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[J.T. Pürstl](https://orcid.org/0000-0001-6022-6878), C. Tian, A. Sharma, [A. Nascimento](https://orcid.org/0000-0003-3996-1928), [N.M. della Ventura](https://orcid.org/0000-0002-4158-1660), [T.E.J. Edwards](https://orcid.org/0000-0002-3089-0062), P. Chartier, M. Vreeswijk, [R.P. Thompson](https://orcid.org/0000-0001-9459-5014), [I.J. Beyerlein](https://orcid.org/0000-0002-5489-5132), J.J. Schwiedrzik, J. Michler, W.J. Clegg, N.G. Jones

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[Cryogenic micropillar compression of Ti3AlC2, Ti3SiC2 and Cr2AlC: A comparative evaluation of composition-dependent dislocation mobility in MAX Phases](https://mdr.nims.go.jp/datasets/54733377-df94-4b2e-a487-783d9ad814a4)

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Cryogenic micropillar compression of Ti3AlC2, Ti3SiC2 and Cr2AlC: A comparative evaluation of composition-dependent dislocation mobility in MAX PhasesActa Materialia 316 (2026) 122432 A1( Contents lists available at ScienceDirectActa Materialiajournal homepage: www.elsevier.com/locate/actamat  Full length articleCryogenic micropillar compression of Ti3AlC2, Ti3SiC2 and Cr2AlC: A comparative evaluation of composition-dependent dislocation mobility in MAX PhasesJ.T. Pürstl a,b ,∗, C. Tian c, A. Sharma c, A. Nascimento b , N.M. della Ventura b,c , T.E.J. Edwards c,d , P. Chartier e, M. Vreeswijk a, R.P. Thompson a , I.J. Beyerlein b , J.J. Schwiedrzik b,f, J. Michler b,g, W.J. Clegg a, N.G. Jones aa University of Cambridge, 27 Charles Babbage Road, Cambridge, CB3 0FS, United Kingdomb University of California, Santa Barbara, Santa Barbara, Santa Barbara, 93116, CA, United States of Americac Laboratory for Mechanics of Materials and Nanostructures, Empa Swiss Federal Laboratories for Materials Science and Technology, Feuerwerkerstraße 39, Thun, 3602, Switzerlandd National Institute for Materials Science, Research Center for Structural Materials, 1-2-1 Sengen, Tsukuba, 305-0047, Ibaraki, Japane Institut Pprime, UPR 3346 CNRS - Université de Poitiers - ISAE-ENSMA, BP 30179, Fututorscope-Chasseneiul Cedex, 86962, Francef Laboratory for High Performance Ceramics, Empa Swiss Federal Laboratories for Materials Science and Technology, Ueberlandstrasse 129, Dübendorf, 8600, Switzerlandg Institute of Materials, EPFL, Lausanne, Lausanne, 1015, SwitzerlandA R T I C L E  I N F OKeywords:MAX phasesMicropillar compressionPeierls stressesActivation parametersCryogenic deformation A B S T R A C TMAX phases serve as an ideal model system for studying the crossover between metallic and ceramic behavior, and improved ceramic ductility. This ductility is primarily linked to the anomalously easy glide of basal plane dislocations, yet a full theoretical understanding of the characteristics governing their mobility remains a subject of continuing research. Following recent efforts using atomistic simulations of MAX phase basal plane dislocation cores, the present study focused on an experimental evaluation of friction and Peierls stresses in three representative MAX phase compounds, Ti3AlC2, Ti3SiC2, and Cr2AlC, using micropillar compression at cryogenic temperatures. The study examines specifically the effects of temperature, size, and pristine dislocation morphology under aid of crystal plasticity finite element simulations to derive the lattice resistance for each compound and compare it with previously simulated results. Measured Peierls stresses of 142 MPa (Ti3AlC2), 150 MPa (Ti3SiC2), and 359 MPa (Cr2AlC) confirm a significant role of core structures and bonding characteristics on MAX phase dislocation plasticity, with Ti-based MAX phases exhibiting markedly lower lattice resistance than Cr-based compounds. The cryogenic tests presented here mark the first such experiments in MAX phases and open new pathways for understanding their deformation behavior at low temperatures.1. IntroductionThe Mn+1AXn phase ternary carbides and nitrides, where M stands for a transition metal, A for an A group element, X for either C or 𝑁 and n = 1–4, have gained widespread interest due to their hybrid ceramic–metallic character [1–3]. Their exceptional properties include high electric and thermal conductivity [1,4–7], high thermal stability as well as pronounced deformability despite limited slip systems [8–14]. The latter is linked to the anomalously easy glide of basal plane ∗ Corresponding author at: University of California, Santa Barbara, Santa Barbara, Santa Barbara, 93116, CA, United States of America.E-mail addresses: jpuerstl@ucsb.edu (J.T. Pürstl), chunhua.tian@empa.ch (C. Tian), amit.sharma@empa.ch (A. Sharma), andersonw@ucsb.edu (A. Nascimento), n_dellaventura@ucsb.edu (N.M.d. Ventura), thomas.edwards@nims.go.jp (T.E.J. Edwards), patrick.chartier@univ-poitiers.fr (P. Chartier), mv299@cantab.ac.uk (M. Vreeswijk), rpt26@cam.ac.uk (R.P. Thompson), beyerlein@ucsb.edu (I.J. Beyerlein), jakob.schwiedrzik@empa.ch (J.J. Schwiedrzik), johann.michler@empa.ch (J. Michler), wjc1000@cam.ac.uk (W.J. Clegg), ngj22@cam.ac.uk (N.G. Jones).dislocations in the hexagonal crystal [15–18], with experimentally determined critical resolved shear stresses (𝜏CRSS) at room temperature of as low as 77MPa [8,19]. While much is known about the electronic structure and functionality of the MAX phases and their 2D derivatives, MXenes [6,20], their basal plane dislocation dynamics remain difficult to resolve. Several concepts regarding dislocation core structures and interactions have been proposed, lately aided by rigorous computa-tional efforts from both density functional theory (DFT) [21,22] and molecular dynamics (MD) [23]. Yet, the exact configurations promoting the observed eased dislocation glide remain under debate.https://doi.org/10.1016/j.actamat.2026.122432Received 1 December 2025; Received in revised form 26 May 2026; Accepted 4 Juvailable online 8 June 2026 359-6454/© 2026 The Authors. Published by Elsevier Inc. on behalf of Act http://creativecommons.org/licenses/by/4.0/ ). ne 2026a Materialia Inc. This is an open access article under the CC BY license https://www.elsevier.com/locate/actamathttps://www.elsevier.com/locate/actamathttps://orcid.org/0000-0001-6022-6878https://orcid.org/0000-0003-3996-1928https://orcid.org/0000-0002-4158-1660https://orcid.org/0000-0002-3089-0062https://orcid.org/0000-0001-9459-5014https://orcid.org/0000-0002-5489-5132mailto:jpuerstl@ucsb.edumailto:chunhua.tian@empa.chmailto:amit.sharma@empa.chmailto:andersonw@ucsb.edumailto:n_dellaventura@ucsb.edumailto:thomas.edwards@nims.go.jpmailto:patrick.chartier@univ-poitiers.frmailto:mv299@cantab.ac.ukmailto:rpt26@cam.ac.ukmailto:beyerlein@ucsb.edumailto:jakob.schwiedrzik@empa.chmailto:johann.michler@empa.chmailto:wjc1000@cam.ac.ukmailto:ngj22@cam.ac.ukhttps://doi.org/10.1016/j.actamat.2026.122432https://doi.org/10.1016/j.actamat.2026.122432http://creativecommons.org/licenses/by/4.0/J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 MAX phase dislocation mobility is predominantly confined to the metallic layers parallel to the basal plane of the hexagonal crystal [10,24]. Nevertheless, generalized stacking-fault (GSF) based Peierls-Nabarro models significantly overestimated the resistance to disloca-tion mobility in the past, with Peierls stresses of ∼1000MPa predicted in Ti2AlN [24] and in Cr2AlC [25]. This was somewhat reconciled by accounting for the pronounced elastic heterogeneity within the MAX phase crystal [26]. By incorporating individual elasticity param-eters from the metallic (M-A) and carbide (M-X) layers determined by DFT, an adapted Peierls–Nabarro framework yielded substantially reduced stress estimates, with for example 26MPa for Ti3SiC2 and 3MPa for Ti3AlC2 [26]. For comparison, experimentally determined critical resolved shear stresses for Ti3SiC2 were estimated to 16MPausing extrapolation from size dependent micropillar compression, and 30MPa for compression of 10 μm pillars in Ti3AlC2. Whilst the pre-dicted values are in reasonably good agreement with experiments, the exceptionally low Peierls stress estimates, particularly the 3MPapredicted for Ti3AlC2, raise questions about whether the continuum elastic framework fully captures the resistance to dislocation motion.Recent reports of non-Schmid effects in MAX phases [11,13] provide experimental evidence that dislocation core structures play a significant role in controlling basal plane dislocation mobility. Plummer et al. [23] and Hossain et al. [21,22] recently used atomistic simulations to in-vestigate different basal plane dislocation core configurations and their Peierls stresses in Ti3AlC2 and Ti3SiC2. Using MD, Plummer et al. [23] predicted Peierls stresses of ∼200MPa for edge and ∼3000MPa for screw dislocations gliding in the M-A layers of Ti3AlC2. The simulations further predicted partial dissociation and the formation of zonal dislo-cations, a relaxed configuration of a basal dislocation pair, in which two adjacent basal-plane dislocations share the Burgers vector and produce a multi-plane spread core. This paired configuration lowers the local lattice resistance, with Peierls stresses of as low as  20MPa for edge character. DFT studies by Hossain et al. [21,22] predicted similar Peierls stresses for edge dislocations in Ti3AlC2 (∼200MPa), as well as ∼70−150MPa for edge or mixed, and ∼3000MPa for screw dislocations in Ti3SiC2. The authors further predicted partial dissociation for both edge and screw characters, yet did not find zonal dislocation formation to be energetically favorable within the DFT framework.The predicted Peierls stresses for edge dislocations in the above studies are broadly consistent with the range of experimentally mea-sured flow stresses, considering that the atomistic values are obtained under athermal conditions (0K relaxation and varying effective strain rates). However, experimental evidence of zonal dislocations was so far only provided in Ti2AlC processed with surface mechanical attrition treatment (SMAT) by transmission electron microscopy (TEM) [27]. Furthermore, no predominance of edge over screw or mixed charac-ters was found during MAX-phase deformation [10,28]. For example, Higashi et al. [10] reported a mix of edge, mixed and screw character after compression of Ti3SiC2, in contrast to the apparent predominance of edge character from simulation.The predicted predominance of edge character by atomistic simula-tions suggests either a possible temperature or rate-dependent enhance-ment of screw dislocation mobility under experimental conditions, or a discrepancy between the predicted core structures and those ac-tive in real materials. This motivates further investigation into MAX phase dislocation core structures, as well as temperature dependent deformation. To date, a targeted experimental evaluation of activation parameters or Peierls stresses, which would aid in accurate prediction of dislocation core structures, is outstanding. Such an evaluation can be achieved by probing the temperature-dependence of the 𝜏CRSS, coupled with TEM analysis of dislocation structures. This additionally allows for an estimate of dislocation–dislocation interactions on MAX phase deformation, which is not captured by DFT or MD simulations and may guide further investigations on the basis of dislocation dynamics simulations. So far, experimental evaluation of basal plane dislocation 2 mobility in MAX phases and the associated 𝜏CRSS has been achieved pri-marily through compression of textured crystals [8] or via micropillar compression [10,11,13] at room temperature.The present study incorporates a combined temperature-dependent micropillar compression - TEM protocol to determine Peierls stresses and activation volumes in the Ti3AlC2, Ti3SiC2 and Cr2AlC MAX Phases. This incorporates: (i) a unified micropillar compressionmethodology to isolate friction stresses based on the study of size effects and crystal plasticity finite element (CPFE) analysis, (ii) testing at cryogenic temperatures (190K–292K) to assess thermally activated dislocation glide, and (iii) correlation of mechanical data with targeted TEM to quantify dislocation sub-structures and slip character. The results deliver the first experimentally-determined cryogenic Peierls stresses for MAX phases, activation-volume estimates determined from thermal activation analysis, as well as an initial experimental bench-mark to determine the validity of current DFT/MD models of MAX phase dislocation cores. The three model systems selected for the study offer a direct comparison to previous atomistic simulations of dislocation cores, while extending the analysis by variation of the transition-metal chemistry (Ti vs. Cr). The latter is predicted to alter bond hybridization, elastic anisotropy, and hence the intrinsic dislo-cation core structure. As such, we further use the data to map the plasticity in MAX phases based on bonding characteristics, to actively inform the design of MAX phases or derived systems on the basis of chemistry.2. Methods2.1. MaterialsPolycrystalline Cr2AlC (∼99% purity), Ti3AlC2 (∼98% purity) and Ti3SiC2 (∼95% purity) samples were fabricated via hot isostatic press-ing (HIP) of elemental powders for the M and A elements, and either carbon graphite (C) or TiC powders for X in stoichiometric quanti-ties [29,30]. Elemental powder stoichiometry and processing param-eters were optimized to minimize the formation of impurity phases, with processing carried out under vacuum to minimize the uptake of impurity elements (O, N, C). The applied processing conditions are summarized in Supplementary Table S.1. To allow for a representative number of pillars to be produced in each selected grain for cryogenic testing, the Ti3AlC2 and Ti3SiC2 samples were further heat treated at 1300 ◦C for 48 h to induce grain growth, as previously applied by Zhan et al. [11].Separate specimens were prepared for testing at room and cryogenic temperatures. Samples were cut in the form of semi or quarter disks, and ground to achieve parallel top and bottom surfaces using SiC paper and a 2000 grit fine diamond grinding disk. One surface was further polished using diamond suspensions with progressively smaller particle sizes (6 μm, 1 μm, and 0.25 μm), followed by a final polish with a H2O2-buffered colloidal silica suspension (OPS, pH 7).2.2. Orientation analysisGrain orientations were determined by electron backscatter diffrac-tion (EBSD). EBSD was carried out in a Tescan Lyra 3 with an Oxford Instruments Symmetry Detector (Cr2AlC, Ti3SiC2) and a Tescan Mira 3 fitted with an EDAX EBSD detector (Ti3AlC2), using an acceleration voltage of 20 kV, a tilt angle of 70◦ and a step size of 2 μm. Kikuchi patterns were indexed with standard reference cell parameters of a = 3.073Å and c = 18.557Å for Ti3AlC2 [31], a = 3.058Å and c =17.623Å for Ti3SiC2 [32], and a = 2.86Å, c = 12.82Å for Cr2AlC [33]. Further orientational analysis was carried out in MTEX [34]. The orientation parameters of selected grains in all three tested compounds are summarized in Supplementary Tables S.2 and S.3.J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 2.3. Micropillar preparationSingle crystal pillars were prepared by focused ion beam (FIB) milling in distinct grains with high Schmid factors for basal plane slip. Given grain size limitations, and to ensure statistical significance, pillars were prepared in multiple grains for testing at each condition. In addition to a high basal Schmid factor, the grain orientations for milling were chosen such that only one of the three possible basal systems would be favored; geometrically, this corresponds to 𝜆 = 90◦−𝜙, where 𝜆 is the angle between the slip direction and loading axis and 𝜙 is the angle between the slip plane and loading axis. To further reduce non-Schmid effects [11,13] to a minimum, pillar orientations were selected to maintain Schmid factors for basal plane slip between 0.45–0.5.Cylindrical pillars with nominal diameters between 1–7 μm and an aspect ratio of 2.5–3 were prepared using annular FIB milling at 30 kV in a Tescan Lyra 3 FIB/SEM and an FEI Helios Nanolab dual beam FIB/SEM. Milling was carried out with gradually reduced milling currents, with a final current of 50 pA for pillars >1 μm in diameter, and 20 pA for pillars 1 μm in diameter, to minimize FIB induced damage and reduce the final pillar taper to below 3◦. For temperature dependent testing, a separate set of pillars with a diameter of 3.5 μm was prepared.2.4. Micropillar compressionSize dependent testing was carried out using an Alemnis nanoin-dentation setup (Alemnis Standard Assembly) operated in displacement controlled mode in a Philips XL30 FEGSEM/Tescan Mira 3 SEM. Flat diamond punches, 5 μm in diameter for the 1 μm pillars and 10 μm in diameter for all other pillar sizes (Synton MDP, Switzerland), were used for compression. Compression was carried out at an initial strain rate of 10−3 s−1 (normalized by pillar height) to a maximum uncorrected strain of 10%.Temperature dependent testing was carried out using the Alemnis Standard Assembly fitted with a cooling unit for testing at liquid nitrogen temperatures [35] in a ZEISS DSM 962 SEM. Cooling of the cryogenic unit is achieved by a cold finger attached to the back of the indenter, through which gaseous nitrogen is pumped from a liquid nitrogen tank outside the chamber. Sample and tip holders are cooled by connection to the cold finger using copper braids. The cooled region is thermally isolated from the indenter frame by ceramic shafts. Resis-tive heating and a temperature feedback control loop further minimize variations in frame temperature and frame-related drift.The measured baseline temperature of the cooling unit were 115Kfor the Cr2AlC and Ti3AlC2 test cycles, and 118K for the Ti3SiC2 cycles. To preclude any effects from thermal drift between the sample surface and the flat punch used for compression, each testing cycle at cryogenic temperatures was preceded by thermal equilibration between the tip and sample surface using thermocouples and resistive heaters attached to the tip and sample holders, respectively [36]. Testing was carried out at nominal temperatures of 115/118K, 200K and 292K, corresponding to effective temperatures of 191 ± 3K, 233 ± 3K and 292K. The discrepancy between effective and nominal cryogenic temperatures is linked to thermal losses across the sample thicknesses. The effective surface temperature for each sample was measured in a separate step by approach with a thermocouple fitted to the nanoindenter rig, as described in [36].Pillars were imaged before and after compression in a Tescan Lyra 3 FIB/SEM. Load–displacement curves were converted to stress–strain data using the pillar height measured for each pillar and pillar-cross section at half the pillar height. In addition to frame compliance, a Sneddon correction [37] was applied to account for pillar sink-in for calculation of strain.3 2.5. Transmission electron microscopyThe dislocation structures in the pristine condition material and in pillars post-mortem were further corroborated by means of weak-beam dark field (WBDF) TEM. The pristine dislocation density was evaluated following a line-intersection approach using randomly drawn lines [38,39]. Diffraction contrast analysis (𝐠 ⋅ 𝐛) was carried out to determine dislocation characters using multiple two-beam conditions corresponding to 𝐠 = ⟨1 1 2 0⟩ and 𝐠 = ⟨3 3 0 0⟩ (basal plane reflections). The selected diffraction vectors allow for analysis of full dislocations (𝐛 = 13 ⟨1 1 2 0⟩), as well as partial dissociation (𝐛 = 13 ⟨1 1 0 0⟩). Details of dislocation density analysis are given in Supplementary Figure S.1 and Supplementary Table S.4; details of diffraction contrast analysis are given in Supplementary Figures S.2 - S.7 and Supplementary Tables S.5 - S.7.Lift-outs for TEM analysis were prepared from pristine Ti3AlC2, Ti3SiC2 and Cr2AlC samples, as well as in Ti3SiC2 micropillars de-formed at room and cryogenic temperatures, using a Tescan Lyra 3 for initial Pt deposition and rough milling and a FEI Helios DualBeam FIB/SEM for fine polishing. Final polishing was carried out at an acceleration voltage of 2 kV and a beam current of 50 pA and a 7◦tilt in-plane. Lift-outs of the as produced and deformed samples were prepared with zone axis [0 0 0 1]. TEM analysis was carried out using a ThermoFischer Themis 200 G3 spherical aberration (probe) corrected TEM operated at 200 kV.2.6. Crystal plasticity simulationsA micropillar crystal plasticity finite element (CPFE) model [40] (Fig.  1(a)) was built in the commercial software package Abaqus to validate the influence of forest hardening on the measured stress–strain responses of the three tested MAX phase compounds, and guide an estimate of friction stresses. The applied mesh reproduced the exper-imentally measured aspect ratio, with boundary conditions applied to mimic uniaxial compression along the average loading axis determined by EBSD for each compound. Pillar dimensions were normalized with respect to absolute size, to allow for application of a scale-independent constitutive formulation.The applied constitutive formulation describes a standard finite deformation, anisotropic elasticity as well as a rate-dependent crystal plasticity approach. For the former, the full anisotropic elasticity law with the five independent hexagonal elastic constants corresponding to each MAX phase compound is employed, where: ⎛⎜⎜⎜⎜⎜⎜⎝𝜎11𝜎22𝜎33𝜎23𝜎13𝜎12⎞⎟⎟⎟⎟⎟⎟⎠=⎛⎜⎜⎜⎜⎜⎜⎝𝐶11 𝐶12 𝐶13 0 0 0𝐶12 𝐶11 𝐶13 0 0 0𝐶13 𝐶13 𝐶33 0 0 00 0 0 𝐶44 0 00 0 0 0 𝐶44 00 0 0 0 0 𝐶66⎞⎟⎟⎟⎟⎟⎟⎠⎛⎜⎜⎜⎜⎜⎜⎝𝜖11𝜖22𝜖33𝜖23𝜖13𝜖12,⎞⎟⎟⎟⎟⎟⎟⎠(1)where 𝐶66 =𝐶11−𝐶122  (Fig.  1(b)).For the later inelastic contribution, deformation is restricted to basal slip mode as the expected predominant deformation mode [10,12,15]. As such, plastic shear was allowed only on the three {0 0 0 1}⟨1 1 2 0⟩basal slip systems. The resolved shear stress (𝜏𝛼) on each active slip system 𝛼 was related to the shear rate 𝛾̇𝛼 by a viscoplastic flow rule, where 𝛾̇𝛼 = 𝛾̇0||||𝜏𝛼𝑔𝛼||||1∕𝑚sign(𝜏𝛼) (2)and 𝛾̇0 is the reference shear rate, 𝑚 the strain rate sensitivity exponent and 𝑔𝛼 the current critical resolved shear stress on slip system 𝛼. The 𝑔𝛼 can be further divided into a friction stress (𝑔𝛼0 ) and a hardening component: 𝑔𝛼 = 𝑔𝛼0 + 𝜅𝐺𝑏√∑𝛼𝛼𝛽𝜌𝛽 , (3)𝛽J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Fig. 1. Outline of CPFE model. (a) Applied pillar mesh (aspect ratio 2.5, no taper) in deformed state, showing activation of a single {0 0 0 1}⟨1 1 2 0⟩ basal slip system. Pillars were oriented to mimick the average orientation for each compound determined by EBSD. Plastic shear is confined to the three {0 0 0 1}⟨1 1 2 0⟩basal slip systems by setting 𝑔0,pyr/pris = 15 × 𝑔0,basal and 𝜌𝛽pyr/pris = 0. (b) Schematic representation of the five independent elastic constants for hexagonal systems. 𝐶44 here relates to shear on basal planes (𝜖13); 𝐶66 =𝐶11−𝐶122 relates to shear on prismatic planes (𝜖12).Table 1Material parameters and interaction coefficients for self and latent hardening for applied CPFE model. Elastic constants from Ref. [43] (Ti3AlC2 and Ti3SiC2) and Ref. [44] (Cr2AlC). Materialparameters𝑏 (Å) 𝐶11 𝐶33 𝐶44 𝐶12 𝐶13   Ti3AlC2 3.073 [31] 355 293 119 85 76   Ti3SiC2 3.058 [32] 370 350 155 97 112   Cr2AlC 2.863 [33] 396 382 173 117 156   Interactioncoefficients𝛼basal-basal 𝛼prism-prism 𝛼pyr-pyr 𝛼basal-prism 𝛼prism-pyr 𝛼basal-pyr  Ti3AlC2 1 1 1 0.5 0.5 0.5   Ti3SiC2 1 1 1 0.5 0.5 0.5   Cr2AlC 1 1 1 0.5 0.5 0.5  where 𝜌𝛽 is the dislocation density on each slip system 𝛽 with stored forest dislocations, 𝜅 and 𝛼𝛼𝛽 are the dislocation interaction coefficient and dislocation interaction matrix for self and latent hardening, re-spectively, 𝐺 denotes the effective isotropic shear modulus and 𝑏 is the Burgers vector. Slip on both pyramidal and prismatic slip systems was here suppressed by assigning an initial critical resolved shear stress 𝑔0,pyr/pris = 15 × 𝑔0,basal and fixing their dislocation densities to 𝜌𝛽 = 0. Within the basal family, one system was treated as mobile (𝛼) and the other two as forest systems (𝛽), each assumed to carry one third of the total initial dislocation density. Eq. (3) accounts for isotropic hardening due to dislocation accumulation. Dislocation-density induced hardening was incorporated by the Kocks–Mecking formulation for dislocation multiplication [41].The applied material parameters are summarized in Table  1. Inter-action coefficients for self (𝛼𝛼𝛼) and latent hardening (𝛼𝛼𝛽) were set to literature-based values for hcp systems [42]. The friction stress 𝜏0 and dislocation interaction coefficient 𝜅 were then varied within expected literature bounds to match bulk critical resolved shear stresses and size-effect corrected initial yield points.3. Results and analysis3.1. Pristine microstructureScanning electron micrographs of as produced samples are shown in Fig.  2. Both Cr2AlC and Ti3SiC2 show largely equiaxed grains, whilst Ti3AlC2 show elongated grains in direction normal to the 𝑐-axis. Impurities of predominantly Al2O3, TiC and Cr7C3 [29,30] can be seen accumulating along grain boundaries. The grain dimensions 4 Table 2Pristine dislocation densities for Ti3AlC2, Ti3SiC2 and Cr2AlC. Pristine dis-locations were solely of type 13⟨1 1 2 0⟩ (Supplementary Figures S.2 - S.7, Supplementary Tables S.5 - S.7). Compound 𝜌tot (m−2) 𝐛   Ti3AlC2 1.48 ± 0.17 × 1014 13⟨1 1 2 0⟩  Ti3SiC2 3.63 ± 0.40 × 1013 13⟨1 1 2 0⟩  Cr2AlC 7.84 ± 0.88 × 1012 13⟨1 1 2 0⟩ ranged between 5–60 μm in width (𝑤) and 20–180 μm in length (𝑙) for Ti3AlC2, 20–180 μm (𝑙, 𝑤) for Ti3SiC2 and 10–150 μm (𝑙, 𝑤) for Cr2AlC.Fig.  2 further shows TEM images of the pristine dislocation struc-tures in the tested MAX phase compounds, imaged along the [0 0 0 1]zone axis. The observed pristine dislocation network in all three com-pounds is formed exclusively by 13 ⟨1 1 2 0⟩-type dislocations, as evalu-ated by 𝐠 ⋅ 𝐛 analysis (Supplementary Figures S.2 - S.7, Supplementary Tables S.5 - S.7). Dislocation densities in each compound are summa-rized in Table  2. The pristine dislocation densities vary significantly among the three compounds, with Ti3AlC2 showing the highest density (1.48 × 1014 m−2), followed by Ti3SiC2 (3.63 × 1013 m−2) and Cr2AlC (7.84 × 1012 m−2). These differences are likely attributed to varying thermal stresses arising during cooling from the synthesis temperature, which scale with the degree of crystallographic anisotropy: the Ti-based compounds exhibit higher c/a ratios (Ti3SiC2: 𝑐∕𝑎 = 6.04; Ti3AlC2: 𝑐∕𝑎 = 5.76) compared to Cr2AlC (𝑐∕𝑎 = 4.48). This anisotropy is also reflected in the grain morphology, which evolves from elongated grains in Ti3AlC2 to more equiaxed grains in Cr2AlC (Fig.  2).The dislocation lines show preferential alignment along the crys-tallographic ⟨1 1 2 0⟩ and ⟨1 1 0 0⟩ directions, an observation previously related to elevated lattice friction in Ti2AlN [28]. The dislocation character observed in Ti3AlC2 and Ti3SiC2 is solely mixed (30◦, 60◦) and edge (90◦). In Cr2AlC, short screw (0◦) segments are visible in addition to mixed (30◦, 60◦) and edge (90◦) dislocations.3.2. Micropillar compressionAll tested micropillars deformed exclusively by basal slip, with no alternative deformation mechanisms observed at any size, temperature or composition. Representative pillar morphologies and corresponding stress–strain curves are shown in Fig.  3 for room temperature tests (292 K). The curves exhibit characteristic load drops, attributed to discrete yield events such as individual dislocation source activation [12]. Yield stresses were determined as the average of the upper yield stresses J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Fig. 2. Pristine microstructure and dislocation network of Ti3AlC2, Ti3SiC2 and Cr2AlC samples. (a) Ti3AlC2 shows elongated MAX phase grains (𝑙 = 20−180 μm, 𝑤 = 5−60 μm), with few Al2O3 globules between grains. A pronounced dislocation network (d) is observed. (b) Ti3SiC2 formed MAX phase grains with sizes 𝑙, 𝑤 = 10−150 μm, with a network of small TiC grains accumulating along grain boundaries. The pristine dislocation network (e) is more localized compared to Ti3AlC2. (c) Cr2AlC shows equiaxed MAX phase grains with 𝑙, 𝑤 = 10−150 μm, with Al2O3 and Cr7C3 accumulating along grain boundaries. The initial dislocaton network (f) consisted of few individual dislocation segments.between 1%–2% plastic strain, in order to avoid artifacts from initial punch alignment [45] and late-stage stress-state breakdown due to pronounced slip activity [12]. To avoid including pillars affected by testing artifacts, data were excluded if the unloading modulus dropped below 70% of the nominal Young’s modulus, or if post-compression imaging revealed slip through the pillar top. Such features are likely indicative of bending caused by misaligned loading or the absence of sufficient pre-existing dislocations on the highest-Schmid factor slip systems [45,46].3.3. Size effectsFig.  4 summarizes the micro-compression test results aimed at investigating size effects, in the form of 𝜏CRSS as a function of pillar diameter (𝐷) for Ti3AlC2 and Ti3SiC2, with results for Cr2AlC re-produced from a previous study by the authors [13]. The evaluated functional relationships 𝜏CRSS = 𝑓 (𝐷) allow for extrapolation to a bulk critical resolved shear stress, and were further used as a baseline for evaluation of friction and Peierls stresses. For this purpose, an empirical power-law relationship, as commonly used to describe size-dependent strength [45,47–51], was employed to fit the experimental data, with the fit overlaid in Fig.  4. The employed fitting function: 𝜏CRSS = 𝜏bulk + 𝐴𝐷−𝑚 (4)describes the experimentally measured 𝜏CRSS by superposition of the bulk critical resolved shear stress, 𝜏bulk, and a size-dependent term de-termined by material constants 𝐴 and 𝑚, with 𝐷 as the pillar diameter. 𝜏bulk, 𝐴 and 𝑚 were treated as fitting parameters to reproduce the experimental data.For materials with negligible bulk strength (𝜏bulk ∼ 0), such as pure metals, the 𝜏bulk term is commonly omitted, reducing Eq. (4) to a two-parameter fit [49]. However, for materials with substantial bulk shear strength, neglecting 𝜏bulk leads to systematic errors in the fitted exponent 𝑚 and prevents meaningful extrapolation to the bulk limit [50]. Given that MAX phases exhibit comparatively high 𝜏bulk val-ues (e.g., ∼70MPa for Ti3SiC2 [8,19]), the three-parameter formulation was employed here. It should be noted that the inclusion of 𝜏  as bulk5 a fitting parameter typically results in higher values of 𝑚 compared to fits that force 𝜏bulk = 0, as the size-dependent term accounts only for the strength increase beyond the bulk value rather than the total measured strength, resulting in a steeper size dependence. The fitted values of 𝜏bulk and the corresponding extrapolation to the bulk limit are summarized in Fig.  4 for all three tested compounds.The extracted 𝜏bulk increase in the order Ti3SiC2 < Ti3AlC2 <Cr2AlC. Based on the pillar deformation morphology, initial disloca-tion density, and the observed stress–strain response, the mechanisms behind the size dependence are most likely source governed behavior or pre-existing dislocation starvation [52–55].3.4. Hardening componentsThe extrapolated 𝜏bulk estimate the stress for basal plane defor-mation of a macroscopic single crystal. This stress can be further decomposed into a stress from dislocation mobility (i.e., the friction stress at finite temperature) and dislocation entanglement (forest hard-ening contributions) [45,49,56]. The latter is classically estimated by a Taylor-type hardening component. This is also incorporated in Eq. (3) in the applied CPFE model, which additionally accounts for dislocation density evolutions during deformation.The term 𝜅 in Eq. (3) is determined by the dislocation interactions within the dislocation forest. In the absence of dedicated dislocation dy-namics simulations for MAX phases, these interactions can be estimated from simulations in hcp metals. Bertin et al. [42] estimate 𝜅 < 0.2for basal-basal interactions in Mg. 𝜅 = 0.1 was hence adopted for the present study.The simulated loading responses are summarized in Fig.  5. Shown are the calculated 𝜏CRSS as a function of slip evolution, as well as the reference stress strain-curves for Ti3SiC2. The 𝜏0 denote the intrinsic lattice resistance (Peierls-type friction stress), which was varied until the predicted slip resistance (𝜏CRSS) matched the experimentally deter-mined 𝜏bulk. This result gives a size-independent calibration, in contrast to fitting directly to size-affected 𝜏CRSS of individual pillars, and is equivalent to decomposing Eq. (3) into friction stress and forest hard-ening components under consideration of an accumulated dislocation J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Fig. 3. Loading curves of compressed micropillars (a–c) and associated post-deformation morphologies (d–f) for all three compounds. Pillars deformed solely by basal plane slip. Examples are here shown for a pillar diameter of 3.5 μm, and 𝑇 = 292 K.Fig. 4. Size effects determined for Ti3AlC2, Ti3SiC2 and Cr2AlC MAX phase compounds. To assess the 𝜏bulk, the data was fitted to a power law, Eq. (4), using 𝐴, 𝑚 and 𝜏bulk as fitting parameters [13]. Ti3AlC2: 𝜏bulk = 145MPa, 𝐴 = 345, 𝑚 = 2.25; Ti3SiC2: 𝜏bulk = 86MPa, 𝐴 = 324, 𝑚 = 1.44; Cr2AlC [13]: 𝜏bulk = 151MPa, 𝐴 = 317, 𝑚 = 1.58.density. The stress–strain curves further confirm that no significant ge-ometric hardening up until 1% strain is present in the deformed pillars, validating the applied methodology for extraction of yield stresses from experimental curves.6 Table 3Results of forest hardening determination in all three compounds. 𝜏bulk signifies the bulk critical resolved shear stress extrapolated from size effect measure-ments, 𝜏0 is the friction stress extracted from CPFE pillar models (Fig.  5). A basal dislocation interaction coefficient 𝜅 = 0.1 was used as a primary estimate for all three compounds. Compound 𝜅 𝜏bulk (MPa) 𝜏0 (MPa)  Cr2AlC 0.1 151 ± 17 133 ± 17   Ti3AlC2 0.1 145 ± 12 100 ± 12   Ti3SiC2 0.1 86 ± 19 65 ± 19  Table  3 lists the determined 𝜏0, as well as the 𝜏bulk and adopted 𝜅values. Among the three compounds, Cr2AlC shows the highest bulk strength, followed by Ti3AlC2 and Ti3SiC2. The intrinsic friction stress 𝜏0 follows the same trend, but reflects differences in initial dislocation density: higher densities increase the Taylor forest hardening compo-nent, thus masking the underlying lattice resistance if only the 𝜏bulkis considered. In the present study, this effect is most pronounced for Ti3AlC2. The uncertainties in 𝜏bulk arise from the three-parameter fitting procedure and propagate to the extracted 𝜏0 values. Uncer-tainty in the measured dislocation densities (±10% from TEM analysis) contributes negligibly to the overall uncertainty compared to 𝜏bulk.3.5. Peierls stress analysisFriction stress analysis was further extended to cryogenic temper-atures to quantify the temperature dependence of slip resistance and to estimate Peierls stresses. Micro-compression tests of pillars 3.5 μm in diameter were performed at effective specimen surface temperatures of 𝑇 = 191 ± 3K, 233 ± 3K and 190K. The results are summarized J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Fig. 5. Forest hardening analysis. (a–c) Critical resolved shear stresses for Cr2AlC, Ti3AlC2, and Ti3SiC2 and (d) associated stress–strain curves for Ti3SiC2determined from CPFE analysis. 𝜏0 was here determined by matching the size effect corrected 𝜏bulk with the 𝜏CRSS established from CPFE analysis. Cr2AlC: 𝜏0 = 133MPa; Ti3AlC2: 𝜏0 = 100MPa; Ti3SiC2: 𝜏0 = 65MPa.in Fig.  6 for all three tested compounds in the form of friction stress versus temperature. Minimal temperature dependency is observed for the Ti-based compounds, with comparably larger temperature depen-dent behavior for Cr2AlC. At each temperature, the friction stresses 𝜏0were again obtained from measured 𝜏CRSS under consideration of the previously determined size effects (Eq. (4)), and subsequent evaluation of forest hardening contributions from CPFE (Section 3.4). Using the CPFE model, the friction stress 𝜏𝛼0 (𝑇 ) was extracted by first removing the size-dependent contribution from the measured 𝜏CRSS(𝑇 ) according to 𝜏𝛼0 (𝑇 ) = 𝜏CRSS(𝑇 ) − 𝐴𝐷−𝑚, followed by adjusting 𝜏𝛼0 (𝑇 ) in the CPFE simulations to match this size-corrected bulk strength. Power law coefficients (𝐴, 𝑚) and dislocation–dislocation interaction coefficients (𝜅) were assumed to show negligible temperature dependence over the cryogenic to room temperature range considered, and were thus retained from room-temperature analysis.Temperature-dependent stress evolution was evaluated using aBoltzmann-type stress-activated process [56,57]: 𝜏0 =𝑘𝑇𝑉sinh−1[𝛾̇2𝜌m𝜈A𝑏2exp(𝜏P𝑉𝑘𝑇)], (5a)where 𝑘 is Boltzmann’s constant, 𝑉  is the activation volume, 𝛾̇ is the applied shear strain rate, 𝜌m is the mobile dislocation density, 𝜈A is the attempt frequency, 𝑏 is the Burgers vector and 𝜏P is the Peierls stress. Eq. (5a) can be derived from the Orowan equation: 𝛾̇ = 𝜌 𝑏𝑣, (5b)m7 considering the dislocation velocity, 𝑣 can be determined from the attempt frequency 𝜈A via 𝑣 = 𝜈A(𝑃F − 𝑃B)𝑏, (5c)with 𝑃F and 𝑃B describing the likelihood of a forward or backward jump of a dislocation segment. The probability of a given jump for a stress-activated process is determined by 𝑃F/P = exp[− 𝑉𝑘𝑇 (𝜏P ± 𝜏0)], such that:𝛾̇ =𝜌m𝑏2𝜈A{exp[− 𝑉𝑘𝑇(𝜏P − 𝜏0)]− exp[− 𝑉𝑘𝑇(𝜏P + 𝜏0)]}=𝜌m𝑏2𝜈A exp(−𝜏P𝑉𝑘𝑇)[exp(𝜏0𝑉𝑘𝑇)− exp(−𝜏0𝑉𝑘𝑇)]=𝜌m𝑏2𝜈A exp(−𝜏P𝑉𝑘𝑇)2 sinh(𝜏0𝑉𝑘𝑇),which can be rearranged to give Eq. (5a).Eq. (5a) describes the temperature dependence of the lattice re-sistance (friction stress), rather than that of dislocation–dislocation interaction. The underlying assumption is that dislocation mobility is predominantly governed by the ability of dislocations to overcome the Peierls barrier (lattice resistance), rather than obstacles from impurities or a dislocation forest [46,58–61]. Such an assumption is supported by the observation of straight dislocation segments aligned with dis-tinct crystallographic directions as observed in TEM (Fig.  2) and by the expectation of limited dislocation interactions for basal slip in a basal-plane dislocation network (𝜅 = 0.1).J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Table 4Input parameters and model identified values for activation volume and Peierls stress following Eq. (5a). 𝜌m = 1∕3𝜌tot; 𝜈A = 𝑘𝛩Dℎ. Theoretical 𝜏P for edge and mixed dislocations determined via MD [23] and DFT [22] were added for comparison. Compound 𝛾̇ (s−1) 𝜌m (m−2) 𝛩D (K) 𝜈A (s−1) 𝑉  (nm3) 𝜏P (MPa) 𝜏P,calc (MPa)   Ti3AlC2 0.002 4.93 × 1013 m−2 758 [63] 1.58 × 1013 1.56 (54𝑏3) 142 ± 16 192 [23]   Ti3SiC2 0.002 1.21 × 1013 m−2 780 [63] 1.63 × 1013 1.14 (40𝑏3) 150 ± 27 70–150 [22]  Cr2AlC 0.002 2.61 × 1012 m−2 675 [64] 1.41 × 1013 0.37 (16𝑏3) 359 ± 63 –  Fig. 6. Temperature dependence of the friction stress measured for Ti3AlC2, Ti3SiC2 and Cr2AlC. The data was fitted to a Boltzmann-type stress-activated process (Eq. (5a)) to assess both 𝜏P and 𝑉 . Ti3AlC2: 𝜏0(292K) = 147 ± 1MPa, 𝜏0(230K) = 156 ± 10MPa, 𝜏0(188K) = 170 ± 6MPa, 𝜏P = 142MPa, 𝑉 = 1.56 nm3; Ti3SiC2: 𝜏0(292K) = 149 ± 8MPa, 𝜏0(235K) = 165 ± 5MPa, 𝜏0(190K) =177 ± 8MPa, 𝜏P = 150MPa, 𝑉 = 1.14 nm3; Cr2AlC: 𝜏0(292K) = 189 ± 23MPa, 𝜏0(236K) = 225±12MPa, 𝜏0(194K) = 277±15MPa, 𝜏P = 359MPa, 𝑉 = 0.37 nm3.Estimates of Peierls stresses from temperature dependent friction stress data were obtained by fitting Eq. (5a) to the temperature de-pendent friction stresses, using 𝜏P and 𝑉  as fitting parameters. The resulting fitting curves are overlaid on the experimental data in Fig. 6. All parameters used for fitting are summarized in Table  4, along with the extracted parameters for 𝜏P and 𝑉 . The 𝜌m were set with 𝜌m = 1∕3𝜌tot, considering slip to occur on one of the three possible basal slip systems. The 𝜈A can be calculated from Debye temperatures 𝛩D via 𝜈A = 𝑘𝛩Dℎ  [62]. 𝑘 and ℎ are the Boltzmann and Planck’s constants re-spectively. The 𝛩D in the three compounds were previously determined via ultrasonic sound velocity and heat capacity measurements [63,64].The highest Peierls stresses were measured in Cr2AlC (𝜏P = 359 ±63MPa), which also exhibited the strongest temperature dependence of the friction stress. In contrast, both Ti3SiC2 (𝜏P = 150 ± 27MPa) and Ti3AlC2 (𝜏P = 142 ± 16MPa) showed lower and comparable Peierls stresses, with a weaker dependence on temperature. The corresponding activation volumes for all three compounds fall within 𝑉 = 16 − 54𝑏3, consistent with values reported for Peierls-barrier controlled plastic-ity in hcp or bcc metals [59,60,65], ordered intermetallics [61], or alkali halides [58]. Uncertainties in the extrapolated Peierls stresses reflect both the scatter in temperature-dependent friction stress mea-surements and the fitting uncertainty in the thermal activation model. Additionally, the absolute magnitudes of 𝜏P depend on the dislocation interaction coefficient 𝜅 = 0.1 assumed in the CPFE model. Variation of 𝜅 within the range 0.05–0.2 would shift 𝜏P by ±20−35MPa, but would preserve both the temperature dependence and the relative ranking among compounds, as 𝜅 introduces only a systematic offset to the friction stress.8 4. DiscussionThe primary focus of this study was the experimental evaluation of temperature dependent friction stresses, activation volumes and Peierls stresses in Ti3AlC2, Ti3SiC2 and Cr2AlC, to provide a reference for validating dislocation-core structures predicted by DFT/MD and to determine how chemical variation influences core structure evolu-tion in MAX phases. This was achieved through a combined protocol: evaluation of size effects at room temperature, assessment of forest hardening by crystal plasticity, micropillar compression at cryogenic temperatures, and targeted TEM analysis.All three compounds showed marked size effects, with predicted bulk critical resolved shear stresses at room temperature of 145±12MPafor Ti3AlC2, 86 ± 19MPa for Ti3SiC2 and 151 ± 17MPa for Cr2AlC. These values are in good agreement with testing of bulk-textured samples [8], where 𝜏CRSS = 77MPa for Ti3SiC2 [8,19]. The evaluated size effects and forest hardening contributions were further used to extrapolate temperature dependent measurements of 𝜏CRSS to friction stresses, eventually used to determine activation volumes and Peierls stresses.The results reveal a clear increase in friction stress with decreasing temperature for all three compounds, confirming thermally activated glide. However, the temperature sensitivity (d𝜏0∕d𝑇 ) diverges sharply among the compounds, highlighting chemistry-specific Peierls barriers. Cr2AlC exhibits the steepest increase in friction stresses as a function of temperature, approximately 2.5 − 3× higher than for the Ti-based MAX phases. Friction stresses in Cr2AlC rise by ∼0.8MPaK−1 in the quasi-linear region, with Ti3AlC2 showing a corresponding rate of ∼0.25MPaK−1, and Ti3SiC2 showing a rate of ∼0.3MPaK−1. This pre-dicts the highest Peierls stresses in Cr2AlC, with 359±63MPa, followed by Ti3SiC2 with 150 ± 27MPa and Ti3AlC2 with 142 ± 16MPa.The experimental Peierls stress predictions for Ti3AlC2 and Ti3SiC2are in good agreement with recent DFT calculations and MD simu-lations of edge dislocation mobility, from which 𝜏P ∼ 200MPa for Ti3AlC2 [21,23] and 𝜏P ∼ 70MPa for Ti3SiC2 [22]. Nevertheless, the Peierls stresses fall below the predicted values for screw dislocations (𝜏P ∼ 3000MPa) [21–23] and above those suggested for basal disloca-tion pairs, or zonal dislocations (𝜏P ∼ 20MPa) [23]. This predominance of edge-type dislocation mobility aligns with the experimental ob-servations from TEM in this work. TEM analysis of pristine Ti3AlC2and Ti3SiC2 confirms the sole presence of edge or mixed dislocations; neither pure screw nor zonal dislocations could be detected (Fig.  2, Figure S2 and S6).To further substantiate the role of edge dislocations in controlling the strength of the Ti-based compounds, TEM analysis was employed post-deformation in Ti3SiC2 to highlight the structure and character of operating dislocations. The results are summarized in Fig.  7, Table 5 and further in Supplementary Figures S3 - S5 and Supplementary Table S5 for pillars tested at room and cryogenic temperatures. All in-vestigated pillars show evidence of source-governed behavior through <a>-type 13 ⟨1 1 2 0⟩ dislocation activity. Whilst closely spaced dislo-cation lines, reminiscent of zonal dislocations with wide dissociation distances [27], are observed, no associated 13 ⟨1 1 0 0⟩ type Burgers vectors could be confirmed. The close spacing of dislocations is likely associated with dislocation arrangement (wall formation) in different 0001 planes. The absence of extensive dissociation and zonal disloca-tions is consistent with DFT predictions of equilibrium core structures J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Fig. 7. Post-mortem WBDF TEM analysis at room and cryogenic temperatures in Ti3SiC2 ([0 0 0 1] zone axis). (a–d) 292K: Parallel dislocation arrays with Burgers vector 𝐛 = 13⟨1 1 2 0⟩ observed after room temperature deformation (292K). (e–h) Isolated dislocation segments (sources) with Burgers vector 𝐛 = 13⟨1 1 2 0⟩ observed at cryogenic temperatures (190K). In both cases, dislocation lines align parallel to ⟨1 1 2 0⟩ and ⟨1 1 0 0⟩ directions.Table 5Results of 𝐠 ⋅ 𝐛 analysis for Ti3SiC2. Diffraction vectors of type 𝐠 = ⟨1 1 2 0⟩ and 𝐠 = ⟨1 1 0 0⟩ were selected to differentiate between full 𝐛 = 13⟨1 1 2 0⟩ and partial 𝐛 = 13⟨1 1 2 0⟩ basal dislocation activity.  Deformed (292K) [1 1 2 0] [1 1 2 0] [2 1 1 0] [3 3 0 0] [0 3 3 0] – 𝐛 Angle between 𝐛 & 𝐥  1 Y Y Y Y N – 13[2 1 1 0] 90◦   2 Y Y Y N Y – 13[1 1 2 0] 60◦   3 Y Y Y N Y – 13[1 1 2 0] 30◦   4 Y Y Y N Y – 13[1 1 2 0] 60◦   5 Y Y Y N Y – 13[1 1 2 0] 60◦   6 Y Y Y N Y – 13[1 1 2 0] 60◦   Deformed (190K) [1 1 2 0] [1 1 2 0] [1 2 1 0] [3 0 3 0] [3 0 3 0] [3 3 0 0] 𝐛 Angle between 𝐛 & 𝐥  1 Y Y Y Y Y Y 13[2 1 1 0] 60◦   2 Y Y Y Y Y Y 13[2 1 1 0] 30◦   3 Y Y Y Y Y N 13[1 1 2 0] 60◦   4 Y Y Y Y Y N 13[1 1 2 0] 60◦   5 Y Y Y N N Y 13[1 2 1 0] 90◦   6 Y Y Y Y Y N 13[1 1 2 0] 90◦  by Hossain et al. [21,22]. As in pristine samples, dislocation lines are preferentially aligned parallel to specific crystallographic directions, highlighting the influence of the lattice resistance on dislocation mo-tion. Contrast analysis again indicates a predominance of edge and mixed (30◦ and 60◦) character.Further insight into the dominant core characteristics for Ti3AlC2and Ti3SiC2, as well as a first estimate of core structures for Cr2AlC in the absence of dedicated atomistic simulations, can be obtained from the extracted activation volumes. Specifically, activation vol-umes of 𝑉Ti3SiC2= 40𝑏3, 𝑉Ti3AlC2= 54𝑏3, and 𝑉Cr2AlC = 16𝑏3 were extracted. Peierls-barrier-controlled mobility, for which the disloca-tion core structure, rather than dislocation–dislocation interactions are the rate-limiting mechanisms in deformation is commonly associ-ated with 𝑉 = 1 − 100𝑏3 [46,58–61,65]. The observed alignment of dislocation segments with densely packed crystallographic directions supports a pronounced influence of dislocation core structure on mo-bility. While the comparatively larger activation volumes in Ti3AlC2and Ti SiC  may link to a transition between a Peierls mechanism and 3 29 dislocation-interaction limited mobility, these can be equally explained by a more extended barrier-crossing event, either involving kink-pair formation over longer segments or the cooperative motion of partials. Such dissociation may also be inferred from the post-deformation TEM observations in Ti3SiC2 (Fig.  7) in the form of slightly broadened dislocation lines, and is in agreement with the proposed dissociated dislocations in Ti-based MAX phases [10,21–23].  While the presence of zonal dislocations has been proposed previously [27], they were not identified in pristine or deformed samples of any composition in the present study.Contrary to the Ti-based compounds, the lower activation volume and higher Peierls stress of Cr2AlC indicate a more localized, ther-mally activated dislocation motion and correspondingly more compact dislocation cores. Although dedicated atomistic simulations of the dis-location core structures in Cr2AlC are not yet available, differences between Cr- and Ti-based systems can be further supported by their contrasting non-Schmid sensitivities under uniaxial loading [11,13]. Specifically, Cr AlC has been reported to exhibit a decrease in 𝜏2 CRSSJ.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Table 6Bond lengths for the p-d hybridized M-A bonds, the correlating M-M and M-X bonds bounding the slip plane, as well as the elastic 𝐶44 constant in Cr2AlC, Ti3AlC2 and Ti3SiC2. Compound M-A (Å) M-X (Å) M-M (Å) 𝐶44 (GPa)  Cr2AlC 2.26 [69] 1.98 [69] 2.22 [69] 173 [44]   Ti3AlC2 2.88 [72] 2.09 [72] 2.99 [72] 119 [43]   Ti3SiC2 2.69 [73] 2.10 [73] 3.05 [74] 155 [43]  with increasing stress normal to the slip plane (𝜎n) [13], whereas Ti3AlC2 shows the opposite trend, i.e., an increase in 𝜏CRSS with increas-ing 𝜎n [11]. A compressive stress normal to the slip plane generally promotes dislocation core widening in plane, thereby lowering the fric-tion stress [66]. This behavior aligns with the observations in Cr2AlC and supports the presence of initially narrow dislocation cores. In contrast, an increase of 𝜏CRSS with 𝜎n, as observed in Ti3AlC2, was previously attributed in L12 and hcp metals to initially wide disloca-tion cores that spread across multiple slip planes of different families (e.g., prismatic and pyramidal) [67,68]. Consequently, the pronounced slip-plane inhomogeneity of 𝜏CRSS among these different families likely restricts dislocation mobility under higher 𝜎n, resulting in the observed increase in 𝜏CRSS. Indeed, dislocation core simulations by MD and DFT support spreading of basal plane dislocations into M-X layers/onto pyramidal planes as an energetically favorable arrangement in Ti-based MAX phases [21,23].The origin of variations in core structure may be hypothesized to be a consequence of differing bonding characteristics in the examined compounds. Plummer et al. [23] previously suggested A-A bonds as a critical factor related to dislocation core structures based on MD simulations in Ti3AlC2. Yet, the present discrepancies between Cr- and Ti-based MAX phases, and specifically between Cr2AlC and Ti3AlC2, suggest the M-element to play a more dominant role. Table  6 lists bond lengths for the p-d hybridized M-A bonds, as well as M-X and M-M bonds in the three investigated MAX phase compounds. Overall, Cr2AlC exhibits shorter bond lengths than both Ti3SiC2 and Ti3AlC2, signifying stiffer and stronger bonds in the Cr-based compound [69]. The variation in bond length is mirrored also in the related elastic constants: for example, the 𝐶44 constant, which relates to shear parallel to the basal plane, is higher for Cr2AlC compared to the Ti-based MAX phases. Enhanced basal plane slip mobility arises primarily from weaker M-A bonds, in line with GSF considerations [10,24], whereas a confinement of dislocation cores and partial dissociation should be governed additionally by M-M and M-X bonds. Differences in charge density distributions around A atoms, which extend parallel to the M-A layer in Cr2AlC [69–71], and into the M-X layer in the Ti-based MAX phases  [72,73], may additionally contribute to the observed discrepancies in dislocation core structure, although a more detailed bonding analysis is required to clarify this role.In summary, the measured Peierls stresses and activation volumes for Ti3AlC2 and Ti3SiC2 are in good agreement with previous pre-dictions of edge and mixed dislocation mobility from MD [23] and DFT [21,22] simulations. TEM analysis of pristine Ti3AlC2 and Ti3SiC2, as well as deformed Ti3SiC2 samples revealed predominantly edge and mixed (30◦,60◦) character, with no clear evidence of screw dislocations in the examined samples. This predominance of edge/mixed character and apparent rarity of screw segments suggests that screws are compa-rably immobile due to their very high Peierls barrier. Screw dislocations are not prominently observed following dislocation generation during thermal stress relief upon cooling from synthesis, nor following active plastic deformation at room temperature and cryogenic conditions, despite their core energies being comparable to those of edge disloca-tions [23]. In contrast, screw dislocations are clearly present in pristine Cr2AlC, indicating that screws are sufficiently mobile to be generated and propagate under thermal stresses during cooling. This is consis-tent with a lower-Peierls screw configuration due to a more compact 10 dislocation core. Experimentally obtained Peierls stresses and activa-tion volumes confirm more compact dislocation core arrangements for Cr2AlC, which were effectively linked to stiffer and stronger M-M and M-X bonding characteristics compared to the Ti-based compounds.While the present experimental findings suggest that dislocation-mediated plasticity in MAX phases is predominantly governed by the Peierls barrier, collective interactions within the dislocation network, in particular with regards to forest hardening, cannot be fully ne-glected. Future modeling efforts that incorporate atomistic simulations or collective dislocation dynamics in these compounds would provide a valuable addition for determination of the dislocation interaction coefficient 𝜅. Large activation volumes and the less pronounced tem-perature dependence observed in the Ti-based compounds could fur-ther be clarified, particularly regarding the transition between Peierls-dominated and interaction-dominated regimes. The remaining open challenge of resolving dislocation core structures in Cr2AlC further define a clear target for first-principles modeling.5. ConclusionsThis study presents systematic cryogenic micropillar compression experiments on MAX phases, coupled with size effect analysis, crystal plasticity finite element modeling and TEM characterization to extract both the Peierls stress and activation volumes across three model compounds: Cr2AlC, Ti3AlC2, and Ti3SiC2. The following conclusions can be drawn:• Despite their structural similarities, the three MAX phases demon-strated marked differences in Peierls stresses and activation vol-umes. Cr2AlC exhibited significantly higher resistance to basal dislocation glide (𝜏P > 360MPa, 𝑉 ≈ 16𝑏3), consistent with more compact dislocation cores and stiffer bonding. In contrast, Ti3SiC2 and Ti3AlC2 showed lower Peierls stresses (𝜏P ≈ 150MPa) and higher activation volumes (𝑉 ≈ 40 − 54𝑏3), suggesting more extended core structures and easier shear due to weaker bonding between specifically M-A and M-M atoms. Previously observed differences in non-Schmid effects between Cr2AlC and Ti3AlC2confirm the likelihood of different core widths in Ti- and Cr-based compounds.• The determined Peierls stresses in Ti-based MAX phases are in good agreement with DFT and MD predictions for edge and mixed dislocations. TEM analysis of pristine and deformed Ti-based compounds revealed exclusively edge and mixed dislocation char-acter, with no observable screw dislocations. In contrast, screw dislocations were observed in pristine Cr2AlC, suggesting suffi-cient mobility to be generated and retained during thermal stress relief upon cooling from synthesis, and consistent with a more compact core structure in this compound. No evidence of zonal dislocations was found in either compound.• The three MAX phase compounds show marked differences in size effects and pristine dislocation densities. These factors showed a non-negligible influence on forest hardening and apparent strength, masking true friction stress variations between com-pounds. As such, a comparison with theoretical predictions of dislocation mobility based on chemistry cannot be meaningfully achieved without separating size and forest hardening-related effects from the intrinsic lattice resistance. Future work incor-porating dislocation dynamics or larger scale atomistic simu-lations could help to further elucidate dislocation–dislocation interactions and their influence on plasticity in MAX phases.CRediT authorship contribution statementJ.T. Pürstl: Writing – review & editing, Writing – original draft, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. C. Tian: Writing – review & editing, J.T. Pürstl et al. Acta Materialia 316 (2026) 122432 Validation, Methodology, Investigation, Formal analysis, Data curation. A. Sharma: Writing – review & editing, Visualization, Validation, Methodology, Investigation, Formal analysis, Data curation, Conceptu-alization. A. Nascimento: Writing – review & editing, Visualization, Software, Methodology, Investigation, Formal analysis, Data curation. N.M. della Ventura: Writing – review & editing, Investigation, Formal analysis, Data curation, Conceptualization. T.E.J. Edwards: Writing – review & editing, Validation, Supervision, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. P. Chartier: Writing – review & editing, Validation, Resources, Methodology. M. Vreeswijk: Writing – review & editing, Validation, Methodology, Investigation. R.P. Thompson: Writing – review & editing, Validation, Supervision, Methodology, Conceptualization. I.J. Beyerlein: Writing – review & editing, Validation, Supervision, Methodology, Funding acquisition, Formal analysis, Conceptualization. J.J. Schwiedrzik: Writing – review & editing, Supervision, Resources, Methodology, Funding acquisition, Data curation. J. Michler: Writing – review & editing, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Conceptualization. W.J. Clegg: Supervision, Project ad-ministration, Methodology, Conceptualization. N.G. Jones: Writing – review & editing, Writing – original draft, Validation, Supervision, Resources, Project administration, Methodology, Funding acquisition, Formal analysis, Conceptualization.Declaration of competing interestThe authors declare the following financial interests/personal rela-tionships which may be considered as potential competing interests: The co-author Irene J. Beyerlein is an Editor for Acta Materialia and was not involved in the editorial review or the decision to publish this article.AcknowledgmentsJ.T.P. thanks the EPSRC for the provision of a Doctoral Training Pro-gramme studentship. T.E.J.E. received funding from EMPAPOSTDOCS-II of the European Union’s Horizon 2020 research and innovation program under the Marie Skłodowska-Curie grant agreement number 754364. A. N. and I.J.B. gratefully acknowledge supported by the ONR, United States under grant number N00014-26-1-2021. Colourscales were adapted from [75].The co-author Irene Beyerlein is an Editor for Acta Materialia and was not involved in the editorial review or the decision to publish this article.Appendix A. Supplementary dataSupplementary material related to this article can be found online at https://doi.org/10.1016/j.actamat.2026.122432.References[1] M.W. Barsoum, The MN+1AXN phases: A new class of solids: Thermodynamically stable nanolaminates, Prog. 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Cryogenic micropillar compression of Ti3AlC2, Ti3SiC2 and Cr2AlC: A comparative evaluation of composition-dependent dislocation mobility in MAX Phases Introduction Methods Materials Orientation Analysis Micropillar Preparation Micropillar Compression Transmission Electron Microscopy Crystal Plasticity Simulations Results and Analysis Pristine Microstructure Micropillar Compression Size Effects Hardening Components Peierls Stress Analysis Discussion Conclusions CRediT authorship contribution statement Declaration of competing interest Acknowledgments Appendix A. Supplementary data References