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Thermal Properties and Ground-state Structures

• f Pure and Alloy Nanoclusters via

Molecular Dynamics Simulations

NAME: ONG YEE PIN MATRIC NO.: P-ZM0007/14(R)

ABSTRACT

• The study of thermal properties of nanoclusters via molecular dynamics simulation is

a common research topic in computational physics. However, the methods of post- processing and determining the pre-melting and melting range of nanoclusters at specific composition differ in every research.

• In this thesis, the study of thermal properties was started by obtaining the ground-

state structure of 38-atoms gold-platinum nanoclusters for various composition via

• PTMBHGA. Bimetallic nanocluster Au32Pt6 with D6h symmetry has been selected as

the nanocluster for further investigation in the thermal properties as it is the most stable bimetallic nanocluster studied in this thesis. The melting mechanism used in this research is BTIMD.

ABSTRACT

• Specific heat, 𝐷𝑤 and Lindemann index, 𝜀 served as the common descriptor used to

monitor the melting behaviour of Au32Pt6 nanoclusters. Both 𝐷𝑤 and 𝜀 curves showed the presence of pre-melting phase in nanoclusters. To further investigate the pre-melting stage, USR has been introduced. The data was plotted into atomic- distance plots and probability distribution function of shape similarity index.

• The three methods shown agreed with each other in determining the pre-melting

and melting range of nanoclusters. However, the USR method had provided detailed insight to the melting behaviour of nanoclusters and proven itself to be a more precise as indicator.

CONTENT

1. Introduction

• Importance of nanoclusters
• Problem statements

2. Theoretical Background & Methodologies

• Structural properties of nanoclusters
• Thermal properties of nanoclusters
• Ultrafast shape recognition

3. Results & Discussions

• Ground-state structures of nanoclusters
• Commonly used post-processing methods
• Post-processing with ultrafast shape

recognition

4. Further Verification for Ultrafast Shape Recognition 5. Conclusion

INTRODUCTION

Nanoclusters

• A group of particles (atoms or molecules) with its size in the order of nanometer

(10-9 m) formed by any countable number of atoms that are combined together.

• Nanoclusters can be formed from identical atoms (homo-atomic) or two or more

types of atoms (hetero-atomic).

• Each type of clusters has their own uniqueness that make them a worthwhile topic

to study.

• Their physical properties generally display a size-dependence behaviour, thus

nanoclusters of different sizes will exhibits different properties despite being formed by the same elements.

INTRODUCTION

Importance of Nanoclusters

• The increasing interest in nanoclusters throughout the past decades is due to the

possibilities of them having distinct physical and chemical properties compared to bulk state.

• To understand the properties of nanoclusters, researchers have searched for the

most stable structures with the lowest potential energy (Baletto et al. 2005). After finding the geometrical and electronic structure of nanoclusters, the results will be branched out to the studies of catalytic, magnetic, optical and thermal properties.

• Since the properties of the nanoclusters are not easily measured in experiments,

theoretical studies and computational methods have become important tools in development and application of nanocluster.

INTRODUCTION

Gold-Platinum Nanoclusters

• Gold (Au) with a filled d-orbital and atomic number 79 is a material which has been

studied intensively due to its unique capability to hold as planar structure from 3 to 14 atoms in gold nanoclusters (Xiao et al. 2004a).

• Platinum (Pt) is a transition element in periodic table with atomic number 78. It is

an important catalyst in various industries.

• Gold-platinum nanoclusters are widely used in industrial as effective catalyst in
• xygen reduction process (Wanjala et al. 2010) and fuel cell electrocatalysis (Maye

et al. 2004).

• The structures of gold-platinum nanoclusters have been investigated while the

results show that they are immiscible in bulk form but experimentally proven that they can exist as nanoclusters (Mott et al. 2007).

PROBLEM STATEMENTS

• In order to know how gold-platinum nanoclusters are affected by temperature

variation, we shall study their possible structures at high temperatures, and they are altered, as well as the melting behaviour of these nanoclusters.

• Conventional methodologies to study thermal instabilities of nanoclusters, such as

Lindemann index and specific heat capacity curve, turn out to be not sufficiently sensitive to capture the detailed mechanism of structural change during the pre- melting phases.

• Quantifying the detail mechanism of structural change in nanoclusters during pre-

melting phases is essential to understand the changes that occur within the nanocluster as temperature varies.

• A novel approach is proposed to quantify and capture these details.

THEORETICAL BACKGROUND AND METHODOLOGIES

Parallel Tempering Multicanonical Basin Hopping plus Genetic Algorithm Ultrafast Shape Recognition Brownian type Isothermal Molecular Dynamics

STRUCTURAL PROPERTIES OF NANOCLUSTERS

Parallel Tempering Multicanonical Basin Hopping plus Genetic Algorithm (PTMBHGA) Gupta many body potential

• To calculate the interactions between many-body atoms.
• Gupta parameters for gold, platinum and gold platinum atoms.

𝒒 𝒓 𝑩(𝒇𝑾) 𝝄(𝒇𝑾) 𝒔𝟏(Å) Au-Au 12.229 4.036 0.2061 1.79 2.884 Pt-Pt 10.621 4.004 0.2795 2.695 2.7747 Au-Pt 10.42 4.02 0.25 2.2 2.8294

PTMBHGA

Start Generate: 20 random configurations Perform: 100 BH steps 10 MBH steps Perform: 500 generations of GA Determine lowest potential energy & configurations of nanocluster Stop

Repeat BH steps with 20 and 30 MBH steps respectively

THERMAL PROPERTIES OF NANOCLUSTERS

Brownian type isothermal molecular dynamics simulation

• The basic idea of this MD simulation approach is built upon canonical ensemble at

classical level, and is designed with the intention to study melting behaviour of clusters (Yen et al. 2007).

• Throughout all simulations, time step of ∆𝑢 which is fixed between 1 × 10−15 to 5 ×

10−15 s was used.

• (𝑈 ≤ 500 K), 1 × 108 steps were performed

(550 K ≤ 𝑈 ≤ 1050 K), 2 × 108 steps were performed (𝑈 ≥ 1100 K), 2 × 107 steps were performed.

• The MD simulations were run at an interval of 50 K throughout all temperatures.

However, in pre-melting and melting regions, which generally lies in the range of 700 K ≤ 𝑈 ≤ 1050 K, a more refined interval of 10 K is adopted.

ULTRAFAST SHAPE RECOGNITION

• Molecular shape recognition technique is widely applied in chemistry field to categorize

molecular structures, especially proteins structure.

• The idea of USR ideology has been inspired S. K. Lai’s team from National Central

University, Taiwan.

• The analysing process of USR involved the shape similarity index and probability of shape

similarity function. It compares the reference ground-state configuration of the original nanocluster at 0K against the configuration at each time step during the simulation. The shape similarity index 𝜂 is the quantifier used to measure the difference between the structures of the nanoclusters 𝑗 = 0.

ULTRAFAST SHAPE RECOGNITION

• 4 different statistical moments, based on the 3D spatial coordinates of the atoms:
• Mean value
• Variance
• Skewness
• Kurtosis
• These moments in turns can be calculated by referring to 4 different reference sites:
• Centre of mass (COM)
• Atom closest to the centre of mass (CCM)
• Atom farthest from the centre of mass (FCM)
• Atom farthest to atom farthest from the centre of mass (FTF)
• Hence, overall, 16 different statistical moment descriptors can be discerned.

RESULTS AND DISCUSSIONS

GROUND-STATE STRUCTURES OF NANOCLUSTERS

Gold nanoclusters

The comparison between the structures of gold nanoclusters obtained from PTMBHGA (left) and reference (right) from Xia Wu et al. 2012.

GROUND-STATE STRUCTURES OF NANOCLUSTERS

The second energy difference plot for gold nanoclusters from size 3-55 atoms.

Second energy difference

• An indicator to monitor the relative stability of nanoclusters.
• A large value at a particular cluster size in second energy difference plot implies higher relative

stability compared to neighbouring cluster sizes.

GROUND-STATE STRUCTURES OF NANOCLUSTERS

Platinum Nanoclusters

The second energy difference plot for platinum nanoclusters from size 3-55 atoms.

Ground-state Structures of Nanocluster

Gold-platinum Nanoclusters

The second energy difference plot for gold-platinum nanoclusters of 38 atoms for every

• composition. 𝑜 refers to the number of gold atom in the bimetallic clusters Au𝑜Pt38−𝑜.

Ground-state Structures of Nanocluster

𝐁𝐯𝟒𝟑𝐐𝐮𝟕

Ground-state structure for Au32Pt6 nanocluster

MELTING BEHAVIOUR OF NANOCLUSTERS

Specific Heat , 𝑫𝒘

• The first indicator used to quantify the melting properties of the binary alloy clusters

is specific heat, 𝐷𝑤, which is one of the most commonly indicators used in the literature.

• 𝐷𝑤 is the measure of energetic changes

Lindemann Index, 𝜺

• The second indicator used in this thesis to quantify the melting behaviour of the

clusters is Lindemann index which also a common tool used to study variation in geometrical properties of a nanocluster in a thermal process.

• 𝜀 is the measure of structural change

MELTING BEHAVIOUR OF NANOCLUSTERS

Test Case: 𝐁𝐯𝟐𝟑𝐃𝐯𝟐

(Left) Specific heat 𝐷𝑤 and (Right) Lindemann Index 𝜀 against temperature for Au12Cu1 obtained by Yen et al., 2009.

MELTING BEHAVIOUR OF NANOCLUSTERS

𝐁𝐯𝟒𝟑𝐐𝐮𝟕

Graph of specific heat 𝐷𝑤 (continuous line) and Lindemann Index 𝜀 (dotted line) against temperature for Au32Pt6 nanocluster.

MELTING BEHAVIOUR OF NANOCLUSTERS

Post-Processing with Ultrafast Shape Recognition USR code was used to produce two types of statistical data useful for analysing the melting mechanism:

• Atomic-distance plot
• obtained from every 500 time-steps of a huge collection of recorded snapshots of cluster

configuration along a simulated MD trajectory, in which the simulation is equilibrated at a fixed temperature 𝑈 by using the CCS thermostat implemented in the BTIMD code.

• The vertical axis in a USR graph represent atomic distances in unit of Angstrom, while the

horizontal axis represents the numerical label attached to a fixed atom in the cluster.

MELTING BEHAVIOUR OF NANOCLUSTERS

Post-Processing with Ultrafast Shape Recognition USR code was used to produce two types of statistical data useful for analysing the melting mechanism:

• Probability of Similarity Index 𝑸 𝜼
• For every trajectory data (which has a fixed temperature), the USR code would calculate

and record the shape similarity index 𝜂𝑗 of the cluster at an interval of every 500 simualtion steps.

• The USR code will then bin the shape similarity index collected 𝜂1, 𝜂501, 𝜂1001, … , 𝜂𝑗, …

to form a normalised histogram with a pre-specified (and narrow) bin width.

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 100 K ≤ 𝑈 ≤ 2000 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 100 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 100 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 100 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 100 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 100 K and 400 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 400 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 100 K and 400 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 400 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 400 K and 700 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 700 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 400 K and 700 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 700 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 700 K and 800 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 800 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 700 K and 800 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 800 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 700 K ≤ 𝑈 ≤ 800 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 760 K and 770 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 770 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 760 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 800 K and 900 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 900 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 800 K and 900 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 900 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 900 K and 1000 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 1000 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 900 K and 1000 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 1000 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 1000 K and 2000 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 2000 K

MELTING BEHAVIOUR OF NANOCLUSTERS

Graph of 𝑄(𝜂) against 𝜂 for Au32Pt6 nanocluster at 𝑈 = 1000 K and 2000 K Atomic distance comparison graphs

• btained

from USR and structure of Au32Pt6 nanocluster at 𝑈 = 2000 K

FURTHER VERIFICATION FOR USR

The purpose to do so:

• To investigate the thermal stability of the cluster, which is a special case of the Au-Pt

cluster with zero Pt atom.

• To use Au38 as another test case to independently justify the use of USR method for

identification of pre-melting and melting phases in a nanosystem.

The calculation procedures as applied to the Au32Pt6 cluster in previous sections will be repeated on Au38

Ground-state structure for 38 atoms gold nanocluster

FURTHER VERIFICATION FOR USR

Specific heat 𝐷𝑤 and Lindemann index plot for Au38. The dotted line is for Lindemann index

FURTHER VERIFICATION FOR USR

Graph of 𝑄(𝜂) against 𝜂 for Au38 nanocluster at 100 K ≤ 𝑈 ≤ 2000 K

FURTHER VERIFICATION FOR USR

Graph of 𝑄(𝜂) against 𝜂 for Au38 nanocluster at 𝑈 = 500 K and 550 K Structure for 38 gold nanocluster at 𝑈 = 550 K

CONCLUSION AND FUTURE STUDIES

• In this thesis, the ground-state structures of pure gold and pure platinum clusters with size from 3 to

55 atoms and the ground state structures of the binary alloy Au𝑜Pt38−𝑜 cluster for 𝑜 ranging from 0 to 38 were obtained with the PTMBHGA code, which was created and made available to us by S. K. Lai’s research team from NCU Taiwan.

• The relative stability of these pure clusters was also analysed by plotting the second energy difference
• f these clusters as a function of size.
• For both pure gold and platinum cluster, the cluster with highest relative stability is that with size 𝑂 =

13 atoms, and a Ih symmetry structure.

• Highly stable gold-platinum nanoclusters, namely that with gold composition 𝑜 = 25, 30 and 32, were

identified, along with their symmetry properties.

• All of the Au𝑜Pt38−𝑜 ground-state structures found display core-shell structure, in which all of the Pt

atoms in the cluster are surrounded by Au atoms.

CONCLUSION AND FUTURE STUDIES

• Due to its high stability and interesting core-shell segregation structure, nanocluster with 32 gold and 6

platinum atoms has been specifically selected as the subject of investigation, in which its melting behaviour was scrutinized via computational simulations.

• Brownian type isothermal molecular dynamics simulation (BTIMD) was the tool deployed to simulate

the melting process of Au12Cu1 and Au32Pt6 for temperature ranging from 100 K to 2000 K.

• Au12Cu1, was also simulated for the purpose of comparison with published results in the literature,

Yen et al., 2009, that was calculated using the same PTMBHGA code. The results of Au12Cu1 calculated in this thesis agrees well with that by Yen et al., 2009.

• The MD trajectories from the simulations were post-processed to obtain the specific heat 𝐷𝑤 and

Lindemann index of the simulated nanoclusters. Specific heat capacity was computed in the MD context as the fluctuation in energy, while Lindemann parameter fluctuation was the averaged distances among the atoms in the system.

• The 𝐷𝑤 and Lindemann curves for Au32Pt6 denoted a signal of pre-melting phase at around 700 K to

800 K. A relatively sharp melting peak at around 1000 K was also displayed in the 𝐷𝑤, but no clear, identifiable feature was seen in the Lindemann curve to indicate melting.

CONCLUSION AND FUTURE STUDIES

• In order to simplify the process, Ultrafast Shape Recognition (USR) approach was introduced. The USR
• perates based on a statistical basis. The post-processing began by recording the atomic coordinates of

each atom in all MD steps at a fixed temperature.

• A total of 16 statistical moments could be calculated from these coordinates in any given time step.

These statistical moments in each time step 𝑗 were then used as input to obtain the numerical value of a descriptor known as shape similarity index, 𝜊𝑗 (with the condition 0 ≤ 𝜊𝑗≤ 1). Similarity index measured the degree of similarity of the structure at an instantaneous MD step 𝑗 to that of a reference structure, which was defined as the ground-state structure at 0 K.

• At any given fixed temperature, a huge amount of 𝜊𝑗 was recorded along a MD trajectory. They were

binned into a histogram, then normalised and approximated into a continuous curve 𝑄(𝜊). Using the 𝑄(𝜂) plot as a measuring tool, it was found that the pre-melting in the Au32Pt6 cluster happened within 760 K to 770 K.

• Quite independently, the collection of atomic coordinates was also used to produce another graph,

namely, the atomic-distance plot. There was a temperature range (i.e., from 760 K to 770 K) where the Pt atoms in the hexagon broke into 3D configurations, yet the cluster, as a whole, still statistically maintained a core-shell segregation.

CONCLUSION AND FUTURE STUDIES

• The ultrafast shape recognition technique can applied into other fields besides determining the

thermal properties of nanoclusters. It can be improve with applying some statistical method added into the USR code.

• For future studies in this topic, the post-processing method can be enhance by produce a structural

index curve that provides a quantitative picture of how the state of the core-shell segregation evolve as a function of temperature in the nanocluster.

PUBLICATION

1. Yee Pin Ong, Tiem Leong Yoon and Thong Leng Lim. Structures of 38-atom Gold-platinum Nanoalloy Clusters. AIP Conf. Proc. 1657, 110005 (2015). doi: http://dx.doi.org/10.1063/1.4915224 2. Yee Pin Ong, Thong Leng Lim and Tiem Leong Yoon. Melting Behaviour of Gold-platinum Nanoalloy Clusters by Molecular Dynamics Simulations. AIP Conf. Proc. 1657, 110007 (2015). doi: http://dx.doi.org/10.1063/1.4915226

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