Materials Science · Resources, reuse, recycling and lifecycle evidence

Impurities, sorting and recovered material quality

Useful background: Energy, stability and environmental context; Measuring and checking material claims. Each worked case explains the quantities it uses.

Back to the chapter

After reading, you can

Explain why recovered material quality depends on sorting and contamination.
Connect unwanted constituents to a specific processing or structural consequence without treating every mixture as unusable.
Balance accepted and rejected classes and copper mass through a defined sorter.
Distinguish accepted-mass yield, desired-class recovery, composition and qualifying output.
Compare upstream separation with dilution, including the added material and its own composition.

Mixtures can limit the next use

Collected material can combine alloys, polymers, coatings or contamination. Some species are difficult to remove economically or technically in a chosen recovery route. Their presence can constrain the properties or applications of the recovered output.

A recovered batch may be mostly the desired family and still miss the next application’s composition requirement. An impurity is an unwanted constituent relative to that intended use; it is not an element that is always harmful. Copper, for example, can be an intentional alloy addition, while residual copper can restrict some recycled-steel routes.

One mechanism is surface hot shortness: surface cracking during hot deformation under susceptible conditions. Preferential oxidation of iron can enrich copper near the steel–oxide interface; a copper-rich liquid phase can then contribute to the problem. Bulk copper content, other alloying elements and the heating/deformation conditions all matter. This is a reason to control the incoming mixture, not a universal copper threshold or a statement that every copper-bearing steel is brittle.

Melting changes the form of a feed; it does not by itself prove selective removal of its elements. Copper is difficult to remove in ordinary steelmaking routes, so preventing unwanted entry can be more useful than expecting a later remelt to purify it. Separating whole objects also cannot extract copper already dissolved within a steel piece. Dismantling or separating attached constituents before they enter one melt addresses a different stage.

Polymer mixtures provide another mechanism. High-density polyethylene (HDPE) and polypropylene (PP) can form distinct domains rather than one molecularly mixed melt. Weak adhesion between domains and changed crystallization can alter the recovered material’s response. A compatibilizer is an added component intended to improve interaction between phases; it does not extract one polymer from the other. Domain shape and processing history matter alongside composition, so a useful treated blend need not be either pure starting polymer. Neither a broad plastic code nor a retained metal family name supplies all the required property evidence.

Follow constituents rather than a single collected total

Consider an original fictional 1000 kg dry recovered-metal lot. Class S contains the desired steel pieces, and class C contains copper-bearing pieces that are unwanted in this next steel batch. Each class has the uniform whole-piece copper mass fraction stipulated in the table. Thus accepting a stated fraction of a class’s mass carries that same fraction of its copper. This is a supplied teaching model, not an observed sorting accuracy or a real scrap grade.

Use w_Cu = M_Cu/M for copper mass fraction, where M_Cu is copper mass and M is total material mass, both in kg. A mass percentage is 100w_Cu. Thus 0.0200 mass% is a fraction of 0.000200, not 0.0200. The S feed contains 900 × 0.000200 = 0.180 kg copper; C contains 100 × 0.200 = 20.0 kg. The complete feed therefore contains 20.180 kg copper, or 2.0180 mass%.

A sorter observes a feature, classifies an object and directs it into an output. Those stages need not be perfect. For plastics, infrared spectra can identify major polymer types, but similar subclasses and additives complicate a complete formulation identification. A correct label for the main polymer is not an assay of every constituent, nor is a laboratory separation result proof of performance at a required throughput.

Here the two sorting modes below are stipulated complete mass-routing records: accepted plus rejected equals input for each class. There is no unrecorded dust, moisture change or third stream. A real process must retain those streams if present. No sorting mechanism is assumed to make missing mass disappear.

Original hypothetical dry input lot. S and C label physical piece classes, not pure chemical elements; all unlisted constituents are retained as the rest of each class.
Input class	Total mass (kg)	Cu (mass%)	Cu mass (kg)
S: desired steel pieces	900.0	0.0200	0.1800
C: unwanted Cu-bearing pieces	100.0	20.0	20.0000
Whole collected lot	1000.0	2.0180	20.1800

A heavier accepted stream can miss the required grade

Mode G accepts 96.0% of S and 5.00% of C. Its accepted mass is 0.960 × 900 + 0.0500 × 100 = 864 + 5 = 869 kg. Copper follows both classes: M_Cu,G = 864 × 0.000200 + 5 × 0.200 = 1.1728 kg. Its accepted copper content is 100 × 1.1728/869 = 0.13496 mass%. Class S is already 99.4246% of this accepted stream, yet that class-based percentage is not its chemical purity.

Mode H accepts 90.0% of S and 1.00% of C: 810 + 1 = 811 kg. It carries 0.1620 + 0.2000 = 0.3620 kg copper, giving 0.04464 mass%. H rejects more S as well as more C. A more selective setting is not a free improvement; it changes which material remains in each stream.

For a deliberately narrow next-use screen, require the homogeneous output’s bulk copper content to be at most 0.100 mass%. Equality is allowed. All other requirements are stipulated satisfied for this calculation. This invented limit is not a steel specification or a universal hot-shortness boundary. Under the stated closed remelt with all accepted mass and copper retained and fully mixed, G fails the copper screen and H passes.

Close both accounts. G rejects 36 kg of S and 95 kg of C, a total 131 kg carrying 0.0072 + 19.0000 = 19.0072 kg copper. H rejects 90 + 99 = 189 kg carrying 0.0180 + 19.8000 = 19.8180 kg copper. Accepted and rejected masses sum to 1000 kg in each mode, and their copper masses sum to 20.1800 kg. Rejected means outside this target stream, not necessarily landfilled or valueless; any subsequent recovery needs its own route and evidence.

Complete original fictional sorting records. Cu percentages are calculated bulk compositions; qualifying refers only to the stipulated 0.100 mass% screen and the declared homogeneous closed output.
Quantity	Mode G	Mode H
Accepted S / C (kg)	864 / 5	810 / 1
Total accepted (kg)	869	811
Accepted Cu (kg)	1.1728	0.3620
Accepted Cu (mass%)	0.13496	0.04464
Rejected total (kg)	131	189
Rejected Cu (kg)	19.0072	19.8180
Qualifying accepted mass (kg)	0 under this screen	811 under this screen

Original hypothetical comparison of alternative sorting modes G and H applied separately to the same dry 1000 kilogram lot. S input is 900 kilograms at 0.0200 mass percent copper and C input is 100 kilograms at 20.0 mass percent copper. In the upper panel, both horizontal bars have a common zero to 1000 kilogram axis. G accepts 869 kilograms and rejects 131 kilograms; H accepts 811 and rejects 189. Hatching distinguishes the accepted portions: diagonal blue for G and horizontal violet for H; the remaining dark portions represent rejected mass. The bars do not separately encode the copper mass or the constituent-class masses. In the lower panel the separate horizontal axis spans zero to 0.160 mass percent copper. G is an orange triangle at 0.13496 mass percent and H a blue square at 0.04464 mass percent. The dashed limit at 0.100 mass percent admits H and excludes G under the supplied closed, homogenized output screen. More accepted mass therefore does not mean more output meeting this target. These are alternative runs, not streams to add together or measured sorter performance.

Yield and quality are separate

A high collected mass does not establish a high yield of material meeting a demanding specification. Track collection, sorting, processing losses and usable grades. Distinguish a laboratory separation demonstration from a functioning recovery pathway at the required throughput.

Define the denominator each time. Accepted-mass yield is accepted total divided by the 1000 kg collected feed: 86.9% for G and 81.1% for H. Desired-class recovery is accepted S divided by its own 900 kg input: 96.0% for G and 90.0% for H. The fraction of accepted mass belonging to S is a third quantity. None equals the copper mass fraction.

Under this target screen and closed-output assumption, the qualifying-output yields on collected mass are 0% for G and 81.1% for H. G’s material has not ceased to exist; it might suit another use or a further treatment. Do not call that alternative use established until its own composition, structure and property requirements have been checked.

The original 100 kg to 60 kg example below remains a qualifying-output statement on collected mass. It does not say which species were recovered or where the remaining 40 kg went. A useful recovery record reports both total streams and the constituents that limit the next use.

Actual remelting can lose material to slag, oxide, dust or other streams, and can introduce contamination from equipment or additions. The closed model here isolates the sorting comparison. If mostly iron is lost while copper is retained, copper concentration can rise even while total output mass falls. A mass loss is not automatically an impurity removal.

Dilution can change a grade without removing the copper

Suppose G’s 869 kg accepted stream is blended with an added material having copper fraction w_a. Assume all material is retained and homogenized; M_a is the added mass in kg. The copper fraction becomes w_final = (1.1728 kg + w_a M_a)/(869 kg + M_a). The numerator is copper mass; the denominator is total output mass. This is a separate original mass-balance case, not a melting recipe.

First stipulate a copper-free addition, w_a = 0. To meet w_final ≤ 0.00100, require 1.1728 ≤ 0.00100(869 + M_a). Thus M_a ≥ 303.8 kg. At equality the output is 1172.8 kg and still contains all 1.1728 kg of the original copper. The concentration fell because the denominator grew, not because copper was separated.

If the addition instead contains 0.0200 mass% copper, w_a = 0.000200. Rearrangement gives 1.1728 − 0.00100 × 869 ≤ (0.00100 − 0.000200)M_a, so M_a ≥ 379.75 kg. The output is then 1248.75 kg, containing 1.1728 + 0.000200 × 379.75 = 1.24875 kg copper. The same target needs more added material because that addition also brings copper.

For an added stream with composition below the target, the general lower bound is M_a ≥ (M_Cu − w_lim M)/(w_lim − w_a), when the original stream exceeds the target. Here w_lim is the required copper fraction. If w_a equals or exceeds w_lim, no finite amount can bring this initially over-limit batch down to the limit by blending alone. The sign of the denominator expresses a physical mixing limit.

The copper-free blend contains 869/1172.8 = 74.10% material from the accepted recovered stream by mass. Calling its 1172.8 kg output a 117.28% recovery of the original 1000 kg collection hides the 303.8 kg addition. Keep that additional input and the rejected 131 kg in the system account. Which route is preferable also needs function, energy, cost, usable properties and other impacts; concentration arithmetic alone does not establish an environmental winner.

Original calculated closed-mixing comparison for 869 kilograms of G material containing 1.1728 kilograms of copper. The horizontal axis is added mass from zero to 500 kilograms and the vertical axis is final copper concentration from 0.070 to 0.150 mass percent. The solid blue curve uses a copper-free addition; the dashed orange curve uses an addition at 0.0200 mass percent copper. Both start at 0.13496 mass percent and each has 201 calculated vertices. A horizontal dashed guide is the invented 0.100 mass percent target. A hollow circle marks the copper-free crossing at 303.8 kilograms added, and a hollow diamond marks the 0.0200 mass percent addition crossing at 379.75 kilograms. The original copper is retained along both curves; the orange case also adds copper. Concentration falls through a growing denominator, not selective removal. No costs, actual process losses, other grade requirements or environmental ranking are represented.

Match the evidence to the claimed output

The feed and routing assumptions are part of the result. If C pieces vary in copper content and the sorter preferentially accepts the copper-rich ones, an overall C average cannot be multiplied by the accepted C mass as if the class were uniform. Measure or justify the composition of the actual accepted and rejected streams. A reported fraction by item count also cannot replace the mass fractions used in this balance.

A bulk assay of a homogenized batch addresses a different question from a surface reading on one fragment or a polymer family classifier. Retain the lot, dry or wet mass basis, sample locations, measured constituents and sampling uncertainty. A small sample passing a limit does not prove that every unmixed piece has that composition. Sampling, scale and extrapolation limits develops this distinction.

Composition is necessary information, not complete property qualification. Recovered metals still have processing state, inclusions and microstructure; recovered polymers can have altered chain distributions, additives and separate phases. A measured output should be tested against the actual next-use quantities and conditions. Record what was demonstrated at the required scale, and keep a prospective recovery route distinct from an operating one.

Worked examples

Work through the case

A process collects 100 kg and produces 60 kg meeting the target specification. What should a useful report retain?

Record 100 kg collection.
Calculate the qualifying-output yield on this collected-mass basis: 60/100 = 0.60, or 60%.
Account for other streams and the quality criterion.

Both collection and usable-output yield; they are different measures.

Compare yield and chemical quality on separate bases

For the supplied G and H records, which gives more accepted mass, and which provides more output meeting the stated copper screen?

G accepts 869 kg; H accepts 811 kg. G therefore has the larger accepted-mass yield, 86.9% versus 81.1%.
G contains 1.1728/869 × 100 = 0.13496 mass% copper, above 0.100. H contains 0.3620/811 × 100 = 0.04464 mass%, below it.
Under the exact homogeneous closed-output assumptions, G supplies no qualifying output to this particular screen and H supplies 811 kg. Do not replace the chemical criterion by the fraction of mass labelled S.

G accepts more material, while H supplies more qualifying output for this defined next use. The comparison does not establish their whole-system cost or environmental ranking.

Account for the addition that changes the concentration

G’s accepted stream is blended with a material containing 0.0200 mass% copper. Find the minimum added mass for the 0.100 mass% screen and the copper mass afterward.

Convert percentages to fractions: w_a = 0.000200 and w_lim = 0.00100. The excess copper relative to the target on the original 869 kg is 1.1728 − 0.00100 × 869 = 0.3038 kg.
Each kg added reduces that excess by only 0.00100 − 0.000200 = 0.000800 kg on the growing total-mass basis. Hence M_a = 0.3038/0.000800 = 379.75 kg.
Total output is 1248.75 kg, with 1.24875 kg copper. Their ratio is 0.00100. Original copper was not removed; an extra 0.07595 kg entered.

Add at least 379.75 kg under the stipulated no-loss mixing model. It reaches the chosen composition boundary, not a demonstrated mechanical property or a purification.

Find how much unwanted class the target can tolerate

Suppose accepted S remains 864 kg but accepted C mass c is only bounded between 2.00 and 5.00 kg. All class compositions are as before. Does that range establish the 0.100 mass% screen?

The accepted stream has total mass 864 + c and copper mass 0.1728 + 0.200c, both in kg.
Require 0.1728 + 0.200c ≤ 0.00100(864 + c). Rearranging gives 0.199c ≤ 0.6912, hence c ≤ (0.6912/0.199) kg, approximately 3.47337 kg.
At c = 2 kg, copper is 0.5728/866 × 100 = 0.06614 mass%; at 5 kg it is 0.13496 mass%. The stated range includes both passing and failing compositions.

No. Under this complete allowed range, the result is unresolved. A justified upper carryover bound at most the unrounded threshold (0.6912/0.199) kg would establish this particular screen; no probability follows from the range.

Try the reasoning

Does recycled content prove future recyclability?
Show the answer and reasoning
No.
The new product may add incompatible constituents.
Why identify alloy or polymer grades?
Show the answer and reasoning
Mixing can change properties.
A broad family label may hide contamination problems.
An analyst enters the S composition 0.0200 mass% as fraction 0.0200, and reports G desired-class recovery as 864/1000. Correct both steps.
Show the answer and reasoning
Use fraction 0.000200 and desired-class recovery 864/900 = 96.0%.
A mass percentage is 100 times a mass fraction. The 900 kg denominator is the input S class; 864/1000 = 86.4% instead reports accepted S mass per total collected feed, a different quantity.
Keep G and the addition at 0.0200 mass% copper, but tighten the invented bulk screen to 0.0800 mass%. Find the minimum addition without losses.
Show the answer and reasoning
796 kg; the resulting total is 1665 kg.
Use w_lim = 0.000800. M_a ≥ (1.1728 − 0.000800 × 869)/(0.000800 − 0.000200) = 0.4776/0.000600 = 796 kg. Copper becomes 1.332 kg, and 1.332/1665 = 0.000800. More input is required for this different target.
Can G be brought to at most 0.100 mass% by adding only a stream containing exactly 0.100 mass% copper, with all mass retained?
Show the answer and reasoning
No finite added mass reaches the limit.
The final excess over the target is [1.1728 − 0.00100 × 869]/(869 + M_a) = 0.3038/(869 + M_a), positive for every finite M_a ≥ 0. The concentration approaches the limit from above; treating equality of addition and target as a zero-cost purification is wrong.
In a separate stipulated process, G loses 50.0 kg of copper-free material and retains all its copper. Find the new copper percentage and decide whether loss improved this screen.
Show the answer and reasoning
0.14320 mass%; it worsened the copper concentration.
Total becomes 819 kg but copper stays 1.1728 kg. 100 × 1.1728/819 = 0.14320 mass%, above the earlier 0.13496. Removing material and removing the limiting constituent are not the same operation.
One accepted unwanted piece weighs 5 kg and 864 accepted S pieces each weigh 1 kg. Does one unwanted piece among 865 establish the same purity as 1/865 by mass?
Show the answer and reasoning
No. Its accepted mass share is 5/869 = 0.5754%, not 1/865 = 0.1156%.
Item counts weight each object equally, whereas composition balances weight its mass. The single unwanted piece carries 1.00 kg copper in this case; many small desired pieces do not make that copper disappear.
In a new lot, accepted S is still 864 kg at 0.0200 mass% copper, but 5 kg accepted C is now 40.0 mass% copper. What changes, and may the old G assay be reused?
Show the answer and reasoning
Copper becomes 2.1728 kg and the accepted stream is 0.25003 mass% copper. The old result cannot be reused.
The total stays 869 kg, but its copper is 0.1728 + 5 × 0.400 = 2.1728 kg. The changed contaminant composition changes the inference even though both accepted class masses are unchanged.
A mixed HDPE/PP output has good strength after a validated compatibilization treatment. Does that establish recovery of chemically pure HDPE, or the same performance after any later remelt?
Show the answer and reasoning
Neither follows.
A useful two-phase blend can remain a mixture. Its interfacial structure, additives and processing history can contribute to the tested response. Keep the actual composition and matched property evidence instead of converting one passed test into a purity or unlimited reprocessing claim.

What to carry forward

Track composition and quality through recovery.
Do not substitute collection mass for usable output.
Define an impurity relative to the intended route and use; composition, phase structure and processing can all matter.
Close total mass and limiting-constituent accounts separately.
State the denominator of each yield, recovery and purity quantity.
Dilution retains unwanted material and adds another input; separation changes its destination.
Qualifying composition is one criterion, not complete property or environmental evidence.

References

Teaching resources and research supporting this lesson’s explanations and examples.