
(a)
Interpretation:
The composition of the solid phase and the liquid phase in wt% and at% are to be calculated for
Concept Introduction:
On the temperature-composition graph of analloy, the curve above which the alloy exist in the liquid phase is the liquidus curve. The temperature at this curve is the maximum temperature at which the crystals in the alloy can coexist with its melt in the
Solidus curve is the locus of the temperature on the temperature composition graph of analloy, beyond which the alloy is completely in solid phase.
Between the solidus and liquidus curve, the alloy exits in a slurry form in which there is both crystals as well as alloy melt.
Solidus temperature is always less than or equal to the liquidus temperature.
The formula to calculate the at% from the wt% for an alloy containing phases
Here,

Answer to Problem 10.54P
Composition of the liquid phase in at% is
Composition of the liquid phase in wt% is
Composition of the solid phase in at% is
Composition of the solid phase in wt% is
Explanation of Solution
The phase diagram for Nb-W alloy is given as:
Now, draw a straight line from temperature
Here, point 'a' represents
Molecular weight of Nb and W are
Use equation (1) to convert wt% to at% for liquid phase as:
Again, use equation (1) to convert wt% to at% for solid phase as:
(b)
Interpretation:
The amount of each phase present in
Concept Introduction:
A matter can exist in different physical forms such as sold, liquid, gas, and plasma. These distinct physical forms are known as a Phase.
A phase has uniform physical and chemical properties and is bounded by a surface due to which two phases can be
The formula to calculate the wt% from the at% for an alloy containing phases
Here,
Amount of each phase in wt% is calculated using lever rule. At a particular temperature and alloy composition, a tie line is drawn on the phase diagram of the alloy between the solidus and liquidus curve. Then the portion of the lever opposite to the phase whose amount is to be calculated is considered in the formula used as:

Answer to Problem 10.54P
Amount of liquid phase in at% is
Amount of liquid phase in wt% is
Amount of solid phase in at% is
Amount of solid phase in wt% is
Explanation of Solution
The phase diagram for Nb-W alloy is given as:
Now, draw a straight line from temperature
Here, point 'a' represents
To calculate amount of liquid phase, lever 'ac' will be used and to calculate amount of solid phase, lever 'ba' will be used. Use equation (3) to calculate the amount of each phase as:
To calculate the amount of liquid and solid phases in at%, first convert the original wt% of W in at% using equation (1) and molecular weights of Nb and W as:
To apply the lever rule, use the corresponding at% for the liquid and solid phases as calculated in part (a) as:
Apply lever rule as:
(c)
Interpretation:
The amount of each phase is to be calculated in vol%.
Concept Introduction:
The formula to convert wt% to vol% using density

Answer to Problem 10.54P
The amount of liquid phase in Vol% is
The amount of solid phase in Vol% is
Explanation of Solution
Given information:
An alloy containing
From part (b), the amount of liquid and solid phases in wt% is calculated as:
Use equation (4) along with the given densities of the phases to calculate the vol% as:
Want to see more full solutions like this?
Chapter 10 Solutions
Essentials of Materials Science and Engineering, SI Edition
- 1- Which TCP/IP protocol is used to convert the IP address to the Mac address? Explain 2-What popular switch feature allows you to create communication boundaries between systems connected to the switch3- what types of vulnerability directly related to the programmer of the software? 4- Who ensures the entity implements appropriate security controls to protect an asset? please do not use AI of any kind. please refrencearrow_forwardthe diagram show 4 motor connected to a k-35 controller. I would like detail explanation to know how the circuit work. Is the controller compatible with the motor? The motor shown is series, parallel or both?arrow_forwardplease draw logic diagram pleasearrow_forward
- Please draw the diagrams please thank youarrow_forwardmatlabarrow_forwardUsing Keras3 Create a Neural Network model with at least two hidden layers. Also, Add a drop out layer after each hidden layer to regularize the neural network model. Use tfruns package to tune your hyper-parameters including the drop out factors. Display the table returned by trfuns.arrow_forward
- Assume a car park facility where the arrival rate is λ customer every minute, and the service process including pressing the button, taking the card, and waiting for the boom to rise leads to service rate of μ customer every minute. a. Assume the arrival and service processes are stochastic. Using any software (Excel, Matlab, or the one you prefer), plot average delay time (including service time) and average queue size (including the vehicle currently being served) for all combinations of λ = {1,2,3,..,10} and p = {0.1,0.3,0.5,0.7,0.9}. Specifically, we ask you to make 2 graphs (one for average delay and the other for average queue size), where the x-axes contains the different values for 1, and where you make one curve for each p. b. Assume the arrival process is stochastic but the service process is deterministic with rate µ. Using any software (Excel, Matlab, or the one you prefer), plot average delay time (including service time) and average queue size (including the vehicle…arrow_forwardA plane wave propagating through a medium with &,,-8 μr = 2 has: E = 0.5 e-j0.33z sin (108 t - ẞz) ax V/m. Determine (a) ẞ (b) The loss tangent (c) Wave impedance (d) Wave velocity (e) H fieldarrow_forwardConsider, M people (aka pax) who want to travel by car from O to D. They all start working at D at Q (e.g., Q-8am). If a person departs at time t, assume the time needed to go from O to D is given by c(t)=A+Bx(t), where x(t) is the flow of people departing at time t [car/unit of time]. In addition, a is the penalty for being early at work (E(t) is how early the person arrived when departing at time t), and ẞ is the penalty for being late at work (L(t) is how late the person arrived when departing at time t). Assume 0 < a < 1 < ß. Further assume the departure time choice problem under the equilibrium conditions. Prove that the arrival time of people who depart when most of the M people start their trips is equal to Q.arrow_forward
- Find the voltage V0 across the 4K resistor using the mesh method or nodal analysis. Note: I have already simulated it and the value it should give is -1.714Varrow_forwardI want to explain my work in Python botnets and it is completely working on the tkinter function with an explanation of how I can work on it with an introduction about what it is and what its benefit isarrow_forward2) The phase voltage at the terminals of a balanced three-phase Y-connected load is 2400 V. The load has an impedance of 16+j12 2/6 and is fed from a line having an impedance of 0.10+j0.80 2/6. The Y- connected source at the sending end of the line has a positive phase sequence and an internal impedance of 0.02+j0.16 2/6. Use the a-phase voltage at the load as the reference. a) Construct the a-phase equivalent circuit of the system b) Calculate the line currents IaA, IbB, and Icc c) Calculate the phase voltages at the terminals of the source, Van, Vbn, Vcn- d) Calculate the line voltages at the source, Vab, Vbc and Vca. e) Calculate the internal phase-to-neutral voltages at the source, Va'n, Vb'n, Ve'n,arrow_forward
- MATLAB: An Introduction with ApplicationsEngineeringISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncEssentials Of Materials Science And EngineeringEngineeringISBN:9781337385497Author:WRIGHT, Wendelin J.Publisher:Cengage,Industrial Motor ControlEngineeringISBN:9781133691808Author:Stephen HermanPublisher:Cengage Learning
- Basics Of Engineering EconomyEngineeringISBN:9780073376356Author:Leland Blank, Anthony TarquinPublisher:MCGRAW-HILL HIGHER EDUCATIONStructural Steel Design (6th Edition)EngineeringISBN:9780134589657Author:Jack C. McCormac, Stephen F. CsernakPublisher:PEARSONFundamentals of Materials Science and Engineering...EngineeringISBN:9781119175483Author:William D. Callister Jr., David G. RethwischPublisher:WILEY





