# TOWARDS THE CONTROL OF THERMAL EXPANSION: FROM 1996 TO TODAY

EDITED BY : Andrea Sanson and Jun Chen PUBLISHED IN : Frontiers in Chemistry

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# TOWARDS THE CONTROL OF THERMAL EXPANSION: FROM 1996 TO TODAY

Topic Editors: Andrea Sanson, University of Padua, Italy Jun Chen, University of Science and Technology Beijing, China

Citation: Sanson, A., Chen, J., eds. (2019). Towards the Control of Thermal Expansion: From 1996 to Today. Lausanne: Frontiers Media. doi: 10.3389/978-2-88945-934-6

# Table of Contents

Fengxia Hu, Feiran Shen, Jiazheng Hao, Yao Liu, Jing Wang, Jirong Sun and Baogen Shen

*34 Mechanisms and Materials for NTE*

J. Paul Attfield

*40 Adjustable Thermal Expansion Properties in Zr2MoP2O12 /ZrO2 Ceramic Composites*

Hongfei Liu, Weikang Sun, Xiang Xie, Lu Yang, Zhiping Zhang, Min Zhou, Xianghua Zeng and Xiaobing Chen

*46 Synthesis of Zr2WP2O12 /ZrO2 Composites With Adjustable Thermal Expansion*

Zhiping Zhang, Weikang Sun, Hongfei Liu, Guanhua Xie, Xiaobing Chen and Xianghua Zeng

*52 Near-Zero Thermal Expansion and Phase Transitions in HfMg1−xZnxMo3O12*

Sailei Li, Xianghong Ge, Huanli Yuan, Dongxia Chen, Juan Guo, Ruofan Shen, Mingju Chao and Erjun Liang

*61 Negative Thermal Expansion Over a Wide Temperature Range in Fe-Doped MnNiGe Composites*

Wenjun Zhao, Ying Sun, Yufei Liu, Kewen Shi, Huiqing Lu, Ping Song, Lei Wang, Huimin Han, Xiuliang Yuan and Cong Wang

*Scattering and Density Functional Calculations* Baltej Singh, Mayanak K. Gupta, Ranjan Mittal, Mohamed Zbiri, Sarah A. Hodgson, Andrew L. Goodwin, Helmut Schober and Samrath L. Chaplot

*112 Control of Uniaxial Negative Thermal Expansion in Layered Perovskites by Tuning Layer Thickness*

Chris Ablitt, Arash A. Mostofi, Nicholas C. Bristowe and Mark S. Senn

*125 Negative Thermal Expansion Near the Precipice of Structural Stability in Open Perovskites*

Connor A. Occhialini, Gian G. Guzmán-Verri, Sahan U. Handunkanda and Jason N. Hancock

Lindsay Young, Jennifer Gadient and Cora Lind

Wei Wang, Huiming Liu, Rongjin Huang, Yuqiang Zhao, Chuangjun Huang, Shibin Guo, Yi Shan and Laifeng Li

# Editorial: Towards the Control of Thermal Expansion: From 1996 to Today

Andrea Sanson1 \* and Jun Chen2

*1 Department of Physics and Astronomy, University of Padua, Padua, Italy, 2 School of Mathematics and Physics, University of Science and Technology Beijing, Beijing, China*

Keywords: thermal expansion control, negative thermal expansion (NTE), materials physics and chemistry, materials science, solid state physics

**Editorial on the Research Topic**

### **Towards the Control of Thermal Expansion: From 1996 to Today**

Most materials expand on heating, known as positive thermal expansion (PTE). Thermal expansion is critical in many technological applications, like precise instruments, glazes and coating materials, optical and electronic devices, high-temperature materials design. As a matter of fact, different materials in contact with each other can have different thermal expansion, giving rise to thermal shock breakage. For this reason, controlling thermal expansion represents a challenge for materials design.

Negative thermal expansion (NTE), that is material contraction on heating over a certain temperature range, is relatively rare but has important technological applications. Since the large isotropic NTE was discovered in zirconium tungstate over a wide temperature range in 1996, the interest in NTE has rapidly grown to become the most promising route to achieve the control of thermal expansion. Since then, many NTE materials have been discovered.

NTE phenomenon is known to arise from a range of different physical mechanisms, such as lowenergy vibrational modes, ferroelectricity, magnetic, and valence transitions. However, this does not lead to straightforward control of thermal expansion. Moreover, composites of negative and positive thermal expansion materials may fail after repeated cycling, so direct control of thermal expansion within a single homogenous phase is desirable and yet difficult to achieve. To date, different methods are under investigation to achieve the control of thermal expansion.

The present Research Topic includes a collection of original research and review (mini review) articles dedicated to the physical-chemical phenomena connected to NTE and to the state-of-theart for control thermal expansion. The collection begins with a review by Takenaka on phasetransition type NTE materials, presenting some recent works related to how giant NTE materials are used as practical thermal expansion compensators. Hu et al. present a second review on the NTE behavior in materials with giant magnetocaloric effects (MCE), including some representative examples of MCE materials. An article perspective is presented by Attfield, where NTE is classified in terms of intrinsic structural and electronic mechanisms, and morphological NTE due to the specific morphology of the sample.

Many articles of the collection are dedicated to developing new materials with zero or adjustable thermal expansion. Liu et al. fabricated Zr2MoP2O12/ZrO2 composites with a variable coefficient of thermal expansion (CTE) from −5.7×10−6 K −1 to +5.6×10−6 K −1 by changing the Zr2MoP2O12 content, reaching a near zero CTE from 25 to 700◦C for the composition ratio Zr2MoP2O12/ZrO2 of 2:1. Similarly, Zhang et al. synthetized Zr2WP2O12/ZrO2 composites and adjusted the CTE

Edited and reviewed by: *Bretislav Friedrich, Fritz-Haber-Institut, Germany*

> \*Correspondence: *Andrea Sanson<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

> Received: *29 March 2019* Accepted: *08 April 2019* Published: *08 May 2019*

#### Citation:

*Sanson A and Chen J (2019) Editorial: Towards the Control of Thermal Expansion: From 1996 to Today. Front. Chem. 7:284. doi: 10.3389/fchem.2019.00284*

**5**

from −3.3×10−6 K −1 to +4.1×10−6 K −1 by varying the mass ratio Zr2WP2O12/ZrO2, obtaining again a zero CTE for the ratio 2:1. Near-zero thermal expansion behavior over a wide temperature range was also found out by Li et al. in HfMg1−xZnxMo3O12 solid solutions, whose phase transition temperature from monoclinic to orthorhombic structure increases with the content of Zn2+. Giant NTE properties were observed in Fe-doped MnNiGe compounds by Zhao et al. with CTE values of about −285×10−6 K −1 and −1167×10−6 K −1 in Mn0.90Fe0.10NiGe and MnNi0.90Fe0.10Ge, respectively. Furthermore, these materials were combined with Cu in order to control their NTE properties. Guo et al. investigated NTE and magnetic properties of anti-perovskite Ga1−xCrxN0.83Mn3 compounds. They observed that Cr doping introduces ferromagnetic order thus giving rise to the broadening of NTE temperature window. Finally, Zhou et al. obtained huge PTE and NTE in fence-like metal organic frameworks obtained with a series of transition metal ions.

Part of the published works have a computational character. By using an efficient approach for obtaining the variation of the dynamical matrix as a function of the lattice constant, Vila et al. obtained that the large NTE of ZrW2O8 arises almost exclusively from the transverse contributions of the O-atoms. A second study was performed by Vila et al. on ZrW2O8, combining theoretical calculations of the structure and vibrational properties with the experimental results from extended x-ray absorption fine structure spectroscopy. Ab initio lattice dynamics calculations were combined with inelastic neutron scattering by Singh et al. to study the NTE dynamics in the metal organic framework compound AgC4N3. Ablitt et al. performed density functional theory simulations in Ruddlesden– Popper layered perovskite series, showing that by changing the fraction of layer interface in the structure one may control the anisotropic compliance necessary for the pronounced uniaxial NTE observed in these systems. Occhialini et al. discussed the broad issue of structural NTE with particular attention on perovskite-structured materials, providing a model treatment beyond mean field theory to identify the key elements that move toward control of NTE. First-principles calculations were performed in NiSi and isostructural compound NiGe by Goel et al. with the aim of studying the phonon modes which give the major contribution to the NTE behavior in NiSi, and reasons for negligible NTE in NiGe.

Lastly, high-pressure synchrotron powder X-ray diffraction studies of Cr2Mo3O12 and Y2Mo3O12 were conducted by Young et al. revealing that the monoclinic polymorphs of these materials do not undergo phase transitions within the studied pressure range, making them unique among the A2M3O12 family of NTE materials. Jiang et al. investigated the thermal expansion properties of the ultraviolet nonlinear optical crystal BaAlBO3F2 and the practical implications were discussed. Wang et al. proposed the new strain gauge method to measure the thermal expansion and magnetostriction of solid materials at low temperatures, opening up an interesting way for exploring potential magnetostrictive and NTE materials.

In summary, the present papers taken together give an overview of research on NTE and on the tuning of thermal expansion. We hope that the different perspectives here reported will inspire new studies and findings toward the design of materials with controlled thermal expansion.

# AUTHOR CONTRIBUTIONS

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2019 Sanson and Chen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Progress of Research in Negative Thermal Expansion Materials: Paradigm Shift in the Control of Thermal Expansion

### Koshi Takenaka\*

*Department of Applied Physics, Nagoya University, Nagoya, Japan*

To meet strong demands for the control of thermal expansion necessary because of the advanced development of industrial technology, widely various giant negative thermal expansion (NTE) materials have been developed during the last decade. Discovery of large isotropic NTE in ZrW2O8 has greatly advanced research on NTE deriving from its characteristic crystal structure, which is now classified as *conventional* NTE. Materials classified in this category have increased rapidly. In addition to development of conventional NTE materials, remarkable progress has been made in *phase-transition-type* NTE materials using a phase transition accompanied by volume contraction upon heating. These giant NTE materials have brought a paradigm shift in the control of thermal expansion. This report classifies and reviews mechanisms and materials of NTE to suggest means of improving their functionality and of developing new materials. A subsequent summary presents some recent activities related to how these giant NTE materials are used as practical thermal expansion compensators, with some examples of composites containing these NTE materials.

Keywords: negative thermal expansion, phase transition, thermal expansion control, composites, microstructural effects

# INTRODUCTION

Control of thermal expansion, an urgent demand in modern industrial technology, is making remarkable progress. Even a minute change of 10−5 in linear distortion fatally degrades the performance of high-precision devices and instruments. Furthermore, for a device comprising multiple materials, mismatched thermal expansion between the constituents themselves can cause severe damage such as exfoliation of interfaces and breakage of wires. In addition to work in fields that have traditionally avoided the adverse influence of thermal expansion such as optical instruments and precise machining equipment, control of thermal expansion has been strongly sought in recent years for advanced electronics such as power semiconductor devices, thermoelectric conversion systems, and fuel cells. Difficulties attributable to thermal expansion control are universal and are difficult to resolve.

The core technology of thermal expansion control is negative thermal expansion (NTE) materials: substances that contract when heated (Chu et al., 1987; Sleight, 1998; Evans, 1999; Barrera et al., 2005; Lind, 2012; Takenaka, 2012; Chen et al., 2015). After discovery of the large isotropic NTE of ZrW2O8 in 1996, for which the coefficient of linear thermal expansion αL (subscript L signifying "linear") reaches −9 × 10−6 K −1 (Mary et al., 1996), the successive discovery of giant

#### Edited by:

*Jun Chen, University of Science and Technology Beijing, China*

#### Reviewed by:

*Ren Zhang, Intel (United States), United States Oh-Hoon Kwon, Ulsan National Institute of Science and Technology, South Korea Cora Lind, University of Toledo, United States*

#### \*Correspondence:

*Koshi Takenaka<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

> Received: *22 March 2018* Accepted: *12 June 2018* Published: *02 July 2018*

#### Citation:

*Takenaka K (2018) Progress of Research in Negative Thermal Expansion Materials: Paradigm Shift in the Control of Thermal Expansion. Front. Chem. 6:267. doi: 10.3389/fchem.2018.00267*

**7**

NTE materials has encouraged remarkable progress of research in this field, particularly during the last decade. Such development has brought a paradigm shift for the control of thermal expansion. For further improvement of the NTE functions and for the development of new materials, the achievements of the last two decades in this field are summarized briefly, particularly addressing recently discovered giant NTE materials (**Figure 1**).

# POSITIVE AND NEGATIVE THERMAL EXPANSION

# Thermal Expansion of Solids

The origin of thermal expansion of solids can be summarized briefly (Cochran, 1973). One might consider atoms connected together by springs as a model of solids, but these springs are anharmonic and do not exactly and simply obey Hooke's law. The atoms are prevented from becoming extremely close to one another because of Pauli's exclusion principle. As a result, excursions to longer interatomic distances occur more readily than those to shorter interatomic distances. Consequently, the average interatomic distance increases concomitantly with increasing temperature T. More intuitively, one can generally infer from Pauli's exclusion principle that as the temperature rises and the thermal vibration of an atom increases, it tries to maintain its distance from other atoms to avoid mutual collision. This increasing distance with vibration explains thermal expansion.

# Conventional NTE Materials

In stark contrast to ordinary materials, some materials contract upon heating. Some examples are those of a silicon oxide family including β-eucryptite (LiAlSiO4) and cordierite (Mg2Al2Si5O18), which were reported in the 1950s (Gillery and Bush, 1959). These silicates have strong covalent bonds such as Al–O and Si–O bonds, and not so strong ionic bonds such as Li–O and Mg–O bonds. The ionic bonds expand on heating, resulting in the expansion of two-dimensional sheets in β-eucryptite, for example. Thermal expansion of these ionic bonds pulls the two-dimensional sheets closer together because these two-dimensional sheets are joined by strong covalent bonds that do not expand when heated (**Figure 2**). For β-eucryptite with a hexagonal crystal lattice, on warming from 293 K to 1073 K, the in-plane (a axis) direction in which the Li–O bond is dominant expands 0.62%, whereas the out-of-plane (c axis) direction, in which the Si–O bond is dominant, contracts 1.39%. This thermal distortion causes unit-cell volume contraction of 0.15%. From another viewpoint, open spaces are filled by the thermal distortion of strong covalent bonds. This concept is exemplified more clearly in the open-framework or flexiblenetwork materials described next. Readers might doubt that the NTE of β-eucryptite is much larger. Details of the discrepancy between the unit-cell volumetric NTE and the bulk NTE are discussed in Chapter 4.

Flexible-network materials are a well-known family of NTE materials that includes ZrW2O8 and vanadates and phosphates of certain kinds (Mary et al., 1996; Pryde et al., 1996; Evans et al., 1997). This network consists of rigid units connected by soft

linkages. The rigid units are formed by strong covalent bonds. For ZrW2O8, W–O covalent bonds are strong. Therefore WO4 units are rigid. They do not expand on heating. By contrast, although the W–O and Zr–O bond distances are not changed, the Zr–O– W linkages are soft. Transverse oxygen displacement is induced easily on heating. These displacements consume open spaces in the crystal structure, resulting in volumetric NTE (**Figure 3**). Different from the silicates, anisotropic lattice thermal expansion is unimportant. The volume change related to NTE is much greater. In fact, ZrW2O8 has attracted great attention because of its large and isotropic NTE of αL = −9 × 10−6 K −1 (Mary et al., 1996). NTE appears at the whole T range below 1443 K. The total volume change related to NTE, 1V/V, reaches 2.7% (Evans, 1999).

Negative thermal expansion that is explainable from the concept that strong atomic bonds and thermally induced deformation fill open spaces in the crystal lattice explains conventional NTE materials (**Figure 1**), which include widely diverse materials. In addition to cyanides (Chapman et al., 2006; Phillips et al., 2008), the fluoride group (Greve et al., 2010; Attfield, 2011; Chatterji et al., 2011; Chen et al., 2017), such as ScF3 and ZnF2, has attracted attention recently. Particularly, Cd(CN)2·xCCl4 shows large NTE of αL = −34 × 10−6 K −1 and 1V/V = 2.1% at T =175–375 K (Phillips et al., 2008).

At present, most industrial thermal-expansion compensators, including β-eucryptite, belong to the group of conventional type oxides. This type of NTE has a structural origin for its phenomena. Therefore, NTE appears in almost the entire T range, which is extremely important industrially. However, when discussing practically used materials, their NTE magnitude, at most αL = −7 × 10−6 K −1 , is not large from today's perspective. Because the coexistence of strong and not strong chemical bonds is fundamentally important for conventional NTE, low thermal conductivity and low stiffness are unavoidable in these materials. Low thermal conductivity and low stiffness are weak points even for some phase-transition-type NTE materials described in the next chapter. Diligent efforts are continuing toward overcoming them. For example, high thermal conductivity is indispensable for rapid heat dissipation of devices. Development of NTE materials with high thermal conductivity is desired.

# PHASE-TRANSITION TYPE NTE MATERIALS

Various attempts have been made to overcome the shortcomings of the conventional NTE materials presented in the preceding chapter. The current trend of NTE material development is to use the phase transition accompanied by volume contraction upon heating. The effectiveness of this approach was recognized widely by discovery of the giant NTE of αL = −25 × 10−6 K −1 in antiferromagnetic antiperovskite Mn3Zn1−xGexN, which uses magnetovolume effects (Takenaka and Takagi, 2005). The giant NTE of manganese nitride strongly influenced subsequent NTE research, leading to the discovery of many NTE materials using magnetic, ferroelectric, charge-transfer, and metal–insulator phase transitions. The phase-transition type NTE concept became dominant in the field (**Figure 1**). The relation between phase transition and NTE might not be a modern concept because NTE accompanying the magnetic transition (Fe-Pt Invar alloy, Wasserman, 1990) and the ferroelectric transition (PbTiO3, Shirane and Hoshino, 1951) has been known for a long time. The novelty of the present method is the modification of the properties of "mother" materials showing a phase transition (in many cases, first-order phase transition), intentionally using chemical approaches such as element substitution (**Figure 4**).

Specifications of the recently discovered giant NTE materials are presented in **Table 1**. Phase-transition type materials have an operating temperature that is limited to several tens to 100 K around the phase transition, but they have a negative αL that is several times to 10 times larger than those of conventional type materials. Although a wide operating temperature window 1T is generally suitable for practical applications, limited 1T presents no difficulty in many cases, such as precision equipment that is expected to operate at room temperatures. Bi0.95La0.05NiO3 exhibits large negative αL of −82 × 10−6 K −1 (Azuma et al., 2015), which is comparable to the magnitude of positive αL of epoxy resin, although the operating-temperature window 1T is not so wide (60 K). Despite that operating temperature window limitation, it is of great importance that it suppresses the thermal expansion of plastics, which has heretofore been difficult.

For phase-transition-type NTE materials, a certain mechanism causes excessive shrinkage that can overcome positive lattice thermal expansion. The mechanisms of prototypical phase-transition-type NTE are described in

phase-transition-type materials. Instead, the total volume change 1*V*/*V* is the intrinsic index indicating the potential of NTE.

*Microstructural effects are not considered. Parameters of materials with phase transition accompanied by large volume contraction upon cooling, not broadened, are also listed for comparison.*

*aAveraged value when the material is anisotropic.*

*bFor NTE region or lower-temperature, larger-volume phase.*

*cCV, conventional; MG, magnetic transition; FE, ferroelectric transition; CT, charge-transfer transition; MI, metal–insulator transition.*

*dD, dilatometry; N, neutron diffraction; X, X-ray diffraction.*

this chapter. It is noteworthy that the mode of classification, including the conventional type, is not absolute. For example, ferroelectric transition and charge-transfer transition have a common point of charge disproportionation. Other phase transitions such as structural phase transition are often coupled with the magnetic transition.

It is noteworthy that slope αL presents a tradeoff relation with the width of operating-temperature window 1T in the case of phase-transition-type NTE materials (**Figure 4**). The total volume change 1V/V is a value that is peculiar to the substance. It is difficult to increase it artificially. As a result, the wider the operating-temperature window 1T becomes, the smaller the negative slope αL becomes. For isotropic materials, we obtain the simple relation of 1V/V = 3αL1T. Therefore, slope αL is not intrinsic for such phase-transition-type materials. Instead, 1V/V is the intrinsic and the most important index indicating the potential of NTE. The word "giant" is customarily used in the field, but no clear definition exists. One important turning point was the discovery of ZrW2O8 in 1996, and a material that surpasses it by the negative coefficient of linear thermal expansion and/or the total volume change related to NTE: a so-called giant NTE material.

# Magnetic Transition

The magnetovolume effect is a phenomenon by which the volume changes according to the amplitude of the magnetic moment in itinerant systems. The relative volume change attributable to magnetism is known as the spontaneous volume magnetostriction ωs . Generally speaking, less-itinerant electrons are necessary for magnetism. Electronic spins are aligned via the exchange interaction. That exchange interaction does not work well when electrons are itinerant. Volume expansion decreases the overlap of electronic orbitals and makes electrons less itinerant. This effect is explainable by the electronic theory of solids as follows: volume expansion suppresses the bandwidth and condenses the density of states near the Fermi level EF, which is helpful for magnetism (**Figure 5**). Therefore, if possible, the system expands the volume to assist magnetism when the magnetic order sets in. This expansion is the magnetovolume effect, which is intimately related with the origin of magnetism in metals. Therefore, it has persisted as a central topic in the field of condensed-matter physics.

The materials classified into this category include 36Ni-Fe alloy (Invar alloy, which has low thermal expansion rather than negative thermal expansion) (Wasserman, 1990), Fe3Pt (Sumiyama et al., 1979), YMn2 (Nakamura et al., 1988) in the past, and Mn3AN (where A is a transition metal or semiconducting elements, Takenaka and Takagi, 2005; Hamada and Takenaka, 2011; Wang et al., 2012; Takenaka et al., 2014), La(Fe, Si, Co)13 (Fujita et al., 2001; Huang et al., 2013), and MnCo0.98Cr0.02Ge (Zhao et al., 2015) in recent years. Mass production technology developed in 2012 for manganese nitrides has made them commercially available (Smartec R ; Kojundo Chemical Lab. Co. Ltd., Japan, Kawahara et al., 2017).

The low thermal expansion of 36Ni-Fe Invar alloy was reportedly explained by the difference in atomic radius in the early stages of research. The concept of the 2γ model (Weiss,

1963) is that upon heating, the spin configuration of Fe changes gradually from a high-spin state with a larger radius to a lowspin state with a smaller radius. A controversy has long persisted (van Schilfgaarde et al., 1999) between this atomic picture and the itinerant-electron picture described in earlier paragraphs, which emphasizes the contribution from electronic density anomaly near EF (Wohlfarth, 1977; Moriya and Usami, 1980). Although details are not included herein, metallic electronic images are regarded as superior in the sense that they can universally explain the magnetovolume effect of various materials, not merely Invar alloys. Nevertheless, differences in atomic radius between highspin and low-spin states can play an important role in volume change in real materials such as cobalt oxides (Burley et al., 2004). The 2γ model, which still holds importance as a possible mechanism of NTE, is closely related to NTE caused by charge transfer in the sense that NTE is induced by a change in the atomic radius.

Negative thermal expansion is reported also for localizedmoment magnets of certain kinds. Actually, NTE is known to appear in the T range of several tens of degrees on the high T side of the magnetic transition with a compound having a certain spinel or breathing pyrochlore structure (Hemberger et al., 2007; Okamoto et al., 2018; Pokharel et al., 2018). In these materials, NTE disappears below the critical temperature at which the magnetic long-range order is formed. From the localized-moment picture, the magnetovolume effect is attributed to the peculiar volume dependence of the magnetic exchange interaction J, ∂J/∂ω (ω = 1V/V) (Hausch, 1973). The generalized framework extended to the strain derivative of J is also discussed (Filippetti and Hill, 2000). The argument based on the Bethe–Slater curve of single J discussed previously is too naive to explain the diverse phenomena of real materials. However, if

there exist multiple (e.g., ferromagnetic and antiferromagnetic) J and competition between them, then the once discarded localized-moment picture might be revived as worthy of consideration.

# Ferroelectric Transition

Actually, NTE is widely known to appear in ferroelectric materials with charge disproportionation such as PbTiO3 (Shirane and Hoshino, 1951), 0.4PbTiO3-0.6BiFeO3 (Chen et al., 2006), Sn2P2S6 (Rong et al., 2016), and Pb(Ti,V)O3 (Pan et al., 2017). From general consideration of the relation between valence and bond length, the averaged bond length in the charge disproportionate case is greater than the bond length in the charge uniform case (Evans, 1999, **Figure 6**). Atomic bonds are readily expanded, but they are difficult to shrink. We can regard that fact as representing a kind of anharmonicity of atomic bonds. It is noteworthy that anisotropy is fundamentally important for NTE materials of this type. Phenomenologically, dielectric polarization corresponds to volume change (Chen et al., 2015), similar to magnetic NTE materials in which magnetic moments are intimately related to the volume change, but their physical origin differs greatly.

# Charge-Transfer Transition

When charge transfer occurs between the constituent elements, atoms with an increasing number of valence electrons become larger. On the other hand, those with a decreasing number of valence electrons become smaller. However, the change in the atomic radius varies according to the atomic species, electronic configuration, etc. In addition, the effect of the atomic radius on the crystal size depends on the atom's position in the crystal structure. If the contribution from atoms with a decreasing number of valence electrons upon heating is greater, then one can expect net NTE.

A famous example of charge-transfer-type NTE materials, bismuth-nickel oxides (Azuma et al., 2011, 2015), is discussed next. When these oxides are warmed, charges are transferred from Ni to Bi. Therefore, the atomic radius of Ni contracts

occurs, because the higher-valence interatomic bond length does not shrink as much as the lower-valence one expands (Bottom), the bond length becomes longer than that of the averaged case (Upper).

and that of bismuth expands on warming, but the atomic radius of nickel dominates the lattice volume because the Ni–O octahedron dominates the lattice volume. For that reason, the net volumetric NTE occurs in the bismuth-nickel oxide. A similar mechanism functions for NTE of LaCu3Fe4O12 (Yamada et al., 2011).

Negative thermal expansion is also induced by intra-atomic charge transfer that increases the 4f electron number with decreasing temperature. For example, Sm1−xYxS (Jayaraman et al., 1975; Alekseev et al., 2006), Sm2.75C60 (Arvanitidis et al., 2003), and YbGaGe (Salvador et al., 2003; Sleight, 2003) are known for negative or low thermal expansion by such a mechanism. In the case of Sm, two electronic configurations of (4f) 5 (5d) 1 and (4f) 6 compete energetically, but the atomic radius is determined mainly by the 4f electron number. Therefore, NTE appears if the electrons are transferred from the 5d to the 4f orbitals with decreasing temperature.

# Metal–Insulator Transition

An example in which the effect of electronic repulsion manifests as an apparent physical property is a Mott insulator (Mott, 1990). In transition metal compounds of a certain kind, the metallic state is often lost because of electronic correlations at low temperatures and the system becomes an insulating state. This transition is called a Mott transition. Generally, a Mott insulating state appears at the lower-T side. The volume of the low-T insulating phase is known to expand upon Mott transition for V2O3 (1.5%) (McWhan and Remeika, 1970) and NiS (1.8%) (Matoba et al., 1991). The mechanism of volume expansion in the insulating state might resemble a magnetovolume effect in the itinerant-electron magnets (**Figure 5**). It can be understood that volume expansion suppresses the bandwidth and that it therefore enhances electronic-correlation effects, which stabilizes the low-T Mott insulating state. Furthermore, Ca2RuO4 (Takenaka et al., 2017a) is classified into this category, as explained in the next chapter.

# Other Factors

Some materials are also known to have volume of the low-T phase which becomes greater than that of the high-T phase with the phase transition because of mechanisms other than the four explained above. They are not understood so systematically as the four above, but they are suggestive for the development of new materials. They are therefore explained here. Silver iodide, AgI (Lawn, 1964; Kumar et al., 2006), which is known as a superionic conductor, undergoes a structural phase transition from β and γ phases with larger volume at low temperatures to α phase and smaller volume at high temperatures near 400 K. The volume change is known to reach 5%. The fact that the relation between NTE and ionic conductivity is discussed (Sleight, 1998) also for the famous NTE material β-eucryptite is suggestive of its importance for future development.

Related to a structural phase transition, certain martensitic transformations accompany volume expansion on cooling. For example, MnCoGe is known to expand by 3.9% in the martensitic transformation from high-T hexagonal phase to low-T orthorhombic phase at around 370 K (Johnson, 1975). Actually, MnCo0.98Cr0.02Ge, with one of the largest total volume change related to NTE found to date, belongs to the same family and shows the same martensitic transformation simultaneously with the magnetic transition (Zhao et al., 2015). Correlation between magnetism and structure in these materials is an interesting subject that has yet to be explored (Kanomata et al., 1995).

Although the relation between NTE and superconductivity is not well understood, Ca0.85La0.15Fe2As2 with the superconducting transition temperature of 43 K exhibits a marked NTE of αL = −16 × 10−6 K −1 and 1V/V = 1.4% at almost all temperatures below 300 K (Robello et al., 2012). Orbital ordering is regarded as involving the Mott transition in Ca2RuO4 (Mizokawa et al., 2001; Qi et al., 2010) and, although weak, NTE appears just above the Verwey transition (ca. 110 K) in Fe3O4 (Wright et al., 2000). These results suggest that an orbital-ordering transition might be a universal mechanism of NTE.

# Mechanism of Broadening Volume Change

From the viewpoint of the mechanism of how the sharp volume change accompanying the first-order phase transition becomes a gradual change with temperature, the phase-transition-type NTE materials are broadly divisible into two categories: "phaseseparation" type and "second-order-transition" type. In the former category, which includes bismuth-nickel oxides (Azuma et al., 2011, 2015), the system separates into the larger-unit-cell L phase and the smaller-unit-cell S phase, while preserving the first-order phase transition. NTE is induced because the volume fraction of the L phase increases concomitantly with decreasing T. In the latter category, which includes magnetic NTE materials such as antiperovskite manganese nitrides (Takenaka and Takagi, 2005; Hamada and Takenaka, 2011; Wang et al., 2012; Takenaka et al., 2014), the phase transition changes from first-order-like to second-order-like. Negative thermal expansion of these materials is characterized by a gradual increase in the unit-cell volume of a single phase with decreasing T without phase separation. For manganese nitrides, a detailed neutron diffraction study (Iikubo et al., 2008) demonstrated that the evolution of the amplitude of the magnetic moment is in one-to-one correspondence with the volume increase due to NTE. For the phase-transition-type materials, the mechanism of broadening the volume change is a key issue dominating the operating-temperatures of NTE. To elucidate the broadening mechanism, a certain kind of diffraction study and microscopic observations are required in addition to dilatometry.

# ANISOTROPIC THERMAL EXPANSION AND MICROSTRUCTURAL EFFECTS

Negative thermal expansion discussed in the former chapters is associated with NTE of the crystallographic unit cell. For these materials, NTE of the unit cell found using a crystallographic technique such as x-ray diffraction and NTE of the bulk measured using a dilatometric technique are fundamentally equal. However, in some cases, the crystallographic NTE and the dilatometric NTE do not coincide. Actually, β-eucryptite, which is a representative practical thermal-expansion compensator, is one example. The colossal NTE measured in the sintered body of layered ruthenium oxide Ca2RuO4 (Takenaka et al., 2017a) reaffirmed this discrepancy as an important subject in NTE research (**Figure 7**). The total volume change 1V/V related to NTE reaches a maximum of 6.7%, exceeding twice the former maximum (3.2%) obtained with MnCo0.98Cr0.02Ge (Zhao et al., 2015). Despite the wide operating-temperature window of 135– 345 K (1T = 210 K), αL shows a remarkable size of −115 × 10−6 K −1 because of this large total volume change.

Originally, Ca2RuO4 was known for unit-cell volume expansion of about 1% at the onset of high-T metallic to low-T insulating phase transition at 360 K (Friedt et al., 2001; Qi et al., 2012). Therefore, Ca2RuO4 is classified as the metal–insulator transition category of NTE described in the preceding chapter. Even in our sample showing a huge bulk NTE, during warming from 150 to 340 K, the c axis expands by 4.6%, whereas the a axis and the b axis shrink respectively by 0.6 and 5.0%. As a result, the unit cell shrinks by 1%. The anisotropic thermal expansion of this unit cell and the fairly large NTE with volume change of 1V/V = 1% are regarded as attributable to the Mott transition coupled with electronic orbital ordering, although the details remain to be explored.

The colossal NTE of Ca2RuO4 ceramics is proposed as explainable by anisotropic thermal deformation of the crystal grain which fills in the volume of pores that are contained in the sintered body (**Figure 8**). Such deformation is trivial in the

FIGURE 7 | Linear thermal expansion of Ca2Ru1−*xM*xO4−*y* (*M* = Fe, Cu). Reference temperature: 500 K. Inset: Linear thermal expansion 1*L/L* of Ca2Ru0.92Fe0.08O3.82 before and after 20 iterations of thermal cycling (reference temperature: 500 K). Data related to the warming process were collected using a laser interference dilatometer. Referred from earlier reports (Takenaka et al., 2017a,b). For comparison, data of MnCo0.98Cr0.02Ge (Zhao et al., 2015) are also shown.

field of ceramics. Moreover, it is not limited to β-eucryptite, for example, also known as MgTi2O5 (Kuszyk and Bradt, 1973; Ohya et al., 1987; Yamai and Ota, 1993). In most cases, however, it is a "one-time" phenomenon that induces microcracks, which is useless as a practical thermal-expansion compensator. One well-known exception is β-eucryptite, the practical use of which was achieved by overcoming the difficulty of advanced control of microcracks (Pelletant et al., 2012; Benavente et al., 2016). Although the NTE characteristics of β-eucryptite vary according to fabrication conditions, the total volume change of the bulk specimen (1.7%) reaches 10 times that of the unit cell (0.15%); also, αL is −7 × 10−6 K −1 .

The ruthenium oxides are characterized by rather low onset temperatures of anisotropic thermal expansion of the unit cell, which is about 500 K. For many other materials including β-eucryptite and MgTi2O5, the onset temperature is close to the sintering temperature, typically over 1,300 K. Therefore, the inner stress accumulates greatly during cooling to room temperature. Compared with those, the accumulated inner stresses are expected to be much smaller for the ruthenates. Indeed, the linear thermal expansion 1L(T)/L of Ca2Ru0.92Fe0.08O3.82 is reproducible after 20 repetitions of thermal cycling of 300 K → 500 K → 300 K (inset of **Figure 7**), which suggests that possible degradation of the characteristics because of the thermal history is avoidable. Recently reported theoretical calculations indicate that the microstructural effects without cracks can reproduce the gigantic NTE observed in the ruthenate sintered body (Takezawa et al., 2018). Enhancement of NTE in the ruthenates occurs at a scale of 10 times that of βeucryptite. Examples for which the material structure is deeply involved in the bulk function of NTE do not exist among recently discovered NTE materials. The concept of microstructural effects provides a strategy for realizing giant NTE. Control of thermal expansion using specific characteristics of materials, particularly in a negative α region, are highly limited in an operating temperature and/or a magnitude of α because of the severe constraints of available materials. To overcome these difficulties, designated structures consisting of two materials having different (positive) thermal expansions and voids are proposed as an artificial materials showing NTE (Takezawa et al., 2015; Wang et al., 2016). The present result is expected to stimulate those activities as a "natural" counterpart of the artificial structures. Structures composed of Structures composed of crystal grains exhibiting anisotropic thermal expansion and voids are expected to be important subjects of future NTE research.

# COMPOSITES CONTAINING GIANT NTE MATERIALS

Forming a composite using a NTE material as a thermalexpansion compensator is an effective method of controlling the thermal expansion of a material. Many commercial materials exist such as zero-expansion glass used for precision optical equipment and a zero-expansion ceramic material used for semiconductor device manufacturing. Many earlier studies have examined composites containing NTE materials, particularly βeucryptite (Xue et al., 2010; Borrell et al., 2012) and ZrW2O8 (Holzer and Dunand, 1999; Matsumoto et al., 2003; Sullivan and Lukehart, 2005; Lind et al., 2011), as thermal expansion compensating fillers.  Because their chemical reactivity is higher at high temperatures than those of conventional NTE materials, phase-transition-type NTE materials are difficult to use as thermal expansion compensating filler, particularly in cases of metal matrix composites (MMCs). However, powder metallurgy, which enables us to form MMCs at lower temperatures and in a shorter time than when using the conventional method, produced MMCs containing manganese nitrides (Ding et al., 2011; Takenaka et al., 2012, 2015). Some concern arose about difficulties arising from a large thermal expansion difference at the interface between the matrix and the gigantic NTE material. Additional research on the interfaces is expected to be indispensable for the development of industrial materials with high reliability, although this difficulty has not arisen for some composites at present (Takenaka and Ichigo, 2014). Here, plastic matrix composites (PMCs) containing manganese nitrides and ruthenium oxides are discussed.

Generally, the operating temperatures of phase-transitiontype NTE materials are not high (ca. 600 K at highest). Therefore, plastics for which the operating temperature range and composite processing temperature are low are indeed the most compatible matrices. In electronic devices, plastics are used in various components such as printed circuit boards, sealing materials, and substrate-chip bonding films. As miniaturization and high integration of integrated circuits progress, problems originating from thermal expansion mismatch between these plastics and inorganic materials such as semiconductors have become more severe. To suppress the large thermal expansion of plastics, conventional thermal expansion compensators such as silica are insufficient. The use of large NTE of phase-transitiontype NTE materials is indispensable. Furthermore, control of thermal expansion at a local region at the micrometer level in an integrated circuit, such as underfill of a three-dimensional integrated circuit (3DIC) is strongly demanded (Kino et al., 2017). It is technically important to miniaturize the particle diameter of a giant NTE material to submicrometer size, or less (Lin et al., 2016; Yang et al., 2016).

Before presenting scientific arguments, to summarize briefly how to evaluate the thermal expansion of composites, the author presents discussion of a simple case in which particles of an isotropic reinforcement are dispersed uniformly in an isotropic matrix for analyzing PMCs containing thermal expansion compensating particles. In that case, thermal expansion of the composite falls between the two bounds: The rule of mixture (ROM) and Turner's model (Takenaka, 2012). A bound, ROM, is given, assuming that thermally induced stress is uniform throughout a composite, which is equivalent to saying that the matrix and the filler exhibit their own thermal expansion independently. Consequently, the thermal expansion of a composite is given as the volume-weighted sum of contributions from the matrix and the dispersed filler.

$$
\alpha\_{\rm c} = \nu\_{\rm m} \alpha\_{\rm m} + \nu\_{\rm t} \alpha\_{\rm t} \tag{1}
$$

Another bound, that of Turner's model, is given as the approximation that strain is uniform throughout a composite as a result of elastic interactions between the matrix and the filler at the interfaces. It gives the following estimation.

$$\alpha\_{\rm c} = (\nu\_{\rm m} E\_{\rm m} \alpha\_{\rm m} + \nu\_{\rm t} E\_{\rm t} \alpha\_{\rm t}) / (\nu\_{\rm m} E\_{\rm m} + \nu\_{\rm t} E\_{\rm t}) \tag{2}$$

In the equations above, subscripts c, m, and t respectively denote a composite, matrix, and thermal-expansion compensator. Also, vm and vt respectively represent the volume fractions of the matrix and thermal-expansion compensator; vm + vt = 1. E represents Young's modulus. In Equation (2), the constituent with the larger elastic modulus contributes more to αc beyond the volume fraction. In the case of PMCs containing NTE filler, the relations αm > αt and Em < Et are always fulfilled. Therefore, Equation (1), ROM, gives the upper bound; Equation (2), Turner's model, gives the lower bound for αc.

**Figure 9** displays a plot of the 1L(T)/L experimental values along with curves calculated assuming ROM and Turner's moles

for 38 vol%-Mn3.25Zn0.5Sn0.25N/polyamide-imide composite (Takenaka and Ichigo, 2014). The typical grain size of the nitride filler is 30–50µm. This nitride thermal expansion compensating filler shows a huge NTE of αL = −45 × 10−6 K −1 at T = 305– 340 K, resulting in NTE (αL = −3 × 10−6 K −1 at T = 315–327 K) for the composite. Displacement in 1L/L is less than 160 ppm at T = 303–333 K, equivalent to the averaged αL of 5.3 × 10−6 K −1 . The obtained 1L(T)/L of the composite is between the ROM and Turner's estimates. This result reflects much larger E of the nitride filler (200 GPa, Nakamura et al., 2009) than the matrix (5 GPa, Reinecke et al., 1996), demonstrating the excellent thermal expansion compensating capability of the manganese nitride.

The results of bis-phenol epoxy resin matrix composite in which the ruthenium oxide particles are dispersed (Takenaka et al., 2017b) can be discussed next. The filler is Ca2Ru0.92Fe0.08O3.82. Although Fe doping somewhat suppresses negative αL to −28 × 10−6 K −1 , the operating temperature window is expanded to 100–500 K. Furthermore, T-linearity of 1L(T)/L is improved. Thermal expansion exhibits almost T-linear behavior, even near the lowest temperature used for the present dilatometry measurements. Therefore, NTE apparently continues down to the lower temperature. In that case, the total volume change 1V/V might become greater than the present estimate of 2.8% (T = 100–500 K). Unfortunately, thermal expansion below 100 K was not measured successfully because of exfoliation of the strain gage. Nevertheless, the composite exhibits low thermal expansion down to 4 K, suggesting NTE of the ruthenate below 100 K.

**Figure 10A** presents a plot of the 1L(T)/L experimental values for the 56 vol%- Ca2Ru0.92Fe0.08O3.82/bis-phenol epoxy resin composite (Takenaka et al., 2017b). For the epoxy resin and the composite, 1L(T)/L was measured down to 5 K using a strain

displayed for comparison. Reproduced from an earlier report (Takenaka et al., 2017b). Copyright (2017) The Japan Society of Applied Physics.

gage. **Figure 10B** depicts an SEM image of the composite. Darkgray and light-gray regions respectively represent the epoxy-resin matrix and the ruthenate filler. The ruthenate filler particles, with average size of 20–30µm, are dispersed uniformly. Each particle is regarded as consisting of smaller crystal grains (ca. 80vol%) and pores (ca. 20vol%). Here, Young's modulus of the epoxy resin is 3.2 GPa (Nabetani et al., 2015). Young's modulus of the ruthenate ceramics particle is estimated as 100 GPa considering the Young's modulus of the related substance Sr2RuO4 of 160

# REFERENCES

GPa (Hao et al., 2014) and sample porosity of 0.2 (Wagh et al., 1991). The obtained linear thermal expansion of the composite falls between Equations (1, 2), similar to reports of many earlier studies (Sullivan and Lukehart, 2005; Takenaka and Ichigo, 2014; Nabetani et al., 2015). Therefore, the ruthenium oxide particles dispersed in the composite have sufficient stiffness and negative αL. They suppress thermal expansion of the matrix effectively via elastic interactions at the interfaces.

# CONCLUDING REMARKS

Because of the phase transition accompanied by large volume contraction on heating, giant NTE beyond that of conventional materials has been realized. That achievement has enabled us to compensate the large thermal expansion of plastics, which has been difficult to date, although the operating temperature ranges of the accomplishments have remained limited. The conventional wisdom of materials science, which has held that "negative CTE cannot be so large," has been rejected. Concepts and technologies related to thermal expansion control are about to change dramatically. One remarkable achievement in recent years is the huge NTE observed for ruthenium oxide sintered bodies. A structure comprising crystal grains exhibiting anisotropic thermal expansion and pores presents fertile ground for the development of new NTE materials. Today, thermal expansion adjustable composites are being fabricated using recently discovered giant NTE materials including the ruthenates.

# AUTHOR CONTRIBUTIONS

The author confirms being the sole contributor of this work and approved it for publication.

# ACKNOWLEDGMENTS

The author is grateful to M. Azuma, Y. Okamoto, N, Katayama, A. Takezawa, and S. Mori for many fruitful discussions and to his students for their enthusiastic conduct of experiments. This work was partly supported by Grants-in-Aid for Scientific Research (Nos. 17H02763 and 18H01351) from MEXT, Japan and by Adaptable and Seamless Technology Transfer Program (A-STEP; No. AS2911907T) from JST, Japan.

compound BiNi1−xFexO3 and zero-thermal expansion composite. Appl. Phys. Lett. 106:061912. doi: 10.1063/1.4908258

**Conflict of Interest Statement:** The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Takenaka. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Negative Thermal Expansion in the Materials With Giant Magnetocaloric Effect

Fengxia Hu1,2 \*, Feiran Shen1,2, Jiazheng Hao1 , Yao Liu1,2, Jing Wang1,2, Jirong Sun1,2 and Baogen Shen1,2

*1 Beijing National Laboratory for Condensed Matter Physics and State Key Laboratory of Magnetism, Institute of Physics, Chinese Academy of Sciences, Beijing, China, 2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing, China*

Negative thermal expansion (NTE) behaviors in the materials with giant magnetocaloric effects (MCE) have been reviewed. Attentions are mainly focused on the hexagonal Ni2In-type MM'X compounds. Other MCE materials, such as La(Fe,Si)13, RCo2, and antiperovskite compounds are also simply introduced. The novel MCE and phase-transition-type NTE materials have similar physics origin though the applications are distinct. Spin-lattice coupling plays a key role for the both effect of NTE and giant MCE. Most of the giant MCE materials show abnormal lattice expansion owing to magnetic interactions, which provides a natural platform for exploring NTE materials. We anticipate that the present review can help finding more ways to regulate phase transition and dig novel NTE materials.

#### Edited by:

*Jun Chen, University of Science and Technology Beijing, China*

#### Reviewed by:

*Jianchao Lin, Institute of Solid State Physics, Chinese Academy of Sciences, China Cong Wang, Beihang University, China*

> \*Correspondence: *Fengxia Hu<EMAIL_ADDRESS>
#### Specialty section:

*This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry*

Received: *02 July 2018* Accepted: *03 September 2018* Published: *25 September 2018*

#### Citation:

*Hu F, Shen F, Hao J, Liu Y, Wang J, Sun J and Shen B (2018) Negative Thermal Expansion in the Materials With Giant Magnetocaloric Effect. Front. Chem. 6:438. doi: 10.3389/fchem.2018.00438* Keywords: negative thermal expansion, thermal compensation, giant magnetocaloric effect, spin-lattice coupling, magnetostructural transition

# INTRODUCTION

Magnetic cooling technique based on magnetocaloric effect (MCE) has attracted an increasing attention for its environmental-friendly and energy-saving superiority compared to conventional vapor compression technique (Annaorazov et al., 1996; Pecharsky and Gschneidner, 1997; Hu et al., 2000a, 2001; Wada and Tanabe, 2001; Tegus et al., 2002; Fujita et al., 2003; Gschneidner et al., 2005; Krenke et al., 2005; Shen et al., 2009; Liu E. K. et al., 2012; Liu J. et al., 2012; Wu et al., 2015).  A common feature of these materials is the strong spin-lattice coupling. In other words, magnetic and structural transition concurrently takes place, and the change of lattice during the transition does contribute to the giant MCE. Note that a number of MCE materials show abnormal lattice expansion owing to magnetic interactions, which provides a natural platform for exploring negative thermal expansion materials. However, not all the giant MCE materials show negative thermal expansion (NTE), some of them still show positive thermal expansion (PTE), depending entirely on the characteristics of the magnetostructural/magnetoelastic transition and the specific physical origin in different systems.

**20**

For example, FeRh alloy shows giant MCE. It crystallizes in the CsCl-type cubic structure and experiences PTE with volume change of 1V/V∼ + 0.9% along with the AFM-FM (antiferromagnetic-ferromagnetic) transition without the change of space group. Gd5Si2Ge2 also exhibits giant MCE (Pecharsky and Gschneidner, 1997), which originates from a coupled magnetostructural transition in which slabs of a well defined arrangement of R and T atoms shift ∼0.5Å with respect to one another along the a-axis when the transition occurs under the influence of temperature (Gschneidner et al., 1997; Morellon et al., 2000). Such a shift gives rise to a PTE with volume change of 1V/V ∼ + (0.4–1)% depending on the compositions. MnFeP1−xAsx (0.15 < x < 0.66) alloys with giant MCE crystallize in hexagonal Fe2P-type structure and undergo a first-order FM-PM (paramganetic) magnetic transition around room temperature (Tegus et al., 2002). The space group (P6 2 ¯ m) keeps unchanged upon the magnetic transition, but the lattice shows an anomaly expansion in the direction of the a and b axes and a contraction of the c axis as the FM phase is formed, which originates from an increase in the intralayer metal-metal bond distance (Liu et al., 2009). As a result, a PTE with 1V/V ∼ + 0.06% was observed with increasing temperature. The FM Heusler alloy Ni2MnGa with L21 structure shows a giant MCE owing to the martensitic magnetostructural transformation from FM austenitic to FM martensitic phase (Wada and Tanabe, 2001). On heating, the alloy displays a PTE with 1V/V ∼ + 1%.

However, the La(Fe1−xSix)13-based materials with giant MCE show NTE with 1V/ V∼ – (1.0–1.6)% around TC, depending on compositions, due to the itinerant ferromagnetic nature of the materials (Shen et al., 2009). The space group (Fm3 c) ¯ keeps unchanged across the magnetic transition. Moreover, the hexagonal MnCoGe/MnNiGe-based compounds also show giant MCE and NTE. The optimal compositions undergo a magnetostructural transition from a Ni2In-type hexagonal PM phase (space group P63/mmc) to a TiNiSi-type orthorhombic FM phase (space group Pnma). The c axis of hexagonal phase expands while the a-axis contracts upon the martensitic structural transition. As a result, NTE as large as 1V/V= –(2.68– 3.9)% occurs depending on compositions (Liu E. K. et al., 2012; Wu et al., 2015; Zhao et al., 2015).

Materials with precise thermal expansion or zero thermal expansion (ZTE) are in urgent demand in modern industry (Rathmann et al., 1968; Namba et al., 2001; Du et al., 2016), such as engineered components, optical mirrors, and printed circuit boards. Generally, ZTE can be reached by combining the materials with PTE and NTE coefficients.  Among these NTE materials, the phase-transition-type materials (Takenaka and Takagi, 2005; Iikubo et al., 2008; Sun et al., 2010a; Song et al., 2011; Huang et al., 2013; Zhao et al., 2015) have attracted specific attention.

In this paper, we mainly review the negative thermal expansion behaviors based on magnetostructural or magnetoelastic transition in the materials showing giant magnetocaloric effect. Here, the magnetostructural transition refers to the concurrent magnetic and structural transition where the lattice structure (space group) changes during the transition, while the magnetoelastic transition refers to the concurrent magnetic and elastic transition where the lattice structure (space group) remains unchanged but lattice parameter changes elastically.

# LA(FE,SI)13-BASED COMPOUNDS

# Crystal Structure

LaFe13 does not exist due to the positive formation enthalpy between La and Fe. To get LaFe13-based alloys, a third element is needed. The first stable LaFe13−xMx compounds were made by Krypiakewytsch et al. (1968) in 1968 when Fe was partially replaced by Si or Al. The compounds show cubic NaZn13-type structure with space-group of Fm3c. In the structure, La atoms occupy the 8a site, while Fe atoms occupy the 8b and 96i sites. Fe atoms at these two sites are denoted as FeI and FeII, respectively. Al or Si randomly substitute for FeII site. Fe atoms at FeI site and La form a CsCl structure. The FeI are surrounded by an icosahedron of 12 FeII, and the FeII are surrounded by nine nearest FeII and one FeI , as shown in **Figure 1**.

# Magnetocaloric Effect

By analyzing phase formation rule of NaZn13-type compounds, LaFe13−xSix compounds with Si content ranging from x = 1.2 to 2.4 were successfully synthesized (Hu, 2002; Shen et al., 2009). In 2001, we firstly reported the large MCE in LaFe11.4Si1.6, originating from a negative lattice expansion and a fieldinduced itinerant-electron metamagnetic transition (Hu et al., 2001). The maximal magnetic entropy change, –1S, reaches

19.4 J kg−1K −1 around 213K under a magnetic field change of 0-5T, largely exceeding that of LaFe10.4Si2.6 with typical second-order transition, as shown in **Figure 2A**. The differential curves given in the inset of **Figure 2A** clearly illustrates the asymmetrical broadening of –1S peak caused by the fieldinduced itinerant-electron metamagnetic transition. **Figure 2B** displays the comparison of lattice change around phase transition between LaFe11.4Si1.6 and LaFe10.4Si2.6. One can notice, for LaFe11.4Si1.6, the negative expansion of lattice parameter can be as much as −0.4%.

Introducing the substitution of Co for Fe or interstitial atoms C/H can both impact the exchange coupling between the magnetic elements. This fact can adjust the temperature of phase transition in a wide temperature range covering room temperature while a large MCE is maintained. The maximal room temperature –1S can reach 12 J kg−1K −1 and 20 J kg−1K −1 under 2 T and 5 T magnetic fields, respectively, for the typical La(Fe,Si)13-based compounds (Hu et al., 2002; Shen et al., 2009). The large MCE make the La(Fe,Si)13-based compounds attractive to be as room temperature refrigerants. For La(Fe1−xCox)11.9Si1.1 (Hu et al., 2002, 2005), the –1S is one times larger than the conventional refrigerant Gd, and is comparable or even exceeds that of Gd5Si2Ge2, the milestone MCE material discovered in 1997 (Pecharsky and Gschneidner, 1997). The large MCE is closely related to negative lattice expansion across phase transition, which can be identified in the temperature dependence of lattice parameter for La(Fe1−xCox)11.9Si1.1 (x = 0.04, 0.06, 0.08) compounds (**Figure 3**).

# Negative Thermal Expansion Behaviors

Although the large MCE of La(Fe,Si)13-based compounds owing to the significant negative lattice expansion was discovered in the early 2000 (Hu et al., 2000b; Shen et al., 2009), these materials have never been considered as negative thermal expansion (NTE) materials till 2013. As NTE materials, Huang et al. firstly reported the giant NTE in La(Fe,Si,Co)13 compounds (Huang et al., 2013).

For LaFe13−xSix, the NTE properties were found to be strongly dependent on the Si contents. A sharp volume change from 170 to 240 K was observed in LaFe11.5Si1.5 with a NTE temperature window (1T) about 70 K. The estimated 1L/L is 3.5 × 10−3 , which is comparable to those of Mn3ZnN (4.6 × 10−3 ) (Takenaka and Takagi, 2005) and Mn3GaN (3.8×10−3 ) (Takenaka et al., 2008). With increasing Si content from x=1.5 to 2.4, the linear expansion becomes broader gradually, leading to a large negative slope in a wider temperature range. This result illustrates that the replacement of Fe by Si can broaden the temperature window of NTE. However, the numerical values of NTE coefficient rapidly drop with the increase of Si content, which is an unfavorable character for practical applications.

To improve the performance of NTE behavior, the substitution of Co for Fe was introduced. **Figure 4** displays linear thermal expansion as a function of temperature and

FIGURE 3 | The temperature dependence of lattice parameter for La(Fe1−xCox)11.9Si1.1 (*x* = 0.04, 0.06, 0.08) compounds. Reprinted with permission from Hu et al. (2005).

its comparison with magnetization for LaFe11.5−xCoxSi1.5. Increasing Co content broadens the temperature window, 1T, of NTE, and drives it to a higher temperature. The 1T width of NTE is 74 K, 90 K, and 110 K for x = 0.2, 0.4, and 1.0, respectively. More importantly, the change of 1L/L within the NTE window reduces less rapidly with Co compared to the case with Si. The composition with x = 0.10 produces an average coefficient of thermal expansion (CTE) of α¯ = −26.1 × 10−6 K −1 from 240 K to 350 K, covering room temperature. This numerical value of α¯ is about 3 times larger than that of the commercial NTE materials ZrW2O8 with α = −9 × 10−6 K −1 . Moreover, the absolute value of the negative CTE reaches those of high-expansion metals such as Al (α = 23 × 10−6 K −1 at room temperature). These findings suggest the potential application of La(Fe,Si)13-based compounds as NTE materials.

More interestingly, zero thermal expansion (ZTE) has been recently reported in La(Fe,Si)13-based compounds in a wide temperature range away from phase transition (Li et al., 2017), which is a fascinating phenomenon in these compounds.

# NI2IN-TYPE MM'X COMPOUNDS

# Crystal Structure

Hexagonal Ni2In-type MM'X (M, M' = transitional element, X = main element) compounds have attracted lots of attention owing to the rich magnetic and structural behaviors. Ferromagnetic or antiferromagnetic coupling occurs depending on the compositions and atomic local environments (Niziol et al., 1981; Caron et al., 2011; Gercsi et al., 2011; Liu E. K. et al., 2012). As a member of family, the stoichiometric MnCoGe alloy undergoes diffusionless martensitic structural transition, Tstru, from Ni2In-type hexagonal (space group: P63/mmc) to TiNiSi-type orthorthombic (space group: Pnma) structure at Tstru ∼420 K and a transition of ferromagnetic ordering at Tc∼345 K (Niziol et al., 1981). Both the martensitic and austenitic phases display ferromagnetic nature, and the orthorhombic phase shows a higher magnetic moment Ms ∼4.13 µB than the hexagonal phase (Ms ∼2.76 µB) (Niziol et al., 1981). On the other hand, the stoichiometric MnNiGe undergoes a similar martensitic structural transformation at Tstru∼470 K, and a magnetic transition at T M N ∼346 K. The martensitic and austenitic phases have distinct magnetic structure. The former shows spiral antiferromagnetic (AFM) coupling with Neel temperature T M N at 346 K while the latter exhibits ferromagnetic (FM) nature with intrinsic Curie temperature T A C at 205 K (Niziol et al., 1981).

**Figure 5** shows the sketches of orthorhombic martensitic and hexagonal austenitic structures for MnCoGe (Wu et al., 2015).

## Magnetocaloric and Barocaloric Effects

For the MM'X compounds, austenitic phase has a smaller volume than martensitic phase. This fact prompts one to think that the introduction of smaller atoms or vacancies may stabilize the austenitic phase and shift Tstru to a lower temperature. Following this way, magnetostructural transition has been indeed realized by introducing smaller atoms or vacancies, such as MnCo1−xGe (Wang et al., 2006), Mn1−xCoGe (Liu et al., 2010), Mn1−xCrxCoGe (Caron et al., 2011). Moreover, It has demonstrated that valence electron concentration (e/a) can also affect Tstru. By introducing Indium (In) atom (2.00 Å, 5s2 5p1 ) with a larger radius but fewer e/a to replace Mn (1.79 Å, 3d5 4s2 ), Co (1.67 Å, 3d7 4s2 ), or Ge (1.52 Å, 4s2 4p2 ), magnetostructural transition is also created in (Liu E. K. et al., 2012). As a result, large MCE has been observed in these MnCoGe-based materials.

On the other hand, it has been found that, for MnNiGe, the AFM coupling in the martensitic structure is not robust. The replacements of Mn or Ni by Fe atom can convert the AFM into FM coupling and stabilize the austenitic phase (Liu E. K. et al., 2012). As a result, the Tstru shifts to low temperature, and magnetostructural transition is realized and hence large MCE appears in an extended temperature window from 350 K down to 70 K in MnFeNiGe alloys.

Moreover, giant barocaloric effect has been demonstrated in MnCoGe0.99In0.01 compound (Wu et al., 2015). Neutron powder diffraction (NPD) studies indicated that the lattice of hexagonal phase expands significantly along the c-axis (cH) by 11.3% while contracts along the a-axis (aH) by −6.8% during the magnetostructural transformation, Tmstru. As a result, negative

orthorhombic structure while the purple lines in (B) enclose the one of Ni2In-type hexagonal structure. The unit cell of hexagonal phase transforms into the zigzag-type structure in the orthorhombic phase, as indicated by purple lines in (A).

lattice expansion as large as 1V/V = (Vortho/2-Vhex)/Vhex ∼ −3.9% occurs for MnCoGe0.99In0.01, as shown in **Figure 6**. Note that the unit cell volume and lattice constants of hexagonal and orthorhombic phases have relations as ao=cH, bo=aH, co= √ 3aH and VO=2VH.

The calorimetric measurements using a differential scanning calorimeter (DSC) revealed that the total change of transition entropy can be as large as 55 J kg−1K −1 contributed by the large difference of internal energy across the transition for MnCoGe0.99In0.01. High resolution NPD studies under hydrostatic pressure revealed that pressure can shift the Tmstr to lower temperature at a rate of 7.7 K/kbar. The large latent heat and high sensitivity of the magnetostructural transition to pressure result in giant inverse barocaloric effect (Wu et al., 2015). The entropy change, 1S, and adiabatic temperature change, 1Tad, under a pressure of 3 kbar reaches 52 J kg−1K −1 and −18 K, which exceed those of most materials, including the giant magnetocaloric effect driven by a magnetic field of 5 T (Gschneidner et al., 2005) that can be only available by superconducting magnets. The refrigeration cooling power (RCP) reaches 1190 J kg−1 .

# Negative Thermal Expansion Behavior

Similar to the case of La(Fe,Si)13-based compounds, the Ni2Intype MM'X compounds have rarely been considered as negative thermal expansion (NTE) materials because of the limited temperature region of phase transition, though they surely have significant negative lattice expansion and large MCE and barocaloric effect owing to the magnetostructural transition.

## Giant Negative Thermal Expansion in MnCoGe-Based Materials

In 2015, Zhao et al. firstly reported giant NTE in bonded MnCoGe-based materials (Zhao et al., 2015). The as-prepared compounds are very brittle and even collapse into powders during preparation. Through introducing a few amounts (3– 4 wt%) of epoxy to bond the powders, residual stress was introduced, hence the structural transition was broadened due to the lattice softening enforced by the stress. Hence, giant NTE has

FIGURE 6 | Lattice constants and unit-cell volume of hex. and orth. structure as a function of temperature for MnCoGe0.99In0.01. The blue and red symbols correspond to the hex. and orth. structure, respectively. The red circle, red square and red rhombus stand for ao, co/ √ 3 and bo, respectively. The blue pentagon and blue star represent the ch and ah , respectively. The unit-cell volume of hex. and half of unit-cell volume of orth. structure are symbolized as blue and red triangle, respectively. Reproduced under a Creative Commons Attribution 4.0 International License from Wu et al. (2015).

been achieved in a wide temperature region. Moreover, excellent mechanical properties and tunable electrical conductivity has been demonstrated for the bonded powders.

Neutron powder diffraction (NPD) studies indicate that the change of lattice volume during the magnetic transition can be as much as 3.9, 3.9, and 3.8% for MnCoGe1−xInx (x = 0.01, 0.02), and MnCoGe0.97Sb0.03, respectively. Accordingly, the evaluated linear expansion is equal to 1L/L ∼10,995 × 10−6 and the average NTE coefficient is about α¯ ∼ −183.3 × 10−6 /K if the polycrystalline powder is supposed to expand isotropically for MnCoGe0.99In0.01.

Linear expansion, 1L/L, was measured using high resolution strain gauge for the bonded plates. It was found that the 1L/L behaves isotropically, independent of the in-plane measured axis. **Figure 7** shows the 1L/L as a function of temperature for some typical compositions. The maximal 1L/L keeps above 10,231 × 10−6 , while the average linear NTE coefficient ranges from −51.5 × 10−6 /K to −94.7 × 10−6 /K in the tunable temperature region from ∼60 to 330 K covering room temperature for the bonded MnCoGe-based materials with different compositions. Because of the significant broadening of phase transition caused by residual stress and the possibly porosities introduced, the 1L/L and α¯ are somewhat smaller than those estimated from the X-ray diffraction (XRD) or NPD measurements. However, the maximal 1L/L measured has reached 93% of the crystallographic value. These novel NTE properties are over the performance of most other reported materials previously. For example, the average α¯ ∼ −51.5 × 10−6 /K with operation temperature window as wide as 210 K was observed in MnCo0.98Cr0.02Ge, which is more than 5 times larger than that of the commercial NTE materials ZrW2O8 with α = −9 × 10−6 /K.1 More interestingly, in the temperature region from 250 to 305 K covering room temperature, the CET α (−119 × 10−6 /K) remains nearly independent of temperature (see **Figure 7A**), and this value is about 40% larger than the that (−82 × 10−6 /K) of Bi0.95La0.05NiO3 (320–380 K) (Azuma et al., 2011), and more than four times larger than the α (−25 × 10−6 /K) of an antiperovskite manganese nitride (316–386 K) (Takenaka and Takagi, 2005).

**Figures 8A,B** presents the temperature dependence of magnetization (M-T curves) measured under a 0.3 T magnetic field for the bonded and as-prepared compositions with and without magnetostructural coupling. From **Figure 8** and the dM/dT plots in the insets, one can distinguish that the structural/magnetostructural transformation (Tstru/Tmstru) was significantly broadened while the pure magnetic transition keeps unchanged around TC for the bonded samples. For the bonded MnCoGe0.99 with magnetostructural transition, the Tmstru shifts by 10 K to low temperature, while for the Mn0.97In0.03CoGe with decoupled Tstru and TC, the Tstru shifts by 7 K to low temperature while TC keeps unchanged (261 K). The significant broadening of the structural/magnetostructural transformation enforced by the residual stress governs the NTE behavior in the bonded samples.

From viewpoint of industry, electrical conductivity is a critical parameter for practical applications. For the bonded MnCoGebased materials, the electrical conductivity can be adjusted through choosing distinct binders. It has been experimentally demonstrated that the electrical resistivity for the materials with Ag-epoxy as binder is lower than the one with epoxy as binder by 3 orders of magnitude. Moreover, the mechanical properties have been largely improved. All these suggest the high potential of MnCoGe-based compounds as NTE materials, which can be used to compensate the materials with high PTE, such as the popularly-used organic or plastic materials.

# Ultra-Low Thermal Expansion Realized in MnCoGe0.99In0.01 Through Self-Compensation

The martensitic structural transition in Ni2In-type MM'X compounds behaves extremely sensitive to pressure compared to magnetic field (Wu et al., 2015). The introduced residual strain and defects during pulverization (Wu et al., 2016) or cold pressing (Liu et al., 2015) can also affect the magnetostructural coupling besides hydrostatic pressure. It has been reported that

FIGURE 8 | The comparison of temperature dependent magnetization under 0.3T for the bonded and as-prepared compositions (A) MnCoGe0.99 with magnetostructural coupling and (B) Mn0.97In0.03CoGe with decoupled *Tstru* and *TC*. The insets show corresponding dM/dT plots. Reprinted with permission from Zhao et al. (2015).

the introduced residual strain in the MnCoGe1−xInx thin slices prepared by cold pressing can stabilize the austenite phase, as a result, the temperature window of martensitic transformation is broadened, the magnetic and structural transition becomes decoupling (Liu et al., 2015). Similarly, with reducing particle size, austenitic phase becomes stable and a high fraction of austenitic phase loses the martensitic transformation, and retains the hexagonal FM structure in the entire temperature range. Considering the large difference of volume between austenitic and martensitic phases, one may prompt to think that adjusting phase fraction and magnetostructural transition through residual strain can lead to controllable NTE or even ZTE.

Indeed, ultra-low thermal expansion has been realized in the giant NTE material MnCoGe0.99In0.01 by controlling the crystallinity degree and phase transition (Shen et al., 2017). A high fraction of sample can be converted into amorphous structure by ball milling, which turns to show PTE while the remained crystallites exhibit decreased NTE in an extended temperature window. Ultra-low thermal expansion can be reached and the NTE can be totally adjusted through selfcompensation effect.

Samples with different particle sizes were made through energetic ball milling. For small particles, high-resolution TEM (transmission electron microscopy) images indicate the mixture of a high fraction of amorphous structures and nanocrystallites full of atomic defects. The amounts of the amorphous structure were estimated by high-resolution neutron powder diffraction (NPD).

**Figure 9** shows 1L/L vs. temperature for the bonded particles compared to the bulk, which was measured by using highresolution strain gauge. One can notice that the maximal 1L/L declines while the operating 1T significantly broadens with reducing particle size. For small particles P3 (2–5µm) and P4 (1–2µm), NTE dominates in the entirely measured temperature range from 310 K to 100 K.

For the smallest particles with size P5 (0.3–1µm), the NTE disappears and turns out to be ultra-low PTE, and the CTE α is as small as + 0.68 × 10−6 /K from 200 to 310 K. This result suggests that the material can be also useful as a ZTE material, in addition to be used as compensators for PTE material. Moreover, one can notice that the low NTE for P4 (1–2µm) and the ultra-low PTE for P5 (0.3–1µm) is nearly independent of temperature in the corresponding temperature region (see the pink lines in **Figure 9**), which is appreciable for practical applications.

The tunable CTE with particle size originates from the coexistence of crystalline phases and amorphous structure, particularly for the small particles. Variable temperature XRD and neutron NPD studies revealed that the phase ratio changes remarkably with crystallite size. About 7, 14.5, 38.5, 44.8, and 55.2% austenitic phase lost the martensitic transformation and remains the hexagonal structure down to low temperature for the particles P1 (10–20µm), P2 (5–10µm), P3 (2–5µm), P4 (1–2µm), and P5 (0.3–1µm), respectively.

**Figure 10** shows the unit cell volume as a function of temperature (V-T curve) for the orthorhombic structure (red dot), hexagonal structure (blue dot), and the weighted average volume V¯ (black dot) calculated based on the refined phase fraction. Moreover, the temperature dependence of lattice volume was fit based on the Grüneisen law, and the results agree well with the refined results for either orthorhombic or hexagonal phase.

FIGURE 9 | Linear thermal expansion 1L/L as a function of temperature for the bonded MnCoGe0.99In0.01 samples with different particle size in comparison to the bulk (the reference temperature is 390 K). Particle size: P1 (10–20µm), P3 (2–5µm), P4 (1–2µm), and P5 (0.3–1µm). The morphology of the bonded sample is shown in the inset. Adapted from Shen et al. (2017). APL Materials, Vol. 5, Article ID 106102, (2017); licensed under a Creative Commons Attribution (CC BY) license.

FIGURE 10 | Refined unit cell volumes of martensitic structure (red dot), austenitic structure (blue dot), and the weighted average (black dot), as a function of temperature for the overall crystalline phases of various particles of MnCoGe0.99In0.01: (A) P1(10∼20µm), (B) P2(5∼10µm), (C) P4(1∼2µm), (D) P5(0.3∼1µm). The fitting curves according to Grüneisen law are represented by the small dots. Adapted from Shen et al. (2017). APL Materials, Vol. 5, Article ID 106102, (2017); licensed under a Creative Commons Attribution (CC BY) license.

From **Figure 10** (black curve), one can notice that PTE occurs below 290 K and turns to be NTE above this point. TEM studies indicated that crystallite size reduces with particle size, and the average crystallite sizes are about 15 nm and 8 nm for P4 (1–2µm) and P5 (0.3–1µm), respectively. With reducing the crystallite size, the both PTE and NTE coefficients decline, which are mainly caused by the instability of magnetostructural transformation due to residual stress and defects.

On the other hand, the contribution from amorphous structure cannot be ignored, noting the amount reaches 40% for the smallest particles P5(0.3∼1µm). Detailed analysis indicated that the amorphous structure shows positive thermal expansion (PTE), and its compensation effect plays an essential role in the realization of ultra-low expansion even if the possible contribution from the small fraction of epoxy was considered. Details were given in the Supplementary Material in Shen et al. (2017).

### Colossal Negative Thermal Expansion in Fine-Powdered Mn0.98CoGe

In 2016, Lin et al. prepared fine-powdered Mn0.98CoGe by two ways of high energy ball milling (BM) and repeated thermal cycling (TC) across the martensitic transformation, and compared the NTE behaviors (Lin et al., 2016). It was found that the both ways can make the temperature window (1T) of NTE broadening. For the powders experienced TC for ten times, the 1T broadens to 90 K (309–399 K), and the CTE is about αL ∼ −141 × 10−6 /K.

The SEM result showed that the average particle size for the powder of Mn0.98CoGe alloy through 10 times of TC treatments is 8.2µm, and for the powder through 0.5, 5, and 12 h of BM process are 7.4, 3.9, and 2.2µm, respectively.

**Figures 11A–D** display the refined phase fractions for both orthorhombic and hexagonal phases based on the variable temperature XRD patterns for typical samples. For the powders experienced TC for 10 times, the transition of two phases is ∼98%. For the powders prepared by BM for 0.5 h, the martensite transformation is broadened, and the transition ratio decreased to ∼93%. With increasing BM time to 5 and 12 h, the martensite transformation window was further broadened, and the transition ratio reduced to ∼60 and 36%, respectively.

**Figures 11E–H** show the corresponding volumetric thermal expansion coefficient (αV) calculated based on the refined phase volume and fraction. For the powders experienced TC for 10 times, NTE effect appears between 309 and 399 K (1T = 90 K), and the corresponding αV is about −423 × 10−6 /K. For the powders prepared by BM for 0.5 h, 1T extends to 135 K (from 258 to 393 K), and αV value becomes −238 × 10−6 /K. Further increasing BM time to 5 and 12 h results in the decreases of both 1T and αV, and the αV values are about −135 × 10−6 /K (236– 366 K, 1T = 130 K) and −93 × 10−6 /K (264–303 K, 1T = 39 K), respectively. The corresponding linear αL values are about −141 × 10−6 /K (1T = 90 K), −79.6 × 10−6 /K (1T = 135 K), −45 × 10−6 /K (1T = 130 K), and −31 × 10−6 /K (1T = 39 K) for the samples experienced TC for 10 times, BM for 0.5 h, BM for 5 h, and BM for 12 h, respectively.

(D) BM for12 h; The temperature dependent volumetric thermal expansions 1*V/V* (the reference temperature is 438 K) for the corresponding samples is shown in (E–H), respectively. The NTE temperature region is highlighted for all samples. Reprinted with permission from Lin et al. (2016).

For the samples experienced TC for 10 times, the both temperature window of NTE and the αL magnitude are larger than those of typical NTE material Bi0.95La0.05NiO3 (αL = −137 × 10−6 /K, 320–380 K) (Azuma et al., 2011). This αL magnitude forthe samples experienced TC for 10 times is several times larger than that of common metals (Takenaka et al., 2012) and even larger than that of most polymers (Sullivan and Lukehart, 2005; Chu et al., 2012; Takenaka and Ichigo, 2014).

The NTE behavior has different origins for the samples prepared by the two ways. For the powder prepared by BM, the broadening of temperature window of martensitic transformation originates from the accumulated residual strain. With increasing the BM time, the overall NTE window first expands and then shrinks. For the powder prepared by TC, the sample does not suffer any external pressure, and the introduced strain is thus weaker than the case by BM, hence leading to the completely different evolution of phase transition with temperature.

All these results suggest the TC or slightly BM treatments can both extend temperature interval and optimize the NTE properties, which have high potential applications as the PTE compensators by forming composites.

# Negative Thermal Expansion in Mn-Co-Ge-In Thin Films

In recent years, many materials with magnetostructural transition, such as Gd5Si2Ge2 (Pires et al., 2015), FeRh (Zhou et al., 2013), metamagnetic NiMn-based Heusler alloys (Akkera et al., 2015), and MnAs (Mosca et al., 2008), have been explored in nanostructured thin films, aiming to activate novel properties and explore applications in micro-scale of these materials. Recently, Liu et al. firstly explored the fabrication of MnCoGebased alloy films, and studied the magnetocaloric effect and thermal expansion behaviors of the films obtained (Liu et al., 2018).

MnCoGe0.995In0.005 films with thickness of 45 nm were successfully grown on (001)–LaAlO3, (001)–SrTiO3, and (0001)– Al2O3 substrates by using pulsed laser deposition (PLD) technique. It was found that the obtained films exhibit three dimensional growth mode, and the island size varies for thin films grown on different substrates. Room temperature XRD patterns imply that the films crystallize in mixed hexagonal and orthorhombic structures, which are textured along the out of plane (001) direction for the hexagonal structure and (h00) orientations for the orthorhombic structure. For all the films, there exists obvious thermal hysteresis between the heating and cooling process in a wide temperature range, indicating that firstorder magnetostructural transformation was retained. Moreover, the temperature window of the transformation for the films significantly broadened compared to that of the bulk alloy.

The broadened magnetostructural transformation of Mn-Co-Ge-In films can be ascribed to the stress effect and crystalline defects. Besides, the commercially supplied Al2O3, SrTiO3, and LaAlO3 substrates have positive linear thermal expansion coefficients + 7.5 × 10−6 /K, + 9.4 × 10−6 /K, and + 1 × 10−5 /K, respectively. Consequently, the different films denote tunable negative thermal expansion due to different island size and strain state of the films along with the compensating effect from substrates. As can be seen from **Figure 12**, for Mn-Co-Ge-In/Al2O3 and Mn-Co-Ge-In/SrTiO3, the NTE coefficients are −6.56 × 10−6 /K (from 270 K to 390 K) and −4.82 × 10−6 /K (from 290 K to 390 K), respectively. These values are a bit smaller in comparison to those of the well-known commercial NTE materials ZrW2O8 (−9 × 10−6 /K). Otherwise, the Mn-Co-Ge-In/LAO with the smallest island size denotes near-zero CTE of −2 × 10−6 /K in the temperature range from 290 to 390 K.

The deposition of films completely overcomes the brittleness nature of Mn-Co-Ge-In alloy and much more durable. Repeated experiments demonstrated that the NTE behavior is completely repeatable between different cycles for the all films (**Figure 12**). All the results denotes that durable thin films with different CTE can be designed through choosing appropriate substrates or introducing a buffer layer, which would be quite useful for practical applications.

### Negative Thermal Expansion in Fe-Doped MnNiGe Composites

Similar to MnCoGe-based alloys, MnNiGe-based alloys also denote NTE due to the martensitic transition from Ni2In-type hexagonal to TiNiSi-type orthorhombic structure. Still, Fe-doped

FIGURE 12 | Temperature dependent linear thermal expansion 1L/L for the Mn-Co-Ge-In thin films grown on Al2O3 (A), SrTiO3 (B), LaAlO3 (C). Each has been repeated at least two times. Reprinted with permission from Liu et al. (2018).

MnNiGe alloys naturally crack into small pieces after annealing. Recently, by preparing the alloy through solid state interaction, Zhao et al. (2018) reported the NTE of MnNiGe-based alloy. The average CTE of Mn0.9Fe0.1NiGe alloy with Fe replacing Mn reaches a giant value of αL ∼ −285.23 × 10−6 K in a temperature window from 192 to 305 K (1T = 113 K), while the αL of MnNi0.9Fe0.1Ge alloy with Fe replacing Ni reaches −1,167 × 10−6 /K in a narrow temperature window (246–305 K, 1T = 59 K). The introduction of Fe changes the magnetic state of martensitic phase from the spiral AFM structure into FM state.

Furthermore, commercial Cu powders with positive thermal expansion has been chosen as the matrix metal, both acting as the compensators to control CTE and bonder to increase the mechanical properties of the alloy. The study (Zhao et al., 2018) revealed that the introduced Cu powers rarely react with the Fe-doped MnNiGe alloy. The cracks and holes can be filled by Cu particles, and the resulted MnNiGe/x%Cu composites is more compact with increasing Cu contents. The CTE of both Mn0.9Fe0.1NiGe and MnNi0.9Fe0.1Ge alloy decreases by introducing 35% Cu, as shown in **Figure 13A**. The linear thermal expansion behavior of Mn0.92Fe0.08NiGe/x% Cu and Mn0.84Fe0.16NiGe/x% Cu are presented in **Figures 13B,C**. The absolute CTE values of the two serials of composites decrease and the NTE temperature windows become narrow with increasing the Cu ratio. Increasing the Cu content to 70%, the composites display near-ZTE behaviors due to the compensation effect between the PTE properties of Cu matrix and the NTE properties of Fe-doped MnNiGe alloys. A low thermal expansion behavior with a CTE αL ∼ −4.73 × 10−6 /K was observed in a temperature

range from 173 to 229 K (1T = 56 K). In MnNi0.92Fe0.08/10%Cu composite, a low αL ∼1.16 × 10−6 /K is also achieved in a wide temperature range from 125 to 215 K (1T = 90 K).

In addition, the mechanical performance can be enhanced for the Fe-doped MnNiGe compounds with Cu as binders. All these suggest the high potential of the composites as NTE materials.

# RCO2 COMPOUNDS

# Crystal Structure

The cubic Laves phases RCo2 (R = rare earth elements) have intensively been studied for the rich magnetic properties, which arise from the highly localized 4f electrons of rare earth elements and the interactions with the itinerant 3d electrons of the transition elements. For the RCo2 with R = Nd, Pr, Sm, Gd, Tb, Tm, the magnetic transition is of second-order in nature, while for R = Dy, Ho, and Er, the magnetic transition becomes of first-order (Khmelevskyi and Mohn, 2000). RCo2 compounds have a cubic Laves C15 structure with space group Fd3m around room temperature. In the cubic C15 structure, rare atoms locate at sites 8(a) (0.125, 0.125, 0.125) and Co atoms at sites 16(d) (0.5, 0.5, 0.5) (**Figure 14A**; Ouyang et al., 2005a). With temperature decreasing, ErCo2 and TbCo2 exhibit a rhombohedral distortion (space group R3m) below Curie temperature TC (Ouyang et al., 2005a; Kozlenko et al., 2015). At low temperature, Er (Tb), Co1, and Co2 atoms occupy Wyckoff sites 6c (0, 0, z), 3b (0, 0, 0.5) and 9e (0.5, 0, 0), respectively. **Figure 14B** shows the crystal and magnetic structure of the TbCo1.9Fe0.1 compound at 10 K, the moments of Tb and Co atoms are antiparallel alignment along the c axis, which is similar to that of ErCo2 and TbCo2. However, NdCo2 and HoCo2 (Ouyang et al., 2005b; Mudryk et al., 2016) undergo two crystallographic transitions: the room temperature cubic lattice (space group Fd3m) transforms into the tetragonal one (I41/amd) at TC, and then becomes orthorhombic (space group: Fddd) below spin orientation TSR.

# Magnetocaloric Effect

Numerous studies have been carried out on phase transition and magnetocaloric effect (MCE) for RCo2 compounds (Wada et al., 1999, 2001; Duc et al., 2002; Gomes et al., 2002; Wang et al., 2002a,b, 2003; Liu and Altounian, 2005). Experimental and theoretical investigations show that the compounds with R = Er, Ho, and Dy show giant MCE owing to the first-order nature of magnetic transition. In 2001, Wada et al. reported the MCE of single crystal ErCo2. The maximum magnetic entropy change, –1S, is as high as 10.6 J mol−1 K −1 (37.2 J kg−1 K −1 ) and the maximal adiabatic temperature change, 1Tad, reaches ∼9.2 K under a magnetic field change of 0–5 T (Wada et al., 1999). Owing

to the large MCE, ErCo2 is usually considered to be a standard material for comparison in the low temperature region around 30 K. Furthermore, the maximum entropy change of DyCo2 and HoCo2 is 11 and 20 J kg−1 K −1 (Duc et al., 2002) under 0–5 T, respectively. The large MCE of RCo2 compounds is relevant to the large magnetic moment of R atoms, and more importantly, the crystallographic transition with negative volume expansion of different amplitudes also plays a key role for the various MCE. A small magnetic moment is induced in Co atoms, which is usually antiparallel to R atoms, resulting in the ferrimagnetic nature of the compounds.

In addition, some studies indicated that the replacement of R atoms by other Lanthanide elements can regulate the phase transition and MCE. Liu et al. (Liu and Altounian, 2005) reported that the Curie temperature of (Er1−xGdx)Co2 increases from 32 to 403 K with the substitution of Er by Gd. However, the maximum value of -1S under 0–5 T decreases from 15.3 J kg−1 K −1 at x = 0.1 to 3.2 J kg−1 K −1 at x = 0.6. Furthermore, it has been found that the substitution of Dy by Gd will rapidly reduce the MCE in DyCo2 (Wang et al., 2002b), but replacing Tb with Er increases the MCE of TbCo2 (Gomes et al., 2002). On the other hand, Wang et al. (2002a) reported that using 7% of Si to replace Co can increase the Curie temperature of DyCo2 up to 168 K, but weakens the first-order phase transition properties and causes a significant reduction in the magnetocaloric effect. It is worth mentioning that the replacement of Co by Ni lowers TC of Ho(Co1−xNix)2, while the large MCE is retained up to x = 0.1 though the phase transition changed from first-order to the second-order in nature (Wada et al., 2001).

## Negative Thermal Expansion Behaviors

In RCo2 compounds with R = Dy, Ho, and Er, the magnetic ordering around TC is accompanied by negative thermal expansion of lattice. Recently, Song et al. reported a wide temperature ZTE in the Tb(Co, Fe)2 and found a negligible thermal expansion coefficient, αL, in TbCo1.9Fe0.1, which is nearly two orders smaller than that of the common alloys (Song et al., 2018).

**Figure 15A** displays the temperature dependent linear thermal expansion (1L/L0) for Tb(Co2−xFex) compounds. It is found that the NTE and PTE can be obtained by adjusting the Fe concentration in Tb(Co2−xFex). Remarkably, the TbCo1.9Fe0.1 compound exhibits a ZTE property over a wide temperature range from 123 to 307 K. The average linear CTE of Tb(Co1.9Fe0.1) is αL = 0.48 × 10−6 K −1 and intrinsic unit cell also confirmed the reliability of ZTE which was determined by SXRD (synchrotron X-ray diffraction), as shown in **Figure 15B**. This CTE of Tb(Co1.9Fe0.1) is about two orders of magnitude smaller than that of the Al (αL = 23.1 × 10−6 K −1 ) and Cu (αL = 17.7 × 10−6K −1 ). Furthermore, this value is also smaller than the CTE of Invar alloys with composition Fe0.65Ni0.35 (αL = 1.5 × 10−6 K −1 , 193–373 K) (Guillaume, 1897).

The magnetic moment of Tb atoms, MTb, plays a dominationg role in the ferrimagnetic nature of the Tb(Co2−xFex) compounds. The spontaneous volume magnetostriction (ωs) was used to quantitatively describe the contribution of magentovolume effect to the abnormal change of lattice. For TbCo1.9Fe0.1, and the ωs is denoted by ωs = ωexp-ωnm,where ωexp is the unit cell volume obtained by NPD, and ωnm is calculated based on the Debye-Grüneisen relationship. A strong correlation between M2 Tb and ωs was denoted by the equation ωs(T) = k C M(T)2 , where k and C represent compressibility and magnetovolume coupling constant, and M(T) the amplitudes of magnetization (Gruneisen and Goens, 1926; Sayetat et al., 1998). That is to say, the spontaneous magnetostriction is closely related to the magnetization. The decrease of magnetization with temperature is responsible for the negative contribution to volume expansion, which neutralizes the normal lattice expansion, and hence produces the ZTE.

 This material has a very large family, which shows rich magnetic and lattice structure depending on compositions and atomic occupations. Experts, such as C. Wang's group and Y.P. Sun's group, have done a lot of excellent studies in the antiperovskite compounds, particularly on the NTE properties. Moreover, fascinating properties were also reported in some compositions, such as baromagnetic (Shi et al., 2016), barocaloric effect caused by spin frustration (Matsunami et al., 2015), and large magnetocaloric effect (Sun et al., 2012). Specifically, C.

# REFERENCES

Wang' group have reported a large amount of research work on NTE and MCE in antiperovskite compounds and also thought that lattice entropy is important to be excited due to large negative thermal expansion behavior driven by magnetic effects in the antiperovskite compounds so as to improve the magnetocaloric effect. A specific review article focusing on the antiperovskite compounds should be summarized separately, and we do not address more here.

# CONCLUSION

In summary, negative thermal expansion (NTE) behaviors in the materials with giant magnetocaloric effects (MCE) have been reviewed. Representative materials including La(Fe,Si)13, MM'X, and RCo2 have been included. Antiperovskite compounds are also briefly introduced. MCE materials are used for magnetic refrigeration while NTE materials for thermal compensation. Although the materials have distinct applications, the physical sources are similar particularly for the novel MCE and phase-transition-type NTE materials, both originating from the strong spin-lattice coupling. A number of MCE materials show abnormal lattice expansion owing to magnetic interactions, which provides a natural platform for exploring negative thermal expansion materials. The magnetostructural transformation in the giant MCE materials can be adjusted by utilizing its sensitivity to chemical/physical pressure, hence abnormal lattice expansion in an extended temperature range can be achieved. The present review provides implications for developing novel NTE materials and multifunctional devices.

## AUTHOR CONTRIBUTIONS

FH wrote the article in cooperation with FS, JH, and YL. All authors reviewed the manuscript.

# FUNDING

This work was supported by the National Key Research and Development Program of China (Grant Nos. 2017YFB0702702, 2018YFA0305704, 2014CB643700, and 2017YFA0303601), the National Natural Sciences Foundation of China (Grant Nos. 51531008, U1832219, 51771223, 51590880, and 11474341), and the Key Program and Strategic Priority Research Program (B) of the Chinese Academy of Sciences.

transitions of the Laves-phase compound NdCo2. Phys. Rev. B 71:064405. doi: 10.1103/PhysRevB.71.064405

**Conflict of Interest Statement:** The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Hu, Shen, Hao, Liu, Wang, Sun and Shen. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Mechanisms and Materials for NTE

### J. Paul Attfield\*

Centre for Science at Extreme Conditions and School of Chemistry, University of Edinburgh, Edinburgh, United Kingdom

Negative thermal expansion (NTE) upon heating is an unusual property but is observed in many materials over varying ranges of temperature. A brief review of mechanisms for NTE and prominent materials will be presented here. Broadly there are two basic mechanisms for intrinsic NTE within a homogenous solid; structural and electronic. Structural NTE is driven by transverse vibrational motion in insulating framework–type materials e.g., ZrW2O8 and ScF3. Electronic NTE results from thermal changes in electronic structure or magnetism and is often associated with phase transitions. A classic example is the Invar alloy, Fe0.64Ni0.36, but many exotic mechanisms have been discovered more recently such as colossal NTE driven by Bi–Ni charge transfer in the perovskite BiNiO3. In addition there are several types of NTE that result from specific sample morphologies. Several simple materials, e.g., Au, CuO, are reported to show NTE as nanoparticles but not in the bulk. Microstructural enhancements of NTE can be achieved in ceramics of materials with anisotropic thermal expansion such as beta–eucryptite and Ca2RuO4, and artificial NTE metamaterials can be fabricated from engineered structures of normal (positive) thermal expansion substances.

#### Edited by:

Andrea Sanson, Università degli Studi di Padova, Italy

#### Reviewed by:

Angus Wilkinson, Georgia Institute of Technology, United States Ranjan Mittal, Bhabha Atomic Research Centre, India Xianran Xing, University of Science and Technology Beijing, China

\*Correspondence:

J. Paul Attfield<EMAIL_ADDRESS>
#### Specialty section:

This article was submitted to Physical Chemistry and Chemical Physics, a section of the journal Frontiers in Chemistry

> Received: 21 June 2018 Accepted: 02 August 2018 Published: 22 August 2018

#### Citation:

Attfield JP (2018) Mechanisms and Materials for NTE. Front. Chem. 6:371. doi: 10.3389/fchem.2018.00371 Keywords: thermal expansion, negative thermal expansion, thermal expansion coefficient, structural NTE, electronic NTE, morphological NTE

# INTRODUCTION

NTE (negative thermal expansion) refers to the unusual phenomenon of volume contraction upon heating. Although most materials display positive thermal expansion (PTE) on heating, NTE is found in a wide variety of substances over varying ranges of temperature. This brief review is an attempt to summarize the mechanisms and prominent materials that show NTE. Further details may be found in more substantial reviews published by other authors in recent years (Lind, 2012; Takenaka, 2012; Chen et al., 2015; Dove and Fang, 2016; Liu et al., 2018; Mittal et al., 2018) and in the other papers in this special issue.

Control of thermal expansion is important for many applications from ceramic cooker hobs to housings for optical devices, with zero thermal expansion (ZTE) materials or composites of PTE and NTE components being particularly useful. Thermal expansion is quantified through the linear or volume (bulk) thermal expansion coefficients (TECs), αL = (1/L)(dL/dT), and αV = (1/V)(dV/dT), which respectively measure the change in length L or volume V of an object with temperature T. αL and αV are typically quoted in 10−6 K −1 units, equivalent to ppm (parts per million) K−1 or MK−1 . Isotropic substances such as simple liquids, glasses, polycrystalline ceramics, and cubic crystals, have the same αL in all directions with αV = 3αL. ZrW2O8 is a famous example of a cubic NTE material (Mary et al., 1996). However uniaxial (tetragonal, hexagonal, or trigonal) crystals may have different linear TECs α|| and α⊥ parallel and perpendicular to the unique symmetry axis, respectively, and crystals with orthorhombic or lower symmetry have three different values α1, α2, and α3 in mutually perpendicular directions. The volume TEC is given by

**34**

αV = α|| + 2α⊥ or αV = α1 + α2 + α3 and when the linear TECs are very different, such as a mix of negative and positive values, then highly anisotropic thermal expansion may be obtained. TECs of crystalline materials are usually measured by determining how unit cell lengths change with temperature from diffraction measurements. Direct strain gauge (dilatometry) measurements of crystals can also be used, and are particularly useful for ceramics and amorphous materials such as glasses. Diffraction and dilatometry expansion measurements can give different results due to the effects of microstructure, as discussed in section Microstructural NTE.

NTE materials have negative αV over some temperature range. Reported αV values vary from −1 to −1,000 × 10−6 K −1 , but it is also important to consider the temperature range to which the quoted αV refers as very large negative αV's may result from modest volume decreases over very narrow temperature ranges at a phase transition. For this reason it is often more useful to consider the overall volume decrease; materials with –1L/L > 1% and so –1V/V > 3% have notably large NTE.

The thermodynamic origin of thermal expansion in solids is expressed through the relation αV = γCV/BV where CV is heat capacity at constant V, B = –V(dp/dV) is the bulk modulus with p being pressure, and γ is the weighted or macroscopic Grüneisen parameter summed over values for the active phonon frequencies ωi as γi = –d(ln ωi)/d(ln V). CV and B always take positive values, hence variations in the sign of αV arise from corresponding variations in the sign of γ. NTE is often associated with other unusual lattice properties such as negative linear compressibility under applied pressure (Mittal et al., 2018) and pressure-induced softening where dB/dp becomes negative (Dove and Fang, 2016).

Conventional PTE arises because γ is usually positive as a consequence of the shape of the interatomic potential for bonding between two atoms, as shown in **Figure 1**. Anharmonicity in the shape of the potential leads to an increase in the average interatomic distance as higher vibrational states become more populated as temperature rises. As this pairwise potential shape applies qualitatively to all type of chemical bonding, it might appear that PTE should be a universal behavior, but NTE can arise from two "escapes" that circumvent the latter argument.

## INTRINSIC NTE MECHANISMS

# Structural NTE

The first "escape" from the universal PTE behavior expected from the interatomic potential in **Figure 1** arises from the more complex vibrational properties of large arrays of atoms. **Figure 2** shows some of the possible motions for a chain of atoms. Longitudinal (L) vibrations in the direction of the bonds (**Figure 2A**) tend to lengthen the chain as temperature increases through thermal expansion of the individual bonds via the anharmonicity of the interatomic potential (**Figure 1**). However, transverse (T) motions perpendicular to the direction of the chain tend to shorten the chain–length as the amplitude of vibration increases with temperature (**Figures 2B,C**) and so can lead to NTE. This is sometimes known as the tension or

FIGURE 1 | The interatomic bonding potential, showing the variation of potential energy with interatomic distance for a pair of bonded atoms. Vibrational energy levels are quantised and with increasing temperature the occupation of higher levels leads to a slight increase in the mean interatomic distance relative to the minimum–energy equilibrium distance as shown.

"guitar string" effect. Lattice vibrations, also known as phonons, are usefully classified as optic (O) with short wavelengths and high frequencies and energies, or acoustic (A) with long wavelengths and low frequencies and energies. Transverse optic (TO) phonons like that shown in **Figure 2B** lead to large chain shortening (NTE) but may only be excited at high temperatures in view of their high energies, whereas transverse acoustic (TA) modes that lead to more modest NTE are excited at lower temperatures. Detailed theoretical and experimental analyses of phonon spectra are needed to assess the contributions of TO and TA vibrations to the NTE of real materials (Dove and Fang, 2016; Mittal et al., 2018).

Structural NTE results when the shortening effects of the transverse phonon amplitudes due to bending or torsional motions outweigh the expansion effects of the longitudinal modes. Low atomic connectivity so that atoms have free space to move into during transverse motions leading to large amplitudes is a necessary feature for NTE to prevail. Planar 3-coordination is the maximum connectivity known to lead to negative expansion, as exemplified by graphene sheets of carbon atoms (Yoon et al., 2011). However when these sheets are stacked in the threedimensional lattice of graphite, conventional PTE arising from soft van der Waals bonding potentials in the stacking (high symmetry) direction gives a large α|| = 23.1 × 10−6 K −1 that outweighs the NTE in the perpendicular directions (α⊥ = −0.6 × 10−6 K −1 ) leading to bulk PTE (αV = α|| + 2α⊥ = 21.9 × 10−6 K −1 ) (Morgan, 1972).

Bulk structural NTE requires a large proportion of 2 coordinate linker groups, connecting more highly-coordinated atoms into a three-dimensional structure. Some representative examples of structural NTE material types, with 2-connected linkers underlined, are ScF3, Ag2O, ZrW2O8, ZrV2O7, LiAlSiO4 (the mineral β-eucryptite), zeolitic forms of SiO2 (e.g., ITQ-4) and related AlPO4 (e.g., AlPO4-17) frameworks, Cd(CN)2, Co3[Co(CN)6]2, and metal organic frameworks such as IRMOF-1 (Zn4O(bdc)3, where bdc is 1,4-benzodicarboxylate). These have αV values of magnitude −20 to −120 × 10−6 K −1 over typical temperature ranges of a few hundred K; details and citations are shown in Dove and Fang (2016). All of these materials have the majority of their atoms in the 2-connected linkers. The metal fluoride and oxide examples have 2-coordinate atoms linking tetrahedral or octahedral units together. These polyhedra tend to be rigid so the transverse vibrations of the lattice may be described in the rigid unit mode (RUM) picture (Dove and Fang, 2016).

The importance of the transverse motions of the linker atoms or groups to NTE is further demonstrated by changes observed when additional molecules or ions are inserted into NTE materials. The inserted species within cavities in the structure are adjacent to the linkers and so reduce the amplitudes of their transverse vibrations. Redox insertion of only 6% Li into Fedoped ScF3 switches the TEC from negative to positive (Chen et al., 2017), and the same change is found when K+ or H2O is inserted into the channels of the cyanide framework material YFe(CN)6 (Gao et al., 2017).

## Electronic NTE

A disparate group of materials, usually dense metal alloys or ceramics, display NTE that is not driven by the structural (transverse vibration) mechanism. Although they have a wide variety of physical properties, and so are sometimes described as having different NTE mechanisms, they have the common feature that NTE results from thermal changes in the interatomic bonding potential, as illustrated in **Figure 3**. Changes in bonding with temperature such that the interatomic potential becomes more strongly bonding can shift the curve to a smaller equilibrium distance at higher temperature. This may occur through a relatively sharp first order phase transition between two distinct states, or the potential may gradually evolve with changing temperature through a second or higher order transition. When the effect of this "escape" outweighs the usual PTE from the anharmonicity of the potentials then NTE may be observed over temperature range of the crossover.

**Figure 4** illustrates the schematic changes in lattice volume with temperature for a material displaying electronic NTE. Both the larger-volume low-T and the smaller-volume high-T states shown in **Figure 3** display conventional PTE behavior, but the change between them in the crossover region with lower and upper temperatures Tl and Tu leads to NTE. Tu often marks an ordering temperature such as a magnetic or ferroelectric Curie transition, and the lower limit Tl is reached where the order parameter (magnetization or electric polarization) is fully saturated. In other cases such as charge transfer materials, Tl and Tu mark the lower and upper limits of the two-phase region where the low-T and high-T phases coexist. The electronically-induced excess volume 1Vex relative to the extrapolated volume of the high-T state, VHT, may be used to calculate the spontaneous volume striction 1Vex/VHT. Variations in the magnitude of 1Vex and in the separation between Tl and Tu may be used to tune electronic materials from reduced PTE, through ZTE to NTE behavior. A famous material that launched the study of unusual thermal expansion properties is the Invar alloy Fe0.64Ni0.36 named for an invariant length with a very small αL = 1 × 10−6 K −1 (effectively ZTE) below magnetic TC = 500 K.

The transitions or changes that give rise to electronic NTE are usually associated with an increase in electron delocalization on passing from the low-T to the high-T phase. The low-T phase is more electron localized or correlated (e.g., magnetically ordered), due to electron-electron repulsions that may be described by the Hubbard U energy, while the more electron delocalized or disordered high-T phase is stabilized by entropy. Electrons near the Fermi level are often in d- or f-states that are non-bonding or weakly antibonding, so their delocalization allows the bonding potential to become more negative and shift to shorter distance as shown in **Figure 3**.

Classes of materials where electronic NTE is found are;

a 0.4% cell volume decrease at 750 K where the orbital orderdisorder transition occurs.

Further details and citations when not shown above are given in the comprehensive review of NTE in functional materials by Chen et al. (2015).

# MORPHOLOGICAL NTE

The structural and electronic mechanisms for NTE described above apply to chemically homogenous materials such as a single crystal. However, there are further instances where NTE can arise or differ from the normal bulk behavior due to the specific morphology of the sample.

# Nanoparticle NTE

A variety of materials that show bulk PTE have been found to display NTE when prepared as small particles, usually in the nanoscale regime. For example, the magnetic insulators CuO and MnF2 show PTE in the bulk but as 5 nm particles they display NTE below their Néel temperatures. CuO has a giant NTE of αV = −110 × 10−6 K −1 between 20 and 170 K (Zheng et al., 2008). Nanoparticles of Au (Li et al., 2002) and TiO2 (Zhu et al., 2016) are also reported to display NTE.

The origin of nanoparticle NTE is usually electronic as, for example, the excess volume of CuO particles above follows the general behavior shown in **Figure 4**. Localization of ordered or correlated states tends to be enhanced at and near surfaces so the associated lattice expansion on cooling can dominate the overall behavior in small particles with a large proportion of surface atoms. The structural NTE mechanism could also play a

part as surface atoms have a lower connectivity than the bulk so transverse vibrational amplitudes may be enhanced.

# Microstructural NTE

Direct measurement of αV for ceramic samples sometimes gives a more negative value than that expected from crystallographic measurement of the linear TECs. The excess negative expansion is achieved by reducing the volumes of microcracks or voids within the ceramic on heating, as illustrated schematically in **Figure 5**. Microstructural NTE was reported in an early study of β-eucryptite (LiAlSiO4) (Gillery and Bush, 1959) and very large effects have recently been discovered in Ca2RuO4 (Takenaka et al., 2017a). These ceramic materials both have anisotropic thermal expansion with one strongly negative coefficient that dominates the expansion of their ceramics. For example, on heating from 150 to 340 K, the orthorhombic a, b, and c axes of Ca2RuO4 show length changes of −0.6, −5.0, and +4.5% respectively, so an overall 1V/V = −1.1% is expected. However an 80% dense ceramic sample gave 1V/V = −6.7% revealing a substantial microstructural NTE effect.

Anisotropic thermal expansion leads to stresses at grain boundaries that result in microcracking in β-eucryptite ceramics on cooling to room temperature after sintering. Reduction of the microcrack volumes on subsequent heating results in bulk NTE and an enhancement of the excess NTE with increasing grain size (and hence internal microcrack volume) has been established (Pelletant et al., 2012). However, this is less problematic for Ca2RuO4-based ceramics, which have been combined with epoxy resin to generate ZTE materials that are stable to microcracking on thermal cycling (Takenaka et al., 2017b).

# Metamaterials NTE

Artificial structures consisting of two or more materials with different TECs (which may all be positive) can be engineered

to contract when heating. A simple example based on bonded strips of two materials with different positive TECs is shown in **Figure 6**. The structure contracts on heating through reduction of the volume of internal voids, which outweighs the increase in volume of the materials themselves. Designs for threedimensional cellular metamaterials with varying TECs based on the use of such bimaterial connectors were proposed by Lakes (2007).

Recent developments in additive manufacturing through three-dimensional printing technologies have enabled metamaterials with bulk NTE to be generated. In a recent example, a two-component polymer metamaterial showed bulk negative expansion with αL = −50 × 10−6 K −1 although the individual components had PTE with an average αL = 40 × 10−6 K −1 (Qu et al., 2017).

# SUMMARY

Although many diverse examples of NTE materials are reported, they may be classified according to two types of intrinsic mechanism. Electronic NTE arises from reduction in first-neighbor distances upon heating due to changes in the interatomic potential. These changes may arise from a variety of physical property transitions such as magnetism, charge transfer, ferroelectricity, and superconductivity that alter the distribution of electron density. Structural NTE occurs through reduction in second- or higher- neighbor distances upon heating due to dominant effects of transverse vibrations such as bending or torsional modes, and is found in many framework-type materials with a high proportion of 2-connected linkers.

The intrinsic NTE mechanisms may be enhanced in nanoparticles, most likely through electronic effects from localization of ordered or correlated states near surfaces. Further morphological mechanisms for NTE of bulk artifacts result from reducing the volume of internal voids upon heating. Microstructural NTE is found for ceramics of materials having anisotropic thermal expansion coefficients. Artificial structures of substances with different expansion coefficients may be used to generate metamaterials with NTE even when the individual components have PTE behavior.

# AUTHOR CONTRIBUTIONS

The author confirms being the sole contributor of this work and approved it for publication.

# REFERENCES

# FUNDING

The author acknowledges financial support from EPSRC.

# ACKNOWLEDGMENTS

This paper is based upon a talk presented at the 2nd International Symposium on Negative Thermal Expansion and Related Materials (ISNTE-II) at Tokyo Institute of Technology, Yokohama, Japan in December 2017. The author thanks the organizers and participants for their contributions that helped to shape the ideas presented in this paper.

**Conflict of Interest Statement:** The author declares that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Copyright © 2018 Attfield. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

# Adjustable Thermal Expansion Properties in Zr2MoP2O12/ZrO2 Ceramic Composites

Hongfei Liu1 , Weikang Sun1 , Xiang Xie1 , Lu Yang1 , Zhiping Zhang2 \*, Min Zhou1 , Xianghua Zeng1 and Xiaobing Chen2