SCIENCE · INVESTIGATE AND EXPLAIN

Construct a material representation without overclaiming evidence

Build individual substitution sites, preserve composition while changing arrangement, and identify what empirical properties cannot determine.

Learning outcome: Construct and critique an atom-count representation using a mass-to-atom reference and distinguish composition, arrangement and mobile charge.

Starting recap

Atom percent counts atoms; mass percent weighs them. A finite drawing has limited composition resolution and need not reveal a real crystal structure.

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Try

The source 10% nickel by mass row contains 10.73% nickel atoms. One nickel among eight sites is 12.5%, so an eight-site drawing cannot match it exactly.

Open the experiment

Predict

Before editing, state how many nickel sites give the nearest eight-site composition. Predict whether moving that site changes the count, real material resistivity, or the information justified by the packet.

Your prediction and reason

Experiment

Build and capture your own diagram. Make a second arrangement with the same count, then a two-nickel arrangement with different adjacent contacts. Explain the difference between a teaching contact count and a measured structure. Transfer to the 5% mass target and explain the coarse nearest-count result.

Build and challenge a particulate representation

Evaluated material reference values · original wire and site representations · Eight editable substitution sites form an original counting cartoon, not the crystal structure of copper–nickel. Site arrangements never generate empirical resistivity.

Source composition to represent: Cu–10% Ni, 293 K case

Reset keeps your prediction, captures and practice history.

Your editable substitution-site diagram

Target Cu–10% Ni, 293 K: 10% nickel by mass corresponds to the source's 10.73% nickel atoms. Select individual sites to replace Cu by Ni. Every site holds one atom; no interstitial site is introduced. Keyboard users can Tab to a site and press Space.

0/8 = 0% nickel sites. Difference from the atomic target: -10.73 percentage points. One site is 12.5 percentage points, so exact matching may be impossible. The nearest count is 1; a zero nearest count for a dilute alloy reflects this coarse representation, not absence of nickel in the material.

The boxes are counting positions, not a square crystal or measured atom sizes. Positive metal cores coexist with delocalized electrons; the labels name the elements, not formal oxidation states. The electron band is a qualitative carrier representation, not a measured electron count, drift rate or trajectory. In a solid ionic model the ions occupy constrained sites; mobile ions in a melt or solution provide another conduction mechanism. Conductivity alone does not uniquely identify bonding.

There are 0 unlike-element contacts among 10 horizontal/vertical edges in this cartoon. Capture a diagram, then move nickel sites while keeping their count fixed. Compare the count and contact ledger. This edge count is not a real coordination number, clustering measurement or resistivity predictor.

The selected empirical resistivity stays 13.89 × 10⁻⁸ Ω m regardless of your drawing. An arbitrary clustered diagram may not represent the source preparation. Explain what diffraction or preparation evidence you would request before claiming a unique structure. Save both diagrams with those explanations as captures.

Material / T	Ni mass % / atom %	ρ / 10⁻⁸ Ω m	Source estimated uncertainty
Pure Cu, 293 K	0 / 0	1.678	±0.5%
Cu–0.5% Ni, 293 K	0.5 / 0.54	2.23	±5%
Cu–1% Ni, 293 K	1 / 1.08	2.85	±5%
Cu–3% Ni, 293 K	3 / 3.24	5.32	±5%
Cu–5% Ni, 293 K	5 / 5.39	7.77	±5%
Cu–10% Ni, 293 K	10 / 10.73	13.89	±5%
Pure Cu, 400 K	0 / 0	2.398	±1%
Cu–10% Ni, 400 K	10 / 10.73	14.81	±3%

Source definitions and comparison limits

Ho et al. (1983), Electrical Resistivity of Ten Selected Binary Alloy Systems, Table 4, printed p. 228. Accessed 2026-10-28. Recommended, smoothed reference values for well-homogenized alloys with low clustering, without severe quenching or cold work. Pure copper is well-annealed and high-purity. Room-temperature dimensions are used without thermal-expansion correction (printed pp. 187–188, 227, 240). Exact impurity concentrations, pressure, common specimen preparation and covariance are not specified for these recommended rows. The stated percentages are source estimated uncertainties, not declared confidence intervals. All selected rows are unstarred; source stars elsewhere flag temperature ranges without experimental data. These values are evaluated recommendations, not a new raw-data cohort. Only selected factual numbers are reproduced; diagrams and tasks are original.

Your diagram has 0 nickel sites among eight.

Compare a second arrangement with the same count. Equal composition does not mean equal microscopic arrangement; the reference does not determine a unique diagram.

Observation to attach to a capture

Captures retain your reference comparison and wire geometry or each editable substitution site. Replay recalculates the source comparison and your counting representation; it does not measure a new alloy, infer a unique structure or grade the explanation.

Understand

Build the representation yourself

A label says “10% nickel.” Does that mean one nickel atom in ten? First ask what the percent counts. The reference table gives this alloy as 10% nickel by mass and 10.73% nickel atoms. Copper and nickel atoms have different masses, so the two percentages differ.

The eight editable sites are your counting representation. Click or keyboard-toggle individual sites between Cu and Ni, rather than choosing a finished picture. Before editing, predict the nearest number of nickel atoms. One nickel among eight gives 12.5 atom%, which is 1.77 percentage points above the reference. It is a coarse approximation, not an exact reconstruction.

Capture the drawing with a note identifying what it preserves and what it leaves out. Resetting the controls preserves that capture. A capture records your settings and explanation, not an independently graded structure solution.

Composition does not determine arrangement

Move the nickel atom to another site without changing the count. Then make two different two-nickel diagrams: adjacent sites and separated sites. Both contain 25 atom% nickel. Compare the horizontal/vertical unlike-neighbor ledger. The count may change with arrangement even though composition stays fixed.

That ledger belongs only to this two-dimensional cartoon. Its eight sites and ten edges are not the actual coordination or crystal structure of a copper–nickel solid. The empirical resistivity is deliberately unchanged when you rearrange sites. There is no fitted function mapping your drawing to conductivity, hardness or strength.

In the earlier alloy cage you compared replacement and interstitial placement. Here you construct alternative replacement patterns yourself and ask what the empirical packet can distinguish. The source’s low-clustering preparation constraint matters: an arbitrary clustered drawing may be incompatible with that population even if its composition matches. A single resistivity value cannot uniquely recover the arrangement.

Add the charge-carrier explanation

Explain the separate band beneath the diagram: delocalized electrons can move while the positive metal cores remain near sites. The symbol Cu or Ni labels element identity, not a formal charge assignment. Neither the number of free electrons nor a drift speed is measured by this cartoon.

Contrast this with an ionic solid representation: oppositely charged ions occupy constrained positions, so those ions are not freely translating charge carriers in the solid. Melting or dissolving may let ions carry current. A real unknown conductor therefore needs more than a resistance measurement: state, composition, structure and carrier evidence can discriminate alternatives. Do not infer “ionic” merely because an alloy has more resistance than copper.

Make a resolution failure explicit

Transfer to the 5% nickel-by-mass row, which has 5.39 atom% nickel. The nearest eight-site count is zero, but that does not mean the source alloy contains no nickel. A picture with only eight sites has 12.5 percentage-point steps and cannot resolve this dilute composition well. Propose a larger drawing or a composition label, rather than silently erasing a real constituent.

An unfamiliar packet reports 2 atom% dopant. A fifty-site counting diagram can represent one dopant exactly; an eight-site picture cannot. Exact count still would not establish random placement, measured dimensions or a transport mechanism.

Combine independent representations

Save two diagrams with the same composition and different arrangements. In your reflection, connect them to one numerical comparison from the material-property investigation. Include a supported claim, a competing explanation and an additional observation that would distinguish them. Use a numerical ratio, a particulate representation and written reasoning together.

This is public guided investigation evidence. It does not complete a mixed Unit 2 assessment, an unseen assignment or an independently reviewed practical project. A reviewer still needs to check your explanation and transfer to new evidence.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Combine a numerical source comparison, two independently constructed diagrams, and a competing explanation. Distinguish mobile metallic electrons from mobile ions in a liquid and propose additional evidence needed for an unfamiliar conducting material.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Test alloy-property claims against matched reference data Next: Distinguish successive bond breaking from a mean bond value

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