*3.2. Alloying*

The differential evaluation of a systematic series of homogenized CuNi alloys with respect to their |α|, σ, *n*, and *SE* at room temperature is shown in Figure 2. Herein, it is the specific situation of alloys that they typically cannot be accurately calculated or predicted by usual band structure models. However, the full alloy series is experimentally accessible. There are no structural phase transitions reported, and, also, all investigated samples were homogenous with respect to their microstructure and composition by scanning electron microscopy and X-ray diffraction. The dependence of σ on the Ni content (Figure 2a) presents two minima at around 30 at.%-Ni and at around 70 at.%-Ni, which are better seen in the inset to Figure 2a, where the data of the main panel are presented in logarithmic vertical scale.

**Figure 2.** Thermoelectric and transport properties across alloy system Cu–Ni at room temperature, alloy composition was obtained with Energy-Dispersive X-Ray spectroscopy: (**a**) electrical conductivity, (**b**) the Seebeck coefficient in absolute values, (**c**) the carrier concentration derived from the Hall coefficient, (**d**) calculated electronic entropy. Lines and shades are guides to the eye.

In the trend of |α| (Figure 2b), a broad maximum can be seen slightly below to the equiatomic composition, close to the composition of the highest chemical disorder, a similar situation to that of other entropic parameters of such alloys [31], but a shoulder at a composition of about 70 at.%-Ni is also evident. This observation of high |α|for a high chemical disorder reflects the general finding that high configurational entropy is a prerequisite for the observation of large |α| [32]. Because of the close relationship between large |α| and high configurational entropy, it was recently suggested to even use configurational entropy as a gene-like performance indicator for the computational search of new thermoelectric materials [33].

The parameters σ and |α| follow inverse trends with respect to one another. Additionally, these trends match the description of α under the Mott formula [13]. Consequently, the investigated alloy series represents a good electronic model system. There is no clear trend in the data of *n*. (Figure 2c) The pure metals Cu and Ni have the highest *n*. Different effects superimpose to a more sophisticated dependence of *n* on the alloy composition: (i) the effect of change in the average lattice parameter by the alloying [31] should create a gradual increase in *n* as the amount of Nickel increases; (ii) additionally, with the addition of Ni (Ni: 3d<sup>8</sup> 4s2; 2 electrons per Ni atom) into the Cu matrix (Cu: 3d<sup>10</sup> 4s1; 1 electron per Cu atom) more charge will also be added [34]. A linear increase is schematically depicted by the dashed line in Figure 2c. The overall result of these measurements is a clear minimum at approximately 65 at.%-Ni. This already indicates that additional degrees of complexity add to this simplified picture.

The combination of |α| and *n* to extract the *SE* allows us to gain additional information compared to the individual transport coe fficients. Figure 2d shows a curve in *SE* with maximum at approximately 30% of Ni and an additional clear minimum at approximately 65% of Ni. Coming from the Cu-side of the phase diagram, the increase in *SE* points out an increase in the available states for the transport electrons, which may be intuitively understood: the disorder in the non-periodic electrostatic potential leads to an increase in the entropy of the transport electrons. This increase in *SE* reaches a maximum close to the point where the maximum chemical disorder is expected, following the trend of |α|. Coming from the Ni-side of the phase diagram, |α| increases and *n* decreases. The |α|, similar to the Cu-side of the phase diagram, shows higher values because of a higher degree of chemical disorder in the system. But the |α| does not follow a monotonic trend; instead, it has a plateau. This, combined with the reduction of *n* in the same composition region, results in a sharp minimum of *SE*. This minimum exactly coincides with the onset of ferromagnetism in the alloy series. Hence, the entropy evaluation provides an insight on how the magnetic ordering mechanism in this alloy a ffects the localization of charges, possibly due to interactions between d- and s-orbitals. While there is no one-to-one correspondence between the experiment and the microscopic origin, it still provides a meaningful measure of the intensity of correlations in the electronic transport system, which are not easily accessible by usual ab-initio methods.
