# SimXRD-4M: Big Simulated X-ray Diffraction Data
Accelerate the Crystalline Symmetry Classification

Bin Cao1,2 , Yang Liu1,311footnotemark: 1, Zinan Zheng1, Ruifeng Tan1,2, Jia
Li1,3, Tong-yi Zhang1,222footnotemark: 2
1Hong Kong University of Science and Technology (Guangzhou)
2Guangzhou Municipal Key Laboratory of Materials Informatics
3Hong Kong University of Science and Technology
<EMAIL_ADDRESS>
<EMAIL_ADDRESS><EMAIL_ADDRESS>
<EMAIL_ADDRESS>Both authors contributed equally to this
research.Corresponding Author.

###### Abstract

Spectroscopic data, particularly diffraction data, contain detailed crystal
and microstructure information and thus are crucial for materials discovery.
Powder X-ray diffraction (XRD) patterns are greatly effective in identifying
crystals. Although machine learning (ML) has significantly advanced the
analysis of powder XRD patterns, the progress is hindered by a lack of
training data. To address this, we introduce SimXRD, the largest open-source
simulated XRD pattern dataset so far, to accelerate the development of
crystallographic informatics. SimXRD comprises 4,065,346 simulated powder
X-ray diffraction patterns, representing 119,569 distinct crystal structures
under 33 simulated conditions that mimic real-world variations. We find that
the crystal symmetry inherently follows a long-tailed distribution and
evaluate 21 sequence learning models on SimXRD. The results indicate that
existing neural networks struggle with low-frequency crystal classifications.
The present work highlights the academic significance and the engineering
novelty of simulated XRD patterns in this interdisciplinary field. SimXRD aims
to advance symmetry identification research and is freely accessible at
http://simxrd.caobin.asia/.

Figure 1: The X-ray diffraction patterns of crystal Tb2BaCoO5 and PbSO4.

##  1 Introduction

Crystals embody a distinct and precisely structured form of matter,
constituted by atoms or molecules arranged in long-range order [21]. Symmetry
identification is a fundamental and crucial step for materials
characterization and design. Specifically, XRD analysis stands out as
exceptionally potent for probing microstructure, due to its sensitivity to
atomic arrangement and the element specificity of atom scattering power. The
diffraction pattern reflects the atomic arrangement of the diffracting
material, as depicted in Figure 1. XRD patterns serve as a fingerprint of the
crystals, and the identification of symmetry has been a fundamental practice
in the decoding process.

The traditional method involves a search-match process [1] among numerous
known powder diffraction patterns. Given a target XRD pattern, it iterates
candidates in databases until satisfactory alignment is achieved. Although
such a method is prevalent, it is time-consuming [1, 34, 19] due to two
issues: (1) high dependency on human intervention. Matching processes rely on
domain-specific programs. Human-assisted tuning is often required during
program execution; (2) diffraction is an intricate multi-physical coupling
processes. The complex interplay between scattering signals and the
convolution of crystalline peaks poses a challenge to structure analysis. The
intensity of each observed peak in the spectrum is influenced by external
conditions such as grain size, temperature and instrument, resulting in peak
broadening [53] that obscures the precise peak location. This complexity
renders pattern symmetry analysis extremely challenging, even for experienced
domain experts.

To address the above problems, recent studies [28, 57, 35, 63, 27, 58, 9, 51]
train neural networks [31] on simulated XRD datasets. They treat XRD patterns
as sequences and aim to classify them to specific symmetry (e.g., crystal
systems or space groups). Despite significant progress, several limitations
exist in current model development and evaluation:

  * •

Lack of a large-scale and high-quality dataset: The ultimate goal of symmetry
identification tasks is to develop a general model capable of recognizing
symmetry from experimental measurements, emphasizing extensive coverage and
high fidelity. Previous research has been largely confined to specific
materials[15, 28, 63]. For example, Lee et al. [28] focus on mixtures of 38
distinct binary and ternary crystals in the Sr-Li-Al-O inorganic compounds.
Additionally, the geometric similarity of crystals and experimental physical
factors can result in XRD patterns with similar peak distributions. Therefore,
sufficient coverage of structures and close alignment with experimental
patterns under different physical conditions is necessary for developing
models with high generalization ability.

  * •

Insufficient comparison of recurrent and transformer models: Transformers have
shown impressive results in sequence modeling applications such as time series
and text classifications. Additionally, recurrent models like Recurrent Neural
Networks (RNNs)[52], Long Short-Term Memory (LSTM)[17], and Gated Recurrent
Units (GRUs)[8] have long been employed as well. These models can be applied
to symmetry identification but a systematic comparison between them and CNNs
is still absent.

Crafting such a high-fidelity simulated XRD pattern dataset is challenging due
to the many domain-specific simulation processes, such as determining crystal
stability, instrumental settings, and physical environments. In this work, we
present SimXRD, the largest open-sourced and physically comprehensive dataset
aimed at advancing this new interdisciplinary domain. It was developed based
on the mature refinement software [4], established by researchers from
material science. We use advanced Material Project as a crystal source and
filter out crystals of broken symmetry, duplication, or discrepancies in space
groups. Consequently, SimXRD comprises 4,065,346 X-ray powder diffraction
patterns covering 119,569 distinct crystal structures simulated under various
conditions, including grain size, orientation, internal stress, inelastic
scattering, thermal vibration, instrumental zero shift, and noise. Through the
analysis of SimXRD, we discovered that the symmetry of real-world crystals, as
exemplified by the Materials Project (MP) [20] database, follows a long-tail
distribution.

Notably, the low-frequency space group is still vital in crystallography.
Benchmarking the model performance on such a long-tailed sequence
classification problem is crucial for the academia-industry need for real-time
crystal analysis. Thus, we evaluate the performance on SimXRD of 20 models,
which can be divided into three types of sequence models: convolution neural
networks (i.e., the backbone of existing symmetry classification models),
recurrent models, and transformers.

In summary, our contributions are:

  * •

We introduce SimXRD, the largest open-source simulation dataset for symmetry
identification, including 4,065,346 XRD patterns of 119,569 high-quality
crystals .

  * •

We highlight the long-tailed distribution in symmetric identification and find
that most existing methods achieve low accuracy in space groups of low
frequency.

  * •

We construct a comprehensive benchmark of 21 models of three types of sequence
models. We integrate SimXRD and all models mentioned in this paper into an
open-source repository.

Table 1: Summaries of existing powder XRD datasets. ICSD refers to the
commercial Inorganic Crystal Structure Database. MP denotes the open-sourced
Material Project.

Dataset | #XRD Pattern | #Structure | Open Access | Simulated | Crystal Source | Year
---|---|---|---|---|---|---
RRUFF [22] | 3,002 | 3,002 | $\checkmark$ | $\times$ | - | 2015
XRDSP [55] | 169,536 | 169,536 | $\checkmark$ | $\checkmark$ | ICSD | 2020
CNN [28] | 1,785,405 | 170 | $\times$ | $\checkmark$ | ICSD | 2020
PQNet [14] | 250,000 | 1 | $\checkmark$ | $\checkmark$ | ICSD | 2021
XRDAutoAnalyzer [57] | 38,250 | 150 | $\checkmark$ | $\checkmark$ | ICSD | 2021
XRDIsAllYouNeed [26] | 328,503 | 189,476&139,027111Union of ICSD and MP database, existing the same structures. | $\times$ | $\checkmark$ | ICSD&MP | 2022
AdvancedXRDAnalysis [27] | 29,569,650 | 197,131 | $\times$ | $\checkmark$ | ICSD | 2023
CrySTINet [7] | 100 | 100 | $\checkmark$ | $\checkmark$ | ICSD | 2024
CPICANN [5] | 692,190 | 23,073 | $\checkmark$ | $\checkmark$ | COD | 2024
SimXRD | 4,065,346 | 119,569 | $\checkmark$ | $\checkmark$ | MP | 2024

##  2 Related Work

###  2.1 Existing datasets

Several datasets have been developed to train neural models for
crystallography. Table 1 provides a summary of these datasets, compared along
several key dimensions:

  * •

Dataset Size: Existing open-source databases either contain relatively small
structures tailored to specific purposes [7, 14, 57, 28] or consider limited
environmental settings [7, 55]. Crystal structure databases form the backbone
of XRD pattern databases. Although the database developed by Lee et al. [26,
27] covers almost all the crystals in the Inorganic Crystal Structure Database
(ICSD) [64] or the Materials Project (MP) [20]. A significant number of
crystals are repeated and with broken symmetries. SimXRD employs the entire MP
database of January 2024, totaling 154,718 crystal structures. During the
generation of the SimXRD database, we applied screening methods to improve
crystal quality. Additionally, we simulate XRD patterns under various
environments to meet the academic-industry requirements.

  * •

Availability: Most pattern datasets are openly available, as indicated in
Table 1, though some datasets can only be retrieved upon reasonable request
[28, 26, 27]. Additionally, published diffraction pattern datasets are saved
in various formats, requiring specific data loaders provided by the authors.
In contrast, the SimXRD-4M dataset developed in our work is fully available
and features an easier workflow for machine learning training, easily
integrable with TensorFlow or PyTorch frameworks.

  * •

Simulation vs. Experiments: Among the existing datasets, only the RRUFF
Project [22] aims to create a comprehensive set of high-quality spectral data
from well-characterized minerals. Since its inception in 2005 [50], RRUFF has
compiled a collection of 3,002 high-quality experimental powder XRD patterns
as of March 2024. However, conducting the experiments is time-consuming. Thus,
recent studies have employed domain-specific software to generate simulated
data. Rather than relying solely on software like Pymatgen [41] and FullProf
[48] to simulate patterns under finite real-world conditions, SimXRD accounts
for a broader range of comprehensive real-world conditions. These include
grain size, internal stress, external temperature variations, grain
orientation, instrument drift, instrument noise, and scattering-induced
background.

###  2.2 Symmetry identification

Existing methods rely on one-dimensional convolutional neural networks for
building classification models. Almost all related research originates from
the materials community due to the lack of easily accessible datasets. The
models developed in recent years have primarily focused on CNN architectures
[14, 63, 42]. In particular, they focus on designing CNNs with deep layers
[26] and large kernel sizes [23], ensemble CNNs [35, 57], and CNNs without
dropout [28] and pooling layers [51]. However, whether CNNs can address long-
tailed distributions and the performance of other sequence models are still
underexplored.

##  3 SimXRD-4M Dataset

In this section, we first introduce the fundamental concepts of the research
problem and then elaborate on the dataset construction process and analysis
results.

###  3.1 Preliminaries

##### Crystal symmetry

Symmetry in crystallography is a fundamental property of the orderly
arrangements of atoms found in crystalline solids. Each atomic arrangement
possesses certain symmetry elements, which are transformations that leave the
arrangement unchanged. These elements include rotation, translation,
reflection, and inversion. The specific symmetry elements present in a
crystalline solid determine its shape and influence its physical properties.
Crystals are classified based on their symmetry elements, falling into one of
7 crystal systems, and could further divided into 230 space groups [12].

##### XRD pattern

Powder XRD patterns offer a one-dimensional representation of the three-
dimensional diffraction pattern and stand as the most common experimental
measurement. Specifically, each one-dimensional powder X-ray diffraction
pattern in SimXRD is presented in the format of d-I (lattice plane distance-
intensity), where the x-axis is lattice plane distances and the y-axis is
corresponding intensities, as shown in Figure 2. Lattice plane distances
denote the detected atomic directions. Some distances lack peaks due to
geometric constraints from the lattice cell and extinction effects [32] under
diffraction. The relative intensity is normalized, with the maximum intensity
value set to 100, making the pattern independent of the incident X-ray
intensity.

##### Symmetry classification

Formally, SimXRD considers the following multi-class sequence classification
problem. Given the XRD pattern
$\bm{X}=[x_{1},x_{2},\cdots,x_{n}]\in\mathbb{R}^{n}$ where $x_{i}$ is the
$i$-th intensity value and $\bm{X}$ is arranged by lattice plane distance, the
object is to predict its symmetry $\bm{Y}\in\mathbb{R}^{k}$. Here $n$ is the
feature dimension which is 3501 in our dataset. $k=7$ for crystal system
classification and $k=230$ for space group classification. We did not consider
practical factors such as average grain size and stress as input variables, as
these are not directly measurable in real-world diffraction experiments.

Figure 2: The transformation from crystal structure to XRD pattern, accounting
for finite grain size, specific orientation, thermal vibrations, zero shift
adjustments, and the scattering background.

###  3.2 Data Generation and Processing

##### Crystal data

The crystal structures utilized in this study were sourced from Material
Project [20], a comprehensive, searchable database containing information
about solid-state materials and molecules. It provides detailed data on these
materials’ physical properties, such as elastic tensors, band structures, and
formation energies, derived from electronic structure calculations, offering a
more comprehensive reference for crystal studies. We utilize the latest
dataset, denoted as MP-2024.1, encompassing a total of 154,718
crystallographic structures of January 2024.

##### Crystal Filtering

To ensure consistency between recorded space group numbers (crystal systems)
and atomic arrangements, and to enhance the quality of crystal structures, we
conducted a thorough examination of each structure in the MP database. We
utilized Spglib [59], a library designed for identifying and managing crystal
symmetries, to check all structures. Structures displaying broken symmetry,
duplication, or discrepancies in space groups were excluded. Additionally,
only structures containing up to 500 atoms per lattice cell were retained,
effectively encompassing nearly all inorganic materials in the MP dataset. A
total of 119,569 crystal structures were screened.

##### Simulation in SimXRD

Figure 2 illustrates the overall simulation process. The experimental XRD
patterns are determined by both the crystal’s intricate structure and
practical factors including the state of the specimen and the instrumental
parameters. Our goal is to simulate this process via domain-specific custom
refinement software WPEM [4]. We first specify environmental settings and then
compute the XRD patterns of given crystals. By varying the environmental
parameters, we construct all samples of SimXRD. We systematically analyze the
physical conditions influencing the XRD profiles, categorized into factors
impacting the specimen’s internal structure and those influencing instrumental
measurements. These parameters, along with their respective value ranges, are
introduced in the Appendix. For each input crystal, we randomly couple these
physical conditions within reasonable ranges, repeating the process 33 times
to simulate XRD patterns in diverse environments. Each XRD pattern is
standardized, with the x-axis values (lattice plane distance) uniformly set
based on the experimental settings, resulting in a vector of 3501 dimensions.
The y-axis values (diffraction intensity) are simulated according to the
crystal structure and diffraction conditions.

##### Dataset availability

The XRD data is stored as standard database (db) files in the Atomic
Simulation Environment (ASE). Each row in the database contains a diffraction
pattern consisting of 3051 d-I pair values (lattice plane distance (d) and
diffraction intensity (I)), along with the chemical formula (string), atomic
elements (list), space group (integer), and crystal system (integer). Users
can utilize a command-line tool called ‘ase db’ to query and manipulate these
databases. Additionally, a Python interface is available, as detailed in the
introduction of the SimXRD documentation.

Figure 3: The statics of dataset. (A) The distribution of structures contained
in the SimXRD database across various space groups (uniformly divided into 5
categories according to the frequency) and (B) crystal systems (C) The
distribution of formation energy/atom of crystals contained in MP-2024.1 and
(D) SimXRD. Space groups 89, 103, and 104 have been excluded from Figure A to
enhance clarity, each appearing only once.

###  3.3 Data Analysis

We analyze the crystal system and space group distribution to provide insights
into building neural network solutions. To investigate the data quality of
SimXRD, we plot the formation energy of its crystals, which reflects the
stability of structures. A case study between experimental and simulated XRD
patterns is displayed to validate our simulation algorithm’s effectiveness.

##### Long-tailed distribution

The distributions of space groups and crystal systems are shown in Figure 3A
and B. We can observe that the classes are highly imbalanced and follow a
long-tailed distribution. Given that MP-2024.1 serves as a comprehensive
database of commonly occurring material systems, this distribution imbalance
is inherent to the physical population of crystals in nature. This imbalance
can lead to biased model performance as the model may be more inclined to
predict the majority class, leading to lower accuracy for the minority
classes. Since minority crystal is also important for material discovery,
addressing long-tailed sequence learning is crucial for symmetry
identification. However, existing models do not consider such a challenge,
evaluating their performance in different classes is necessary.

##### Formation Energy

The formation energy ($E_{f}$) of a configuration represents the energy
required or released to generate that configuration. Thus, the formation
process can be either endothermic or exothermic. The more negative the
formation energy of a structure, the more stable the structure, indicating its
thermal stability [60]. Figures 3C and D illustrate the formation energy per
atom across 154,718 crystal structures in MP-2024.1 and 119,569 crystal
structures in SimXRD. Figure 3C highlights the high-quality crystal data in
MP-2024.1, with 90.33% of structures exhibiting negative formation energy.
Sequentially, the crystal data in SimXRD shows a negative formation energy
rate of 92.18%, indicating that the excluded crystals are mainly relatively
unstable structures. This high-quality structural data serves as the
cornerstone of XRD pattern databases.

Figure 4: The comparison between experimental measurement patterns and
generated XRD patterns using WPEM, based on a Li-rich layered oxide cathode
structure with a primary phase of Li2MnO3.

##### Case study

A case study is conducted to investigate the difference between experimental
and simulated XRD patterns of Li2MnO3. Initially, the physical states of the
tested specimens and the experimental settings were obtained using a
refinement method (see Appendix). Subsequently, the XRD pattern was generated
inversely through the WPEM. Figure 4 shows their results where we can observe
that the generated profile exhibits extreme similarity to the experimental
measurements[29]. Therefore, by altering the physical states within a
reasonable range, other patterns that correspond to different experimental
settings can be generated. Such simulation allows us to obtain high-quality
data in a relatively efficient way, compared to experimental patterns.

##  4 Use Cases of SimXRD Datset

To further demonstrate the practical utility and applicability of SimXRD, we
explore its use in two critical tasks: crystal system classification and space
group classification. We concentrate on in-library classification, a
fundamental task in crystallography, which aims to precisely identify crystal
types by analyzing XRD patterns across various physical coupling conditions.
Therefore, the dataset is randomly split according to the types of simulated
environments, resulting in 119,569 × 30 training instances, 119,569 × 1
validation instances, and 119,569 × 2 testing instances. The data recorded for
training, validation, and testing include crystals from different simulated
environments (e.g., grain size, stress, temperature).

##### Baselines

We consider the following three types of sequence classification models:

  * •

CNN-based Models: We evaluate all existing CNN architectures that are proposed
for symmetry identification. Since most of models do not have specific names,
we classified them based on their number of convolution layers, pooling
layers, and whether they use ensemble learning and dropout layers. Table 2
summarizes the existing 11 CNNs.

  * •

Recurrent Models: We select three basic recurrent neural networks: RNN [37],
LSTM [17], and GRU [11]. Moreover, since XRD patterns can be viewed from both
forward and backward, we also evaluate the bidirectional RNN, LSTM, and GRU
performance [52].

  * •

Transformers: Transformers have proven effective in diverse sequence modeling
tasks. We evaluate the performance of raw transformer [62] and two advanced
transformer models - iTransformer [30] and PatchTST [40].

Besides these models, we further add MLP as a straightforward baseline. For
recurrent models and transformers, we first use them to learn sequence
representations, and then employ an MLP to predict the symmetry.

##### Implementation details

We use the following hyper-parameters across all experiments: Batch size 128,
learning rate $2.5\times 10^{-4}$. All models are trained for 50 epochs with
an early stopping patience of 3. We use the Cross-Entropy function to measure
the loss between prediction and the ground truth. We use accuracy, macro
F1-score, macro precision, and macro recall as our metrics to measure the
performance of the models. All models are implemented based on the Pytorch
[43] library, trained on GeForce RTX 3090 GPU.

##### Overall performance

Table 2 displays the baseline performance and inference time for the
classification of crystal systems and space groups. Based on the results, we
have the following observations:

  * •

Most existing CNN models are unsuitable for symmetry identification within the
large scale of SimXRD database. It is clear that the crystal system
classification accuracies of multiple CNNs, e.g., CNN 4 and 6 are on par with
that of MLP. The reason, as shown in the next paragraph and Figure 3, is that
their predictions are heavily biased by classes of high frequency, thus they
can not predict the low-frequency classes. Such weakness is more obvious in
space group classification where the accuracy of most CNNs (i.e., CNN 1-4, 6,
and 8) is 0.241, indicating their outputs are almost fixed to the most
frequent space group.

  * •

Convolutional neural networks without pooling have achieved the best
performance in most tasks, consistent with the findings of previous work [51].
Since the peak maximum and the relative value among peaks of XRD patterns are
highly related to the atom arrangement of crystals, employing pooling layers
may cause information loss, affecting the identification of peaks and leading
to lower accuracy.

  * •

Bidirectional recurrent models consistently outperform their unidirectional
counterparts. These results reveal an important physical attribute of XRD
patterns. That is, ensure the consistent retrieval of crystal information
through bidirectional pattern reading. Such property differs from previous
sequence tasks such as text and time-series classification, which requires
further model designs.

  * •

The raw transformer encounters difficulties when dealing with this long-tailed
sequence problem. Nevertheless, compared to it, we can observe that PatchTST
achieves significant performance improvement, demonstrating subsequence-level
patches are beneficial to identify peaks and further improve classification
performance.

Table 2:  Results of crystal system classification and space group
classification. Inference time is measured for a batch size of 100 samples and
experiments are run on a GeForce RTX 3090 GPU.

Model | # Conv. | # Dropout | # Pooling | # Ensemble | Ref. | Accuracy | F1 | Precision | Recall | Time (ms) | Accuracy | F1 | Precision | Recall | Time (ms)
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
CNN1 | 3 | ✓ | AvgPool | $\times$ | [42] | 0.559 | 0.418 | 0.427 | 0.431 | 3.2 | 0.241 | 0.002 | 0.001 | 0.005 | 3.4
CNN2 | 2 | $\times$ | MaxPool | $\times$ | [28] | 0.466 | 0.236 | 0.222 | 0.283 | 1.8 | 0.241 | 0.002 | 0.001 | 0.005 | 1.9
CNN3 | 3 | $\times$ | MaxPool | $\times$ | [28] | 0.531 | 0.328 | 0.315 | 0.369 | 3.5 | 0.241 | 0.002 | 0.001 | 0.005 | 3.6
CNN4 | 7 | ✓ | MaxPool | $\times$ | [63] | 0.316 | 0.069 | 0.045 | 0.143 | 1.4 | 0.241 | 0.002 | 0.001 | 0.005 | 1.4
CNN5 | 3 | ✓ | AvgPool | ✓ | [35] | 0.517 | 0.394 | 0.489 | 0.378 | 0.6 | 0.295 | 0.022 | 0.025 | 0.026 | 0.6
CNN6 | 7 | ✓ | MaxPool | $\times$ | [14] | 0.316 | 0.069 | 0.045 | 0.143 | 65.0 | 0.241 | 0.002 | 0.001 | 0.005 | 65.0
CNN7 | 6 | ✓ | MaxPool | ✓ | [57] | 0.862 | 0.863 | 0.887 | 0.845 | 6.8 | 0.588 | 0.124 | 0.147 | 0.130 | 6.9
CNN8 | 14 | ✓ | MaxPool | $\times$ | [26] | 0.377 | 0.162 | 0.148 | 0.221 | 3.1 | 0.241 | 0.002 | 0.001 | 0.005 | 3.1
CNN9 | 3 | ✓ | MaxPool | $\times$ | [23] | 0.795 | 0.817 | 0.826 | 0.810 | 1.9 | 0.599 | 0.597 | 0.681 | 0.556 | 1.9
CNN10 | 4 | ✓ | MaxPool | $\times$ | [23] | 0.870 | 0.888 | 0.892 | 0.885 | 1.8 | 0.705 | 0.792 | 0.853 | 0.759 | 1.8
CNN11 | 3 | ✓ | None | $\times$ | [51] | 0.902 | 0.922 | 0.932 | 0.914 | 4.8 | 0.758 | 0.750 | 0.735 | 0.828 | 4.8
| MLP | 0.316 | 0.069 | 0.045 | 0.143 | 1.6 | 0.241 | 0.002 | 0.001 | 0.005 | 1.6
| RNN | 0.381 | 0.183 | 0.200 | 0.202 | 8.0 | 0.245 | 0.003 | 0.002 | 0.007 | 8.1
| LSTM | 0.728 | 0.743 | 0.762 | 0.728 | 14.6 | 0.515 | 0.156 | 0.224 | 0.151 | 14.6
| GRU | 0.765 | 0.788 | 0.802 | 0.777 | 15.1 | 0.575 | 0.273 | 0.400 | 0.251 | 15.1
| Bidirectional-RNN | 0.365 | 0.155 | 0.197 | 0.185 | 14.7 | 0.245 | 0.003 | 0.002 | 0.007 | 14.7
| Bidirectional-LSTM | 0.791 | 0.814 | 0.825 | 0.805 | 29.1 | 0.559 | 0.384 | 0.533 | 0.346 | 29.1
| Bidirectional-GRU | 0.800 | 0.826 | 0.840 | 0.816 | 30.3 | 0.627 | 0.451 | 0.609 | 0.408 | 30.3
| Transformer | 0.338 | 0.127 | 0.172 | 0.155 | 83.4 | 0.241 | 0.002 | 0.001 | 0.005 | 83.5
| iTransformer | 0.627 | 0.611 | 0.652 | 0.599 | 1.9 | 0.388 | 0.135 | 0.320 | 0.118 | 1.9
| PatchTST | 0.720 | 0.752 | 0.766 | 0.740 | 3.3 | 0.631 | 0.811 | 0.850 | 0.784 | 3.3

##### Performance w.r.t. long-tailed distribution

To further investigate the model performance, we display the accuracy of each
crystal system and space group of different frequencies in Figure 5. To better
visualize the model performance on space group, we divided the results of 280
space groups into 5 categories according to their frequency (the same as
Figure 3). From the results, we can observe:

  * •

In crystal system classification, the performance of most CNN models, the raw
RNN, and transformers is affected by the frequency of crystal systems. They
can not predict the XRD patterns of Cubic and Hexagonal symmetry (their
accuracies are almost zero). In contrast, multiple domain-specific CNN (i.e.,
CNN 7, 9, 10, 11), LSTM, GRU, and advanced Transformers (i.e., iTransformer
and PatchTST) can mitigate long-tail distributions.

  * •

Space group classification is more challenging than crystal system
classification. Most models can only predict space groups with high frequency
and hardly predict most low-frequency space groups. Surprisingly, PatchTST
achieves comparable performance with the best models in all low-frequency
space groups. Given that PatchTST is a model specifically tailored for time
series forecasting, its performance on XRD pattern classification has
considerable room for improvement.

Figure 5: Classification accuracy of each model w.r.t. crystal systems and
space groups. The same as Figure 3(A), Space groups are classified into 5
categories based on their frequency. $N$ denotes the number of crystals.

##  5 Conclusion

In this paper, we propose SimXRD, the largest open-source XRD pattern dataset
for symmetry identification. Through data analysis, we find that the symmetry
follows a long-tailed distribution. Our evaluation of 21 models shows that
most existing models can not work well in predicting the symmetry of low
frequency, limiting their real-world applications. Our results underline the
importance of modeling long-tailed sequence classification and comprehensive
comparison in accurately understanding the capabilities of various models. We
make SimXRD open-source to facilitate further research and improvement of
symmetry identification algorithms.

##### Limitations

Although SimXRD enhances prior datasets from multiple perspectives (e.g.,
sample size, crystal quality, and accessibility), long-tailed and imbalanced
label distribution is its inherent limitation. The distribution of
crystallographic symmetry arises through natural processes and is invariant to
human intervention. Such biases are difficult or even impossible to address in
any dataset. Thus, possible solutions are to develop specific class-imbalanced
algorithms or employ additional information on target crystals.

##### Future works

We regard SimXRD as a long-term evolving project and are dedicated to its
continuous development. At present, we focus on in-library identification,
which is predominant in the materials science community. In the future, we
plan to (1) develop long-tailed sequence classification models through data
augmentation [10] or enhance features via multi-model inputs; (2) evaluate the
out-library symmetry classification performance of existing models.

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##  Appendix A Appendix

###  A.1 More details about crystal symmetry

The seven crystal systems are triclinic, monoclinic, orthorhombic, tetragonal,
trigonal, hexagonal, and cubic system. Crystals can be diagrammatically
represented by an orderly stacking of lattice cells, whose shape determines
the crystal system to which they belong. Unit cells of identical shape can
have lattice points, representing an atom or group of atoms, at their centers
or faces, in addition to the corners. These additional lattice points further
divide the seven crystal systems into 14 Bravais lattices, which are then
subdivided into 32 crystal classes, or point groups. Each point group
corresponds to a possible combination of rotations, reflections, inversions,
and improper rotations. When translational elements are included, these point
groups yield the 230 space groups [12].

###  A.2 In-library and Out-of-library Tasks

In-library identification is a fundamental task in crystallography that aims
to accurately identify crystal types based on XRD patterns measured in various
environments. Since 1938, crystallographers have been documenting all
discovered structures and archiving them as Powder Diffraction Files (PDFs) .
By comparing and retrieving these PDFs, researchers can determine the
structures of studied materials by matching them with historical data. With
advancements in computing, numerous software programs have been developed to
assist in the search-match process.

A related concept is out-of-library identification, which involves discovering
previously unknown structures that lack any recorded information. This process
relies on symmetry identification to determine the basic space group
information and subsequent refinement processes. Traditionally, the crystal
system to which a crystal belongs can be determined based on the crystal’s
physical properties, such as electrical conductivity, optical behavior, and
thermal characteristics. Subsequently, the space group can be identified by
examining extinction effects . This is followed by determining the ideal
chemical formula according to the estimated number of atoms and Wyckoff
positions . Validation is conducted through Rietveld refinement and site
optimization, among other techniques.

We recommend two types of data splits:

  * •

In-library Classification: This approach uses the default splitting in SimXRD.
As shown in our benchmark, the dataset is split according to different
simulation environments. Both training and testing datasets contain the same
structures but under different simulation environments, corresponding to the
in-library identification in XRD phase identification.

  * •

Out-of-library Classification: We also recommend splitting the dataset
according to crystal types. Both the training and testing datasets contain
different structures, corresponding to the out-of-library identification in
XRD phase identification. We provide the code for generating such splits based
on SimXRD in the OutlibDataProcessor tool available here.

###  A.3 Search-Match approach

Conventionally, the predominant method for in-library phase identification in
X-ray powder diffraction patterns is the search-match approach, which
comprises three main steps. Initially, (d, I) values, representing interplanar
spacing (d) and intensity (I) of each peak, are extracted from the pattern.
Subsequently, potential phases are sought from diffraction databases based on
characteristic d values, such as Hanawalt indexes [61]. Following this,
candidate phases are compared to the (d, I) values of the pattern using a
scoring system to assess alignment, aiding in selecting the most suitable
candidate phase. This process iterates until satisfactory alignment is
achieved for most (d, I) values. A recent study [33] employs a distinct
approach utilizing the Rietveld method for conducting a Full Profile Search-
Match (FPSM). Crystal structures selected from databases are automatically
aligned with raw data via the Rietveld method, culminating in a score
determined by $R_{wp}$ [38]. The phase with the highest score is acknowledged,
and this iterative procedure persists until specified criteria are met.
Subsequently, a Rietveld quantification is executed to ascertain the weight
fraction of each phase. Despite advancements in computer technology enabling
novel qualitative analysis methods, the core objective remains consistent: to
match experimental data with database entries and calculate a corresponding
score.

In-library query strategies, such as the search-match approach, can retrieve
reference structures for subsequent refinement. These references are based on
lattice geometry and include some information about atomic locations, thereby
reducing the burden of subsequent optimization. However, this approach is
ineffective for determining out-of-library structures. In contrast, using the
space group helps determine the lattice structure, and subsequent optimization
of atomic sites can be performed during the refinement process, which provides
a general method for structural measurement practices.

###  A.4 XRD Pattern Simulation

Powder XRD offer a one-dimensional representation of the three-dimensional
diffraction pattern and stand as the most common experimental measurement, as
depicted in Figure 1. These patterns mirror the relative arrangement of atoms
in real three-dimensional space. The interaction of X-rays with condensed
materials during diffraction entails elastic collisions between photons and
electrons. Therefore, conditions affecting atom arrangement and electron
behavior influence the pattern shape.

The diffraction vector $\mathbf{G}^{*}$ is defined as

$|\mathbf{G}^{*}|=\frac{2\sin{\theta}}{\lambda},$ (1)

where $\lambda$ is the wavelength of the scattered particle and
$\theta=2\theta/2$, with $2\theta$ being the angle between the incident and
diffracted beams. In three dimensions, scattering occurs only at a discrete
set of reciprocal vectors, $\mathbf{K}$, forming the reciprocal lattice,

$\mathbf{K}=h\mathbf{a}^{*}+k\mathbf{b}^{*}+l\mathbf{c}^{*},$ (2)

where $\mathbf{a}^{*}$, $\mathbf{b}^{*}$, and $\mathbf{c}^{*}$ are the
reciprocal lattice vectors, and $h$, $k$, and $l$ are constants. The
diffraction condition is defined as

$2\pi\mathbf{G}^{*}=\mathbf{K}.$ (3)

The x-axis of simulation patterns $d$ is the reciprocal of $|\mathbf{G}^{*}|$,
i.e., $d=1/|\mathbf{G}^{*}|$.

The diffraction intensity $I^{WPEM}$ on each diffraction vector
$\mathbf{G}^{*}$ for a single phase is determined by

$I^{\text{WPEM}}(\mathbf{G}^{*})=SF_{k}^{*}F_{k}\varnothing
LPOD+I^{\text{BG}},$ (4)

where $S$ denotes the scale factor, $F_{k}$ is the structure factor,
$F_{k}^{*}$ is the complex conjugate of $F_{k}$, $\varnothing_{k}$ is the
profile function, $L_{k}$ is the Lorentz-polarization factor, $P_{k}$ is the
multiplicity, $O_{k}$ is the preferred orientation factor, $D_{k}$ is the
Debye-Waller factor, and $I^{\text{BG}}$ is the background intensity. The
structure factor is computed as:

$F_{k}=\sum_{j=1}^{N}f_{j}e^{2\pi i\mathbf{G}^{*}\cdot\mathbf{R}},$ (5)

where $f_{j}$ is the form factor [18] in XRD, $\mathbf{R}$ is the lattice
coordinate of atom $j$, and $N$ is the total number of atoms in a lattice
cell. The profile function ($\varnothing_{k}$) is a Voigt function [2],

$\varnothing_{k}=\frac{1}{\sigma\sqrt{2\pi}}\int_{-\infty}^{\infty}\left[\frac{\gamma}{(2\theta-t)^{2}+\gamma^{2}}\right]\exp\left(-\frac{(2\theta-t)^{2}}{2\sigma^{2}}\right)dt,$
(6)

where $\theta=\arcsin{\left(\frac{\lambda|\mathbf{G}^{*}|}{2}\right)}$. Peak
broadening is correlated with the Full Width at Half Maximum (FWHM, $\Gamma$),
where $2\gamma=2\sqrt{2\ln{2}}\sigma=\Gamma$ [3]. $\Gamma$ is calculated by
Scherrer’s equation [39] related to finite grain size.

The Lorentz-polarization $L_{k}$ is calculated by,

$L_{k}=\frac{1+\cos^{2}{2\theta}}{\sin^{2}{\theta}\cos{\theta}}.$ (7)

The multiplicity $P_{k}$ is determined by counting the number of diffraction
vectors present within an Ewald diffraction sphere. The Debye-Waller factor
$D_{k}$ is calculated by ,

$D_{k}=e^{-2M},$ (8)

where
$M=\frac{6h^{2}T}{mk\Theta^{2}}\left(\varnothing\left(\frac{\Theta}{T}\right)+\frac{\Theta}{4T}\right)\left(\sin^{2}{\theta}\right)/\lambda$,
$h$ is Planck’s constant, $m$ is atom mass, $k$ is Boltzmann constant,
$\Theta$ is the average characteristic temperature, $T$ is absolute
temperature, and $\varnothing(\Theta/T)$ is the Debye function. The
diffraction pattern, expressed as a function of $d$, is independent of
$\lambda$.

The state of the specimen is simulated by:

  * •

Finite grain size: the average grain size is set as a random number in the
range of 2 nm to 50 nm to replicate the degree of experimental broadening
[36]. Instrumental broadening becomes apparent in the experimental patterns as
convolution with the crystal peak occurs. Typically, in the refinement
process, it is common to separate observed peaks into Voigt and instrumental
components. However, quantifying the instrumental component proves challenging
as it varies with the diffraction angle. Therefore, in our simulations, we opt
for a smaller grain size than realistic to accurately replicate the degree of
experimental broadening.

  * •

Orientation: the ideal powder specimen is assumed to have no orientation,
however, this is impossible. The orientation effect arises from the uneven
distribution of small grains in the incident beam, leading to an uneven
distribution of reciprocal sites across the reciprocal spheres of the powder
specimen. To simulate the impact of orientation, we set the intensity by
perturbation within a 40% range based on the ideal simulation to mimic the
orientation randomness.

  * •

Thermal vibration: the temperature is converted to the kinetic energy of
atoms, which is simulated by allowing atoms to shift from their average
positions within a range of 0.01-0.5 angstrom.

  * •

Internal stress: internal stress is simulated by applying elastic deformation
of the recorded lattice constant by up to 10%.

  * •

Instrument zero shifting: the zero shift is simulated by randomly translating
$2\theta$ within -1.2 to 1.2 degrees.

  * •

Instrument noise: 2% Gaussian white noise is added to the entire pattern to
reflect instrument noise.

  * •

Inelastic Scattering: A sixth-order polynomial function is employed to
simulate the background distribution, encompassing phenomena such as Compton
scattering, fluorescence, and multiple scattering. This simulated background
is then integrated into the XRD pattern with a 2% ratio.

###  A.5 Crystal and diffraction

Among various investigative methods, diffraction analysis stands out as
exceptionally potent for probing microstructure, primarily due to its
sensitivity to atomic arrangement and the element specificity of atom
scattering power. Each intensity maximum, termed a line profile or peak,
within a diffraction pattern reflects the atomic arrangement along certain
direction of the diffracting material, as depicted in Figure 6.

Powder X-ray diffraction, in particular, furnishes a remarkably diverse array
of structural details, encoded in the material- and instrument-specific
distribution of coherently scattered monochromatic wave intensity, with
wavelengths corresponding to lattice spacing. The X-rays are generated by a
cathode ray tube, filtered to produce monochromatic radiation, collimated for
concentration, and directed towards the sample. When conditions satisfy
Bragg’s Law, which relates the wavelength of electromagnetic radiation to the
diffraction angle and lattice spacing in a crystalline sample, the incident
rays interact with the sample to produce constructive interference and a
diffracted ray.

The diffracted X-rays are subsequently detected, processed, and quantified. By
scanning the sample across a range of diffraction angles, all possible
diffraction directions of the lattice are accessible due to the random
orientation of powdered material.

Conversion of diffraction peaks to d-spacings facilitates mineral
identification, since each mineral possesses a unique set of d-spacings. This
identification is typically accomplished through comparison with standard
reference patterns.

###  A.6 Symmetry recognition in structure determination

Pattern refinement [46, 47] is essential for accurately determining the
crystal structure in diffraction practices. In XRD refinement, the critical
initial step involves identifying the crystalline phase of the given pattern.
This phase identification is crucial as it facilitates the calculation of the
static structure factor [56], which aids in determining atom sites during
refinement. The primary step in refinement is establishing the geometry of the
crystal lattice cell by solving the diffraction indices corresponding to a set
of lattice planes for each diffraction peak, a process known as indexing
calculation [49].

Utilizing existing crystal databases, the commonly employed search-match
approach retrieves potential structures that match the observed pattern,
essentially performing in-library identification. The matched structure, along
with basic crystallographic information, including crystal symmetry, serves as
a foundational element for further analysis.

Whether the observed patterns are from in-library or out-of-library crystals,
symmetry identification combined with indexing is a generic method for
determining lattice geometry to initiate the refinement process. This is why
many researchers in materials science and physics pursue a general method to
derive the symmetry of structures based on diffraction patterns. Once the
fundamental crystallographic information is acquired, techniques such as
pattern decomposition and Rietveld refinement [46, 47, 24] come into play.
These methodologies facilitate the determination of atom sites, temperature
factors, grain sizes, residual stress, and other intricate structural details
from the diffraction patterns on a case-by-case basis, thereby contributing to
the comprehensive elucidation of a crystal structure.

Figure 6: Experimental procedure for recording XRD patterns.

###  A.7 Whole Powder Pattern Fitting and Refinement

Structure refinement is an effective method for determining crystal
structures. Traditionally, refinement begins with a set of reasonably
estimated parameters with physical significance. Accurately identifying the
structure’s space group aids in establishing rational parameters. However,
without prior structural knowledge, this process becomes trial and error.
Although identifying the space group initiates the process, its validation
relies on refinement outcomes.

A significant advancement in powder diffraction fitting for structure
refinement emerged with the Rietveld method[46, 47], which pioneered whole
pattern fitting over the analysis of individual, non-overlapping Bragg
diffraction peaks. The Whole Powder Pattern Fitting (WPPF) approach within the
Rietveld method uses profile intensity calculations and a least-squares
algorithm for structure refinement. By minimizing the disparities between
observed experimental profiles and theoretical profiles, it extracts all
structural information. Once fitting reaches its limit, the parameters in the
theoretical model represent the only determinable physical information.
SimXRD’s pattern simulation also relies on the structural information
contained within the theoretical model. The Pawley[44] and Le Bail[25]
methods, two widely used WPPF techniques, are developed after the Rietveld
method.

These parameters with physical significance are diverse, and one important
type is peak shape parameters. The parameters of each diffraction peak
(positions, intensities, and shapes) within a whole XRD pattern offer detailed
structural insights from different aspects, making their quantitative and
accurate extraction from the overall XRD profile highly significant. This
quantification of peak information and the subsequent derivation of physical
parameters constitute the essence of the refinement endeavor.

Numerous factors influence diffraction peak shapes, creating a multiphysical
coupling effect (see Figure 7). The full pattern fitting in the commercial
TOPAS package[13], also known as the fundamental parameters approach, employs
a convolution function to describe peak shapes, as illustrated by the
equation:

$y(x)=[W(x)*G(x)]*S(x)$ (9)

where * denotes the convolution process, and $W(x)$, $G(x)$, and $S(x)$
represent contributions to the observed XRD pattern from the emission source,
instrumental factors, and the tested specimen, respectively.

The simulation process of SimXRD considers the multiphysical coupling process
to generate a wide range of diffraction patterns.

Figure 7: The emission (W), instrumental factor (G), and the tested specimen
(S) are convoluted to form the diffraction peak.

###  A.8 Dataset Card

#### Motivation

  1. 1.

For what purpose was the dataset created? Was there a specific task in mind?
Was there a specific gap that needed to be filled? Please provide a
description.

     * •

The dataset addresses a fundamental task in crystallography: identifying
crystal types by analyzing XRD patterns. Traditional methods involve a time-
consuming search-match process through known diffraction patterns. Recent
studies have advanced this by training neural networks on simulated XRD
datasets to classify patterns by specific symmetries, though these often focus
on specific materials. To improve generalization, models need comprehensive
coverage of structures and alignment with experimental patterns under various
conditions. Creating such high-fidelity simulated datasets is challenging due
to the complex simulation processes involved. SimXRD-4M was developed to
overcome these challenges and fill this gap.

  2. 2.

Who created the dataset (e.g., which team, research group) and on behalf of
which entity (e.g., company, institution, organization)?

     * •

The authors created the dataset.

  3. 3.

Who funded the creation of the dataset? If there is an associated grant,
please provide the name of the grantor and the grant name and number.

     * •

N/A

  4. 4.

Any other comments?

     * •

No.

#### Composition

  1. 1.

What do the instances that comprise the dataset represent (e.g., documents,
photos, people, countries)? Are there multiple types of instances (e.g.,
movies, users, and ratings; people and interactions between them; nodes and
edges)? Please provide a description.

     * •

Each row in the SimXRD dataset represents a diffraction pattern, consisting of
3051 pairs of values representing lattice plane distance (d) and diffraction
intensity (I). Additionally, each instance includes information such as
chemical formula (string), atomic elements (list), space group (integer), and
crystal system (integer).

  2. 2.

How many instances are there in total (of each type, if appropriate)?

     * •

SimXRD-4M consists of 4,065,346 simulated powder X-ray diffraction patterns

  3. 3.

Does the dataset contain all possible instances or is it a sample (not
necessarily random) of instances from a larger set? If the dataset is a
sample, then what is the larger set? Is the sample representative of the
larger set (e.g., geographic coverage)? If so, please describe how this
representativeness was validated/verified. If it is not representative of the
larger set, please describe why not (e.g., to cover a more diverse range of
instances, because instances were withheld or unavailable).

     * •

SimXRD-4M does not contain all possible instances of XRD patterns. However, it
covers all the crystals contained in the latest Material Project [20] (almost
all inorganic crystals), denoted as MP-2024.1. The diffraction pattern for a
given crystal varies depending on various physical settings. We provided 33
coupling conditions for diffraction. Since many physical settings affecting
diffraction patterns are continuous values, it is impossible to provide all
real situations. The specific settings are determined based on our domain
knowledge and experience in XRD practice.

  4. 4.

What data does each instance consist of? “Raw” data (e.g., unprocessed text or
images) or features? In either case, please provide a description.

     * •

The each instance includes:

     * •

element: A list of chemical symbols representing the elements in the crystal
(e.g., [’S’, ’Pb’, ’O’]).

     * •

latt_dis: A list of lattice plane distances.

     * •

intensity: A list of diffraction intensities.

     * •

spg: An integer representing the space group number.

     * •

crysystem: An integer representing the crystal system number.

  5. 5.

Is there a label or target associated with each instance? If so, please
provide a description.

     * •

SimXRD has clearly categorized labels of crystal systems (integers, 1-7) and
space groups (integers, 1-230).

  6. 6.

Is any information missing from individual instances? If so, please provide a
description explaining why this information is missing (e.g. because it was
unavailable). This does not include intentionally removed information but
might include, e.g., redacted text.

     * •

No.

  7. 7.

Are relationships between individual instances made explicit (e.g., users’
movie ratings, social network links)? If so, please describe how these
relationships are made explicit.

     * •

No.

  8. 8.

Are there recommended data splits (e.g., training, development/validation,
testing)? If so, please provide a description of these splits, explaining the
rationale behind them.

     * •

No.

  9. 9.

Are there any errors, sources of noise, or redundancies in the dataset? If so,
please provide a description.

     * •

No.

  10. 10.

Is the dataset self-contained, or does it link to or otherwise rely on
external resources (e.g., websites, tweets, other datasets)? If it links to or
relies on external resources, a) are there guarantees that they will exist and
remain constant over time; b) are there official archival versions of the
complete dataset (i.e., including the external resources as they existed at
the time the dataset was created); c) are there any restrictions (e.g.,
licenses, fees) associated with any of the external resources that might apply
to a dataset consumer? Please provide descriptions of all external resources
and any restrictions associated with them, as well as links or other access
points, as appropriate.

     * •

SimXRD relies on the crystal database. Currently, it contains all the recorded
data in the Material Project (MP) crystal database. The MP database is open-
sourced. Further development of SimXRD may require supplementing new crystal
structures after a certain period when significant new crystals are added to
the MP database.

  11. 11.

Does the dataset contain data that might be considered confidential (e.g.,
data that is protected by legal privilege or by doctor– patient
confidentiality, data that includes the content of individuals’ non-public
communications)? If so, please provide a description.

     * •

No, there are no confidential datapoints in SimXRD.

  12. 12.

Does the dataset contain data that, if viewed directly, might be offensive,
insulting, threatening, or might otherwise cause anxiety? If so, please
describe why.

     * •

No.

  13. 13.

Does the dataset identify any subpopulations (e.g., by age, gender)? If so,
please describe how these subpopulations are identified and provide a
description of their respective distributions within the dataset.

     * •

No.

  14. 14.

Is it possible to identify individuals (i.e., one or more natural persons),
either directly or indirectly (i.e., in combination with other data) from the
dataset? If so, please describe how.

     * •

No.

  15. 15.

Does the dataset contain data that might be considered sensitive in any way
(e.g., data that reveals race or ethnic origins, sexual orientations,
religious beliefs, political opinions or union memberships, or locations;
financial or health data; biometric or genetic data; forms of government
identification, such as social security numbers; criminal history)? If so,
please provide a description.

     * •

No.

  16. 16.

Any other comments?

     * •

No.

#### Collection Process

  1. 1.

How was the data associated with each instance acquired?Was the data directly
observable (e.g., raw text, movie ratings), reported by subjects (e.g., survey
responses), or indirectly inferred/derived from other data (e.g., part-of-
speech tags, model-based guesses for age or language)? If data was reported by
subjects or indirectly inferred/derived from other data, was the data
validated/verified? If so, please describe how.

     * •

The crystal structures in this study were sourced from the Materials Project
database. We used the latest dataset, MP-2024.1, containing 154,718 structures
as of January 2024. To ensure data quality, we used Spglib to check for
consistency in space group numbers and atomic arrangements, excluding
structures with broken symmetry, duplication, or discrepancies. We retained
only structures with up to 500 atoms per lattice cell, covering nearly all
inorganic materials, resulting in 119,569 screened structures. The XRD
patterns, influenced by the crystal’s structure and practical factors like
specimen state and instrumental parameters, were simulated using custom
software WPEM.

  2. 2.

what mechanisms or procedures were used to collect the data (e.g., hardware
apparatus or sensor, manual human curation, software program, software
API)?How were these mechanisms or procedures validated?

     * •

The crystal database MP and screening package Spglib are open-sourced. The
simulation software is WPEM, homemade and not completely open-sourced yet, but
its effectiveness has been recognized by multiple peer researches in material
and physical communities[29, 6, 54, 45, 16]. Additionally, the details of the
simulation process are provided in mathematics in Appendix A.4.

  3. 3.

Over what timeframe was the data collected? Does this timeframe match the
creation timeframe of the data associated with the instances (e.g., recent
crawl of old news articles)?If not, please describe the timeframe in which the
data associated with the instances was created.

     * •

Crystal data recorded in the MP database up to January 2024 were retrieved.
The simulated data were generated between January and May 2024.

  4. 4.

Were any ethical review processes conducted (e.g., by an institutional review
board)?If so, please provide a description of these review processes,
including the outcomes, as well as a link or other access point to any
supporting documentation.

     * •

No ethical problems were involved.

  5. 5.

Did you collect the data from the individuals in question directly, or obtain
it via third parties or other sources (e.g., websites)?

     * •

The crystal database MP is open for acquisition.

  6. 6.

Did the individuals in question consent to the collection and use of their
data?If so, please describe (or show with screenshots or other information)
how consent was requested and provided, and provide a link or other access
point to, or otherwise reproduce, the exact language to which the individuals
consented.

     * •

Not applicable.

  7. 7.

If consent was obtained, were the consenting individuals provided with a
mechanism to revoke their consent in the future or for certain uses?If so,
please provide a description, as well as a link or other access point to the
mechanism (if appropriate).

     * •

Not applicable.

#### Preprocessing/cleaning/labeling

  1. 1.

Was any preprocessing/cleaning/labeling of the data done (e.g., discretization
or bucketing, tokenization, part-of-speech tagging, SIFT feature extraction,
removal of instances, processing of missing values)?If so, please provide a
description. If not, you may skip the remainder of the questions in this
section.

     * •

All spectrum data contained in SimXRD provide full information with XRD
features and labels. We did not perform any further preprocessing of the data.

  2. 2.

Is the software used to preprocess/clean/label the instances available?If so,
please provide a link or other access point.

     * •

We provide a data loader associated with our dataset as dataloader.

#### Uses

  1. 1.

Has the dataset been used for any tasks already?If so, please provide a
description.

     * •

Not yet. We offer benchmarks to illustrate its potential in library space
group and crystal system classification tasks, as illustrated in the section :
Use Cases of SimXRD Dataset.

  2. 2.

Is there a repository that links to any or all papers or systems that use the
dataset?If so, please provide a link or other access point.

     * •

Please refer to SimXRD-4M.

  3. 3.

Is there anything about the composition of the dataset or the way it was
collected and preprocessed/cleaned/labeled that might impact future uses?For
example, is there anything that a future user might need to know to avoid uses
that could result in unfair treatment of individuals or groups (e.g.,
stereotyping, quality of service issues) or other undesirable harms (e.g.,
financial harms, legal risks) If so, please provide a description. Is there
anything a future user could do to mitigate these undesirable harms?

     * •

Not applicable.

#### Distribution

  1. 1.

Will the dataset be distributed to third parties outside of the entity (e.g.,
company, institution, organization) on behalf of which the dataset was
created?If so, please provide a description.

     * •

Yes, the dataset will be open-source.

  2. 2.

How will the dataset be distributed (e.g., tarball on website, API,
GitHub)Does the dataset have a digital object identifier (DOI)?

     * •

The dataset can be acquired from the website SimXRD-4M.

  3. 3.

When will the dataset be distributed?

     * •

Starting from June 1, 2024.

  4. 4.

Will the dataset be distributed under a copyright or other intellectual
property (IP) license, and/or under applicable terms of use (ToU)? If so,
please describe this license and/or ToU, and provide a link or other access
point to, or otherwise reproduce, any relevant licensing terms or ToU, as well
as any fees associated with these restrictions.

     * •

CC-BY-4.0

  5. 5.

Will the dataset be distributed under a copyright or other intellectual
property (IP) license, and/or under applicable terms of use (ToU)?If so,
please describe this license and/or ToU, and provide a link or other access
point to, or otherwise reproduce, any relevant licensing terms or ToU, as well
as any fees associated with these restrictions.

     * •

No.

  6. 6.

Have any third parties imposed IP-based or other restrictions on the data
associated with the instances?If so, please describe these restrictions, and
provide a link or other access point to, or otherwise reproduce, any relevant
licensing terms, as well as any fees associated with these restrictions.

     * •

No.

  7. 7.

Do any export controls or other regulatory restrictions apply to the dataset
or to individual instances?If so, please describe these restrictions, and
provide a link or other access point to, or otherwise reproduce, any
supporting documentation.

     * •

No, the dataset is open for any application.

#### Maintenance

  1. 1.

Who will be supporting/hosting/maintaining the dataset?

     * •

SimXRD-4M will host the dataset and we will maintain the dataset.

  2. 2.

How can the owner/curator/manager of the dataset be contacted (e.g., email
address)?

     * •

The authors can be contacted via<EMAIL_ADDRESS>
  3. 3.

Is there an erratum?If so, please provide a link or other access point.

     * •

No

  4. 4.

Will the dataset be updated (e.g., to correct labeling errors, add new
instances, delete instances)?If so, please describe how often, by whom, and
how updates will be communicated to users (e.g., mailing list, GitHub)?

     * •

There are no older versions of SimXRD-4M.

     * •

If any updates are necessary in future development, we will provide essential
updates and communicate all revisions and changes through the database website
SimXRD-4M. We will provide the updated version and maintain a history of
versions.

  5. 5.

If the dataset relates to people, are there applicable limits on the retention
of the data associated with the instances (e.g., were individuals in question
told that their data would be retained for a fixed period of time and then
deleted)?If so, please describe these limits and explain how they will be
enforced.

     * •

Not applicable.

  6. 6.

Will older versions of the dataset continue to be
supported/hosted/maintained?If so, please describe how. If not, please
describe how its obsolescence will be communicated to users.

     * •

There are no older versions of SimXRD-4M.

     * •

If any updates are necessary in future development, all older versions of the
dataset will continue to be supported/hosted/maintained. The database website
SimXRD-4M will record all historical datasets and the newest dataset versions
along with commit histories.

  7. 7.

If others want to extend/augment/build on/contribute to the dataset, is there
a mechanism for them to do so?If so, please provide a description. Will these
contributions be validated/verified? If so, please describe how. If not, why
not? Is there a process for communicating/distributing these contributions to
other users? If so, please provide a description.

     * •

Yes, we accept user contributions to extend/augment/build on/contribute to the
dataset. If any user wishes to contribute, they need to provide crystal data
and simulation software for strict screening by us to ensure data quality. The
application can be launched by submitting a pull request on our dataset GitHub
repository SimXRDGithub or by contacting the author directly for data merging.

#### Croissant metadata

  1. 1.

URL to Croissant metadata record documenting the dataset/benchmark available
for viewing and downloading by the reviewers. You can create your Croissant
metadata using e.g. the Python library available here:
https://github.com/mlcommons/croissant.

     * •

A sample dataset is available for viewing and downloading, hosted by Hugging
Face Datasets: SimXRDreview.

     * •

The sample dataset contains 5,000 training patterns, 1,000 validation patterns
and 2,000 test patterns.

     * •

The code to access the dataset metadata is provided below:

⬇

1 pip install mlcroissant

⬇

1 import mlcroissant as mlc

2

3 url =
"https://huggingface.co/datasets/caobin/SimXRDreview/raw/main/simxrd_croissant.json"

4 dataset_info = mlc.Dataset(url).metadata.to_json()

5 print(dataset_info)

Listing 1: Example Python code