Mineral Identification and the Diopside–Anorthite Phase Diagram: 18-Geol-A1 Mineralogy and Petrology, December 2013, Q2

Question 2: Mineral Identification and the Diopside–Anorthite Phase Diagram (18 total)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

a) Diagnostic hand-specimen properties (8 minerals, 1 mark each)

Mineral identification — diagnostic hand-specimen properties
Mineral	Formula	Diagnostic properties
(a) Selenite	$\text{CaSO}_4\cdot 2\text{H}_2\text{O}$ (gypsum variety)	Very soft (H = 2, scratched by a fingernail); one perfect cleavage giving thin, flexible but inelastic, colourless to transparent sheets; vitreous to pearly luster.
(b) KCl	$\text{KCl}$ (sylvite)	Cubic crystals/cleavage (3 directions at 90°, like halite); H = 2; distinctly bitter/salty taste (more bitter than halite — a standard hand-specimen test); readily soluble in water.
(c) Citrine	$\text{SiO}_2$ (yellow quartz variety)	H = 7 (scratches glass); no cleavage, conchoidal fracture; vitreous luster; hexagonal prismatic habit with pyramidal terminations; pale yellow to golden-brown colour.
(d) Fe₂SiO₄	Fayalite (Fe-rich olivine)	H = 6.5–7; olive-green to brown/black colour; vitreous luster; conchoidal fracture, poor cleavage; unusually high density for a silicate; occurs in Fe-rich rhyolites/granites and some mafic rocks.
(e) Cu₃(CO₃)₂(OH)₂	Azurite	Distinctive intense azure-blue colour; H = 3.5–4; effervesces in dilute HCl (carbonate); commonly intergrown with green malachite in the oxidized (gossan) zone above copper sulphide deposits.
(f) An_90-100	Bytownite–anorthite (Ca-rich plagioclase)	H = 6–6.5; two cleavages near 90° (86°/94°, distinguishing plagioclase from orthoclase); fine parallel striations (polysynthetic albite twinning) visible on the best cleavage face — the single most diagnostic hand-specimen test for plagioclase; white to grey; typical of mafic/anorthositic rocks.
(g) Mg₃Si₄O₁₀(OH)₂	Talc	Softest common mineral (H = 1, the Mohs scale reference); one perfect cleavage giving flexible, non-elastic, greasy-feeling sheets; pale green to white; pearly luster; distinctive soapy/greasy feel is the standard field test.
(h) Antigorite	Serpentine group, ≈ $\text{Mg}_3\text{Si}_2\text{O}_5(\text{OH})_4$	H = 2.5–3.5 (soft); yellow-green to dark green, sometimes mottled; waxy to greasy luster; platy/massive (non-fibrous) habit — distinguishes it from the fibrous serpentine polymorph chrysotile (asbestos); forms by hydrothermal alteration of olivine/pyroxene in ultramafic rocks.

b) Crystallization sequence from 20% anorthite liquid, 1500°C

Given. A simple binary eutectic phase diagram for the Diopside (Di, $\text{CaMgSi}_2\text{O}_6$) – Anorthite (An, $\text{CaAl}_2\text{Si}_2\text{O}_8$) system: Di melts at 1391°C (0% An), An melts at 1553°C (100% An), and the eutectic is at 1274°C, 42% An. Starting liquid: 20% An, 1500°C.

Find. The equilibrium and fractional crystallization sequences, and the final crystalline assemblage.

Diopside–Anorthite binary eutectic diagram. Green dashed path: 20% An liquid cools from 1500°C to the liquidus (≈1335°C, where diopside begins crystallizing), then the residual liquid migrates along the liquidus to the eutectic (42% An, 1274°C) as diopside is progressively removed.

Approach. Read the crystallization path off the diagram and check the final mass balance with the lever rule; since Di and An have no solid solution, compare whether removing crystals from the melt (fractional) changes the outcome versus keeping them in contact with the melt (equilibrium).

Cool the liquid to the liquidus. The 20% An liquid cools at constant composition (vertical path on the diagram) from 1500°C until it intersects the diopside liquidus. Interpolating linearly between the Di melting point (0%, 1391°C) and the eutectic (42%, 1274°C): $$T_{liq}(20\%) = 1391 + \dfrac{1274-1391}{42-0}\times 20 \approx 1335\ ^\circ\text{C}$$ Below this temperature the liquid is saturated in diopside and pure diopside begins to crystallize — it is always the first phase to appear from any starting composition on the Di-rich side of the eutectic (0–42% An).
Equilibrium crystallization. As diopside crystallizes and remains in continuous chemical contact/equilibrium with the melt, removing pure Di (0% An) from the liquid drives the residual liquid composition progressively toward higher %An, following the liquidus curve down and to the right as temperature falls further. This continues until the residual liquid reaches the eutectic (42% An, 1274°C), at which point anorthite joins diopside crystallizing simultaneously from the fixed-composition eutectic liquid (an invariant, three-phase assemblage: liquid + Di + An) at constant temperature until the liquid is entirely consumed. By the lever rule on the bulk composition (20% An) versus the removed pure-Di crystals (0% An): $$f_{\text{liquid at eutectic}} = \dfrac{20}{42} \approx 0.476,\qquad f_{\text{primary Di}} = 1-0.476 = 0.524$$ i.e. ≈52% of the rock's mass crystallizes as primary diopside before the eutectic is reached; the remaining ≈48% of the original liquid (now at 42% An) then crystallizes at the eutectic into a Di:An intergrowth in the eutectic's own 58:42 mass ratio. The final assemblage is $\boxed{\approx 80\%\ \text{diopside} : 20\%\ \text{anorthite by mass}}$ — exactly the starting bulk composition, since no material leaves the system.
Fractional crystallization. If instead each diopside crystal is physically removed from contact with the liquid as soon as it forms (e.g. by settling), the residual liquid still evolves along exactly the same liquidus path (0% An crystals are being subtracted either way) and still reaches the same eutectic at 42% An, 1274°C, crystallizing the same final Di+An eutectic intergrowth from the last liquid. Because the Diopside–Anorthite system is a simple eutectic with no solid solution and no intermediate compound, equilibrium and fractional crystallization therefore follow an identical path and produce an identical final assemblage — the two mechanisms only diverge in systems where early-formed crystals can either react back with the melt or be isolated from it (e.g. plagioclase or olivine solid-solution series, or a system with a peritectic reaction), which is not the case here. The practical difference in a Di–An rock is textural, not mineralogical: equilibrium crystallization tends to leave primary diopside crystals rimmed/overgrown or zoned as the eutectic assemblage nucleates around them, while fractional crystallization (settled Di crystals separated from the melt) can produce a cumulate layer of diopside physically segregated from the later eutectic-textured Di+An intergrowth.

Final Results — Q2b
Quantity	Value
Liquidus temperature at 20% An (onset of Di crystallization)	≈ 1335 °C
Mass fraction crystallizing as primary diopside (before eutectic)	≈ 52.4%
Mass fraction of original liquid remaining at the eutectic	≈ 47.6% (42% An)
Final bulk assemblage (equilibrium AND fractional)	≈ 80% diopside : 20% anorthite by mass

Topic. Hand-specimen mineral identification, and crystallization paths on a simple binary eutectic phase diagram.

Key relations. Linear liquidus interpolation; lever rule $f_{liquid} = \dfrac{X_{bulk}-X_{solid}}{X_{liquid}-X_{solid}}$.

Why this works. In a system with no solid solution, the identity of the crystallizing solid(s) and the path the liquid follows on the diagram depend only on which liquidus field the bulk composition starts in and on simple mass balance — not on whether earlier crystals stay in contact with the melt — so equilibrium and fractional crystallization are indistinguishable in final result for a Di–An type system, even though they are famously NOT indistinguishable in systems with solid solution (e.g. olivine or plagioclase), where fractional crystallization drives the liquid to more evolved compositions than equilibrium crystallization would.

Common pitfall. Assuming fractional crystallization always changes the final mineral assemblage relative to equilibrium crystallization — true for solid-solution systems, but not for a simple eutectic like Di–An; and misreading the lever rule's numerator/denominator (the fraction of liquid remaining is proportional to the distance from the BULK composition to the crystallizing solid, divided by the total tie-line length).

Source. Winter, Principles of Igneous and Metamorphic Petrology, 2nd ed., §6.3–6.5 (binary eutectic systems, equilibrium vs. fractional crystallization); Klein & Dutrow, Manual of Mineral Science, 23rd ed., ch.1–20 (hand-specimen diagnostic properties).

Question 2 of 3: Mineral Identification and the Diopside–Anorthite Phase Diagram

Question 2: Mineral Identification and the Diopside–Anorthite Phase Diagram (18 total)

a) Diagnostic hand-specimen properties (8 minerals, 1 mark each)

b) Crystallization sequence from 20% anorthite liquid, 1500°C