For the same silver-copper alloy, tin-copper alloy, and copper-nickel alloy, why does the resistivity change when transitioning from the hard state before annealing to the soft state after annealing?
Is there any pattern to this change?
How much can it change?
Can it exceed 10%?
And a more practical question:
Why are some materials very stable, with a regular change between the hard state and the soft state? While for some materials, their resistivity changes from high today to low tomorrow, and there is no discernible pattern among different batches?
In the end, we reached a relatively consistent view:
The change in resistivity between the hard state and the soft state is of course important, but for materials that are truly used in large quantities, what is more important is "stability".
To sum up: After annealing, the resistivity generally decreases, but this is not an absolute rule.
For materials of the same composition and batch, if they only go through:
cold processing hardening such as drawing and rolling → followed by normal annealing softening,
the most common trend is:
the resistivity in the hard state is relatively higher, and after annealing, the resistivity decreases while the conductivity increases.
Why?
Because the current travels through the metal, essentially it is the movement of electrons.
Anything that can "obstruct" the movement of electrons will increase the resistivity.
In simple terms, the resistivity in metals mainly comes from several factors:
temperatures causing lattice vibrations, alloy elements, impurities, as well as crystal defects such as dislocations, vacancies, and grain boundaries.
This is the basic logic behind the classic Matthiessen's rule: alloy elements and crystal defects both increase the scattering of electrons, thereby contributing to additional resistivity. Related materials also divide the metal resistivity into parts caused by thermal vibrations and residual resistivity due to chemical impurities and physical defects.
And what happens when an alloy wire is subjected to extensive drawing?
The grains are elongated, the density of dislocations increases significantly, and a large amount of deformation energy is stored internally. There may also be various defects such as vacancies, residual stress, etc.
So the material becomes harder and the strength increases.
But these defects also scatter electrons.
Therefore, the resistivity of many cold-worked hard materials also increases.
After annealing, there is recrystallization and recovery, the number of dislocations decreases, internal stress is released, and the crystal structure is re-adjusted.
The defect scattering of electrons decreases, so:
The strength decreases, the elongation increases, and the resistivity often decreases as well.
This is the most fundamental rule.
Is annealing always going to reduce it? Not necessarily.
This is the most easily misunderstood part.
If it is a very pure copper piece, the logic is relatively simple.
But we are discussing:
Silver-copper, tin-copper, copper-nickel, these "alloys".
Alloys are much more complex.
Because in addition to dislocations and grain boundaries, there is another more important variable:
What state do the alloy elements exist in within the copper matrix?
For example, if Ag, Sn, Ni atoms are largely dissolved in the copper matrix, they themselves will form a strong electron scattering.
But after some annealing, some alloys may:
precipitate, segregate, phase transform, recrystallize or solute concentration change.
So the resistivity is no longer only affected by "softness or hardness", but begins to be influenced by multiple factors such as:
dislocation density + solute atom content + precipitated phase + grain + impurities.
This is why:
There is no fixed formula applicable to all copper alloys that states how much the resistivity will be lower in the soft state compared to the hard state.
For example, a study on a Cu-15%Ag silver-copper alloy found that during annealing, both recovery and recrystallization occur, and Ag precipitates; as the dislocation density and solute Ag concentration decrease, the resistivity significantly decreases. The study even found that the resistivity of the Cu-Ag alloy after complete recrystallization is significantly related to the residual Ag solute concentration in the copper matrix.
This shows one thing:
For alloys, it is not simply "hard" or "soft", but what exactly happens inside the material after annealing determines the resistivity.
Can the resistivity change by more than 10% before and after annealing?
The answer is:
It is entirely possible.
But "10%" should not be understood as a unified normal or abnormal dividing line.
Take an example closer to our industry.
There is a study that specifically conducted drawing and annealing experiments on Cu-1%Ag silver-copper alloy wires.
The resistance of a φ0.08mm Cu-1%Ag wire after cold processing is approximately:
1.931×10⁻⁸ Ω·m
After annealing, it drops to:
1.723×10⁻⁸ Ω·m
The decrease is approximately 10.8%.
In another set of continuous annealing conditions, the resistivity further drops to approximately:
1.635×10⁻⁸ Ω·m
Relative to the original cold processing state, the change is over 15%.
So:
A change of more than 10% from the hard state to the soft state is completely possible from the material mechanism perspective.
But this does not mean:
The silver-copper alloy "should be reduced by 10%" after annealing.
These two concepts must be kept separate.
Different silver contents, different processing quantities, different wire diameters, different annealing temperatures, and different annealing times will all result in different final outcomes.
Tin-copper is more complex.
Research has found that in the annealing process of Cu-Sn alloys, in addition to recovery and recrystallization, in some materials with higher Sn content, there may also be the precipitation of phases such as Cu₃Sn, so the change in resistivity may show obvious stages, and it is not just a simple continuous decline.
Why do the changes in different alloys vary completely?
This question is actually quite easy to understand.
Because in different alloys, which factor dominates is different.
For example, silver-copper.
In some low-silver-copper alloys, the conductivity itself is still relatively high, so the dislocations generated by cold processing and the changes in the microstructure have a relatively easier manifestation on the total resistivity.
While copper-nickel is completely different.
After adding Ni to Cu, the effect on resistivity is very obvious.
For example, in the publicly available Cu-Ni material data, under annealing conditions:
The resistivity of CuNi2 is approximately 0.05 Ω·mm²/m;
CuNi6 is approximately 0.10;
CuNi10 is approximately 0.15;
Up to CuNi44, it has reached approximately 0.49 Ω·mm²/m.
That is to say, as the Ni content increases, the electronic scattering caused by the alloy elements themselves has become the major factor in the resistivity.
At this time, even if the number of dislocations reduced during annealing, when viewed in the overall resistivity, the relative change ratio may not be as obvious as some high-conductivity low-alloy materials.
So, different alloys cannot be simply compared horizontally:
Why did the annealing of silver-copper change by 8%, while tin-copper only changed by 3%, and copper-nickel only 1%?
This does not represent which one is better or worse.
First, you need to look at the material system.
But if the same material "fluctuates up and down", it is worth paying attention to.
This is actually the most important issue that I think I should focus on after communicating with the client today.
For example, the same tin-copper alloy CuSn0.6%.
Same specifications;
Same hard state;
Same annealing process.
This batch of materials has a 5% drop in resistivity from the hard state to the soft state;
The next batch drops by 1%;
The next batch instead increases by 4%;
The next batch drops by 8%.
If this situation occurs over a long period, I think it cannot simply be explained as:
"After annealing, the resistivity is inherently without a pattern."
No.
The material mechanism can be complex, but a stable material combined with a stable process should ultimately exhibit statistical regularities.
It may not be fixed at 3%.
It may not be fixed at 5%.
However, there should be a relatively stable range.
If it fluctuates wildly, one should first check several aspects.
One is whether there is any fluctuation in the composition.
Especially for us who produce ultra-fine alloy wires, one cannot only look at the average content of the main elements.
The actual contents of Sn, Ag, Ni, oxygen, impurities, and the uniformity of the material at different positions all affect the resistivity.
The second is whether the hard-state processing history is the same.
The same term "hard state" does not mean the dislocation density is the same.
90% cold deformation and 50% cold deformation are both hard states, but the internal state of the material may be completely different.
The third is whether the annealing regime is truly consistent.
The furnace temperature is 400℃, but this does not mean the actual temperature of the wire is 400℃.
Continuous annealing also includes:
line speed, current, tension, actual residence time, cooling method, etc.
These slight changes will result in different final structures.
Another issue that is often overlooked is: it may not be that the material has changed, but that the "measurement has changed".
This problem is particularly important for those who make fine wires.
The volume resistivity is not simply measured by a single resistance value.
It essentially is:
ρ = R × A / L
That is to say:
Resistance R, cross-sectional area A, test length L, any inaccurate data will result in a change in the final resistivity.
Especially for ultra-fine wires.
Assuming the diameter measurement error is only 1%.
Because the cross-sectional area is related to the square of the diameter, the final error brought about by the cross-sectional area is approximately 2%.
For wires with diameters of 0.05, 0.03, or even 0.01mm, this is particularly noteworthy.
There is also temperature.
The resistance itself changes with temperature.
Therefore, when conducting resistivity measurements according to national standards, it is required to record parameters such as measurement temperature, sample length, average cross-sectional area, etc., and usually convert to the standard state of 20℃ for comparison. GB/T 351-2019 also clearly requires that the test records include cross-sectional area, measurement temperature, resistance value, and converted volume resistivity, etc.
So if:
One batch is measured at 22℃;
One batch is measured at 28℃;
One laboratory uses the actual cross-sectional area;
Another directly uses the nominal diameter;
Even for soft and hard states using different equipment;
The "hard and soft state resistivity changes" obtained at the end may already have mixed in measurement errors.
So the statement made by the customer today, I completely agree: Stability may be more important than a certain numerical value.
When we do materials, we often fall into a misconception:
Pursuing a particularly beautiful indicator.
For example:
The lower the resistivity, the better;
The higher the tensile strength, the better;
The higher the elongation, the better.
But when it comes to actual continuous production by the customers, they will find that:
What they really fear is not having slightly lower indicators, but instability.
Today the resistivity is 0.030;
Tomorrow it is 0.033;
The day after tomorrow it is 0.029;
The next batch suddenly becomes 0.036.
For the customers, this might be more troublesome than stabilizing at 0.032.
Because all the subsequent processes such as drawing, electroplating, twisting, welding, signal transmission and the entire process parameters all need to be re-adjusted.
So I increasingly feel that:
The real threshold of high-end materials is not achieving one specific indicator to the extreme, but maintaining a set of indicators in a very narrow range of stability over a long period.
Today the resistivity is 0.030;
Tomorrow it is 0.033;
The day after tomorrow it is 0.029;
The next batch suddenly becomes 0.036.
For the customers, this might be more troublesome than stabilizing at 0.032.
Because all the subsequent processes such as drawing, electroplating, twisting, welding, signal transmission and the entire process parameters all need to be re-adjusted.
So I increasingly feel that:
The real threshold of high-end materials is not achieving one specific indicator to the extreme, but maintaining a set of indicators in a very narrow range of stability over a long period.
The final answer might not be 3%, 5% or 10%.
What is more worthy of questioning is:
After fixed composition, fixed processing volume, fixed annealing regime and fixed detection conditions, can this change be repeated in every batch?
If it can be repeated,
even if it changes by 7%, it is a controllable material.
If today it is +5%, tomorrow it is -3%, and the day after tomorrow it is +10%, there is no pattern to be found.
Even if each batch is "barely in line with the standard", it may not be a truly useful material for high-end customers.