This Perspective describes the phonon transport engineering with one-dimensional defects, i.e., dislocations, from both theoretical and experimental points of view. The classical models, modern atomistic simulations, and advanced experimental investigations on thermal conductivity reduction by dislocations are discussed. Particularly, the complex stress field induced by dislocations, the phonon–dislocation interaction mechanisms, and the anisotropic thermal transport in materials with well-oriented dislocations are emphasized. Further investigations of phonon–dislocation interactions in both theory and experiments are prospected at the end of the work.

A dislocation, which is defined as a boundary between deformed and non-deformed regions in a crystalline structure, has been widely studied in relation to the mechanical properties of materials. The motion, multiplication, and interaction of dislocations cause strain hardening, a common phenomenon in which continued deformation increases the strength of a crystal. As an important lattice defect, dislocations were recognized as the main sources of phonon scattering in the early days.1 Understanding the phonon–dislocation interaction is extremely important since dislocations can naturally appear during the deformation and growth of materials. Actually, using lattice defects to control the heat transport in materials has become an important direction in many frontier fields, such as thermoelectric energy conversion2–5 and novel computations based on heat.6–9 

Dislocations distort crystals in a complex manner. The region close to the dislocations is highly distorted and plastic, which is inaccessible to continuum models and it is largely treated on an empirical basis. Away from the dislocation line, the deformation field can be well described with elastic theory and the strain field strongly depends on the distance to the dislocation line. Due to their spatially extended character, dislocations have the most severe impacts. But the complex non-homogeneous strain fields created by the dislocation make the interactions between phonons and dislocations much different from other scattering sources, such as point defects. Such complex phonon–dislocation interactions bring serious theoretical difficulties. The early studies were based on analytical theories/models, which provide a great deal of insight into the effect of dislocations on thermal conductivity (TC). However, such analytical models based on Boltzmann transport equation (BTE) can only qualitatively predict the TC in dislocated systems and it could not help to understand the detailed mechanisms. Nowadays, atomistic simulations are playing a prime role in understanding complex materials.10–12 Microscopic simulations can provide direct insights into phonon–dislocation interactions from the atomistic level, which is beneficial for better control of thermal transport based on dislocations.

Apart from bulk materials, dislocations have also been observed in nanowires (NWs) and nanotubes. In fact, screw dislocations have been found to be an important growth mechanism of one-dimensional structures, where the Burgers vector could also be well controlled.13 It can provide an endless source of crystal steps to enable nanostructure growth. As yet, screw dislocations have been identified in a variety of quasi-one-dimensional materials including PbS, GaN, PbSe, PbTe, ZnO, In2O3, InP, Cu2O, and CdS.14–20 On the other hand, the development of modern technology could allow measuring how the TC is affected by dislocations more accurately. In this Perspective, we will provide a complimentary summary on the phonon–dislocation interaction and its impact on thermal transport from both experimental and theoretical aspects.

Unlike other defects, dislocations lead to inhomogeneous distorted lattice and stress fields. The non-homogeneous stress field induced by dislocations makes the interactions between phonons and dislocations much more complicated than other scattering sources like point and plane defects. According to the stress distributions, the stress field induced by dislocations can be divided into two regions, i.e., the plastic deformation region within a critical radius rc and the elastic deformation region beyond the critical radius rc, where rc denotes the distance away from the dislocation line. The elastic deformation region can be well described by the linear elastic theory. However, the stress field distribution in this region is different from screw and edge dislocations. According to the dislocation theory, the stress field beyond the critical radius of a dislocation gradually decreases with the distance away from the dislocation line.

A dislocation is often characterized by the Burgers vector, which represents the magnitude and direction of the lattice distortion generated by a dislocation in a crystal lattice. A screw dislocation can be visualized by cutting a crystal along a plane and slipping one half across the other by a lattice vector [Fig. 1(a)], the boundary of the cut is defined as a screw dislocation. Around a screw dislocation, the atoms are arranged in a helical pattern and the dislocation line is parallel to the Burgers vector. For an edge dislocation, it is a defect where an extra half-plane of atoms is introduced midway through the crystal, distorting nearby planes of atoms. The boundary of the half-plane is defined as the dislocation line, which is perpendicular to the Burger vector. Wang et al.22 studied the stress distribution of a screw dislocation embedded in the middle of a Si NW, which is along the z direction, based on molecular dynamics (MD) simulations. Figures 1(c) and 1(d) report the non-zero stress components σxz and σyz in the Cartesian coordinate, respectively. The stress field is reduced to one component σθz in polar coordinates, which depends only on the distance away from the dislocation center as shown in Fig. 1(e). As can be observed in polar coordinates, maximum stress appears at a critical radius rc. In the region of radii below rc, the stress is relatively small, which corresponds to the plastic deformation region. In the outer shell regions with radius beyond rc, the stress is radius dependent and decreases with the increase in radius, which can be well described by the classical dislocation theory.23 For the elastic deformation region, there are only two shear stresses σxz and σyz, which are not zero while all other components vanish in the Cartesian coordinates. The two components can be expressed as23 

σxz=Gb2πsinθr,
(1)
σyz=Gb2πcosθr,
(2)

where G and b represent the shear modulus and the Burgers vector, respectively. r is the distance away from the dislocation center. The non-zero elastic stress component in polar coordinates above rc is expressed as

σθz=Gb2πr.
(3)
FIG. 1.

Model of a pristine NW (a) and a NW with a screw dislocation in the middle of the NW (b). Reproduced with permission from Ni et al., Phys. Rev. Lett. 113, 124301 (2014).21 Copyright 2014 American Physical Society. The color map of the stress field (σ) distribution for a screw dislocation situated in the middle of a NW. The side length of the NW cross section is 4.34 nm. (c) The xz component σxz and (d) the yz component σyz; (e) the total stress and (f) the radius-dependent stress of different Burgers vectors. The NW axis and dislocation are both oriented along the z direction ([100] direction). Reproduced with permission from Wang et al., Phys. Rev. B 103, 058414 (2021).22 Copyright 2021 American Physical Society.

FIG. 1.

Model of a pristine NW (a) and a NW with a screw dislocation in the middle of the NW (b). Reproduced with permission from Ni et al., Phys. Rev. Lett. 113, 124301 (2014).21 Copyright 2014 American Physical Society. The color map of the stress field (σ) distribution for a screw dislocation situated in the middle of a NW. The side length of the NW cross section is 4.34 nm. (c) The xz component σxz and (d) the yz component σyz; (e) the total stress and (f) the radius-dependent stress of different Burgers vectors. The NW axis and dislocation are both oriented along the z direction ([100] direction). Reproduced with permission from Wang et al., Phys. Rev. B 103, 058414 (2021).22 Copyright 2021 American Physical Society.

Close modal

The radius-dependent stress field in polar coordinates obtained by Wang et al.22 can be well fitted with Eq. (3) as shown in Fig. 1(f). Moreover, they found that the critical radius rc between elastic and plastic deformation is very close to the magnitude of the Burgers vector as demonstrated by the vertical dashed lines in Fig. 1(f). Verschueren et al.24 studied the injection process of a screw dislocation into a tungsten crystal, and they also confirm the stress field can be described by Eq. (3) through atomistic simulations.

For edge dislocations, there are both tensile and shear stresses. For an edge dislocation along the z direction and the Burgers vector along the x direction, the deformation is a plane strain deformation on the xy plane and the tensile stresses are found to be23 

σxx=Gb2π(1ν)y(3x2+y2)(x2+y2)2,
(4)
σyy=Gb2π(1ν)y(x2y2)(x2+y2)2,
(5)

while the shear stress is expressed as

σxy=σyx=Gb2π(1ν)x(x2y2)(x2+y2)2,
(6)

where ν is the Poisson ratio. The other stress components are zero. The stress field produced by an edge dislocation is much more complicated than that induced by a screw dislocation. Based on MD simulations, Soleymani et al.25 found that the stress field shape of edge dislocations could be well described by Eqs. (4)–(6), even different potentials were used. The induced stress field by dislocations can strongly interact with phonons, hence it can reduce the TC of the material. The stress field simulated by MD and especially the obtained critical radius rc could be helpful for understanding the complex phonon–dislocation interactions.

The plastic deformation core region and the elastic deformation shell region have different effects on phonon scattering. In the classical theory of phonon–dislocation interactions, they were treated in different ways. In the early work of Klemens,1 the scattering of low-frequency phonons by lattice imperfections was considered, including substitutional atoms, vacancies, dislocations, and grain boundaries.26 Since only the low-frequency phonons are considered, the Debye approximation for phonon dispersion is adopted and the TC can be integrated over all possible phonon frequencies ω as follows:

κ=16π2v0ωdCV(ω)τ(ω)ω2dω,
(7)

where CV and v are the heat capacity at constant volume and the averaged phonon group velocity, ωd is the Debye frequency, and τ is the phonon lifetime. For phonon-defect scattering, the lifetime is the key parameter to be evaluated, which is considered with the perturbation method by Klemens. As for dislocations, since they create plastic core and elastic shell regions, the effects on phonon lifetimes from the two regions are treated differently. When the temperature gradient is perpendicular to the dislocation line, the lifetime τc of the plastic deformation region is cast as1,26

1τc=Nda4v2ω3.
(8)

Here, Nd is the dislocation density, a represents the lattice constant, and v is the phonon group velocity. The above lifetime expression can be applied to both screw and edge dislocations. Klemens obtained the lifetime of the dislocation core region by assuming a line of vacancies. For randomly distributed vacancies, the lifetime decreases according to ω4. However, when the vacancies are organized as a line, which is assumed as the dislocation core, the overlap effect of atomic mass and spring constant perturbations eventually enhances phonon-vacancy scattering. Consequently, the phonon relaxation time in the dislocation core region decreases as ω3. If the orientation of dislocations is randomly distributed, a factor of 0.55 needs to be added in Eq. (8) to take account of the average effect.

Compared to the size of the dislocation core, the elastic deformation region induced by dislocations is much larger. Hence, it contributes significantly to phonon–dislocation interactions. In the elastic deformation region, the perturbation on both bond length and third order force constants needs to be considered.

In the case where the temperature gradient is perpendicular to the dislocation line, the lifetime of the shell region is expressed as1,27

1τs=0.06αNdb2γ2ω.
(9)

Here, b is the magnitude of the Burgers vector. α=1 for screw dislocations and α=0.5+0.04(12μ1μ)2(1+2vl2vt2)2 for edge dislocations with μ, vl, and vt referring to the Poisson ratio, the longitudinal, and transverse group velocities. γ stands for the Grüneisen parameter. Similar to the relaxation time in the core region, 1/τs multiplied by a factor of ∼0.55 if the dislocations are randomly arranged. For the scattering of phonons due to the long-range elastic field, Klemens argued that most of the scattering arises at regions about one wavelength λ from the dislocation line, which might make τs scale with ω1.

The two scattering terms in Eqs. (8) and (9) represent the static phonon–dislocation interactions. However, the motion of dislocations can also contribute to the scattering of phonons. The effect of dislocation dynamics on phonon lifetime is more complicated than the effect produced by static strains. Assuming that dislocations are damped oscillating strings, the energy of phonons can convert into the oscillating energy of dislocations after interactions. After solving the motion equation of dislocations with some approximations, the dynamic scattering term of dislocations in Klemen's theory can be written as28,29

1τd=Bω,
(10)

where B is related to bulk modulus, dislocation density, Burgers vector, and the ratio of the shear stress to the total stress. This scattering describes the rate at which the incident wave transfer its energy to the dislocations. Dynamic scattering is insignificant for heat transport at elevated temperatures.28 With the above three terms of lifetimes, one can count the total phonon–dislocation scattering lifetime according to the Matthiessen rule.30 

Based on similar models, Kotchetkov et al.27 calculated the TC in wurtzite GaN with different dislocation densities. They found that the TC of GaN was enhanced from 1.31 to 1.97 W/m K when the dislocation density reduces from 1012 to 1010 cm−1, indicating that the dislocation plays an important role in determining the TC of a material. The analytical theory of Klemens correctly predicts a decrease in TC. However, as it is well recognized nowadays, it can only produce qualitative predictions. This theory fails by at least one order of magnitude in comparison with the experimental data. For example, Sproull et al.31 measured the impact of dislocations on the TC of LiF crystals and they found that the reduction of TC is much larger than Klemens' predictions.

With the rapid improvement of the computational speed of modern CPUs, atomic simulations have become an important and popular method to investigate the thermal transport phenomena in dislocated systems. Atomistic simulations can provide an in-depth picture on phonon–dislocation interactions.

Based on MD, the temperature effect on thermal transport properties in materials with dislocations were investigated in UO2 by Deng et al.34 After building microstructure models with various edge dislocation densities, Deng et al.34 found that the effect of dislocations on the thermal transport properties was independent of temperature between 800 and 1600 K. Such a phenomenon indicates that dislocations can interact with phonons, and the strength is even stronger than the temperature-induced anharmonic effect. Later on, Xiong et al.32 considered the effect of the Burgers vector size on thermal transport in NWs and NTs with a screw dislocation embedded in the middle of the structure. They found that the TC of both NW and NT was dependent on the Burgers vector magnitude, as shown in Fig. 2(a). For a Si NW of diameter ∼4.0 nm, i.e., ri:ro = 0:2 nm, TC is reduced from 10.5 W/mK to 8.8, 7.0, and 5.8 W/mK with the Burgers vector of 1b, 2b, and 3b, respectively. The corresponding reduction percentages are 16.2%, 33.3%, and 44.8%. The increase in the Burgers vector size makes the dislocation store more energy, leading to the decrease in TC with Burgers vector magnitude. Moreover, they also considered the effect of the cross section size of dislocated NW on thermal transport. With the increase in NW diameter, the TC reduction percentage due to dislocation decreases. However, the absolute TC reduction value still increases at specific Burgers vectors, which indicates that the region impacted by elastic stress is larger than the maximum considered diameter (∼10 nm).

FIG. 2.

(a) TC of Si NWs and NTs (nanotubes) with different Burgers vectors. ri and ro, respectively, denote the inner and outer radii of a NT with ri = 0 corresponds to a NW. Reproduced with permission from Xiong et al., Small 10, 1756 (2014).32 Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA. (b) TC of GaN with different dislocation types. 4E, 5/7E, and 8E are edge dislocations with the dislocation origin located at the position I, II, and III as shown in the inset figure, respectively. While S6S and D6S correspond to screw dislocations with origin positioned at IV and I, respectively. Reproduced with permission from Termentzidis et al., Phys. Chem. Chem. Phys. 20, 5159 (2018).33 Copyright 2018 The Royal Society of Chemistry. (c) Phonon relaxation time of pristine and screw dislocated Si NWs. Reproduced with permission from Wang et al., Phys. Rev. B 103, 058414 (2021).22 Copyright 2021 American Physical Society. (d) Thermal boundary resistance varies with coordinates perpendicular to the dislocation line in a screw dislocated SiC NW. Reproduced with permission from Ni et al., Phys. Rev. Lett. 113, 124301 (2014).21 Copyright 2014 American Physical Society.

FIG. 2.

(a) TC of Si NWs and NTs (nanotubes) with different Burgers vectors. ri and ro, respectively, denote the inner and outer radii of a NT with ri = 0 corresponds to a NW. Reproduced with permission from Xiong et al., Small 10, 1756 (2014).32 Copyright 2014 Wiley-VCH Verlag GmbH & Co. KGaA. (b) TC of GaN with different dislocation types. 4E, 5/7E, and 8E are edge dislocations with the dislocation origin located at the position I, II, and III as shown in the inset figure, respectively. While S6S and D6S correspond to screw dislocations with origin positioned at IV and I, respectively. Reproduced with permission from Termentzidis et al., Phys. Chem. Chem. Phys. 20, 5159 (2018).33 Copyright 2018 The Royal Society of Chemistry. (c) Phonon relaxation time of pristine and screw dislocated Si NWs. Reproduced with permission from Wang et al., Phys. Rev. B 103, 058414 (2021).22 Copyright 2021 American Physical Society. (d) Thermal boundary resistance varies with coordinates perpendicular to the dislocation line in a screw dislocated SiC NW. Reproduced with permission from Ni et al., Phys. Rev. Lett. 113, 124301 (2014).21 Copyright 2014 American Physical Society.

Close modal

According to the elastic theory and Klemen's theory of dislocations, the plastic and elastic deformation regions have different impacts on thermal transport. In the plastically deformed core region, the lattice structures are altered. The changed lattice structure enlarges the thermal resistance around the dislocation center as demonstrated by Ni et al.21 [Fig. 2(d)]. Moreover, such an enhanced resistance eventually leads to temperature jumps around the dislocation region in non-equilibrium molecular dynamics (NEMD) simulations as observed by Sun et al.35 The increased thermal resistance of the core region can strongly reduce the TC. Actually, with a comparison of TC in screw dislocated NWs and NTs, Xiong et al.32 demonstrated that the TC reduction by dislocations mostly originated from the dislocation core region. After removing the core regions of dislocated Si NWs, the TC reduction is much weaker as shown in Fig. 2(a). Furthermore, based on the harmonic phonon Green's function calculations, Xiong et al.32 found that the phonon transmission was slightly reduced by a much smaller amount than what was found by MD simulations. These results demonstrate that the screw dislocation itself almost does not scatter phonons directly, instead, it can strongly enhance the anharmonicity of the structure. The enhanced lattice anharmonicity is attributed to the dislocation-induced long-range inhomogeneous stresses. The elastic stress by dislocation can induce slight variations in bond lengths, which will not change the harmonic properties as they arise mostly from the two-body interactions. However, the shear displacement induced by screw dislocations can change the bond angles more significantly than the bond length, which finally causes the change in anharmonicity.22,36 The enhanced anharmonic scattering by dislocations was further approved by Ni et al.21,37 and Wang et al.,22 where they both showed that the harmonic properties such as phonon group velocity in dislocated structures were almost unchanged when compared to that in pristine structures. However, the phonon relaxation time can be greatly reduced by dislocations. Interestingly, from Fig. 2(c) one can find that at low frequencies (<4 THz), the relaxation time is reduced by approximately one order of magnitude, which is much larger than the effect on high-frequency modes. With such effect, one could expect that dislocations have a larger effect on TC at lower temperatures, where only low-frequency phonons are populated. At high temperatures, TC reduction percentage will decrease due to the small effect of dislocation on high-frequency phonon relaxation time.

Recently, Termentzidis et al.33 comparably studied the effect of edge and screw dislocations on the thermal transport in wurtzite GaN [Fig. 2(b)]. They considered three types of edge dislocations and two types of screw dislocations, i.e., four-atom ring (4E), five/seven-atom ring (5/7E), and eight-atom ring (8E) core atomic configurations, which is corresponding to the edge dislocation origin at positions I, II, and III [inset of Fig. 2(b)], respectively. Similarly, for the screw dislocation, the single six-atom ring (S6S) and the double six-atom ring configuration (D6S) corresponds to the origin of the screw dislocation positioned on IV and I. They found that TC could be reduced by a factor of two by screw dislocations, while the influence of edge dislocations is less pronounced [Fig. 2(d)]. To characterize the different effects by edge and screw dislocations, they analytically calculated the strain energy of an infinite straight dislocation in a perfect crystal using linear elasticity theory. After a detailed analysis, they found that the calculated TC was found to be inversely proportional to the stored elastic energy for the two perfect threading dislocations. Since screw dislocations store more energy than edge dislocations, the impact of screw dislocations on TC is more pronounced than that of edge dislocations. Besides, the introduction of dislocations can lead to an anisotropic transport, which makes the TC in the direction perpendicular to the dislocation line smaller than that along the dislocation line. The magnitude of anisotropy grows with increasing density of dislocations and it becomes more pronounced for the systems with edge dislocations. Moreover, they also found that the indium decoration of the dislocation core could lead to a further decrease in TC.38 

Experimentally, dislocations can be easily formed during the epitaxial growth due to inclusions and lattice mismatch.39 The dislocation density can be well controlled via the growth techniques, allowing for tuning the material properties through the variation of dislocation concentration. Regarding the effect of dislocations on TC, the experimental measurements were mainly focused on materials like GaN, InN, AlN40,41 and GaSb/GaAs, Si/Ge interfaces.42,43 Based on the 3-Omega method, Mion et al.40 measured the TC in GaN with dislocation density ρD up to 1010 cm−2. It was shown that the TC is independent of dislocation density when ρD is smaller than 106 cm−2. However, when ρD exceeds 106 cm−2, the TC decreases with a logarithmic dependence with dislocation densities. Li et al.41 synthesized three GaN films with varying dislocation densities based on different fabrication methods. The dislocation densities of the three samples are ρD = 1.80 × 1010 cm−2 (77% edge, 23% mixed), ρD = 2.36 × 109 cm−2 (50% edge, 50% mixed), and ρD ∼ 2–5 × 107 cm−2 (relative character concentrations are unknown), respectively. Although the measured in-plane TC also decreases with the increase in dislocation density, the obtained TC is much larger than that obtained by Mion et al.40 with similar dislocation density. Su et al.44 also find more than twofold TC decrease in AlN with a large dislocation density of 4 × 1010 cm−2. Such a large reduction of TC might result from the cooperation with defective interfaces.

Since dislocation is a line defect, the stress field it creates is anisotropic. Consequently, the interaction between phonons and dislocations is direction dependent. Normally, phonons are scattered more strongly when their transport direction is perpendicular to the dislocation line compared to the parallel direction. Such a character offers an opportunity to design materials with enhanced anisotropic thermal transport if the dislocations are highly oriented along a specific direction. To demonstrate such dislocation can induce anisotropic thermal transport, Sun et al.45 synthesized the InN films on GaN substrate with the plasma-assisted molecular beam epitaxy technique. The as-grown InN film contains highly oriented dislocations along the [0001] direction. They find that both cross-plane and in-plane TC can be reduced by dislocations [Fig. 3(a)]. However, the cross-plane TC of InN is almost tenfold higher than the in-plane TC at 80 K when the dislocation density is ∼3 × 1010 cm−2 [Fig. 3(b)]. The anisotropic transport is more pronounced at lower temepratures, which should be due to the fact that dislocations can significantly reduce the low-frequency relaxation time22 as only low-frequency modes are populated at low temperature. The large thermal transport anisotropy induced by highly oriented dislocations is not predicted by conventional models. Moreover, it was demonstrated that the in-plane TC is strongly dependent on dislocation density at low temperatures while the cross-plane TC is almost dislocation density-independent, which again illustrates that the effect of dislocation on TC is larger in the direction perpendicular to the dislocation line.

FIG. 3.

(a) Temperature-dependent in-plane κ (filled symbols) and cross-plane κ (open symbols) TC of InN films with dislocation densities of 1.1 × 1010 cm−2 (green diamonds) and 2.9 × 1010 cm−2 (red circles). (b) Temperature-dependent TC anisotropy ratios of InN films with a dislocation density of 1.1 × 1010 cm−2 (green diamonds) and 2.9 × 1010 cm−2 (red circles). Reproduced with permission from Sun et al., Nat. Mater. 18, 136 (2019).45 Copyright 2019 Nature Publishing Group. (c) Temperature-dependent thermal boundary conductance of GaSb/GaAs with different dislocation densities. Reproduced with permission from Hopkins et al., Appl. Phys. Lett. 98, 161913 (2011).43 Copyright 2011 American Institute of Physics.

FIG. 3.

(a) Temperature-dependent in-plane κ (filled symbols) and cross-plane κ (open symbols) TC of InN films with dislocation densities of 1.1 × 1010 cm−2 (green diamonds) and 2.9 × 1010 cm−2 (red circles). (b) Temperature-dependent TC anisotropy ratios of InN films with a dislocation density of 1.1 × 1010 cm−2 (green diamonds) and 2.9 × 1010 cm−2 (red circles). Reproduced with permission from Sun et al., Nat. Mater. 18, 136 (2019).45 Copyright 2019 Nature Publishing Group. (c) Temperature-dependent thermal boundary conductance of GaSb/GaAs with different dislocation densities. Reproduced with permission from Hopkins et al., Appl. Phys. Lett. 98, 161913 (2011).43 Copyright 2011 American Institute of Physics.

Close modal

Except for the TC of materials, dislocations can also tune the thermal boundary conductance.42 Hopkins et al.43 studied the effects of dislocation density on thermal boundary conductance in well-characterized GaSb/GaAs interfaces. Unlike the large reduction of TC by dislocation, the thermal boundary conductance is only reduced by a factor of two when the dislocation density is increased by two orders of magnitude, as shown in Fig. 3(c). The weak effect of dislocation on thermal boundary conductance might associate with other defects at interfaces. Actually, the formation of dislocations at interfaces could lead to poor crystalline quality and thus hinder thermal transport.46 Such poor crystallized structures can possibly take over the effect of dislocations on TC.

In many cases, dislocations appear with other defects automatically during the growth process. For example, dislocation usually appears in twinning boundaries.47 The coexistence of other defects with dislocation might induce new phenomena in thermal transport and in sometimes, they can be used to synergistically engineer heat transport. Karthikeyan et al.48 found that doping of rare earth elements into thermoelectric material β-Zn4Sb3 can generate numerous dislocations. The coexistence of point defects and dislocations strongly hinders the phonon transport and eventually results in a very low TC of 0.15 W/m K. Simulations demonstrated that perfect twinning boundaries have a weak effect on phonon transport.49 However, the involvement of dislocations on twinning boundaries can dramatically enhance the phonon scattering at the interface.47 The introduction of screw dislocations in SiGe superlattices can lead to unexpected phonon propagation in the interface region. Hu et al.37 demonstrated that the screw dislocation along the direction perpendicular to the Si–Ge interface could even reduce the thermal boundary resistance due to the increased Si–Ge bonds. Moreover, unlike inhomogeneous materials, where a dislocation does not affect the phonon group velocities, the introduced screw dislocations in superlattices can dramatically reduce the phonon group velocity.37 The synergistic engineering of TC by dislocations together with phonon resonances was demonstrated by Wang et al. in Si NWs.22 By embedding a screw dislocation inside a Si NW and involving resonant pillars on surfaces, ultralow TC can be obtained in Si NWs, which arises from the different frequency response of phonon on dislocations and resonances. With dislocations, high-frequency phonons can be hindered more efficiently compared to the case of resonant structures. However, it becomes opposite at the low-frequency region. As a result, the involvement of both dislocation and resonant structures can effectively hinder the phonon transport in the entire frequency range, which provides an important strategy for phonon engineering and is beneficial for high performance thermoelectric materials design.

In this perspective, we systematically summarized the phonon–dislocation interactions and their impacts on thermal transport from both theoretical and experimental aspects. The early analytical model of Klemens accounts for the interaction between low-frequency phonons and dislocations and it can qualitatively describe the TC reduction induced by dislocations. However, due to the complex stress field induced by dislocations, modern atomistic simulations are necessary to make quantitative predictions. It was found that TC decreases rapidly with the increase in the Burgers vector magnitude due to more energy stored by dislocations with larger Burgers vectors. Besides, the increase in dislocation density also enhances the energy stored by a crystal, hence it makes TC strongly correlate with dislocation density, i.e., TC reduces rapidly with the increase in dislocation density. Compared to edge dislocations, screw dislocations can store more energy and thus have a larger impact on thermal transport. Unlike other scatterers, dislocations do not scatter phonons directly but enhance the lattice anharmonicity through the generated inhomogeneous stress field. The created non-uniform stress field not only reduces the relaxation time of high-frequency phonons but also hinders low-frequency phonon transport. This is considered as the key phonon–dislocation interaction mechanism. Experimental studies not only confirm the reduction of TC by dislocations but also illustrate the possibility of tuning the anisotropic phonon transport by growing well-oriented dislocation threads. The effect of dislocations on thermal boundary conductance is much weaker than the effect on TC. At the end of the Perspective, engineering the thermal transport via the combination of dislocation and other defects such as twinning boundaries and point defects is discussed.

Although the investigation of dislocation–phonon interactions has been started a long time ago, current studies are still unable to understand the detailed mechanisms comprehensively, especially the accurate predictions of TC with simple models. First, in terms of modeling, the Klemens model is the only one that can consider phonon–dislocation interactions. However, this model only considers the interactions between low-frequency phonons and dislocations while fully neglected the dislocation effect on high-frequency modes. As a result, the simple Debye approximation of linear phonon dispersion was adopted in calculations. However, as illustrated by MD simulations, although the reduction of relaxation time at high frequencies is weaker than that at low frequencies, the relaxation time can still be reduced by a factor of two. Consequently, the high-frequency phonons can still contribute non-negligible TC reduction, especially at high temperatures. On the other hand, the plastic deformation region is modeled as a line of atomic vacancy in Klemens' theory. The considered plastic deformation size is much smaller than what is illustrated by MD simulations and thus could underestimate the impact of dislocation core. As a result, to improve the accuracy of Klemens' model, it is necessary to adopt real phonon dispersion in calculations and re-examine the dislocation core-phonon interaction strengths. More importantly, we should also consider the interaction between optical phonons and dislocations. Such considerations in modeling are essential for accurate predictions of TC reduction by different types of dislocations.

Second, although the atomistic simulations could provide more details on phonon–dislocation interactions, current simulation models mainly contain single type straight dislocations, which is different from the experimental situations. As a result, a possible direction to study the phonon–dislocation interaction could be to build simple models to account for the TC reductions by dislocations based on the mechanisms obtained by atomistic simulations. Besides, current MD simulations have mainly focused on the static interactions between phonons and dislocations, i.e., the scattering by plastic and elastic deformations. The dislocation dynamics have not been observed possibly due to the relatively short simulation time (typically nanoseconds). It might also be interesting to perform long time simulations in specifically designed small systems to observe the energy exchange between dislocations and phonons. Another point in MD simulation is that its fundamental physical basis is classical which makes it difficult to investigate phonon transport at low temperatures. While it has been shown that a dislocation has a larger impact on low-frequency modes, it could be more convincing to adopt other methods such as the Boltzmann transport equation (BTE) to investigate phonon transport in dislocated structures at low temperatures.

Third, in most of the cases, the experimentally synthesized samples contain both edge and screw dislocations with random orientations, which can only illustrate the average effect produced by different dislocation types and orientations. As a result, controlling the dislocation type and orientations in materials experimentally could also be very helpful for the investigation of detailed phonon–dislocation interaction mechanisms. Besides, current experimental studies on phonon–dislocation interactions have focused on bulk materials. Since dislocated NWs have been successfully synthesized in many materials,14,15 the studies on thermal transport in dislocated one-dimensional structures are worthy investigating, especially for the applications of low-dimensional thermoelectric materials.

Finally, up to now, almost all studies have focused on the interaction between phonons and screw or edge dislocations. Other types such as partial dislocations including Frank and Shockley partial dislocations are also commonly found in materials. A partial dislocation could have a different effect on phonons as it associates with stacking faults. Besides, dislocations can be pinned by other defects. It, however, remains unclear whether the pinning of dislocations could affect the dislocation–phonon interactions or not.

This work was supported by the National Natural Science Foundation of China (NNSFC) under Grant No. 11804242 and the CREST JST under Grant No. JPMJCR19I1.

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

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