Colossal negative thermal expansion over a wide temperature span in dynamically self-assembled MnCo(Ge,Si)/epoxy composites

The achievement of significant negative thermal expansion (NTE) over a wide temperature range (ΔTNTE) has posed a formidable challenge for NTE materials. In the present study, textured MnCo(Ge,Si)/epoxy composites were prepared by magnetic field-assisted dynamic self-assembly of multi-component Mn0.945Co1.055Ge1-xSix particles. The utilization of multi-component particles with tunable transition temperatures significantly amplifies the temperature range over which the NTE occurs, surpassing the limitations of conventional single-component composites. The textured microstructure enables the extension of lattice-level NTE to reach the macroscopic level, which is manifested by a remarkably large NTE coefficient of −328.7 × 10−6/K between 288.2 and 431.1 K. GRAPHICAL ABSTRACT IMPACT STATEMENT Colossal NTE with a coefficient αL of −328.7 × 10−6/K is achieved over a wide temperature range of 142.9 K between 288.2 and 431.1 K, representing the largest αL among all reported NTE materials.


Introduction
Negative thermal expansion (NTE) materials are a fascinating group of materials that contract as their temperature increases, which is opposite from the typical positive thermal expansion (PTE) behavior exhibited by most materials.NTE materials can be incorporated with PTE materials to create composites that have zero or reduced thermal expansion, which is of crucial importance to a variety of technological applications, e.g.thermal stress management, high-precision engineering, thermal barrier coating and aerospace industry [1][2][3][4].
The origin of NTE can be attributed to various underlying mechanisms that make a negative contribution to the overall thermal expansion against anharmonic vibration of atoms.For instance, NTE has been observed in framework materials that are characterized by phonondriven structural distortions or asymmetric vibration and rotation of structural units within the crystal lattice [5][6][7][8][9][10].The NTE phenomenon can also be a macroscopic manifestation of the strong coupling between lattice, electron and spin degrees of freedom at the microscopic scale.
The microscopic charge transfer in BiNiO 3 [11], local chemical ordering in PtNi nanoparticles [12], magnetovolume effect in magnetic alloys [4,[13][14][15][16][17][18][19][20], and ferroelectric ordering in PbTiO 3 -based compounds [21] also lead to a macroscopic NTE behavior.Apart from that, the abrupt increase in the unit-cell volume across the martensitic transition brings a giant/colossal NTE in the MM'X (M, M' = Mn, Fe, Co, Ni; X = Si, Ge) [22][23][24][25][26], Fe 3 NiB x [27] and Fe 44−x Mn 28 Ga 28 + x [28,29] alloys.Among the diverse classes of NTE materials, the MM'X family has attracted considerable attention due to their exceptionally large NTE.For example, the (Mn 0.95 Ni 0.05 )CoGe alloy shows an NTE coefficient (α L ) of about −207 × 10 −6 /K [30], which is almost one order of magnitude larger than that of most NTE materials [1,2].However, such a large NTE can only be obtained in a narrow temperature span ( T NTE ) of about 50 K [30].The T NTE can be enlarged to ∼ 195 K by compositional variation in Fe-doped MnNiGe alloys, whereas this is realized at the expense of a significant reduction of the α L [25].Therefore, it has been a great challenge to achieve both large NTE and a wide temperature span for the MM'X materials.
One prominent feature of the MM'X materials is the anisotropic structural deformation close to the martensitic transition temperature (T t ).The orthorhombic lattice shrinks along the a Ort axis by ∼ 10% upon heating, while it expands along the b Ort and c Ort axes by ∼ 7% and ∼ 0.4%, respectively [25,31].As a result, a colossal NTE with a potential maximum α L of ∼ 2000 × 10 −6 /K may be developed in < 100 > Ort -textured MM'X materials, but the T NTE will still be limited by the sharp martensitic transition.In the present work, we successfully fabricated < 100 > Ort -textured MnCo(Ge,Si)/epoxy composites by dynamical self-assembly in a magnetic field [32][33][34].In order to tackle with the narrow T NTE , multi-component Mn 0.945 Co 1.055 Ge 1−x Si x particles with variable T t s were used in the composites, which yielded martensitic transitions in tandem over a wide temperature range and thus a significantly enlarged T NTE .

Materials and methods
Polycrystalline samples with nominal compositions of Mn 0.945 Co 1.055 Ge 1−x Si x (x = 0.09, 0.12, 0.15, 0.17, 0.19 and 0.21) were prepared by arc melting under high-purity argon atmosphere.The ingots were remelted four times to ensure compositional homogeneity and subsequently annealed at 1123 K for 4 days in evacuated quartz tubes before being quenched in water.
The annealed Mn 0.945 Co 1.055 Ge 1−x Si x ingots were pulverized through multiple thermal cycles in liquid nitrogen.The pulverized powders with diameters between 20 and 50 μm from 6 different compositions (i.e.x = 0.09, 0.12, 0.15, 0.17, 0.19 and 0.21) were mixed in an equal ratio and used for the subsequent dynamic selfassembly process (see the illustration in Figure 1).The multi-component design aims at enlarging the temperature span of the NTE since the lattice-level NTE appears only in a narrow temperature range around T t for a single composition.The multi-component powders were then suspended in epoxy.The amount of epoxy was set to be 10, 12.5 and 15 wt.% with respect to the weight of the multi-component powders.The suspension after degassing in a vacuum was transferred into a cylindrical plastic mould that was subsequently rotated along its long axis at a speed of 30 r/min for 10 h.A static magnetic field of 1 T was applied perpendicular to the long axis of the mould during the rotation.Self-assembled multi-component Mn 0.945 Co 1.055 Ge 1−x Si x /epoxy composites with a diameter of 5 mm and a length of 15 mm were finally obtained after curing at room temperature for 10 h.
A vibrating sample magnetometer (VSM, Lakeshore 7400s) and a differential scanning calorimeter (DSC, PerkinElmer DSC 6000) were employed to characterize the magnetic and structural transitions.In situ temperature-dependent X-ray diffraction (XRD) measurements were performed using a PANalytical Empyrean diffractometer with Cu-Kα radiation.The morphology and crystallographic orientation of the dynamically self-assembled multi-component composites were examined using a scanning electron microscope (SEM, JSM 7200F) equipped with electron backscatter diffraction (EBSD) detectors.The micro-and nano-scale structural analyses on the dynamically self-assembled composite were carried out using a transmission electron microscope (TEM, FEI Tecnai G2 F20).The linear thermal expansion ( L/L 0 ) curves were measured by a thermal dilatometer (Linseis DIL L75 VS).Uniaxial compression tests were performed using a universal test machine (INSTRON 5982) with a strain rate of 1 × 10 −4 s −1 .

Results and discussion
Figure 2(a) shows the temperature-dependent magnetization (M-T) curves, where a sharp paramagneticferromagnetic (PM-FM) transition with noticeable thermal hysteresis ( T hys ) was observed in the x = 0.09 sample.Besides, the FM transition is accompanied by a strong endothermic or exothermic peak in the DSC curves (Figure 2(b)).This suggests the occurrence of a first-order magnetostructural transition, where the hexagonal-orthorhombic structural transition coincides with the PM-FM transition.According to the M-T and DSC curves, the T t rises with increasing Si content from 0.09 to 0.17, while the magnetostructural transition is retained.In contrast, a different phase transition character is observed in the x = 0.19 and 0.21 samples.Although endothermic and exothermic peaks are still present in the DSC curves (Figure 2(b)), the x = 0.19 and 0.21 samples show a second-order FM transition with negligible T hys in the M-T curves (Figure 2(a)).This suggests the decoupling of the structural and magnetic transitions.Based on the magnetometry and calorimetry analyses, a magnetic and structural phase diagram has been constructed for the Mn 0.945 Co 1.055 Ge 1−x Si x series  of materials (see Figure 2(c)).According to the phase diagram, all of the samples are in the FM orthorhombic state at room temperature, which offers the potential to manipulate the orientation of the free powders using a magnetic field.
Figure 2(d) displays a contour plot of the XRD patterns from the x = 0.12 sample as an example.A structural transition from TiNiSi-type orthorhombic (space group Pnma) to Ni 2 In-type hexagonal (space group P6 3 /mmc) is detected at around 340 K, in agreement with the magnetometry and calorimetry results.Thermal evolution of the lattice parameters across the structural transition is derived from Rietveld refinement and displayed in Figure 2  This lamellar structure is ascribed to the complex interplay between magnetic force from the external magnetic field, dipole-dipole interaction between neighboring particles, viscous drag from the epoxy and centripetal force during the field-assisted self-assembly process [32][33][34].The thickness of the epoxy layer increases as the epoxy content rises from 12.5 to 15 wt.% (Figure 3(c)).
XRD and EBSD analyses were performed to explore the grain orientation in the multi-component Mn 0.945 Co 1.055 Ge 1−x Si x /epoxy composites.Figure 3(h) displays the XRD patterns collected from the multicomponent powders and the transverse cross section of the dynamically self-assembled multi-component composites.The diffraction peaks of the powders can be mainly indexed by the TiNiSi-type orthorhombic phase.There are also a couple of weak reflections from the Ni 2 In-type hexagonal phase, which is originated from the Mn 0.945 Co 1.055 Ge 0.91 Si 0.09 particles showing a hexagonal-orthorhombic transition around room temperature (Figure 2 (a) and (b)).In contrast with the XRD pattern of the multi-component powders, the XRD patterns of the dynamically self-assembled composites with 12.5 and 15 wt.% epoxy are characterized by strong {H00}-type reflections (e.g. ( 200) and ( 400)), suggesting a strong < 100 > Ort texture along the long axis of cylindrical-shaped samples.Nevertheless, the preferred grain orientation is less significant in the composite with 10 wt.% epoxy, which may arise from the large constraints between neighbouring particles suspended in a limited amount of epoxy.Additionally, the preferred orientation of the Mn 0.945 Co 1.055 Ge 1−x Si x particles in the composites with 12.5 wt.% epoxy has also been verified by the EBSD orientation maps, pole figures and inverse pole figures in Figure 3(i).
Consequently, the XRD and EBSD results reveal a strong < 100 > Ort texture in the multi-component Mn 0.945 Co 1.055 Ge 1−x Si x /epoxy composites with 12.5 and 15 wt.% epoxy.Our previous neutron diffraction experiments reveal that the magnetic moments in MnCoGebased alloys are aligned along the c-axis of the orthorhombic structure [31].As a result, < 001 > Ort texture was obtained by means of aligning the Mn 0.6 Fe 0.4 NiGe 0.5 Si 0.5 particles in a static magnetic field [26].In contrast, here we applied a magnetic field perpendicular to the rotation axis of the Mn 0.945 Co 1.055 Ge 1−x Si x particles (see Figure 1).Therefore, the particles are reoriented with the c-axis perpendicular to their rotation axis, leading to the desirable preferred orientation of < 100 > Ort parallel to the rotation axis (see Figure 3(g) and (h)).
Figure 4 shows the TEM observations on a thin specimen lifted out from the multi-component composite with 12.5 wt.% epoxy by focused ion beam (FIB).Thin and parallel laths can be observed in the bright-field (BF) TEM image in Figure 4(a), manifesting itself as the orthorhombic martensite, which has also been observed in other MM'X-type materials [35][36][37][38].The TiNiSi-type orthorhombic structure is also confirmed by the selected area electron diffraction (SAED) pattern in Figure 4(b), which was taken from the [102] Ort zone axis (Z.A.).The EDS elemental maps (Figure 4(c)) reveal compositional homogeneity in the area enclosed by dotted lines in Figure 4(a).Figure 4(d) and (e) present a highresolution TEM (HRTEM) image and a corresponding fast Fourier transform (FFT) pattern, respectively.The atomic arrangement along the [010] Ort and  Ort crystallographic directions can be unambiguously distinguished in the HRTEM image (see the schematic illustration in Figure 4(f)).Additionally, the lattice parameter b of the orthorhombic phase is estimated to be 3.82 Å by the periodicity of the intensity profile (see Figure 4(g)) along the [010] Ort direction, which is consistent with the neutron diffraction results and literature reports [31,39].
Figure 5(a) presents the temperature-dependent linear thermal expansion ( L/L 0 ) along the long axis of the single-component Mn 0.945 Co 1.055 Ge 1−x Si x /epoxy composites.A large NTE coefficient (α L ) of about −1756.1 × 10 −6 /K is realized in the single-component composites due to the martensitic transition.This is the largest reported magnitude of α L among NTE materials.However, the temperature span of the NTE is less than 50 K in the single-component composites due to the relatively sharp martensitic transition (see Figure 2).The narrow T NTE has been a common issue for metallic materials whose NTE property is induced by martensitic phase transitions [1].In strong contrast to the narrow T NTE in single-component composites, a wide T NTE up to 163.1 K is obtained in the multi-component composites that contain Mn 0.945 Co 1.055 Ge 1−x Si x particles from six different compositions and 10 wt.% epoxy.The design of multi-components takes advantage of the martensitic transition from each composition and results in consecutive martensitic transitions over a wide temperature range.Besides, both α L and T NTE are influenced by the amount of epoxy.The magnitude of α L increases from 252.8 × 10 −6 /K to 328.7 × 10 −6 /K as the amount of epoxy rises from 10 to 12.5 wt.%, while it shows a decrease with further increase in the amount of epoxy to 15 wt.%.The non-monotonic change in α L with respect to the amount of epoxy can be attributed to the competition between crystallographic texture and PTE of epoxy itself.As shown in Figure 3(h), the < 001 > Ort orientation of the Mn 0.945 Co 1.055 Ge 1−x Si x powders is enhanced with an increase in the epoxy content from 10 to 12.5 wt.% due to the improved mobility of the Mn 0.945 Co 1.055 Ge 1−x Si x powders during the field-assisted self-assembly process.As a result, stronger NTE is observed in the composites with 12.5 wt.% epoxy as compared to that with 10 wt.% epoxy.Nevertheless, the NTE of the composite is weakened with a further increase in the epoxy content to 15 wt.%, which is ascribed to the increased contribution of epoxy with PTE.The Ashby-like plot in Figure 5(c) compares the T NTE and α L for various NTE magnetic materials.A combination of colossal NTE and a large temperature span makes the dynamically self-assembled multi-component Mn 0.945 Co 1.055 Ge 1−x Si x /epoxy composites highly competitive among all reported NTE magnetic materials [16,17,[22][23][24][25][26]28,29,[40][41][42][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57][58].It is worth noting that the wide variety of compounds within the MM'X family provides the flexibility to adjust the T t across a wide temperature range.This capability opens up the potential for further expanding the T NTE .
Additionally, mechanical properties are also critical for practical applications of NTE materials.The compressive stress-strain curves of the dynamically selfassembled multi-component Mn 0.945 Co 1.055 Ge 1−x Si x / epoxy composites are shown in Figure 5(d).It can be found that the composite with 12.5 wt.% epoxy exhibits a maximum compressive stress of 143 MPa, remarkably higher than the Ag-epoxy-bonded MnCoGe 0.99 In 0.01 (70.4 MPa) [22] and In-bonded Mn 0.6 Fe 0.4 NiGe 0.5 Si 0.5 (48 MPa) [26] composites.

Conclusions
In summary, this work demonstrates a new strategy to achieve both a large NTE coefficient and a wide temperature range for MM'X materials.This is realized by dynamic self-assembly of multi-component Mn 0.945 Co 1.055 Ge 1−x Si x /epoxy composites in a magnetic field, which leads to a preferred < 100 > Ort orientation for the Mn 0.945 Co 1.055 Ge 1−x Si x particles.The colossal NTE along the a Ort axis of the orthorhombic lattice across the martensitic transition manifests in the macroscopic level due to the strong < 100 > Ort texture.As a result, a linear NTE coefficient of −328.7 × 10 −6 /K has been obtained in the dynamically self-assembled multi-component MM'X/epoxy composites, which represents one of the highest α L values among all reported NTE materials.Furthermore, the integration of multicomponent Mn 0.945 Co 1.055 Ge 1−x Si x particles with gradually varying martensitic transition temperatures substantially broadens the NTE temperature range, achieving an impressive T NTE of 142.9 K between 288.2 and 431.1 K. Consequently, the remarkable synergy between colossal NTE and a wide temperature span makes the dynamically self-assembled multi-component MM'X/epoxy composites highly competitive within the realm of NTE materials.

Figure 1 .
Figure 1.Schematics of the field-assisted self-assembly process.

Figure 2 .
Figure 2. (a) M-T and (b) DSC curves, (c) magnetic and structural phase diagram of the Mn 0.945 Co 1.055 Ge 1−x Si x alloys.(d) Contour plot of temperature-dependent XRD patterns of the x = 0.12 sample.(e) and (f) Temperature-dependent lattice parameters of the x = 0.12 sample.The errors on lattice parameters are smaller than the symbol sizes.

Figure 3 .
Figure 3. SEM images collected from (a-c) longitudinal and (b-f) transverse cross sections of dynamically self-assembled multicomponent composites.The insets in (a), (b) and (c) are EDS mappings of the Mn element.(g) 3D and 2D XCT images of the multicomponent composite with 12.5 wt.% epoxy.(h) XRD patterns collected from the multi-component powders and composites.(i) EBSD analysis of the transverse cross section of the multi-component composite with 12.5 wt.% epoxy.

Figure 3 (
a)-(f) present images taken from the longitudinal and transverse cross sections of the composites.The microstructure of the composite with 10 wt.% epoxy is characterized by a uniform distribution of Mn 0.945 Co 1.055 Ge 1−x Si x powders in the epoxy matrix (Figure 3(a) and (b)).Interestingly, lamellar structure appears in the longitudinal cross section of the composite with 12.5 wt.% epoxy (Figure 3(b)), which is also visualized in the EDS (the inset of Figure 3(b)) and X-ray computed tomography (XCT) analyses (Figure 3(g)).

Figure 4 .
Figure 4. BF-TEM image and (b) SAED pattern taken from a specimen lift out from the dynamically self-assembled multi-component composite with 12.5 wt.% epoxy.(c) EDS maps of selected region in (a).(d) HRTEM image and (e) corresponding FFT of the region enclosed by solid lines in (a).(f) Schematic representation of the atomic configuration viewing along the [102] Ort direction.(g) Intensity profiles of the region enclosed by the dashed line in (d).