We can understand it with the metaphor of a balance:

One end of the balance: It is the mechanism that causes resistance to rise with temperature.

On the other end of the balance lies the mechanism that causes resistance to decrease with temperature.

Objective: By adjusting the composition and structure of the alloy, achieve a perfect or near-perfect balance at both ends within the required working temperature range.

Now let's analyze in detail these two mechanisms at both ends of the balance:

Mechanism One: Factors causing increased resistance (making TCR positive)

This is a universal phenomenon that all metallic materials possess.

Lattice vibration scattering: Metal atoms are not stationary at lattice points but are constantly vibrating. The higher the temperature, the more intense the vibration.

Electron transport is blocked: Electrons moving in a specific direction (forming an electric current) will collide with these violently vibrating atoms when passing through the lattice, and thus be scattered. This is like a person moving through a crowded and constantly shaking crowd, and their speed will slow down.

Increased resistance: This scattering effect hinders the directional flow of electrons, which is manifested macroscopically as an increase in resistance.

Conclusion: This mechanism is the "base plate", which always attempts to increase the resistance as the temperature rises, contributing a positive TCR.

Mechanism Two: Factors leading to reduced resistance (making TCR negative)

This is a characteristic possessed by certain special alloys and also the key to achieving a low TCR. There are mainly the following two theories to explain:

Kondo Effect - mainly used to explain certain alloys containing magnetic atoms (such as Cu-Mn series manganese-copper)

In some diluted alloys (such as when a small amount of manganese (Mn) atoms are doped into a copper-Cu matrix), manganese atoms have a local magnetic moment, just like a tiny magnet.

At low temperatures: The spins of these magnetic atoms will have a strong interaction with the spins of conducting electrons, "binding" the electrons and causing them to be strongly scattered, resulting in very high resistance.

When the temperature rises: Thermal motion disrupts this ordered magnetic interaction and weakens the scattering ability of conducting electrons. Electrons have instead become more "free".

Result: The resistance decreases as the temperature rises, contributing a negative TCR.

2. Short-range order and residual resistance - A more universal explanation, especially applicable to non-magnetic alloys (such as Cu-Ni constantan)

In solid solutions, the arrangement of atoms is not completely disordered.

The ideal state: Atoms A and B are completely randomly distributed at the lattice points, which is called a "completely disordered solid solution".

Actual state: During the preparation and heat treatment of alloys, atoms tend to form some kind of tiny local ordered structure (for example, an A atom is more likely to be surrounded by a B atom).

Strong scattering at low temperatures: In this short-range ordered structure, the periodicity of the lattice is disrupted, forming a very effective scattering center for conducting electrons and generating a very high "residual resistance".

When the temperature rises: Thermal vibration intensifies, which will disrupt this short-range order and cause it to transform into a more disordered state. The periodicity of the lattice is restored to a certain extent, and the scattering of electrons is weakened instead.

Result: The residual resistance caused by short-range order decreases as the temperature rises, also contributing a negative TCR.

Exquisite Balance: How to Achieve Near-Zero TCR

Now, we combine the two mechanisms:

Mechanism One (lattice vibration scattering) contributes positive TCR.

Mechanism Two (Kondo effect/short-range ordered destruction) contributes negative TCR.

The work of materials scientists and engineers is to precisely adjust the "composition" and "heat treatment process" of the alloy to "fine-tune" the strength and range of this negative TCR, so that within a specific temperature range, it exactly cancelling out the positive TCR.

For instance, classic manganese-copper alloys (such as Cu-Mn-Ni-Fe, etc.)

By adjusting the precise proportions of elements such as manganese and nickel, their magnetic states and the interaction forces between atoms can be altered, thereby regulating the magnitude of that "negative TCR".

The degree of short-range order within the alloy can be controlled through specific heat treatments (such as quenching and annealing). Rapid quenching can "freeze" the disordered state at high temperatures, while slow cooling or annealing will promote the formation of short-range order. This provides engineers with another "knob" for fine-tuning the TCR.

Ultimately, within a wide temperature range (for instance, from 0°C to 60°C), the positive and negative TCR compensate for each other, resulting in a negligible change in the overall resistance of the alloy and achieving the near-zero low-temperature drift characteristics we require.

Summary

Why can precision resistance alloys achieve low TCR? The answer is:

They do not "resist" physical laws, but rather "utilize" more complex physical laws. By designing the alloy composition and microstructure, a mechanism that reduces resistance with rising temperature (derived from the Kondo effect or short-range ordered destruction) is introduced to counter and counteract the widespread mechanism that increases resistance with rising temperature (lattice vibration scattering), thereby achieving high stability of resistance values on a macroscopic level.

This precisely demonstrates the superb wisdom of humanity in the field of materials science: not opposing the laws of nature, but guiding multiple laws to balance each other in order to achieve the goals we desire.