2

Magnesium hyd ide o ene gy s o age applica ions: The kine ics o
dehyd ogena ion unde di e en wo king condi ions
An onio Pe ejóna,b,*, Ped o E. Sánchez-Jiméneza, José M. C iadoa, Luis A. Pé ez-
Maquedaa,*
aIns i u o de Ciencia de Ma e iales de Se illa (C.S.I.C.-Uni . Se illa). C. Amé ico
Vespucio 49, Se illa 41092. Spain
bDepa amen o de Química Ino gánica, Facul ad de Química, Uni e sidad de Se illa,
Se illa 41071, Spain
Abs ac
A new app oach o he kine ics o magnesium hyd ide dehyd ogena ion is conside ed. A
model able o p edic he dehyd ogena ion unde di e en expe imen al condi ions has
been p oposed. A new combined kine ic analysis me hod, which conside s he
he modynamic o he p ocess acco ding o he mic o e e sibili y p inciple, has been
used o pe o ming he kine ic analysis o da a ob ained unde di e en he mal
schedules a hyd ogen p essu es anging om high acuum up o 20 ba .
The kine ic analysis shows ha he dehyd ogena ion mechanism o magnesium hyd ide
depends on he expe imen al condi ions. Thus, he eac ion ollows a i s o de kine ics,
equi alen o an A a mi-E o ee kine ic model wi h an A ami coe icien equal o 1,
when ca ied ou unde high acuum, while a mechanism o idimensional g ow h o
nuclei p e iously o med (A3) is ollowed unde hyd ogen p essu e. An explana ion o
he change o mechanism is gi en. I has been shown ha he ac i a ion ene gy is closed
o he Mg-H bond b eaking ene gy independen ly o he hyd ogen p essu e su ounding
he sample, which sugges s ha he b eaking o his bond would be he a e limi ing s ep
o he p ocess. The eliabili y o he calcula ed kine ic pa ame e s is es ed by
compa ing simula ed and expe imen al cu es.
Keywo ds: magnesium hyd ide; hyd ogen s o age; he mal ene gy s o age; kine ic analysis;
dehyd ogena ion-hyd ogena ion eac ions; kine ic model
3

1. In oduc ion
Magnesium hyd ide is a ma e ial o he mos in e es o a numbe o echnical
applica ions, mainly as hyd ogen s o age ma e ial o PEM uel cells, due o i s la ge
e e sible s o age capaci y (7.6 mass%) o high pu i y hyd ogen [1-5], and as a he mal
ene gy s o age sys em in he mosola plan s due o he high en halpy o he
hyd ogena ion-dehyd ogena ion eac ions [6-10]. Mo eo e , magnesium has a ela i ely
high abundance in ea h. Fo any o hese wo applica ions, he kine ics o he
dehyd ogena ion-hyd ogena ion eac ions is o pa amoun impo ance. I has been
epo ed in li e a u e ha he dehyd ogena ion eac ion is a e y sensi i e p ocess ha
depends on a numbe o pa ame e s such as he mal his o y o he sample ( o example,
ac i a ion cycles o hyd ogena ion-dehyd ogena ion) [4],s uc u al de ec s in he
sample p oduced by mechanical milling [11], p esence o addi i es wi h o wi hou
ca aly ic e ec [12-16], gas p essu e [17-18], e c. Mo eo e i has been shown in
li e a u e ha he in luence o he anspo o hyd ogen h ough he Mg/MgH2 bed on
he kine ics o hyd ogena ion/dehyd ogena ion eac ions mus be conside ed when
ei he la ge o compac ed samples a e being p ocessed [18-20]. This is no he case o
his wo k, in which e y small amoun s o powde samples will be used o minimizing
he in luence o gas anspo phenomena on he o wa d eac ion.
A deep knowledge o he kine ics o abso p ion and deso p ion p ocesses in
nonca alyzed MgH2-based ma e ials is c ucial o u u e applica ions bo h as hea
s o age o hyd ogen s o age ma e ial and is o he mos in e es o be e unde s and he
beha io o milled and ca alyzed MgH2.
A e y la ge numbe o s udies o abso p ion and deso p ion o hyd ogen in MgH2 and
ela ed compounds ha e been pe o med employing ei he olume ic analysis unde
iso he mal condi ions o he mog a ime y (TG) and di e en ial scanning calo ime y
(DSC) a linea ising empe a u e unde a low o hyd ogen o an ine gas [11, 17-18,
21-28]. Howe e , in mos o he cases he hyd ogen p essu e has no been ca e ully
con olled and, p o ided ha he dehyd ogena ion o MgH2 is e e sible, he
uncon olled g adien s o hyd ogen p essu e gene a ed du ing he eac ion could lead o
un ealis ic kine ic models and alse kine ic pa ame e s. Mo eo e , in many cases he
kine ic analysis has been ca ied ou by p e iously assuming a gi en kine ic model o
i ing he expe imen al da a, bu i is known, i s ly, ha a same se o expe imen al
da a can be simul aneously i ed by a numbe o kine ic models and, secondly, ha he
4

ac i a ion ene gy is s ongly dependen on he kine ic model p e iously assumed [29-
33]. A p ope kine ic analysis o e e sible he mal decomposi ion eac ions unde a
gi en cons an p essu e o he gas sel -gene a ed in he eac ion would imply o conside
he he modynamic o he p ocess by aking in o accoun he mic o e e sibili y p inciple
[26, 30, 34-35]. On he o he hand, i would be ad isable o associa e he
mic o e e sibili y p inciple wi h me hods o kine ic analysis ha would allow
de e mining bo h he kine ic pa ame e s and he kine ic model obeyed by he eac ion
wi hou any p e ious assump ion on he kine ic model.
The objec i e o his wo k is he s udy o he dehyd ogena ion kine ics o magnesium
hyd ide a p essu es anging om high acuum up o 20 ba s o hyd ogen in o de o ge
a uni ied eac ion mechanism ha would allow p edic ing he kine ic beha io o he
dehyd ogena ion o magnesium hyd ide as a unc ion o he hyd ogen p essu e.
2. Expe imen al
Comme cially a ailable magnesium hyd ide pu chased om Ald ich (p oduc numbe
683043, wi h a e age pa icle size o 50 μm) was used o pe o ming he s udy. In all
cases, he powde s we e weigh ed inside a glo e-box, aken ou o i and immedia ely
placed in he co esponding ins umen in o de o minimize he exposi ion o he
samples o he ai .
The mog a ime ic measu emen s we e pe o med using a high sensi i i y (2 × 10-7 g)
CI Elec onics he mobalance and a as esponse u nace connec ed o a high- acuum
sys em ( o a y and u bomolecula pumps) ha is able o educe p essu e o ~5 × 10-5
mba . A se o calib a ion weigh s whe e used o calib a e he mass ou pu o he
hemobalance, while he empe a u e calib a ion was pe o med using hyd ous calcium
oxala e hea ed a 10 K min-1. The expe imen s we e pe o med a ~5 × 10-5 mba in
con en ional linea hea ing a e condi ions, a 0.2 K min-1, 0.5 K min-1 and 1 K min-1.
The s eady-s a e o he sys em was eached a e ou gassing o e nigh a oom
empe a u e and ull pumping a e. A quad upole mass spec ome e (P ism, P ei e )
was employed o pe o m he e ol ed gas analysis. A shu o al e allows ca ying ou
he expe imen s ei he unde high acuum o in a gas low. Typical sample size was ~85
mg, which was placed in alumina pan.
Di e en ial scanning calo ime y (DSC) expe imen s we e pe o med unde 10 ba and
20 ba o hyd ogen p essu e on a p essu e DSC sys em (Q20P, TA Ins umen s,
5

C awley, UK) ha p o ides hea low measu emen s on p essu e sensi i e ma e ials.
The p essu e cell employs s anda d hea lux DSC echnology and inco po a es p essu e
con ol al es, a p essu e gauge, and o e -p essu e p o ec ion. The sys em was
connec ed o a mass low con olle and a p essu e con olle in o de o ca y ou he
expe imen s unde 50 cm3 min-1 hyd ogen low and a cons an p essu e. The hea low
and empe a u e calib a ion we e ca ied ou employing s anda d sapphi e discs and
indium. The me al was hea ed h ough i s mel ing ansi ion and he calcula ed hea o
usion compa ed o he heo e ical alue. Mo eo e , he eco ded mel ing poin o his
s anda d is compa ed o he known mel ing poin and he di e ence is calcula ed o
empe a u e calib a ion. The DSC expe imen s we e ca ied ou in open alumina pans a
di e en hea ing a es, β: 1 K min-1, 2.5 K min-1, 5 K min-1 and 7.5 K min-1. Typical
sample size was ~5 mg. Be o e pe o ming he expe imen s, he sys em was ou gassed
using a o a y al e du ing 20 min, o p e en sample oxida ion. The expe imen al DSC
cu es we e no malized in such a way ha he o al a ea enclosed co esponds o ull
con e sion (i.e; α = 1). Thus, he alues o dα/dT a a gi en empe a u e a e equal o he
alue o he o dina e (y axis) a his empe a u e and he co esponding alue o dα/d is
ob ained h ough he exp ession dα/d = β(dα/dT). The α-T plo s we e ob ained by
nume ical in eg a ion o he no malized DSC plo s.
X- ay di ac ion pa e ns we e eco ded in acuum in a Philips X’Pe P o
di ac ome e wo king a 45 kV and 40 mA, using CuKα adia ion and equipped wi h
an X’Cele a o de ec o and a g aphi e di ac ed beam monoch oma o .
3. Theo e ical
The dehyd ogena ion o magnesium hyd ide akes place acco ding o he ollowing
e e sible eac ion:
←
→ (1)
Acco ding o he mic o e e sibili y p inciple, in a e e sible eac ion he mechanism in
one di ec ion is exac ly he e e se o he mechanism in he o he di ec ion. This
p inciple has been employed by di e en au ho s o s udy he in luence o p oduc gas
6

p essu e on e e sible eac ions, leading o he ollowing exp ession o he eac ion a e
[26, 30, 34-37]:


󰇛󰇜1
∗󰇛2󰇜
whe e α is he eac ed ac ion calcula ed no malizing he mass loss in
he mog a ime y o in eg a ing and no malizing he DSC cu es, A is he
p eexponen ial ac o , E he ac i a ion ene gy, (α) he kine ic model ollowed by he
eac ion, p he p essu e o he gas gene a ed in he eac ion (which is main ained
cons an in ou expe imen s) and p* is he equilib ium p essu e o he gas (hyd ogen in
ou case). I he eac ion is ca ied ou unde high acuum in such a way ha he
p essu e p is ex emely low wi h ega d o he equilib ium p essu e, he e m p/p* would
be close o ze o and equa ion (2a) becomes:


󰇛󰇜󰇛2󰇜
The equilib ium p essu e in equa ion (2a) would be de e mined as a unc ion o he
empe a u e om he Van’ Ho equa ion:
ln∗
∆
∆
󰇛3󰇜,
whe e p* is he equilib ium p essu e a he absolu e empe a u e T, p0 is he a mosphe ic
p essu e, H and S a e he en halpy and en opy o hyd ide o ma ion and R is he
uni e sal gas cons an .
3.1. Model ee me hods
F iedman isocon e sional me hod allows de e mining he ac i a ion ene gy as a
unc ion o α wi hou conside ing he kine ic model o he p ocess [38-39]. Thus,
equa ion (2a) can be ea anged in loga i hmic o m as ollows:

7


ln1
∗󰇟󰇛󰇜󰇠
󰇛4󰇜
I we a e a om equilib ium like in he expe imen s conduc ed unde high acuum we
ge om equa ion (2b):

󰇡
󰇢󰇟󰇛󰇜󰇠
 (4b)
The ac i a ion ene gy a a cons an α is calcula ed om he slope o he plo o he le -
hand side o ei he equa ion (4a) o (4b) agains he in e se o empe a u e a a gi en
alue o α.
3.2. Combined kine ic analysis
The combined kine ic analysis is a me hod o ob aining bo h he kine ic model and he
kine ic pa ame e s associa ed o a p ocess om he simul aneous analysis o a se o
da a ob ained unde di e en he mal schedules wi hou p e iously assuming nei he o
he kine ic pa ame e s o he kine ic model o he p ocess [40-41]. The modi ied Ses ak-
Be gg en equa ion, i.e. 󰇛󰇜󰇛1󰇜, has been conside ed o his pu pose.
This is because his empi ical equa ion beha es like an umb ella ha i all he kine ic
equa ions p oposed in li e a u e o desc ibing solid s a e eac ions, including de ia ions
om ideal models [40, 42-43].Thus, he equa ion o Ses ak–Be gg en simpli ies
conside ably he kine ic analysis, allowing he disc imina ion o he kine ic model in a
second s ep wi h he help o mas e plo s.
The equa ion o he combined kine ic analysis is ob ained ea anging he equa ion (2a)
in loga i hmic o m a e eplacing he (α) unc ion by he Ses ak-Be gg en equa ion:
󰇯 /
󰇛1󰇜󰇡1
∗󰇢󰇰ln󰇛󰇜
󰇛5󰇜
o
 /
󰇛1󰇜ln󰇛󰇜
󰇛5󰇜,
8

when a om equilib ium (i.e.; p/p* = 0). The se o expe imen al da a, co esponding
o di e en hea ing schedules, is subs i u ed ei he in o equa ion (5a) o (5b) and he
le -hand side o he equa ions is plo ed e sus he in e se o empe a u e. The Pea son
linea co ela ion coe icien is se as an objec i e unc ion o op imiza ion, and he
alues o he pa ame e s n and m ha p o ide he bes linea i o he plo a e
de e mined. The alues o E and ln(cA) a e calcula ed om he slope and in e cep
espec i ely.
4. Resul s and discussion
4.1. Kine ics o magnesium hyd ide dehyd ogena ion in acuum.
Figu e 1 p esen s he XRD pa e n o he as ecei ed magnesium hyd ide eco ded in
acuum a oom empe a u e in he 2θ ange om 25° o 50°. The Rie eld e inemen
o he XRD p o ile shows ha he sample is cons i u ed by a mix u e o 86% o MgH2
and 14 % o me allic magnesium. The la ice pa ame e s de e mined om he Rie eld
me hod a e a = 0.4518(4) and c = 0.3019(3) ha a e in excellen ag eemen wi h he
alues epo ed o he e agonal β-MgH2 phase acco ding o he powde di ac ion ile
JCPDS 12-0697. These esul s sugges ha he sample is cons i u ed by quasi-
s oichiome ic MgH2 and un eac ed magnesium. I is no ewo hy o poin ou ha i has
been heo e ically demons a ed in li e a u e ha he β-MgH2 phase is capable o
accommoda ing only e y small concen a ions o hyd ogen acancies ha a e mainly
isola ed a he han o ming clus e s [44]. I has been sugges ed ha he o ma ion o
non-s oichiome ic magnesium hyd ide is es ic ed o nanome ic pa icles, al hough
s uc u al e idence has no been epo ed un il now [3, 22, 45]. On he o he hand, i is
known ha , o bulk mic on sized pa icles a shell o magnesium hyd ide is o med,
which p e en s he hyd ogena ion o he emaining me al co e a e he maximum
hyd ogena ion o magnesium is achie ed [3, 45-47]. Thus, i can be conside ed ha he
pe cen age o magnesium p esen in he sample is no coming om he pa ial
decomposi ion o MgH2 du ing he s o age unde ine a mosphe e bu i co esponds o
un eac ed me al. The e o e, i is easonable o pe o m he kine ic analysis in he o e all
eac ed ac ion ange, conside ing ha α = 0 o he s a ing sample and α = 1 o he
comple ely dehyd ogena ed ma e ial.
9

Figu e 1. XRD pa e n o he as ecei ed magnesium hyd ide eco ded in acuum a oom empe a u e.
The kine ics o MgH2 dehyd ogena ion was i s s udied by he mog a ime y unde
high acuum o p e en oxida ion a he ime o app oach o ze o he a io p/p* in o de
o ob ain di ec ly he ac i a ion ene gy o he o wa d eac ion (1) om equa ion (4b)
and o pe o m he combined kine ic analysis by means o equa ion (5b). Expe imen s
we e pe o med a low hea ing a es wi h a double pu pose: i s ly, o educe he
decomposi ion empe a u es in o de o a oid Mg sublima ion and secondly, o
minimize he in luence o hea and mass ans e phenomena on he o wa d eac ion.
Figu e 2 shows he mass loss and he a e o mass loss p o iles o he he mal
dehyd ogena ion o magnesium hyd ide eco ded unde ~5 × 10-5 mba a 0.2 K min-1,
and he co esponding e olu ion o he H2 signals egis e ed by mass spec ome y as a
unc ion o empe a u e. I is clea om Figu e 2a ha hyd ogen is eleased in a single
p ocess and he mass loss is 6.5%, wha indica es ha he s a ing sample is cons i u ed
by 86% o MgH2, which con i ms he esul p e iously ob ained om he XRD analysis
by he Rie eld me hod. Figu e 2b con i ms ha H2 is e ol ed in a single s age, as
obse ed in he he mog a ime ic ace.
10

Figu e 2. (a) In eg al TG (mass loss) and di e en ial TG cu es o he he mal dehyd ogena ion o
magnesium hyd ide eco ded unde ~5 × 10-5 mba a 0.2 K min
-1. (b) Co esponding H2 signals
egis e ed by mass spec ome y as a unc ion o empe a u e.
Figu e 3 p esen s he he mog a ime ic cu es eco ded a 0.2 K min-1, 0.5 K min-1 and
1 K min-1. Mass losses ha e been no malized o u n i in o eac ed ac ions.
Ne e heless, an o e all mass loss equal o 6.5% was ob ained in he whole se o
expe imen s shown in Figu e 3. The shape o he α-T plo s included in his igu e
suppo s ha he dehyd ogena ion o MgH2 occu s h ough a single s ep. The ac ha
some au ho s ha e obse ed mo e han one s ep pe haps would be explained
conside ing he con amina ion o hei samples wi h Mg(OH)2 coming om a ce ain
hyd olysis o he hyd ide [17, 21]. Thus, he he mal decomposi ion o MgH2 and
Mg(OH)2 could be o e lapping.
The appa en ac i a ion ene gy o MgH2 dehyd ogena ion as a unc ion o he eac ed
ac ion was calcula ed by means o he F iedman isocon e sional me hod desc ibed in
sec ion 3.1, analyzing simul aneously all expe imen al cu es included in Figu e 3 a
di e en α alues by means o equa ion (4b), p o ided ha p/p* is close o ze o. In ac ,
17

Figu e 6. Tempe a u e dependence o he p essu e co ec ion e m (1-p/p*) a p essu es o 10 ba and 20
ba .
Figu e 7. No malized dα/d plo s o he dehyd ogena ion o magnesium hyd ide, calcula ed om he
DSC aces shown in igu e 5 (do ed lines). a) Hyd ogen p essu e o 10 ba s; b) hyd ogen p essu e o 20
ba s. The cu es econs uc ed using he kine ic pa ame e s ob ained om he kine ic analysis a e plo ed
as solid lines.

18

Table 2. Ac i a ion ene gy alues as a unc ion o α, ob ained om he F iedman isocon e sional analysis
o he expe imen al cu es shown in Figu e 7 wi hou accoun ing o he p essu e e m (1-p/p*).
Table 3 shows he ac i a ion ene gies ob ained by he isocon e sional me hod om he
expe imen al cu es included in Figu e 7 acco ding o equa ion (4a), namely
conside ing he p essu e e m. The ac i a ion ene gies a e easonably cons an du ing
he en i e p ocesses and, he e o e, magnesium hyd ide dehyd ogena ion unde 10 ba
and 20 ba o hyd ogen p essu e can be desc ibed as a single eac ion wi h ac i a ion
ene gies a e aging 124±7 kJ mol-1 and 127±4 kJ mol-1 espec i ely. These ac i a ion
ene gies ma ch inside he e o ange a ained. Hence, when he p essu e e m is aken
in o accoun , he ac i a ion ene gy ob ained is p ac ically cons an be ween 10 and 20
ba s and jus sligh ly highe han ha calcula ed o magnesium hyd ide
dehyd ogena ion unde high acuum.
Table 3. Ac i a ion ene gy alues as a unc ion o α, ob ained om he F iedman isocon e sional analysis
o he expe imen al cu es shown in Figu e 7 accoun ing o he p essu e e m (1-p/p*).
dehyd ogena ion a 10 ba
α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.996 0.996 0.997 0.998 0.997 0.998 0.998 0.998 0.999
E
(kJ mol-1) 226 ± 9 208 ± 8 201 ± 9 197 ± 7 195 ± 6 195 ± 6 197 ± 5 201 ± 8 208 ± 11
dehyd ogena ion a 20 ba
α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.970 0.991 0.994 0.994 0.994 0.995 0.996 0.997 0.996
E
(kJ mol-1) 292 ± 11 291 ± 9 283 ± 7 275 ± 8 268 ± 7 263 ± 6 259 ± 8 255 ± 8 252 ± 10
dehyd ogena ion a 10 ba
α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.995 0.999 0.999 0.999 0.999 0.999 0.999 0.999 0.997
E
(kJ mol-1) 131 ± 11 123 ± 6 119 ± 5 118 ± 7 118 ± 5 120 ± 5 125 ± 4 127 ± 7 135 ± 12
dehyd ogena ion a 20 ba
α 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
0.968 0.991 0.993 0.994 0.994 0.995 0.996 0.997 0.996
E
(kJ mol-1) 121 ± 7 128 ± 4 129 ± 5 127 ± 3 126 ± 3 125 ± 3 126 ± 4 128 ± 5 131 ± 8
19

The combined kine ic analysis, desc ibed in Sec ion 3.2, was applied o he cu es
egis e ed unde 10 ba and 20 ba o H2 sepa a ely. Figu e 8 shows he plo s o he le
hand side o equa ion 5a, using each se o expe imen al da a, e sus he e e se o
empe a u e. The en i e con e sion ange can be easonably i ed o he model o bo h
expe imen s unde 10 ba and 20 ba . The alues ob ained o n and m om he
op imiza ion p ocedu e a e n = 0.881 and m = 0.864 a 10 ba and n = 0.83 and m =
0.745 a 20 ba o hyd ogen p essu e. The slopes o he plo s lead o ac i a ion ene gy
alues o 124 ± 2 kJ mol−1 and 121 ± 4 kJ mol−1 o 10 ba and 20 ba , espec i ely,
while he in e cep s yield o alues o cA o 5.4 (±1.5) × 109 min−1 and 2.9 (±0.8) × 109
min−1. The alue o c canno be disc imina ed bu a combined cA is ob ained ins ead.
The ac i a ion ene gy alues a e in good ag eemen wi h hose calcula ed by he
isocon e sional analysis (Table 3), which demons a es he eliabili y o he alues
ob ained.
Figu e 8. Combined kine ic analysis plo s o he expe imen al cu es p esen ed in Figu e 7, eco ded in
10 ba and 20 ba o hyd ogen p essu e.
Compa ison wi h he heo e ical kine ic unc ions is needed o de e mine he kine ic
model ollowed by he eac ion. In igu e 9, he con e sion unc ions es ima ed by he
combined kine ic analysis a e plo ed oge he wi h he mos commonly used kine ic
models, such as nuclea ion and g ow h, i s o de and di usion. The compa ison
e idences ha he calcula ed (α) unc ions ob ained o MgH2 dehyd ogena ion unde
10 ba and 20 ba ma ch he mas e plo co esponding o he A3 A ami-E o ee
20

kine ic model. I is no ewo hy ema k ha hese esul s ha e been ob ained wi hou any
p e ious assump ion abou he kine ic models o he ac i a ion ene gies. F om a
physical poin o iew, his model implies he ins an o ma ion o idimensional nuclei
ollowed by he g ow h o hese nuclei [61].
In he same way as was done in he p e ious sec ion o MgH2 dehyd ogena ion unde
high acuum, he kine ic pa ame e s calcula ed by he kine ic analysis we e used o
econs uc ing he expe imen al cu es nume ically, in eg a ing he gene al kine ic
equa ion and conside ing he hea ing condi ions used in he di e en expe imen s. Then,
he cu es we e di e en ia ed wi h espec o ime and he esul ing dα/d cu es a e
included in Figu e 7. The kine ic pa ame e s a e alida ed by he close ma ch be ween
he simula ed dα/d -T cu es and he expe imen al ones.
Figu e 9. Compa ison o he (α) unc ions (lines) no malized a α = 0.5 co esponding o some o he
ideal kine ic models wi h he (α) unc ions esul ing om he combined analysis o MgH2
dehyd ogena ion in (a) 10 ba o hyd ogen p essu e and (b) 20 ba o hyd ogen p essu e.
21

The dehyd ogena ion mechanism is modi ied by he expe imen al condi ions in which
he expe imen s a e pe o med. Thus, a change om i s -o de d i en p ocess
(equi alen o A1) in high acuum o an A3 nuclea ion mechanism in hyd ogen p essu e
is obse ed. This change o mechanism would be explained aking in o accoun he
la ge inc ease o he decomposi ion empe a u e imposed by he equilib ium
displacemen unde hyd ogen p essu e. This no iceably inc ease o he decomposi ion
empe a u e o he hyd ide would p omo e he g ow h o he po en ial nucleus o ming
si es, un il collapsing in nuclei o idimensional shape. Thus, once ha he equilib ium
empe a u e o he dehyd ogena ion o MgH2 unde a gi en hyd ogen p essu e is
o e passed, he dehyd ogena ion eac ion akes place h ough he idimensional g ow h
o he nuclei p e iously o med.
On he o he hand, i is no ewo hy o poin ou ha he di e ence be ween he
ac i a ion ene gies ob ained unde high acuum and unde hyd ogen p essu e is only
abou a 12%. The ac ha he ac i a ion ene gy o he o wa d eac ion ob ained unde
hyd ogen p essu e ho oughly ag ee wi h he alue o 127 kJ mol-1 epo ed o he Mg-
H bond ene gy sugges s ha he b eaking o his bond is he a e limi ing s ep o
magnesium hyd ide he mal dehyd ogena ion [62]. The ex a ene gy s o ed as la ice
de ec s on he s a ing sample would accoun o he sligh ly lowe ac i a ion ene gy
ob ained o he dehyd ogena ion o MgH2 unde high acuum.
Finally, he ac ha ac i a ion ene gies closed o 120 kJ mol-1 we e de e mined o he
dehyd ogena ion kine ics unde iso he mal condi ions using as aw ma e ials MgH2
samples supplied by di e en manu ac u e s, as shown in a ecen e iew [3], would
sugges ha he Mg-H bond-b eaking could be he a e limi ing s ep o he eac ion as
we ha e p oposed. This would be ue in spi e ha di e en kine ic models we e
assumed o de e mining he ac i a ion ene gies collec ed in he Va in e al. e iew [3].
I has been demons a ed in a ecen pape ha he same ac i a ion ene gy is ob ained
om a se o iso he mal da a, wha e e would be he kine ic model p e iously assumed,
which is no ue i kine ic da a ob ained om ising empe a u e expe imen s a e
conce ned [63].
5. Conclusions
Kine ics o MgH2 dehyd ogena ion has been s udied in h ee di e en expe imen al
condi ions. The kine ic analysis has been pe o med using model- ee isocon e sional
22

analysis ha p o ides he alue o he ac i a ion ene gy as a unc ion o he eac ion
ac ion, and he combined kine ic analysis p ocedu e ha allows ob aining all he
kine ic pa ame e s a oiding any kind o assump ion abou he kine ic model obeyed by
he eac ion, and he e o e he isk o model- i ing he expe imen al da a wi h an
e oneous kine ic model. The eliabili y o he calcula ed kine ic pa ame e s has been
es ed by compa ing simula ed and expe imen al cu es.
In e es ingly, esul s ob ained show ha dehyd ogena ion mechanism o MgH2 depends
on he expe imen al condi ions used o ca y ou he eac ion. Thus, i he eac ion is
pe o med unde high acuum, i ollows a i s o de kine ics, equi alen o an A ami-
E o ee kine ic model wi h an A ami coe icien equal o 1, while a idimensional
g ow h o nuclei p e iously o med (A3) is ollowed when he expe imen is ca ied ou
unde 10 ba o 20 ba o hyd ogen p essu e. A uni ied heo y ha explains his
beha io is gi en. The ac i a ion ene gy o he eac ion is less in luenced by he
expe imen al condi ions, and he alues ob ained ag ee wi h he alue epo ed o Mg-
H bond ene gy, which sugges s ha he b eaking o his bond could be he a e limi ing
s ep o he MgH2 he mal dehyd ogena ion.
6. Acknowledgemen s
I is acknowledged he suppo om p ojec s CTQ2014-52763-C2-1-R (MINECO-
FEDER), TEP-7858 (Jun a Andalucía-FEDER) and TEP-1900 (Jun a Andalucía-
FEDER). The au ho s also hank VPPI-US o he AP cu en con ac . Addi ionally,
one o he au ho s (PESJ) is suppo ed by a Ma ie Cu ie-Jun a de Andalucía Talen ia
g an .
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