just fantastic, Ewald sphere remained elusive in my physics course, until now that you explained it in a couple of minutes! But I think there is 1 mistake: the length of G*hkl vector should be 2pi/dhkl instead of just 1/dhkl, in order for the scattering condition G*T = 2 pi m, where m is integer and T is lattice vector, to hold. Correspondingly the length of CO or any other of those scattering vectors has to be 2 pi / lambda instead of just 1/lambda
Actually there are two different conventions which are used. I am using he convention most commonly used in crystallography text. Here the reciprocal lattice vectors and the wave vectors are defined without the factor 2 Pi. Thus reciprocal basis vector a*=bXc/V, b*=cXa/V, c*=aXb/V and k=1/lambda. Correspondingly, G*_hkl = 1/d_hkl. The other convention is used most commonly in physics texts where the factor 2 Pi is introduced in the reciprocal lattice vectors and the wave vectors. Thus a*= 2 Pi bXc/V, b*= 2 Pi cXa/V, c*= 2 Pi aXb/V and k=2 Pi/lambda. Correspondingly G*_hkl = 2 Pi/d_hk. So physicist's reciprocal lattice vectors, wave vectors and the radius of Ewald sphere are all linearly expanded by 2 Pi in comparison to the corresponding quantities of the crystallographer. However, if a crystallographers reciprocal lattice vector lies on the his/her Ewald sphere then a physicist's reciprocal lattice vector will also lie on his/her Ewald sphere. Thus both will agree whether in a given experimental setting diffraction happens or not.
Thank you sir for this video. Sir can you please share the video lecture related to stereograhic projections of cubic as well as hcp metals. With regards, Deepankar Panda
Dear sir, at 11:41, in step number 2, you mentioned taking the incident wave vector Ki with its head at O. If suppose, the direction of incident beam is along [111] of a Cubic P lattice in real space, how to consider the direction of wave vector Ki in reciprocal space?
This will be a specific application of the general principle explained in the video. In cubic P lattice direct and reciprocal space directions with same indices coincide. So [111] in real space is parallel to [111] in reciprocal space. So k_i vector will be drawn along [111] direction in reciprocal space with its head at the origin of the reciprocal space.
Sir at 7:28 you have chosen the origin as 'O' but the diffracted wave at reciprocal lattice point 'Q' is drawn w.r.t to 'C', why is it so? Sir also plz elaborate the difference b/w point O and C??
Sorry to have missed your comment earlier, so this very delayed response. You might have already found the answer by now, but I am still replying so as to help others who may have similar doubts. The difference between O and C is critical in the construction of Ewald's sphere. O is the origin of the reciprocal lattice. But it is not the centre of the Ewald's sphere. C is the centre of the Ewald's sphere. All wave vectors are drawn from the centre C of the Ewald's sphere. The wave vector CO represents direct beam. Since we are considering elastic scattering, any diffracted beam will have the wave vector CP of the same length as CO and thus P should lie on the Ewald's sphere. Also, by the vector form of Bragg's law the difference between the diffracted wave vector CP and the incident wave vectorCO, i.e. OP=CP-CO should be a reciprocal lattice vector. Thus OP is a reciprocal lattice vector and therefore P is a reciprocal lattice point. We thus conclude that whenever a reciprocal lattice point P lies on the sphere there will be a corresponding diffracted beam whose wave vector will be defined by the vector from the centre C of the sphere (not the origin O of the reciprocal space) to the reciprocal lattice point P , i.e. the vector CP. The planes from which this diffraction happen are defined by the reciprocal lattice vector OP.
Sir what an excellent explanation
No hurry no tension
Peacefully explained
Enjoyed your lecture
Much satisfied with your lecture. Thank you sir 😊
very very good explanation, very easy to follow and with all the concepts explain clearly, thank you very much!
I hated solid state physics at first, you made me fall in love with it.
just fantastic, Ewald sphere remained elusive in my physics course, until now that you explained it in a couple of minutes! But I think there is 1 mistake: the length of G*hkl vector should be 2pi/dhkl instead of just 1/dhkl, in order for the scattering condition G*T = 2 pi m, where m is integer and T is lattice vector, to hold. Correspondingly the length of CO or any other of those scattering vectors has to be 2 pi / lambda instead of just 1/lambda
Actually there are two different conventions which are used. I am using he convention most commonly used in crystallography text. Here the reciprocal lattice vectors and the wave vectors are defined without the factor 2 Pi. Thus reciprocal basis vector a*=bXc/V, b*=cXa/V, c*=aXb/V and k=1/lambda. Correspondingly, G*_hkl = 1/d_hkl. The other convention is used most commonly in physics texts where the factor 2 Pi is introduced in the reciprocal lattice vectors and the wave vectors. Thus a*= 2 Pi bXc/V, b*= 2 Pi cXa/V, c*= 2 Pi aXb/V and k=2 Pi/lambda. Correspondingly G*_hkl = 2 Pi/d_hk. So physicist's reciprocal lattice vectors, wave vectors and the radius of Ewald sphere are all linearly expanded by 2 Pi in comparison to the corresponding quantities of the crystallographer. However, if a crystallographers reciprocal lattice vector lies on the his/her Ewald sphere then a physicist's reciprocal lattice vector will also lie on his/her Ewald sphere. Thus both will agree whether in a given experimental setting diffraction happens or not.
@@rajeshprasadlectures okkay, good
So alternatively we can say that diffraction occurs when one end of incident wave vector touches the bragg plane or the brilluone zone boundary.
Thanku sir so much.... I was struggling alot to understand this topic...
Now I can able to feel this. Thank u sir🥰
Thank you sir for this video. Sir can you please share the video lecture related to stereograhic projections of cubic as well as hcp metals.
With regards,
Deepankar Panda
ua-cam.com/video/uRMMfo74hSg/v-deo.html
@@rajeshprasadlectures thanks a lot sir.
Thanks for the nice lecture. How can we correlate the Ewald's sphere construction with TEM diffraction patterns?
Please see:
ua-cam.com/video/ku2YjCO_8cE/v-deo.html
@@rajeshprasadlectures Awesome video, thank you very much sir!
Thank you!
Dear sir, at 11:41, in step number 2, you mentioned taking the incident wave vector Ki with its head at O. If suppose, the direction of incident beam is along [111] of a Cubic P lattice in real space, how to consider the direction of wave vector Ki in reciprocal space?
This will be a specific application of the general principle explained in the video. In cubic P lattice direct and reciprocal space directions with same indices coincide. So [111] in real space is parallel to [111] in reciprocal space. So k_i vector will be drawn along [111] direction in reciprocal space with its head at the origin of the reciprocal space.
Thank you sir!
Thank you sir
Sir at 7:28 you have chosen the origin as 'O' but the diffracted wave at reciprocal lattice point 'Q' is drawn w.r.t to 'C', why is it so?
Sir also plz elaborate the difference b/w point O and C??
Sorry to have missed your comment earlier, so this very delayed response. You might have already found the answer by now, but I am still replying so as to help others who may have similar doubts.
The difference between O and C is critical in the construction of Ewald's sphere. O is the origin of the reciprocal lattice. But it is not the centre of the Ewald's sphere. C is the centre of the Ewald's sphere.
All wave vectors are drawn from the centre C of the Ewald's sphere. The wave vector CO represents direct beam. Since we are considering elastic scattering, any diffracted beam will have the wave vector CP of the same length as CO and thus P should lie on the Ewald's sphere. Also, by the vector form of Bragg's law the difference between the diffracted wave vector CP and the incident wave vectorCO, i.e. OP=CP-CO should be a reciprocal lattice vector. Thus OP is a reciprocal lattice vector and therefore P is a reciprocal lattice point.
We thus conclude that whenever a reciprocal lattice point P lies on the sphere there will be a corresponding diffracted beam whose wave vector will be defined by the vector from the centre C of the sphere (not the origin O of the reciprocal space) to the reciprocal lattice point P , i.e. the vector CP. The planes from which this diffraction happen are defined by the reciprocal lattice vector OP.
Perfect
Can anyone tell how this type of simple videos can be made ?
For this one I have just used powerpoint.
Nice accent. Just like Einstein
how is it possible to talk so slow? Nearly fell asleep
Thank you sir