Importance and Composition of Metal Alloys
📌 Metal alloys are crucial for applications like coins, requiring properties such as distinguishability, security against counterfeiting, ease of manufacture, wear resistance, corrosion resistance, and anti-bacterial qualities (e.g., copper's natural property).
🪙 The 2 euro coin uses two alloys: an outer ring of 75% copper and 25% nickel, and an inner ring of 75% copper, 20% zinc, and 5% nickel.
🥉 Lower denomination coins (5, 2, 1 cent) are copper-plated steel to reduce cost, preventing their metal value from exceeding the coin's face value.
🔩 Alloying different elements, like copper with tin (bronze) or zinc (brass), drastically changes properties (hardness vs. malleability) compared to the base metals.

Phase Diagram Concepts
⚙️ An alloy is a mixture of metals, classified as binary (2 elements) or ternary (3 elements); a phase is a region with uniform physical and chemical properties (e.g., ice vs. water in the H₂O diagram).
🔗 Solid solutions form when solute atoms mix homogeneously with solvent atoms; complete solid solubility means the components are miscible at all proportions (e.g., Copper-Nickel).
🧱 In limited solid solubility systems (e.g., Aluminum-Copper, Silver-Copper), a second phase precipitates out when the solute concentration exceeds a solubility limit, creating a more thermodynamically stable state.
📉 Phase diagrams define boundaries: the liquidus line (all liquid), the solidus line (no liquid remains), and the solvus line (solid solubility limit between two solid phases, like $\alpha$ and $\beta$).

Applying the Lever Rule
⚖️ The Lever Rule quantifies the mass fractions of each phase ($\text{mass}_{\text{solid}}$ or $\text{mass}_{\text{liquid}}$) within a two-phase region of a binary alloy system.
🧮 The mass fraction of a phase is calculated by taking the ratio of the segment length from the overall composition to the opposite phase boundary, divided by the total length of the horizontal tie line.
🧪 For a complete solid solubility system with 50% Nickel (Ni) at a temperature where boundaries are at 20% Ni (solid) and 80% Ni (liquid), the mass fraction of solid is $(0.50 - 0.20) / (0.80 - 0.20) = 0.5$, meaning $50\%$ solid.
📊 For limited solubility systems like Silver-Copper (Ag-Cu) at 40 wt% Ag and $600^\circ \text{C}$, the compositions of the $\alpha$ phase (4% Ag) and $\beta$ phase (97% Ag) must first be determined using the solvus lines before applying the lever rule to find mass fractions ($w_{\alpha} = 61\%$, $w_{\beta} = 39\%$).

Calculating Volume Fractions
➗ To find volume fractions after determining mass fractions and phase compositions, the density of each phase must be calculated by averaging the densities of the constituent elements (e.g., $\rho_{\text{Ag}} = 10.49 \text{ g}/\text{cm}^3$, $\rho_{\text{Cu}} = 8.96 \text{ g}/\text{cm}^3$).
📏 The volume fraction is calculated by dividing the volume of a single phase by the combined total volume of all phases, requiring the use of calculated phase densities and known mass fractions.

Key Points & Insights
➡️ Alloying materials allows engineers to customize material properties (strength, malleability, corrosion resistance) far beyond those of pure elements.
➡️ Phase diagrams are essential tools for predicting the equilibrium microstructure (phases present) of an alloy based on its temperature and composition.
➡️ The Lever Rule provides a quantitative method to determine the relative amounts (mass fractions) of each phase present in a two-phase region of a system.
➡️ Understanding density differences helps transition from mass fractions to volume fractions, which is critical as mechanical properties are often dependent on volume distribution.

📸 Video summarized with SummaryTube.com on Nov 17, 2025, 02:05 UTC