Final answer:
The question pertains to an Al-Li alloy's phase composition and involves calculating phase amounts using a phase diagram, the Lever Rule, and known densities for weight and volume fractions. Calculations of atomic fractions for primary, eutectic, and total β phases also require specific phase diagram data.
Step-by-step explanation:
The student's question deals with an Al-Li alloy and requires an understanding of phase diagrams, particularly concerning the eutectic system at a given temperature (860K). This involves determining the composition of different phases and calculating their amounts in weight fraction, volume fraction, and atomic fraction. Since the exact phase diagram is not provided, a general explanation will be given, but the calculation of specific values cannot be performed without additional data.
Composition of Phases
The composition of the phases in a binary alloy system at a specific temperature can be found by consulting the phase diagram for that specific alloy system. Typically, you would locate the alloy composition on the horizontal axis and move upwards to the given temperature. The phase regions intersected (e.g., α, β, or liquid) will give you the phase compositions at equilibrium.
Calculating Amounts of Phases
Once the phase compositions are known, the Lever Rule can be applied to find the weight fractions of each phase. The procedure requires calculating the lengths of the tie-line segments from the overall composition to the composition of each phase. Volume fractions can be calculated if the densities of the phases are known. Atomic fractions would be found by considering the atomic percentages of each element within the phases.
Total β Phase Calculation
The total β phase would include both the primary β (existing before reaching the eutectic temperature) and the eutectic β (formed at the eutectic composition during cooling). Atomic fractions for each of these can be computed based on their respective compositions and amounts.