Crystal Structure Theory and Applications, 2012, 1, 100-106
http://dx.doi.org/10.4236/csta.2012.13019 Published Online December 2012 (http://www.SciRP.org/journal/csta)
Analysis of Inhomogeneities in Hydrogen Storage Alloys:
A Comparison of Different Methods
Francesco Massimino1,2
1Università degli Studi, Dipartimento di Chimica IFM, Turin, Italy
2NTT—New Tera Technology, Turin, Italy
Received October 26, 2012; revised November 22, 2012; accepted November 30, 2012
ABSTRACT
In this work we have realized a simplified model to analyze compositional inhomogeneities in commercial hydrogen
storage alloys. We have used it to evaluate the effect of the thermal annealing, together with calorimetric, PCIs and
XRD measurement. We have compared results with composition distribution histograms based on Rietveld refinement
of XRD patterns. Finally we studied the variation of α and β phases crystallographic parameters with H2 pressure.
Keywords: Hydrogen Storage; Alloys; Inhomogeneities; Sloping Plateau
1. Introduction
Pressure-Composition Isotherms (PCIs) are one of the
most informative data when performances of hydrogen
storage alloys need to be determined. Basically these
curves should be composed, at least for simple systems,
of three branches: a stiff rise at the beginning, a flat and
wide plateau central region and a second stiff rise at the
end. The first and the last part are related to hydrogen
solubility, respectively in metal and in hydride. The cen-
tral flat part is due to transition of metal into hydride
phase: as every two-phase equilibrium at a certain tem-
perature it should lay at one well-defined pressure. It is
common to obtain a sloping plateau instead of a flat one.
Many hypotheses have been proposed to explain it, in-
cluding kinetic effects and establishment of local equilib-
riums [1], microstructure and internal stresses [2] and
inhomogeneities of the alloy: Park et al. [3] proposed to
use this feature of the PCIs as a diagnostic method for
inhomogeneities.
In the following we tried to implement a simplified
and easily applicable version of this model in the analysis
of a commercial LaNi4.8Al0.2 alloy and we compared re-
sults with the ones we obtained from other adhoc ex-
periments based on Rietveld refinement of XRD pattern
of both metal powder and partially hydrided powder.
2. Experimental
Experiments have been carried on LaNi4.8Al0.2 from Pal-
can Energy Corporation and 5.0 grade hydrogen has been
used.
As-received alloy has been observed in SEM and EDS
microanalysis has been used to determine coarsely the
average composition of the alloy.
Part of the alloy has been annealed in Ar for one week
at 1000˚C.
XRD patterns of as-received and annealed alloys have
been collected both in vacuum and at different hydrogen
pressures, PCIs and calorimetric curves have been meas-
ured (see below for further details of each part).
Alloys have been activated following this general pro-
cedure for hydrogen applications:
 Preliminary coarse grinding;
 In-vacuum heating to 100˚C;
 Soak in high hydrogen pressure (15 - 50 bar depend-
ing on the apparatus used);
 Cooling down to room temperature after one hour.
This procedure has been repeated twice after each air
exposure of samples.
2.1. Pressure-Composition Curves
PCIs curves have been measured with two different ap-
paratus.
The first one is an automatic Sievert AMC Unit, used
to trace PCI curves at temperatures in the range of 25˚C -
120˚C. The instrument is equipped with an oven and a
temperature controller and provides corrections for ∆T
between hydrogen reservoir and specimen region. Hy-
drogen sorbed amounts are calculated using modified Be-
nedict-Webb-Rubin equation for real gases.
The second apparatus is a simplified version of the
first one: it consists of a manually operated high pressure
steel line, in which ideal gas law is used to evaluate hy-
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F. MASSIMINO 101
drogen sorbed amount. In this case there is no ∆T correc-
tion: it is accurate for measurement at room temperature,
but it tends to overestimate/underestimate sorbed amounts
at temperatures lower/higher than room temperature. The
same apparatus is equipped with a C80 calorimeter that
allows to measure reaction enthalpies. Pressure is meas-
ured with a capacitive transducer.
Reaction enthalpies and entropies can also be esti-
mated from Van’t Hoff equation, mathematically operat-
ing on PCI curves at different temperatures.
2.2. C80 Calorimeter
Setaram C80 DTA calorimeter is used together with the
steel high pressure line previously mentioned. The refer-
ence cell is identical to the specimen one; the two cells
are connected, so they undergo the same pressure condi-
tions. Signal has been amplified and collected through a
LabView custom interface. All measures have been done
at constant temperature, thanks to a heater and a tem-
perature controller.
A considerable quantity of sample (6 g) has been used
in experiment: in this way it was possible to observe
good S/N ratio in the thermal signal and to minimize
error in determining sorbed amount, without changing
too much hydrogen concentration in the material. In or-
der to improve reproducibility and standardization of the
measurement, a fixed cut-off has been introduced in the
thermal peak: this avoids as much as possible the effect
of thermal oscillation but it may introduce some error,
especially in measurements in the plateau region, that is
very temperature-dependent; the recovery of the initial
temperature may take a really long time due to thermal
ballast action operated by hydrides: cut-off may elimi-
nate part of the signal, but at least this error is systematic
for all measurement.
Ratio between the integral of thermal peak and the
sorbed quantity of hydrogen, that represents enthalpy of
reaction, is converging with time and someway reduces
the negative effect of the introduction of the cut-off.
Empty cell tests confirmed that heat involved with gas
expansion in and from the cell region is negligible in
those experiments.
Generally each part of the specimen is considered as it
has sorbed the same hydrogen amount at the end of each
sorption step; this fact may not be true: due to hysteresis
phenomena and really quick reaction rate, for instance,
upper part of the sample may absorb more than the lower
one and not returning hydrogen at the considered pres-
sure, causing non-homogeneities along the vertical axis.
2.3. X-Ray Diffraction
XRD has been performed with a Phillips X’pert in
Bragg-Brentano configuration, equipped with plate sam-
ple-holder or XRK900 reactive stage, with Cu X-ray tube;
XRK900 has Be windows, Ni filter has been removed in
this case to maximize signal and improve acquisition
speed.
The sample region is linked to a high pressure and
vacuum line that allows imposing a specific hydrogen
pressure. Pressure is measured with a capacitive trans-
ducer; we have estimated a pressure drop between trans-
ducer and cell of 0.5 bar in the 1 - 3 bar region due to
resistive effect of the pipes.
We have performed XRD at different fractions of the
plateau region. Measures have been executed at the same
temperature of the calorimetric one.
For each sorption step several XRD pattern has been
collected quickly (0.75˚/min) and consequently in a short
degree range (2θ = 38˚ ~ 44˚) containing the two major
peaks of α and β phases; when XRD pattern was not
changing any more, a large degree range (2θ = 25˚ ~ 75˚)
XRD patterns have been collected, also with longer ac-
quisition time (0.33˚/min).
With plate sample-holder we averaged four acquisi-
tions in an even wider range (2θ = 20˚ ~ 100˚) with
longer acquisition time (0.33˚/min).
Rietveld analysis has been accomplished using MAUD
software [4] on large XRD patterns. Instrumental broad-
ening function has been built using standard LaB6. Due
to the removal of Ni filter, also kβ has been introduced in
the Rietveld simulation for XRD pattern acquired with
reactive chamber stage.
First we have refined Rietveld simulation of a single
phase for in vacuum XRD pattern and from this step we
have obtain single phase cell parameters. Then we have
introduced in the simulation more metal phases with
slightly different Al contents. In the second case we have
kept constant B factors and microstructure parameters in
addiction to previous ones. Relative phase fraction has
been achieved from the computation.
In the case of reactive chamber XRD patterns, Riet-
veld refinement has been performed introducing two
phases, α-solution and β-hydride; Al occupancy has been
fixed to reach nominal stoichiometry of the alloy. Cell
parameters and phase ratio have been obtained from the
computation.
3. Data Treatment and Calculation
For the following calculations we needed functions de-
scribing


pl Al
px ,


Al
ax and and where

Al
cx
p
l
p is plateau pressure, a and c are cell parameters and
Al
x
is the Al content. We have described
p
l
p with
Van’t Hoff equation.
ln pl
H
S
pRT R

  (1)
so we had also to determine

Al
H
x and


Al
Sx.

F. MASSIMINO
102
We data mined in literature [5-8] and in our previous lab
measurements for these parameters and we elaborated
linear expressions for desired functions. Available data
allowed us to determine solidly

Al

H
x and


Al
Sx
for absorption process only.
Linear parameters are shown in Table 1.
Low resolution PCIs, hydrogen wt% vs.


pln , have
been fitted with a sigmoidal curve to better obtain their
derivative curve: with this assumption we hypothesize
gaussian distribution of inhomogeneities as Fujitani et al.
[9] did.
The complete expression (2) Park et al. [3] proposed
has been significantly simplified, once they have verified
the distribution character of their function.
 
ddl
lnfp nk
p





 
In this expression θ indicates H/M atom ratio, α and β
are metal and hydride phase and θα and θβ are phase
boundaries.

 

ba
ba ab
kk
k
kk kk














 


(3)
In Equation (3) kb and ka are the slopes of the


ln p 
PCI in first and last branch; because of the almost hori-
zontality of these branch in our case the numerical value
is very low and even more their difference that may be
considered zero. K(θ) is almost constant and it lowers the
value of

ln

f
p, amplifying the central values of the
distribution and narrowing the function. If K(θ) is ne-
-glected the curve obtained may result broadened propor-
tionally to the values of kb and ka in respect to the one
obtained from the full calculation.
The denominator




  assumes just a normal-
izing role and the derivative ddlnp

remains the only
fundamental factor; the normalization of the distribution
can be imposed a posteriori at the end of the data treat-
ment.
Note that the usage of H/M atom ratio is no longer re-
quired and one can choose his preferred unit, e.g. hydro-
gen wt%.
The last step was converting into
f(xAl) using
the Van’t Hoff equation and linearized

flnp



H
x and
Table 1. Cell and thermodinamic parameters vs. Al con-
tents, linearized expressions.
a c ΔH ΔS
Intercept 5.0175(8) 3.976(3) –31.10(6) –109.0(1.6)
Slope 0.0362(6) 0.0889(6)16.6(4) –9.7(3)


Sx expressions.
For what concerns the calorimetric curve, we have de-
fined an average weight percent to avoid problems cited
at the end of C80 paragraph: we have associated each
measured
H

to the mean value between current hy-
drogen wt% and the one related to previous step, that is
lower for absorption and higher for desorption.
In the multi-phase Rietveld refinement we have avoid-
ed to simulate the presence of too many phases, this
would have introduced too many degree of freedom. We
have used a maximum of five phases, fixed in Al content
and cell parameters; they have been “prepared” using the
linearized function for a(x) and c(x). The phases differ by
a constant Al
x

value and each one is representative of
a class of the same width. We have repeated the refine-
ment using a different sampling of the phase space,
namely “preparing” other phases differing 2
Al
x from
each one of the previous. After that we averaged the par-
tially superposed classes, obtaining a histogram com-
posed of classes with half broadness.
Finally in order to build a distribution based on the re-
active chamber experiments, we used hydride-metal
phase ratio obtained from the Rietveld computations and
we associated each increment in the hydride quantity to
the reached pressure. Then we converted pressure into xAl
as done in the previous. The classes obtained in this way
are not of the same wideness and cannot be used to plot a
distribution histogram: for that reason we have normal-
ized the value of each class dividing it by the class
wideness and we normalized the whole distribution a
posteriori.
4. Results
SEM imaging could not highlight inhomogeneities both
in the as-received and annealed alloy. Also EDS analysis
variability stays widely inside experimental uncertainly
and gives atomic composition of La 18.6%, Ni 78.8%
and Al 2.6%, corresponding to an Al/(Al + Ni)*5 ratio of
0.16, a bit lower than nominal one of 0.2.
XRD peaks, as shown in Figure 1, broaden for as-re-
ceived alloy: this is particularly evident for (00l) peaks.
Sharper peaks may be an index of less strained micro-
structure, as expected after annealing.
PCIs plateau flatten after annealing; PCIs of as-re-
ceived and annealed alloys cross exactly at midpoint of
plateau and hysteresis remains of the same magnitude. In
Figure 2 PCIs collected at 313 K with manual instrument
for both alloys are shown. The flattening of the plateau
after annealing is a clear clue suggesting the presence of
inhomogeneities in the received alloy.
As shown in Figure 3, reaction enthalpy, determined
with C80, is constant for the annealed alloy and it is
about 33.8 kJ/mol, while the result for the as-received
alloy is higher for first-absorbed (or last-desorbed) hy

F. MASSIMINO 103
41,0 41,5 42,0 42,545,045,5
(200)
(111)
(002)
As received
Annealed
Intensity (a.u.)
2
Figure 1. XRD peaks of as-received and annealed alloys.
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6
0,1
1
10
0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6
Annealed
As received
p (Atm)
% w
Figure 2. PCIs at 313 K of as-received and annealed alloys.
0,00 0,25 0,50 0,75 1,00 1,25
30
31
32
33
34
35
36
|H| (kJ/mol)
< % w >
As Received Annealed
Abs Abs
Des Abs
Figure 3. Calorimetric determined |∆H| at 313 K as-re-
ceived and annealed alloys; this data have been collected
contemporary to the PCIs of Figure 4.
drogen molecules and lower toward the final part of pla-
teau. High heat of reaction is related to higher Al-content.
Calorimetric curve is confirming that the modification of
PCIs after annealing is not a merely kinetic effect.
Execution of the experiment with reactive chamber
was greatly more problematic in the case of the annealed
alloy: in fact the presence of a sloping plateau allowed us
to explore more systematically the sample in the whole
central range, while the flat plateau forces the alloy to
pass abruptly from an almost pure α solid solution to a
completely hydrided material β. For this reason there is a
gathering of data to the sides of the plateau.
Figure 4 sums up the results of Rietveld refinement
coming from this experiment.
Cell volume of the α phase suddenly increases after
the first hydrogen load; α cell volume of as-received al-
loy shrinks with the rise of hydrogen pressure after the
same initial expansion. In the case of β phase, for as-re-
ceived there is a gradual increment of volume, while in
the annealed alloy it remains almost constant until a stiff
rise in the last part.
The same trend can be directly and qualitatively ob-
served from the XRD pattern; the main peaks of both
phases are shown in Figure 5 that underlines also the
high variability of (002) hydride peak in relation to the
increasing H2 pressure.
Figure 6 presents the distributions and the histograms
obtained from the various techniques previously described.
Every distribution shows a narrowing effect of the an-
nealing process. Manual and automatic PCI instrument
results are almost perfectly superposing, in particular for
as-received sample. Centers of XRK and sloping plateau
distributions coincide while the multi-phase Rietveld
refinement gives results at substantially higher xAl values.
(a)
050100
-6
-2
-1
0
1
2
 phase
% hydride phase
cell volume %
As received Annealed
Abs Abs
Des Des
(b)
Figure 1. Cell volume variation: α phase take 0 bar phase as
reference (a); β phase take 10 bar phase as reference (b).

F. MASSIMINO
104
(a)
(b)
(c)
(d)
Figure 5. Main XRD peaks of α and β phase during
the reactive chamber experiment.
5. Discussion
Almost all the analyses performed on the bought alloy
suggest that the material is not homogeneous; variations
in Al content, and consequently on Ni one, change mo-
lecular weight of the unit formula of the alloy of 33
g/mol per unitaryAl
x
: even hypothesizing a variation of
(a)
(b)
Figure 6. Distributions from various techniques: (a) histo-
grams from reactive chamber experiment, lines from slop-
ing plateau simplified model, dashed and continuous ones
come from manual and automatic instrument data respec-
tively; (b) histograms come from multi-phase Rietveld re-
finement.
0.3 on xAl it is not enough to appear with SEM imaging
or to be clearly detected with EDS micro-analysis. For
this reason we have no information about the spatial dis-
tribution of the inhomogeneities. Repeating of the PCIs
measurement on specimen taken from other parts of the
ingot brings to the same results: inhomogeneities are
substantially equally spread all over the material.
The source of inhomogeneities is still not clear, but
one hypothesis may be segregation acting on each grain
during solidification from the melt.
c cell parameter exhibits a greater dependency from
both xAl and hydrogen concentration (i.e. pressure), as
shown by the higher value of slope for linearized cxAl and
shift of the (00l) peaks. Notice that percent variation of
c(xAl) is even greater due to smaller dimension of c com-
pared to a. This relative stability of the a parameter al-
lows the growth of phases with slightly different xAl with
relative low strain, at least in some direction. As a con-
sequence XRD pattern is not so different after annealing,
expecially for (hk0) peaks.
Calorimetric measurement confirmed the presence in
the as-received alloy of Al-richer and Al-poorer fractions,
fraction that tends to the average composition after the
annealing: this fact is supported by the midpoint inter-
ception of PCIs collected both before and after annealing.
Trend of cell volume of α and β is the result of three

F. MASSIMINO 105
different phenomena:
1) H2 rising pressure increments the gas solubility in
both α and β phase, the higher is the hydrogen dissolved
in a phase the bigger is its crystalline cell;
2) In inhomogeneous alloys Al-richer fractions are re-
acting at lower H2 pressure, and the more pressure rise,
the more unreacted fraction is made of Al-poorer phases,
which are the last to transform into β phase; Al-poorer
has smaller cell parameters, so the average a and c de-
crease in both α and β phases, increasing H2 pressure for
this effect;
3) As every material, this alloy may shrink due to in-
creasing hydrostatic pressure and re-expand when pres-
sure lowers; considering the low pressures involved this
factor may be the less important, at least in the plateau
region.
Observing cell volume ε% trends one may conclude
that:
1) Effect is very strong for β phase and really low, ex-
cept for first hydrogen load, for α solid solution; this ef-
fect is basically the only one observed in the right ab-
sorption branch of annealed alloy; this difference of be-
havior may correspond to a dissimilarity in Sievert’s con-
stants;
2) Effect is present in as-received alloy for α phase but
is overcome by i. effect for β phase;
3) Effect may explain the increase of hydride cell
volume as a relaxation while pressure is lowered after a
complete hydrogen load.
There is agreement between sloping plateau model
distributions and the ones based on reactive chamber
experiments. In those cases the conversion between
and xAl is based on the same thermodynamic literature
data ΔH and ΔS. The automatic instrument curve of the
annealed alloy is a bit broadened respect to the one com-
ing from manual measurement: in the second apparatus
the time between one step and the following is extremely
longer than in the first one, due to the waiting needed to
have the calorimeter correctly settled; for this reason the
automatic measure may be influenced by some kinetic
effects and same effects propagate to the distribution
curve.
ln p
The multi-phase Rietveld distribution overestimates
average xAl. This problem seems to be intrinsic of the
method. If one tries to simulate a single phase XRD over
the same experimental data, obtained cell parameters
correspond to a correct xAl (0.17 in this case); once more
phases have been introduced, the ones with bigger cell
size gain in scale factor during the refinement and higher
<xAl> is obtained at the end of the process. Al content has
not as its only effect the increase of the cell size, but it
also changes relative heights of the XRD peaks in a
nonlinear way. According to this statement the best
agreement between experimental data and simulated
curve may be found in different conditions in the single-
phase refinement respect to the multi-phase one. Litera-
ture data come from a “single-phase library” and it may
be not so correct to use it for a multi-phase simulation.
Considering this, the only information this multi-phase
simulation is correctly furnishing is that there is an effec-
tive narrowing of the inhomogeneities distribution after
annealing.
6. Conclusions
Commercial hydrogen storage alloys may have composi-
tional inhomogeneities related to their production proc-
esses.
The simplified model we proposed seems to be a quick,
good and simple way to estimate the variations in com-
position of one element x in an alloy belonging to a sys-
tem in which the function ppl(x) is known. A low resolu-
tion PCIs is sufficient for the whole calculation. This
simplified model could be extended, with the knowledge
of more functions (e.g. ΔΗ(x) and ΔS(x)) and the avail-
ability of PCIs at different temperatures, to a more com-
plex system with three or more varying atomic species.
Three effects are acting in the variation of the crystal-
lographic parameters with H2 pressure and their trends
may be very complex.
Multi-phase Rietveld refinement is probably not a
fully trustable analytical technique with the available
data for this kind of material; however it may be an in-
teresting field into systematically inquire to build an al-
ternative data library for future studies.
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