What is 10¹⁰ times smaller than us?

Jingxuan Ding

Harvard, SEAS

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Long table physics journal club

09/23/2023

Probing atomic motions through neutron/x-ray scattering

A regular dog ~ 1 m

A dog vs an atom

A regular dog ~ 1 m

10¹⁰ time smaller ~ 0.1 nm or 1 Å

A dog vs an atom

An atom

A regular dog ~ 1 m

10¹⁰ time smaller ~ 0.1 nm or 1 Å

A dog vs an atom

What are they doing?

An atom

Outline

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• How to describe the motion of atoms?
• Small solid-state physics lecture

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• How do we probe them experimentally?
• Neutron/x-ray scattering principles
• Virtual tour to facilities

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• Why are they important?
• Application in emergent energy materials

Motion of atoms

Q: Are the motion of a group of atoms in a periodic crystal lattice random?

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A: No! They are determined by the forces that atoms exert on each other.

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The subject of lattice dynamics is to formally describe such motions

1D monoatomic chain model

Dove, Introduction to lattice dynamics. Vol. 4, P. 18-21, Cambridge university press, 1993.

Harmonic approximation

Dove, Introduction to lattice dynamics. Vol. 4, P. 18-21, Cambridge university press, 1993.

Force constant (FC)

1D monoatomic chain model

Harmonic approximation

1D monoatomic chain model

Dispersion relations

Dove, Introduction to lattice dynamics. Vol. 4, P. 86-88, Cambridge university press, 1993.

Lattice dynamics (3D)

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Si crystal structure

Dove, Introduction to lattice dynamics. Vol. 4, P. 86-88, Cambridge university press, 1993.

Lattice dynamics (3D)

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Si crystal structure

Si phonon dispersion

TA

LA

TO

LO

0 0.1 0.2

DOS (1/THz)

(0,0,0) (0.5,0,0.5) (0.75,0.5,0.75) (0.5,0.5,0.5)

Phonons in crystal

Phonons are quantized normal-modes of vibration of a (harmonic) crystal:

TA

LA

TO

LO

0 0.1 0.2

DOS (1/THz)

(0,0,0) (0.5,0,0.5) (0.75,0.5,0.75) (0.5,0.5,0.5)

Phonons are quantized normal-modes of vibration of a (harmonic) crystal:

TA(X)

Phonons in crystal

A little anharmonicity

Energy

Interatomic distance

Harmonic

Add 3^rd order term

r

r₁

r₂

Thermal expansion

• Anharmonicity is important to explain many phenomena

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• Thermal expansion, thermal conductivity, phase transition …

Motion of atom 2 – ionic diffusion

He, X., Zhu, Y., & Mo, Y. 8(1), 15893 (2017).

Take away

Phonon: collective vibrations, periodic,

and time correlated

Ionic diffusion: stochastic, long-range, decaying correlation in time

Outline

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• How to describe the motion of atoms?
• Small solid-state physics lecture

​

• How do we probe them experimentally?
• Neutron/x-ray scattering principles
• Virtual tour to facilities

​

• Why are they important?
• Application in emergent energy materials

Why can we use neutron/x-ray as probes?

Advantages and disadvantages

Inelastic scattering

— what are the atoms doing

Elastic scattering (diffraction)

— where the atoms are

Squires, Introduction to the theory of thermal neutron scattering. Cambridge university press, P. 60-65, 2012.

http://www.oxfordneutronschool.org/2013/Lectures/GarciaSakai-QENS.pdf

Neutron/x-ray scattering

Energy transfer

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http://www.oxfordneutronschool.org/2013/Lectures/GarciaSakai-QENS.pdf

Map of dynamical modes

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http://www.oxfordneutronschool.org/2013/Lectures/GarciaSakai-QENS.pdf

QENS AgCrSe₂ powder

INS AgCrSe₂ powder

IXS AgCrSe₂ single crystal

Map of dynamical modes

Energy transfer

https://neutrons.ornl.gov/sns

Spallation Neutron Source (SNS)

Oak Ridge National Laboratory

Neutron and X-ray facilities

Beamlines

Linac

Accumulator ring

• Front end generates H^-
• Linac accelerates H^- to 0.88c, 1GeV
• H^- passes through a foil striping 2 e^-
• H⁺ hits liquid mercury and generate neutron (spallation)

Front-end

Neutron and X-ray facilities

Isotope reactor

High Flux Isotope Reactor (HFIR)

Oak Ridge National Laboratory

https://neutrons.ornl.gov/hfir

By MikeRun - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=60375907

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Slow neutron

fission

chain reaction

https://www.aps.anl.gov/About/Welcome

Advance Photon Source (APS)

Argonne National Laboratory

Neutron and X-ray facilities

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Linac

Synchrotron ring

• 250 MeV electron Linac
• 450-MeV positron Linac
• 450-MeV positron accumulator ring
• 0.4 to 7-GeV booster synchrotron
• 7-GeV positron storage ring

Booster/injector

E_i

E_f

Sample

Georg, Rev. Sci. Instrum. 82.8: 085108, (2011)

Time-of-flight (TOF) for phonon/diffusion

Direct TOF

Indirect TOF

E_i

E_f

Sample

Powder samples in Al can

(a few grams)

Georg, Rev. Sci. Instrum. 82.8: 085108, (2011)

Example scan on powder AgCrSe₂

(thermoelectric material)

300 K

Time-of-flight (TOF) for phonon/diffusion

Mamontov, Rev. Sci. Instrum. 82.8: 085109, (2011)

Example dataset and fitting of Li₆PS₅Cl

(solid-state electrolyte material)

Time-of-flight (TOF) backscattering for diffusion

Said, J. Synchrotron Radiat. 27.3: 827-835 (2020)

https://neutrons2.ornl.gov/nxs/2015/lectures/resources/Alp_NX_Schol_2015_IXS.pdf

High-resolution monochromator

Mounted Single Crystal

(a few hundreds micron size)

E_i=23.7 keV

Example scan on a specific Q

High Energy Resolution Inelastic X-ray

Outline

​

• How to describe the motion of atoms?
• Small solid-state physics lecture

​

• How do we probe them experimentally?
• Neutron/x-ray scattering principles
• Virtual tour to facilities

​

• Why are they important?
• Application in emergent energy materials

Harmonic:

delta functions

Spectral signatures of anharmonicity

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• Quasi-harmonic phonons: 𝛅 -functions on dispersions
• Stronger anharmonicity:

phonon peaks broadened (damping)

no-longer well-defined quasiparticles in extreme cases

Harmonic:

delta functions

Weakly Anharmonic:

damped harmonic oscillators

Lorentzian-like, shifted

Spectral signatures of anharmonicity

​

• Quasi-harmonic phonons: 𝛅 -functions on dispersions
• Stronger anharmonicity:

phonon peaks broadened (damping)

no-longer well-defined quasiparticles in extreme cases

• Quasi-harmonic phonons: 𝛅 -functions on dispersions
• Stronger anharmonicity:

phonon peaks broadened (damping)

no-longer well-defined quasiparticles in extreme cases

Harmonic:

delta functions

Weakly Anharmonic:

damped harmonic oscillators

Lorentzian-like, shifted

PbTe, Mg₃Sb₂

(Ag/Cu)CrSe₂, Li₆PS₅Cl

Strongly Anharmonic:

strong renormalization,

complex spectra (eg. satellites),

quasi-elastic from damped fluctuations

Niedziela, Nature Physics 15, 73 (2019)

Ding, PNAS 117, 3930 (2020)

Gupta, Energy Environ. Sci. 14.12: 6554-6563 (2021)

Delaire, Nat. Mater. 10, 614 (2011)

Ding, Sci. Adv., 7:eabg1449, (2021)

Spectral signatures of anharmonicity

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Ding, PNAS, 117.8: 393-3937, (2020)

Niedziela, Nature Physics 15, 73 (2019)

Ding, Spin and lattice dynamics in MCrX2 (under preparation)

(Ag/Cu)CrSe₂

Ding, (under review)

Li₆PS₅Cl

Thermoelectrics

Solid-state electrolytes

Cu₇PSe₆

Ag₈SnSe₆

Gupta, Advanced Energy Materials, 12(23), 2200596 (2022).

Ren, Q, Nature Materials, 1-8 (2023).

Na₃PS₄

Gupta, Energy Environ. Sci., 14 (12), 6554-6563 (2021)

Combining neutron/x-ray scatter with soft anharmonic phonons

Non-Debye behavior reveals liquid-like dynamics

Debye frequency has quadratic relation in low-E DOS

https://www.researchgate.net/publication/278020916_Lecture_Note_on_Phonon-II_thermal_properties_Solid_State_Physics/figures?lo=1

• Quadratic relation applied at 200K (no long-range diffusion)
• At 600K, a linear relation (red) is observed, similar to instantaneous normal modes in liquid
• The fast stochastic Li⁺ jumps on a dynamic result in a linear frequency dependence, and a finite spectral weight at the zero-frequency limit.

Neutron measurements on a solid-electrolyte material

Summary

• Atomic dynamics include lattice vibration and ionic diffusion

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• The time- & length-scales are at the order of ps (10^-12 s) & Å (10^-10 m)

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• We can probe atomic dynamics through neutron/x-ray scattering

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• The method is very useful in study the atomistic mechanism in energy materials

Thanks!