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Artemon [7]
2 years ago
5

Consider an infinite lattice with coordination number z in which every site is occupied by a molecule. (As a reminder, the coord

ination number is the number of neighbors each site has). Each molecule can be in one of two states: an 'up' state, and a 'down' state. A system interacts only with adjancet particles that share its state (i.e. ups interact with ups and downs interact with downs). Each interaction of this kind contributes an interaction energy of -epsilon to the system's energy. Using a mean-field approach, compute the following. (a) The fraction of molecules in the up state as a function of reduced temperature kT/(epsilon*z) (b) The mean energy per site as a function of reduced temperature. Here are some hints. In doing this, you will want to use the perturbation (mean field) approach retaining only F0 and F1. To obtain F0, just compute the entropy of the lattice in the absence of interactions. To obtain F1, compute the energy that is then introduced to the system by the attractions, using the configurational probabilities from the reference (noninteracting state). For this second part, you will have to use the idea I introduced in class that in a non-interacting lattice the site probability is just given by a mole fraction. When you determine the fraction of molecules in the up state, the easiest way will be to use the criterion that F is at a minimum at equilibrium, i.e. dF/dX = 0. In this case, you will want to minimize with respect to the fraction of up or down sites. This equation will require some numerical solution near the end. Note also that below some temperature, there should be two solutions to this minimization, in terms of two possible equilibrium values of the mole fraction of up sites (or down sites). This leads to the final part of this problem: (c) Determine the reduced temperature below which two different fractions of 'up' molecules are possible at the same temperature.
Engineering
1 answer:
ratelena [41]2 years ago
4 0
I am just questing to point a ok ok ok this might not be right
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Sever21 [200]

Answer:

a) Solid solution strengthening and alloying,  Precipitation hardening, work hardening

b) Absence of enough  crystallographic misalignment in the grain boundary region for a small-angle

Explanation:

<u>A) strengthening mechanism</u>

i) Solid solution strengthening and alloying:

In solid solution strengthening and alloying mechanism there is an addition of one atom of solute to another during this process, there might be substitution of interstitial point defect in crystal

also the shear stress required can be represented as:  Δz = Gb√Ce^3/2

where : C = solute concentration , e = strain on material

ii) Precipitation hardening:

During precipitation hardening the alloying above the concentrate will lead to the formation of a second phase also under precipitation hardening a second phase can also be created via thermal treatments

particle bowing cab be written as :  Δz = Gb / L-2x

iii) work hardening :

Dislocation caused by stress fields been generated hardens metals under the work hardening mechanism

dislocation can be represented as ; Gb √ p

where : G = shear modulus , b = Burgess vector, p = dislocation density

B) The small angle grain boundaries are not effective enough because there is less crystallographic misalignment in the grain boundary region for a small-angle

3 0
3 years ago
Explain what will happen if the series circuit is closed?
irakobra [83]

Answer:

When the circuit switch is off, no electricity will flow and then the circuit is called an open circuit. Electricity will not flow in open circuit.

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3 years ago
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The raw plastic that will be molded into a brick shape actually
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Answer:

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For the above-cited practical reasons and because it is also an aesthetically pleasing medium, brick has been used as a building material for at least 5,000 years. The first brick was probably made in the Middle East, between the Tigris and Euphrates rivers in what is now Iraq. Lacking the stone their contemporaries in other regions used for permanent structures, early builders here relied on the abundant natural materials to make their sun-baked bricks. These, however, were of limited use because they lacked durability and could not be used outdoors; exposure to the elements caused them to disintegrate. The Babylonians, who later dominated Mesopotamia, were the first to fire bricks, from which many of their tower-temples were constructed.

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Read more: http://www.madehow.com/Volume-1/Brick.html#ixzz6JyObrRwm

Explanation:

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Answer:

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Explanation:

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Explanation:

There are 10 millimeters in a centimeter.

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