Thermal Tuning of Thermophysical Properties of Single Cu-Ni Alloy

Abstract

The great majority of metallic materials in use are not single crystals but disordered. We model such a material specimen as being composed of nanoclusters, each cluster being a small mutually interacting cluster of atoms. In this modeling, a material specimen is then treated as a mixture of nanocrystalline and glassy-state atoms. If we define the degree of crystallinity of the object by the probability that an atom is a member of a crystallite existing within the specimen, the probability would be smaller than unity. Structural disorder in such metallic alloys affects thermophysical properties of the alloy specimen in myriad ways. Transport properties in turn impact material utilization in significant ways to the extent that the specimen could behave as possessing completely different alloy properties. This approach to changing alloy properties can serve useful purposes. We show how one might approach such modification of alloy properties without changing alloy composition with a sample of copper-nickel alloy.

1. Introduction

A general theory [1] has been developed for a wide class of metallic alloys. In this theory, such a specimen codifies the structural disorder by means of broad size distributions of nanocrystallites and population of glassy-state atoms of the given alloy elements. It has been established by experiment that the functional form of the nanocrystallite size distribution depends sensitively on the alloy’s elemental composition. A model material specimen is then represented by a compactified mixture of nanocrystallites as large molecules, intermixed with constituent atoms in glassy state. A large system of reaction equilibrium equations is solved numerically iteratively to follow the growth or shrinkage of nanocrystallites as the temperature of the alloy medium is varied.

In this approach, an alloy specimen is regarded as a randomly close-packed (RCP) mixture of a population of nanocrystallites and constituent atoms in glassy state. The disorder is then represented by the size distribution function of the nanocrystallites. Under sustained exposure to thermal, stress, nuclear, or chemical forcing at an elevated temperature, the distribution function becomes modified, and this process is predictable for a given forcing condition and thus controllable. Transport of excitations is affected by the detail of the distribution function, making it possible to control transport properties, all at a fixed alloy composition. The modeling and experimental support will be presented [2].

The reaction of 2-D randomly close-packed (RCP) structures to thermal forcing through a simulated oven experiment was described in previous work [1, 3]. The suggested dissociation of nanocrystallites seen in this experiment lent itself to a modeling approach for the dissociation of nanocrystallites in a RCP system. The treatment of this dissociation is handled by the law of mass action. To start, we must define the room temperature basis for our binary alloy. We model a metallic binary alloy as a mixture of nanocrystallites and glassy atoms. At room temperature, we define the structure of our binary alloy as having a certain mix of these two states. The degree of crystallinity at the binary alloy composition will determine the ratio of glassy matter to nanocrystallites. To define the structure of the nanocrystallites, we use the crystallite size distribution found by combination of our simulated experiment and numerical simulation study for the composition. These parameters for the structure of the binary alloy are composition-dependent, and we use the lessons learned from RCP modeling to determine the room temperature structure of each binary alloy we investigate.

In this study, the nanocrystallite size distribution is changed by sustained thermal forcing at a temperature close to but below the melting point of the given alloy. The specimen is quenched to capture the new equilibrium size distribution of the nanocrystallites at this temperature, and its thermophysical properties are measured. The protocol as described is used at different forcing temperatures for a single copper-nickel alloy specimen at fixed elemental composition. In this chapter, theoretical modeling and forcing experiments will be presented together with measured thermophysical properties resulting from the forcing runs.

2. Thermal forcing

When we acquire a sample of an alloy from a vendor, it is never clearly known what its thermal history is except that we do have reliable pedigree (composition of 55 W% Cu and 45 W% Ni). Experimentally, we do know from alloy structure study [1] that our new theory gives rise to the average value of the degree of crystallinity at room temperature [1]. Figure 1 shows how the degree of crystallinity of the specimen would be expected to change after each round of thermal annealing. We define the degree of crystallinity by the average probability that an atom remains to be part of nanocrystallites within the specimen. Figure 1 is obtained from our theory [1] making use of the Lennard-Jones constants [4, 5], available in the literature for Cu and Ni.

Figure 1.

The dimensionless number density ρ of glassy-state atoms, where ρ = n/n₀ and n is given per unit volume, versus dimensionless temperature for the alloy $T/T_{\mathit{mp}}$. $T_{\mathit{mp}}$ denotes the melting point of the alloy; the intersection of the green line with the blue line in the figure corresponds to unity in dimensionless temperature. $n_0$ denotes the number of single isolated atoms in glassy state at melting point per unit volume.

We note that we view specimen, which is in the form of a wire, 40.5000 cm long and 1.5875 mm in diameter, is often not straight. It contains many small curved segments, which result from unwinding out of the spool and putting in and out of an electric furnace (Fisher Muffle Furnace). For precise measurements, the specimen has been stretched between two end point locations on an optical bench as follows. The end of the copper-nickel wire specimen was flared by a small hammer to serve as an anchor by means of a metal-ceramic latch in an electrically insulating manner. The opposite end is held in a similar manner. One end of the specimen is struck by the bob of a charged pendulum made of a conductor to charge a grounded capacitor (ceramic capacitor, 0.02 microfarad), generating a short pulse from the pendulum in order to generate a narrow electrical pulse to trigger an oscilloscope (digital oscilloscope 400 MHz bandwidth at 400 M bites per second digitization rate). At the end of the wire, specimen is pressed by a spring-loaded transducer (piezoelectric), whose output is displayed in the oscilloscope, thus making the determination of the time of flight of the mechanical pulse (acoustic pulse) to travel the full length of the specimen [6].

On further consideration of any bends in the wire specimen, we have prepared a fixture for straightening the wire specimen. The fixture is designed not to compress nor to stretch the specimen after each annealing treatment, as follows. Two long slabs of an optical bread board made out of aluminum, each with a full row of a straight groove machined out between the two rows of threaded holes, and the heat-treated specimen is sandwiched along the full length of the boards, facing each other. The wire specimen is trapped within the two long 90-degree V-grooves facing each other, the two sides of the wire specimen pressed by aluminum walls gently against each other by means of long screws threaded into the rows of holes on either side of the long grooves. This arrangement allows the measurement of the length of the specimen before and after each annealing round. This type of fixtures can be readily prepared in a machine shop.

The interior of a furnace is typically three-dimensional chamber and cube-shaped, and, consequently, the specimen must be bent into a winding roll to be within a furnace. The above-mentioned wire straightener fixture resolves the chores of reshaping the wire specimen before and after the annealing run, while the annealing could be carried out in an inert atmosphere.

As the temperature the specimen may encounter the effect of oxidation as one approaches the melting temperature of the alloy, we developed a method of putting the specimen within a long stainless tubing capped with all-metal (stainless steel) Swagelok’s (Parkin-Hannifin). The protective tubing used was 6 mm in outer diameter. The protective tubing can be evacuated and filled with argon and sealed after the wire specimen is inserted. The assembly may easily rolled up in order to insert into the furnace and retrieve the annealed specimen after annealing.

3. Theoretical considerations

The size of nanocrystallites that make up a real alloy specimen changes as a result of annealing. The very interesting question is what happens to the length and volume of the specimen due to annealing and quenching of the specimen. It is also important to know how stable would the size distribution of nanocrystallites be because the new distribution function determines the thermophysical properties of the alloy specimen. The motion of an atom is governed by the size of the energy that binds it to a site relative to available thermal energy, whereas energy variation experienced in normal applications is usually very small.

Another to ask is how the thermal evolution of the nanocrystallite population impacts the thermophysical properties of disordered metallic solids as the temperature is raised. The model calculations have clearly shown that not only the number of the nanocrystallites diminishes in population but also the functional form of their size distribution undergoes significant changes at elevated temperatures. These changes lead to changes in packing fraction of the alloy specimen. From the definition of the degree of crystallinity, which measures the probability that an atom belongs to a nanocrystallite, we can derive the packing fraction of glassy matter, η_gl, expressed in terms of the degree of crystallinity, $\gamma$, the packing fraction η_cp when the alloy medium is crystalline and the packing fraction η_rcp when the medium is disordered. We use the composite value for the average packing fraction as compiled by Berryman [7] for the latter. The expression for the packing fraction of fully glassy matter can be found as follows:

$${\eta }_{\mathit{gl}}=\frac{\left(1-\gamma \right){\eta }_{\mathit{rcp}}{\eta }_{\mathit{cp}}}{{\eta }_{\mathit{cp}}-\gamma {\eta }_{\mathit{rcp}}}.$$E1

For a given alloy specimen η_gl is always smaller than either η_cp or η_rcp, and a transition of crystalline particles into the glassy state of matter directly leads to a volume expansion. It thus impacts thermal expansion of the specimen; this contribution is new and additional to the usual definition of thermal expansion. We propose that the simplest way to incorporate the contribution into the alloy model is to treat the thermal expansion in nanocrystallites and in glassy matter separately from the change of the relative populations of atoms within nanocrystallites and atoms in glassy state of matter. Upon heating, the nanocrystallites within the specimen expand according to the crystalline expansion coefficient. Glassy matter of the specimen would also expand but according to the average expansion coefficient of metallic glass. Both of these expansion coefficients are knowable in principle from the literature.

In prescribing the linear expansion coefficient for a disordered alloy in a functional form, one can express the contributions from these effects to the volume of the specimen as a function of temperature in the following form:

$$V\left(T\right)=V\left(T_o\right)\left[\gamma \left(T\right)\left\{(1+{\beta }_{\mathit{cr}}\left(T\right)\left(T-T_o\right)\right\}+\left\{1-\gamma \left(T\right)\right\}\left\{(1+{\beta }_{\mathit{gl}}\left(T\right)\left(T-T_o\right)\right\}\right]$$E2

V(T) and V(T_o) denote the volume of the specimen at temperature T and at a reference temperature T_o, respectively. ${\beta }_{\mathit{cr}}\left(T\right)$ and ${\beta }_{\mathit{gl}}\left(T\right)$ are the volume expansion coefficient at temperature T of the crystallites and glassy matter, respectively. The volume expansion is written out as the sum of the expansions of the nanocrystallites and glassy matter. The new contribution is included into $\gamma \left(T\right)$, which measures the movement of the population of ordered crystalline atoms in the specimen when the temperature is raised [3].

In the conventional treatment, no distinction is made of the nanocrystallites separately from the glassy matter in writing out the linear expansion coefficient; their relative populations are assumed to remain fixed. In the present treatment, the fraction of nanocrystallites in the specimen changes when the temperature is raised, and this change can be determined by first-principle calculation.

4. Concluding remarks

Theoretical analyses of the above kind were carried out for the following singe-atom metals: Ag, Al, Au, Ca, Ce, Cu, Ir, Ni, Pb, Pd, Pt, Rh, Th, Ba, Cr, Fe, K, Li, Na, Nb, Rb, Ta, V, W, Be, Cd, Co, Dy, Er, Hf, Mg, Re, Ru, Ti, Tl, Y, Zn, and Zr.. Similar calculations were carried out for binary disordered metallic alloys AlTi, ${\mathit{Al}}_3\mathit{Ti},$Al${\mathit{Ti}}_3$, AuCu, and $\mathit{Au}{\mathit{CU}}_3$. All calculations showed results of the types consistent with those shown in Figure 1 with varying degrees of agreement for the melting points with known experimentally determined melting point data.

We had a successful thermal forcing run. A 0.382-M-long wire specimen of 55 W% in copper and 45%W% in nickel was used for this run. When forced at 940 K for 16.45 h and the specimen was quenched in water at 10°C, the measured speed of longitudinal sound pulse at room temperature was found to be increased to 5744.36 M/s from the speed of sound in untreated specimen, off the shelf, at 4235.03 M/s. This is an increase by 35.64 percent.

The change of metallic alloy’s thermophysical properties stems from the modifications of the equilibrium distribution functions of nanocrystallites within the system by slow thermal forcing (over 15 hours at a selected temperature) at high temperatures (at temperatures above one half of the melting point), and therefore, it is reasonable to expect that the thermophysical property of the system will most likely to remain as modified throughout normal utilization of the material. The melting point of the alloy used here is given to be 1507 K.

The structural disorders that are pertinent in the context of the present discussion may arise partly from the rough (approximate) handling in material processing stages or partly from trace-level impurities that remain within the alloy-making, and these should be considered intrinsic to the industry, and therefore, the current state of the art may present many useful opportunities to be exploited.