Autonomous analysis of synchrotron X-ray experiments withapplications to metal nanoparticle synthesis

Anthony Fong, Lenson Pellouchoud, Sathya Chitturi, Christopher Tassone
Stanford University & Stanford Synchrotron Radiation LightsourceOutline
1. Pipeline for nanoparticle optimization based on Small-Angle X-ray
Scattering (SAXS) data (Anthony/Lenson)- Automatic analysis of SAXS data
- Bayesian optimization of reaction conditions
2. Automatic analysis of powder diffraction / Wide-angle X-ray scattering(WAXS) data
- Lattice parameter estimation using CNNs
- Effects of experimental non-idealities on predictions- Approaches for tackling multiphase data!2

Introduction
Project Goals

TEM of Pd NPs with different sizes

1) Synthesize libraries of monodisperse Pd nanoparticles with user
specified sizes2) Determine synthetic conditions for desired nanoparticle sizes
3) Perform these experiments in an autonomous fashion using aflow-reactor setup

Automatic Synthesis Schematic

Bayesian Optimization

Choose:{Temperature, Flow Rate,
Reagent Concentrations}

Measure physical properties
via X-ray experiments:{NP size, polydispersity}

Fong, A et al. Utilization of machine learning to accelerate colloidal synthesis and discovery (in review).

!3Matching the Probe to the Metric
Small Angle X-ray Scattering (SAXS) characterizes
ShapeSize

Polydispersity

1000
100
10
10 .10 .0 10 .0 0 123

4

5

67 8 90 .1

2

3

4

56

7

Wide-angle X-ray scattering (WAXS) characterizes
••
•
•
•

Phase
Composition
Degree of Crystallinity
StrainCrystallite Size!4

Automated Fitting of SAXS data

SAXS data populations

Data Fitting Approach-- Dilute spherical NPs (desired)-- Condensed / disordered-- Superlattice-- Precursor (metal ligand)!5

Using ML to improve SAXS Fitting!6

Bayesian Optimization to find synthesis conditions!7

Bayesian Optimization to find synthesis conditions!8

Individual GPs

Details of Bayesian Optimization

Enforceo Sizeo Monodispersity
o Large Yieldo Desired Population (dilute)!9Acquisition Function Details
Constraints Coded into Acquisition Functions

Closest training example
target!10

Automating Understanding of Synthesizability
We don’t want to synthesize a single catalyst, we want to synthesize a library
Iteration 1

Iteration 2

Iteration 3!11Sample Results for NP synthesis!12

Future Directions: Binary and Ternary Systems

o Multimodal SAXS/WAXS experiments

Wide-angle X-ray scattering (WAXS) characterizes• Optimize for desired phase, composition andparticle size
• E.g. make NPs of Pt4Sn alloyo Automate analysis of 1D powder/WAXS data using ML• Crystal System / Lattice parameters• Predict phases in data based on known priors•••••

PhaseComposition
Degree of Crystallinity
StrainCrystallite Size!13

Intensity

Introduction to WAXS / Powder Diffraction

q or 2➢ Peak locations: crystal system / lattice
parameters➢ Peak shape: sample / instrument
effects➢ Peak intensities: space group / positionof atoms, texturing➢ Phase Identification: fingerprinting!14

Conventional Analysis Pipeline

PeakFinding

Indexing

Refinement

Bottleneck
Multiple Phases

Overlapping Peaks!15

Problem Formulation

Intensity

Goal: Develop machine learning models to directly estimate lattice
parameters from powder diffraction dataq or 2Previous Work

Potential Advantages
Robust to Noise➢

1Automatic space group and crystalsystem prediction➢ 2Lattice parameter prediction for neutron
diffraction data
1. Park, W. B. et al., IUCrJ (2017).
2. Doucet, M. et al., Machine Learning: Science and Technology 2.2 (2020).

No Intervention Needed
Fast!16

Previous ML Analysis of Powder Diffraction Data• Determination of Space Group and Crystal System
directly from diffractogram- 230 Space Groups, 7 Crystal Systems
MethodAccuracy

TypeOutput

Dataset Size

Datasets

Park et al.
2017

CNN

81.14%

Sim

230 spacegroups150000

ICSD

Oviedo etal. 2018

CNN +physics
augmentation

89%

Sim/Exp

7 Crystal

164 + 115

ICSD/Exp

Vecsei etal. 2018

FCNN

57%

Sim/Exp

230 spacegroups128404 + 800

ICSD/RRUFFSuzuki etal. 2018

RF - 10 peak
positions83.62%

Sim

230 spacegroups188607

ICSD

Systems

Simulation Details➢ ~ 1 million patterns simulated from CIF structure files from Inorganic
Crystal Structure Database and Cambridge Structural Database
Cambridge Structural Database

Ibuprofen~ Large Unit Cells~ Low symmetry

Inorganic Crystal Structure Database

NaCl~ Small Unit Cells~ High symmetry!18

Simulation Details

Crystal Structure
Factor

Lorentz-Polarization
Intensity

Multiplicity

192!19Performance of Baseline Models on Simulated Data
ML Models: 1D Convolutional Neural Networks trained and tested on
simulated intensity arrays for each crystal system
Crystal System

Independent Parameters Mean Percentage Error (%)

Cubic

7.4

Hexagonal

6.4

Trigonal

14.8

Tetragonal

11.6

Orthorhombic

10.0

Monoclinic

11.8

Triclinic,

3.1
Are these predictions good enough?
!20

Machine Learning + Refinement Pipeline

MachineLearning

Estimate}

1Lp-Search

Crystal System
Knowledge

Refinement

Refined}ML can provide the initial guess required for refinement
1. Coelho, A. A., Journal of Applied Crystallography (2017).

!21

Monte Carlo Pawley Refinement (Lp Search)
Pawley Refinement•

Minimize difference between calculated and observed (experiment) diffractogram•Method does not rely on the structure factor

Parameters

Interpretation

Lattice Parameters Dictates peaks via Bragg Equation
I(hkl)

Intensities for each (hkl)

2θzeroZero-offset (instrument)

U,V,W

Peak-widthη
Lp Search is a Monte Carlo minimization of the objective:• Not used so much due to large parameter range• Lattice parameter ranges for {}- 3<- < 120• Space Group

Other detector, peak shape parameters

Automatic Unit-Cell RefinementChemical Formula: 1C48H62Er N7O2Si2

Crystal System: Hexagonal

Lattice Parameters: {a = 13.11, b = 13.11, c = 57.64, = 120}

CNN Estimate{a = 13.71, b = 13.71, c = 57.74}

After Refinement
Peaks for c lattice parameter✓ {a = 13.11, b = 13.11, c = 57.64}

Possible to fully automate the analysis of challenging powder diffraction patterns
1. Huang, Z. et al., Inorganic chemistry (2018).

!23Modelling Realistic Non-idealities• There is normally exists a generalization gap between training on simulated dataand predicting on experimental data

Train on Simulated / Test on Simulated Train on Simulated / Test on Experimental• Experimental data has extra non-idealities that may need to modelled➢ Peak Intensity Variation➢ Zero-Offset Error➢ Peak Broadening➢ Impurity Phases➢ Baseline Noise!24

Modelling Realistic Non-idealities
Intensity Variation

Non-ideality models preferential orientation effects!25Modelling Realistic Non-idealities
Zero-Offset Error

Non-ideality models detector drift!26

Modelling Realistic Non-idealities
Impurity Phases

Non-ideality models the addition of extra impurity phases!27Modelling Realistic Non-idealities
Baseline Noise

Non-ideality models various sources of baseline noise!28

Modelling Realistic Non-idealities
Peak Broadening

Non-ideality models broadening due to size and microstrain effects!29

Effect of Realistic Non-idealities

Baseline CNN models are unstable against some non-ideal conditions!30

Stabilization against Realistic Non-idealities

Using non-idealities during training greatly improves performance!31Multiphase analysis: Predicting phases and phase fractions

Phase identification/fraction using CNNs

Prior knowledgeof possible phases!32

Future Work❖ Nanoparticle Optimizationo Other systems beyond Pd
o Extension to multicomponent systems using SAXS/WAXS
o Analysis of other optimization methods beyond Bayesian optimization❖ Powder Diffraction Anaysis
o Incorporation of more realistic physical models for preferred orientation,microstrain, crystallite size and temperature dependenceo Adding atomic / geometrical features based on plausible compositionso Capturing additional information in the 2D area datao Using prior information to analyze multiphase data!33

Acknowledgements
Lenson Pellouchoud

Kevin Stone

Anthony Fong

Daniel Ratner

Malcolm Davidson

Richard Walroth

Carena Church
Ekaterina Tcareva
Liheng Wu

Vivek Thampy
Evan ReedMike Dunne
Chris Tassone

Kyle Peterson
Bryce Meredig!34

Supplementary Slides!35

Learning Nanoparticle Design Rules• TOP, oleylamine, oleic acid are ligands which can bind and control nucleation and growth- TOP slows nucleation kinetics by increasing Pd precursor- Oleylamine can enhance nucleation kinetics- ODE is just a diluting solvent• Higher Temperatures + Lower Flow Rates give bigger NPs- Large T accelerates growth kinetics- Low Flow-rate increase growth duration!36