Talk:Electron diffraction

Please, stop vandalizing the article

Lets's be minimalistic. Dear Ldm1954, feel free to continue with personal offenses and humiliations, feel free to improve the article, but please stop vandalizing it. After your edits, there are errors, empty sections, references to removed images, not mentioning the content. Klingm01 (talk) 14:58, 7 February 2023 (UTC)

The prior version would fail any decent TEM class at a strong university. Sorry, but that is reality. It is not "personal offenses", this is scientific rigor.

The current version is adequate, although I would still only give it a B-. I have to go and teach TEM, and will add more references later and further clarifications -- they are needed. Ldm1954 (talk) 16:06, 7 February 2023 (UTC)

Ldm1954, do stop vandalizing the article

Dear Ldm1954, your expertise is most welcome. Instead of using it to disparage others and their contributions, please use it to improve the article. As mentioned before, the article is not necessarily perfect, but this does not mean, you can freely remove its substantial parts without providing better alternative.

Repeated removal of substantial content and claims of incorrect information

Above, you claim the "relativistic form is incorrect" and you say

"While I understand that you want to give people a simple explanation so they can use simple codes, that takes knowledge backwards. The whole theory section must be removed. Electron diffraction is not simple."

You have removed all the formulas claiming they were wrong and too simple. What have you left there instead? Nothing. Your repeated removal of Theory section leaves an impression that there is no theory behind the diffraction. This is what "takes knowledge backwards".

Moreover, you claim the relativistic wavelength formula and/or table to be incorrect. I have just checked the formula in the article and it equals to the one stated in Prof. Kirkland's book (see the references). If there is a mistake, please fix it in the article and inform Prof. Kirkland accordingly. If there is a mistake in the wavelength table, please tell us where. Carter&Williams, Karlík, de Graef - I have just checked their books and they all state exactly the same values you have deleted for being incorrect.

Article structure

The structure of the article had its purpose:

1. History
2. Theory - Non-relativistic, relativistic, material structure (singe/poly-crystal) etc.
3. Applications - TEM (SAED, CBED etc.), SEM, Gases

This structure guided the reader from the History (from the first experiments up to de Brogile), then via the Theory (the reader could read the de Brogie's formula mentioned in the history, see its place in theory, via non-relativistic to the relativistic etc.), showing the impact of material structure on the diffractogram (single- vs. poly-crystal). The the Applications decribed TEM (it's importance from ED point, the beam and image formation, and individual experimental techniquies like SAED or CBED etc.), followed by SEM and gases.

As you know, the strengths and traps of the diffraction imaging originate from the fact, that the image is formed by so many factors at once - if we stay very simple, it's material structure, beam parameters and detectors. Please note here, that the original structure kept those factors separated instead of mixing them all together. This is crucial for understanding the influence of the individual aspects on the resulting diffraction.

Please note also, that the structure allowed the article to be read in whole (with a continuous flow and gradual information develpment) as well as in parts (individual subsections as self-supporting as possible).

After you "rationalized" the structure we have:

1. History
2. Types of electron diffraction

In the giant, unstructured section called Types of electron diffraction, you put together different instrument, phenomena or techniques with no respect to their functional or causal relations. At the same level in one single section, you mix together

• experimental instruments (TEM, SEM, RHEED)
• experimental techniques (CBED, 4D STEM, Precession etc.)
• material structure (singe- vs. poly-crystalline samples)
• general information specific to TEM (formation of image in TEM)
• theory (double diffraction)
• diffractogram features (Kikuchi lines)

This looks as if the Scanning electron microscope shared the category and level with Kikuchi lines. This is extremely confusing. Of course, experts can orient themselves in this chaos, but beginners or cross-disciplinary people will be lost and confused. And this is encyclopedia - it should be readable for a broader audience.

Summary

These are just the major areas of arguments qualifying your activities as vandalism. I am not mentioning particularities like that you should prepare your edits in your sandbox instead of continuously editing the article visited by the readers meanwhile or that the non-realistic wavelength, which is mentioned in all relevant books, is relevant here, it allows to bridge the History and Theory and it's extent is proportional.

Please, do not repeat your vandalizing activity. As mentioned repeatedly, you are welcome to improve the articles. Try to focus on smaller, gradual changes. This does not mean, however, removing each Theory subsection individually (12:23, 7 February 2023‎ and later) instead of removing it at once (19:13, 2 February 2023). It means correcting particular mistakes as you spot them and can prove them. Before more substantial edits, feel free to contact the original authors or discuss them here on the talk page.

Your knowledge is needed, but use it constructively.

Klingm01 (talk) 12:56, 8 February 2023 (UTC)

I will give you a hint, have a look at https://scholar.google.com/citations?user=zmHhI9gAAAAJ

Also, please say hello for me to Marianna, and ask if I will see her at IMC20 in September. Ldm1954 (talk) 16:01, 8 February 2023 (UTC)

I posted this on my talk page, I will repeat it here:

I am afraid that you have misunderstood. The full formulation for the energy and mass is standard and can be found in main sources such as HHPNW & JMC. Scientific rigor says cite the key early papers/books, not later ones. For instance from my class notes (you will find it elsewhere as well):

"The total energy is

Et2 = c2p2 +mo2c4

where mo is the rest mass of the electron, c the speed of light and Et is the sum of the rest energy and the kinetic energy of the electron, i.e.

Et = eE + moc2

The relativistically corrected mass to use is

m = mo + eE/2c2

(this is not the true mass of the electron, which is m0+eE/c2, but instead a value used to eliminate the relativistic terms)."

There is no real reason to go into this in the page, or the original Archie Howie explanation of how to reduce the Klein-Gordon/Dirac to the Schroedinger that is normally used in multislice/Bloch waves. (I intend to add selected refs)

For reference Marc's theory is strong, Earle's is good on multislice although I prefer the original work of Mike O'Keefe. I learnt a lot of my multislice theory from Mike O'Keefe over tea breaks back when my hair was black. Ldm1954 (talk) 15:20, 8 February 2023 (UTC)

Ldm1954 (talk) 15:28, 8 February 2023 (UTC)

You're avoiding the answer because you took on yourself a very difficult task. Showing incorrectness of something which is correct is quite difficult.

You're standing alone against all these heavy weights of electron crystallography: Kirkland, Egerton , Carter&Williams, De Graef... how many names do you need?

References

Let me remind you your own words: "Self criticism is an art not many are qualified to practice", Joyce Carol Oates

Klingm01 (talk) 16:37, 8 February 2023 (UTC)

To repeat, your formulation was incorrect.

The equations in those texts are almost certainly right.

However, the wavelength is not theory, and what was there was very much not kinematical. There is certainly no place in this section for the full Green's function derivation, e.g. http://www.numis.northwestern.edu/460/Notes/kinematical.docx or Hirsch et al. Ldm1954 (talk) 16:45, 8 February 2023 (UTC)

"Also, please say hello for me to..."

...OK so now you're even threatening me with my boss. OK... Klingm01 (talk) 16:46, 8 February 2023 (UTC)

When I said "say hello" that is what I meant.

N.B., my identity is somewhat obvious and I just edited my home page. Ldm1954 (talk) 16:57, 8 February 2023 (UTC)

Ooops! The whole theory section is gone! That was the only place in the whole English Wikipedia that stated it at that level of detail, and I miss it. As far I can say, it was fully correct once contrasted all my available sources. I can't understand Ldm1954 when he says: However, the wavelength is not theory[...] (???) For sure it was theory, and it was only theory since De Broglie to Davisson. And it was non-relativistic at first. Once confirmed, it saw a quick development, of course. I agree with Klingm01's original vision for the article, as it was it was a perfect starting point to everyone interested on such development's history.

And it is a very interesting case in history of physics, one of the few where correct theories aforehead facts. Electromagnetic theory by Maxwell predicted electromagnetic waves produced by Hertz. Mass-energy equivalence theory by Einstein ultimately lead to nuclear power plants and weapons. And we all here know De Broglie anticipated electron microscopy (to be succint). Will you, Ldm1954, mutilate those "dated theories" in the corresponding articles? Then you can delete all Ptolomy related articles as well. Even Kepler's and Newton's formulations are all outdated by today's knowledge. Strip away them all from Wikipedia!

But I'm surprised the most with your notes: The relativistically corrected mass to use is m =m₀ + e_E/2c² (this is not the true mass of the electron, which is m₀+e_E/c², but instead a value used to eliminate the relativistic terms). How you derived this? I assume e_E = m/c² – m₀/c² here, as per E_t = e_E + m₀c², so, Where that "corrected mass" came from? I've never heard on this, although it means nothing, of course, Wikipedia is meant to teach people about things like this, and I want to learn the more. And, How that "corrected mass" influences the wavelength? By using non-relativistic De Broglie, maybe, as that value "elimitate relativistic terms"?

Please, can some editor re-state the whole theory section as it prevously was? And then, may Ldm1954 or whoever extend it with appropriate material to explain about "corrected mass", and how it is used to compute wavelength. Thank you. 37.134.90.176 (talk) 08:43, 13 February 2023 (UTC)

For completeness, the relevant references and explanation are now included. The original Bethe paper in 1928 was non-relativistic, based upon Scroedinger's equation. The paper by Fujiwara in 1961 & the note by Howie in 1962 are the standard references on how relativistic diffraction is converted to non-relativistic using an effective mass -- the form is in the revised page. All of the hundreds of papers on swift electron diffraction use this fact, although it is very rarely mentioned; the Fujiwara paper has been, according to Google Scholar, only cited 176 times. Ldm1954 (talk) 14:33, 15 February 2023 (UTC)

You, Ldm1954, do not state the units for k wavevector. As per "The wavelength of the electrons is 1/k", the reader must to deduce by him/herself k is given in m^–1. Also, you do not say what eE stands for. As it is spelt, it seems it is the product of elementary charge e, which is mentioned (or even the e number as per the exponential function also mentioned) and some energy E, which is quite confusing to the reader.

But eE (or better, E_e here, for "electron energy") comes from the difference of E_t, "total energy", minus E₀, or energy equivalent of the electron rest mass m₀, that is, E₀ = m₀c². So, E_e = E_t – E₀, as per your notes E_t = E_e + m₀c², then E_t = E_e + E₀. Right?

Well. From your notes again, E_t² = c²p² + m₀²c⁴, which is OK (c·p is given in Joules). Then, E_t² = c²p² + E₀². As E₀ and c are constant (as m₀ is), the variable here is p, the kinetic momentum of the electron as a particle of a given mass. The momentum is function of velocity v, so that mass must have been accelerated to attain that velocity. How the electron has been accelerated, in first place?

Of the many ways an electron can be accelerated, De Broglie choose the energy the electron gets when under a given potential V, that is, E = e·V, being here e the elementary charge. This is how an electron gun works, Right? Asuming non-relativistic mechanics, that energy E is the classic kinetic energy, E_k = ½mv², which is a good approximation for low voltages. But assuming relativistic mechanics, it is c·p, so c·p = e·V, and thus E_t² = E₀² + e²V². From here on, the theory follows all what you, Ldm1954, have stripped out.

As you left it, there is no way for the reader to know how to compute 1/k (the wavelength λ, the magnitude we're interested to get) from the applied voltage V. Plus, you're using k as an input value, not the output one.

Conclusion: the former theory section must be re-stated at least as an introductory reasoning. Then, that "effective mass adjusted to cancel out the relativistic terms" can be addresed, if necessary, but in such way k being the resulting, deduced value. 37.134.90.176 (talk) 21:40, 17 February 2023 (UTC)

Thankyou for noting the typo, which is now corrected.

Please read the work by Fujiwara (1961), that of Howie (1962) and also other papers such as the more recent Watanabe et al (1996) cited. All electron diffraction theory start from either the Dirac equation or Schroedinger with the effective mass. They do not start with the work of De Broglie, they start with quantum mechanics. Sorry. Ldm1954 (talk) 23:49, 17 February 2023 (UTC)

Dirac's equation (1928) derived from Schrödinger wavefunctions (1925-1926) for (non-relativistic) both planar waves (leading to Klein–Fock–Gordon equation, 1926) and the hydrogen atom, which in turn extend De Broglie's hypothesis (λ = h/p, 1924) and his hydrogen atom's model (electron as stationary wave with λ_n = 2πna₀, being n the principal quantum number, with n ∈ ℕ), which in turn explain Bohr's hypothesis (1913) of quantized states and angular momentum of the hydrogen atom (L_n = m₀r_nv_n = nh/2π), to be succint. So yes, De Broglie's work IS quantum mechanics, check the years. In fact, the starting point of quantized wave mechanics was De Broglie, not Schrödinger. This is stated in every high school physics' book since then, and elsewhere here in the Wikipedia, of course.

I agree De Broglie himself didn't anticipate electron diffraction (as he didn't anticipate the electron microscope, to say), but the famous Davisson–Germer experiment (1927), the first evidence of the particle-wave duality postulated by De Broglie, was by the discovery that electrons diffract for real, which it is possible only if accelerated electrons behave as De Broglie said. This is the key link.

After your last edit, there are now two flaws:

• By substituting m^eff in the first of the two equations involving E and m^eff (BTW, I would prefer a subscript for m_eff), being here E = e·V Joules and the wavelength λ = 1/k, one reach finally ${\frac {1}{k}}=\lambda ={\frac {hc}{\sqrt {eV(2m_{0}c^{2}+eV)}}}$ (try it by yourself), which is exactly the same conclussion in the former "theory" section, "Relativistic" sub-section, that what you say it is "wrong". It's not (or if yes, yours too).
• You stated that E is typically given in electronvolts (eV), but the shown formulae are for energy in Joules (SI). This only gets the unaware audience more confused.

The main conclusion here is that, essentially, you've vandalized the whole article, as me and others complain about. Your exposition is not superior than previous, so please desist. 37.134.90.176 (talk) 02:32, 18 February 2023 (UTC)

Unfortunately you are still missing the key point. Let me try and explain it differently.

Yes, De Broglie's work was important. Nobody has ever said it was not.

However, it is not central to 21st century understanding of electron diffraction. The key paper is by Bethe (1928), as cited in the article and in articles/textbooks on dynamical diffraction. He starts with the non-relativistic Schroedinger equation, from which by assuming plane wave solutions he derives the basic form of the secular equations for a periodic potential and reciprocal lattice. He even has mean inner potential effects and aspects of the dispersion surface.

The effective mass is how the errors in the Schroedinger equation are handled for elastic scattering. (Inelastic is different.) This is the foundation of all modern methods such as multislice and channeling. The wavelength has some relevance, but is not in fact a constant inside a solid, as we know from band structure -- but this is well, well beyond what is relevant here.

Please read Bethe's paper. Sorry, but this matters. Ldm1954 (talk) 03:45, 18 February 2023 (UTC)

Addendum: I have added back the equation for the wavelength. I don't think it is useful, but Klingm01 thinks it is. It is not an important change. Ldm1954 (talk) 04:17, 18 February 2023 (UTC)

Still far from being satisfactory, specially for introducing the topic to a broader audience and students. It seems you only address those who already know about the subject. The article is not about 21st century understanding of electron diffraction only, you know.

• De Broglie's key formula, $\lambda =h/p$ should be cited, at least, along with his original non-relativistic deduction of the wavelength for electrons accelerating under a potential V, with $E_{K}=e\cdot V$, leading to $\lambda ={\frac {h}{\sqrt {2m_{0}eV}}}$, and noting this is a good approximation only for low voltages, of about 100V or so.
• The general, relativistic formula can be summarized as follow: given in special relativity both:

$E_{t}=m_{0}c^{2}+E$ and $E_{t}={\sqrt {m_{0}^{2}c^{4}+p^{2}c^{2}}}$

for the total energy $E_{t}$ of a single electron, then

$m_{0}c^{2}+E={\sqrt {m_{0}^{2}c^{4}+p^{2}c^{2}}}$.

By squaring, cancelling the resulting $m_{0}^{2}c^{4}$ at both sides and extracting $E$ as common factor at left side,

$E(2m_{0}c^{2}+E)=p^{2}c^{2}$.

As per De Broglie, $\lambda =h/p$, so $p=h/\lambda$. By substituting $p^{2}$ and solving for $\lambda ^{2}$ we get:

$\lambda ^{2}={\frac {h^{2}c^{2}}{E(2m_{0}c^{2}+E)}}$. (1)

With $E=e\cdot V$, electron wavelength is

$\lambda ={\frac {hc}{\sqrt {eV(2m_{0}c^{2}+eV)}}}$.

• The original table of wavelengths by potential, which is fully correct, should be restored.
• Notice: if $E$ is given in electronvolts, then one must use $m_{0}c^{2}\approx 0.511$ MeV, not joules.
• To the wavefunction: continuing from (1), lets introduce a convenient value $k={\frac {1}{\lambda }}$, and extracting $2c^{2}$ as common factor in the divisor:

${\frac {1}{k^{2}}}={\frac {h^{2}}{2E(m_{0}+{\frac {E}{2c^{2}}})}}$.

Lets introduce a new convenient value $m^{*}=m_{0}+{\frac {E}{2c^{2}}}$, sometimes called the electron "effective mass" by some authors [refs here]. Note this value is a shorthand akin to concepts like the reduced mass for solving the two-body problem, or the Lorentz factor in special relativity, not a true physical magnitude.

Then, by substituting with $m^{*}$ and solving for $E$:

$E={\frac {h^{2}k^{2}}{2m^{*}}}$.

And etc., up to $\psi (r)$, showing $k$ is the so-called wavevector.

This way, the full historical path is shown step-by-step, giving the complete picture without too much overload. Then you can discuss diffraction formulae next.

Plus, wavelength IS relevant to understand how accelerated electrons reach the sample where diffraction occurs. If not, there would be no difference as if discussing pure X-rays diffraction here. 37.134.90.176 (talk) 02:22, 23 February 2023 (UTC)

Please check the established literature

To repeat, please read the seminal paper by Bethe (1928) in order to understand more about the foundations. This is the established explanation, and starts from the Schroedinger equation, not the De Broglie relationship. It appeared within months of the experiments. Indeed, if you look at the original experimental papers (cited in the document) you will see that they hedge between using the De Broglie approach, and what was call undulatory mechanics, what we now call quantum mechanics or wave mechanics.

Also, please read up on effective mass using, for instance, Ashcroft and Mermin and semiconductor theory. It is far from what you are suggesting, and has real physics behind it, for instance holes in solid-state physics. It is not close to reduced mass or similar. Strictly speaking it is a tensor $h^{2}/m_{ij}^{*}=d^{2}E(k)/dk_{i}dk_{j}$, but we can simplify to $h^{2}/m^{*}=d^{2}E(k)/dk^{2}$ except in elements of dynamical theory -- but this is a big digression.

Maybe an example will help. We all know about shock waves and sound, also the sound waves in solids which are called phonons. These are collective oscillations of atoms, and can be described as both particles and waves. They have mass, which is not that of individual atoms but an effective mass as mentioned above. Almost every on has an effective mass, for instance plasmons, magnons -- see List_of_quasiparticles. Tricky physics which is beyond the scope of this article IMHO. Ldm1954 (talk) 03:12, 23 February 2023 (UTC)

History Section revised

The 2022 History section had a number of major issues. Parts of it appear to have been copied verbatim from other Wikipedia pages, some major contributions were not mentioned, many of the links were inaccurate or broken.

The current version is based upon searching various sources which are quoted in the article. Whereas the 2022 version had 11 cites, the current one has 63. The current version:

• Has a more general description of electrons in vacuum, with more accurate citations.
• Puts the work of de Broglie and Schroedinger better into context, including a quote on this from de Broglie.
• Provides credit to at least some of the founders of electron optics.
• Provides more extensive cites to the issues about who invented the TEM, which is not straightforward. I have attempted to be unbiased.
• Added the critical paper by Boersch on SAED.
• Added a bit about LEED/RHEED
• Added something about how ED was viewed for many years using a quote from John Cowley,
• Added a bit about advances. I do not think this is the place for more.

N.B., There might be duplicate references. Ldm1954 (talk) 20:53, 18 February 2023 (UTC)

Just a note, the tidbit which in turn is connected to the observations of electrostatic charging by Thales of Miletus around 585 BCE. references this paper which says in its abstract "there is no basis to believe [Thales] discovered, carried out experiments on, or systematically observed electrostatic charging." I haven't read the paper; it just caught my attention as I was skimming the History section. Wanted to make sure it's as intended. Ajpolino (talk) 05:02, 28 February 2023 (UTC)

Ajpolino it's a tricky point, and I deliberately used the word connected rather than discovered. As Daniel Lacks indicates, there is no proof -- but then our records are incomplete. For certain Thales knew of Triboelectricity charging, and the source of electron is the Greek word for amber. There is a Greek stamp with him, charging and amber, and many cites with stronger connections.

Please feel free to wordsmith this is sentence, it is generally accepted color rather than being critical. Ldm1954 (talk) 09:51, 28 February 2023 (UTC)

Unsourced comments added

User:Ldm1954 has made a large number of unsourced edits, the user still doesn’t seem to understand how Wikipedia works. Adding comments here [1] with no sources. Theroadislong (talk) 18:56, 26 February 2023 (UTC)

The statement by Theroadislong is inaccurate. The relevant information is within a sentence or less of every statement that was added. Everything has stated sources.

User:Theroadislong, an apology would be appropriate.

Ldm1954 (talk) 19:16, 26 February 2023 (UTC)

Adding content AFTER a source is not how we do it, if the edit was covered by a previous source then the source should have been repeated. Theroadislong (talk) 21:15, 26 February 2023 (UTC)

User:Theroadislong the source was in the sentence before or the same paragraph, and clearly indicated. Please admit error. Ldm1954 (talk) 21:28, 26 February 2023 (UTC)