Using the lever rule in a phase diagram to determine phase fraction

Taylor Sparks
3 Sept 202005:12
EducationalLearning
32 Likes 10 Comments

TLDRThe video script explains the concept of phase diagrams in materials science, focusing on the microstructure of ceramics. It introduces the lever rule to determine the weight fraction of different phases in a two-phase region, using a binary isomorphous phase diagram of forsterite and fayalite as an example. The script demonstrates how to calculate the weight percentage of olivine and liquid phases at a given temperature, emphasizing the importance of understanding phase diagrams for material properties and composition.

Takeaways
  • 📚 Phase diagrams are essential for understanding the microstructure of materials, especially in multi-phase regions.
  • 🔍 The lever rule is introduced to determine the proportions of different phases in a two-phase region of a phase diagram.
  • 💠 The example given uses a binary isomorphous phase diagram for two ceramics, forsterite (Mg2SiO4) and fayalite (Fe2SiO4), which have a complete solid solubility.
  • 📉 When cooling a material with a specific composition, the phase diagram can indicate the composition of the first solid to form and the changing composition of the liquid phase.
  • 📏 The lever rule calculates the weight fraction of phases by using the lengths of segments on the phase diagram corresponding to the composition of interest.
  • 🔢 The calculation involves determining the total length between the end members and the lengths of the segments representing the phase of interest.
  • 🧐 For the example given, the weight fraction of olivine is calculated as the difference between the right-hand side composition (71%) and the initial composition (50%), divided by the total range of compositions (71% - 38%).
  • 📈 The weight fraction of olivine is found to be approximately 63.6%, with the remaining being the liquid phase.
  • 🔄 The process is reversed to find the weight fraction of the liquid phase, using the left-hand side composition and the total range.
  • 📝 The example concludes with the weight fraction of liquid being approximately 36.4%, demonstrating the application of the lever rule.
  • 📋 The takeaway emphasizes the importance of understanding phase diagrams and the lever rule for material science, especially in the context of ceramics and solid-state chemistry.
Q & A

  • What do phase diagrams reveal about the microstructure of materials?

    -Phase diagrams reveal the microstructure of materials by showing the presence of multiple phases and how they come together under different conditions.

  • What is the lever rule used for in phase diagrams?

    -The lever rule is used to determine the amount of different phases present in a two-phase region within a phase diagram.

  • What are the two ceramics mentioned in the script, and what do they have in common?

    -The two ceramics mentioned are forsterite (Mg2SiO4) and Fe2SiO4. They both have an olivine crystal structure but differ in their cation composition, with Mg2+ versus Fe2+.

  • What does complete solid solubility mean in the context of phase diagrams?

    -Complete solid solubility means that the two components can dissolve in each other in any proportion without forming distinct phases.

  • How does the lever rule calculate the weight fraction of a phase in a two-phase region?

    -The lever rule calculates the weight fraction of a phase by dividing the length of the segment representing that phase by the total length between the two end members.

  • What is the initial composition of the olivine when the material is first cooled down to the phase diagram point at 50-50?

    -The initial composition of the olivine is about 20 weight percent Fe2SiO4 and 80 weight percent Mg2SiO4.

  • How does the composition of the liquid change as the material cools down?

    -As the material cools down, the composition of the liquid changes, with the mole or weight percentage of the components shifting towards the composition of the solid phase that is forming.

  • What is the weight fraction of olivine at the point where the composition is 38 weight percent Fe2SiO4?

    -At that point, the weight fraction of olivine is approximately 63.6%, as calculated using the lever rule.

  • What is the weight fraction of liquid at the same point where the olivine fraction is 63.6%?

    -The weight fraction of liquid at that point is the remainder of the total, which is 36.4%, since the total must add up to 100%.

  • How does the lever rule apply differently when calculating for the liquid phase versus the solid phase?

    -When calculating for the liquid phase, you take the left-hand segment (representing the liquid) over the total length, and for the solid phase, you take the right-hand segment (representing the solid) over the total length.

  • Why is it important to know the weight fraction of phases in materials science?

    -Knowing the weight fraction of phases is important as it helps in understanding the material's properties, behavior during processing, and its final application.

Outlines
00:00
🔬 Lever Rule in Phase Diagrams

This paragraph introduces the concept of the lever rule, which is used to determine the proportion of different phases present in a two-phase region of a phase diagram. The example uses a binary isomorphous phase diagram for two ceramics, forsterite (Mg2SiO4) and Fe2SiO4, both having the olivine crystal structure. The explanation focuses on how the lever rule can be applied to a composition at a specific temperature to find the weight fraction of solid (olivine) and liquid phases. The process involves drawing a line across the phase diagram at the given composition and using the lever rule to calculate the weight percentage of each phase by comparing the lengths of the segments on either side of the line.

05:01
📊 Calculating Weight Fractions with the Lever Rule

The second paragraph continues the discussion on the lever rule, emphasizing the calculation of weight fractions in phase diagrams presented in weight percent. It explains that if the phase diagram is based on atomic percent, one would calculate mole or atomic fractions instead. The paragraph provides a step-by-step guide on how to use the lever rule to find the weight fraction of olivine and liquid phases at a given temperature, using the difference in composition between the initial and final points of the line drawn across the phase diagram. The summary includes the actual calculations performed to determine the weight percentages of both phases, illustrating the practical application of the lever rule in material science.

Mindmap
Keywords
💡Phase Diagrams
Phase diagrams are graphical representations that show the equilibrium conditions between different phases of a material system at various temperatures and pressures. In the context of the video, phase diagrams are used to understand the microstructure of materials, particularly how multiple phases come together and their compositions at different temperatures. The script uses a binary isomorphous phase diagram to illustrate the solid solubility between two ceramics, forsterite and fe2 sio4.
💡Microstructure
Microstructure refers to the small-scale structure of a material, which can be observed with the aid of a microscope. It is crucial in determining the physical properties of materials. In the script, the microstructure is discussed in relation to how different phases appear when viewed under a microscope, emphasizing the importance of understanding phase diagrams for analyzing the composition and arrangement of phases in materials.
💡Lever Rule
The lever rule is a method used to calculate the amounts of different phases present in a two-phase region based on a phase diagram. It is central to the script's explanation of how to determine the weight fractions of phases in a material. The rule is applied by measuring the lengths of the tie lines on the phase diagram and using them to find the proportion of each phase, as demonstrated with the example of cooling a material with a 50/50 composition of forsterite and fe2 sio4.
💡Binary Isomorphous Phase Diagram
A binary isomorphous phase diagram specifically represents the phase relationships between two components that have complete solid solubility, meaning they can dissolve in each other in any proportion. In the script, such a diagram is used to illustrate the phase behavior of forsterite (mg2 sio4) and fe2 sio4, which both have the olivine crystal structure but differ in their cation composition.
💡Olivine Crystal Structure
The olivine crystal structure is a specific type of mineral structure found in certain silicate minerals, characterized by a repeating pattern of cations and anions. In the video script, forsterite and fe2 sio4 are mentioned as examples of minerals with this structure. The script discusses how the phase diagram can be used to understand the formation of the first solid phase in materials with this structure when cooled from a melt.
💡Solid Solubility
Solid solubility is the ability of one solid material to dissolve in another solid material to form a solid solution. The script explains that forsterite and fe2 sio4 have complete solid solubility, meaning they can form a continuous range of solid solutions across the entire composition range of the phase diagram.
💡Weight Percent
Weight percent is a measure of the weight of a particular component in a mixture compared to the total weight of the mixture. It is used in the script to describe the composition of the first solid phase that forms during cooling and to calculate the weight fractions of olivine and liquid phases using the lever rule.
💡Weight Fraction
Weight fraction is the ratio of the weight of a component to the total weight of the mixture. The script uses the lever rule to calculate the weight fraction of olivine and liquid phases in a material at a specific temperature, providing a clear example of how to apply this concept in the context of phase diagrams.
💡Cooling
Cooling is the process of reducing the temperature of a substance. In the script, the process of cooling a material down from a melt is used to illustrate how the phase diagram can predict the formation of solid phases and the changes in composition of both the solid and liquid phases as the temperature decreases.
💡Composition
Composition refers to the makeup of a substance in terms of the types and amounts of its constituent elements or compounds. The script discusses how the composition of a material changes as it cools, using the phase diagram to predict these changes and to calculate the amounts of different phases present at a given temperature.
Highlights

Phase diagrams reveal the microstructure of materials, including the arrangement of multiple phases.

Introduction of the lever rule for determining the amount of different phases in a two-phase region.

Binary isomorphous phase diagram example using foresterite (Mg2SiO4) and Fe2SiO4 with complete solid solubility.

Demonstration of how to use the phase diagram to determine the composition of the first solid formed during cooling.

Explanation of the process to continue cooling and track changes in the composition of solid and liquid phases.

Application of the lever rule to calculate the weight fraction of olivine at a specific temperature.

Calculation method using the lever rule involving the length of the total line between end members.

Determination of the weight percent of olivine using the lever rule with a specific example calculation.

Calculation of the weight fraction of liquid by using the opposite segments of the lever rule.

Explanation of the total weight fraction being 100% and how to deduce the amount of liquid from the amount of solid.

Clarification on calculating the weight percent of liquid using the left-hand segment over the total.

The importance of correctly identifying which phase's weight fraction to calculate based on the position on the diagram.

Illustration of how the lever rule applies differently for calculating the right and left-hand segments.

The distinction between calculating mole or atomic fraction versus weight fraction based on the units of the diagram.

Practical application of the lever rule in understanding phase compositions in materials science.

Summary of the lever rule's utility in determining the proportions of different phases in a binary system.

Transcripts

Browse More Related Video

FE Exam Review - FE Mechanical - Material Properties - Phase Diagrams

Uses of phase diagrams

Phases present in the system

Microstructure evolution during solidification in isomorphous systems

Solid-Liquid Phase Diagrams

Proportion of phases present in the system

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Phase DiagramsLever RuleCeramicsOlivine CrystalSolid SolubilityWeight FractionMg2+Fe2+Cooling ProcessMicrostructureMaterial Science