LIGHTWEIGHT MATERIALS CROSS-REFERENCE TO RELATED APPLICATION

This claims the benefit of the earlier filing date of U.S. Provisional Application

No.62/412,729, filed October 25, 2016, which is incorporated herein by reference in its entirety. FIELD

This invention concerns ultra-hard multicomponent alloys and methods for making the alloys. BACKGROUND

Developments in new generation of materials for high-speed machining and light-weight materials applications have been motivated by demands from the cutting tool and aerospace industries. A need exists for advanced materials as an alternative to conventional carbide and ceramic cutting tools and lightweight materials. SUMMARY

Embodiments of ultra-hard multicomponent alloys and methods for designing and making the alloys are disclosed. The alloys are useful in many applications including, but not limited to, cutting tools and lightweight materials, such as aerospace materials and structural materials.

Embodiments of a computer-implemented method for designing an alloy include (i) putting identities of four to six metallic elements A, B, C, D, E, and F into a computer system configured to execute an algorithm for determining an alloy composition of the four to six metallic elements, the alloy composition having a minimum Gibbs free energy,∆G _mix , wherein

∆Gmix =∆Hchem +∆Hels– T*∆Smix,

∆Hchem =∑4*∆Hij*Xi*Xj,

∆H _els =∑X _i *X _j * (X _j *E _ij + X _i *E _ji ), and

∆Smix = -R*∑Xi*ln(Xi),

where ΔHchem is enthalpy of mixing due to chemical interaction,∆Hels is enthalpy of mixing due to strain energy of atomic size misfit, E is elastic strain energy,∆S _mix is entropy of mixing, T is temperature, R is 8.314 J/mol∙K, X is atomic fraction, and i and j represent metallic elements; (ii) inputting thermodynamic values for each pair of metallic elements into the algorithm, wherein the thermodynamic values are ΔH _ij and E _ij ; (iii) calculating, using the algorithm and based upon the thermodynamic values and a temperature T, the atomic fraction X of each metallic element in the alloy where

X _A + X _B + X _C + X _D + X _E + X _F = 1; and (iv) displaying to a user the calculated atomic fraction X of each metallic element in the alloy. In some embodiments, the method includes calculating atomic fractions for each metallic element in the alloy at each of two or more temperatures to provide an atomic fraction range for each metallic element in the alloy.

In any or all of the above embodiments, the method may further include combining powders of the metallic elements in amounts corresponding to the calculated atomic fraction X of each metallic element to form a combined powder; forming an alloy precursor by (i) ball milling of the combined powder, or (ii) melting the combined powder via vacuum arc melting or vacuum induction melting to provide a melt and cooling the melt to provide a solid; and heating the alloy precursor at a temperature of 1000-1500 °C for at least one hour to form the alloy.

Embodiments of the disclosed alloys comprise at least four metallic elements, each metallic element comprising at least 1 at.% of the alloy, the alloy having a melting temperature T _M and a Vickers hardness of at least 650 HV at temperatures within a temperature range of from 0.5 × TM up to TM, wherein hardness is measured by ASTM method E384 using a 200-gram load and a duration time of 15 seconds. In some embodiments, the alloy has a Vickers hardness of at least 700 HV over the temperature range. In any or all of the above embodiments, the alloy may be a solid solution of the at least four metallic elements.

In any or all of the above embodiments, the metallic elements may comprise (a) iron, chromium, and titanium; and (b) 1-3 metallic elements selected from the group consisting of vanadium, aluminum, and manganese. In certain embodiments, the alloys comprise Fe-Cr-V-Ti, Fe-Cr-V-Ti-Al, Fe-Cr-Mn-Ti, or Fe-Cr-Mn-Ti-Al.

The foregoing and other objects, features, and advantages of the invention will become more apparent from the following detailed description, which proceeds with reference to the accompanying figures. BRIEF DESCRIPTION OF THE DRAWINGS FIG.1 is a flowchart of software codes to solve the thermodynamic analytical model.

FIG.2 depicts a generalized example of a computing system.

FIG.3 is a system diagram depicting an example mobile device including a variety of optional hardware and software components. FIG.4 depicts a generalized example of a cloud-supported environment.

FIG.5 is a graph of the atomic concentration of each element versus temperature in the Fe- Cr-V-Ti alloy system.

FIG.6 is a graph of the atomic concentration of each element versus temperature in the Fe- Cr-V-Ti-Al alloy system.

FIG.7 is a graph of the atomic concentration of each element versus temperature in the Fe- Cr-Mn-Ti alloy system.

FIG.8 is a graph of the atomic concentration of each element versus temperature in the Fe- Cr-Mn-Ti-Al alloy system. DETAILED DESCRIPTION

Embodiments of ultra-hard multicomponent alloys and methods for designing and making the alloys are disclosed. Embodiments of the disclosed alloys exhibit ultra-high hardness (e.g., > 600 HV) and thermal stability over a broad range of temperatures up to the melting point of the alloy. Advantageously, embodiments of the disclosed alloys may be produced from common, abundant metallic elements, making them less expensive to produce than other high-performance alloys used in demanding applications, such as cutting tools and lightweight materials (e.g., aerospace and other lightweight structural materials). I. Definitions and Abbreviations

The following explanations of terms and abbreviations are provided to better describe the present disclosure and to guide those of ordinary skill in the art in the practice of the present disclosure. As used herein,“comprising” means“including” and the singular forms“a” or“an” or “the” include plural references unless the context clearly dictates otherwise. The term“or” refers to a single element of stated alternative elements or a combination of two or more elements, unless the context clearly indicates otherwise.

Unless explained otherwise, all technical and scientific terms used herein have the same meaning as commonly understood to one of ordinary skill in the art to which this disclosure belongs. Although methods and materials similar or equivalent to those described herein can be used in the practice or testing of the present disclosure, suitable methods and materials are described below. The materials, methods, and examples are illustrative only and not intended to be limiting. Other features of the disclosure are apparent from the following detailed description and the claims. Unless otherwise indicated, all numbers expressing quantities of components, percentages, temperatures, times, and so forth, as used in the specification or claims are to be understood as being modified by the term“about.” Accordingly, unless otherwise implicitly or explicitly indicated, or unless the context is properly understood by a person of ordinary skill in the art to have a more definitive construction, the numerical parameters set forth are approximations that may depend on the desired properties sought and/or limits of detection under standard test

conditions/methods as known to those of ordinary skill in the art. When directly and explicitly distinguishing embodiments from discussed prior art, the embodiment numbers are not

approximates unless the word“about” is recited.

In order to facilitate review of the various embodiments of the disclosure, the following explanations of specific terms are provided:

Alloy: A solid or liquid mixture of two or more metals.

Atomic fraction: The fraction of atoms of one kind of atom (e.g., a metal) relative to the total number of atoms in a composition, such as an alloy. The sum of the atomic fractions of the elements in the composition is equal to one.

Atomic percent (at.%): A percentage of one kind of atom (e.g., a metal) relative to the total number of atoms in a composition, such as an alloy.

Multicomponent alloy: As used herein, the term multicomponent alloy refers to an alloy comprising at least four metallic elements, each metallic element comprising at least 1 at.% of the alloy.

Input: Enter information into a computer for processing, wherein information is entered from a keyboard, from a touchscreen, via a voice receiver, from a file stored in a database (a file composed of records, each containing fields together with a set of operations for searching, sorting, recombining, and other functions), or a combination thereof.

Solid solution: As used herein, the term“solid solution” refers to a solid, homogeneous mixture of substances.

Vickers Hardness: A hardness measurement determined by indenting the test material with an indenter subjected to a load of 1 to 100 kgf for a period of time. Vickers hardness may be expressed in units of HV– the Vickers Pyramid Number. Hardness measurements reported herein were determined by ASTM (American Society for Testing and Materials) method E384 using a Vickers indenter with a 200-gram load and a duration time of 15 seconds. II. Method of Designing and Making Alloys

Embodiments of the disclosed method include a computer-implemented solution model to predict the solubility of each metallic element in a multinary system and determine whether the elements can maintain a stable concentration in the alloy as the temperature increases up to the melting point of the alloy. The computer-implemented model can be employed to design any multinary system and to understand the core effect of high entropy. As this model incorporates the atomic size misfit effects, the competition between the enthalpy and the entropy at an equilibrium state are elucidated. The entropy effect is not a predominant effect in many cases. Embodiments of the disclosed method determine the optimum alloy composition at a given temperature in lieu of simply choosing an equimolar composition.

Per general definition, the Gibbs free energy of a system is:

The enthalpy of mixing, ΔHmix, is broken into two elements– ΔHchem (enthalpy of mixing due to chemical interaction) and ΔHels (enthalpy of mixing due to strain energy of atomic size misfit):

The enthalpy of mixing due to chemical interaction, ΔHchem, is taken as follows using the regular solution model where Xj and Xj are the atomic mole fractions of elements i and j, respectively: ∆

where

The due to the binary mixing of ith and jth atoms is estimated from the Miedema model. For example, when six metallic elements A, B, C, D, E, and F are present, equation (3) is expressed as:

The enthalpy of mixing due to the strain energy of atomic size misfit can be expressed as follows:

(6) By the use of continuum theory approximation of Friedel model, the strain energy stored in the system due to the atomic size misfit of i _th atoms surrounded by the j _th atoms as denoted by ^^ _{^^ ^^} and vice versa for ^^ _{^^ ^^} can be calulated. Therefore, for the six metallic elements of A, B, C, D, E, and F, equation (6) is expressed as:

Assuming an ideal solution of multinary mixture, the entropy of the mixing is summed up as:

(8) Hence, the equation (8) is constructed as follows for the six-element system of A, B, C, D, E, and F: In order to find an equilibrium state of the solution at a given temperature, the total Gibbs free energy is minimized with respect to each of the atomic concentrations. Due to the complexity of this final result, the Lagrange Multiplier method is used to find the minimum point of the Gibbs free energy at which the alloy composition will be at equilibrium state. This gives: Hence, the equilibrium composition at the given temperature is given by:

(11)

This approach for a six-element system is expressed as follows in the equations of (12) - (19):

These equations can be solved through a computer-executed algorithm (a set of rules to be followed in calculations by a computer, or computer-implemented instructions describing a computation that when executed proceeds through a finite number of successive states, producing an output and terminating at a final ending state) at a given temperature using a computer system configured to execute the algorithm. A summary of the method is shown in the flowchart of FIG.1. The algorithm includes inputting identities of metallic elements, such as four to six metallic elements A, B, C, D, E, F, into a computer system configured to execute an algorithm for determining an alloy composition of the four to six metallic elements, wherein the alloy composition has a minimum Gibbs free energy,∆Gmix, wherein

∆G _mix =∆H _chem +∆H _els – T*∆S _mix ,

∆Hchem =∑4*∆Hij*Xi*Xj,

∆Hels =∑Xi *Xj* (Xj*Eij + Xi*Eji), and ∆S _mix = -R*∑X _i *ln(X _i ),

where ΔHchem is enthalpy of mixing due to chemical interaction,∆Hels is enthalpy of mixing due to strain energy of atomic size misfit, E is elastic strain energy,∆Smix is entropy of mixing, T is temperature, R is 8.314 J/mol∙K, X is atomic fraction, and i and j represent metallic elements. Thermodynamic values, i.e.,∆H _ij and E _ij , are inputted into the algorithm for each pair of metallic elements. For example, where there are six metallic elements, thermodynamic values for the pairs AB, AC, AD, AE, AF, BA, BC, BD, BE, BF, CA, CB, CD, CE, CF, DA, DB, DC, DE, DF, EA, EB, EC, ED, and EF are inputted into the algorithm. The thermodynamic values may be inputted using any suitable method including, but not limited to, data entry by a user or importation from a database of thermodynamic values stored in the computer system and accessible by the algorithm. Using the algorithm, and based upon the inputted thermodynamic values and a temperature T, the atomic fraction of each metallic element in the alloy is calculated where X _A + X _B + X _C + X _D + X _E + XF = 1. The calculated atomic fraction of each metallic element is displayed to a user, e.g., via a printout or on a display such as a computer monitor.

The atomic fraction of each metallic element can be calculated by solving the polynomial function L as shown in equation 12 above where λ is a multiplier, e.g., a Lagrangian multiplier. Solving the polynomial function L comprises determining λ by solving the first derivative∂L/∂XA for metallic element A using equation 13. The multiplier λ is then substituted into the first derivative∂L/∂XB,∂L/∂XC,∂L/∂XD,∂L/∂XE,∂L/� ��XF, for each metallic element B, C, D, E, and F (equations 14-18), and each first derivative is solved to determine the atomic fraction X of each metallic element.

It is understood that if the alloy will include fewer than six metallic elements, the above equations are modified accordingly. For example, if the alloy will include only four metallic elements A, B, C, and D, then (i) only thermodynamic values pertaining to combinations of A, B, C, and D will be inputted into the algorithm, (ii) X _E and X _F will be zero, and (iii) the first derivatives∂L/∂XE and∂L/∂XF will not be calculated.

In some embodiments, atomic fractions are calculated for each metallic element in the alloy at two or more temperatures to provide an atomic fraction range for each metallic element in the alloy. For instance, two or more temperatures within an expected temperature range of use for the alloy may be used. In some examples, a plurality of temperatures over a range from 1500 K below an expected melting temperature of the alloy to 500 K above the expected melting temperature are used to determine an atomic fraction range for each metallic element in the alloy over a wide temperature range. The computer-designed alloys are made by conventional alloy preparation techniques. In some embodiments, powders of the metallic elements are combined in amounts corresponding to the calculated atomic fraction X of each metallic element to form a combined powder. The combined powder may be formed into an alloy precursor by mechanical alloying or

melting/solidification, among other methods. In one embodiment, the alloy is mechanically formed by high-energy ball milling, i.e., ball milling with sufficient energy to cause cold welding and fracturing of the powder particles. High-energy ball milling may be performed, for example, with a planetary ball mill or shaking ball-mill. The ball milling may be performed under an inert atmosphere, such as under an argon atmosphere, or under negative pressure. In other embodiments, the combined powder is formed into an alloy precursor by vacuum arc melting or vacuum induction melting, as is known to one of ordinary skill in the art of alloy preparation, to provide a melt and then cooling the melt to provide a solid precursor alloy.

In some embodiments, the alloy precursor is subsequently sintered, or heat treated, to form the alloy. Sintering may be performed at a temperature within a range of 500-2000 °C, such as a temperature of 1000-1500 °C, for at least one hour. Sintering may be performed in an inert or reducing atmosphere, such as in an argon or argon-hydrogen atmosphere. III. Ultra-Hard Multicomponent Alloys and Uses Thereof

An ultra-hard multicomponent alloy comprises at least four metallic elements, each metallic element comprising at least 1 at.% of the alloy. In some embodiments at least two of the metallic elements each comprise at least 15 at.% of the alloy or at least 25 at.% of the alloy, such as 15-50 at.%, 25-50 at.%, or 30-50 at.%. In certain embodiments, the alloy may comprise only four metallic elements, and each metallic element comprises at least 5 at.% of the alloy.

Embodiments of the disclosed alloys are in the form of a solid solution. In some

embodiments, the solid solution is substantially crystalline, i.e., at least 90% of the solid solution, such as 90-100% or 95-100% of the solid solution, is crystalline. Average grain size may be determined by any suitable means, such as x-ray diffraction or transmission electron microscopy.

The disclosed alloys have a Vickers hardness of at least 650 HV, such as a hardness of at least 700 HV, at temperatures within a temperature range of from 0.5 × TM up to TM, where TM is the melting point of the alloy. Hardness is measured by ASTM method E384 using a 200-gram load and a duration time of 15 seconds. In some embodiments, the alloy has a hardness from 650- 1200 HV over the temperature range, such as a hardness from 650-1100 HV, 700-1100 HV, 750- 1100 HV, 800-1100 HV, or 900-1100 HV. The hardness may vary less than 25%, less than 15%, less than 10%, or less than 5% over the temperature range of from 0.5 × TM up to TM.

Embodiments of the disclosed alloys comprise at least four metallic elements, such as from four to six metallic elements. Exemplary ultra-hard multicomponent alloys include iron, chromium, titanium, and from one to three additional metallic elements. For instance, an ultra-hard multicomponent alloy may comprise Fe-Cr-Ti-V, Fe-Cr-Ti-V-Al, Fe-Cr-Ti-Mn, Fe-Cr-Ti-Mn-Al, Fe-Cr-Ti-Mn-V, Fe-Cr-Ti-V-Co, or Fe-Cr-Ti-Mn-Co. Other exemplary iron-containing alloys include, but are not limited to, Fe-Cr-Mn-Co-Mo and Fe-Co-Mn-Ti-V.

Other ultra-hard multicomponent alloys may include Ti-Mg-Al, Ti-V-Cr, Ti-Zr-Mo, or Ti- Zr-Nb plus one to three additional metallic elements. For example, the alloy may comprise Ti-Mg- Al-Li-Sc, Ti-Mg-Al-Li, Ti-Mg-Al-Sc, Ti-V-Cr-Zr, Ti-V-Cr-Nb, Ti-V-Cr-Mo, Ti-Zr-Nb-Hf-Ta, Ti- Zr-Mo-Nb, Ti-Zr-Mo-Ng-Hf, Ti-Zr-Mo-Nb-Ta, or Ti-Zr-Mo-Nb-W.

In some examples, the alloy comprises iron, chromium, titanium, and the additional metallic elements are selected from the group consisting of vanadium, aluminum, and manganese. One exemplary alloy comprises 31-39 at.% iron, 9-18 at.% chromium, 16-22 at.% vanadium, and 29-36 at.% titanium. Another exemplary alloy comprises 1-12 at.% iron, 1-6 at.% chromium, 1-10 at.% vanadium, 34-50 at.% titanium, and 38-50 at.% aluminum. Still another exemplary alloy comprises 30-38 at.% iron, 7-18 at.% chromium, 10-19 at.% manganese, and 33-43 at.% titanium. Yet another exemplary alloy comprises 1-10 at.% iron, 1-5 at.% chromium, 1-11 at.% manganese, 35- 50 at.% titanium, and 39-50 at.% aluminum.

Embodiments of the disclosed ultra-hard multicomponent alloys are useful for any application where hardness and/or temperature stability are advantageous. Exemplary applications include, but are not limited to, cutting tools and lightweight materials, such as aerospace materials and other lightweight structural materials.

Conventional carbide and ceramic cutting tools have disadvantages, such as limited tool life due to wear and/or chemical reactions between the cutting tool and the material being cut. In some embodiments, a cutting edge or cutting portion of a cutting tool is constructed of or at least partially coated with an alloy as disclosed herein. For example, at least 50%, such as 50-100%, 70-100%, 90-100%, or 95-100% of a cutting edge may be coated with the alloy. The alloy coating has a sufficient thickness to provide a useful tool life. The alloy coating may have an average thickness of at least 0.1 mm, such as from 0.1-20 mm or 0.5-10 mm. In other embodiments, the cutting edge or cutting portion is constructed of the alloy. Exemplary cutting tools and cutting portions include, but are not limited to, cutting wheels, saw blades, cut-off tools, annular cutters, angle cutters, drill bits, router bits, scissors, and snip cutters, among others.

Embodiments of the disclosed alloys are also useful as aerospace and/or other lightweight structural materials. Aerospace materials have demanding specifications, including exceptional performance, strength, and heat resistance. Desirably, aerospace materials are also lightweight. Some embodiments of the disclosed alloys are suitable for use in constructing aerospace airframes and structures, engine parts, fasteners, actuators, landing gear components, and wing and fuselage skins, among others. The alloys also may be used anywhere that conventional alloys are used, e.g., as structural materials, for example, in vehicles and buildings, among others. IV. Computer System

FIG.2 depicts a generalized example of a suitable computing system 100 in which the described innovations may be implemented. The computing system 100 is not intended to suggest any limitation as to scope of use or functionality, as the innovations may be implemented in diverse general-purpose or special-purpose computing systems.

With reference to FIG.2, the computing system 100 includes one or more processing units 110, 115 and memory 120, 125. In FIG.2, this basic configuration 130 is included within a dashed line. The processing units 110, 115 execute computer-executable instructions, e.g., an algorithm for performing embodiments of the disclosed method for determining an alloy composition of four to six metallic elements, the alloy composition having a minimum Gibbs free energy. A processing unit can be a general-purpose central processing unit (CPU), processor in an application-specific integrated circuit (ASIC), or any other type of processor. In a multi-processing system, multiple processing units execute computer-executable instructions to increase processing power. For example, FIG.2 shows a central processing unit 110 as well as a graphics processing unit or co- processing unit 115. The tangible memory 120, 125 may be volatile memory (e.g., registers, cache, RAM), non-volatile memory (e.g., ROM, EEPROM, flash memory, etc.), or some combination of the two, accessible by the processing unit(s). The memory 120, 125 stores software 180

implementing one or more innovations described herein, in the form of computer-executable instructions suitable for execution by the processing unit(s).

A computing system may have additional features. For example, the computing system 100 includes storage 140, one or more input devices 150, one or more output devices 160, and one or more communication connections 170. An interconnection mechanism (not shown) such as a bus, controller, or network interconnects the components of the computing system 100. Typically, operating system software (not shown) provides an operating environment for other software executing in the computing system 100, and coordinates activities of the components of the computing system 100.

The tangible storage 140 may be removable or non-removable, and includes magnetic disks, magnetic tapes or cassettes, CD-ROMs, DVDs, or any other medium which can be used to store information and which can be accessed within the computing system 100. The storage 140 stores instructions for the software 180 implementing one or more innovations described herein.

The input device(s) 150 may be a touch input device such as a keyboard, mouse, pen, or trackball, a voice input device, a scanning device, or another device that provides input to the computing system 100. The output device(s) 160 may be a display, printer, speaker, CD-writer, or another device that provides output from the computing system 100.

The communication connection(s) 170 enable communication over a communication medium to another computing entity. The communication medium conveys information such as computer-executable instructions, audio or video input or output, or other data in a modulated data signal. A modulated data signal is a signal that has one or more of its characteristics set or changed in such a manner as to encode information in the signal. By way of example, and not limitation, communication media can use an electrical, optical, RF, or other carrier.

The innovations can be described in the general context of computer-executable

instructions, such as those included in program modules, being executed in a computing system on a target real or virtual processor. Generally, program modules include routines, programs, libraries, objects, classes, components, data structures, etc. that perform particular tasks or implement particular abstract data types. The functionality of the program modules may be combined or split between program modules as desired in various embodiments. Computer-executable instructions for program modules may be executed within a local or distributed computing system.

The terms“system” and“device” are used interchangeably herein. Unless the context clearly indicates otherwise, neither term implies any limitation on a type of computing system or computing device. In general, a computing system or computing device can be local or distributed, and can include any combination of special-purpose hardware and/or general-purpose hardware with software implementing the functionality described herein.

Terms like“determine” and“use” are used to describe computer operations in a computing system. These terms are high-level abstractions for operations performed by a computer, and should not be confused with acts performed by a human being. The actual computer operations corresponding to these terms vary depending on implementation. FIG.3 is a system diagram depicting an example mobile device 200 including a variety of optional hardware and software components, shown generally at 202. Any components 202 in the mobile device can communicate with any other component, although not all connections are shown, for ease of illustration. The mobile device can be any of a variety of computing devices (e.g., cell phone, smartphone, handheld computer, Personal Digital Assistant (PDA), etc.) and can allow wireless two-way communications with one or more mobile communications networks 204, such as a cellular, satellite, or other network.

The illustrated mobile device 200 can include a controller or processor 210 (e.g., signal processor, microprocessor, ASIC, or other control and processing logic circuitry) for performing such tasks as signal coding, data processing, input/output processing, power control, and/or other functions, including execution of the alloy design algorithm. An operating system 212 can control the allocation and usage of the components 202 and support for one or more application programs 214. The application programs can include common mobile computing applications (e.g., email applications, calendars, contact managers, web browsers, messaging applications), or any other computing application. Functionality 213 for accessing an application store can also be used for acquiring and updating application programs 214.

The illustrated mobile device 200 can include memory 220. Memory 220 can include non- removable memory 222 and/or removable memory 224. The non-removable memory 222 can include RAM, ROM, flash memory, a hard disk, or other well-known memory storage

technologies. The removable memory 224 can include flash memory or a Subscriber Identity Module (SIM) card, which is well known in GSM communication systems, or other well-known memory storage technologies, such as "smart cards." The memory 220 can be used for storing data and/or code for running the operating system 212 and the applications 214. Example data can include web pages, text, images, sound files, video data, or other data sets to be sent to and/or received from one or more network servers or other devices via one or more wired or wireless networks. The memory 220 can be used to store a subscriber identifier, such as an International Mobile Subscriber Identity (IMSI), and an equipment identifier, such as an International Mobile Equipment Identifier (IMEI). Such identifiers can be transmitted to a network server to identify users and equipment.

The mobile device 200 can support one or more input devices 230, such as a touchscreen 232, microphone 234, camera 236, physical keyboard 238 and/or trackball 240 and one or more output devices 250, such as a speaker 252 and a display 254. Other possible output devices (not shown) can include piezoelectric or other haptic output devices. Some devices can serve more than one input/output function. For example, touchscreen 232 and display 254 can be combined in a single input/output device.

The input devices 230 can include a Natural User Interface (NUI). An NUI is any interface technology that enables a user to interact with a device in a“natural” manner, free from artificial constraints imposed by input devices such as mice, keyboards, remote controls, and the like.

Examples of NUI methods include those relying on speech recognition, touch and stylus recognition, gesture recognition both on screen and adjacent to the screen, air gestures, head and eye tracking, voice and speech, vision, touch, gestures, and machine intelligence. Thus, in one specific example, the operating system 212 or applications 214 can comprise speech-recognition software as part of a voice user interface that allows a user to operate the device 200 via voice commands.

A wireless modem 260 can be coupled to an antenna (not shown) and can support two-way communications between the processor 210 and external devices, as is well understood in the art. The modem 260 is shown generically and can include a cellular modem for communicating with the mobile communication network 204 and/or other radio-based modems (e.g., Bluetooth 264 or Wi-Fi 262). The wireless modem 260 is typically configured for communication with one or more cellular networks, such as a GSM network for data and voice communications within a single cellular network, between cellular networks, or between the mobile device and a public switched telephone network (PSTN).

The mobile device can further include at least one input/output port 280, a power supply 282, a satellite navigation system receiver 284, such as a Global Positioning System (GPS) receiver, an accelerometer 286, and/or a physical connector 290, which can be a USB port, IEEE 1394 (FireWire) port, and/or RS-232 port. The illustrated components 202 are not required or all- inclusive, as any components can be deleted and other components can be added.

FIG.4 illustrates a generalized example of a suitable cloud-supported environment 300 in which described embodiments, techniques, and technologies may be implemented. In the example environment 300, various types of services (e.g., computing services) are provided by a cloud 310. For example, the cloud 310 can comprise a collection of computing devices, which may be located centrally or distributed, that provide cloud-based services to various types of users and devices connected via a network such as the Internet. The implementation environment 300 can be used in different ways to accomplish computing tasks. For example, some tasks (e.g., processing user input and presenting a user interface) can be performed on local computing devices (e.g., connected devices 330, 340) while other tasks (e.g., storage of data to be used in subsequent processing) can be performed in the cloud 310.

In example environment 300, the cloud 310 provides services for connected devices 330, 340 with a variety of screen capabilities. Connected device 330 represents a device with a computer screen. For example, connected device 330 could be a personal computer such as desktop computer, laptop, notebook, netbook, or the like. Connected device 340 represents a mobile device. For example, connected device 340 could be a mobile phone, smart phone, tablet computer, and the like. One or more of the connected devices 330, 340 can include touchscreen capabilities. Devices without screen capabilities also can be used in example environment 300. For example, the cloud 310 can provide services for one or more computers (e.g., server computers) without displays.

Services can be provided by the cloud 310 through service providers 320, or through other providers of online services (not depicted). For example, cloud services can be customized to the screen size, display capability, and/or touchscreen capability of a particular connected device (e.g., connected devices 330, 340). V. Examples

Compositions of four exemplary alloys 1-4 were determined by the method disclosed herein. Mole fractions of each element were determined for temperatures ranging from 1500 K below an expected melting temperature of the alloy to 500 K above the expected melting point.

One exemplary algorithm for determining an alloy composition of up to six metallic elements, i.e., the Maple (a symbolic and numeric computing environment, and multi-paradigm programming language) sheet coding for the system of six metallic elements A-B-C-D-E-F (where A = Co, B = Cr, C = Fe, D = Ni, E = Cu, and F = Al), is presented at the given temperature of T as follows:

FIGS.5-8 show the calculated mole fractions for alloys A-D, respectively, over the temperature range. The compositions of alloys A-D are provided below:

The composition of Alloy 1 is as follows (FIG.5): The composition of Alloy 2 is as follows (FIG.6):

Alloy precursors were prepared by combining powders of the metallic elements in the calculated ratios and ball milling. Ball milling was performed at room temperature for 1-2 hours in an argon atmosphere or under negative pressure. The alloy precursors were heat treated at a temperature of 1000-1500 °C for one hour in an argon atmosphere. Hardness was measured at ambient temperature by ASTM method E384 using a 200-gram load and a duration time of 15 seconds. The hardness results are shown below in Table 1:

Table 1 In view of the many possible embodiments to which the principles of the disclosed invention may be applied, it should be recognized that the illustrated embodiments are only preferred examples of the invention and should not be taken as limiting the scope of the invention. Rather, the scope of the invention is defined by the following claims. We therefore claim as our invention all that comes within the scope and spirit of these claims.