synthesis and tuning of multifunctional materials at high...

ACTAUNIVERSITATIS

UPSALIENSISUPPSALA

2020

Digital Comprehensive Summaries of Uppsala Dissertationsfrom the Faculty of Science and Technology 1883

Synthesis and Tuning ofMultifunctional Materials at HighPressure

LEI LIU

ISSN 1651-6214ISBN 978-91-513-0825-8urn:nbn:se:uu:diva-397718

Dissertation presented at Uppsala University to be publicly examined in Axel Hambergsalen,Geocentrum, Villavägen 16, Uppsala, Tuesday, 28 January 2020 at 10:00 for the degree ofDoctor of Philosophy. The examination will be conducted in English. Faculty examiner:Professor Ronald Miletich-Pawliczek (Universität Wien).

AbstractLiu, L. 2020. Synthesis and Tuning of Multifunctional Materials at High Pressure. DigitalComprehensive Summaries of Uppsala Dissertations from the Faculty of Science andTechnology 1883. 71 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0825-8.

At the present stage, human society is developing at an unprecedented speed, facing anemergence of highly pressing challenges, e.g., information explosion, energy productionproblems, environmental pollution, climate problems. Functional materials with tailoredproperties are considered as holding a key to solving these problems. In this thesis, high-pressuretechniques were employed to synthesize and tune the properties of multiferroic materialsrelevant to spintronic and light-harvesting applications, and multifunctional high-entropy alloys.

Melanostibite (Mn2FeSbO6, MFSO) is a very rare mineral discovered in Sweden. Previousstudies indicate it is a potential multiferroic material with foreseen applications in informationstorage and spintronic devices. However, its multiferroic phase has not been synthesized yet.Herein, the structural evolution of MFSO was studied up to ~50 GPa, and the LiNbO3-typeMFSO was synthesized at high pressure and moderate temperature. As a polar structure material,the LiNbO3-type MFSO represents a promising candidate for multiferroic materials. The doubleperovskite, Pb2CoTeO6, was also compressed to ~60 GPa, while no polar phase was discovered.The obtained results provide guidance to the synthesis of new multiferroic double perovskite.

Solar energy is a promising alternative to fossil fuels and thus a viable solution to theglobal energy problem. Light-harvesting materials, which absorb sunlight and transform itinto electricity by the photovoltaic effect, represent the core part of solar cells. Currently,the dominant commercial light-harvesting material is silicon. However, silicon and recentlyemerged organic-inorganic perovskites have several drawbacks. Multiferroic oxides areconsidered as stable and nontoxic light-harvesting materials. But, their bandgap energies aregenerally too large for photovoltaic applications. Herein, high-pressure technique was appliedto treat Mn3TeO6, and a quenchable phase of Mn3TeO6 displaying a greatly narrowed bandgapwas synthesized. The measured absorption spectrum of the quenched phase reveals that it maybe suitable for photovoltaic applications. The present research opens a green way to tune thebandgap energy of multiferroic.

High-entropy alloys (HEAs) were first synthesized in 2004. However, knowledge of thisnew class of promising alloys is still very limited, even in very fundamental aspects. Thepresent results reveal that lattice distortion plays important roles in the phase transition of HEAs,and demonstrate the future possibility of designing the Invar high-entropy alloy, a promisingstructural material. The results show that it is possible to combine several practical propertiesin a single alloy, which will widen the range of applications of HEAs.

The presented research demonstrates that high-pressure represents an effective way to tunevarious properties of materials, as well as can be applied for the synthesis of materials withexotic properties which are usually not stable or attainable at ambient conditions.

Keywords: double perovskite, multiferroic, bandgap engineering, high-entropy alloy, highpressure

Lei Liu, Department of Earth Sciences, Mineralogy Petrology and Tectonics, Villav. 16,Uppsala University, SE-75236 Uppsala, Sweden.

© Lei Liu 2020

ISSN 1651-6214ISBN 978-91-513-0825-8urn:nbn:se:uu:diva-397718 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-397718)

Dedicated to my wife Lei for her

endless love and support!

List of Papers

This thesis is based on the following papers, which are attached in the end.

I Pressure-induced polymorphism and piezochromism in Mn2FeSbO6. Liu, L., Song, H.X., Li, X., Zhang, D., Mathieu, R., Ivanov, S., Skogby, H., Lazor, P., Applied Physics Letters, (2019). 114:162903.

II Pressure tuning of octahedral tilt in the ordered double perovskite Pb2CoTeO6. Liu, L., Ivanov, S., Mathieu, R., Weil, M., Li, X., Lazor, P., Journal of Alloys and Compounds, (2019). 801:310-317.

III Bandgap engineering in Mn3TeO6: giant irreversible bandgap re-duction triggered by pressure. Liu, L., Skogby, H., Ivanov, S., Weil, M., Mathieu, R., Lazor, P., Chemical Communications, (2019). 55:12000-12003.

IV Lattice distortion-induced sluggish phase transition in CoCrFe-NixAl1-x (x = 0.5, 0.75) high-entropy alloys at high pressures. Liu, L., Lazor, P., Li, X., High Pressure Research, (2019). DOI: 10.1080/08957959.2019.1653865.

V Pressure-induced magnetovolume effect in CoCrFeAl high-en-tropy alloy. Liu, L., Huang, S., Vitos, L., Dong, M., Bykova, E., Zhang, D., Almqvist, B.S.G., Ivanov, S., Rubensson, J.E., Varga, B., Varga, L.K., Lazor, P., Communications Physics, (2019). 2:42.

Reprints were made with permission from the respective publishers.

Personal Contributions

My contributions to the published papers are listed as follows: Paper I: I conceived the project with P. Lazor. I performed the Raman exper-iment and part of the synchrotron XRD experiment. I analyzed the data and I carried out data interpretation in collaboration with co-authors. I drafted the main text of the manuscript. Paper II: I conceived the project with P. Lazor. I performed the Raman and synchrotron XRD experiments. I analyzed the data and I carried out data in-terpretation in collaboration with co-authors. I drafted the main text of the manuscript. Paper III: I conceived the project with P. Lazor. I performed the Raman and UV-vis experiments. I analyzed the data and I carried out data interpretation in collaboration with co-authors. I drafted the main text of the manuscript. Paper IV: I conceived the project. I performed the synchrotron XRD experi-ments. I analyzed the data and I carried out data interpretation in collaboration with co-authors. I drafted the main text of the manuscript. Paper V: I conceived the project with P. Lazor. I performed the magnetic measurement and part of the synchrotron XRD experiments. I analyzed the data and I carried out data interpretation in collaboration with co-authors. I drafted the main text of the manuscript.

Contents

1. Introduction ........................................................................................... 9

2. Methodology ........................................................................................ 12 2.1 Diamond anvil cell ............................................................................. 12

2.1.1 Diamond anvils ........................................................................... 12 2.1.2 Gaskets ........................................................................................ 14 2.1.3 Pressure transmitting medium .................................................... 14 2.1.4 Pressure scales ............................................................................ 15 2.1.5 Sample preparation in DAC ........................................................ 16

2.2 In situ Synchrotron X-ray diffraction ................................................. 19 2.2.1 Synchrotron radiation source ...................................................... 21 2.2.2 X-ray diffraction ......................................................................... 22 2.2.3 High-pressure X-ray diffraction beamline .................................. 23 2.2.4 XRD data processing .................................................................. 24

2.3 Raman scattering ................................................................................ 25 2.3.1 Principle of Raman scattering ..................................................... 26 2.3.2 Raman spectroscopic system ...................................................... 29

2.4 UV-vis absorption spectroscopy ........................................................ 30

3. Double perovskites (A2BB´O6) at high pressures ................................. 33 3.1 Perovskite oxides ................................................................................ 33 3.2 Double perovskite polar magnets ....................................................... 35 3.3 Polymorphism and piezochromism in Mn2FeSbO6 ............................ 35 3.4 Pressure-induced octahedral tilting in Pb2CoTeO6 ............................. 38

4. Bandgap engineering in multiferroic oxide Mn3TeO6 ......................... 40 4.1 Perovskite solar cells .......................................................................... 40 4.2 Photovoltaics with multiferroic oxides ............................................... 42 4.3 Bandgap engineering in Mn3TeO6 ...................................................... 42

5. Pressure-induced phase transitions of high-entropy alloys .................. 45 5.1 The concept of high-entropy alloy ..................................................... 45 5.2 Phase selection rules of HEA ............................................................. 46 5.3 Lattice distortion ................................................................................ 49 5.4 Lattice distortion-induced phase transition ........................................ 51 5.5 Magnetovolume effect in HEAs ......................................................... 52

6. Conclusions and perspectives .............................................................. 54

7. Summary in Swedish ........................................................................... 57

Acknowledgments......................................................................................... 60

References ..................................................................................................... 62

9

1. Introduction

Historically, the use of progressively more advanced materials promoted the development of human civilization, which is even reflected in the names of several important archeological periods in human history: Stone Age, Bronze Age, Iron Age… and now the Information Age called also the Silicon Age. Nowadays, in the time of a rapidly developing modern society with a growing population, various challenges have emerged, e.g., sustainable energy produc-tion, a radically increasing pace of environmental pollution, and climatic change. In order to address these negative developments, on the materials science side, great efforts are devoted to designing novel functional materials that hold a promise to enable the emergence of new green technologies miti-gating if not eliminating these problems. In today´s Information Age, a massive amount of data is continuously pro-duced, calling for cheaper and smaller storage devices. Multiferroic oxides, which simultaneously exhibit properties of ferromagnetism and ferroelectric-ity, may hold the future for the ultimate information storage devices (Scott, 2007; Spaldin and Ramesh, 2019; Manipatruni et al., 2019) if the magnetoe-lectric coupling is sufficiently strong. In such a class of materials, the ferroe-lectric state can be switched by a magnetic field and vice versa. This property offers the possibility of a low-power electrical write and non-destructive mag-netic read operations in multiferroic memories. However, the multiferroic ox-ides are rare because of incompatible electronic requirements for dipole and spin orderings (Cai et al., 2017; Hill, 2000; Benedek and Fennie, 2013). Re-cently, double perovskites emerged as a promising platform for designing multiferroic oxides, especially at high pressures (Li et al., 2013; Gilioli and Ehm, 2014). So far, the synthesis of these highly distorted multiferroic double perovskites under high pressure is still a high-cost and low-efficient trial-and-error process, partly due to the very limited knowledge of pressure effect on their structure and properties. In this thesis, the pressure effect on Mn2FeSbO6 and Pb2CoTeO6 was studied, in order to investigate the structural evolution, as well as to search for novel polar multiferroic phases. The energy from fossil fuels (oil, natural gas, and coal) constitutes a major part of the world´s energy consumption today. The atmospheric emissions of CO2 resulting from burning these fuels contribute in a major way to the ob-

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served global warming phenomenon. In addition, at the projected rate of con-sumption, the fossil fuel reserves on the Earth will run out in about a century. Consequently, human society faces an urgent task of searching for green and renewable alternatives to fossil fuels. One of the most promising candidates is solar energy which can be transformed into electricity by the photovoltaic ef-fect in solar cells without negative impacts on the environment. The core part of solar cells is built around light-harvesting materials. The dominant light-harvesting material in commercial solar cells is silicon. However, the fabrica-tion and performance drawbacks of theses photovoltaic materials stimulate a search for the next generation of photovoltaic materials. During the last dec-ade, organic-inorganic hybrid metal perovskites have been widely investi-gated as a very promising alternative to the presently used commercial solar technologies due to their high absorption coefficient, tunable bandgap energy, long charge carrier diffusion length, high defect tolerance, abundant elemental composition, and low-cost and low-temperature fabrication methods (Bakr and Mohammed, 2017; Li et al., 2019; and reference therein). The power con-version efficiency (PCE) of perovskite solar cells (PSCs) surpasses the top PCE of semiconductors and reaches a value as high as 23.7 % (reported by NREL), making it comparable to the top efficiency of silicon. But several dis-advantages of PSCs remain to be overcome before their viability for commer-cial applications. These include chemical instability and serious environmen-tal toxicity of lead. Recent research identified multiferroic oxides as represent-ing a stable and nontoxic alternative to organic-inorganic hybrid metal perov-skites. However, the bandgap energies of multiferroic oxides are generally too large for photovoltaic applications. In the present research, multiferroic oxide Mn3TeO6 was subjected to a high-pressure in order to explore the possibility of tuning its bandgap energy. In some applications, engineering materials are exposed to extreme conditions (e.g., intense irradiation and high temperature), which make these materials becoming soft or lead to their failure. Materials with specifically tailored su-perior properties are needed to address the challenge of withstanding the ad-verse effect. In 2004, two groups (Yeh et al., 2004; Cantor et al., 2004) intro-duced a new class of alloys – high-entropy alloys with revolutionary metal-lurgy principles and properties superior to conventional alloys (such as high fracture toughness, excellent strength, superconductivity, high resistance to corrosion, and good catalytic performance). However, current knowledge about this group of materials is incomplete in many aspects, including those pertaining to an efficient synthesis and understanding of fundamental proper-ties. These limitations hinder HEAs from finding the way from research la-boratories to industries. Local lattice distortion (LD), originating from an atomic size mismatch, represents the intrinsic and essential characteristics of HEAs, and significantly influences the phase stability, microstructure, me-chanical, and transport properties of HEAs. Consequently, the LD holds a key

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to understanding the structure-property relationships in HEAs. In the present study, the LD effect on the phase stability of CoCrFeNixAl1-x (x = 0.5, 0.75) was investigated at high pressure. Moreover, our study on CoCrFeAl HEA demonstrated the possibility of combining excellent mechanical properties with exotic functional properties in a single HEA. In this thesis, the polar-structure Mn2FeSbO6, representing a potential polar multiferroic material, was synthesized under high pressure and moderate tem-perature conditions. These achieved results will benefit the synthesis of double perovskite multiferroic materials in the future. The high-pressure treated mul-tiferroic oxide Mn3TeO6 turned out to possess a much narrowed bandgap, suit-able for photovoltaic applications. This demonstrates that the high-pressure treatment has the potential of providing green and effective methods to tune the bandgap of multiferroic oxides. The LD was discovered to play an im-portant role in the phase stability of HEAs. The present research reveals that CoCrFeAl possibly is an Invar high-entropy alloy featuring the merits of both types of these alloys. This points out the feasibility of designing alloys that combine exotic functional properties with excellent mechanical properties. The results presented in this thesis provide several examples of using high pressure for the synthesis of multifunctional materials and for refining their properties. In a broader perspective, they also imply that high-pressure tech-niques will likely play an important role in the search for advanced materials, the use of which will aid human society in finding its way towards a sustain-able development.

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2. Methodology

2.1 Diamond anvil cell Diamond Anvil Cell (DAC) was invented by Alvin Van Valkenburg, Charles E. Weir, Ellis R. Lippincott, and Elmer N. Bunting at the National Bureau of Standard (today National Institution for Standards and Technology, NIST) in 1958 (Weir et al., 1959; Bassett, 2009). Since then, DAC has become the most powerful and versatile tool for probing the various properties of materials at high pressures and/or high temperatures. The simplicity of DAC and the trans-parency of diamond to a broad range of electromagnetic waves (IR, visible light, X-ray), makes it possible to employ various techniques for probing a sample compressed between two diamond anvils, i.e., subjected to high pres-sures. Owing to the developing contributions of the high-pressure community for over six decades, the DAC represents a tool enabling to explore science in the terapascal (TPa) range (Dubrovinsky et al., 2012; 2015; Dubrovinskia et al., 2016; Dewaele et al., 2018; Jenei et al., 2018).

Many different types of DAC have been designed for optimizing the various measurements. However, the heart of DAC remains unchanged since the in-troduction of the gasket. As illustrated in Fig. 2.1, the core of DAC consists of two opposing diamond anvils, between which is the gasket enclosing a sam-ple chamber. The sample, pressure transmitting medium (PTM), and pressure gauge are loaded in the sample chamber. The force applied on the tables of diamond anvils is transmitted directly to the tips of anvils. The pressure on the tips of diamonds is greatly magnified because of the large table/culet area ra-tio.

2.1.1 Diamond anvils Single-crystal diamond is a widely used anvil material because of its excep-tional hardness and transparency to a broad range of electromagnetic waves (ultraviolet, visible, and infrared radiation below 5 eV, as well as X-ray above 5 keV). In addition, its chemical inertness and high melting temperature make it a perfect sample container for the high-pressure and high-temperature re-search. A typical diamond anvil features a small flat culet parallel to the (100) crystallographic plane of the diamond. In the flat geometry, the culet size gen-erally determines the maximum pressure that a DAC can achieve.

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Figure 2.1. Schematic diagram of the essential components of DAC.

In the last several decades, researchers continued optimizing the geometry of diamond anvil, striving to achieve ever-higher pressures. A bevel was first added to the flat anvil and what resulted in achieved pressures higher than 100 GPa (Mao et al., 1976; 1977). The bevel angle was further optimized with the help of finite element simulations and pressures as high as 300 - 400 GPa were generated (Moss et al., 1986; Mao et al., 1989). This design of anvil remains the most popular one up to date, and the pressure limit of this conventional DAC is around 400 GPa (Li et al., 2018). Dubrovinsky et al. invented the double-stage anvil (dsDAC), which features a half-spherical micro-anvil sit-ting on top of the conventional anvil serving as a secondary anvil and intro-ducing an additional compression on the sample (Dubrovinsky et al., 2012). They claimed pressures of 600 GPa, and later 1065 GPa, achieved by employ-ing their design (Dubrovinsky et al., 2015; Dubrovinskia et al., 2016). How-ever, this technique is very challenging, and such high pressures were not re-produced by other groups despite great efforts (Sakai et al., 2015; 2018; Lobanov et al., 2015; Vohra et al., 2015). The technical challenge and difficult sample preparation may limit dsDAC´s application as a routine way of gener-ating high pressures. Recently, Dewaele et al. (2018) changed the geometry of the conventional anvil by introducing a toroidal tiny tip. Pressure of 600 GPa was achieved after optimizing the geometry of the anvil by a trial-and-error procedure. Also, Jenei et al. demonstrated that the toroidal-DAC had the capability to generate pressure beyond 500 GPa (Jenei et al., 2018). Their to-roidal-DAC appears to be more convenient and easier to handle than the dsDAC. At the same time, these results indicate a possibility that the best ge-ometry of anvil has not been discovered yet. Finite Element Method (FEM) can be used to further optimize the geometry of anvils though it already has been employed for optimizing the angle of beveled anvils (Moss et al., 1986; Feng et al, 2016).

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For some experiments, e.g., single-crystal diffraction, a large aperture of DAC is crucial for collecting a broader d-spacing range of diffraction signals. Boeh-ler et al. introduced a new design of anvil with a conical crown that is embed-ded in the conical cavity of the WC seat (Boehler and De Hantsetters, 2004; Boehler, 2006). This conical design enlarges the X-ray aperture to around 85o. Furthermore, the conical support with a larger area allows a significantly higher force load.

In addition to diamond, cubic zirconia (Xu et al., 1996a), sapphire (Xu et al., 1996b), and moissanite (Xu and Mao, 2000) have been used as anvil materials in DAC, while with much lower maximally attainable pressures.

2.1.2 Gaskets The introduction of the gasket represented a large progress in the development of DAC techniques. Bassett stated `Van´s use of gaskets especially for encap-sulating fluids was almost as important a contribution as the invention of the diamond anvil cell itself ` (Bassett, 2009). The gasket placed in between two opposite diamond anvils serves multiple purposes in DAC, including: (1) encapsulating sample assemblage (sample + PTM + ruby chips) in the sample chamber, (2) sustaining pressure, especially a large pressure gradient, through the force of friction between gasket surface and culets, (3) supporting the anvils by the extruded part which encircles the tips of diamonds, (4) preventing the touching of culet rims because of cupping effect at high pressure. The general-use gaskets are selected for their strength and inertness. The T301 stainless steel, Re, and W foils with a thickness of 200-250 μm are commonly used as the materials for gaskets. For specific experiments, e.g., radial diffrac-tion for texture (Merkel et al., 2013), measurement of mechanical properties (Kavner, 2008), or spectroscopic experiments using low energy X-ray < 5 keV (Badro et al., 1999), gasket serves also as an X-ray window. In these experi-ments, X-ray transparent gasket (e.g., Be (Badro et al., 1999; Kavner, 2008), Kapton (Merkel and Yagi, 2005), or composite gaskets (Merkel et al., 2013)) are used.

2.1.3 Pressure transmitting medium Pressure, more exactly, the hydrostatic pressure which means equal pressure in all directions at a given point, is a fundamental thermodynamic variable. Such a hydrostatic pressure state can be achieved in fluids lacking the shear strength. However, commonly, the melting lines of materials as a function of pressure display a positive slope, leading to the inevitable solidification of

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PTM and loss of hydrostatic environment. In experiments, materials with a low strength are chosen as PTM, as well as taking into account their inertness, degree of nonhydrostaticity, and operational convenience. It is not an easy task to measure the degree of hydrostaticity of different PTM. The deviation of pressure across the sample chamber was proposed as an in-dicator of the degree of hydrostaticity (Klotz et al., 2009):

= 1 ( − ) where is the average pressure measured from N different ruby balls distrib-uted in the sample chamber. The hydrostatic limits of commonly used PTM determined according to this criterion are listed in Table 2.1.

Table 2.1. Commonly used pressure transmitting media, along with their hydrostatic limit and the standard deviation of pressure σ at 10 and 20 GPa.

PTM Hydrostatic li-

mit (GPa)

σ @ 10 GPa (GPa)

σ @ 20 GPa (GPa)

NaCla 1.0 0.18 0.5 KBra 2.0 0.20 1.3 CsIa 2.0 0.25 0.5 Silicone oilb 3.0 0.3 2.3 Daphne 7474 @20 °Cb 4.0 0.32 -- 4:1 methanol-ethanolb 10.5±0.5 0 2.2 16:3:1 methanol-ethanol-waterb 10.5±0.5 0 2.0 Nitrogenb >10 0 0.25*, 0.4* Argonb 2.0 0.1 0.2 Neonb 15 0 0.15 Heliumb 23 0 0.05

a Celeste, A., Borondics, F., Capitani, F., 2019. High Pressure Research, https://doi.org/10. 1080/08957959.2019.1666844. b Klotz, S., Chervin, J-C., Munsch, P., Le Marchand, G., 2009. Journal of Physics D: Applied Physics. 42, 075413. * From two independent runs.

2.1.4 Pressure scales Pressure scales represent calibrated relationships P(x) between pressure P and various variables x (e.g., unit cell volume, positions of fluorescence lines and Raman bands). In the early days of modern high-pressure research, the iso-therms P(V) of metals reduced from Hugoniot curves were used as pressure scales. In 1972, Forman et al. proposed that the red-shift of the R lines of ruby fluorescence P(λ) can serve as a pressure gauge in DAC experiments (Froman

16

et al., 1972). Indeed, this P-λ relationship was calibrated against the isotherms of metals under nonhydrostatic (Cu, Mo, Pd, and Ag; Mao et al., 1978) and quasi-hydrostatic (Cu, Ag; Mao et al., 1986) conditions up to around 100 GPa:

= (1 + ∆/ ) − 1 where P is the pressure in GPa, λ0 and ∆λ are the wavelength at ambient pres-sure and pressure-induced shift of the ruby R1 line, respectively, and A = 1904 GPa, B = 5 (nonhydrostatic condition, Mao et al., 1978), A = 1904 GPa, B = 7.665 (quasihydrostatic condition, Mao et al., 1986). These are the most widely used pressure scales in the last several decades. The typical ruby fluorescence spectra and its pressure-induced red-shift are illus-trated in Fig. 2.2.

Figure 2.2. Ruby fluorescence spectra and its pressure-induced red-shift effect.

Following research has shown that calibrating the ruby pressure scale against the reduced isotherms from the shocking wave data introduces too many un-certainties (Holzapfel, 2010). To overcome this drawback, an absolute MgO pressure scale has been proposed by combining the Brillouin scattering and single-crystal X-ray diffraction (XRD) data without any theoretical assump-tions (Zha et al., 2000).

2.1.5 Sample preparation in DAC In this section, sample preparation in a symmetric piston-cylinder DAC is briefly described. Experimental studies presented in this thesis employed the Mao-Bell DACs of so-called symmetric design, equipped with flat diamond anvils and standard WC seat. A stereomicroscope featuring an ample working distance and equipped with a bright light source was used in the alignment and

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loading procedures described below. The DAC and preparation tools are shown in Fig. 2.3.

Figure 2.3. DAC and preparation tools. 1-screw and washers, 2-gasket, 3-WC seats, 4-needle, 5-tweezer, 6-screw drivers, 7-knife, 8-anvil mounting jig, 9-cylinder part of DAC, 10-piston part of DAC.

The following procedures were applied: (1) Cleaning the diamond anvils, the seats, and the cell body thoroughly. (2) Mounting the diamond anvils on the seats.

a. Place the WC seat in the cylinder part of the anvil mounting jig. Make sure that the seat is almost in the center of the jig, then tighten the screw to fix the seat.

b. Place the anvil on top of the seat and roughly in the center of the seat. c. Put the piston part of the jig into the cylinder part and make sure its

tip presses the culet of the anvil. Tighten the screw to apply a moder-ate force on the anvil.

d. Adjust the position of the seat so that the culet of the anvil is in the center of the hole or slit of the seat.

e. Glue the anvil to the seat. In the current studies, the Stycast 2850 FT thermally conductive epoxy with Catalyst 23 LV as a curing agent (the mix ratio is 100:7.5 in weight) was used as a glue. Apply the mixed epoxy (prepared immediately before the diamond mounting) around the anvil. Normally, the epoxy should cover the girdle and not exceed ½ height of the anvil. Wait until the epoxy becomes hard. The jig may be placed on a heating plate in order to shorten the waiting time.

(3) Align the diamond anvils with respect to each other. The anvils should be very well aligned in order to minimize the risk of premature failure of diamonds under pressure.

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a. Adjust the seat positions so that the center of two anvils, in the cylin-der and piston parts of DAC, are well aligned.

b. Rotate the piston part 180° relative to the cylinder part. Usually, the two anvils are not aligned after the rotation. Adjust the two anvils with the same amount until the centers of the two anvils are well aligned again.

c. Rotate the piston part 180° relative to the cylinder part again, and make sure they are in the right rotational orientation. Adjust the two anvils with the same amount until the centers of the two anvils are well aligned again. Then the rotational axes of the two anvils coincide with the rotational axis of the cylindrical cell body.

d. Gently and slowly bring the two diamond culets in contact. Check the degree of parallelism of the culets by looking for the optical interfer-ence fringes. If the two culets are not parallel enough, multiple peri-odic colorful interference fringes appear. If more than two full fringes are visible, the alignment process should be repeated.

(4) Preparing the gasket. As gasket materials, we used the T301 stainless steel circular blanks and square-cut Re foils with the initial thickness of around 250 μm. a. Make a visible mark on the edge of the gasket in order to ensure keep-

ing its correct orientation throughout the sample preparation. b. Use the DAC to compress the gasket until the thickness of the in-

dented region is around 30 μm (dependent on the gasket materials). c. Drill a sample hole in the center of the pre-indented region. Generally,

the diameter of the sample hole is ⅓ to ½ of the culet diameter. In our preparation laboratory, we use an electrical discharge machining to drill the sample hole.

(5) Place the indented and drilled gasket back into DAC. Observing its correct orientation, the gasket will fit the anvil exactly.

(6) Load the sample, ruby balls, and pressure medium. Ideally, the sample is positioned in the center of the sample chamber. Two or three ruby balls are placed in close proximity to the sample in order to measure the repre-sentative pressure (pressure gradient at high pressures may be large). The solid (e.g., NaCl) and liquid (e.g., silicone oil) PTMs are loaded easily. In several experiments, I loaded argon as a PTM using the cryogenic method, which uses liquid nitrogen to liquidity Ar gas (Fig. 2.4). Compressed neon was also loaded as PTM (Liu et al., 2019e) using the COMPRES-GSECARS gas-loading system at GSECARS, sector 13 at the Advanced Photon Source (Rivers et al., 2008).

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Figure 2.4. Setup of loading argon using the cryogenic method. (a) gas loading with the lid closed. The cryo-loader is surrounded by liquid nitrogen. (b) after gas loading with the lid open. The DAC is immersed in liquid argon.

2.2 In situ Synchrotron X-ray diffraction Two important intrinsic features of the DAC technique are: (1) the sample is encapsulated by wall materials of the sample chamber (two diamond culet plus gasket), and (2) there is a tradeoff between the obtained pressures and culet sizes of diamonds – increasingly higher maximum pressures are achieved at the expense of culets sizes of diamonds - increasingly higher maximum pres-sures are achieved at the expense of progressively smaller culet sizes. Hence, sample sizes in DAC experiments span the range from sub-μm to several hun-dred μm. Probing materials of such small volumetric amounts and linear di-mensions requires the exploitation of highly penetrating, intense, and well-collimated radiation sources. These must provide capabilities to probe sam-ples at a high spatial resolution through the massive walls of pressure cham-bers while avoiding the signal contamination by materials of the surrounding environment. The synchrotron X-ray source perfectly matches these require-ments: (1) synchrotron provides high-energy X-rays (up to 500 keV) to which the diamond anvils are highly transparent; (2) the brilliance of a third-genera-tion undulator (∼1020 photons/s/mrad2/mm2/0.1%bandwidth) is some tens or-ders of magnitude higher than that of a rotating Cu Kα X-ray machine; (3) synchrotron X-rays can be highly focused to a spot of only several μm, or even smaller. In addition, the tunable energy of the synchrotron radiation facilitates the X-ray spectroscopy measurements. Nowadays, numbers of synchrotrons operate dedicated high-pressure beamlines, which are equipped for measure-ments by a variety of X-ray techniques (scattering, spectroscopy, and imag-ing). The marriage of DAC technique and synchrotron X-ray source has been accelerating the development of high-pressure science since the late 1970s (Buras et al., 1977). Some of these dedicated beamlines (DAC techniques only) are summarized in Table 2.2.

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Table 2.2. Summary of part of the high-pressure beamlines (DAC technique only) of Synchrotrons around the world.

Synchrotron Beamline Techniques Energy (keV)

Advanced Photon Source (APS), Argonne, IL, USA

3-ID-B,C,D Nuclear resonant inelastic X-ray scattering; Inelastic X-ray scattering; Synchrotron Moessbauer spectroscopy

7-27

13-ID-D Powder diffraction; Single-crystal diffraction 4.9-75

13-BM-C Powder diffraction; Single-crystal diffraction 29

13-BM-D Powder diffraction; Single-crystal diffraction; Imaging

37, up to 70

16-BM-B Energy-dispersive X-ray diffraction 10-120

16-BM-D

Powder diffraction; Single-crystal diffraction; X-ray absorption; Tomography

6-45

16-ID-B Powder diffraction; Single-crystal diffraction 18-60

16-ID-D Nuclear resonant scattering; Inelastic X-ray scattering; X-ray emission spectroscopy

5-37

Beijing Synchrotron Radiation Facility, (BSRF), Beijing, China

4W2 Powder diffraction; Single-crystal diffraction 20

Diamond Light Source, Didcot, UK

I15 Powder diffraction; Pair Distribution Function 20-80

I19 Single-crystal diffraction 5-25

European Synchro-tron Radiation Facil-ity (ESRF), Greno-ble, France

ID15B Powder diffraction; Single-crystal diffraction; Diffuse X-ray scattering

30

ID18 Nuclear resonance techniques 7-80

ID24

X-ray absorption spectroscopy; X-ray magnetic circular dichroism; Fourier transform infrared spectros-copy/microscopy

5-27

ID27 Powder diffraction; X-ray fluorescence; X-ray Raman scattering

20-90

PETRA III Hamburg, Germany P02.2

Powder diffraction; Single-crystal diffraction; Pair Distribution Function

25.6, 42.7, 60

Spring-8, Hyōgo Prefecture, Japan BL10XU Powder diffraction 6-61

Shanghai Synchro-tron Radiation Facil-ity, (SSRF), Shang-hai, China

BL15U1 Powder diffraction 5-20

21

2.2.1 Synchrotron radiation source In the 1940s, the circular high-energy electron accelerator was built. However, the maximum energy of the electrons was limited because of energy loss due to the emission of electromagnetic radiation when the electrons follow a curved orbit. Later, this radiation was observed at the General Electric Re-search Laboratory and called synchrotron radiation. The potential advantages of synchrotrons were not realized until almost a decade later. Nowadays, sci-entists from almost all research fields and many industries benefit from the advantages of synchrotron radiation sources. Over a period of more than 60 years, synchrotron radiation facilities were built all over the world. Today these synchrotron radiation sources are grouped into four generations: (1) The first generation synchrotron radiation sources are parasitic facilities

because the synchrotrons were primarily designed for high energy physics research. The `waste` (by-product) synchrotron radiation was used by other physicists.

(2) The second-generation synchrotron radiation sources are dedicated facil-ities optimized for the synchrotron radiation.

(3) The third-generation synchrotron radiation sources employ the insertion devices (IDs, wigglers or undulators) to optimize their brilliance. The rep-resentative third-generation synchrotron radiation sources are ESRF (France), APS (USA), and Spring-8 (Japan).

(4) There are two types of the fourth-generation synchrotron radiation: the Diffraction-Limited Storage Rings (DLSR) and the X-ray Free-Electron Lasers (XFEL). The emittance of the electron beam of DLSR is smaller or about the same as the photon emittance, thus significantly improving their brilliance and coherence fraction relative to the third-generation syn-chrotron radiation sources. XFEL is based on linear accelerators and gen-erates coherent, high-brilliance (∼9 orders magnitudes higher than the third-generation synchrotron radiation sources), and short X-ray pulses (femtoseconds).

Fig. 2.5 shows the schematic of a third-generation synchrotron source with essential components. The electrons from a source are first accelerated by the linac and further accelerated by the booster ring. The accelerated electrons are injected into the storage ring, where they circulate in a closed path controlled by the bending magnets. The radiation produced due to the effect of the bend-ing magnets and the IDs is optimized by various optical elements and finally delivered to the sample in the experimental hutch.

22

Figure 2.5. Schematic of a synchrotron radiation source. A beamline consists of the front end, optic hutch, and experimental hutch.

2.2.2 X-ray diffraction Although a variety of synchrotron-based X-ray techniques are applied today, the main working horse in the high-pressure research field is still the XRD technique, which represents a non-destructive method of determining the atomic structure of materials. In the present study, we focus on crystalline materials, which possess a long-range order with the periodicity of length scales of the order of Ångströms, comparable to the X-ray wavelength. When impinging on a crystal, X-ray is scattered by electrons, whose density has the same periodicity as crystal lattice. The scattered X-rays add up constructively in certain directions, which are revealed by high-intensity counts on a detector. The purpose of XRD techniques is to collect two dimensional diffraction pat-terns, from which a three-dimensional periodic atomic arrangement is deci-phered. A diffraction peak position is described by Bragg´s law:

2 =

where dhkl is the d-spacing of (hkl) planes, θhkl is the diffraction angle, and λ is the wavelength of the incident X-ray. The kinematical scattering theory leads to a result that the (hkl) diffraction peak intensity is:

∝ | | where Fhkl is the structure factor,

= exp 2 ( + + )

23

where Nj is the fraction of every equivalent position that is occupied by atom j, fj is the structure factor of atom j, and xj, yj, and zj are fractional coordinates of atom j.

2.2.3 High-pressure X-ray diffraction beamline A typical high-pressure beamline in the third-generation synchrotron source is sketched in Fig. 2.6. IDs placed in the straight sections between bending magnet arc segments produce a high-flux and high-brilliance whitebeam, ei-ther a high power X-ray beam with a broad energy spectrum from the wiggler or a series of sharp harmonics from the undulator. The white beam is mono-chromatized by a set of double single crystals (usually silicon) in the mono-chromator. After being focused horizontally and vertically by a pair of Kirk-patrick Baez (KB) mirrors, a small and intense X-ray beam with a selected wavelength is delivered to the sample. The diffraction signal is usually col-lected by a 2D detector. A real picture of a high-pressure XRD setup using the DAC technique is shown in Fig. 2.7.

Figure 2.6. Schematic of a typical high-pressure X-ray diffraction beamline using the DAC technique.

24

Figure 2.7. The setup for high-pressure XRD at the P02.2 beamline of PETRA III.

2.2.4 XRD data processing In the present study, XRD images were integrated using software packages Fit2D (Hammersley et al., 1996) or Dioptas (Prescher et al., 2015) in order to obtain 2θ - intensity curves for further analyses (Fig. 2.8). Some set of the XRD patterns were fitted by the Fityk software (Wojdyr, 2010) with the Voigt function to get the peak width information. Fullprof (Rodríguez-Carvajal, 1993) or GSAS II (Toby et al., 2013) were used for the structural refinement. The equation-of-sate parameters of the studied materials were determined by fitting the pressure-volume (P-V) data points with Vinet equation of state (Vinet, 1987) using the EosFit7-GUI software (Gonzalez-Platas et al., 2016): = 3 [1 − ] 32 ( ` − 1)[1 − ] where V0 is the equilibrium volume, K0 and K`0 are bulk modulus and its pres-sure derivative at ambient pressure, respectively.

25

Figure 2.8. The working window of Dioptas software. The left part is the XRD im-age and the lower right part is the integrated 2θ -intensity curve.

2.3 Raman scattering In 1921, Sir Chandrasekhara Raman was attracted by the fascinating blue color of seawater on the ship back to India from England. In the next seven years, he studied the light scattering effect by liquids, and discovered the fre-quency change in the scattered light in addition to the elastic Rayleigh signal. The frequency change in the scattered light originates from the energy transfer between the incident light and the scattering system. In 1928, he reported `a new type of secondary radiation` (Raman and Krishnan, 1928) which is now called the Raman scattering. Two years later in 1930, Sir Chandrasekhara Ra-man was awarded the Nobel Prize in Physics `for his work on the scattering of light and for the discovery of the effect named after him` (Nobel Prize web-site). Raman scattering is an inelastic scattering of light by various (quasi-)excita-tions (vibrons, phonons, or magnons). Raman spectroscopy provides infor-mation on the composition, symmetry, stress, and strain in materials. How-ever, the extremely weak Raman signal (generally 10-6 -10-12 of the incident light) limited its applications until the advent of the laser in the 1960s. Nowa-days, in science, Raman scattering is a widely used spectroscopic technique in research fields including physics, chemistry, material science, biology and medicine, Earth and environmental science, and cultural heritage.

26

2.3.1 Principle of Raman scattering The principle of Raman scattering presented in this section is adapted from the description of Long (2002) and Zhang (2008).

A. The classical theory of Raman scattering The classic description of the Raman scattering does not discuss all aspects of the effect, nevertheless, it provides valuable insights into the nature of the phenomenon, including the frequency dependence and the selection rules. In the classical theory, the electric dipole moment p induced by an excitation electric field E can be written as:

= ( ) + ( ) + ( ) + ⋯ where ( ) = ∙ ( ) = 12 ∙

( ) = 16 ∙

where α is the polarizability tensor which is a second-rank tensor, β and are the first and second hyperpolarizabilities with α » β » . The contributions from p(2) and p(3) are much smaller than that of p(1) unless E is very high. Ra-man scattering phenomenon can be observed even the electric field E is very low. Thus, only the contribution from p(1) is taken into consideration in the classical treatment. To simplify the description, the scattering system is con-sidered as one molecule with a vibrational degree of freedom while without the rotational degree of freedom. Then the component (αij) of the polarizabil-ity tensor α can be expressed in a Taylor series with the normal coordinates of vibration (Qk, Ql…):

= ( ) + ( ) + 12 ( ), + ⋯ where (αij)0 is the value of αij at the equilibrium configuration, Qk, Ql … are normal coordinates of vibration with vibrational frequency ωk, ωl …. The magnitude of vibration near the equilibrium position is usually small thus har-monic approximation can be applied. Thus we ignore the terms involving powers of Q higher than one. In the following, we focus on the normal vibra-tional harmonic mode Qk and get

( ) = ( ) + ( )

27

and = cos ( + ) Combining the above two equations, the time dependence of the polarizability tensor originated from the vibration mode Qk is

= + ´ cos ( + ) Consequently, the dipole moment p(1) induced by the electric filed =

can be expressed as ( ) = + ´ cos ( + )

and be rewritten as ( ) = + 12 ( ) cos(( + ) + )+ 12 ( ) cos (( − ) − )

The last expression provides several fundamental insights into the Raman scattering: (1) The induced dipole moment involves three distinct frequencies if ( ) ≠ 0. These frequencies correspond to the Rayleigh scattering (ω1,

the same as that of the incident electric field), the anti-Stokes scattering (ω1 + ωk), and the Stokes scattering (ω1 - ωk).

(2) The Rayleigh scattering has the same phase as the incident radiation, while the Stokes and anti-Stokes scattering are shifted by relative to the phase of the incident radiation.

(3) The vibrational mode of a molecule is Raman active when ( ) ≠ 0, which is determined by the symmetry of the system.

Although the classical theory provides a fundamental insight into the phenom-enon of Raman scattering, it also has several limitations. For example, (1) The classic theory cannot deal with the rotations of molecules, (2) The classic theory cannot provide information on the intensity of the

Stokes and anti-Stokes peaks, (3) The classic theory does not provide the relationship between ´ and the

properties of molecules.

28

B. Quantum mechanical theory of Raman scattering The quantum mechanical treatment of the Raman scattering is performed in the framework of time-dependent perturbation theory. The induced transition electric dipole moment from the initial state ( ´ = ( ) + ( ) + ⋯) to the final state ( ´ = ( ) + ( ) + ⋯) in the perturbed system is:

( ) = ´ ̂ ´ ( ) = ( ( )) + ( ( )) + ⋯ where ( ( )) = ( ) ̂ ( ) ( ( )) = ( ) ̂ ( ) + ( ) ̂ ( ) If the following assumptions apply: (1) the perturbation is first order, (2) the interaction Hamiltonian only involves the electric dipole, and (3) the perturb-ing radiation is a plane monochromatic electromagnetic wave with frequency of ω1, the ρ component of (p(1))fi can be expressed as

( ) = 12ħ ( ) ̂ ( ) ( ) ̂ ( )− − + ( ) ̂ ( ) ( ) ̂ ( )+ +

∗ exp +, + 12ħ ( ) ̂ ( ) ( ) ̂ ( )+ +

+ ( ) ̂ ( ) ( ) ̂ ( )− − exp − −, +

where ωrf =ωr -ωf, and 2Γr relates to the full width of level r. This expression implies two frequency dependence in the transition electric dipole moment. The (ω1 + ωfi) term describes the process involving two quanta (ω1 + ωfi and ω1) if (ω1 + ωfi) > 0. This term will not be taken into account. The second term involving (ω1 - ωfi) corresponds to the origination of the Rayleigh and Raman scattering if (ω1 - ωfi) > 0: (1) (ω1 - ωfi) > 0 will be always satisfied if ωf = ωi, indicating the initial and

final states have the same energy. This corresponds to the Rayleigh scat-tering;

(2) (ω1 - ωfi) > 0 will be always satisfied if ωf <ωi, indicating the final state has lower energy than the initial state. This is the anti-Stokes scattering;

(3) (ω1 - ωfi) > 0 will be always satisfied if ω1 > ωf -ωi and ωf > ωi, indicating the incident radiation has sufficient energy to reach the final state | from the initial state | . This represents the Stokes scattering.

So, the Raman part of the ρ component of (p(1))fi is ( ) = 12ħ ( ) ̂ ( ) ( ) ̂ ( )+ +

+ ( ) ̂ ( ) ( ) ̂ ( )− − exp − −, +

29

and the general transition polarizability tensor is ( ) = 1ħ ( ) ̂ ( ) ( ) ̂ ( )+ +

+ ( ) ̂ ( ) ( ) ̂ ( )− − , This expression shows that the transition polarizability is determined by the wave function and energy levels of the system.

2.3.2 Raman spectroscopic system Typically, a Raman spectroscopic system consists of the following compo-nents: (1) Monochromatic light source. Lasers represent an ideal excitation source

for the Raman spectroscopy by virtue of their high intensity, good mono-chromaticity, polarization, and coherence.

(2) Spectrometer is used to spatially disperse (resolve) the inelastically scat-tered light according to its spectral components and focus it on the at-tached detector.

(3) Detector. Converts photons into an electric signal. Because of the weak nature of Raman scattering, detector featuring a high quantum efficiency and a low dark signal is required.

(4) Optics. The optics in the Raman spectrometer fulfil three functions: deliv-ering and focusing the laser on the sample, collecting and transporting the scattering light to the dispersion system, and suppressing the Rayleigh light.

(5) XYZ sample stage for finely adjusting the position of the sample. An es-sential component when the micro-Raman technique is applied to minia-ture samples in DAC.

At the Department of Earth Sciences, Uppsala University, a dedicated Raman system for high-pressure studies using the DAC technique has been built (Fig. 2.9). This system operates in the backscattering geometry and uses a DPSS laser (Cobolt Samba, 532.42 nm, maximum power 150 mW) as the excitation source. The laser is focused on the sample by a long working distance objec-tive (20×, w.d. = 20.5 mm, Nikon) to a spot size of about 2 - 4 µm. Two hol-ographic notch filters (Semrock) suppress the Rayleigh light. The scattered light is dispersed by the high-throughput single-stage imaging spectrometer (HoloSpec f/1.8i, Kaiser Optical Systems, Inc.) on the CCD detector (Newton, Andor Technology, 1600 × 400 pixels, thermoelectrically cooled to -55 °C). Raman spectra are collected in the range of from -700 cm-1 to 3850 cm-1. The spectral axis is calibrated with the help of a neon fluorescence lamp and the stability of calibration frequently checked using the first-order Raman line of single-crystal silicon (521 cm-1). The spectral resolution of the system is around 4 cm-1 and the accuracy estimated from the calibration procedure is

30

about 2 cm-1. An example of Raman spectrum collected by this system from a crystalline sample in DAC is shown in Fig. 2.10.

Figure 2.9. Raman system for high-pressure research using the DAC technique built at the Department of Earth Sciences at Uppsala University. The imaging and pressure measurement units are combined with the Raman system. The typical ruby fluores-cence spectra, the Raman spectrum, and sample image are also shown in the figure.

2.4 UV-vis absorption spectroscopy The magnitude of the bandgap of semiconductors is determined by the energy difference between the bottom of the conduction band and the top of the va-lence band. The bandgap is a critical parameter of semiconductors as it deter-mines the wide range of their applications (Ning et al., 2017). In semiconduc-tors, there are two types of bandgap – the direct bandgap and the indirect bandgap (Fig. 2.11). In the indirect bandgap semiconductors, the bottom of the conduction band and the top of the valence band lie at the same value of k space. Consequently, only energy changes for electrons excited from valence

31

Figure 2.10. An example of Raman spectrum of a crystalline sample (Cu3TeO6) com-pressed to 13.6 GPa in DAC. The spectrum was collected using the Raman system at the Department of Earth Sciences, Uppsala University.

band to conduction band, and phonon is not required to conserve the momen-tum. However, in the indirect bandgap, the bottom of the conduction band and the top of the valence band are not aligned in the k space, which leads to en-ergy and momentum change of electrons excited from valence band to con-duction band. Thus, phonons participate in this excitation process to conserve the momentum.

Figure 2.11. Direct and indirect energy bandgaps.

UV-vis absorption spectroscopy is a convenient method for measuring the bandgap of semiconductors. Photons with energy larger than the bandgap have the ability of exciting electrons from the valence to the conductive band. Thus,

32

the red edge of the UV-vis absorption spectrum determines the bandgap en-ergy of semiconductors. The wavelength dependence of the absorbance coef-ficient is described by the following equation:

( ) = ( − )

where α is absorption coefficient, Eg is bandgap energy, B is a constant, and n is the power factor of the transition mode which equals 2 for direct band sem-iconductors and ½ for indirect band semiconductors, respectively. Conse-quently, the intercept of the (αhν)n - hν plot (Tauc plot) determines the bandgap energy of materials. According to the Beer-Lambert law, the absorp-tion coefficient α is determined by the absorbance and the thickness of mate-rial: = 10 = 2.303 = where A is absorbance, t is the thickness of the sample, I0 and I are the inten-sities of the incident and transmitted light, respectively. The UV-vis absorption experimental setup is sketched in Fig. 2.12. The light from the source is collimated by the entrance slit and dispersed by dispersive devices (prism or diffraction grating). The dispersed light of a selected wave-length illuminates the sample, and the transmitted light intensities are recorded by the detector (I(λ)). The intensity of the transmitted light through the refer-ence is recorded as I0(λ). In the present study, the in situ UV-vis absorption spectroscopy experiment was performed at the Swedish Museum of Natural History. The spectra were collected from 280 nm to 1100 nm using a custom-ized visible microscope system in the transmission mode. The transmitted light through the two anvils and the PTM is recorded as I0(λ).

Figure 2.12. Schematic picture of the UV-vis experiment.

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3. Double perovskites (A2BB´O6) at high pressures

3.1 Perovskite oxides Perovskite is a mineral with the composition of calcium titanate (CaTiO3), which is named after Russian mineralogist Lev Perovski. In a broader mean-ing, term `perovskite` represents a class of materials adopting crystal structure related to that of the mineral perovskite CaTiO3. The general chemical formula of perovskite oxides is ABO3, where A site accommodates larger cations which are 12-coordinated while B site accommodates smaller cations which are 6-coordinated. In the ideal cubic perovskite structure (SrTiO3, s.g. Pm-3m, Z = 1), the A site Wyckoff position is 1b, (0.5, 0.5, 0.5), the B site position is 1a, (0, 0, 0), and O atoms occupy the 3d position (0.5, 0, 0), (0, 0.5, 0), (0, 0, 0.5). The cubic perovskite structure is shown in Fig. 3.1.

Figure 3.1. Cubic perovskite crystal structure. The cyan, green and orange atoms oc-cupy the A, B, and O sites, respectively. The BO6 and AO12 polyhedral are also illus-trated. Dash orange lines indicate the cubic unit cell.

The ionic radii in the ideal cubic perovskite structure with unit cell parameter a meet the following relationship

= √2( + ) = 2( + ) Thus their tolerance factor

34

= ( + )√2( + ) equals to 1. However, the relative ion size requirements of the ideal cubic per-ovskite structure are stringent, so distortion of the cubic structure is introduced in order to accommodate A and B ions with various sizes, and consequently lower the structural symmetry. Previous studies indicate that the structure of perovskite can be roughly predicted using their t values, though also other factors affect their crystal structures (Vasala and Karppinen, 2015). The most common distortion arising from the cation size mismatch is the tilting or rota-tion of BO6 octahedra relative to one another as rigid corner-linked units. Glazer (1972) developed a set of notations to describe the different tilting pat-terns with implications for the investigation of the unit cell symmetries (Glazer, 1975; Howard and Stokes, 1998). Group theoretical analysis reveals 15 different space groups in perovskite materials, arising from the octahedral tilting (Howard and Stokes, 1998). In addition to the size effect, the Jahn-Teller effect and the deviations from the ideal composition can also lead to distortion of the cubic perovskite structure, e.g., tilting of the octahedra, and cations shifting away from the center of their coordination polyhedra what introduces ferroelectricity in perovskites (King and Woodward, 2010). Besides their structural flexibility, perovskites can accommodate a considera-ble degree of compositional flexibility. Partial cation substitution can take place in either A and B sites. The substituted cations can arrange orderly or randomly in both A and B sites. There are three kinds of A/B site ordering: rock-salt, columnar and layered ordering (King and Woodward, 2010). This cation substitution expands the perovskite family to double, triple, quadruple perovskite, and so on. The A or B sites in perovskite-related structures can accommodate almost all the elements in the periodic table (Schlom et al., 2008). The combination of two or more cations in one site significantly tailors existing and introduces new interesting and exotic properties in perovskites. Perovskite oxides are the most widely studied owing to their fundamentally interesting chemical and physical properties, including ferroelectricity, mag-netism, ferromagnetism, colossal magnetoresistance, piezoelectricity, metal-insulator transition, superconductivity, catalytic activity, as well as some com-bined properties like multiferroicity (Vasala and Karppinen, 2015). Because of their structural flexibility and a distinct variety of properties, perovskite oxides have a wide range of applications, e.g., as thin-film capacitors, non-volatile memories, and photo-electrochemical cells.

35

3.2 Double perovskite polar magnets Polar magnets possess an electric polarization and magnetization simultane-ously in a single phase, as well as a strong coupling between them. In these materials, the electric polarization can be tuned by a magnetic field, and the magnetization can be tuned by an electric field. This electric-to-magnetic link makes them very attractive for potential applications in information storage and spintronic devices (Dong et al., 2015; Spaldin et al., 2010; Wang et al., 2009). However, polar magnets are rare because of the contradicting elec-tronic arrangement requirement for electronic polarization and for magnetism (Hill, 2000; Benedek and Fennie, 2013). In the last decade, B site substituted double perovskites A2BBÒ6 have been emerging as a promising platform for polar magnets design for two reasons (Li et al., 2013): (1) The structural flexibility of A2BBÒ6 double perovskites allows them to

crystallize in non-centrosymmetric structures (e.g., LiNbO3-type, Ni3TeO6-type, and ordered ilmenite-type structures as shown in Fig. 3.2), introducing an electric polarization. The electric polarization originates from the cations off-centering in their coordinated polyhedra triggered by the Coulombic repulsion (Li, et al., 2014; 2015; Hoel et al., 2010);

(2) The compositional flexibility of A2BBÒ6 double perovskites allows A, B, and B` sites to be occupied by transition-metal cations, which can further enhance the magnetoelectric coupling. This highly distorted A2BBÒ6 double perovskites are usually not stable at ambient conditions. Thus, the high-pressure technique is generally needed for stabilizing the highly dis-torted structure (Li, et al., 2013; 2014; 2015; Wang et al., 2015; Zhou et al., 2017).

3.3 Polymorphism and piezochromism in Mn2FeSbO6 Melanostibite, Mn2FeSbO6 (MFSO), is a rare mineral discovered in the Sjö mine in Sweden. This mineral was named by L.J. Igelström in 1893 for its color and composition (melano = black, and stibium = antimony in Greek). Melanostibite crystallizes in the ilmenite structure (IL, s.g. R-3) and displays ferromagnetic order below 270 K (Mathieu et al., 2011; 2013a). Though found in nature, its synthesis at ambient conditions has not yet been accomplished despite several efforts. The ilmenite-type and perovskite-type (s.g. P21/n) MFSO can be synthesized as-quenched samples from high-pressure and high-temperature conditions (Bazuev et al., 1996). However, both types are sym-metric structures, and thus no or only very week electric polarization effect occurs in these materials. For A2BBÓ6 materials with tolerance factor t smaller than 0.85, the polar LN structure can be synthesized as a retrograde product of high-pressure perovskite phase upon decompression. The tolerance factor of MFSO is 0.78, thus an appearance of the polar LN-type MFSO would

36

Figure 3.2. Possible crystal structures of the B site substituted double perovskite with small cations occupying the A sites (adapted from Wu and Li, 2018). (a) Al2O3 corun-dum structure (s.g. R-3c). Centrosymmetric structure with cations randomly distrib-uted in A, B, and B` sites; (b) LiNbO3 structure (LN, s.g. R3c). Polar structure with B and B` sites randomly occupied; (c) Ni3TeO6 structure (s.g. R3). Polar structure with A, B, and B` sites occupied orderly. There are two distinct crystallographic A sites. (d) FeTiO3 structure (ilmenite, s.g. R-3). Centrosymmetric structure with B and B` sites randomly occupied; (e) ordered ilmenite structure (s.g. R3). Polar structure with A, B, and B` sites occupied orderly. There are two distinct crystallographic A sites; (f) dis-torted GdFeO3 perovskite structure (s.g. P21/n).

not be unexpected. In the present study, the crystal structure evolution of MFSO is investigated by the XRD and Raman scattering techniques, along with the density functional theory (DFT) calculations, in order to search for the foreseen polar structure (e.g., of the LN-type) (Liu et al., 2019a). The powdered MFSO was compressed to a pressure of around 50 GPa using Ar as PTM, and was XRD-probed. The in situ XRD results reveal a phase transition commencing at 34.74 GPa and completing at 39.65 GPa. The XRD patterns of the high-pressure phase can be well reproduced using the structural model of the synthetic perovskite-type MFSO. The volume collapse during the transition is 2.6% (Fig. 3.3). Upon decompression, the high-pressure phase transformed back to the IL structure at 19.50 GPa. No polar LN-type phase was detected in the course of these quasi-hydrostatic compression and decom-pression runs. The determined bulk moduli of the IL and the Pv phases are 211 ± 4 GPa and 229 ± 4 GPa respectively.

37

Figure 3.3. Pressure-volume data and the equation of states of ilmenite and the per-ovskite phases of MFSO.

In contrast to the XRD results, the high-pressure Raman study of the MFSO single crystal reveals two phase transitions at 30.78 and 36.15 GPa. Upon compression, the color of MFSO crystal gradually changes from yellow to black. These two phase transitions reoccurred at 32.29 GPa and 9.46 GPa upon decompression. The inconsistent results of the XRD and Raman experiments introduce two questions: (1) why the phase transition routes are different when two different probing techniques are employed? (2) what is the structure of the new intermediate phase?

The analysis of possible reasons for the observed inconsistency reveals that the heating effect of the excitation laser is responsible for the different phase transition routes. The bandgap energy of MFSO at ambient pressure is 2.04 eV, a value smaller than the photon energy of the laser of 2.33 eV (wavelength of ∼532 nm). However, upon a pressure increase, the bandgap narrows as is visually demonstrated by the sample´s progressively darker color (Fig. 3.4), and as corroborated by the DFT calculations. The bandgap narrowing en-hances the laser energy absorption due to which the local temperature of the sample increases to around 400 K, facilitating the phase transition. The Raman results indicate that the intermediate phase adopts the LN structure for the following reasons: (1) The calculated Raman modes of LN-type MFSO agree fairly well with experimental result at 35 GPa; (2) The high-pressure Raman spectra of LN-type ZnTiO3 are similar to the measured Raman spec-trum of MFSO at 35 GPa (Ruiz-Fuertes et al., 2015); (3) The evolution of

38

Raman spectra of ZnTiO3 during the LN-to-Pv phase transition resembles what is observed during the second phase transition of MFSO at 36.75 GPa. Consequently, the intermediate phase is proposed to be the missing polar LN structure.

Figure 3.4. Piezochromic effect of MFSO observed through diamonds in transmitted light under compression and decompression.

3.4 Pressure-induced octahedral tilting in Pb2CoTeO6 Pb2CoTeO6 (PCTO) double perovskite crystallizes in the R-3 structure at am-bient conditions. The localization of Pb2+, Co2+, and Te6+ in A, B, and B´ sites of PCTO suggests that it is a good candidate for a polar magnet (Ivanov et al., 2010). Similar to MFSO, the crystal structure evolution of PCTO was inves-tigated by the XRD and Raman scattering up to around 60 GPa, in order to search for the polar structure at high pressure (Liu et al., 2019b). A subtle phase transition from the R-3 structure to the monoclinic I2/m structure was observed at around 20 GPa (Fig. 3.5). Accordingly, the tilt system changed from a-a-a- to a0b-b-, and the octahedral tilt axis was altered from the pseudo-cubic [111] axis to the [100] axis. Unfortunately, the I2/m structure is also centrosymmetric. Ivanov et al. (2010) reported a phase transition sequence of PCTO upon temperature decrease: Fm-3m → R-3 → I2/m → P21/n. The pre-sent results indicate that increasing pressure and decreasing temperature im-pose a similar effect on the crystal structure of PCTO - promoting the distor-tion of the structure. Raman results indicate also a further phase transition from I2/m to P21/n structure above 40 GPa, which calls for further investiga-tion in the future.

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Figure 3.5. (a) XRD patterns of PCTO. The dashed blue and red lines show the dif-fraction peaks from the Ar PTM and CoO impurity, respectively. (b) Pressure depend-ence of the peak width (FWHM) of the four main reflections highlighted in (a). (c) the c/a ratio as a function of pressure when using the R-3 structural model to refine the XRD patterns.

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4. Bandgap engineering in multiferroic oxide Mn3TeO6

4.1 Perovskite solar cells The energy problem belongs to one of the greatest challenges the human so-ciety is facing today. Great efforts are being devoted to searching for alterna-tives to fossil fuels. Intuitively, solar energy, which is the most abundant ex-ploitable renewable energy source, springs to mind. This safe and environ-ment-friendly energy has been attracting tremendous attention as a promising solution for the energy problem without a negative impact on the global envi-ronment. The solar radiation received by Earth is more than three orders of magnitude higher than annual global energy consumption. The spectra of sun-light are shown in Fig. 4.1. The ideal way of harvesting solar energy is to convert it into electricity by the photovoltaic effect. Consequently, searching for proper photovoltaic materials represents the primary task in solar cell re-search. The dominant commercial photovoltaic material is silicon, whose power con-version efficiency (PCE) reaches 25.3% in a laboratory while it varies between 16-20 % in commercial cells (Service 2016). In addition, thin-film polycrys-talline semiconductors (CdTexSe1-x (Poplawsky et al., 2016), CuInxGa1-xSe2 (Kronik et al., 1998), etc.), quantum dots (CdSe (Huynh et al., 1999), InP (Blackburn et al., 2003), etc.), and dyes (crocetin, cosmos, etc.) (Gratzel, 2005) have also been developed for use as photovoltaic devices. However, the high fabrication cost or poor performance of theses photovoltaic materials drives the search for the next generation of solar cells.

In 2009, Kojima et al. proposed a new class of materials, organic-inorganic halide perovskite, as a light-harvesting material for the next generation of so-lar cells. This kind of perovskite is considered the most promising alternative to the presently used commercial solar technologies due to its high absorption coefficient, tunable bandgap energy, long charge carrier diffusion length, high defect tolerance, abundant elemental composition, and low- cost and low-tem-perature fabrication methods (Bakr and Mohammed, 2017; Li et al., 2019; and reference therein). In the past decade, the performance of organic-inorganic halide perovskite solar cells (PSCs) improved rapidly. The PCE of PSCs sur-

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Figure 4.1. Spectra of sunlight (adapted from Oku, 2016). The spectrum at the upper atmosphere is Air Mass 0 (AM-0). When going through the atmosphere, part of the solar radiation is absorbed or scattered by air and water in the atmosphere. The spec-trum of sunlight reaching the ground perpendicular to the land surface is AM-1. The incident angle of sunlight is generally smaller than 90o. The spectrum of sunlight reaching the ground with an incident angle of 41.8o is AM-1.5, which is used for eval-uating solar cells.

pass the top PCE of semiconductors and reaches a value as high as 23.7 % (reported by NREL), comparable to the top efficiency of silicon. Although impressive progress in the evolution of PSCs has been accomplished in the last decade since the first report in 2009 (Kojima et al., 2009), several disadvantages of PSCs have to be addressed before commercial applications. The first problem is the chemical instability of perovskite photovoltaic mate-rials, which usually degrades in humid conditions and high temperatures. Moreover, UV light, ion/electro- migration, and interfacial reactions can cause degradation of perovskite photovoltaic materials (Berhe et al., 2016). Another critical problem is the serious environmental toxicity of lead, though lead-based perovskite photovoltaic materials have good stability and performance. Replacing the lead cation without sacrificing the conversion efficiency and chemical stability represents one of the grand challenges in solar cell research (Zhang et al., 2018).

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4.2 Photovoltaics with multiferroic oxides The photovoltaic effect of ferroelectric oxides was discovered more than half a century ago (Chynoweth, 1956; Chen, 1969). In addition, their low fabrica-tion cost and stability in a wide range of mechanical, chemical and thermal conditions of ferroelectric oxides attract attention for photovoltaic applica-tions. However, their extremely low photocurrents ascribed to the large bandgap energy, and consequently the low PCE (< 1%) inhibit the commercial applications. Recently, Nechache et al. (2014) introduced a new photovoltaic material double perovskite oxide Bi2FeCrO6 and achieved a PEC value as high as 8.1%, which indicated that multiferroic oxides offer the possibility to over-come the drawbacks of organic-inorganic halide perovskite thus representing promising alternatives. However, the bandgap energy of multiferroic oxides generally spans a range of 2.7 - 4.0 eV, which is too large for photovoltaic materials because only a small portion of the solar energy can be absorbed. Finding efficient means for tuning the bandgap of multiferroic oxides for pho-tovoltaic applications represents another important research goal in solar cell research.

4.3 Bandgap engineering in Mn3TeO6 A3TeO6 (A = Cu, Co, Mg, Mn, Ni, Zn) compounds possess similar values of tolerance factor t while adopting four different types of structures as shown in Fig. 4.2: (a) cubic bixbyite-type (s.g. Ia-3, Cu3TeO6); (b) β-Li3VF6-type (s.g. C2/c, Co3TeO6 and Zn3TeO6); (c) Mg3TeO6-type (s.g. R-3, Mn3TeO6); and (d) Ni3TeO6-type (polar corundum, s.g. R3). These materials show interesting magnetic and/or dielectric properties, representing a platform for designing potential multiferroic materials (Mathieu et al., 2013b; Selb et al., 2019).

Figure 4.2. Four typical structures of A3TeO6 (A = Cu, Co, Mg, Mn, Ni, Zn) com-pounds. The cyan, green, and orange atoms represent the A, Te, and O atoms, respec-tively. The black lines show the corresponding unit cells.

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In the present study, high-pressure treatment was employed for tuning the bandgap energy of multiferroic oxide Mn3TeO6 (MTO) (Liu et al., 2019c). The MTO was compressed to ∼40 GPa and probed by the Raman scattering and UV-vis absorption techniques. The Raman results revealed a phase tran-sition at ∼17 GPa, and significantly, the high-pressure phase was found to be quenchable to the ambient pressure, surviving the decompression. The phase transition was accompanied by a pressure-induced piezochromic effect – the initially colorless MTO crystal turned brown and became increasingly darker as the pressure was increased. The observed piezochromic effect reveals a bandgap narrowing of MTO at high pressure. UV-vis absorption experiments were performed in order to quantify the bandgap energy change during the phase transition. Analysis of the absorption spectra reveals a major bandgap narrowing by about 1 eV, from 3.15 eV at 18.03 GPa to 2.17 eV at 21.28 GPa (Fig. 4.3). Upon further compression to 34.45 GPa, the bandgap energy further decreased and reached a value of 2.07 eV. Surprisingly, upon decompression, the bandgap energy continued to diminish, attaining its minimum value of 1.86 eV when the pressure dropped close to ambient conditions. These results demonstrate that the high-pressure treatment may represent a tool for the green-way tuning of the bandgaps of multiferroic oxides, which would open for their use as stable and nontoxic photovoltaic materials.

Figure 4.3. The UV-vis absorption spectra of MTO. (a) The UV-vis absorption spec-trum of MTO at low pressure. The AM-1.5 solar spectrum is included as a reference. The insert picture shows the colorless MTO crystal at 2.67 GPa upon compression. (b) The UV-vis absorption spectrum of quenched MTO. The insert picture shows that the pressure-quenched MTO turns dark brown.

In order to understand the underlying mechanism behind the observed bandgap narrowing in MTO, in situ high-pressure X-ray diffraction experi-ments were conducted up to 37 GPa. The MTO was first compressed to ∼37.03 GPa in a quasi-hydrostatic environment using SO as a PTM. The sample as-sembly was the same as in the optical studies described above, except a pow-dered sample was used instead of a single crystal. The XRD patterns illus-

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trated in Fig. 4.4 (b) evidence a phase transition at 18.99 GPa upon compres-sion (Fig. 4.4 (b) and (c)). The onset pressure of the phase transition agrees with that determined by Raman scattering (∼16-18 GPa) and UV-vis absorp-tion spectroscopy (∼18 GPa) (Liu et al., 2019c). The XRD pattern of the high-pressure phase can be indexed as originating from the structure of a mono-clinic symmetry. In the A3TeO6 series of compounds, Co3TeO6 (s.g. C2/c) adopts the monoclinic structure (Becker et al., 2006). The perovskite-type MTO (s.g. P21/n) has been synthesized recently (Su et al., 2019). The XRD patterns of the high-pressure phase cannot be well reproduced using the struc-tural model of perovskite-type MTO. Consequently, we suggest the high-pres-sure phase adopts the Co3TeO6 structure and crystallizes in the C2/c space group (Fig. 4.4(d)). Upon decompression, the C2/c phase transformed into an-other recently reported monoclinic phase of the P21/n space group (Su et al., 2019) at ∼9.60 GPa, indicating an irreversible phase transition. This subtle phase transition from C2/c phase to P21/n was further demonstrated by the change of slope in the pressure dependence of the Raman band positions (Fig. 1(d) in Liu et al., 2019c), as well as by a kink in the plot showing bandgap-pressure relationship (Fig. 4(b) in Liu et al., 2019c) at around 10 GPa upon decompression. The quenched P21/n phase with the energy gap of 1.86 eV remained stable for at least eight months, indicating a promising potential for solar energy harvesting applications.

Figure 4.4. XRD patterns of MTO at high pressures using SO as a pressure medium. (a) and (b) Contour plot of XRD pattern upon decompression and compression, re-spectively. A clearly visible phase transition is determined at 18.99 GPa. (c) Integrated 1D XRD patterns upon compression and decompression. Cyan, orange, and green pat-terns represent the R-3, C2/c, and P21/n phases, respectively. (d) Refinement of MTO with the C2/c phase at 37.03 GPa. (e) Refinement of MTO with the P21/n phase at 4.35 GPa upon decompression.

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5. Pressure-induced phase transitions of high-entropy alloys

5.1 The concept of high-entropy alloy Metallic materials play an important role in the history of human civilization. Humans have been able to tune the properties of metals using the alloying strategy – adding minor property-tuning elements in one principal metallic element – since the Bronze Age. This strategy is used to produce multifarious alloys, from the swords of Rome soldiers to the engines of aircraft, and re-mains unchanged over millennia. This principle-element dominated approach produces limited types of alloys (e.g., ferrous alloys, aluminum alloys, nickel alloys, titanium alloys), most of which have been identified and well ex-ploited. Innovative approaches are necessary to design novel alloys with ex-cellent properties meeting the emerging needs and satisfying critical require-ments. In 2004, two groups independently proposed a new strategy for alloy design – mixing five or more elements with (near) equiatomic concentrations (Yeh et al., 2004; Cantor et al., 2004). These multi-principal-element alloys are coined `high-entropy alloys (HEAs)` (Yeh et al., 2004). Comparing to conventional alloys with only one or two principal elements, HEAs contain at least 5 prin-cipal elements whose concentrations span a range of 5-35 at% (Zhang et al., 2014; Yeh et al., 2004; Ye et al., 2016). The first reports about HEAs were published only 15 years ago (Yeh et al., 2004; Cantor et al., 2004). Since then, HEAs have been attracting intense and ever-increasing attention because of their scientific significance as well as practical applications (Zhang et al., 2014; Miracle and Senkov, 2017; George et al., 2019). The new concept of HEAs ushers material scientists to the uncharted center of the compositional phase diagram (Fig. 5.1). This contrasts with conventional physical metal-lurgy corner-focused approaches, which have been essentially limited to only a small portion of the compositional space. For example, using 12 principal elements results in a formation of 12 conventional alloy systems, in which only one element dominates. On the other hand, by alloying 5-12 principal elements, it is possible, in principle, to produce as many as 3302 systems. Not only this revolutionary metallurgical concept dramatically extends the terri-

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tory of alloys but also introduces unconventional alloys with unique proper-ties, such as high fracture toughness (Gludovatz et al., 2014), excellent strength (Youssef et al., 2015), superconductivity (Kozelj et al., 2014; Guo et al., 2017), high resistance to corrosion (Lee et al., 2007), and good catalytic performance (Yao et al., 2018; Xie et al., 2019). The term High-Entropy Alloy stresses the high-configuration-entropy effect (Yeh et al., 2004), which is thought to be the main reason why these alloys crystallize into a single phase (fcc, bcc, and hcp), other than an intermetallic phase. In addition to the high-entropy effect, the sluggish diffusion effect, the severe lattice distortion effect, and the cocktail effect are four core effects that determine the promising properties of HEAs (Yeh, 2006).

Figure 5.1. The contour map of the configuration entropy of a ternary alloy system (ABC). The configuration entropy increases per mole due to the formation of a solid solution by mixing n principal elements with the molar fraction ci is ∆ = − ∑ , where R is the gas constant (Yeh et al., 2004). In this compositional space, the conventional alloys with one or two principal elements are located in the corners.

5.2 Phase selection rules of HEA The formation of single-phase HEAs is counter-intuitive because the conven-tional view is that the probability of intermetallic compounds formation in-creases with the number of principal elements. Consequently, researchers would like to identify a criterion for the formation of single-phase HEAs, which will guide the HEAs design in the future. This criterion is also called

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the phase selection rule (Ye et al., 2016). Several phase selection rules have been proposed:

(1) Atomic size difference and mixing enthalpy According to the Hume-Rothery rules, Zhang et al. (2008) suggested that the size effect and the enthalpy of mixing play a critical role in the for-mation of single-phase HEAs:

= (1 − ∑ ) ∆ = 4∆,

where ci and ri are the molar fraction and atomic radius of the ith element, and ∆ is the mixing enthalpy of binary liquid alloy. Zhang et al. (2014) proposed that HEAs tend to form a single-phase solid solution when -10 kJ/mol < ∆ < 5 kJ/mol and 0 < < 4, while Ye et al. (2016) suggested a quantitative criterion -15 kJ/mol < ∆ < 5 kJ/mol and 0 <

< 5 after summarising the and ∆ values of 90 reported HEAs.

(2) Thermodynamics rules There is a competition between the formation of solid solutions and inter-metallic components. Thermodynamically, this competition is controlled by the relative free energy change. Yeh et al. (2004) suggested that a ther-modynamic system tends to form a single-phase solid solution if

∆ ≫ |∆ | where ΔS represents the entropy increase during the formation of a solid solution, and ΔHi is the formation enthalpy of the ith intermetallic phase. Ye et al. (2015a; 2015b) reformulated this inequality and introduced a new parameter:

= ∆ − |∆ |/|∆ | where ΔSE is the excessive entropy relative to the contribution of an ideal solution, and Tm is the average melting temperature estimated through the rule of mixing (Yang and Zhang, 2012). ΔSE is a function of atomic size and atomic packing fraction. They suggested that a single-phase solution forms when φ > 20.

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(3) Intrinsic residual strain When HEAs with different atomic sizes crystallize into a single-phase solid solution, the atomic sizes are altered in order to be accommodated into the simple lattice. This atomic size alteration leads to an intrinsic re-sidual strain (ε) in the alloys, which is proportional to the elastic energy stored in the lattice. The lattice will be destabilized if the intrinsic strain is too large. In this point of view, Ye et al. (2015c) proposed a geometric model to estimate ε and suggested that the system tends to crystallize into a single-phase solid solution when the root-mean-square residual strain εRMS is smaller than 5%.

(4) Valence electron concentration (VEC) The single-phase HEAs usually crystallize into three structures: body-cen-tered cubic (bcc), face-centered cubic (fcc), and hexagonal close-pack (hcp) structures. The aforementioned parameters present several indica-tors for the formation of the single-phase solid solution to some extent. However, which effect determines exactly the structure of the single-phase HEAs? Guo et al. (2011) proposed the valence electron concentra-tion

= ( ) including d-electrons as a good indicator for fcc or bcc solid solution. Ye et al. (2016) suggested that single-phase HEA adopted fcc structure with VEC of 8.5 ± 1.0, bcc structure with VEC of 5.0 ± 0.7, and hcp structure with VEC of 2.8 ± 0.2.

In the previous studies, the values of the aforementioned parameters of re-ported HEAs were summarized in order to reveal the underlying relationship between these parameters and HEA phases (structures). The parameters have been found mutually entangled with the response to their variations. When the principal elements change, the atomic size difference (δ) changes conse-quently, so do the mixing enthalpy (∆ ), the thermodynamics parameter (φ), the intrinsic residual strain (ε), and the valence electron concentration (VEC). A clean tool is desired for tuning a selected parameter. As known, pressure represents a fundamental thermodynamic variable, which can be ap-plied as a tool to tune the structural, elastic, and electronic properties of mate-rials pronouncedly (Shen and Mao, 2017). It also represents a “chemically clean tool” which can be applied for selectively probing the desired effect, helping to disentangle related and crossover phenomena.

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5.3 Lattice distortion Lattice distortion (LD), representing one of the four core effects of HEA, orig-inates from the deviation of equilibrium atomic positions away from the ideal lattice sites because of the large atomic size mismatch. Akin to the Hume-Rothery rules, LD is considered as a decisive factor in the phase selection rules for HEAs. LD impedes the movement of dislocations and thus results in an additional strengthening in HEAs (Song et al., 2017). LD and/or the local chemical disorder enhance the capability of scattering the electrons and pho-nons, hence reduce the electrical and thermal conductivities of HEAs (Zhang et al., 2015; Fan et al., 2017). Though it influences the structure and various properties of HEA significantly, there is no widely accepted quantitative def-inition of the lattice distortion to date, which hinders the investigation of lat-tice distortion effect on related properties. Some of the proposed models are as follows:

(1) Atomic size mismatch (Zhang et al., 2008):

= (1 − ∑ ) where ci and ri are the molar fraction and atomic radius of the ith element.

(2) Intrinsic residual strains (Ye et al., 2015b):

= 12 [1 − ( + 2)+ 1 ] where xij is the atomic size ratio.

(3) Deviation of lattice coordination (Song et al., 2017): ∆ = 1 ( − ´) + ( − ´) + ( − ´)

where (xi, yi, zi) and (xi´, yi´, zi´) are the reduced coordinates of the unre-laxed and relaxed positions of atom i.

(4) Distribution of interatomic distance (Toda-Caraballo et al., 2015): = ,

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where is the mean value of all first neighbor distances. All the models mentioned above are too complicated and impractical, espe-cially at high pressure in a DAC, because they are based on the parameters that are very difficult to measure. Assessing the magnitude of LD experimen-tally is challenging, as proved by the rigorous analysis performed by Owen et al. (2017; 2018). The direct consequence of LD is the variation of the first neighbor distance, and subsequently the lattice constant, which is an experi-mentally measurable parameter. Thus, a better approach may be to evaluate the magnitude of LD using lattice constant a:

= 1 1 ( − )

where ai are the real edge length of the unit cell, and ai0 are the lattice constants of the undistorted ideal unit cell. The measurement of ai is still almost impos-sible, and the X-ray diffraction technique determines the average value of all ai acquired as a. Consequently, the above equation can be rewritten as (for cubic HEA):

= | − | The undistorted ideal unit cell is imaginary. So Zhou et al. (2008) used the lattice constant of original elemental crystals (OEC) aOEC to replace a0, and get

= | − | The physical implication of this model leads to the evaluation of the deviation of a HEA from the undistorted ideal lattice. According to the principles of selecting the OEC ((1) being one of the principal elements; (2) adopting the same crystal structure as the HEA; (3) distributing homogeneously in HEA; and (4) having the moderate atomic radius) (Zhou et al., 2008), the value of aOEC can represent the lattice parameter of an ideal undistorted lattice to some extent. Furthermore, the results presented in the original paper (Zhou et al., 2008) partly demonstrated the validity of using this model for presenting the lattice distortion of HEA at ambient pressure. Moreover, this model is con-veniently applicable to high pressure.

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5.4 Lattice distortion-induced phase transition In the present study, the pressure was employed for tuning the LD of CoCrFe-NixAl1-x (x=0.5, 0.75) HEAs (Liu et al., 2019d). The CoCrFeNixAl1-x (x=0.5, 0.75) HEAs were compressed up to around 50 GPa and XRD-probed. The degree of LD of CoCrFeNixAl1-x (x = 0.5, 0.75) HEAs was assessed using the parameter of εintr. Several important conclusions are summarized as follows: (1) At ambient pressure, the CoCrFeNixAl1-x HEAs adopt the fcc structure

with low LD (low content of Al), while high LD (high content of Al) sta-bilizes the bcc structure.

(2) The determined EOS parameters of CoCrFeNixAl1-x HEA are listed in Ta-ble 5.1. With the Al concentration increasing, the average atomic volume increase, while the bulk modulus decrease. The reason is that Al atom oc-cupies an atomic volume which is much larger (16.573 Å3/atom) (Dewaele et al., 2004) than those of Co, Cr, Fe, and Ni (11.096, 12.011, 11.760, and 10.942 Å3/atom, respectively) (Dewaele et al., 2008; Ming and Manghnani, 1978). The introduction of Al atom increases the `free volume`, which is easily squeezed out upon compression and conse-quently lowers the bulk modulus (Zhang et al., 2017).

Table 5.1. EOS parameters of CoCrFeNixAl1-x HEAs at ambient conditions.

Sample V0 (Å3/atom)

K0 (GPa) K0´ PTM Ref.

CoCrFeNi 11.42 206.5 4 (fixed) ME∗ Zhang et al., 2017 CoCrFeNi0.75Al0.25 11.66 194 4 (fixed) NaCl Liu et al., 2019d CoCrFeNi0.5Al0.5 11.84 190 4 (fixed) NaCl Liu et al., 2019d CoCrFeAl 12.06 144.6 4 (fixed) neon Liu et al., 2019e CoCrFeAl 11.94 176.1 4 (fixed) NaCl Liu et al., 2019e

∗ Methanol-ethanol mixture. (3) The fcc-CoCrFeNi0.75Al0.25 and bcc-CoCrFeNi0.5Al0.5 transform to the hcp

structure at high pressures. The transformation to the hcp structure com-menced at 20.12 GPa for fcc-CoCrFeNi0.75Al0.25 and at 14.64 GPa for bcc-CoCrFeNi0.5Al0.5. Both phase transitions are sluggish and do not complete at the highest experimental pressure. The sluggishness may originate from the local energy variation caused by the chemical disorder in HEAs. These pressure-induced phase transitions are sketched in Fig. 5.2.

(4) The magnitudes of LD of fcc-CoCrFeNi0.75Al0.25 and bcc-CoCrFeNi0.5Al0.5

are evaluated through εintr. According to the criteria of OEC selection, bcc Fe and fcc Ni were selected as OEC of bcc-CoCrFeNi0.5Al0.5 and fcc-CoCrFeNi0.75Al0.25, respectively. The results indicate that the phase tran-sition commenced when the corresponding εintr values reached their max-ima, implying that LD plays a central role in the phase transition of HEAs. The underlying mechanism is that the lattice distortion introduces extra

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elastic energy which leads to the instability of fcc-CoCrFeNi0.75Al0.25 and bcc-CoCrFeNi0.5Al0.5 lattices.

Figure 5.2. Schematic picture of the phase transition of CoCrFeNixAl1-x (x = 0.5, 0.75) HEAs. HEAs transformed to the hcp structure at high pressures when their LDs reached maximum values.

5.5 Magnetovolume effect in HEAs Controlled expansion alloys, exhibiting a very low coefficient of thermal ex-pansion (CTE), have wide applications in electronics, aerospace engineering, telecommunications, and cryogenic components, where the thermal expansion of engineering structures needs to be critically considered. In 1897, Guillaume discovered a nickel-iron (FeNi36) alloy with uniquely low CTE. This kind of nickel-iron alloy is named Invar alloy, which reflects its invariable dimen-sions over a specific temperature range. Nowadays, more than a century later after the discovery, the underlying mechanism of Invar alloy is still under de-bate. The two popular proposed models are 2γ model (Weiss, 1963) and non-collinear model (van Schilfgaarde et al., 1999). The 2γ model suggests the conventional thermal expansion is counteracted by the volume collapse of iron atoms during the high spin to low spin transition. However, van Schilfgaarde et al. proposed that the extremely low CTE of Invar alloys originated from the volume decrease when the directions of magnetic moments change from par-allel to non-collinear. On all accounts, both models claim that the dependence of volume on magnetism, the so-called magnetovolume effect, is responsible for the Invar effect. HEAs with excellent mechanical properties are promising structural materials. It would be of great advantage if one could design HEAs in which superior mechanical properties are combined with the Invar effect. In the present study (Liu et al., 2019e), the bcc-CoCrFeAl HEA was com-pressed to around 60 GPa, both hydrostatically and non-hydrostatically. The bcc lattice remained stable up to the highest experimental pressure. The mag-netovolume effect was discovered at high pressure by the XRD technique, and

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confirmed and explained by the DFT calculation. This effect was ascribed to the successive collapse of the local magnetic moments of Co and Fe. Upon hydrostatic compression, CoCrFeAl transformed from the ferromagnetic (FM), to paramagnetic (PM), and to non-magnetic (NM) state (Fig. 5.3). The NM state transformed back to the FM state directly without the appearance of the PM state. During the non-hydrostatic compression, only the reversible FM to PM state phase transition was detected. The CTE of CoCrFeAl at ambient pressure was also measured. The values of CTE shows a pronounced and sharp minimum (approaching nearly zero within experimental resolution) at around 770 K, which originates from the volume collapse during the PM to NM phase transition.

Figure 5.3. The magnetic phase transition of CoCrFeAl in hydrostatic (a and b) and nonhydrostatic (c and d) experiments. The calculated magnetic moments of Fe, Co, and the total magnetic moment are also shown.

These results indicate that many unique properties of the newly emerging HEAs await further exploration. Once established, these advantageous prop-erties will widen the range of applications of HEAs. The present results also demonstrate the possibility to design the Invar high-entropy alloys, which could serve as structural materials in precise instruments.

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6. Conclusions and perspectives

Considering all the results as a whole, the presented research demonstrates that high-pressure represents an effective way to tune various properties (structural, electronic, magnetic and so on) of materials, as well as can be ap-plied for the synthesis of materials with exotic properties which are usually not stable or attainable at ambient conditions. B site substituted A2BB`O6 double perovskites represent a class of materials possessing various functional properties, thus have a broad range of applica-tions. In the present study (Liu et al., 2019a), Mn2FeSbO6 was compressed to a pressure of around 50 GPa and probed by techniques of XRD and Raman spectroscopy. Density functional calculations (DFT) aided the interpretation of the experimental data. The results show that the polar LiNbO3-type Mn2FeSbO6, a promising candidate for multiferroic material, can only be syn-thesized at high pressure and moderate temperatures (∼400 K, as estimated from the Raman signal). Another perovskite, Pb2CoTeO6, was compressed to around 60 GPa in searching for the polar structure at high pressure (Liu et al., 2019b). The reversible phase transition between the two centrosymmetric R-3 and I2/m structures was detected, while no polar structure of Pb2CoTeO6 was discovered. These results demonstrate that high-pressure offers an effec-tive way to tailor the structure of double perovskites, and is critical for the synthesis of promising multiferroic materials. However, the pressure effect on the structural evolution of double perovskites is not well studied. Considering various combinations of transition metallic cations on B and B` site, orderly or randomly distributed, a large number of double perovskites with exotic functional properties is expected to be discovered, especially at high pressures and when involving also the A site in the substitution schemes. These materials are worth further investigations in the future. Bandgap energy is one of the decisive parameters of semiconductor materials. Multiferroic oxides, which are considered as nontoxic and stable alternatives of hybrid metallic perovskites in photovoltaic applications, have an intrinsic drawback of a too-large bandgap. In the present study (Liu et al., 2019c), the high-pressure technique was employed for tuning the bandgap energy of mul-tiferroic oxide Mn3TeO6 (MTO). Results of the Raman spectroscopic meas-urements and optical observations reveal a phase transition at high pressure, which is accompanied by the change of visual appearance from colorless to

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dark brown. Analysis of the sequence of UV-vis absorption spectra indicates a bandgap narrowing from 3.15 eV at 18.03 GPa to 2.17 eV at 21.28 GPa. Significantly, the high-pressure phase is quenchable to ambient pressure, where it displays bandgap energy of 1.86 eV, much suitable for photovoltaic applications. The present research outlines a green way of tuning the bandgap energy of multiferroic oxides. However, high-pressure research on these ma-terials is rare to date. Furthermore, the underlying electronic mechanism of the observed bandgap narrowing is unclear. Further investigations with the help of DFT calculations are required for understanding the phenomenon and guiding future experiments. As one of the four core effects controlling the properties of HEA, lattice dis-tortion (LD) is believed to influence the structural and mechanical properties of HEA significantly. In the present study aimed at understanding the LD ef-fect, we used high pressure as a tool for introducing an additional LD in HEA, the structural stability of which was examined in situ by the synchrotron-based XRD technique. The results show that bcc-CoCrFeNi0.5Al0.5 and fcc-CoCrFeNi0.75Al0.25 transform to hcp structure when their LDs reaches a maxi-mum value. The underlying mechanism is that the pressure-induced LD in HEA increases the elastic energy stored in the lattice, and eventually destabi-lizes the lattice, triggering a structural phase transition. These results demon-strate LD plays a critical role in the phase stability of HEA (Liu et al., 2019d). However, the method used in the present study to evaluate the degree of LD is not sufficiently precise. Further investigation is necessary in order to estab-lish a robust and accurate method for the evaluation of LD at high pressure (Owen et al., 2017; Owen and Jones, 2018). HEAs are attracting tremendous and ever-increasing attention since its advent in 2004. So far, investigations have just scratch the surface and many proper-ties of HEAs await characterization. In the present study, the magnetovolume effect of CoCrFeAl HEA has been discovered (Liu et al., 2019e). This effect arises from the collapse of magnetic moments Co and Fe. The volume collapse during the magnetic state transition counteracts the volume expansion from the anharmonic vibrations, thus leading to an extremely small CTE of CoCrFeAl at high temperatures. These results indicate that CoCrFeAl HEA is a potential Invar high-entropy alloy, which combines excellent mechanical and thermal properties in a single material. The present study paves a way for designing HEAs displaying an unprecedented combination of various func-tional properties and superior mechanical properties. However, other func-tional properties, except for the mechanical ones, have rarely been studied to date. In addition to HEA, high-entropy oxides (Rost et al., 2015; Berardan et al., 2017; Sarkar et al., 2018), carbides (Harrington et al., 2019), nitrides (Hsieh et al., 2018), and diborides (Tallarita, et al., 2019) are emerging as promising materials. For example, high-entropy perovskite oxides crystallize

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in the perovskite structure, as well as have a high configuration entropy orig-inating from the random distribution of multi-cations in B and/or A structural sites. Hence, this class of materials bridges two fascinating fields, multiferroic oxides and high-entropy materials (Jiang et al., 2018; Witte et al., 2019). There is no doubt that high-pressure techniques will play a critically important role in synthesizing and tuning the properties of these high-entropy multifunctional materials, in order to meet the requirements of diverse technological applica-tions.

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7. Summary in Swedish

Med beaktande av alla resultat i sin helhet visar den presenterade forskningen att högtryck representerar ett effektivt sätt att optimera olika egenskaper av material (strukturella, elektroniska, magnetiska och så vidare), liksom kan an-vändas för syntes av material med exotiska egenskaper som vanligtvis inte är stabila eller kan uppnås vid rumsförhållanden. B-platssubstituerade A2BB`O6-dubbla perovskiter representerar en klass av material som har olika funktionella egenskaper, och således har ett brett an-vändningsområde. I den aktuella studien (Liu et al., 2019a) komprimerades Mn2FeSbO6 till ett tryck av cirka 50 GPa och undersöktes med hjälp av rönt-gendiffraktion (X-Ray Diffraction, XRD) och Raman spektroskopi. Densitets-funktionella beräkningar (Density Functional Theory, DFT) hjälpte till att tolka experimentella data. Resultaten visar att den polära LiNbO3-typen Mn2FeSbO6, är en lovande kandidat som ett multiferroiskt material, vilket endast kan syntetiseras vid högt tryck och måttliga temperaturer (∼400 K, en-ligt uppskattning från Ramansignalen). En annan perovskit, Pb2CoTeO6, kom-primerades till cirka 60 GPa för att leta efter den polära strukturen vid högt tryck (Liu et al., 2019b). Den reversibla fasövergången mellan de två centro-symmetriska R-3 och I2/m-strukturerna upptäcktes, medan ingen polär struk-tur av Pb2CoTeO6 upptäcktes. Avhandlingens resultat visar att högtryck erbju-der ett effektivt sätt att skräddarsy strukturen för dubbla perovskiter, och är avgörande för syntesen av lovande multiferroiska material. Tryckseffekten på den strukturella utvecklingen av dubbla perovskiter är emellertid inte väl stu-derad. Med tanke på olika kombinationer av övergångsmetalliska katjoner på B- och B’-platsen, organiserade eller slumpmässigt fördelade, förväntas ett stort antal dubbla perovskiter med exotiska funktionella egenskaper upp-täckas, särskilt vid höga tryck och även när A-platsen involveras i substitut-ionsscheman. Dessa material är värda ytterligare undersökningar i framtiden. Bandgapsenergi är en av de avgörande parametrarna för halvledarmaterial. Multiferroiska oxider, som betraktas som icke-toxiska och stabila alternativ av hybridmetalliska perovskiter i fotovoltaiska applikationer, har en innebo-end nackdel i och med ett för stort bandgap. I den aktuella studien (Liu et al., 2019c) användes högtryckstekniken för att justera bandgapsenergin för den multiferroiska oxiden Mn3TeO6. Resultaten av Ramans spektroskopiska mät-ningar och optiska observationer avslöjar en fasövergång vid högt tryck, vilket

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åtföljs av förändringen av det visuella utseendet från färglöst till mörkbrunt. Analys av sekvensen av UV-vis absorptionsspektra indikerar att bandgapet minskar från 3.15 eV vid 18.03 GPa till 2.17 eV vid 21.28 GPa. Markant, högtrycksfasen bevaras vid tryckminskning till ett omgivningstryck, där den visar en bandgapsenergi på 1.86 eV, mycket lämplig för fotovoltaiska appli-kationer. Den nuvarande forskningen beskriver ett miljövänligt sätt för att fin-justering av bandgapsenergin för multiferroiska oxider. Högtrycksforskningen på dessa material är emellertid begränsad. Vidare är den underliggande elektroniska mekanismen för den observerade bandgapsminskningen oklar. Ytterligare undersökningar med hjälp av DFT-beräkningar krävs för att förstå fenomenet och vägleda framtida experiment. Som en av de fyra kärneffekterna som styr egenskaper hos högentropilege-ringar (High Entropy Alloy, HEA), tros gitterförvrängning (Lattice Distortion, LD) påverka de strukturella och mekaniska egenskaperna hos HEA avsevärt. I den aktuella studien som syftar till att förstå LD-effekten, använde vi hög-tryck som ett verktyg för att införa en ytterligare gitterförvrängning i HEA, vars strukturella stabilitet undersöktes in situ med den synkrotronbaserade XRD-tekniken. Resultaten visar att bcc-CoCrFeNi0.5Al0.5 och fcc-CoCrFeNi0.75Al0.25 transformerar till hcp-struktur när deras gitterförvrängning når ett maximivärde. Den underliggande mekanismen är att den tryckinduce-rade gitterförvrängning i HEA ökar den elastiska energin lagrad i gittret och så småningom destabiliserar gittret, vilket utlöser en strukturell fasövergång. Dessa resultat visar att LD spelar en kritisk roll i fasstabiliteten hos HEA (Liu et al., 2019d). Metoden som användes i den här studien för att utvärdera gra-den av LD är emellertid inte tillräckligt exakt. Ytterligare studier är nödvändig för att upprätta en robust och korrekt metod för utvärdering av LD vid hög-tryck (Owen et al., 2017; Owen och Jones, 2018). Högentropilegeringar lockar en enorm och ständigt ökande uppmärksamhet sedan dess upptäcktes i 2004. Hittills har forskningsstudier bara skrapat ytan och många egenskaper hos dessa typ av legeringar väntar på karakterisering. I den aktuella studien har magnetovolymeffekten av CoCrFeAl HEA upp-täckts (Liu et al., 2019e). Denna effekt uppstår från kollaps av magnetiska moment av järn och kobolt. Volymkollapsen under den magnetiska tillstånds-övergången motverkar volymutvidgningen från de anharmoniska vibration-erna, vilket leder till en extremt liten värmeutvidgningskoefficient av CoCrFeAl vid höga temperaturer. Dessa resultat indikerar att CoCrFeAl HEA är en potentiell Invar-högentropilegering, som kombinerar utmärkta meka-niska och termiska egenskaper i ett enda material. Den nuvarande studien ba-nar väg för ett sätt att designa legeringar som visar en aldrig tidigare skådad kombination av olika funktionella egenskaper, inklusive överlägsna meka-niska egenskaper. Emellertid har andra funktionella egenskaper, förutom de mekaniska egenskaperna sällan studerats. Förutom HEA, högentropioxider

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(Rost et al., 2015; Berardan et al., 2017; Sarkar et al., 2018), karbider (Har-rington et al., 2019), nitrider (Hsieh et al., 2018), och diborider (Tallarita et al., 2019) framträder också som lovande material. Exempelvis kristalliserar högentropi perovskitoxider i perovskitstrukturen såväl som de har en högkon-figurationsantropi som härrör från slumpmässig fördelning av multikatjoner i B- och / eller A-strukturella platser. Därför överbryggar denna klass av material två fascinerande fält, multiferroiska oxider och material med hög entropi (Jiang et al., 2018; Witte et al., 2019). Det råder ingen tvekan om att högtryckstekniken kommer att spela en kritiskt viktig roll i syntes och juste-ring av egenskaperna hos dessa högentropiska multifunktionella material för att uppfylla kraven i olika teknologiska tillämpningar.

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Acknowledgments

First of all, I would like to express my deepest gratitude to my supervisors Prof. Peter Lazor, Prof. Roland Mathieu, Dr. Guoyin Shen, and Dr. Viktor Struzhkin for their support and encouragement, without which I could not ac-complish the goal of this Ph.D. project. I learned a lot from you, e.g., how to think like a scientist and how to work as a scientist. My most sincere thanks go to Peter. I still remember the very cold midnight when you picked me up at Arlanda airport in January of 2016. Your appear-ance and your kindness made me felt very warm on the cold night. Thank you for performing the synchrotron XRD experiment when I had visa problems. Thank you for always be positive to my ideas. You always can find time to discuss the scientific problems with me even you are very busy. Thank you for the delicious dinners and thank Lucia and Anna for the great cookies and cakes they made. Thank you all for the nice moments we had with Nasse, Domino, Karamell, Piff, and the fish. I would like to express my sincere gratitude to my colleagues, without whom this Ph.D. study would never be accomplished. I would like to thank Sergey Ivanov (UU and Karpov’s Institute of Physical Chemistry, Russia) for provid-ing high-quality crystals, characterizing the HEA samples, as well as for his help with analyzing the XRD data. Shuo Huang (KTH), Levente Vitos (KTH), and Hongxing Song (NYU) are acknowledged for the DFT calculations. I am grateful to Dongzhou Zhang (University of Hawaii at Manoa), Elena Bykova (PETRA III), Xiaodong Li (BSRF), Minjie Dong (UU), Jan-Erik Rubensson (UU) for their help with the XRD experiments. Special thanks go to Henrik Skogby (Swedish Museum of Natural History) for providing the natural MFSO single crystal and help with the UV-vis absorption experiment. I am indebted to Bjarne Almqvist (UU) for his help with the magnetic measurement on HEA, and Matthias Weil (TU Wien) for providing high-quality samples. Bela Varga (Transilvania University) and Lajos Varga (Wigner Research Cen-ter for Physics) are appreciated for the CTE measurement of HEA samples. The in situ high-pressure XRD experiments were performed at several high-pressure beamlines at the synchrotron photon source around the world, includ-ing the 4W2 high-pressure beamline of Beijing Synchrotron Radiation Facil-ity, the 15U hard X-ray micro-focusing beamline of Shanghai Synchrotron

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Radiation Facility, the P02.2 extreme conditions beamline of PETRA III, and GeoSoilEnviroCARS of the Advanced Photon source. The beamlines men-tioned above are appreciated for providing the indispensable beamtime for our research. Thanks are due to the beamline scientists for their support and assis-tance during the experiments. I am grateful to all my colleagues in the MPT program, Department of Earth Sciences, Uppsala University for every great moment we had in the corridor. Special thanks go to Hemin Koyi for your wise advice and encouragement during the nice conversations in your office. I would like to thank Valentin Troll for sharing your opinions and your experience of scientific research at Beijing Capital International Airport. I hope the chicken claw did not scare you too much. I would like to thank the friends (you know who you are) I met in Uppsala. Thank you all for the great memories we shared in the last four years. I thank my parents, my parents-in-law, my brother and my sisters for their support. You are always behind me whenever I meet any problems.

Last but not least I would like to thank my wife Lei for her endless love and support. It is a tough time for the last four years because we lived ∼7000 km away, more than the distance from the surface to the core of Earth. Finally, we made it. Anything is meaningless without your love.

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