Crystal Interfaces This animation is about the various kinds of interfaces between boundaries of...

Crystal Interfaces

This animation is about the various kinds of interfaces between boundaries of solid substances, that occur when two different orientations (in most cases two different types of substances) are brought in contact with each other.

Course Name: Phase Transformations

Author Name: Sharth Mandan,

10d110004,

Undergraduate Dual Degree Student,

MEMS Department.

Mentor Name: Prof. M. P. Gururajan

MEMS Department

Learning Objectives To explain the meanings of Coherent, Semi Coherent and

Incoherent Interfaces. To explain the concept of Coherency Strains. To explain the formation of dislocations that occur in the

semi-incoherent interface and also to explain their properties.

Here show the slides number 1 and 2 as they are shown.

For slide 1, no audio narration. For slide 2, audio same as text.

Definitions:

• Interface: The boundary between two adjoining crystals having different or same crystal structure.

• Interface Coherence: When the two crystals match perfectly at the interface plane so that the lattices plane are continuous across the interface, then a coherent interface is said to be formed.

• Coherency Strains: When there is a slight mismatch in the inter-atomic distances of two adjoining crystals, the coherent interface can occur resulting in lattice distortions known as coherency strains.

• Semi-Coherent Interface: When difference in inter-atomic distances in the two crystals becomes relatively large, more than 5%, then semi-coherent interface is formed in which the misfit is periodically countered by dislocations (generally, edge dislocations).

• Interfacial Energy: The energy of atoms in the bulk is less as it is surrounded by the neighbouring same atoms. But at the interface, each atom is partly bonded to other atoms. This increases the energy of the interfacial atoms and this increase is known as interfacial energy.

• Incoherent Interface: When two randomly oriented crystals are joined across any interfacial plane such that they either have completely different pattern of atoms in both phases or their inter-atomic distances differ by more than 25%, then the interface formed is known as incoherent interface.

Coherent Interfaces

• When the crystals of the two adjoining atoms are such that the inter-atomic distances between them is very small(less than 1-2%) and also their lattices are such that the adjoining planes are parallel, then the interface formed is known as coherent interface.

• In this type of interface, the planes and directions in which the crystals are joined to each other should be parallel to each other.

• For this type of interface the increase in interfacial energy is equal to the coherent interfacial energy which is usually up to about 200 mJ m-2.

ϒ(coherent)=ϒch

Theory Part

• Example:

1.) HCP packed Si and Ge with a diamond cubic crystal structure, form a interface which is coherent in nature. The atomic structures of both the elements are such that the interface formed is coherent without any strains 2.) The interfacial boundaries of Ga and Al in GaAs and AlAs structures also form coherent interfaces. • Coherency Strains:When the interatomic distances is slightly non-identical between the two crystals at the interface (between 2-3%), coherency is maintained by straining one or both of the lattices. The distortions caused in the lattice are known as coherency strains.

Theory Part

Semi-coherent Interfaces

• As the strains in the coherent interface increase the total energy of the system, it becomes energetically more favourable, for large atomic misfit in inter-atomic distance or sizes, to replace the coherent interface with semi-coherent in which the misfit is periodically compensated by dislocations.

• It occurs when the difference in sizes of the atoms of both crystals is in between 3% to 25%. Also, the planes and directions in which the crystals are joined to each other should be parallel to each other.

• In the term for interfacial energy, apart from the increase in energy of atoms, a term for the increase in energy because of distortions is also added.ϒ(semi-coherent)=ϒch + ϒst

• The energies of semi-coherent interfaces is normally in range of 200-500 mJ m-2.

Theory Part

Example:The formation of steel takes place by the semi-coherent interface forming. The interface between iron-nickel or iron-chromium in steel is semi-coherent interface.

Also, edge dislocation is the most common type of dislocation occurring in the semi-coherent interface. Image 4:

Semi Coherent Interface and Dislocations in it

Let the inter-atomic distance in one crystal be dα and that in other crystal

on other side of plane is dβ. Then the misfit is between two lattices (Δ) is defined by,

Δ= dβ -dα

dα In one dimension, this misfit can be accommodated by a set of edge dislocations with a spacing D between them, given by,

D= dβ Δ

Theory Part

Incoherent Interfaces

• When the atomic configuration on both sides of the interface is different and pattern of atoms arranged is very different or the inter-atomic distance is more than 25%, the interface formed is incoherent interface.

• Incoherent interface arises because of joining two randomly oriented crystals. The features of incoherent interfaces are very much similar to high end grain boundaries

• The energy of incoherent interface is in range of 500 to 1000 mJ m-2. Also the atomic structure at the interface is highly disordered and they also possess step-like structure caused by low-index planes protruding into the interface.

Theory Part

Step 1: Coherence interface.

• Difference in atomic sizes is less than 2%

• The planes are parallel in direction

Description of action Audio narration Text to be displayed

First bring in the orange circles on the left of the arrow. Then the green circles. Then show the arrow and then bring in the image on the right side of the arrow.

{ Dimensions for Figure:Radius of the circles: about 0.5 cm each, with lines joining each circle of length 0.2 cm each}

Also show the bullet points one by one after the image is displayed on the screen.

When the crystals of the two adjoining atoms are such that the inter-atomic distances between them is very small and also their lattices are such that the adjoining planes are parallel, then the interface formed is known as coherent interface. For this type of interface the increase in interfacial energy is equal to the coherent interfacial energy which is usually up to about 200 mJ m-2. ϒ(coherent)=ϒch

When the crystals of the two adjoining atoms are such that the inter-atomic distances between them is very small (less than 1-2%) and also their lattices are such that the adjoining planes are parallel, then the interface formed is known as coherent interface. In this type of interface, the planes and directions in which the crystals are joined to each other should be parallel to each other.For this type of interface the increase in interfacial energy is equal to the coherent interfacial energy which is usually up to about 200 mJ m-2. ϒ(coherent)=ϒch

Step 2: Examples of coherent interface:

• HCP packed Si shown in blue color.

• Diamond- Packed Ge shown in green color.

• The coherency exists because of the suitable plane directions without any strains


Show the image when the audio narration No.1 is running. But for the audio narration No.2, show only the text on the screen

Also show the bullet points one by one after the image is displayed on the screen for audio narration No. 1.

Dimensions for figure:Radius of the circles: about

0.5 cm each for bigger circles and 0.3 cm each for smaller, with lines joining each circle of length 0.2

cm each, angle inclination of blue circles is 45° from normal. colors same as

given.

No.1: HCP packed Si and Ge with a diamond cubic crystal structure, form a interface which is coherent in nature. The atomic structures of both the elements are such that the interface formed is coherent without any strains

No.2The interfacial boundaries of Ga and Al in GaAs and AlAs structures also form coherent interfaces.

No.1: HCP packed Si and Ge with a diamond cubic crystal structure, form a interface which is coherent in nature. The atomic structures of both the elements are such that the interface formed is coherent without any strains

No.2The interfacial boundaries of Ga and Al in GaAs and AlAs structures also form coherent interfaces.

Step 3: coherency strains


First show the left most image. Then by animation, show as if the first image turns into the second image by straining of atoms. After that, show the third image in same way after straining the third image.

Dimensions:Radius of the circles: about 0.5 cm each, with lines joining each circle of length 0.2 cm each. Distance of each column of green circles from

other column is 0.2 cm in figure on left. Distance of each column of blue circles from other column is 0.15 cm in figure on left. In

figure on the right, the upper green and lower blue circles of all the rows should be in same vertical line while the lower green and upper blue circles of the rows should be kept same

as before. So the other circles in between should be aligned as needed so that above

purpose is achieved.

When the interatomic distances is slightly non-identical between the two crystals at the interface (between 2-5%), coherency is maintained by straining one or both of the lattices. The distortions caused in the lattice are known as coherency strains.

When the interatomic distances is slightly non-identical between the two crystals at the interface (between 2-5%), coherency is maintained by straining one or both of the lattices. The distortions caused in the lattice are known as coherency strains.

Step 4: Semi-coherent Interface

• Difference in atomic sizes is between 3 to 25%

• There is energy increase of the atoms due to the strains that are developed because of the semi-coherent interface.


First show the brown part on the left side of the arrow. Then show the green circles. Then by animation, make the green circles move towards brown such that image on right side is formed.


0.5 cm each for green circles and 0.45 cm each

for blue, with lines joining each circle of length 0.2 cm each. colors same as given.


As the strains in the coherent interface increase the total energy of the system, it becomes energetically more favourable to replace the coherent interface with semi-coherent in which the misfit is periodically compensated by dislocations. It occurs when the difference in sizes of the atoms of both crystals is in between 3% to 25. Apart from the increase in energy of atoms, a term for the increase in energy because of distortions is also added.

As the strains in the coherent interface increase the total energy of the system, it becomes energetically more favourable to replace the coherent interface with semi-coherent in which the misfit is periodically compensated by dislocations. It occurs when the difference in sizes of the atoms of both crystals is in between 3% to 25%. Apart from the increase in energy of atoms, a term for the increase in energy because of distortions is also added. ϒ(semi-coherent)=ϒch + ϒst The energies of semi-coherent interfaces is normally in range of 200-500 mJ m-2.

Description of action Audio narration Text to be displayedDescription of action Audio narration Text to be displayed

Show the above on the screen with each bullet point appearing on screen after a gap o1 second after the previous one. Also keep the second and fourth bullet points blinking all the time.

Same as above text.

Step 5: dislocations in Semi-coherent Interface

• Let the inter-atomic distance in one crystal be dα and that in other crystal on other side of plane is dβ. Then the misfit is between two lattices (Δ) is defined by,

• Δ= dβ -dα dα

• In one dimension, this misfit can be accommodated by a set of edge dislocations with a spacing D between them, given by,

• D= dβ Δ

Step 6: Examples of Semi-coherent Interface


During the audio of point 1), don’t show any image on screen. Just the text for it should be displayed. During the audio for point 2), show the above image on the screen with the text in the image blinking.


0.45 cm each for green circles and 0.5 cm each for blue, with

lines joining each circle of length 0.2 cm each. Angle of line joining blue and green

circles should be accordingly tilted. colors same as given.

1)The formation of steel takes place by the semi-coherent interface forming. The interface between iron-nickel or iron-chromium in steel is semi-coherent interface. 2)Also, edge dislocation is the most common type of dislocation occurring in the semi-coherent interface

1)The formation of steel takes place by the semi-coherent interface forming. The interface between iron-nickel or iron-chromium in steel is semi-coherent interface. 2) Also, edge dislocation is the most common type of dislocation occurring in the semi-coherent interface

Step 7: Incoherent Interface

• Difference in atomic sizes is more than 25%

• It is similar to high end grain boundaries.


Show the above image as it is on the screen


0.5 cm each for green circles and 0.3 cm each for

blue, with lines joining each circle of length 0.2

cm each, angle inclination of blue circles is 45° from normal. colors same as

given.


When pattern of atoms arranged is very different or the inter-atomic distance is more than 25%, the interface formed is incoherent interface. Incoherent interface arises because of joining two randomly oriented crystals. The features of incoherent interfaces are very much similar to high end grain boundaries The energy of incoherent interface is in range of 500 to 1000 mJ m-2. Example: the interface in silicates particles is incoherent interface.

When pattern of atoms arranged is very different or the inter-atomic distance is more than 25%, the interface formed is incoherent interface. Incoherent interface arises because of joining two randomly oriented crystals. The features of incoherent interfaces are very much similar to high end grain boundaries The energy of incoherent interface is in range of 500 to 1000 mJ m-2. Example: the interface in silicates particles is incoherent interface.

Animation 1: Change dβ or dα and get the distance between the nearest two set of edge dislocations!!!

dα

dβ

Dimensions( only for the animation maker):Radius of the circles: about dβ cm each for green circles and dα cm each for blue, with lines joining each circle of length 0.2 cm each.

Angle of line joining green and blue circles should be tilted accordingly in animation. colors same as given.


When user presses next tab, Show 3 rulers on the screen. One for value of dα , other for dβ and third showing value of D. The scale of the ruler should be ranging from 100pm to 500pm. (Here pm=Pico Meter) [Note: in drawing diagram on screen, take 10 pm= 0.05 centimeter and draw accordingly]Now the user should be allowed to vary the values of dα and dβ. Accordingly, the value of D should be displayed on scale after calculating the value according to the following formulas: Δ= dβ -dα

dα

and, D= dβ Δ Show this value of ‘D’ on the third scale.

Also, |dα -dβ|, i.e. the difference between interatomic distances in both planes should be in between 5% to 25%. If it’s out of range, then adjacent audio should be played.

Select the sizes of dα and dβ on the scale. U will get the corresponding distance ‘D’ between the dislocations on the other scale.

If the value of |dα -dβ|is out of range, the AUDIO should be: For given dα and dβ , it does not form semi-coherent interface!!!

Change dα and dβ and see what happens..

If the value of |dα -dβ|is out of range, the TEXT should be should be: For given dα and dβ , it does not form semi-coherent interface!!!

Animation- 2: Choose the interatomic distance and the type of crystal structure. U will get the interface between both the crystals. (only for simple interfaces not involving the coherent interface between FCC and HCP.)

FCC BCC HCP

dα

dβ

Type of crystal 1: FCC BCC HCP

Type of crystal 2: FCC BCC HCP

Image 1

Image 2

Image 3


Show 2 rulers on the screen with the scale as shown in previous animation. Also show the rulers under different headlines, one for dα and other for dβ. [ the ruler dimensions and conversions as before]Now under each head line, also make a “choose one from list type of radio buttons” with three options: - FCC - BCC - HCP

Now, there are following conditions to be applied to show the results: -If the difference between the values of dα and dβ is less than 5% and the chosen radio buttons are of same options, i.e., either both are FCC or BCC or HCP, then display the image 1 on the right. If the chosen values are not same, then if the values are FCC and BCC or vice versa, then also show image 1.

Select the values of dα and dβ . Also select the crystal structures.

-Audio for image 1: The result is coherent interface.

- Audio for image 2: The result is semi-coherent

- Audio for image 3: The result is incoherent

Select options see what you get.

We are considering simple examples and so example of FCC crystal forming interface with HCP crystal for coherent interface is ignored.

If the difference between the values of dα and dβ is between 5% and 25% and the chosen radio buttons are of same options, i.e., either both are FCC or BCC or HCP, then display the image 2 on the right. If the chosen values are not same, then if the values are FCC and BCC or vice versa, then also show image 2. If the difference between the values of dα and dβ is more than 25%, then show the image 3. Also if chosen values are FCC and HCP or BCC and HCP, then also show image 3.

Table continued…

Questions:

Something to think upon!!!!

1) What is the relation between the Gibbs free energy and the interfaces formed between two surfaces?{Hint: The interfaces formed between the surfaces depend on the bulk energy and the interfacial energy.}

2) Which of following can form semi-coherent interface? A) High angle grain boundary B) Low angle grain boundary C) Both of the above

3)Which of the following planes form the coherent interface?(Multiple answers may be correct)

A) {110}bcc and {111}fcc B) <001>bcc and <101>fccC) {110}bcc and {111}fcc D) <111>bcc and <101>fcc

4) In the semi-coherent interface, if δ is small, then the formula for D becomes “ D=b “. What is “b” here? δA) b=dα + dβ B) b=dα – dβ

C) b=(dα + dβ)/2 D) b=(dα -dβ)/2

Summary:

When an interface forms between two surfaces, it can be of three types: -- Coherent Interface-- Semi-coherent Interface-- Incoherent Interface

Of all the interfaces, the most important interface is the coherent interface which is seen in several metal alloys and also in the semi-conductors.

The interfacial energy forms a very important role in formation of interfaces.

Additional references:

1) Interfaces in Materials (1997), James M. Howe, Wiley Interscience.2) Phase transformations in metals and alloys by David A. Porter.

Crystal Interfaces This animation is about the various kinds of interfaces between boundaries of...

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