Magnesium (Mg) hydride is a promising hydrogen storage material, yet its application has been limited by the slow hydrogen sorption kinetics. Recently, Mg nanoparticles have shown significant improvement of hydrogen storage properties in terms of dimensional stability upon cycling with the trend that the smaller the particle, the better the sorption kinetics. Since the volume change during sorption generates stress, leading to plastic deformation, the fundamentals of the mechanical deformation of the Mg particles are a significant issue. By using in situ transmission electron microscope compression tests and atomistic simulations on Mg nanoparticles, it was observed that deformation in the larger particles was dominated by the nucleation of ⟨a⟩-type dislocations from stress concentrations at the contact surface, while the smaller particles deformed more homogeneously with greater distribution of multiple types of dislocation sources. Importantly, this improvement of plastic deformation with decrease in size is orientation-independent. First-principles calculations suggest that this improved plasticity can be explained by the nearly-isotropic ideal shear strength for Mg, which becomes more important in smaller nanoparticles. As a result, the smaller Mg nanoparticles demonstrated better plastic stability to accommodate volume change upon hydrogen storage cycling.

Metal hydrides are traditionally thought to be one of the leading candidates for hydrogen storage materials due to their low cost, lightweight, and high hydrogen storage capacity. Yet the high bond formation enthalpies result in comparatively slow hydrogen sorption kinetics and high operating temperature.1–3 Recently, nanoengineering of these materials have shown great influence on their hydrogen sorption kinetics.4 Mg nanoparticles and nanocomposites have been reported to have both higher hydrogen storage capacity and more rapid kinetics,2,5 which is mainly attributed to the increase of surface-to-volume ratio and decrease of diffusion path length of hydrogen with decreasing size. However, no matter what size, the absorption and desorption of hydrogen involves volume expansion and contraction that leads to significant mechanical deformation.1–3,6 During this process, the Mg particles undergo cyclic plastic deformation resulting in fracture and eventual decrepitation of the structure. Moreover, characteristic internal imperfections that define the microstructure of the hydride grains1,7 and the defect evolution lead to changes in the hydrogen diffusion. All of these factors have a strong impact on the cycling stability and hydrogen sorption kinetics, making the investigation of the mechanical properties and the dynamic defect evolution during deformation of Mg particle important for understanding the optimization of hydrogen storage in Mg nanoparticles. In addition, the mechanical issue may even affect the thermodynamics. For example, it was reported that the thermodynamics of hydrogen absorption in Mg could be tuned by means of elastic clamping.8 

Mg has hexagonal closed packed crystal structure. Bulk Mg shows significant deformation anisotropy since the critical resolved shear stress for various slip system is quite different. Therefore, the ability of plastic deformation is considered as low, and the deformation is highly orientation-dependent. However, it is well known that nanostructured materials have significantly different mechanical properties as compared to bulk materials. In FCC (face centered-cubic) metals, for example, smaller particles usually have higher strength but lower plastic stability due to more intermittent plastic instability as compared to bulk materials.9,10 However, this trend is not directly applicable for hexagonal close-packed (HCP) materials such as Mg due to their inherently more anisotropic dislocation plasticity.11 Here, we have used in situ transmission electron microscope (TEM) compression tests on individual Mg nanoparticles with different sizes to study the dynamic defect evolution during deformation and investigate their plastic stability as a function of particle size. In contrast to FCC metals, our results show that the smaller Mg nanoparticles demonstrate both higher strength and improved plastic stability. The improvement of plasticity is also proved to be orientation-independent.

To investigate the effect of size on plastic deformation, Mg nanoparticles were produced by a direct current (DC) arc plasma method.12 As shown in Figures 1(a) and 1(b), the nanoparticles displayed a 3-dimensional structure with six fold-symmetry. The surface planes were {0001}, {101¯0}, and {101¯1}, respectively. The 2-dimensional projection of the nanoparticles from the top view displayed the hexagonal shape, as shown in the TEM image in Figure 1(a). The morphology of nanoparticles was analyzed by employing diffraction and HRTEM analysis.13 Figure 1(c) demonstrates the crystallography of the nanoparticles. The nanoparticles were further dispersed on to a silicon device with a sharp wedge for mechanical testing, similar to previous studies.14In situ TEM compression tests were performed in a JEOL 3010 microscope by using a Hysitron PI95 nanoindentation with a flat diamond tip. For comparison, nanoparticles with diameters of 300–400 nm and 100–120 nm were tested, respectively. The load was applied along different orientations to test the possible orientation-dependence of the plasticity. Over 25 tests were performed in total to make sure that trends were repeatable and convincing. Dislocation analysis was performed before and after the deformation. The experimental results of the observed plastic deformation characteristics were analyzed with the help of Molecular Dynamics (MD) simulations and density functional theory (DFT) calculations.13 

FIG. 1.

(a) TEM image and (b) SEM image of the as-grown Mg nanoparticles. (c) Schematic of the morphology and crystallography of the nanoparticles.

FIG. 1.

(a) TEM image and (b) SEM image of the as-grown Mg nanoparticles. (c) Schematic of the morphology and crystallography of the nanoparticles.

Close modal

The experimental results demonstrated that the nanoparticles with different sizes behaved quite differently in terms of both the dislocation dynamics and the measured mechanical properties, consistent with previous work on nanoscale compression and tension experiments of FCC metals.15 Figure 2(a) shows a typical mechanical curve of a large particle with a diameter of about 400 nm. For selected points during the test, a simple estimation of the contact pressure/stress was calculated from F/A, where F is load and A is the contact surface area under the corresponding load F. From the mechanical testing curves, it can be observed that there was a catastrophic load drop during the deformation where the load directly dropped to zero. This is regarded as the peak stress where plastic instability occurred. From the movies (refer to Figures 2(b) and 2(c)), it was clear that the deformation of large particles was mainly controlled by the operation of a dominant dislocation source at the contact surface. If one defines a simple engineering strain as the displacement of the indenter punch in the direction parallel to the load divided by the initial particle height, the corresponding engineering strain up to instability was about 10%. Figure 2(b) shows a large particle compressed along the normal of {101¯1} pyramidal plane. Some random dislocation activity was detected at the very beginning. Shortly thereafter, a dislocation source at the contact surface started to generate new dislocations but the new dislocations did not escape from the sample surface immediately; instead, they formed dislocations entanglements inside the particle. Following this entanglement stage, the stress increased to approximately 0.7 GPa (contact stress) and a remarkable strain burst occurred due to a dislocation avalanche. The dislocation analysis in the deformed particles demonstrated that the remaining dislocations were almost all ⟨a⟩ type. This phenomenon was consistent across all of the particles in this size regime and showed no significant orientation-dependence. Figure 2(c) demonstrates an example of a compression of a large particle with loading direction parallel to the normal of {101¯0} prismatic plane. It was observed that one dominant dislocation source at the contact surface was operating, generating dislocations on the plane which was marked by the dash line in red. Similar to the previous example in Figures 2(a) and 2(b), shear localization occurred after the initial dislocation operation regime, resulting in a sudden strain burst and significant load drop from ∼60 μN to zero.

FIG. 2.

(a) Load-displacement curve of a compression test on a 400 nm-sized particle. The blue dots represented the contact pressure at selected points in the test. (b) TEM images from the movie of a nanoparticle compression test where the loading direction was along the normal of {101¯1} plane, g = [11¯00], and the data for this test are shown in Figure 2(a) see movie1). Figure 2(b) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (c) TEM images captured from the movie of the compression test on a different nanoparticle with ∼400 nm size, g = [101¯0]. The loading direction was along the normal of {101¯0} plane (see movie2). Figure 2(c) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4921003.1] [URL: http://dx.doi.org/10.1063/1.4921003.2]

FIG. 2.

(a) Load-displacement curve of a compression test on a 400 nm-sized particle. The blue dots represented the contact pressure at selected points in the test. (b) TEM images from the movie of a nanoparticle compression test where the loading direction was along the normal of {101¯1} plane, g = [11¯00], and the data for this test are shown in Figure 2(a) see movie1). Figure 2(b) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (c) TEM images captured from the movie of the compression test on a different nanoparticle with ∼400 nm size, g = [101¯0]. The loading direction was along the normal of {101¯0} plane (see movie2). Figure 2(c) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4921003.1] [URL: http://dx.doi.org/10.1063/1.4921003.2]

Close modal

In contrast to the behavior exhibited by the larger size regime and detailed in Figure 2, the smaller Mg particles deformed more continuously with what can be described as extended plastic stability. Figure 3(a) shows a typical mechanical curve of a 100 nm-sized particle. Even though stress serrations occurred, their amplitudes were less than 100 MPa, and no catastrophic load drops were observed. The contact stress kept increasing until ∼1.16 GPa; beyond this point, stress decreased with increasing strain as marked by blue dot in Figure 3(a), indicating that plastic instability occurred, although no obvious shear localizations could be observed. The corresponding engineering strain along the loading direction before the instability was about 30%. From the in situ movie (refers to Figure 3 (c), Multimedia view), it was observed that the dislocation activities were more homogenous, which were not only observed near the contact surfaces but also in the interior of the particle. Specifically, the deformation mainly occurred through the activation of small segments of pre-existing defects, a phenomenon that was rarely seen in large particles and bulk materials. Those short dislocations could be the strongly pinned segments of dislocations produced by the intersection of long dislocations, which are commonly observed in bulk materials as well. Those dislocations can be considered as “hard” sources and rarely contributed to plastic deformation, because their critical resolved shear stress (CRSS) can be very high due to their small length and certain crystallographic defects such as sessile segments. Interestingly, here, these hard sources become quite mobile in the smallest particles where the plastic flow occurs at a high stress. Figure 3(b) shows the dislocation dynamics corresponding to the mechanical curve in Figure 3(a), where the load was applied along the normal of {101¯1} pyramidal plane. The dislocation analysis before the test showed a pre-existing ⟨c + a⟩ dislocation and another even shorter segment of ⟨a⟩ dislocation, which is labeled as single arm source in Figure 3(b). Figure 3(b) shows the TEM images captured from the in situ movie displaying the dynamic dislocation activities. The ⟨c + a⟩ source is usually considered as a “hard” source because of the large Burgers vector; it started to operate at very beginning of plastic deformation. Simultaneously, the extremely tiny single armed source was operating as well, generating multiple dislocations. Figure 3(c) shows another example of the compression of a small particle loaded along the normal of {101¯0} prismatic plane. Consistent with the plasticity shown in Figure 3(b), the dislocation activities were observed throughout the whole volume. The operation of a short pre-existing single-arm source was observed near the contact surface at the bottom. Moreover, at the central plane where the engineering stress was lower due to the larger cross section, dislocation nucleation occurred as shown in Figure 3(c) (middle image), very likely by surface nucleation. Similar event occurred at the bottom of the particle. After compression tests, dislocation analysis revealed that some dislocations were ⟨c + a⟩ type as shown in Figures 3(b) and 3(c) (after), indicating the participation of “hard”sources during the deformation.

FIG. 3.

(a) Load-displacement curve of a compression test on 100 nm-sized particle. The blue dots represented the contact pressure at selected points in the test. (b) TEM images captured from the movie of the compression test on the nanoparticle with data shown in Figure 3(a), g = [11¯00]. The loading direction was along the normal of {101¯1} plane. Figure 3(b) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (c) TEM images captured from the movie of the compression test on another nanoparticle with ∼100 nm size, g = [101¯0]. The loading direction was normal to the {101¯0} plane (see movie3). Figure 3(c) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4921003.3]

FIG. 3.

(a) Load-displacement curve of a compression test on 100 nm-sized particle. The blue dots represented the contact pressure at selected points in the test. (b) TEM images captured from the movie of the compression test on the nanoparticle with data shown in Figure 3(a), g = [11¯00]. The loading direction was along the normal of {101¯1} plane. Figure 3(b) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (c) TEM images captured from the movie of the compression test on another nanoparticle with ∼100 nm size, g = [101¯0]. The loading direction was normal to the {101¯0} plane (see movie3). Figure 3(c) (after) shows the ⟨a + c⟩-type of dislocations in this particle after deformation. (Multimedia view) [URL: http://dx.doi.org/10.1063/1.4921003.3]

Close modal

Comparing the behavior of small particles and large particles, one observes two major differences: (1) If we roughly estimate the energy absorption per volume before the plastic instability in the form of ρ=0εIσdε, where σ is the stress and εI is the strain to instability, the value of ρ for small particles was almost six times higher than that for the large particles. The significant improvement is attributed to the higher stress as well as the much larger strain to instability in smaller particles. (2) The large particles deformed by the operation of one dominant dislocation source, which was ⟨a⟩-type dislocation nucleated from the contact surface, and the corresponding yield/flow stress is relatively smaller (<=0.7 GPa before εI); the small particles deformed with contribution from truncated “easy” dislocations, pre-existing “hard” dislocation, and the nucleation of new basal/non-basal dislocations, and the corresponding yield/flow stress is much higher (>1.0 GPa before εI), a phenomenon known as “smaller is stronger.”

There are several possible mechanisms to explain that the smaller nanoparticle samples are stronger, such as source truncation model and dislocation surface nucleation model.10,15 As shown in our large nanoparticle samples, the dislocation nucleation becomes the limiting factor of plastic deformation and controls the flow stress. For nanoparticles, it was proposed that the critical compressive stress to nucleate a dislocation loop at nanoparticle surface decreases with the increase in particle dimensions as R−n, where R is the sample size and n is the exponent in the power law.10 Consistent with previous results, our MD simulations on Mg nanoparticles as shown in Fig. 4(a) with different sizes also demonstrated that the dislocation nucleation occurred at higher stress with decreasing particle sizes. The size effect on the nucleation stress can be seen in Figure 4(b) that shows that the nucleation stress increases with the decrease in particle size. Fitting a straight line to the corresponding log-log plot suggested n ≈ 0.63, similar to the value from previous simulation in Au nanoparticles.10 In general, this can be understood that for the nanoparticle with smaller volume, larger elastic energy density has to be accumulated to pay the activation energy for the nucleation of individual dislocation.

FIG. 4.

(a) The Mg nanoparticle model used for the MD simulations. (b) The log-log plot showing that the increase of dislocation nucleation stress as the particle size D decreases is in a power law relation with n ≈ 0.6. Here, compression strain is applied perpendicular to pyramidal facet in (a). (c) Stress-strain relations for prefect Mg crystal when shear strain is applied along different slip systems. The ideal shear strength is the maximum shear stress achieved in each curve.

FIG. 4.

(a) The Mg nanoparticle model used for the MD simulations. (b) The log-log plot showing that the increase of dislocation nucleation stress as the particle size D decreases is in a power law relation with n ≈ 0.6. Here, compression strain is applied perpendicular to pyramidal facet in (a). (c) Stress-strain relations for prefect Mg crystal when shear strain is applied along different slip systems. The ideal shear strength is the maximum shear stress achieved in each curve.

Close modal

The orientation-independent activation of different deformation modes under high stress condition in the smaller nanoparticles can be explained by the nearly isotropic ideal shear strength of Mg. At relatively low strength, the deformation is usually dominated by the slip mechanism with the minimum activation barrier, such as basal slip of ⟨a⟩-type dislocations in large particles. As the strength of nanoparticle increases with the decreasing size, other type of deformation modes, such as pre-existing “hard” dislocation and the nucleation of non-basal dislocations, become active. The critical stress required to activate those deformation modes should be limited by the ideal shear strength of the corresponding slip systems.16,17 We applied DFT calculations to obtain the ideal shear strength of Mg along different slip systems on basal, prismatic, and different pyramidal planes. The results in Fig. 4(c) show that the ideal shear strength of all these slip systems are all located in a small region from 1.55 to 1.85 GPa, which is different from the high anisotropy of CRSS for existed dislocations in Mg.18 The nearly-isotropic ideal shear strengths is also consistent with the nearly-isotropic elastic shear modulus,19 since the former value is usually proportional to the later one the along corresponding shear direction. These nearly-isotropic ideal shear strengths are comparable with the contact pressure measured in small nanoparticles (Here, the contact pressure is an average stress value. Locally, the shear stress could be much higher than the contact pressure multiplied by Schmid factor due to the stress concentration at local defects.). Under such high contact pressure, it is possible to activate different slip systems from either surface or certain internal sources simultaneously in various crystal orientations.17 

In hydrogen storage application, since there is significant volume expansion as MgMgH2, the Mg core is always under pressure.1 Our results indicate that the better plastic stability, heavier dislocation activities in smaller particles, and less orientation-dependent plastic deformation would lead to greater dislocation storage and therefore be beneficial to the volume change as well as the diffusion kinetics. In addition, the absorption/desorption process in the coherent system is triggered when the single phase is unstable with respect to the formation of the first incrementally small portion of second phase. The generation of large amount of dislocations can dissipate energy and help the phase transformation, though its impact on the thermodynamic hysteresis for the cyclic absorption/desorption needs further discussion.20 Therefore, from the mechanics point of view, the better plastic stability upon cycling and the improved kinetics can be considered to substantially contribute to the better hydrogen storage properties observed experimentally.2,4–6

This research was supported by the General Motors Research and Development Center and performed at the Molecular Foundry at Lawrence Berkeley National Laboratory, which is supported by the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.

1.
A.
Zaluska
,
L.
Zaluski
, and
J. O.
Ström-Olsen
,
Appl. Phys. A
72
,
157
(
2001
).
2.
K.-J.
Jeon
,
H. R.
Moon
,
A. M.
Ruminski
,
B.
Jiang
,
C.
Kisielowski
,
R.
Bardhan
, and
J. J.
Urban
,
Nat. Mater.
10
,
286
(
2011
).
3.
L.
Schlapbach
and
A.
Züttel
,
Nature
414
,
353
(
2001
).
4.
M.
Fichtner
,
Adv. Eng. Mater.
7
,
443
(
2005
).
5.
L.
Pasquini
,
E.
Callini
,
E.
Piscopiello
,
A.
Montone
,
M. V.
Antisari
, and
E.
Bonetti
,
Appl. Phys. Lett.
94
,
041918
(
2009
);
H.
Shao
,
Y.
Wang
,
H.
Xu
, and
X.
Li
,
Mater. Sci. Eng. B
110
,
221
(
2004
);
J.
Zheng
,
R.
Yang
,
L.
Xie
,
J.
Qu
,
Y.
Liu
, and
X.
Li
,
Adv. Mater.
22
,
1451
(
2010
).
[PubMed]
6.
C.
Zlotea
,
J.
Lu
, and
Y.
Andersson
,
J. Alloys Compd.
426
,
357
(
2006
).
7.
S.
Singh
,
S. W. H.
Eijt
,
M. W.
Zandbergen
,
W. J.
Legerstee
, and
V. L.
Svetchnikov
,
J. Alloys Compd.
441
,
344
(
2007
);
L. G.
Harrison
,
Trans. Faraday Soc.
57
,
1191
(
1961
);
R. A.
De Souza
,
M. J.
Pietrowski
,
U.
Anselmi-Tamburini
,
S.
Kim
,
Z. A.
Munir
, and
M.
Martin
,
Phys. Chem. Chem. Phys
10
,
2067
(
2008
);
[PubMed]
A.
Atkinson
,
Solid State Ionics
12
,
309
(
1984
).
8.
A.
Baldi
,
M.
Gonzalez-Silveira
,
V.
Palmisano
,
B.
Dam
, and
R.
Griessen
,
Phys. Rev. Lett.
102
,
226102
(
2009
).
9.
O.
Kraft
,
P. A.
Gruber
,
R.
Monig
, and
D.
Weygand
, in
Annual Review of Materials Research
(
Annual Reviews
,
Palo Alto
,
2010
), Vol. 40, p.
293
;
M. D.
Uchic
,
D. M.
Dimiduk
,
J. N.
Florando
, and
W. D.
Nix
,
Science
305
(
5686
),
986
(
2004
);
[PubMed]
Z.-J.
Wang
,
Q.-J.
Li
,
Z.-W.
Shan
,
J.
Li
,
J.
Sun
, and
E.
Ma
,
Appl. Phys. Lett.
100
,
071906
(
2012
);
Z.-J.
Wang
,
Z.-W.
Shan
,
J.
Li
,
J.
Sun
, and
E.
Ma
,
Acta Mater.
60
,
1368
(
2012
).
10.
D.
Mordehai
,
S.-W.
Lee
,
B.
Backes
,
D. J.
Srolovitz
,
W. D.
Nix
, and
E.
Rabkin
,
Acta Mater.
59
,
5202
(
2011
).
11.
G.
Partridge
,
Met. Rev.
12
,
169
(
1967
).
12.
S.
Phetsinorath
,
J.-x.
Zou
,
X.-q.
Zeng
,
H.-q.
Sun
, and
W.-j.
Ding
,
Trans. Nonferrous Met. Soc. China
22
,
1849
(
2012
).
13.
See supplementary material at http://dx.doi.org/10.1063/1.4921003 for detailed analysis.
14.
Z. W.
Shan
,
G.
Adesso
,
A.
Cabot
,
M. P.
Sherburne
,
S. A.
Syed Asif
,
O. L.
Warren
,
D. C.
Chrzan
,
A. M.
Minor
, and
A. P.
Alivisatos
,
Nat. Mater.
7
,
947
(
2008
).
15.
D. M.
Norfleet
,
D. M.
Dimiduk
,
S. J.
Polasik
,
M. D.
Uchic
, and
M. J.
Mills
,
Acta Mater.
56
,
2988
(
2008
);
D.
Kiener
and
A. M.
Minor
,
Nano Lett.
11
,
3816
(
2011
).
[PubMed]
16.
A.
Kelly
and
N. H.
MacMillan
,
Strong Solids
, 3rd ed. (
Clarendon
,
Oxford
,
1986
).
17.
Q.
Yu
,
L.
Qi
,
R. K.
Mishra
,
J.
Li
, and
A. M.
Minor
,
Proc. Natl. Acad. Sci. USA
110
(
33
),
13289
(
2013
).
18.
S. R.
Agnew
and
O.
Duygulu
,
Int. J. Plast.
21
(
6
),
1161
(
2005
).
19.
D.
Tromans
,
Int. J. Res. Rev. Appl. Sci.
6
(
4
),
462
(
2011
), available at http://www.arpapress.com/volumes/vol6issue4/ijrras_6_4_14.pdf.
20.
R. B.
Schwarz
and
A. G.
Khachaturyan
,
Acta Mater.
54
,
313
(
2006
).

Supplementary Material