Cerium Containing Copper Based Shape Memory Alloy

Description

CROSS-REFERENCE TO RELATED PATENT APPLICATIONS

This patent application claims the benefit of U.S. Provisional Patent Application No. 63/662,506, filed Jun. 21, 2024, the entire teachings and disclosure of which are incorporated herein by reference thereto.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH AND DEVELOPMENT

This invention was made with government support under DE-AC02-06CH11358 awarded by the United States Department of Energy. The government has certain rights in the invention.

FIELD OF THE INVENTION

This invention generally relates to a shape memory alloy (SMA) and, in particular, to a copper (Cu)-based shape memory alloy.

BACKGROUND OF THE INVENTION

Shape memory alloys (SMAs) have been considered a promising technology for a variety of different applications. In one example, NASA targeted SMAs as a potential material for tires in developing the Mars Rover. This novel tire was designed to run on a harsh terrain covered with razor sharp rocks. Such tires were puncture-free, offered optimum tire-road contact, and provided lightweight advantages over the then current state-of-the art tire constructions. Current SMA-tire technology uses NiTi, a well-developed shape memory alloy that possesses the desired mechanical properties for the tire application.

Unfortunately, while potentially cost-justified for missions to Mars, NiTi is prohibitively expensive for most consumer tire applications. In 2022, the lowest price of non-medical grade NiTi wire was about $250/kg, while each tire for a passenger car would need at least 2 kg of SMA, costing about $500 per tire for just the raw materials. In comparison, a top-grade 225/50R17 tire costs only $200 in retail price. Moreover, when a rubber tread is used on the SMA tire to minimize road wear, the SMA must be compatible with rubber for the adhesion between the two materials. NiTi is not compatible with rubber and often a copper coating is needed.

In view of the foregoing, a cost-effective SMA material is needed for the SMA-tire technology to be widely adopted by the auto industry. Cu-based SMA is much cheaper than NiTi SMA. The cost of copper, which typically makes up >80% of the material, is only about $10/kg (Bloomberg Markets: Precious and Industrial Metals, May 3, 2022). Cu—Al—Mn (Al 16-18 at %, Mn 9-13 at %) was shown to have sub-ambient austenite finishing temperatures which allow its usage for commercial vehicle tires that can be subject to room and freezing temperatures. Most Cu-based SMAs are brittle and difficult to process. But the Cu—Al—Mn SMA with Al 16-18 at % and Mn 9-13 at % is different. It exhibits excellent workability, significantly reducing its processing cost and enhancing its reliability. However, its transformation stress (140 MPa) is significantly lower than that of the NiTi (700 MPa), which imposes a difficult challenge when designing a tire for high load conditions and other critical design considerations for wide operation temperature range, overload protection, and safety.

BRIEF SUMMARY OF THE INVENTION

Embodiments of the present disclosure relate to novel compositions of Cu-based SMAs and to thermal-mechanical processes for improving their shape memory properties. More particularly, the present disclosure relates to compositions, processes, microstructures, and properties of rare earth containing Cu-based SMAs that exhibit a combination of tunable transformation stress, recoverability, transformation temperatures, and fabricability.

In a first aspect, embodiments of the present disclosure relate to a shape memory alloy. The shape memory alloy comprises from about 5 at % to about 30 at % aluminum, from about 0.05 at % to about 30 at % manganese, from about 0.05 at % to about 10 at % of a rare earth element, from 0 at % to about 10 at % of a transition metal element, and balance copper.

In a second aspect, embodiments of the present disclosure relate to the shape memory alloy of the first aspect in which the rare earth element increases a strength of the shape memory alloy.

In a third aspect, embodiments of the present disclosure relate to the shape memory alloy of the first aspect or the second aspect in which the rare earth element is selected from a group consisting of cerium, lanthanum, yttrium, scandium, or a combination of two or more thereof.

In a fourth aspect, embodiments of the present disclosure relate to the shape memory alloy of any of the first aspect to the third aspect in which the shape memory alloy comprises at least 0.05 at % of the transition metal element and in which the transition metal changes the phase transformation temperature and ductility of the shape memory alloy.

In a fifth aspect, embodiments of the present disclosure relate to the shape memory alloy of the fourth aspect in which the transition metal element is selected from a group consisting of tin, nickel, silver, zinc, iron, cobalt, chromium, vanadium, titanium, calcium, or a combination of two or more thereof.

In a sixth aspect, embodiments of the present disclosure relate to the shape memory alloy of any of the first aspect to the fifth aspect in which the shape memory alloy comprises a transformation stress for the induced martensite transformation of at least 150 MPa.

In a seventh aspect, embodiments of the present disclosure relate to the shape memory alloy of any of the first aspect to the sixth aspect in which the shape memory alloy comprises a peak stress of at least 170 MPa.

In an eight aspect, embodiments of the present disclosure relate to the shape memory alloy of any of the first aspect to the seventh aspect in which a microstructure of the shape memory alloy comprises intermetallic compounds of aluminum and cerium at grain boundaries.

In a ninth aspect, embodiments of the present disclosure relate to the shape memory alloy of any of the eighth aspect in which the intermetallic compounds comprise at least one of Al₃Ce and Al₁₁Ce₃.

In a tenth aspect, embodiments of the present disclosure relate to the shape memory alloy of any of the first aspect to the ninth aspect in which the shape memory alloy comprises an austenite start temperature and an austenite finish temperature both within a range from −40° C. to 0° C.

In an eleventh aspect, embodiments of the present disclosure relate to a device comprising the shape memory alloy according to any of the first aspect to the tenth aspect in which the device is an elastocaloric heat pump, a smart structure, or an actuator.

In a twelfth aspect, embodiments of the present disclosure relate to a device comprising the shape memory alloy according to any of the first aspect to the tenth aspect in which the device is an elastocaloric refrigerant, a non-pneumatic tire, anti-earthquake rebar, or robotic muscle.

In a thirteenth aspect, embodiments of the present disclosure relate to a thermomechanical process to optimize microstructure and shape memory properties of the shape memory alloy according to any of the first aspect to the tenth aspect. In the thermomechanical process, an ingot of the shape memory alloy is solution treated at a temperature in a range of 750° C. to 950° C. for a time in a range of 0.5 hours to 5 hours followed by cooling.

In a fourteenth aspect, embodiments of the present disclosure relate to the thermomechanical process of the thirteenth aspect in which the cooling comprises water quenching.

In a fifteenth aspect, embodiments of the present disclosure relate to the thermomechanical process of the thirteenth aspect or the fourteenth aspect in which the process further comprises hot deforming the ingot, after solution treating, to reduce defects and obtain uniform microstructure and quenching the hot deformed ingot.

In a sixteenth aspect, embodiments of the present disclosure relate to the thermomechanical process of the fifteenth aspect in which the process further comprises tempering the ingot, after hot deforming, at a temperature in a range from 150° C. to 350° C. for a time in a range of 15 minutes to 60 minutes and quenching the tempered ingot to achieve a disorder state and improved ductility.

In a seventeenth aspect, embodiments of the present disclosure relate to the thermomechanical process of the sixteenth aspect in which the process further comprises cold working the ingot to obtain optimum microstructure and residual stress, thereby improving stress plateau and adjusting phase transformation temperature.

In an eighteenth aspect, embodiments of the present disclosure relate to the thermomechanical process of the sixteenth aspect or the seventeenth aspect in which the process further comprises isothermal, thermomechanically stabilizing the ingot to obtain optimum microstructure and residual stress thereby improve stress plateau.

In a nineteenth aspect, embodiments of the present disclosure relate to the thermomechanical process of the seventeenth aspect or the eighteenth aspect in which the process further comprises hot deforming and tempering the ingot one or more additional times to achieve a desired grain size and microstructure.

In a twentieth aspect, embodiments of the present disclosure relate to the thermomechanical process of any of the thirteenth aspect to the nineteenth aspect in which the shape memory alloy comprises <1 at % of the rare earth element.

Other aspects, objectives and advantages of the invention will become more apparent from the following detailed description when taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The accompanying drawings incorporated in and forming a part of the specification illustrate several aspects of the present invention and, together with the description, serve to explain the principles of the invention. In the drawings:

FIG. 1 provides room temperature tensile curves (loaded up to 2% strain then unloaded unless fracture occurs) of Cu—Al—Mn alloys with different levels of Ce (in at %) additions, according to exemplary embodiments;

FIGS. 2A and 2B provide DSC curves showing the melting points and the austenite start and finish temperatures of the Cu—Al—Mn alloys, respectively, according to exemplary embodiments;

FIGS. 3A-3F provides backscattered electron micrographs of Cu—Al—Mn alloys with different levels of Ce additions in which graphs represent 0%, 0.1%, 0.25%, 0.5%, 1%, and 2% (at) of Ce addition, respectively, according to exemplary embodiments;

FIGS. 4A-4E provide Energy Dispersive Spectroscopy (EDS) maps showing the partitioning of elements, highlighting that the intermetallic precipitates formed are rich in Al and Ce, according to exemplary embodiments; and

FIG. 5 provides X-ray diffraction (XRD) patterns of Cu—Al—Mn alloys with different levels of Ce additions (in at %), according to exemplary embodiments.

While the invention will be described in connection with certain preferred embodiments, there is no intent to limit it to those embodiments. On the contrary, the intent is to cover all alternatives, modifications and equivalents as included within the spirit and scope of the invention as defined by the appended claims.

DETAILED DESCRIPTION OF THE INVENTION

Referring generally to the figures, various embodiments of a copper (Cu)-based shape memory alloy (SMA) having alloying additions of at least one rare earth and, optionally, at least one transition metal are provided. In particular, the Cu-based SMA is a Cu—Mn—Al alloy including additions of rare earth elements, such as Ce and La, among others, and transition metals, such as Sn, Ni, and Ag, among others, to increase its strength for use, e.g., in applications involving superelasticity and shape memory effect. Advantageously, embodiments of the presently disclosed Cu-based SMA exhibits strength and recovery performance close to NiTi but at a much lower cost. Exemplary embodiments of the Cu-based SMA will be described in greater detail below and in relation to the figures provided herewith. These exemplary embodiments are provided by way of illustration and not by way of limitation.

SMAs exhibit large recoverable deformation. Such property makes SMAs suitable for many applications requiring large recoverable deformation. For example, a non-pneumatic tire made of shape memory alloy can sustain higher load, maintain optimum contact area, and more importantly it is immune to puncture. Leveraging SMA materials in tire technologies will make vehicles safer, lighter, more reliable, and more environmentally friendly. Currently, the state-of-the-art SMA is the near equiatomic nickel-titanium alloy which contains expensive elements and is difficult to process. Cu-based SMAs, including those according to the present disclosure, are comparatively low-cost and easy to process, but the superelastic stress of conventional Cu-based SMAs is relatively low compared to NiTi SMA, which limits the load capability and the power density that the conventional Cu-based SMA materials can deliver. As will be discussed more fully below, embodiments of the presently disclosed Cu-based SMAs provide improved strength, recoverable strain, and ductility, which opens new application spaces for Cu-based SMAs.

In one or more embodiments, the Cu-based SMA is a Cu—Mn—Al alloy with additions of one or more rare earth elements and, optionally, one or more transition metal elements. Generally, the Cu-based SMA can be described as a series of ternary Cu-based SMAs, such as Cu—Mn—Al—X—Y, with fourth (X) and fifth (Y) elements from the transition metals and rare earth metals added to the main alloys for shape memory applications. In one or more embodiments, the rare earth element is selected from a group comprising Ce, La, Y, Sc, and combinations of two or more thereof. In one or more embodiments, the transition metal element is selected from a group comprising Sn, Ni, Ag, Zn, Fe, Co, Cr, V, Ti, Ca, and a combination of two or more thereof.

In one or more embodiments, the Cu—Mn—Al alloy comprises from about 5 at % to about 30 at %, in particular about 10 at % to about 24 at %, aluminum. In one or more embodiments, the Cu—Mn—Al alloy comprises from about 0.05 at % to about 30 at %, in particular about 4 at % to about 18 at %, manganese. In one or more embodiments, the Cu—Mn—Al alloy comprises from about 0.05 at % to about 10 at % of the rear earth element. In one or more embodiments, the Cu—Mn—Al alloy comprises from about 0.05 at % to about 10 at % of the transition metal element. In one or more embodiments, the balance of the Cu—Mn—Al alloy comprises copper, which may be in a range from about 50 at % to about 90 at % of copper.

The addition of the rare earths and transition metals to the Cu—Mn—Al alloy contribute to the solid solution strengthening and precipitation hardening of the alloy. Solid solution strengthening and precipitation hardening are well known mechanisms to improve the strength of metals and alloys. Earlier works have shown that Ni and Sn addition can significantly increase the room temperature strength of Cu—Mn—Al by lowering the phase transformation temperature thereby increasing the stress required for inducing the phase transformation. This effect is linear and is governed by the Clausius-Clapeyron relation.

According to the present disclosure, however, the main contributor to the precipitation hardening of the Cu—Mn—Al alloy is the rare earth component, in particular Ce. Ce is a highly reactive rare earth element, and Ce tends to react with elements that have high electronegativity such as oxygen (O) and aluminum (Al). It has been shown that Ce can purify an alloy by combining with O impurities. As an example, Ce has been added to Al alloys to form small and uniformly distributed Al—Ce intermetallic compound precipitates. These precipitates cannot be dissolved even at 300° C. thereby retaining the alloy's strength at high temperature. As will be demonstrated in the experimental examples below, the Ce also forms Al—Ce intermetallic compounds with the Cu—Mn—Al alloy to provide precipitation hardening of the Cu—Mn—Al alloy.

Higher Ce additions (e.g., >10 at %) further increase the stress levels and absorbed energy on cyclic loading but may reduce recovery strain. Once the precipitates exceed the critical size and volume fraction, they start to impede martensite twin motion causing a debit to improved properties.

In addition, a wide use of Ce can help address the criticality issue for other more valuable rare earth metals. Unlike neodymium (Nd), praseodymium (Pr), dysprosium (Dy), terbium (Tb), and gadolinium (Gd), Ce is not widely used in energy efficient and/or renewable energy applications such as magnets. Notwithstanding, in some rare earth mineral ores, Ce is the most abundant element mined (such as >50% in bastnaesite ore in Mountain Pass, California, USA), and companies seeking the relatively more valuable rare earth elements often discard or offload their Ce wherever they can. Adding value to Ce reduces the cost of other high value critical rare earth elements. Lu et al. (“Effect of Ce addition on the microstructure and damping properties of Cu—Al—Mn shape memory alloys.” Journal of Alloys and Compounds 480, no. 2 (2009): 608-611) investigated Ce addition in Cu—Al—Mn alloy, but the focus of this work was on damping applications that use the material in its martensite state with transition temperature well above room temperature.

In addition to Ce, lanthanum (La) is another non-critical rare earth metal that is of relatively low value. Due to the similarity of the electronic structure, La and Ce have similar physical and chemical properties. Other rare earth elements that can be used include yttrium (Y) and scandium (Sc). In combination with the addition of rare earth elements, transition metals such as tin (Sn), nickel (Ni), and silver (Ag) zinc (Zn), iron (Fe), cobalt (Co), chromium (Cr), vanadium (V), titanium (Ti), and calcium (Ca) provide simultaneous improvement in strength and tuning of shape memory properties according to embodiments of the present disclosure.

In one or more embodiments, the Cu—Mn—Al alloy has a transformation stress for the induced martensite transformation of at least 150 MPa, in particular at least 175 MPa, and most particularly at least 200 MPa. In one or more embodiments, the transformation stress of the Cu—Mn—Al alloy is up to 275 MPa. In one or more embodiments, the Cu—Mn—Al alloy has a peak stress of at least 170 MPa, in particular at least 200 MPa, and most particularly at least 230 MPa. In one or more embodiments, the peak stress of the Cu—Mn—Al alloy is up to 300 MPa, in particular up to 350 MPa.

Embodiments of the present disclosure also relate to a method of preparing the Cu—Mn—Al alloy in which the Cu—Mn—Al is processed and thermo-mechanically heat treated to optimize its mechanical properties. In one or more embodiments, the Cu—Mn—Al alloy comprising additions of rare earths and, optionally, transition metals are prepared by casting a melt of molten alloy into a cast product, such as an ingot. In one or more embodiments, the cast product may be further processed into a particular metal stock, such as rod or wire. In one or more embodiments, the metal stock undergoes a solution treatment at a temperature in a range from 750° C. to 950° C. for a time in a range from 0.5 hours to 5 hours followed by cooling, such as water quenching. Thereafter, in one or more embodiments, the solution treated and quenched metal stock is tempered at a temperature in a range from 150° C. to 350° C. for a time in a range from 15 minutes to 60 minutes followed by cooling, such as water quenching or air cooling. In one or more embodiments, the metal stock is further processed by hot deformation (such as hot extrusion, hot drawing, or hot rolling), followed by quenching, annealing, cold deformation (extrusion, drawing or rolling), and isothermal, thermomechanical stabilization as described in U.S. Pat. No. 8,409,372 (issued Apr. 2, 2013), U.S. Pat. No. 9,273,369 (issued Mar. 1, 2016), and in U.S. Pat. No. 9,476,113 (issued Oct. 25, 2026), the entire contents of both of which are incorporated in their entireties herein by reference thereto.

Additionally, changes in processing can further enhance the useful properties associated with these alloys. By balancing the new chemical composition and the process, one can achieve significant improvements over conventional approaches for the base Cu—Mn—Al alloys. With much improved shape memory properties, the low-cost, high strength Cu-SMA may replace the expensive NiTi-based SMA for a range of applications involving thermally and/or mechanically induced phase transformations such as elastocaloric heat pump, smart structures, actuators, etc. Specific example applications are elastocaloric refrigerant, non-pneumatic tire (e.g., as described in U.S. Pat. No. 10,427,461, issued on Oct. 1, 2019, the contents of which are incorporated in their entirety herein by reference thereto), anti-earthquake rebar, and robotic muscles.

Experimental Examples

For purpose of illustration, Cu₇₂Al₁₇Mn₁₁ (at %) based alloys with Ce added in the amount of 0 at %, 0.1 at %, 0.25 at %, 0.5 at %, 1 at %, and 2 at % were synthesized using arc melting. Arc melt buttons of the obtained alloys were vacuum-sealed in quartz tubes and back-filled partially with inert gas, then homogenized at 800° C. followed by quenching into ice brine water. The quenched samples were aged at 200° C. for 10 minutes followed by air cooling.

Tensile Properties

Tensile tests were conducted using a Zwick tensile tester equipped with a laser extensometer for the strain measurement. The strain rate for both loading and unloading was set at 1×10⁻³ s⁻¹. The dog-bone shaped samples for the tensile test were prepared using EDM with a gauge dimension of 3 mm×6 mm.

FIG. 1 provides tensile curves for Cu—Al—Mn alloyed with 0 at %, 0.1 at %, 0.25 at %, 0.5 at %, 1 at %, and 2 at % of Ce. The tensile curves in FIG. 1 show that the Ce addition resulted in a significant increase in the transformation stress, i.e., the stress required to induce the phase transformation. The transformation stress for the induced martensite transformation is ˜140 MPa for the Cu—Al—Mn alloy (without Ce addition) in agreement with the literature. The samples containing 0.25 at % Ce and 0.5 at % of Ce additions to the Cu—Al—Mn alloy resulted in 28.5% and 71.4% of improvement in the transformation stress, reaching a level of 180 MPa and 240 MPa, respectively.

The peak stress also increased for samples containing Ce additions. The peak stress increased from 160 MPa for the Cu—Al—Mn alloy with 0 at % Ce to 174 MPa, 252 MPa, and 284 MPa for the samples containing 0.1 at %, 0.25 at %, and 0.5 at % of Ce, respectively. While larger amounts of Ce resulted in further strength increases, the resulting alloys become more brittle under current processing conditions. The strain hardening rate and the area enclosed in the load-unload curve are also increasing with increasing Ce amount, which means Ce containing alloys are stronger and are more resilient in energy absorption.

The inventors expect that a proper amount of cold work or isothermal, thermomechanical stabilization may further improve the plateau stress of the developed Cu—Mn—Al alloy to levels of 350 MPa or higher.

Thermal Properties

The melting characteristics of the alloys were measured using Netsch 404C high temperature Differential scanning calorimetry (DSC), and the transformation characteristic of the alloys were measured using Netsch Polyma 214 DSC. The heat/cool rates were 10° C./min for both DSCs.

FIGS. 2A and 2B provide DSC curves showing the melting points and the austenite start and finish temperatures, respectively, of the Cu—Al—Mn alloys having 0 at %, 0.1 at %, 0.25 at %, 0.5 at %, 0.5 at %, 1 at %, and 2 at % of Ce. From FIG. 2A, it can be seen that, for the zero Ce alloy, the melting onset temperature Tm (onset) was about 950° C., and from FIG. 2B, it can be seen that the austenite start temperature (As) was −50° C., and the finish temperature (Af) was −25° C. DSC reveals that the phase transformation temperatures of the alloys did not change with Ce addition, and therefore, the strengthening effect can be attributed to precipitation strengthening. This is fundamentally different from the strengthening effect caused by Sn and Ni, which can be attributed to decreasing phase transformation temperature.

The DSC thermograms reveal an additional endothermal peak in the 800° C.-900° C. region in FIG. 2A, suggesting the formation of an additional phase. In the 900° C.-1000° C. region, there is a minor decrease in the melting point (Tm) of the alloy. The decrease in Tm is a combined effect of Al coming out from the solution and minor Ce dissolution in the solid solution.

As shown in FIG. 2B, Ce addition results in a minor change in martensitic phase transformation temperature. Below 0.25 at % Ce, the phase transformation temperature increases with Ce addition, after that it drops almost linearly. This effect on phase transformation should result in a decrease in the stress plateau. However, as discussed above and shown in FIG. 1, the fact that it increases this plateau implies that the strengthening effect should be attributed to precipitation strengthening effects. The austenite finish temperature of all samples remained below 0° C. except for 2% Ce added sample where no transition was observed from −100° C. to 100° C. The formation of Ce-containing precipitates likely impeded the coordinated atomic shear movement delaying the martensite start temperature (the As temperature also decreases). While at the same time, the addition of Ce pulls Al atoms out of the solid solution, where lower Al content in this alloy is known to cause higher martensite start temperatures as reported by Sutou et al. (“Ductile Cu—Al—Mn based shape memory alloys: general properties and applications.” Materials Science and Technology 24, no. 8 (2008): 896-901).

Microstructure Characterization

The microstructure and elemental distribution of the samples were characterized by Scanning Electron Microscopy (SEM) and Energy Dispersive Spectroscopy (EDS). FIGS. 3A-3F provide micrographs of Cu—Mn—Al alloy showing the formation of precipitates and differences in volume fractions of precipitates with increasing Ce content going from FIG. 3A to FIG. 3F: 0 at %, 0.1 at %, 0.25 at %, 0.5 at %, 1 at %, and 2 at %.

The added Ce has a strong tendency to precipitate from the matrix as shown in FIGS. 3B-3F. The precipitates are clearly visible even with just 0.1 at % Ce addition as shown in FIG. 3B. It starts to prevail throughout and appears to be interconnected when the Ce addition is ≥1 at % as shown in FIGS. 3E and 3F. Fine precipitates assist in blocking or pining down both twin boundary and dislocation movement which helps increase strength. Conversely, coarse and interconnected precipitates become incoherent with the matrix, providing easy pathways for microcracks to grow, resulting the brittleness of samples with >1 at % Ce additions.

The precipitates formed are rich in Al and Ce, as confirmed by the EDS maps in FIGS. 4A-4E. In particular, FIG. 3F (2 at % Ce) was analyzed using EDS, and the elemental analysis is shown in FIGS. 4A-4E. The EDS point scans revealed that the chemical composition of the precipitates is Al₃Ce.

Phase Analysis

The phase analysis of the alloys was done using a Bruker X-ray diffractometer with a copper target. FIG. 5 provides X-ray diffraction (XRD) patterns of Cu—Mn—Al alloys with different levels of Ce additions (in at %), and XRD suggests the formation of the beta phase (with minimum Ce dissolution) and Ce rich intermetallic phases.

In particular, the as-quenched samples show the formation of disordered beta phase with a minor amount of alpha phase as expected from the Cu—Mn—Al ternary phase diagram due to mutual solubility of all three elements above 600° C. at the tested composition. There is a minimum dissolution of Ce in the matrix as the shift of the peaks of the beta phase (to the left in FIG. 5) is extremely small. The XRD patterns confirm the formation of Al₃Ce and a minor amount of Al₁₁Ce₃ intermetallic in agreement with the SEM and EDS results discussed above.

All references, including publications, patent applications, and patents cited herein are hereby incorporated by reference to the same extent as if each reference were individually and specifically indicated to be incorporated by reference and were set forth in its entirety herein.

The use of the terms “a” and “an” and “the” and similar referents in the context of describing the invention (especially in the context of the following claims) is to be construed to cover both the singular and the plural, unless otherwise indicated herein or clearly contradicted by context. The terms “comprising,” “having,” “including,” and “containing” are to be construed as open-ended terms (i.e., meaning “including, but not limited to,”) unless otherwise noted. Recitation of ranges of values herein are merely intended to serve as a shorthand method of referring individually to each separate value falling within the range, unless otherwise indicated herein, and each separate value is incorporated into the specification as if it were individually recited herein. All methods described herein can be performed in any suitable order unless otherwise indicated herein or otherwise clearly contradicted by context. The use of any and all examples, or exemplary language (e.g., “such as”) provided herein, is intended merely to better illuminate the invention and does not pose a limitation on the scope of the invention unless otherwise claimed. No language in the specification should be construed as indicating any non-claimed element as essential to the practice of the invention.

Preferred embodiments of this invention are described herein, including the best mode known to the inventors for carrying out the invention. Variations of those preferred embodiments may become apparent to those of ordinary skill in the art upon reading the foregoing description. The inventors expect skilled artisans to employ such variations as appropriate, and the inventors intend for the invention to be practiced otherwise than as specifically described herein. Accordingly, this invention includes all modifications and equivalents of the subject matter recited in the claims appended hereto as permitted by applicable law. Moreover, any combination of the above-described elements in all possible variations thereof is encompassed by the invention unless otherwise indicated herein or otherwise clearly contradicted by context.