US20060086432A1

US20060086432A1 - Low hysteresis materials and methods

Info

Publication number: US20060086432A1
Application number: US10/973,196
Authority: US
Inventors: Zhiyong Zhang; Richard James
Original assignee: University of Minnesota
Current assignee: University of Minnesota
Priority date: 2004-10-26
Filing date: 2004-10-26
Publication date: 2006-04-27

Abstract

A method is provided for predicting material properties and creating or modifying materials to exhibit desired properties. Materials and devices are described that are formed using the methods. Using embodiments described above, a number of advantages are realized. One advantage includes an ability to predict hysteresis in a multiple phase material. One embodiment includes an ability to modify or create a material to exhibit low hysteresis. Using embodiments described above to predict material properties and modify material properties, a number of materials can be created. An improved shape memory alloy with low hysteresis can be created. Additionally, a material that exhibits any of a number of properties that are normally mutually exclusive can be created.

Description

TECHNICAL FIELD

This application relates to solid materials that undergo phase transformations in at least a fraction of their volume. Several properties of the materials can be affected by the phase transformations with low hysteresis as discussed below. Specifically one example of a low hysteresis property includes low stress hysteresis in response to an applied strain or stress.

BACKGROUND

Materials such as shape memory alloys operate by changing from one crystallographic phase to another and back again in response to a stimulus such as an imposed stress, or a temperature change, etc. However a loss, or hysteresis, is typically observed after a cycle of transformation from the first phase to the second phase, and back to the first phase. In the example of a shape memory alloy, one property exhibiting hysteresis is stress. In the stress context, hysteresis measures the difference between the stress needed to transform the material and the stress recovered when the material transforms back to the original phase. Ideally, if hysteresis were zero, a shape memory alloy would return to exactly the same shape it had in the first phase, after cycling to the second phase and back again.
Although a shape memory alloy is used as an example, the concept of hysteresis in materials extends to any number of possible material properties that are present in one phase and absent or lessened in another. Examples of other material properties include, but are not limited to ferromagnetism, ferroelectricity, ferroelasticity, solubility of hydrogen gas, optical properties, electrical conduction/insulation, thermal conduction/insulation, luminescence, etc. Additionally, the change in phases can be triggered by a number of possible stimuli. Some applied stimuli include, but are not limited to, stress, applied magnetic field, applied electrical field, temperature, etc.
It is desirable to know criteria for identification of materials having properties that change with low hysteresis. It is also desirable to create materials based on known criteria that will possess properties with low hysteresis.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1A shows a three dimensional crystal structure of a phase according to an embodiment of the invention.
FIG. 1B shows a three dimensional crystal structure of another phase according to an embodiment of the invention.
FIG. 2A shows a two dimensional crystal structure of a phase according to an embodiment of the invention.
FIG. 2B shows a two dimensional crystal structure of another phase according to an embodiment of the invention.
FIG. 3A shows a three dimensional crystal structure of a phase according to an embodiment of the invention.
FIG. 3B shows a three dimensional crystal structure of another phase according to an embodiment of the invention.
FIG. 4A shows a two dimensional crystal structure of a phase according to an embodiment of the invention.
FIG. 4B shows a two dimensional crystal structure of a phase variant according to an embodiment of the invention.
FIG. 4C shows a two dimensional crystal structure of another phase variant according to an embodiment of the invention.
FIG. 4D shows a two dimensional crystal structure of another phase variant according to an embodiment of the invention.
FIG. 5A shows a two dimensional view of phase interfaces according to an embodiment of the invention.
FIG. 5B shows a two dimensional view of other phase interfaces according to an embodiment of the invention.
FIG. 6 shows a flow diagram of a method for predicting properties and modifying a material according to an embodiment of the invention.
FIG. 7 shows a block diagram of a device according to an embodiment of the invention.

DETAILED DESCRIPTION

In the following detailed description, reference is made to the accompanying drawings which form a part hereof, and in which is shown, by way of illustration, specific embodiments in which the invention may be practiced. In the drawings, like numerals describe substantially similar components throughout the several views. These embodiments are described in sufficient detail to enable those skilled in the art to practice the invention. Other embodiments may be utilized and structural, logical changes, etc. may be made without departing from the scope of the present invention.
FIG. 1A shows a unit cell 100 of a first phase of a crystalline material. Crystalline materials includes single crystal materials as well as polycrystalline materials. In one embodiment, the crystalline material includes a metal alloy. The example shown in FIG. 1 illustrates a body centered cubic unit cell, although the invention is not so limited. Other unit cell configurations include hexagonal, tetragonal, rhombohedral, orthorhombic, monoclinic, triclinic, etc. The unit cell 100 includes a number of corner atoms 110, and a center atom 120. A number of sides 112 form the edges of the unit cell. A number of crystallographic parameters are also labeled in FIG. 1. A first side length “a”, a second side length “b”, and a third side length “c” are shown. Further a first internal angle “α”, a second internal angle “β” and a third internal angle “γ” are shown.
FIG. 1B shows a unit cell 101 of a second phase of a crystalline material. In one embodiment, the second phase unit cell 101 is transformed from the first unit cell 100 shown in FIG. 1A. In one embodiment, an external stimuli such as a stress 130 is applied to the unit cell 100 to transform it into the unit cell 101. Other stimuli such as an applied electrical field, an applied magnetic field, a change in temperature, etc. are also possible stimuli for triggering a change in phase. In one embodiment, the corner atoms 110 and center atom 120 remain the same species, however the internal angle α is changed in unit cell 101. Similar to the example unit cell 100 described above, the particular second phase unit cell 101 is only as an example. Other crystallographic structures are possible, and only the concept of a phase change from the first phase 100 to the second phase 101 is intended.
Materials such as shape memory alloys use phase transitions from a first phase to a second phase to accommodate large strains that are reversible to an extent. The difference between the strain imposed in passing from the first phase to the second phase and the strain recovered through the reverse transformation is a measure of reversibility. Another measure of reversibility is hysteresis as defined above. In shape memory materials the two phases have different strains. The phases can have different properties such as different polarization, magnetization, solubility for hydrogen or different optical properties. Because each phase can have unique material properties, these properties can effectively be switched on and off at will by utilizing a phase change.
A number of crystallographic criteria have been discovered to provide insight into a level of reversibility in phase changes such as those in shape memory alloys. When a number of the criteria are met, the phase change becomes increasingly reversible and hysteresis is low.
One criterion includes determining a difference in volume between the first phase and the second phase. In one embodiment, a low difference in volume between the unit cell in one phase and the unit cell of the other phase to which it is transformed is desired. FIGS. 2A and 2B illustrate the concept of a phase change with little or no area change. The same concept can be extended to three dimensions to show little or no volume change between phases. FIG. 2A shows a first two dimensional rectangular unit cell 200. The unit cell 200 has edges 212 with a length 213 and a width 214. The unit cell 200 therefore has an area of length×width. FIG. 2B illustrates a second two dimensional rectangular unit cell 201 that illustrates a second phase material formed from the first unit cell 200. The length 213 in unit cell 201 is increased, and the width 214 in the unit cell 201 is decreased. The area of unit cell 201 (equal to length×width) however, has not changed.
Another criterion includes determining a degree of matching at an interface between the first phase and the second phase. In one embodiment, a high degree of matching at an interface between the first phase and the second phase is desirable. FIGS. 3A and 3B illustrate the concept of a phase change with a high degree of matching at the interface between phases. FIG. 3A shows a first phase unit cell 300. The unit cell 300 includes a number of comer atoms 310, a center atom 320 and a number of sides 312. A first interface side 330 is shown with a first length 334 and a first width 332. The interface side further includes a first internal angle 336.
Likewise, FIG. 3B shows a second phase unit cell 301. The unit cell 301 includes a number of comer atoms 311, a center atom 321 and a number of sides 313. A second interface side 331 is shown with a second length 335 and a second width 333. The interface side further includes a second internal angle 337.
As shown in FIGS. 3A and 3B, the first interface side 330 substantially matches the second interface side 331. The matching exists because the first length 334 substantially matches the second length 335; the first width 332 substantially matches the second width 333; and the first internal angle 336 substantially matches the second internal angle 337. Although the matching interfaces shown in FIGS. 3A and 3B show sides of unit cells, the matching plane need not be a crystallographic plane.
Another criterion includes determining a number of configurations that satisfy one or more of the criteria listed above. In one embodiment, the criterion includes determining a number of configurations that satisfy a low volume difference between the first phase and the second phase. In one embodiment, the criterion further includes determining a number of configurations that satisfy a high degree of matching at the interface between the first phase and the second phase.
FIGS. 4A-4C illustrate conversion of a first phase to a number of variants of a second phase that enable a high number of configurations in one embodiment. FIG. 4A shows an example of a first phase in a two dimensional cubic crystal structure unit cell 400. A number of atoms 410 are located at corners of the cell 400 with sides 412. A length 413 is shown that is equal to a width 414.
FIG. 4B shows a tetragonal phase unit cell in a first variant 401 as converted in a phase change from the unit cell 400 in FIG. 4A. In the first variant 401, the length 413 is increased, while the width 414 is decreased to form the tetragonal structure. In contrast, in FIG. 4C, a tetragonal phase unit cell in a second variant 402 as converted in a phase change from the unit cell 400 in FIG. 4A. In the second variant 402, the length 413 is decreased, while the width 414 is increased to form the tetragonal structure.
In FIGS. 4B and 4C, the first variant 401 and the second variant 402 are the same chemically and geometrically, however the orientations are different. In one embodiment, a number of variant geometries are used together in a number of volume fractions of a second phase to accommodate a number of configurations that satisfy low volume difference criteria and high degree of interface matching criteria. FIG. 4D shows another example in which two variants 401 and 402 of the second phase co-exist. The vector “n” of FIG. 4A defines the interface normal, and the vector “a” defines the distortion needed to convert variant 401 into 402. Although FIGS. 4A-4C are shown in two dimensions, one of ordinary skill in the art, having the benefit of the present specification will recognize that the concepts are also extended to three dimensions. One of ordinary skill in the art, having the benefit of the present specification will be able to define the vectors “a” and “n” for any pairs of variants.
FIG. 5A shows a portion of material with a first phase portion 510 and a second phase portion 511. In one embodiment, the second phase portion 511 includes a first variant 520 and a second variant 522. An interface 512 is shown between the first phase portion 510 and the second phase portion 511. In martensitic materials the structure of FIG. 5A is often called an austenite/martensite interface or habit plane.
FIG. 5B shows a structure like FIG. 5A, but the volume fractions of the first variant 520 and the second variant 522 are different from those of FIG. 5A. The volume fraction of a variant of a phase is the proportion of volume of that phase occupied by that variant expressed as a percentage. FIGS. 5A and 5B show two values of the volume fraction of the first variant 520 of the second phase 511. In one embodiment, the volume fraction of the first variant 520 of the second phase 511 can have any value between 0 and 100%. In one embodiment, due at least in part to multiple configurations with multiple volume fractions of the second phase 511, hysteresis is reduced and the reversibility of the transformation is increased.
In one embodiment, hysteresis is predicted by measuring at least one of the criteria described above, including volume difference between a first phase and a second phase. A flow diagram is shown in FIG. 6 that illustrates one example of a method to predict hysteresis in a material. A property such as strain in a shape memory alloy is selected and a material is chosen for evaluation. In one embodiment, the material exhibits a phase change between a first phase and a second phase where the property such as strain is different in the two phases. The material is then evaluated based on a number of criteria.
In one embodiment, the criteria include determining the difference in volume between the first phase and the second phase as described above. In one embodiment, the criteria include determining a degree of matching at the interface between the first phase and the second phase as described above. In one embodiment, the criteria include determining the number of possible volume fractions of variants of a phase that meet another phase. In one method as shown in FIG. 6, the criteria are ranked 1-3. In one embodiment, the importance of the criteria are evaluated with number 1 having the highest priority and number 3 having the lowest priority. Other embodiments include alternative rankings.
In one embodiment, low hysteresis for any of several properties of interests is indicated by a low volume difference in criterion 1, a high degree of matching in criterion 2, and a high number of possible configurations in criterion 3. Although three criteria are shown, other embodiments include evaluating one of the criteria shown, or two of the criteria shown.
In one embodiment, a material composition is selected based on at least one of the criteria shown to produce a material with low hysteresis. In one embodiment, a crystallographic geometry is modified by introducing various elements to the crystal structure in selected amounts. The modifying elements in one embodiment are substitutional on lattice sites. In one embodiment, the modifying elements are in solid solution. In one embodiment a combination of substitutional elements and solid solution elements are used to modify the crystallographic geometry. Other mechanisms of modifying crystallographic geometry to meet the criteria discussed above are also within the scope of the invention.
One of ordinary skill in the art, having the benefit of the present disclosure, will recognize that varying a concentration of any one element, or a number of elements in an alloy will affect crystallographic geometry. In one embodiment, a resulting alloy formed to meet requirements as described above will include titanium and nickel. In one embodiment a resulting alloy will include titanium and copper. In one embodiment a resulting material will include titanium, nickel and copper. In one embodiment a resulting material will include titanium, nickel, copper and zirconium, etc. Other alloy systems are also within the scope of the invention. Although, as discussed above, material design/modification can be accomplished through concentration adjustment of other elements, in one embodiment hafnium and palladium are used to modify a resulting alloy. Addition of hafnium to many alloy systems has the effect of increasing phase transformation temperature. Other effects of hafnium and palladium on crystallography and hysteresis are discussed below.
In one embodiment, addition of heavier atomic elements such as hafnium (atomic number 72), palladium (atomic number 46), or platinum (atomic number 78) is beneficial for imaging purposes. A further advantage of elements such as platinum is that it is not very reactive in a bio-environment such as inside a human body. In applications such as stents in the medical device industry, a high atomic number provides a clearer image within a patient's body using techniques including, but not limited to x-ray imaging. Stents are an important product that uses shape memory alloys.
In one embodiment, a low hysteresis material also exhibits a high fatigue life through cycles of transformation between phases. High fatigue life is desirable in a number of device applications. In stents, for example, high fatigue life ensures that a device will withstand high numbers of cyclic loading such as heart beats, or other muscle contractions, etc.
In one embodiment, phase transformation properties are described using a distortion matrix as shown below: $U_{1} = (\begin{matrix} t_{1} & t_{2} & t_{3} \\ t_{2} & t_{4} & t_{5} \\ t_{3} & t_{5} & t_{6} \end{matrix})$
U₁is a symmetric linear transformation matrix (in an orthonormal basis) between two phases in a reversible phase change, for example between austenite and martensite phases. Although austenite and martensite are used as an example transformation, the invention is not so limited. Other phase transitions are within the scope of the invention. Values for transformations (in this general example t₁-t₆) depend on the material and respective phases being evaluated.
When looking at a specific alloy, the linear transformation matrix is a useful tool for evaluating the three criteria discussed above. Eigenvalues for the transformation matrix and the determinant for the transformation matrix can be used to evaluate specific alloys for low hysteresis. The eigenvalues for the transformation matrix are denoted as λ₁, λ₂, λ₃, and we order them so that λ₁≦λ₂≦λ₃. The determinant is denoted as “det”.
In one embodiment, if det=1, there is no volume change, and the first criteria is optimized. In one embodiment, if λ₂=1 there is no interface mismatch, and the second criteria is optimized. In one embodiment, addition of hafnium to an alloy has an effect of decreasing λ₂. In one embodiment, addition of palladium to an alloy has an effect of increasing λ₂.
In one embodiment, the third criterion of arbitrary volume fraction of the variants of the second phase (limited by atomic scale) is satisfied if the following conditions are satisfied.
λ₂=1 i)
trU ₁ ² detU ₁ ²2−¼|a| ²>0 ii)
a·U ₁ cof(U ₁ ² −I)n=0 iii)
where cofA denotes the cofactor of the matrix A, and the vectors a and n describe the shape change that relates the first and second variants.
In such a system where the conditions i), ii) and iii), stated above are satisfied, it is possible to have a highly reversible phase transformation between the first and the second phases. In such a system it is possible to have two phases that are reversible with each other in a single material, with any volume fraction between 0 and 1 of variants of the first phase meeting with the second phase. In one embodiment, the reversible phases are austenite and martensite. In one embodiment, the conditions i), ii) and iii) are satisfied together with the condition det U₁=1.
One specific alloy with desirable values for criteria discussed above includes Ti₅₀Ni_36.5Cu₃Pd_10.7with a λ₂=1.0000±0.0005. Another example of a specific alloy with desirable values for criteria discussed above includes Ti₅₀Ni_30.3Cu₁₀Pd_9.7with a λ₂=1.0000±0.0005. Another example of a specific alloy with desirable values for criteria discussed above includes Ti₅₀Ni_26.2Cu₁₅Pd_8.3with a λ₂=1.0000±0.0005.
FIG. 7 shows a block diagram of an example device 700 using a low hysteresis material as described in embodiments above. A first electronic device 702 is shown coupled to a second device 704 using electrical interconnect circuitry 706. In one embodiment, the first electronic device includes an active region formed from a low hysteresis material as described in embodiments above. In one embodiment, a change in properties between phases that exhibits low hysteresis includes one phase of ferromagnetism and a second phase of ferroelectric behavior. In one embodiment, the second device includes a conventional electronic device such as logic circuitry, individual transistors, etc.

Conclusion

Using embodiments described above, a number of advantages are realized. One advantage includes an ability to predict hysteresis in a multiple phase material. One embodiment includes an ability to modify a material or create a new material that exhibits low hysteresis. Although low hysteresis is discussed in the descriptions above, using the criteria described, a high hysteresis material can also be created (i.e. |λ₂−1| is large). Using embodiments described above to predict material properties and modify material properties, a number of materials can be created. An improved shape memory alloy with low hysteresis can be created. Additionally, a material that exhibits any of a number of properties that are normally mutually exclusive can be created. One phase of a material exhibits one property, while another phase of the material exhibits a second property. A low hysteresis phase change enables a high efficiency transformation between material properties in such a material. Although selected advantages are detailed above, the list is not intended to be exhaustive. Although specific embodiments have been illustrated and described herein, it will be appreciated by those of ordinary skill in the art that any arrangement which is calculated to achieve the same purpose may be substituted for the specific embodiment shown. This application is intended to cover any adaptations or variations of the present invention. It is to be understood that the above description is intended to be illustrative, and not restrictive. Combinations of the above embodiments, and other embodiments will be apparent to those of skill in the art upon reviewing the above description. The scope of the invention includes any other applications in which the above structures and fabrication methods are used. The scope of the invention should be determined with reference to the appended claims, along with the full scope of equivalents to which such claims are entitled.

Claims

1. A shape memory alloy, comprising:

a first phase component, wherein an amount of the first phase component is adapted for a substantially reversible transformation to a second phase component;

wherein a determinant of U₁is between 0.995 and 1.005; and

wherein a second eigenvalue is between 0.9995 and 1.0005.

2. The shape memory alloy of claim 1, wherein the shape memory alloy includes:

49.5-52.0 atomic % titanium

2.1-25.0 atomic % copper;

(10.8−0.011 Cu²)±0.2 atomic % palladium, where Cu is the atomic % copper; and

a balance of nickel.

3. The shape memory alloy of claim 1, wherein the shape memory alloy includes:

25-35 atomic % nickel;

(50-Ni) atomic % palladium, where Ni is the atomic % nickel;

5-8 atomic % hafnium; and

a balance of titanium.

4. A shape memory alloy, comprising:

25-35 atomic % nickel;

(50-Ni) atomic % platinum, where Ni is the atomic % nickel;

5-10 atomic % hafnium; and

a balance of titanium.

5. A shape memory alloy, comprising:

25-35 atomic % nickel;

(50-Ni) atomic % platinum, where Ni is the atomic % nickel;

5-10 atomic % zirconium; and

a balance of titanium.

6. A multiferroic device, comprising:

an active region formed from a material having a reversible phase transformation, including:

a first phase with a ferroelectric behavior;

a second phase with a ferromagnetic behavior;

wherein, the phase transformation from the first phase to the second phase exhibits low hysteresis;

an actuating system to cause transformation between the first phase and the second phase.

7. The multiferroic device of claim 6, wherein the actuating system is chosen from a group consisting of an electric field, a magnetic field, and mechanical stress.

8. A stent, comprising:

a metal support structure, having a constricted state and an expanded state;

wherein the support structure is formed from a shape memory alloy, the alloy including:

wherein a determinant of U₁is between 0.995 and 1.005; and

wherein a second eigenvalue is between 0.9995 and 1.0005.

9. The stent of claim 10, wherein the shape memory alloy includes:

49.5-52.0 atomic % titanium

2.1-25.0 atomic % copper;

a balance of nickel.

10. The stent of claim 10, wherein the shape memory alloy includes nickel, titanium, copper, and platinum.

11. A hydrogen storage device, comprising:

a first phase with high solubility for hydrogen;

a second phase with a low solubility for hydrogen, wherein the phase transformation from the first phase to the second phase exhibits low hysteresis;

12. A method of forming a material, comprising:

modifying crystallographic parameters of a material capable of at least partially changing from a first phase to a second phase, wherein:

volume change between the first phase and the second phase is reduced; and

a degree of interface matching is increased between the first phase and the second phase.

13. The method of claim 12, further including modifying crystallographic parameters to allow for a continuum of volume fractions of pairs of variants of the second phase.

14. The method of claim 12, wherein modifying crystallographic parameters of a material includes modifying a NiTiPdHf alloy capable of at least partially changing from austenite to martensite.

15. The method of claim 12, wherein modifying crystallographic parameters of a material includes modifying a NiTiCuPd alloy capable of at least partially changing from austenite to martensite.

16. The method of claim 12, wherein modifying crystallographic parameters of a material includes modifying a CuAlZnNi alloy capable of at least partially changing from austenite to martensite.

17. A method of forming a material, comprising:

a degree of interface matching is increased between the first phase and the second phase, and

a continuum of volume fractions of pairs of variants of the second phase are available.

18. The method of claim 17, wherein a difference in volume between phases is maintained to accommodate selective solid solution storage of a gas.

19. The method of claim 18, wherein the gas includes hydrogen.