Heat capacity and thermodynamic properties of
alkali and alkali-earth borohydrides
Erika M. Dematteis,a)# Steffen R. Jensen,b) Torben R. Jensen b) and Marcello Bariccoa)*
a)Department of Chemistry and Inter-departmental Center Nanostructured Interfaces and Surfaces
(NIS), University of Turin, Via Pietro Giuria 7, 10125 Torino, Italy
b)Department of Chemistry, Center for Materials Crystallography (CMC) and Interdisciplinary
Nanoscience Center (iNANO) Aarhus University, Langelandsgade 140, DK-8000 Aarhus C, Denmark
# Present address
Université Paris Est, ICMPE (UMR7182), CNRS, UPEC, 2-8 rue Henri Dunant, 94320 Thiais, France
*Corresponding author Marcello Baricco
E-mail address: marcello.baricco@unito.it Tel.: +39 011 6707569
Abstract
In this work, the above room temperature heat capacity for different polymorphs of alkali and alkali-earth (i.e. Na, K, Rb, Cs, Mg, Ca) borohydrides has been measured by DSC as a function of temperature. The above room temperature measured Cp values have been compared with available
extrapolated literature data, and they have been modelled as a function of temperature according to the Calphad method. The variations of Cp values for different polymorphs were studied in details
and they have been related to the corresponding crystal structures, considering the mobility of the BH4- group. From the whole set of assessed thermodynamic data, possible correlations with
dynamics and structural properties have been estimated.
Introduction
A wide variety of borohydrides and closoboranes, and their relative polymorphs, have been investigated in the past years as promising compounds for both solid-state hydrogen storage and solid-state electrolytes in batteries.[1,2] Furthermore, thermochemical energy storage systems based on metal hydrides gained great interest for having high energy densities and good reversibility.[3] Borohydrides possess a wide range of attractive properties and they were recently widely studied. [1] So, the precise knowledge of their thermodynamic properties is crucial to evaluate phase stability and to describe phase transitions in the temperature range of interest.
The heat capacity is a basic thermodynamic property for any material and its knowledge is necessary for many engineering applications. In addition, Cp experimental values are highly
desirable for a full thermodynamic description of compounds. For compounds with no available values of heat capacity, it is common to apply the Neumann–Kopp Rule (NKR)[4] which suggests that the heat capacity of a compound can be expressed by the weighted average of the heat
capacities of the constituent pure elements.
Concerning alkali borohydrides, only few values are available for the heat capacity at low
temperatures (LT), i.e. below 350 K, which were determined in the 50s,[5] while the above room temperature (HT) heat capacity was investigated only for LiBH4.[6–8] Regarding alkali-earth
borohydrides, no experimental literature data were available for Mg(BH4)2 and Ca(BH4)2. For this
reason, in this work, calorimetric measurements, performed by DSC, of molar heat capacity of various alkali and alkali-earth (i.e. Na, K, Rb, Cs, Mg, Ca) borohydrides will be reported, together with new insight on polymorphic transitions.
All alkali borohydrides show a polymorphic transition (PT).[9] Starting from CsBH4, that has the
lowest PT temperature at 26 K, than the PT can be observed in RbBH4 at 48 K, KBH4 at 77 K,
temperature,[6,10] transforming from an orthorhombic to a hexagonal structure. They all present anomalies of heat capacity through the PT.[9]
Several polymorphs are known for Mg(BH4)2 (i.e. α, β, γ, δ, ε and ζ)[11] and analogies with silica
(SiO2) have been pointed out.[12] In fact, Mg(BH4)2 structures can be described as arrangement of
tetrahedral, in which the magnesium in the centre is coordinated to four anions BH4-, similarly to Si
and O in the units SiO44- of the silicates.[13] The Mg-BH4 interaction is directional and partially
covalent.[12] The α polymorph of Mg(BH4)2, which is stable at room temperature, has a large
hexagonal unit cell and a P6122 symmetry. It can be described as constituted by MgH8 polyhedra
linearly coordinated by H2BH2 units and organized in a 3D network of five terms ring (-Mg-BH4-)n.
[11] It contains an unoccupied volume equal to 6.4% and turns into the β polymorph at around 457 K, with a polymorphic transition enthalpy (ΔHPT) reported equal to 11.3 kJ mol-1.[14,15] The β
polymorph is metastable at room temperature and less dense than α-Mg(BH4)2.[12] It displays an
orthorhombic primitive cell with symmetry Fddd, characterized by two different types of MgH8
polyhedra, coordinated by (-Mg-BH4-)n rings, for which n cannot assume odd values.[11]
α-Mg(BH4)2 also turns into the stable high-pressure polymorph δ (tetragonal, P42nm) at 1.1-1.6 GPa. [12] Wet-chemistry methods of synthesis have led to the discovery of γ-Mg(BH4)2 (cubic, Ia ´3 d).
[12] Its structure is highly porous (33% of the material volume is not occupied) and it is responsible for a high surface area (1160 m2 g-1), which makes it capable of storing hydrogen as a physisorbed
molecule[16] and to convert CO2 into chemicals.[16,17] γ-Mg(BH4)2 transforms into a
non-crystalline phase, called δ-Mg(BH4)2, between 0.4-0.9 and 2 GPa.[18] The ζ polymorph is
hexagonal with symmetry P3112. Finally, ε-Mg(BH4)2 has been observed for the first time by
Paskevicius et al.[19] in a study on the decomposition of γ-Mg(BH4)2.[19]
Ca(BH4)2 presents the polymorphs α, β and γ, which are structurally related to those of titanium
dioxide (TiO2), containing all Ca2+ ions in octahedral coordination with six BH4- groups.[12]
Although these structures might show an ionic bond, the existence of non-compact packaging polymorphs suggests a certain degree of directionality in the Ca-BH4 bond.[12] α-Ca(BH4)2 is
characterized by an orthorhombic cell, with a F2dd symmetry, and it turns into β-Ca(BH4)2, which
presents a tetragonal cell with P- ´4 symmetry, at 437 K with ΔHPT = 8.6 kJ mol-1.[14,20]. So, it is
metastable at room temperature.[21] γ-Ca(BH4)2 is orthorhombic (Pbca) as well.[22] According to
the Riktor et al.[23] study on phase transitions and decomposition of Ca(BH4)2, γ-Ca(BH4)2 should
transform into a new polymorph (δ) at high temperature. However, it was later discovered, that the δ phase is actually an oxidation product of Ca(BH4)2 at high temperature.[24]
In this work, Cp data have been obtained by calorimetric measurements, performed by DSC, as a
function of temperature for different polymorphs of various alkali and alkali-earth (i.e. Na, K, Rb, Cs, Mg, Ca) borohydrides using the height method. The same temperature program was run on the sample, the empty pan (baseline) and a reference (sapphire) on heating and cooling. It consists in linear temperature ramps, reaching different temperature at 5 K min-1 with a temperature step of 30
K and an isotherm of 20 minutes before and after each step. The above room temperature measured Cp values have been compared with available extrapolated literature data,[5,6] and they have been
modelled as a function of temperature according to the Calphad method.[25] The variations of Cp
values for different polymorphs were studied in details and they have been related to the
corresponding crystal structures, considering the mobility of the BH4- group. From the whole set of
assessed thermodynamic data, possible correlations with dynamics and structural properties have been estimated.
Experimental
Commercial sodium borohydride (NaBH4, purity 99.99% from Sigma-Aldrich, CAS 16940-66-2),
potassium borohydride (KBH4, purity 99.9% from Sigma-Aldrich, CAS 13762-51-1), rubidium
borohydride (RbBH4, purity >99% from KatChem, CAS 20346-99-0), caesium borohydride
(CsBH4, purity >99% from KatChem, CAS 19193-36-3) and α-magnesium borohydride
(α-Mg(BH4)2, purity >99% from KatChem, CAS 16903-37-0) have been used without further
chemistry, following a procedure already reported in the literature.[26,27] A brief description of the synthesis is given here in supplementation to the ref.[26,27]. Synthesis of Mg(BH4)2 was performed
by reacting n-butyl magnesium and dimethyl sulphide borane complex at room temperature (RT). The excess solvent was removed by filtration and dynamic vacuum at RT. The γ polymorph was synthesized by heating to 90 °C under dynamic vacuum for 4 hours followed by a second heating to 80 °C for 4 hours with magnetic stirring. The synthesis of α-Ca(BH4)2 was performed by reacting
ball milled CaH2 with dimethyl sulphide borane complex at 40 °C for 3 days. The solvent was
removed by filtration followed drying under dynamic vacuum at RT. The purity of the synthesized compounds was analyzed with powder X-ray diffraction (PXD) at Aarhus University using a Rigaku Smart Lab diffractometer using a Cu source and conversion beam mirror (Cu Kα1 radiation,
λ = 1.540593 Å). The measurement collected data in the 2θ range 10-80° with 3°/min using D/tex
detector. The samples were packed and sealed in borosilicate 0.5 mm capillaries, which sometimes can be detected as a halo in the diffraction patterns (e.g. for β-Ca(BH4)2 and β-Mg(BH4)2, Figure S1). The diffraction patterns of γ-Mg(BH4)2 and α-Ca(BH4)2 can be seen in Figure S1. The
diffraction pattern of the two reveal that phase pure samples have been prepared as the only polymorphs of Mg(BH4)2 and Ca(BH4)2 is γ-Mg(BH4)2 and α-Ca(BH4)2. In the γ-Mg(BH4)2 pattern
only reflections from this compound is observed, which indicate a purity >97%. For the α-Ca(BH4)2
a reflection (35.4 °) which is not originating from α-Ca(BH4)2 is observed, but this reflection is very
small and for this reason the PXD indicate a purity >97% as well. Since β polymorphs of both Mg(BH4)2 and Ca(BH4)2 are metastable,[1] thus can be stabilized at room temperature, pure β
polymorphs were obtained after thermal treatment above their polymorphic transition. Five cycles of heating and cooling at 5 K/min were performed into the HP-DSC to fully convert the α
polymorphs. Pure β phases were observed by XRD (Figure S1) after the cycling, and DSC curves show no peak of the polymorphic transition upon cycling (not shown). All preparations and manipulations of the samples were performed in an argon-filled glove box, with a circulation purifier, p(O2, H2O) < 1 ppm. Details on investigated samples are reported in Table 1.
A high-pressure 204 Netsch DSC (HP-DSC) was used to experimentally measure the heat capacities of the investigated compounds. The instrument was calibrated in temperature and heat flow using the melting enthalpy and temperature of high purity standards (Bi, CsCl, In, Sn, Zn) at the same conditions used for the experiment. The onset temperature (Tonset) and the integration of
melting peak of the standard materials during heating were calculated and compared with literature values to generate a sensitivity and temperature calibration curve. Temperature uncertainty is u(T) = 0.01 K.
The experimental determination of the molar heat capacity has been obtained with a well-defined temperature program, which consisted in several heating and cooling ramps, separated by
isotherms, used as equilibrium point and baseline. Once the temperature program was defined, three measurements have been performed. The measurement on the empty crucible worked as baseline, then a well-known heat capacity reference material was measured and, finally, the measurement was performed on the sample. The evaluation of heat capacity of investigated borohydrides was calculated by the height method, using the following formula:[28]
Cp , ms =Crefp ,m· ∆Y0+∆ Ys ∆Y0+∆ Yref ·nref ns Eq .1
where ΔY0, ΔYref, ΔYs are the height of empty crucible, reference and sample, respectively, and nref and ns are the mole numbers of the reference and sample, respectively.
Approximately 10 to 15 mg of sample were loaded into aluminium crucibles with lid. The
instrument was placed inside the glove box to ensure sample handling under inert atmosphere. The temperature program consisted in linear temperature ramps at different temperatures, at constant 0.2 MPa H2 pressure (pressure standard uncertainty u is u(P) = 10 kPa), at 5 K min-1, with a temperature
step of 30 degrees, and an isotherm of 20 minutes before and after each step (Figure S2). After the baseline subtraction to the sample and sapphire DSC signals, comparing the height of the sample signal with that of the reference (bulk sapphire in form of a disc), which as a known heat capacity,
the heat capacity of the sample has been determined. The authors verified that the use of a sapphire standard in powder form has no significant change in the measurements accuracy (not shown). According to ref. [29], The values for the molar heat capacity of sapphire (Al2O3) used as a
reference were taken from thermochemical tables [30] and calculated using the following formula:
Cp=4.1868 ·((25.48+0.00425 ·T )−682000 ·T −2)
101.961 Eq . 2
The good calibration of the instrument was validated by the calculation of the cell constant, which turned out to be within a relative uncertainty of ur(K) = 0.02 on each measurement. For this reason,
all the data reported in the results have a relative uncertainty of ur(Cp) = 0.02 (Figure S3).
Results
NaBH4
The experimental heat capacity values of cubic NaBH4 are reported in Figure 1, a and Table 2 as a
function of temperature. They are similar to the ones reported in the literature,[7,31–33] but present lower values and a different slope. It has to be noticed that the literature values were measured below room temperature, but were estimated above it, as reported in dotted and dashed lines in Figure 1, a, so they have not been experimentally determined. The NaBH4 literature estimated
above room temperature heat capacity values have been used in the literature for further estimations and calculation of heat capacity of borohydrides by the NKR for Mg(BH4)2[15] and Ca(BH4)2[34] as
described in Eq. 4.
KBH4, RbBH4 and CsBH4
Results of heat capacity measurements for KBH4,[30,32,33] RbBH4,[35] and CsBH4,[36] are
reported as a function of temperature in Table 1 and Figure 1 b, c, d, respectively. After an
increasing trend at low temperatures, an inflection towards lower values is observed for all samples, leading to a maximum value around 100 J mol-1 K-1. The heat capacity reaches a nearly constant
value at temperatures higher than 300 K.
α and γ polymorphs of Mg(BH4)2 show similar values of heat capacity, with a linear trend as a
function of temperature, as reported in Figure 2, a and Table 3. It is worth noting that it was possible to measure the heat capacity of the β phase below the PT, i.e. in metastable conditions, down to room temperature. β-Mg(BH4)2 displays also a linear behaviour, but with lower values,
compared to α and γ.
The Cp of Mg(BH4)2 was estimated by Pinatel et al.[15] using a modified Neumann-Kopp rule,
where the contribution to the heat capacity of the BH4- anion was defined as a function of
temperature as: −¿
BH4¿
¿
Cp¿
Then the heat capacity of Mg(BH4)2 has been estimated as:
BH4¿2 −¿ BH¿4 ¿ Mg(¿)=2· Cp¿ Cp¿
The assessed values by Pinatel et al.,[15] obtained by the modified Neumann-Kopp rule are also reported in Figure 2, a as dashed line, and they are comparable those α and γ phases, but with a different slope as a function of temperature.
Ca(BH4)2
The heat capacity of α-Ca(BH4)2 shows rather high values, as reported in Figure 2, b and Table 3.
A fast increase of heat capacity as a function of temperature can be observed close to the PT. This transition was reported to be of a second order type.[23] However, it was shown later[20] to be a first order transition, since the crystal structures all have a common symmetry supergroup, i.e. I4/mmm, but no order parameter can be used to describe the transitions from the α to the β
structure. Furthermore, the impact of low-energy phonons at high temperature was discovered to be the origin of a vibrational entropy driven phase transition.[20] Also the β phase of Ca(BH4)2 is
metastable below the PT temperature and it presents a linear trend of the heat capacity as a function of temperature, with a value similar to the α phase at room temperature.
The modified Neumann-Kopp rule was also used by Udovic et al.[34] to estimate the heat capacity of Ca(BH4)2, the results have been compared with the standard Neumann-Kopp rule using the heat
capacity of gaseous hydrogen, and DFT calculations. Dotted and dashed lines in Figure 2, b report the estimated values of heat capacity for Ca(BH4)2 reported by Udovic et al.,[34] obtained from
DFT calculations (dots and short dots line), Neumann-Kopp rule (short dash line) and modified Neumann-Kopp rule (dashed line). The best estimation of the heat capacity is obtained with the modified Neumann-Kopp rule, which is in a quite good agreement with obtained experimental values for the β phase.
Discussions
Parametric description of Cp
From experimental values of heat capacity reported in Figure 2, it can be generally observed that the α and γ polymorphs show an higher value of heat capacity than the β polymorph, while there is a change in the Cp value around the temperature of the polymorphic transition toward lower values
(β phase). Cp values of the β phase have a linear dependence as a function of temperature, and can
be measured down to room temperature because of the metastability of these phases. Considering a polynomial expression for the Gibbs Free Energy (GFE) as a function of temperature[25] G= A+BT +CT lnT +D T2+E T3+F T+… Eq . 5 and since Cp=−T
(
δ 2G δ T2)
p , Ni Eq . 6Cp=−C−2 DT −6 E T2−2 F
T2 +…Eq . 7
where the parameters A–F can be optimized on the basis of the available experimental or computed data.
The expressions reported in Eq. 1 and 3 are suitable for expressing the GFE and heat capacity for a limited temperature range and above the Debye temperature. At lower temperatures, a more
complex expression of GFE, based on the Einstein or Debye models for the molar heat capacity has to be considered.[25]
According to the Calphad approach, the heat capacity can be modelled by a parametric equation (Eq. 3). The number of parameters to be introduced in the equation depends on the behavior of the heat capacity as a function of temperature and it should be chosen in order to obtain a good
agreement with experimental data. For this reason, the number of assessed parameters have been selected in order to obtain a reasonable fit and the results are reported in Table 4.
The assessed expressions are reported on experimental data in Figure 1 and 2, they are valid in the limited temperature range on the basis of experimental data (i.e. from 300 to 600 K).
Starting from NaBH4, Figure 1 a, the linear behavior of the heat capacity can be easily assessed by
using a two-parameter equation (Table 4). For KBH4, RbBH4 and CsBH4, Figure 1 b, c, d, a
four-parameter equation should be used to well fit the experimental heat capacity values in the
temperature range 300-600 K, in order to describe the particular inflection that was observed (Table 4). The data can be part of a large plateau and so constant values of heat capacity seems to be the best description of the data above the experimental temperature range.
α,β-Mg(BH4)2 and β-Ca(BH4)2 have an almost linear behavior, that can be described by a two
parameters equation (Figure 2 and Table 4). In the case of α-Ca(BH4)2, a three parameters equation
should be use, to have a best fit of the rapidly growing heat capacity values towards the polymorphic transition (Table 4).
On the basis of the heat capacity fitted values, the entropy (∆S) and enthalpy (∆H) increments, namely S(T)-S(298.15 K) and H(T)-H(298.15 K), were calculated at smooth temperature intervals. Results are given in Tables 5 and 6.
Cp and mobility of the BH4- group
A collection of heat capacity values for alkali and alkali-earth borohydrides, both taken from the literature and experimentally determined, is reported as a function of temperature in Figure 4. The shape of the Cp values as a function of temperature around the PT is rather similar for investigated
compounds. It reminds a λ shape in CsBH4,[5,9,36] NaBH4,[5,7,9,31–33] LiBH4,[5–10] Ca(BH4)2
and Mg(BH4)2, suggesting a role of the BH4- anion in the structural transition across the PT. In the
case of RbBH4,[5,9,35] experimental data are not enough to well define the shape of the Cp across
the PT.
It can be observed that, in general, the Cp of borohydrides can be described as a function of
temperature by three segments. The first segment has an almost linear trend and a PT is present. Then there is an inflection or change in the slope and the last segment shows an almost constant value of Cp. Depending on the PT temperature, a shift in temperature of the inflection for the
different borohydrides is observed. The values of heat capacity for alkali-earth borohydrides are higher with respect to those of alkali borohydrides, because of the presence of two BH4- groups. The
Cp of alkaline earth borohydrides have been investigated in the temperature range related to the
segment containing the PT, showing a liner trend of the Cp.
The observed inflection in the heat capacity values as a function of temperature for KBH4, RbBH4,
and CsBH4 could be related to a continuous reorientation of the BH4- group.[33] In fact, the heat
capacity reflects the lattice dynamics, lattice expansion as a function of temperature, and it is strictly related to vibrational characteristics (transational, rotational, librational, intraionic
vibration), especially for complex anions in ionic compounds. In solids, different vibrational modes are excited consecutively as the temperature is raised, after the polymorphic transition, the
plateau of heat capacity values.[8] The rotational disorder of the BH4- complex anion is also
responsible of the first order phase transition in all studied borohydrides.[37] Structural local order-disorder transition is evidenced from the orthorhombic-to-hexagonal structure in LiBH4, and from
the tetragonal-to-cubic structure in NaBH4, KBH4, RbBH4 and CsBH4, because of the increase in the
dynamic reorientational disorder and short-range ordered arrangements of BH4-.[37] Higher
temperature of the phase transition are observed with smaller cations, because the entropic term needs to compensate energy as the lattice parameter decreases.
In the case of borohydrides, the Neumann-Kopp rule should take into account the contribution of the metal, of the boron and of hydrogen. However, since H is in a gas phase, the contribution to the heat capacity at room temperature (Cp0) of the BH4- anion was calculated by subtracting the value of
Cp of the metal from that of the borohydride at 298 K, as suggested in the modified Neumann-Kopp
rule. Table 7 reports the values of the heat capacity of the BH4- anion at room temperature for the
investigated samples. Slightly increasing values have been obtained for increasing atomic number of alkali borohydrides. Concerning alkali-earth borohydrides, α-Mg(BH4)2 shows a value similar to
that of LiBH4, but Ca(BH4)2 has values comparable with those of CsBH4 and RbBH4. The use of the
modified Neumann-Kopp equation to estimate the Cp values of borohydride might be useful in case
of unknown experimental values. However, because of the variety of crystal structures,
coordination number, temperature and type of polymorphic transition of these materials, it is not always reliable, and the calculated values should be used with care.
The temperature of the PT shows an inverse proportionality with the size of the cation.[38] The study of the heat capacity of the alkali metal borohydrides[5] showed that the polymorphic transition is related to the orientation of the BH4- anion. The temperature of the PT in alkali metal
borohydrides increases when the distance of B-B atom decreases.[8] This trend is confirmed even for alkali-earth metal borohydrides, as reported in Figure 3.[38] The correlation is related to the coordination of the cation in the high temperature polymorph structure[38] and it can be extended to Mg(BH4)2 and Ca(BH4)2. This result evidenced that the complex anion plays a role in the occurrence
of the polymorphic transition, and different rotation and reorientation of it in the crystal lattice may explain the improved ion mobility and enhanced conductivity.[5] In fact, the study and
understanding of the behavior of complex ions is aimed to assess parameters of ionic motion in lattice sites for further improvement of those compounds as solid-state electrolytes.
In conclusion, the Dulong–Petit law states the classical expression for the molar specific heat capacity of chemical elements at high temperatures.[39] The heat capacity of solids approaches a value of 3R per mole of atoms, where R is the gas constant, because full vibrational-mode degrees of freedom amount to 3 degrees of freedom per atom, each corresponding to a quadratic kinetic energy term and a quadratic potential energy term:
¿
Cp ,max=n ° ·3 R Eq . SEQ Eq . 8
Despite its simplicity, Dulong–Petit law offers good prediction for the specific heat capacity of many elementary solids with simple crystal structures at high temperatures. As a consequence, the maximum reachable value (i.e. the plateau value) of the heat capacity (Cp,max) should be close to 25 J
mol-1 K-1, multiplied for the number (n°) of atoms in the structural unit (Eq. 8).
In the case of alkali borohydrides, a total of 6 atoms are present in the compound and the plateau in the heat capacity reached in KBH4, RbBH4 and CsBH4, is approximately equal to 100 J mol-1 K-1.
Considering the metal as a vibrating unit, this result suggests that, according to the Dulong-Petit law, the BH4- anion should be considered as a “3 atoms unit”. In fact:
¿
n °=Cpmax
3 R
100
25 4 Eq . SEQ Eq . 9
Considering Ca(BH4)2, where an almost constant heat capacity value equal to 180 J
mol-1 K-1 is reached at 580 K, the contribution of the BH
4- anion can be considered as a “3 atoms
unit” as well. In fact:
¿
n °=Cpmax
3 R
180
The presence of a relative strong bond between boron and hydrogen may be related to the apparent fault of the Dulong-Petit law. In fact, the BH4- group cannot be easily considered as composed by
five independent oscillators. The presence of strong chemical bonds may induce a limitation of degrees of freedom for the oscillation of single atoms, contributing less (i.e close to half) to the heat capacity of the complex anion.
Conclusions
Experimental Cp values above room temperature for pure borohydrides have been compared with
available literature data and modelled as a function of temperature, according to the Calphad method. The Neumann-Kopp rule has been used to define the heat capacity of the borohydride anion.
Phase transitions and trends of the heat capacities as a function of temperature have been compared and could be linked to different role and dynamics of the borohydrides anion and related to the shape of the Cp across the polymorphic transition. The observed inflection in Cp could be related to
a continuous order-disorder orientation of the BH4- group and the observed plateau at 300 K, for
KBH4, RbBH4 and CsBH4, to a hindered rotation of BH4- anion. The temperature of the
polymorphic transition is related to the coordination of the BH4- anion to the metal cation in the HT
phase and its spacing (B-B distance). No further correlations have been observed suggesting a key role of crystal structure and ion coordination in the polymorphic transition mechanism.
Acknowledgement
Financial support from the European Fuel Cells and Hydrogen Joint Undertaking in the framework of the ECOSTORE (Grant agreement n° 607040) is thankfully acknowledged.
Supporting Information Description
PXD patterns of synthetized materials, example of temperature program used for measurements and calculated DSC cell constant as a function of temperature in the investigated temperature range.
Tabulated values of experimental heat capacities as a function of temperature are reported as separate file (Table S1).
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Figure 1 – Literature,[5,7,9,30–33,35,36] experimental and fitted Cp values of a) NaBH4, b) KBH4,
c) RbBH4, d) CsBH4 as a function of temperature at 0.2 MPa H2 pressure. Standard uncertainties u
are u(P) = 10 kPa, u(T) = 0.01 K, and relative uncertainty ur is ur(Cp) = 0.02, taking into account the
variation of the cell constant reported in Figure S3. Open points show experimental literature data, closed points the new experimental data from this study. The dashed and dotted lines report extrapolated calculates values from the literature, solid line the fitted values from this study.
Figure 2 – Literature, experimental and fitted Cp values of a) α,β,γ-Mg(BH4)2 and b) α,β-Ca(BH4)2
as a function of temperature at 0.2 MPa H2 pressure. Standard uncertainties u are u(P) = 10 kPa,
u(T) = 0.01 K, and relative uncertainty ur is ur(Cp) = 0.02, taking into account the variation of the
cell constant reported in Figure S3. Close points show experimental data of the α phase, while open points refer to the β phase. The dashed and dotted lines report the literature estimated values obtained from DFT calculations or the Neumann-Kopp equation. Literature data of Mg(BH4)2 from
Figure 3 – Correlation between the PT temperatures of different borohydrides [M(BH4)x, M= Li,
Na, K, Rb, Cs, Mg, Ca] as a function of the minimum B-B distance in the high temperature structure and coordination of the cation. Adapted from ref.[8].
Figure 4 – Resume of M(BH4)x (M= Li, Na, K, Rb, Cs, Mg, Ca) literature[5–10,15,30–36] and
experimental heat capacities values as a function of temperature, together with temperature of polymorphic transitions.
Table 1 – Details on all compounds used in the work.
Chemical
Name CAS Source Fraction PurityInitial Mole 1 PurificationMethod Fraction PurityFinal Mole 1 AnalysisMethod2
NaBH4 16940-66-2 Sigma-Aldrich 0.9999 None - XRD, IR
KBH4 13762-51-1 Sigma-Aldrich 0.999 None - XRD, IR RbBH4 20346-99-0 KatChem >0.99 None - XRD, IR CsBH4 19193-36-3 KatChem >0.99 None - XRD, IR -Mg(BH α 4)2 16903-37-0 KatChem >0.99 None - XRD, IR -Mg(BH γ 4)2 16903-37-0 Synthesis - Recrystallization >0.97 XRD, IR -Mg(BH β 4)2 16903-37-0 Annealing - None >0.97 XRD, IR -Ca(BH α 4)2 17068-95-0 Synthesis - Recrystallization >0.97 XRD, IR -Ca(BH β 4)2 17068-95-0 Annealing - None >0.97 XRD, IR
Argon 7440-37-1 Sapio 0.999995 None -
-Hydrogen 1333-74-0 Sapio 0.99995 None -
1no water was detected in any sample
Table 2 – Tabulated values of experimental (EXP) and fitted (FIT) heat capacities (Cp/J∙mol-1∙K-1)
as a function of temperature (T/K) at 0.2 MPa H2 pressure for NaBH4, KBH4, RbBH4, CsBH4.
Experimental data have been obtained both on heating and cooling conditions. Fitted values have been obtained using parameters listed in Table 4. Standard uncertainties u are u(P) = 10 kPa, u(T) =
0.01 K, and relative uncertainty ur is ur(Cp) = 0.02.
T Cp Cp T Cp Cp T Cp Cp T Cp Cp NaBH 4 EXP FIT KBH 4 EXP FIT RbBH 4 EXP FIT CsBH 4 EXP FIT 314 88.52 89.18 314 98.41 99.16 314 104.18 102.02 314 97.95 97.72 325 89.14 89.63 325 99.62 99.28 324 101.02 101.32 324 97.25 96.77 335 89.45 90.06 335 99.48 99.26 335 101.01 100.73 335 96.60 96.05 346 90.96 90.54 346 99.27 99.12 345 100.14 100.19 345 95.15 95.45 356 91.10 90.98 356 99.19 98.91 356 99.52 99.75 356 94.67 95.04 367 91.76 91.41 366 99.47 98.63 366 99.35 99.38 366 94.92 94.75 378 92.43 91.90 378 99.22 98.28 377 97.73 99.04 377 93.97 94.55 388 92.09 92.33 388 98.76 97.93 387 97.51 98.77 387 94.82 94.46 396 92.59 92.65 395 97.71 97.66 395 98.64 98.60 395 95.50 94.45 401 92.48 92.87 400 98.37 97.47 400 98.60 98.50 400 94.11 94.46 406 92.77 93.11 406 97.86 97.27 406 97.21 98.41 406 93.52 94.49 411 94.03 93.33 411 97.35 97.08 411 99.01 98.33 411 93.59 94.53 417 93.92 93.54 416 97.02 96.90 416 99.22 98.26 416 95.23 94.59 422 93.16 93.76 421 96.23 96.72 421 96.72 98.20 421 93.93 94.65 427 93.68 94.00 427 97.06 96.52 427 98.21 98.15 427 95.69 94.74 432 93.73 94.22 432 96.67 96.35 432 98.01 98.11 432 95.05 94.82 438 94.10 94.46 438 95.17 96.17 437 98.00 98.07 437 97.19 94.93 443 94.94 94.68 443 96.33 96.01 442 97.77 98.04 442 94.94 95.04 448 94.54 94.90 448 95.31 95.86 447 97.28 98.02 447 94.82 95.15 454 95.07 95.14 454 97.53 95.70 453 99.03 98.01 453 94.98 95.28 459 95.43 95.35 459 97.07 95.57 458 99.51 98.00 458 97.48 95.40 465 95.68 95.60 464 95.60 95.43 463 99.67 98.00 463 95.81 95.54 470 95.28 95.81 469 96.43 95.32 469 98.04 98.00 469 94.10 95.68 475 95.23 96.03 474 95.78 95.21 474 98.34 98.02 474 95.93 95.82 480 96.07 96.25 479 95.37 95.12 479 98.20 98.03 479 96.11 95.97 486 96.62 96.49 485 95.35 95.03 485 97.62 98.06 485 97.07 96.13 491 96.34 96.70 490 95.30 94.96 490 97.79 98.08 490 97.47 96.27 496 95.99 96.95 496 95.20 94.90 495 97.45 98.12 495 94.46 96.44 502 97.03 97.16 501 95.43 94.86 500 99.19 98.16 500 96.33 96.59 507 97.21 97.38 506 95.81 94.84 505 97.20 98.20 505 96.61 96.74 512 97.91 97.60 511 95.89 94.82 510 98.51 98.24 510 96.17 96.89 517 98.18 97.84 517 94.70 94.83 516 98.05 98.30 517 97.85 97.08 522 98.68 98.05 522 96.28 94.84 521 97.80 98.35 522 97.34 97.23 528 97.37 98.29 527 95.14 94.88 527 97.77 98.42 527 97.46 97.40 533 98.57 98.51 532 96.82 94.93 532 98.56 98.48 532 97.25 97.55 538 98.61 98.73 538 95.66 94.99 537 98.28 98.55 538 99.43 97.70 545 99.45 99.02 544 96.03 95.10 542 98.96 98.62 543 100.96 97.86 557 99.37 99.51 555 94.68 95.34 552 97.79 98.77 553 99.49 98.15 567 100.73 99.94 565 95.36 95.64 563 99.56 98.95 564 97.41 98.44 577 100.55 100.37 579 97.56 96.15 576 98.78 99.16 576 97.70 98.76
Table 3 – Tabulated values of experimental (EXP) and fitted (FIT) heat capacities (Cp/Jmol-1∙K-1)
as a function of temperature (T/K) at 0.2 MPa H2 pressure for α,β,γ-Mg(BH4)2 and α,β-Ca(BH4)2.
Experimental data have been obtained both on heating and cooling conditions. Fitted values have been obtained using parameters listed in Table 4. Standard uncertainties u are u(P) = 10 kPa, u(T) =
0.01 K, and relative uncertainty ur is ur(Cp) = 0.02.
T Cp Cp Cp T Cp Cp T Cp Cp T Cp Cp Mg(BH4) 2 EXP α-Mg(BH4)2 EXP γ-Mg(BH4)2 FIT β-Mg(BH4) 2 EXP FIT α-Ca(BH4) 2 EXP FIT β-Ca(BH4) 2 EXP FIT 314 131.18 135.22 129.10 305 102.32 100.75 316 165.19 162.33 306 161.23 160.41 318 128.19 132.29 130.4 3 312 103.3 5 102.2 3 321 165.7 1 164.4 0 321 162.3 2 161.5 3 324 134.68 131.71 132.2 8 317 105.1 6 103.2 9 326 167.7 8 166.4 5 332 161.9 5 162.2 7 329 132.09 134.06 133.65 320 104.79 104.02 331 169.21 168.48 355 164.32 163.96 334 139.33 133.69 135.4 0 324 105.5 1 104.7 4 337 171.5 9 170.5 6 366 164.2 9 164.8 1 339 134.66 138.31 136.7 9 327 105.7 9 105.4 6 342 173.9 6 172.7 1 375 165.4 5 165.4 6 344 142.39 139.59 138.50 331 106.93 106.35 347 176.96 175.33 386 165.94 166.20 350 137.95 141.74 140.3 1 335 106.4 9 107.0 7 351 178.9 2 176.9 5 391 164.7 6 166.5 7 354 145.69 146.63 141.5 9 338 106.6 3 107.7 9 354 179.8 6 178.6 3 396 166.3 6 166.9 4 360 140.84 144.99 143.5 0 341 107.4 7 108.5 0 358 180.8 1 180.3 8 405 167.1 1 167.6 2 364 147.11 145.84 144.6 8 346 109.1 6 109.3 9 361 182.7 0 182.1 9 409 167.2 8 167.8 7 370 144.00 149.58 146.6 3 349 107.5 9 110.1 1 364 186.4 1 184.0 8 412 167.2 3 168.1 2 379 147.61 148.02 149.2 6 352 107.2 9 110.8 2 368 186.4 2 186.0 8 419 167.6 8 168.6 1 382 147.51 150.54 150.1 5 356 109.7 8 111.5 4 371 187.1 5 188.1 4 423 168.6 9 168.8 9 389 149.38 147.1 152.3 9 360 112.2 0 112.4 3 375 192.5 3 190.7 2 427 170.0 3 169.1 8 392 150.63 156.85 153.3 2 367 115.3 5 113.8 7 379 194.8 8 193.2 9 435 169.1 1 169.8 1 402 154.27 161.08 156.4 4 370 112.9 0 114.5 8 382 197.2 9 195.7 4 439 169.0 8 170.0 6 414 159.78 162.84 160.10 374 118.37 115.42 385 199.46 198.28 442 170.06 170.30 424 163.04 177.12 163.2 6 378 120.3 6 116.1 9 389 202.0 6 200.9 7 449 169.7 5 170.8 0 385 117.05 117.61 392 204.41 203.75 453 171.41 171.08 388 118.90 118.35 396 204.54 206.69 457 171.78 171.36 393 117.22 119.23 399 212.20 209.74 466 174.66 172.04 396 119.21 119.94 403 215.06 213.96 470 175.41 172.33 403 119.78 121.36 408 220.14 218.24 474 172.21 172.63 406 126.91 122.15 411 223.10 221.77 483 175.90 173.26 410 122.69 122.86 414 225.54 225.48 488 173.57 173.60 413 122.18 123.57 418 231.35 229.31 493 171.36 173.98 421 126.26 125.18 421 234.28 233.33 502 176.75 174.62 424 128.22 125.89 424 238.90 237.45 506 173.57 174.91 428 125.36 126.61 429 245.66 242.70 510 175.22 175.21 431 125.79 127.32 519 175.84 175.89
439 132.15 128.94 525 175.55 176.29 442 132.86 129.65 529 175.98 176.61 446 129.33 130.36 537 176.07 177.20 450 131.29 131.24 542 179.49 177.52 474 136.07 136.25 547 178.48 177.88 480 136.65 137.63 556 178.59 178.60 484 137.96 138.35 561 181.12 178.89 487 137.76 139.06 565 180.05 179.19 494 141.52 140.60 581 179.04 180.38
Table 4 – Values of the parameters used for the best fit of the experimental heat capacities, at 0.2 MPa H2 pressure, of M(BH4)x (M= Li, Na, K, Rb, Cs, Mg, Ca) and relative polymorphs. Standard
errors on fitting parameters have been determined with a confidence level of 95%.
C [J mol-1 K-1] D·10 -3 [J mol-1 K-2] E·10 -6 [J mol-1 K-3] F·10 5 [J K mol-1] NaBH4 -75.80±0.04 -21.30±0.04 KBH4 -258.4±2.0 260±3 -74.9±0.9 19.85±0.31 RbBH4 -79.4±3.5 -9.27±5.32 -2.26±1.50 -7.62±0.53 CsBH4 10.6±4.1 -135±6 29.3±1.8 -20.13±0.62 , -Mg(BH α γ 4)2 -31.8±0.2 -155±0.3 -Mg(BH β 4)2 -36.8±0.2 -105±0.2 -Ca(BH α 4)2 -538.6±2.7 1282±7 -728±3 -Ca(BH β 4)2 -138.2±0.1 -36.30±0.07
Table 5 – Heat capacity and increments of enthalpy and entropies, namely ∆S=S(T)-S(298.15 K) and ∆H=H(T)-H(298.15 K), for smoothed values of temperature (T/K) at 0.2 MPa H2 pressure for
NaBH4, KBH4, RbBH4, CsBH4. Values have been obtained using parameters listed in Table 4.
Relative uncertainties ur on calculated thermodynamic functions have been determined with a
confidence level of 95%: max. values ur(Cp) = 0.15, ur(S) = 0.12, and ur(H) = 0.13.
NaBH4 KBH4 RbBH4 CsBH4
T Cp ∆S ∆H Cp ∆S ∆H Cp ∆S ∆H Cp ∆S ∆H
/K /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1 /J∙mol-1∙K-1/J∙mol-1∙K-1/J∙mol-1 /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1 /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1
320 89.4 6.3 1944 99.2 7.0 2164 101.6 7.2 2237 97.1 6.9 2147 330 89.9 9.1 2840 99.3 10.1 3156 101.0 10.4 3250 96.3 9.9 3114 340 90.3 11.7 3741 99.2 13.0 4149 100.5 13.4 4257 95.7 12.8 4074 350 90.7 14.4 4646 99.0 15.9 5140 100.0 16.3 5260 95.2 15.6 5028 360 91.1 16.9 5555 98.8 18.7 6129 99.6 19.1 6258 94.9 18.2 5979 370 91.6 19.4 6469 98.5 21.4 7116 99.2 21.8 7252 94.6 20.8 6926 380 92.0 21.9 7387 98.2 24.0 8100 99.0 24.4 8243 94.5 23.4 7872 390 92.4 24.3 8309 97.9 26.6 9080 98.7 27.0 9231 94.4 25.8 8816 400 92.8 26.6 9235 97.5 29.0 10057 98.5 29.5 10217 94.4 28.2 9761 410 93.3 28.9 10165 97.1 31.4 11030 98.3 31.9 11201 94.5 30.5 10705 420 93.7 31.2 11100 96.8 33.8 11999 98.2 34.3 12184 94.6 32.8 11651 430 94.1 33.4 12039 96.4 36.0 12965 98.1 36.6 13166 94.8 35.0 12598 440 94.5 35.5 12982 96.1 38.3 13928 98.1 38.9 14147 95.0 37.2 13546 450 95.0 37.7 13930 95.8 40.4 14887 98.0 41.1 15127 95.2 39.4 14497 460 95.4 39.8 14882 95.5 42.5 15844 98.0 43.2 16107 95.4 41.4 15450 470 95.8 41.8 15838 95.3 44.6 16798 98.0 45.3 17087 95.7 43.5 16406 480 96.2 43.8 16798 95.1 46.6 17750 98.0 47.4 18067 96.0 45.5 17364 490 96.7 45.8 17763 95.0 48.5 18701 98.1 49.4 19048 96.3 47.5 18325 500 97.1 47.8 18732 94.9 50.4 19650 98.2 51.4 20029 96.6 49.5 19289 510 97.5 49.7 19705 94.8 52.3 20598 98.2 53.4 21011 96.9 51.4 20256 520 98.0 51.6 20682 94.8 54.2 21546 98.3 55.3 21994 97.2 53.2 21226 530 98.4 53.5 21664 94.9 56.0 22495 98.5 57.1 22978 97.5 55.1 22199 540 98.8 55.3 22650 95.0 57.7 23445 98.6 59.0 23963 97.7 56.9 23175 550 99.2 57.1 23640 95.2 59.5 24396 98.7 60.8 24950 98.0 58.7 24154 560 99.7 58.9 24634 95.5 61.2 25349 98.9 62.6 25938 98.3 60.5 25136 570 100.1 60.7 25633 95.8 62.9 26305 99.1 64.3 26928 98.6 62.2 26120 580 100.5 62.4 26636 96.2 64.6 27265 99.2 66.0 27919 98.8 64.0 27107
Table 6 – Heat capacity and increments of enthalpy and entropies, namely ∆S=S(T)-S(298.15 K) and ∆H=H(T)-H(298.15 K), for smoothed values of temperature (T/K) at 0.2 MPa H2 pressure for
α,β,γ-Mg(BH4)2 and α,β-Ca(BH4)2. Values have been obtained using parameters listed in Table 4.
Relative uncertainties ur on calculated thermodynamic functions have been determined with a
confidence level of 95%: max. values ur(Cp) = 0.15, ur(S) = 0.12, and ur(H) = 0.13.
α- γ-Mg(BH4)2 β-Mg(BH4)2 α-Ca(BH4)2 β-Ca(BH4)2
T Cp ∆S ∆H Cp ∆S ∆H Cp ∆S ∆H Cp ∆S ∆H
/K /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1 /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1 /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1 /J∙mol-1∙K-1 /J∙mol-1∙K-1 /J∙mol-1
320 131.0 9.0 2788 104.0 7.2 2222 165.4 11.6 3574 161.4 11.4 3510 330 134.1 13.1 4114 106.1 10.4 3273 168.2 16.7 5241 162.2 16.3 5128 340 137.2 17.2 5470 108.2 13.6 4344 171.8 21.8 6940 162.9 21.2 6753 350 140.3 21.2 6858 110.3 16.8 5437 176.3 26.8 8680 163.6 25.9 8386 360 143.4 25.2 8276 112.4 19.9 6550 181.7 31.8 10469 164.3 30.5 10025 370 146.5 29.1 9726 114.5 23.0 7685 187.9 36.9 12316 165.1 35.1 11672 380 149.6 33.1 11206 116.6 26.1 8840 195.0 42.0 14229 165.8 39.5 13327 390 152.7 37.0 12718 118.7 29.2 10017 203.0 47.2 16219 166.5 43.8 14988 400 155.8 40.9 14260 120.8 32.2 11214 211.9 52.4 18293 167.2 48.0 16657 410 158.9 44.8 15834 122.9 35.2 12433 221.6 57.8 20459 168.0 52.1 18333 420 162.0 48.7 17438 125.0 38.2 13672 232.2 63.2 22728 168.7 56.2 20016 430 165.1 52.5 19074 127.1 41.2 14933 243.7 68.8 25107 169.4 60.2 21707 440 168.2 56.3 20740 129.2 44.1 16214 170.1 64.1 23405 450 171.3 60.2 22438 131.3 47.0 17517 170.9 67.9 25110 460 133.4 49.9 18840 171.6 71.7 26822 470 135.5 52.8 20185 172.3 75.4 28542 480 137.6 55.7 21550 173.0 79.0 30268 490 139.7 58.6 22937 173.8 82.6 32002 500 141.8 61.4 24344 174.5 86.1 33744 510 143.9 64.2 25773 175.2 89.6 35492 520 146.0 67.1 27222 176.0 93.0 37248 530 176.7 96.3 39012 540 177.4 99.6 40782 550 178.1 102.9 42560 560 178.9 106.1 44345 570 179.6 109.3 46137 580 180.3 112.4 47936
Table 7 – Heat capacity at room temperature (Cp0) values of the studied M(BH4)x (M= Li, Na, K,
Rb, Cs, Mg, Ca), of the metal and of the BH4- anion, calculated by the Neumann-Kopp rule. Red
values are the new experimental values at 0.2 MPa H2 pressure. Standard uncertainties u are u(P) =
10 kPa, u(T) = 0.01 K, and relative uncertainty ur is ur(Cp) = 0.02. While the others were already
reported in the literature.[5]
Compound Cp0 Cp0 Cp0
[J mol-1 K-1] [J mol-1 K-1] [J mol-1 K-1]
MBH4 M BH4 LiBH4 80.46 24.62 55.84 NaBH4 86.48 28.15 58.33 KBH4 96.06 29.57 66.49 RbBH4 100.30 31.03 69.27 CsBH4 97.35 29.80 67.55 α,γ-Mg(BH4)2 β-Mg(BH4)2 124.10 ± 2.5 102.31 ± 2.0 24.85 49.63 38.73 , -Ca(BH α β 4)2 161.23 ± 3.3 25.93 67.65
SUPPLEMENTARY INFORMATION
Figure S1 – PXD patterns of synthetized pure γ-Mg(BH4)2, β-Mg(BH4)2, α-Ca(BH4)2. and
β-Ca(BH4)2.Bars in the bottom are markers to index reflection positions for phase identification.
Reference XRD patterns from ICSD database (Inorganic Crystal Structure Database, NIST Stand. Ref. Database Number 3. 2019. doi:10.18434/M32147).
Figure S2 – DSC measurement of empty crucible, reference sapphire disk and sample in a selected temperature ramp between 40 °C and 70°C. Each ramp of 30 °C step was performed at 5 °C/min
Figure S3 – Calculated DSC cell constant using sapphire disk as a reference. Calculation performed both on heating and cooling. Relative uncertainties ur on cell constant value turns out to be equal to
ur(K) = 0.02.
Table S1 – Tabulated values of experimental heat capacities as a function of temperature at 0.2 MPa H2 pressure. Standard uncertainties u are u(P) = 10 kPa, u(T) = 0.01 K, and relative
