Good Vibrations Studying phonons with momentum resolved spectroscopy. D.J. Voneshen 20/6/2018

Transcription

1 Good Vibrations Studying phonons with momentum resolved spectroscopy D.J. Voneshen 20/6/2018

2 Overview What probe to use? Types of instruments. Single crystals example Powder example Thing I didn t talk about because they were tricky.

3 Select your probe. Lets say we want to measure the phonons in Aluminium. We need ~1 mev resolution. We also want information at many wavevectors.

4 Select your probe. Image pinched from: Spec/EMSpec2.html

5 So, x-rays it is. Good news, we can produce lots! Bad news, for 1 Å wavelength the energy is around 10 7 mev. So for 1 mev resolution we wont have many left. Image pinched from: Anything else?

6 Neutrons! Typical energy mev. 1 Å wavelength. Hard to produce, but we wont have to waste many. Image pinched from:

7 Where can we find neutrons? Nuclear reactors Spallation sources

8 Nuclear reactor, now what? Neutrons from reactor have many energies following some profile. Emitted continuously. Profile depends on what bit of the reactor you look at. For spectroscopy, we need to know how much energy was transferred so we need to know incident and final energies. Image pinched from:

9 In diffraction we use a monochromator for Ei.

10 So why not use another!

11 The triple axis spectrometer

12 Spallation, what is different? Most spallation sources are pulsed. So time integrated flux is much lower. But, the pulsed nature gives a big advantage. We can use the neutron Time-Of-Flight (TOF) to determine either Ei or Ef.

13 Chopper spectrometers For phonons we normally use the TOF to give us Ef. To get Ei we use a neutron absorber with a hole cut in it. Detector Sample Chopper By spinning this we get a chopper.

14 Chopper spectrometers For phonons we normally use the TOF to give us Ef. To get Ei we use a neutron absorber with a hole cut in it. By spinning this we get a chopper.

15 A chopper spectrometer

16 A return to x-rays We can do inelastic x-ray scattering. It s basically a TAS. But, instead of varying angles, we vary the temperature of the monochromator!

17 Doing a single crystal measurement

18 Where do we look? We have two options. We could use diffuse scattering to tell us where the signal should be strong. We can think about the phonon scattering cross section. Lets go with the second.

19 One phonon scattering cross section I Q, E = Nħ 2 ν 1 ω Q, ν j b j m j 1 2 Q e j k, ν n ω Q, ν, T + 1 δ E + ħω(q, ν) e iq R jt j Q 2 + n ω Q, ν, T δ E ħω(q, ν).

20 One phonon scattering cross section I Q, E = Nħ 2 ν 1 ω Q, ν j b j m j 1 2 Q e j k, ν n ω Q, ν, T + 1 δ E + ħω(q, ν) e iq R jt j Q 2 + n ω Q, ν, T δ E ħω(q, ν). We know this bit, its just the normal elastic scattering equation.

21 One phonon scattering cross section I Q, E = Nħ 2 ν 1 ω Q, ν j b j m j 1 2 Q e j k, ν n ω Q, ν, T + 1 δ E + ħω(q, ν) e iq R jt j Q 2 + n ω Q, ν, T δ E ħω(q, ν). This looks horrible, but its just telling us that we have more phonons at high temperatures (they follow Bose-Einstein statistics).

22 One phonon scattering cross section I Q, E = Nħ 2 ν 1 ω Q, ν j b j m j 1 2 Q e j k, ν n ω Q, ν, T + 1 δ E + ħω(q, ν) e iq R jt j Q 2 + n ω Q, ν, T δ E ħω(q, ν). Phonons at higher energy are weaker.

23 One phonon scattering cross section I Q, E = Nħ 2 ν 1 ω Q, ν j b j m j 1 2 Q e j k, ν n ω Q, ν, T + 1 δ E + ħω(q, ν) e iq R jt j Q 2 + n ω Q, ν, T δ E ħω(q, ν). This is the only complicated bit. e is the phonon eigenvector, physically, you can think of this as the direction atoms are moving in.

24 Things to remember Phonons are strong when Q is parallel to direction of atomic motion. Phonon intensity goes up with Q 2. Phonons are weaker at high energy. Strong Bragg reflections often have strong phonons around them. Phonons can be stronger at high temperature (but care needed here).

25 Measuring a longitudinal acoustic phonon We want to measure a longitudinal phonon along 00L. Which peak would be best to measure around?

26 Measuring a longitudinal acoustic phonon We want to measure a longitudinal phonon along 00L. Q Which peak would be best to measure around?

27 Measuring a transverse acoustic phonon What about a transverse phonon?

28 Measuring a transverse acoustic phonon Q What about a transverse phonon?

29 Exploiting Q e, an example We were looking for a phonon around 12 mev. However, the background from the cryostat/mount was huge. Rotate sample 90. Suppresses, phonon but background unchanged

30 Exploiting Q e, an example We were looking for a phonon around 12 mev. However, the background from the cryostat/mount was huge. Rotate sample 90. Suppresses phonon but background unchanged

31 TOF, what do we get? With TOF we get an excellent survey. However, we are normally struggling for statistics. Data here was at 300 K counted for two days. Need at least 1 cm 3 single crystal.

32 Comparison to DFT

33 A quick example of this with IXS and We were interested in Na 0.8 CoO 2 as a thermoelectric. INS We wanted to show that the Na vacancy order has a big impact on the phonons. We also wanted to relate this to the thermal conductivity.

34 A quick example of this with IXS and We were interested in Na 0.8 CoO 2 as a thermoelectric. INS We wanted to show that the Na vacancy order has a big impact on the phonons. We also wanted to relate this to the thermal conductivity. Voneshen, D.J. et al. Nature Mater. 12, 1028 (2013).

35 A quick example of this with IXS and We were interested in Na 0.8 CoO 2 as a thermoelectric. INS We wanted to show that the Na vacancy order has a big impact on the phonons. We also wanted to relate this to the thermal conductivity. Voneshen, D.J. et al. Nature Mater. 12, 1028 (2013).

36 A quick example of this with IXS and We were interested in Na 0.8 CoO 2 as a thermoelectric. INS We wanted to show that the Na vacancy order has a big impact on the phonons. We also wanted to relate this to the thermal conductivity. Voneshen, D.J. et al. Nature Mater. 12, 1028 (2013).

37 A quick example of this with IXS and We were interested in Na 0.8 CoO 2 as a thermoelectric. INS We wanted to show that the Na vacancy order has a big impact on the phonons. We also wanted to relate this to the thermal conductivity. Voneshen, D.J. et al. Nature Mater. 12, 1028 (2013).

38 Powders! Good news, powders are simpler! Much simpler. With them we can extract the neutron weighted phonon density of states. But, going beyond that is hard.

39 Powders, what are we doing? We are averaging over a sphere at some Q. So, for small values of Q we are covering just a few (or even 1) Brillouin zones. But, for large Q we are covering many zones, essentially capturing everything in 1 shot. This means for high Q we can no longer see the effect of Q e and the signal is the same as incoherent scattering.

40 Powders, what are we doing? We are averaging over a sphere at some Q. So, for small values of Q we are covering just a few (or even 1) Brillouin zones. But, for large Q we are covering many zones, essentially capturing everything in 1 shot. This means for high Q we can no longer see the effect of Q e and the signal is the same as incoherent scattering.

41 The neutron weighted phonon density of states PDOS neut E = A j b j 2 m j PDOS j E, We normally correct the data for the effects of Bose statistics, 1 ω and Q 2. Then, in the incoherent approximation, the real Phonon Density of States (PDOS) is related to the PDOS we see via the above. This means we cannot obtain the true PDOS for anything other than a monoatomic system.

42 A quick powder example Another thermoelectric. This time, the idea was that superionic diffusion would dramatically change the phonons, leading to a very low thermal conductivity. It doesn t. Instead the low thermal conductivity is caused by regular anharmonic effects.

43 A quick powder example Another thermoelectric. This time, the idea was that superionic diffusion would dramatically change the phonons, leading to a very low thermal conductivity. It doesn t. Instead the low thermal conductivity is caused by regular anharmonic effects.

44 A quick powder example Another thermoelectric. This time, the idea was that superionic diffusion would dramatically change the phonons, leading to a very low thermal conductivity. It doesn t. Instead the low thermal conductivity is caused by regular anharmonic effects.

45 A quick powder example Another thermoelectric. This time, the idea was that superionic diffusion would dramatically change the phonons, leading to a very low thermal conductivity. It doesn t. Instead the low thermal conductivity is caused by regular anharmonic effects. Phys. Rev. Lett. 118,

46 The thing I was scared to talk about Measuring phonon dispersions from time resolved diffuse scattering. Still very early, but really cool. Nature Communications, 7, (2016)

47 The thing I was scared to talk about Measuring phonon dispersions from time resolved diffuse scattering. Still very early, but really cool. Nature Communications, 7, (2016)

48 Summary Momentum resolved spectroscopy is great! We have options, TOF for surveys, TAS for focussed studies and x-rays for tiny samples. Remember that the intensity of phonons depends on Q e 2. If you have questions, me! David.voneshen@stfc.ac.uk