ERB222 Chap.3 Partial Melting and Trace Element Behaviour
Partial Melting and Trace Element Behaviour
Two workshops, one Problem-Solving Task
Workshops 2 and 3 turn the Week 2 melting story into numbers, and Problem-Solving Task 1 asks for a one-page explanation of how partial melting of the mantle creates diverse magmas using those results. Workshop 2 works with major elements: experiments on garnet lherzolite at several pressures and a mass-balance equation for the residue left after melt extraction.
Workshop 3 moves to trace elements and a batch-melting forward model.
The model in brief
Each mineral's partition coefficient, weighted by its abundance, gives a bulk D for the source. The batch equation then predicts the melt concentration for any melt fraction, and a companion equation predicts the residue.
Elements with D far below 1 are concentrated strongly in small melts, while compatible elements such as nickel stay in the solid.
Re-melting the depleted residue, and normalising the result to primitive mantle, tests whether ridge and ocean island basalts need different sources or only different degrees of melting.
What the marker looks for
The task rubric splits marks between workshop observations, interpretation, figures or tables, and communication within one page.
What this chapter covers
- 01
Partition coefficients and bulk D
- 02
Batch melting of the melt
- 03
Residual solid after batch melting
- 04
Major element residue mass balance
- 05
Lherzolite to harzburgite depletion
- 06
Primitive mantle normalisation
- 07
Degree of melting versus mantle heterogeneity
Worked example · free
Batch melting of a compatible element
- 1Bulk D = 0.70 x 10 + 0.20 x 3 + 0.10 x 2 = 7.8, so the element is compatible.
- 1Denominator D + f(1 - D) = 7.8 + 0.10 x (-6.8) = 7.12.
- 1Melt: cl = 2000 / 7.12 = 280.9 ppm.
- 1Residue: cs = 2000 x 7.8 / 7.12 = 2191 ppm.
- 1Check: 0.10 x 280.9 + 0.90 x 2191 = 2000 ppm, matching the source.
Key terms
- Partition Coefficient
- The ratio of an element's concentration in a mineral to its concentration in the coexisting melt, written Kd.
- Batch Melting
- A melting model in which the melt stays in equilibrium with the solid until it is extracted as a single batch.
- Compatible Element
- An element with a partition coefficient above 1, such as nickel in olivine, that stays in the solid during melting.
- Depleted Mantle
- Residual mantle that has lost incompatible elements to earlier melt extraction and so yields depleted melts when melted again.
- Melt Fraction
- The proportion of the source that has melted, written f and running from 0 to 1 in the batch-melting equations.
Partial Melting and Trace Element Behaviour FAQ
How do I calculate bulk D for a mantle rock?
Multiply each mineral's partition coefficient by that mineral's fraction of the rock and add the products. The workshop lherzolite uses 60% olivine, 30% orthopyroxene and 10% clinopyroxene and ignores the 1 to 3% aluminous phase. A mineral with a high Kd can dominate D even when it is scarce.
Why are ocean island basalts more enriched in incompatible elements than MORB?
Batch melting concentrates incompatible elements most strongly at small melt fractions. The workshop links alkali ocean island basalts to roughly 2.5 to 5% melting and ridge basalts to about 10 to 20%, so the larger ridge melts dilute the same elements. Re-melting depleted residue then tests whether source differences also matter.
What should a one-page partial melting report contain?
Use your own workshop numbers as observations, explain how melt fraction, pressure and source depletion change melt composition, and support it with at least one labelled figure or table. The rubric weights observations and interpretation at 30% each, figures or tables at 20% and writing within the page limit at 20%.
Exam move
Rebuild the Workshop 3 spreadsheet from a blank sheet: bulk D, the batch melt and residue equations, then primitive mantle normalisation. Add a row at f = 1 that must return the source and a mass-balance column that must return co. Plot cl/co against f for three D values, then rehearse a one-page explanation that uses those plots as evidence.
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