What is the nature of the origin of reciprocal space, please?

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Discussion Overview

The discussion centers on the nature and origin of reciprocal space, particularly in the context of diffraction phenomena and transmission electron microscopy (TEM). Participants explore the physical significance of the origin point in reciprocal space and its relationship to diffraction patterns observed in powder samples and electron diffraction images.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant questions the physical nature of the origin of reciprocal space, suggesting it may relate to diffraction and the behavior of parallel planes.
  • Another participant asserts that reciprocal space is a mathematical construct linked to a plane wave of zero frequency, indicating that the origin corresponds to a situation where the light's direction remains unchanged.
  • A later reply supports the idea that the origin of reciprocal space is associated with diffraction, specifically noting that it aligns with the head of an incident wave vector in Ewald’s sphere.
  • Participants discuss the bright spot observed in electron diffraction patterns, questioning whether it relates to both transmission and diffraction processes.
  • One participant mentions that in TEM, the reciprocal lattice is evident in both diffraction and imaging modes, highlighting the differences in scale between the two types of observations.
  • Another participant emphasizes that in TEM, the electron must be transmitted through the sample to obtain either diffraction or imaging results.

Areas of Agreement / Disagreement

Participants express differing views on the nature of the origin of reciprocal space and its relationship to diffraction. Some suggest it is fundamentally linked to diffraction phenomena, while others emphasize its mathematical aspects. The discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants reference various concepts such as Ewald’s sphere and the reciprocal lattice, but the discussion does not clarify all assumptions or definitions, leaving some aspects open to interpretation.

wangasu
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Hi, all

I got a question about the origin of reciprocal space..what is the physical nature of the special point? Does that originate from diffraction? or Is that a diffraction points? We know that a 'normal' reciprocal point designates a group of parallel plane. How about the origin of reciprocal space?

In a powder diffraction, we observed only ONE origin of reciprocal space from a huge number of small single crystals. By contrast, the other points which correspond to a CERTAIN plane form a sphere surrunding the origin of reciprocal space..Why does all the origin of reciprocal space for all the single crystal in the power sample come into one point? What factors determine the location of the special point? Is that associated with the direction of the incident beam? Thank you.
 
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Your concepts seem a bit convoluted. The reciprocal space is a mathematical construct. There is a connection between its origin and a plane wave of zero frequency (i.e. a constant) In diffraction the incident light can only change its k vector by the value of a point on the reciprocal lattice. If that is the origin, the light's direction doesn't change and it goes straight through. The reciprocal lattice is a set of points from the reciprocal space.
 
Thanks Ox..It sounds that it is true that the origin of reciprocal space comes from diffraction, and the diffraction holds the same direction as the incident light with diffraction vector being zero. So, the origin can be easily located as the head of an incident wave vector in Ewald’s sphere. Here is one more question. In practice, the origin of electron diffraction patterns is always a bright spot, can we say it concerns both transmission and diffraction? Thanks.

0xDEADBEEF said:
Your concepts seem a bit convoluted. The reciprocal space is a mathematical construct. There is a connection between its origin and a plane wave of zero frequency (i.e. a constant) In diffraction the incident light can only change its k vector by the value of a point on the reciprocal lattice. If that is the origin, the light's direction doesn't change and it goes straight through. The reciprocal lattice is a set of points from the reciprocal space.
 
Hi,
reciprocal lattice are often seen in transmission electron microscopy. Just look at the web for the two modes of operation (transmission and diffraction mode)..In fact both are same (both images you get after the electron passes the crystal sample)..but one changes the plane to view whether the DP or Image. In a diffraction pattern (may be you know it- bright dots) the distance between point are given in inverse units (like 1/cm, or 1/nm, etc)...But if you take a image..scale will be like 1 cm=1 nm.
Little bit helps you.
 
Right..an electron diffraction image of TEM is the projection of the crossection between the reciprocal lattice points and Ewald's sphere. it seems that the origin of the electron diffraction image definitely explains both transmission AND diffraction, NOT just transmission..does it make sense?
 
But don't forget..in TEM for getting diffraction or image, the electron is transmitted through sample. THatz why transmission electron microscopy.
 

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