identifiable. At 19 degrees there is a very broad lump that can barely be characterized as a peak. Dr. Jenkins testified about how he performed a phase identification of the NO-SOx-PC material. (Tr. 367-372). He made a list of the peaks in terms of decreasing intensity, and starting with the strongest peak attempted to identify the phases. The strongest peak was at 28-29 degrees, which is one of the strong lines of ceria. He consulted the reference card for ceria (PTX-266) and was able to identify the lines of 28.55, 33.08, 47.47, and 56.33. Dr. Jenkins then eliminated the ceria lines from any further analysis. After eliminating the ceria lines, the next phase Dr. Jenkins identified was magnesium alumínate spinel. Dr. Jenkins found lines at 65.2, 59.37, 44.83, 36.85, and 31.27. Dr. Jenkins also identified the 19.03 peak as “this broad reflection of low angles.” (Tr. 371). Then Dr. Jenkins identified the magnesium oxide peaks at 63 degrees and 43 degrees. After eliminating all of those peaks, Dr. Jenkins then found “a small amount of bastnae-site-type material.” (Tr. 372). Dr. Jenkins was unable to identify phases other than ceria, magnesium alumínate spinel, magnesium oxide, and the bastnaesite material. (Tr. 378). Dr. Jenkins believed that there was also a small amount of amorphous material present, stating that “there may be a couple percent.” (Tr. 379). According to Dr. Jenkins, no free aluminum oxide was present. (Tr. 379). This Court fully credits Dr. Jenkins’s testimony. Dr. Uhlmann located the three major peaks for magnesium alumínate spinel, but noted the discrepancies in relative intensity between NO-SOx-PC and the reference card. (Tr. 1332). The primary problem with the intensity levels of the three major peaks in the NO-SOx-PC sample is that the 37 degree peak is too small. The peaks at 45 degrees and 65 degrees are about right in intensity compared to each other, but one would expect to see the 37 degree peak be two or three times larger than it is. In addition, Dr. Uhlmann testified that there was no clear evidence of peaks at 19 degrees or at 31 degrees. (Tr. 1333). Although Dr. Uhlmann did not find a peak at 31 degrees, Dr. Uhlmann admitted that one could find a small peak there if one wanted to do so. (Tr. 1335). Dr. Uhlmann’s conclusion from his analysis was that there was a magnesium alumínate phase or phases present in the NO-SOx products but that the magnesium alumínate phase was metastable rather than spinel. (Tr. 1633-36). In addition to the XRD evidence, the parties introduced other evidence regarding the presence or absence of spinel which is of decidedly lesser value. Perhaps the most probative of this other evidence is the lattice cell parameter chart created by Dr. Jenkins. (PTX-307). Using the peaks shown on the XRD analysis, Dr. Jenkins calculated that the magnesium alumínate of NO-SOx-PC had a cubic, face-centered structure, which is the lattice structure of magnesium alumínate spinel. (Tr. 375-76). The transmission electron microscopy (“TEM”) analysis by Dr. Wuensch is of little probative value. First, TEM is a relatively recent technique that was not commonly used before 1990. (Tr. 1198). Moreover, it has been stipulated that a person of skill in the art at the time the patent application was filed would have relied on XRD analysis. If persons skilled in the art at the time the patent application was filed would have understood a material to be spinel based upon XRD analysis, such a material would be spi-nel within the meaning of the patent even if advanced electron microscopy that was then unavailable, or at least not widely utilized, would demonstrate that those persons of skill in the art to have been erroneous in their phase identification. Dr. Wuensch’s trial testimony regarding the conclusions to be reached from, the TEM was shaken by his own deposition testimony. At his deposition, Dr. Wuensch testified that the NO-SOx materials were crystalline and contained no amorphous material. (Tr. 1223-24). At trial, Dr. Wuensch testified that NO-SOx-PC contained 50% amorphous material. (Tr. 1224-25). Dr. Wuensch attempted to explain the discrepancy by stating that at the time of the deposition he had not had a chance to analyze the samples completely. (Tr. 1124-25). This Court is not satisfied by that explanation