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Thermal desorption spectra of hydrogen from the bulk: ZrV2Hx
0038-1098/81/440837-05502 00/0
Sohd State Commumcataons, Vol 40, pp 837-841 Pergamon Press Ltd 1981 Printed m Great Britain
THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2Hx* A Stern, S R Kreltzman, A Resmk, D Shaltlel and V Zevm Center of Energy and the Racah Institute of Physics, The Hebrew Umverslty of Jerusalem, Jerusalem, 91904, Israel
(Recen,ed 30July 1981 by A R Mtedema) Thermal desorpUon of hydrogen from the bulk of the system ZrV2Hx, 0 3 <~x ~< 4 27, shows spectra which develop from a single peak, f o r x < 1, to a spectrum that consasts of 3 peaks and a shoulder for x ~< 4 27 A model is proposed to explain the ongm of these peaks and relates them to a consequaUve desorptaon of the hydrogens from the different mterstmal rues, m agreement wath neutron daffracUon data on the rues' occupancy However, neutron diffraction mdxcates that up to x ~ 2 5 the hydrogens occupy the tetrahedral sites formed by 2 Zr and 2 V, nevertheless our results show that there is a large difference m the bonding energy of these sites for hydrogens with x < 1 and hydrogens with 1 < x < 2 5 1 INTRODUCTION
2 EXPERIMENTAL
THERMAL DESORFrlON SPECTRA (TDS) is a techtuque where the gas adsorbed on a metal surface is released into a very low external pressure (10-Ttorr) whale the temperature is increased hnearly The pressure as a funcUon of temperature gwes a spectrum wluch is related to the bonding energaes and to the occupatton of the surface sites A review on surface physics of hydrogen on metal including TDS ts found m [1] Thas teehmque may also be apphed to the desorptlon of hydrogen from the metal bulk [2], but here the external pressure Is a few orders of magmtude tugher (~ I torr), but nevertheless low compared to the equfllbrmm pressures We have used this techmque for the ZrV2H x system (0.3 ~< x ~< 4 27) and measured its thermal desorptlon spectra for various mxtaal concentrattons The hydride of ZrV2 has been extenswely mvestagated with regard to thermodynamics [3], the different kind of hydrogen mtersUtaal sites [4], their occupation [5, 6] and daffuslon [7] Therefore one can correlate our results to other data and use the ZrV2 as a suxtable compound for thts newly developed techmque It wxll be shown that the spectrum reflects the denvaUve dx]dls, where/a is the chemical potentaal of the hydrogen m the bulk Peaks m the spectrum can be correlated with the filling of the various sites, that differ either m symmetry or m bonding energies Tlus techmque, by its use of derivative, ~s sensitive to minor changes m the chemical potential, and are therefore difficult to detect by other techmques
The compound ZrV2 was prepared by melting the Zr and the V (both of purity 3N supphed by Lelco Inc ) m an arc furnace m argon atmosphere X-ray analysis showed that the samples consast mainly (above 90%) of the C15 cubic Laves phase The hydrogenataon was done m a reactor made of 5 mm O D quartz tubes m which the sample, m a form of powder, was first heated to ~ 900°C under a rotataon pump vacuum Then the hydrogen (99 995%, Matheson, prod ) was introduced at pressures ~ 1 - 3 0 at and cooled slowly to room temperature m 2 h The amount of hydrogen absorbed was calculated by the pressure drop wluch was measured by a Setra pressure transducer gauge The error m the amount of absorbed hydrogen is estamated to be + 5% The sine of the particles m the powder after a few mltlal absorptlon-desorptlon cycles was between 10 and 100/am The desorptaon was done m the same apparatus The desorptlon spectra were recorded on an x - y recorder The y-axas recorded the lower pressure ( 0 - 2 torr) m the tube leading to a rotataon pump The low pressure was measured by a prectslon dafferentlal pressure gauge (Vahdyne 0 7 cm H20 full range) with sensmvaty of 10 -3 torr The x-axas recorded the temperature wluch was measured by a chromel-alumel thermocouple The thermocouple was mounted outside the quartz reactor m the same posllaon with regard to the heater as the sample Tlus was done m order to mmxmlze the temperature differences between the sample and the thermocouple By inserting the thermocouple reside the reactor, it was found that the temperature chfference is 10°C when the temperature is larger than 300°C, or when the hydrogen gas pressure is larger than 0 2 torr Otherwxse, larger temperature differences up to 90°C were observed But, as seen from Fig 1 (see below) the
* Partially supported by the Hebrew Umverslty Research Center for Hydrogen and Redox Fuels Synthesis, Utdlzatlon and Storage
837
THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV:H x Vol 40, No 8
838
T i m e (x 4 7 se¢) 0
i
2
3
414
4
~
5
6
•
8
£
i0
ii
12 i~ 14
~
~ >~
'~
411 0
4 27~
o
I00
200
300
4 Jo
500
600
700
800
900
Temperature (C)
Fig 1 The desorptlon spectra for various initial concentrations which are denoted by the numbers beside each spectrum The graphs were plotted as a function of temperature (lower horizontal scale) and time (upper scale) The pressure units on the left scale are approximately 1 torr The pressure is proportional to -- dx/dt which is also approximately proportional to -- dx/dT The proportion factor was derived by mtegratlon and was used for calculating the scales on the right side difference between the measured and the sample temperatures could affect only the onset of desorption when the pressure is less than 0 2 torr An almost linear increase in temperature was achieved by applymg a constant voltage to the heater 3 EXPERIMENTAL RESULTS The spectra for the samples with initial hydrogen content of 0 3 ~
Fig 2 The Fnauf polyhedron, formed by 12 V atoms, around the Zr atom at the center Also shown, 3 of its 4 nearest nelghbours Zr atoms which are situated opposite the hexagonal faces outside the polyhedron Also shown, 18 of the 24 ( 2 - 2 ) hydrogen tetrahedral sites which are located on the hexagonal faces 4 DISCUSSION The ZrV2Hx system has either the cubic C15 or hexagonal C14 Laves-phase structures In both structures, each Zr atom Is surrounded by 12 V atoms at the corners of a Fnauf polyhedron which has four triangular faces and four hexagonal ones, as illustrated m Fig 2 The hydrogens are located m tetrahedral mterstltlal sites There are 17 tetrahedra per ZrV2 unit, where 12 tetrahedra are composed of 2 Zr and 2 V atoms (type 2 - 2 ) , 4 tetrahedra are composed of 3 V and 1 Zr (type 3 - 1 ) and 1 tetrahedron is composed of 4 V atoms (type 4 - 0 ) The ( 2 - 2 ) sites are located on the hexagonal faces of the Fnauf polyhedron (see Fag 2), and the ( 3 - 1 ) sites are located mslde the Frlauf polyhedron m the tetrahedra formed by its tnangular faces and the Zr m the center The ( 4 - 0 ) sites are situated outside the polyhedron oppomte its triangular faces Pressure-composlUon isotherms [3] show that the ZrV2Hx forms an homogeneous system m which no phase separation occurs at room temperature and above Neutron diffraction data for the deutrlde [5] show that at room temperature the ( 2 - 2 ) site is the only occupied one up to x ~ 2 5 At x ~ 2 5 the occupancy of the ( 3 - 1 ) site starts to budd up while that of the ( 2 - 2 ) site increases more slowly for x > 2 5 For higher D concentration it was found recently [6] that ZrV2D36 undergoes a structural phase transition at ~ 325 K The tugher temperature phase is cubic and the low temperature phase is tetragonal, in which the 12 ( 2 - 2 ) are no longer equivalent The D atoms in the low temperature phase are ordered and occupy only a partial set of 4 ( 2 - 2 ) sites which are no longer equivalent to the other ( 2 - 2 ) sites because of the change m symmetry We shall present in the next section a tentative model m which the peaks are budt up by hydrogens desorbmg from the various sites which differ with their
Vol 40, No 8 THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2Hx bonding eneqpes, the larger the bonding energy, the higher the positron of the peak m temperature From this model we suggest the following pmture winch correlates with the above experimental data [4-6] We shall assume slmdar behavmur for the hydride and deutnde For x < 2 5 the hydrogens occupy only the ( 2 - 2 ) sites m which the main contnbutmn for the bonding energy comes from the Z r - H bond For x < 1 there is less than one hydrogen atom per Zr atom or per each polyhedron When x > 1 the excess hydrogen wall have to share Zr atoms with another H atom, thereby reducing the bonding energms of both hydrogen This may be described m the framework of the Rees model [9] by a formataon of a new kind of sites out of the ( 2 - 2 ) sites that were mmally equwalent, and the existence of a stable ZrV2HI phase The amount of hydrogen desorbed under the fully developed first peak is about x = 1 We therefore assocmte the hydrogens desorbed under this peak as those singularly assocmted wxth each polyhedron and therefore have stronger bondmg energy and are desorbed at the highest temperatures The hydrogens desorbed under the second peak are associated with these excess hydrogen atoms (x > 1) which have weaker bonds m the ( 2 - 2 ) sites The third peak is assocmted with hydrogens desorbed when the ( 3 - 1 ) sites are also occupied Fmally, it seems that the appearance of the tlurd shoulder can be correlated to the order-&sorder phase transataon wtuch appears at high H concentratmns [6] 5 OUTLINES FOR A MODEL AND CONCLUSIONS We shall describe a tentatave model whtch can explain the ongm of the peaks m the spectra and relates them to various sites, their occupancies and energms A more detatled work is now under progress The kmetm of desorptmn Is composed of at least two steps [10] I Dfffusmn from the bulk sites to the surface sites II Recombmahon of 2 protons at the surface and the release of a hydrogen molecule In our case it is step II that is the rate deterrmnmg as we shall show below An upper hmlt for the maximum vanatmn of the concentratmn m the bulk, Ax, can be obtained through AX
=
rde
c
--
ax =
6D
dt
ax'
where Zdee lS an approximate decay time for the &ffusmn process [11], (-- d x / d t ) m a x is the maximum rate of concentratmn change obtained from the expenment, L is the hnear dlmensmn of the partmles and D is the dfffusmn constant. Taking D ~ 10 -s cm 2see -~ [11 ], (-- d x / d t ) m a ~ ~ 10 -2 H atoms/ZrV2- see and L ~ 5 x 10-3 cm, one obtains Ax ~ 0 001H atoms/ZrV2
839
H-I
>, or, o~
o~ Es E2
EI Surface
Gas
Dlsfance
Bulk from
surface
Fig 3 Schematm potentaal energy chagram of the hydrogen atom between the gas phase and the bulk el and e2 are the lowest energy levels m the bulk sites, e s is the level of the surface site and e. is the lowest energy level in the excited state whtch is located m a saddle point (EssentlaUy these levels are higher - by ½heo in the case of the parabohc potential well - than the bottom of the appropriate well ) Ea = ea -- e, is the actlvaUon energy, and Ea Is half of the dassoclatlon energy of the H2 molecule (~ 2 2 eV) which ts small compared to the x range Therefore, we assume an equfllbrmm of the hydrogen throughout the bulk and step II is rate deternunmg The potential energy of the hydrogen near the surface is described schematlcaUy m Fig 3, where E. is the actwataon energy for the recombination process H + H -* H2 The rate equation for tlus process can be written [8] d'x s dt - v ° ~
^-E/k
T.
a
2
(2)
xs,
where x s = N J M s for N s hydrogens m Ms surface sxtes, k ~s the Boltzman factor and Vo Is some attempt frequency taken to include entropy contnbutmn Vo is temperature dependent [8, 12, 13] when the spacing, hw between the energy levels at the surface s~te is much greater than k T This temperature dependence (oc T) is Irrelevant for our purposes On the case hco .~ k T , Vo does not depend on T) [12] d'N = Msd'x is the change m N s due to recombmatmn process alone, therefore d'N = d(N + Ns) where N is the number of hydrogens m the bulk Then we obtain d,xs _
d ' Ns _ Ms
d ( N + N s ) ~- dN _ Ms
Ms
M
dx,
17Ms
where M is the number of bulk sites (x = 17 . N / M ) Then dx __ __ -Ea/k T 2 dt = ve xs,
(3)
840 v -
THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2H x 17M s Uo
(3a)
M
The chemical potential/.t as equal throughout the bulk and will also determine the occupancy x s o f the surface sates by the latrine gas formula [13]
:
-o
"~
-6
e~-es)lkT xs -
1 + e Oa-es)lkT
(4)
where e s is the lowest energy level o f the proton m the surface site and we neglect excited states Let us now analyze the consequences o f the rate equation (3) Generally speaking, it predicts a curve which is exponentmlly zero at low temperature and goes to zero at htgh temperatures when all the hydrogens have desorbed and x , -+ 0 (see also [8]) In order to understand the shape o f the curve and the temperature regmns where it nses, we consider two extreme situations almost fully occupied, x . ~ 1 and the spectra will be deterrmned only b y the acttvatmn energy E a Substltutmg xs = 1 and taking the logarithm o f equation (4), we obtain In
{/( v
E
A:: 0
,, x r
x
,
dx/d/~
Fig 4 (a) Schematic diagram o f the chemical potentmls ta(x, Ta), #(x, Tz) where T1 < / ' 2 for two-sites system, where e l , e2 are the lowest energy level o f the sites and x, are the corresponding stolctuometnc concentratmns (b) The derivative d x / d # ~ (3x/a/~)r (see text)
2p ~ - - c o n s t ' T + E -
,,x%
Concentration,
order o f magnitude as an the bulk where It was found to be [7] vo ~ 101Ssec -1 Using the above values an equatmn (3a) to calculate v we obtain from equatmn (5) that E ~ / T vanes between 25 and 26, thus essentmlly constant Therefore
I # -- e s > 2 k T m this case the surface sites are
--& kT
Vol 40, No 8
(5)
A condltmn for the onset o f desorptlon will be taken as -- d x / d t > 10 -a H atom/ZrV~ see Therefore, equatmn (5) predicts a fixed onset temperature gwen by kTo = & / l n [u/(10 -a sec -1)] independent o f initial concentration This kind o f behavlour may be found for spectra (Fig 1) wathx0 ~> 3 5 where To ~ 100°C and where the onset o f desorptmn is the same for x0 between 4 27 and 3 5 II ~ { e, (or even # < e, where the following conclusmns stall stand to a good approxamatmn) This happens when the surface sates are dflutely occupied, and xs ~ e ~u-es)/kT, which after substltutmn in equation (3), and taking the logarithm, we get again equation (5) where E~ is replaced b y an effective activation energy E~ = E a + 2e, - - 2ta that depends on ts Unhke the previous case hme the onset temperature To depends on the mltml concentrations Xo through/a I n m e a s m g x o increases/~ and decreases E~ and To This b e h a ~ o u r is found for the spectra with Xo < 3 A simple interpretation for the ongm o f peaks can be obtained m case II Consider one of the spectra for xo between 0 62 and 3 0 Except for the beginning and the end o f the spectrum, -- d x / d t varies between 3 x i 0 -a and 9 x 10-3H atoms/ZrV2sec F r o m the size o f the partmles we estimate 17(Ms/M) ~ 10 -6 vo which as defined for a surface site is assumed to be o f the same
a+2%
(6)
This conclusmn stands even if errors were made an the estlmatmns o f v as long as In [v/(-- d x / d t ) ] >> 1 It is a consequence of the form of the rate equation (2) an which the term an the exponent E ~ / T dominates the desorptlon Equation (6) gives also d# cx -- dT and therefore dx
-----
dT
cc
dx -
(7)
-
d#
We conclude that, in a case o f a ddute surface, the desorptlon spectra samply reflect the reciprocal o f the denvatwe o f the chermcal potentml with regard to hydrogen concentration Therefore the mamma appear when the change m/a is small and the maxima when the change in p is large There are few models which calculate the chemical potential for a multaslte system [9, 14] Following the ideas o f these papers we may wnte the chemical potential o f the hydrogen in the tth well in the following simplified form (see also [13]) la, = k T l n
n,
+e,,
(8)
1 --n,
where n, = N,/M, as the occupaUon o f the lth type o f sites, e, as ats lowest energy level and 34, as the number o f these sites For the case o f two types of sates with equal M z we
Vol 40, No 8 THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2Hx
Acknowledgements - We wish to thank W Kohn for a helpful discussion and A Grayevsky for tus technical assistance
obtain that n2 = 2n -- nl and nl is the root of the equation +l - - 2n) (1 -- n 1)(2n --nl)
In nl(nl
_
841
e 2 -- e 1
kT
(9)
where n = (N1 + N2)/(M1 + M:) The last equation is the consequence of the equality of the chermcal potentials/al =/z2 A schematic plot of the chermcal potential vs x on the base of equations (8) and (9) for the case (e2 -- el)/kT>> 1 is presented in Fig 4 It is easy to see that m this case nl "" 2n when n < ½and nl ~-- 1, n2 = 2n -- n i when n > 12,i e only when site 1 is filled site 2 begins to be occupied The derivative (aX/~IZ)T wtuch was plotted in the right side of Fig 4 demonstrates a spectrum where the maxima occur when the sites are half-full, and the nummum occurs at the transition between the two sites, when the first one is almost full and the seond is all but empty Since/~ = T the position of the maxima in temperature wall be proportional to e, In the ZrV2H x case we have both, sites with chfferent symmetry, and sites that have the same symmetry but their bonding energies are different 0 e sites ( 2 - 2 ) occupied by hydrogens with x < 1 and sites ( 2 - 2 ) occupied by x > 1) The above picture presents an ideal situation In reahty one has to introduce corrections due to the following
REFERENCES 1
2 3
4 5 6 7 8 9 10 11
(a) An interactaon between the hydrogens must be taken into account, 1 e e I : e ~ ( x ) (b) dla/dx = (OI~/aX)T + (aMaT)~dT/dx The second additive can be neglected during the desorptlon
12
The combined result of all these corrections smooths the transition between the sites and broadens the peaks Efforts to verify these conclusions, experimentally by equilibrium measurement of the chermcal potential, and theoretically by numencal calculations based on a statistical model, are in progress now
14
13
R Burch, Chemical Physics o f Sohds and their Surfaces (Reported by W A Roberts & J M Thomas), Vol 8. The Royal Society of Chermstry, Burlington House, London (1980) M H Mendelsohn & D M Gruen, Miami lnt Symp on Metal Hydrogen Systems, p 62 (April 1981) A Pebler & E A Gulbransen, Tranz Met Soc AIME 239, 1594 (1967), H W Newkark, A Literature Survey o f Metalhc Ternary and Quaternary Hydrides, UCRL-51244 (1974) D P Shoemaker & C B Shoemaker, J Less Common Met 68, 43 (1979) J J Dldlshelm, K Yvon, P Fischer & D Shaltlel, J Less CommonMet 73,355 (1980) J J I:hdlshelm, K Yvon, P Fischer & P Tlssot, Sohd State Commun 38,637 (1981) J Shlnar, Ph D Thesis, The Hebrew University of Jerusalem (1981) AW Srmth&S Aranoff, J Phys Chem 62, 684 (1958) A L G Rees, Trans Faraday Soc 50, 335 (1954) C Wagner, Z Phystk Chem A159, 459 (1932) J V o l k l & G Alefeld, ToptcstnApphedPhystcs, Vol 28, Hydrogen m Metals I, Chapter 12 Springer Verlag, Berhn-Heidelberg-New York (1978) K W Kehr, Topics in Apphed Physws, Vol 28, Hydrogen in Metals L Chapter 8 Spnnger Verlag, Berlin-Heidelberg-New York (1978) T L Hall, An Introduction to StattstTcal Thermodynamws Addison-Wesley, New York (1961) H A Klerstead, J Less Common Metals 71,303 (1980), H A Kxerstead,J Less Common Metals 75,267 (1980)
Sohd State Commumcataons, Vol 40, pp 837-841 Pergamon Press Ltd 1981 Printed m Great Britain
THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2Hx* A Stern, S R Kreltzman, A Resmk, D Shaltlel and V Zevm Center of Energy and the Racah Institute of Physics, The Hebrew Umverslty of Jerusalem, Jerusalem, 91904, Israel
(Recen,ed 30July 1981 by A R Mtedema) Thermal desorpUon of hydrogen from the bulk of the system ZrV2Hx, 0 3 <~x ~< 4 27, shows spectra which develop from a single peak, f o r x < 1, to a spectrum that consasts of 3 peaks and a shoulder for x ~< 4 27 A model is proposed to explain the ongm of these peaks and relates them to a consequaUve desorptaon of the hydrogens from the different mterstmal rues, m agreement wath neutron daffracUon data on the rues' occupancy However, neutron diffraction mdxcates that up to x ~ 2 5 the hydrogens occupy the tetrahedral sites formed by 2 Zr and 2 V, nevertheless our results show that there is a large difference m the bonding energy of these sites for hydrogens with x < 1 and hydrogens with 1 < x < 2 5 1 INTRODUCTION
2 EXPERIMENTAL
THERMAL DESORFrlON SPECTRA (TDS) is a techtuque where the gas adsorbed on a metal surface is released into a very low external pressure (10-Ttorr) whale the temperature is increased hnearly The pressure as a funcUon of temperature gwes a spectrum wluch is related to the bonding energaes and to the occupatton of the surface sites A review on surface physics of hydrogen on metal including TDS ts found m [1] Thas teehmque may also be apphed to the desorptlon of hydrogen from the metal bulk [2], but here the external pressure Is a few orders of magmtude tugher (~ I torr), but nevertheless low compared to the equfllbrmm pressures We have used this techmque for the ZrV2H x system (0.3 ~< x ~< 4 27) and measured its thermal desorptlon spectra for various mxtaal concentrattons The hydride of ZrV2 has been extenswely mvestagated with regard to thermodynamics [3], the different kind of hydrogen mtersUtaal sites [4], their occupation [5, 6] and daffuslon [7] Therefore one can correlate our results to other data and use the ZrV2 as a suxtable compound for thts newly developed techmque It wxll be shown that the spectrum reflects the denvaUve dx]dls, where/a is the chemical potentaal of the hydrogen m the bulk Peaks m the spectrum can be correlated with the filling of the various sites, that differ either m symmetry or m bonding energies Tlus techmque, by its use of derivative, ~s sensitive to minor changes m the chemical potential, and are therefore difficult to detect by other techmques
The compound ZrV2 was prepared by melting the Zr and the V (both of purity 3N supphed by Lelco Inc ) m an arc furnace m argon atmosphere X-ray analysis showed that the samples consast mainly (above 90%) of the C15 cubic Laves phase The hydrogenataon was done m a reactor made of 5 mm O D quartz tubes m which the sample, m a form of powder, was first heated to ~ 900°C under a rotataon pump vacuum Then the hydrogen (99 995%, Matheson, prod ) was introduced at pressures ~ 1 - 3 0 at and cooled slowly to room temperature m 2 h The amount of hydrogen absorbed was calculated by the pressure drop wluch was measured by a Setra pressure transducer gauge The error m the amount of absorbed hydrogen is estamated to be + 5% The sine of the particles m the powder after a few mltlal absorptlon-desorptlon cycles was between 10 and 100/am The desorptaon was done m the same apparatus The desorptlon spectra were recorded on an x - y recorder The y-axas recorded the lower pressure ( 0 - 2 torr) m the tube leading to a rotataon pump The low pressure was measured by a prectslon dafferentlal pressure gauge (Vahdyne 0 7 cm H20 full range) with sensmvaty of 10 -3 torr The x-axas recorded the temperature wluch was measured by a chromel-alumel thermocouple The thermocouple was mounted outside the quartz reactor m the same posllaon with regard to the heater as the sample Tlus was done m order to mmxmlze the temperature differences between the sample and the thermocouple By inserting the thermocouple reside the reactor, it was found that the temperature chfference is 10°C when the temperature is larger than 300°C, or when the hydrogen gas pressure is larger than 0 2 torr Otherwxse, larger temperature differences up to 90°C were observed But, as seen from Fig 1 (see below) the
* Partially supported by the Hebrew Umverslty Research Center for Hydrogen and Redox Fuels Synthesis, Utdlzatlon and Storage
837
THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV:H x Vol 40, No 8
838
T i m e (x 4 7 se¢) 0
i
2
3
414
4
~
5
6
•
8
£
i0
ii
12 i~ 14
~
~ >~
'~
411 0
4 27~
o
I00
200
300
4 Jo
500
600
700
800
900
Temperature (C)
Fig 1 The desorptlon spectra for various initial concentrations which are denoted by the numbers beside each spectrum The graphs were plotted as a function of temperature (lower horizontal scale) and time (upper scale) The pressure units on the left scale are approximately 1 torr The pressure is proportional to -- dx/dt which is also approximately proportional to -- dx/dT The proportion factor was derived by mtegratlon and was used for calculating the scales on the right side difference between the measured and the sample temperatures could affect only the onset of desorption when the pressure is less than 0 2 torr An almost linear increase in temperature was achieved by applymg a constant voltage to the heater 3 EXPERIMENTAL RESULTS The spectra for the samples with initial hydrogen content of 0 3 ~
Fig 2 The Fnauf polyhedron, formed by 12 V atoms, around the Zr atom at the center Also shown, 3 of its 4 nearest nelghbours Zr atoms which are situated opposite the hexagonal faces outside the polyhedron Also shown, 18 of the 24 ( 2 - 2 ) hydrogen tetrahedral sites which are located on the hexagonal faces 4 DISCUSSION The ZrV2Hx system has either the cubic C15 or hexagonal C14 Laves-phase structures In both structures, each Zr atom Is surrounded by 12 V atoms at the corners of a Fnauf polyhedron which has four triangular faces and four hexagonal ones, as illustrated m Fig 2 The hydrogens are located m tetrahedral mterstltlal sites There are 17 tetrahedra per ZrV2 unit, where 12 tetrahedra are composed of 2 Zr and 2 V atoms (type 2 - 2 ) , 4 tetrahedra are composed of 3 V and 1 Zr (type 3 - 1 ) and 1 tetrahedron is composed of 4 V atoms (type 4 - 0 ) The ( 2 - 2 ) sites are located on the hexagonal faces of the Fnauf polyhedron (see Fag 2), and the ( 3 - 1 ) sites are located mslde the Frlauf polyhedron m the tetrahedra formed by its tnangular faces and the Zr m the center The ( 4 - 0 ) sites are situated outside the polyhedron oppomte its triangular faces Pressure-composlUon isotherms [3] show that the ZrV2Hx forms an homogeneous system m which no phase separation occurs at room temperature and above Neutron diffraction data for the deutrlde [5] show that at room temperature the ( 2 - 2 ) site is the only occupied one up to x ~ 2 5 At x ~ 2 5 the occupancy of the ( 3 - 1 ) site starts to budd up while that of the ( 2 - 2 ) site increases more slowly for x > 2 5 For higher D concentration it was found recently [6] that ZrV2D36 undergoes a structural phase transition at ~ 325 K The tugher temperature phase is cubic and the low temperature phase is tetragonal, in which the 12 ( 2 - 2 ) are no longer equivalent The D atoms in the low temperature phase are ordered and occupy only a partial set of 4 ( 2 - 2 ) sites which are no longer equivalent to the other ( 2 - 2 ) sites because of the change m symmetry We shall present in the next section a tentative model m which the peaks are budt up by hydrogens desorbmg from the various sites which differ with their
Vol 40, No 8 THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2Hx bonding eneqpes, the larger the bonding energy, the higher the positron of the peak m temperature From this model we suggest the following pmture winch correlates with the above experimental data [4-6] We shall assume slmdar behavmur for the hydride and deutnde For x < 2 5 the hydrogens occupy only the ( 2 - 2 ) sites m which the main contnbutmn for the bonding energy comes from the Z r - H bond For x < 1 there is less than one hydrogen atom per Zr atom or per each polyhedron When x > 1 the excess hydrogen wall have to share Zr atoms with another H atom, thereby reducing the bonding energms of both hydrogen This may be described m the framework of the Rees model [9] by a formataon of a new kind of sites out of the ( 2 - 2 ) sites that were mmally equwalent, and the existence of a stable ZrV2HI phase The amount of hydrogen desorbed under the fully developed first peak is about x = 1 We therefore assocmte the hydrogens desorbed under this peak as those singularly assocmted wxth each polyhedron and therefore have stronger bondmg energy and are desorbed at the highest temperatures The hydrogens desorbed under the second peak are associated with these excess hydrogen atoms (x > 1) which have weaker bonds m the ( 2 - 2 ) sites The third peak is assocmted with hydrogens desorbed when the ( 3 - 1 ) sites are also occupied Fmally, it seems that the appearance of the tlurd shoulder can be correlated to the order-&sorder phase transataon wtuch appears at high H concentratmns [6] 5 OUTLINES FOR A MODEL AND CONCLUSIONS We shall describe a tentatave model whtch can explain the ongm of the peaks m the spectra and relates them to various sites, their occupancies and energms A more detatled work is now under progress The kmetm of desorptmn Is composed of at least two steps [10] I Dfffusmn from the bulk sites to the surface sites II Recombmahon of 2 protons at the surface and the release of a hydrogen molecule In our case it is step II that is the rate deterrmnmg as we shall show below An upper hmlt for the maximum vanatmn of the concentratmn m the bulk, Ax, can be obtained through AX
=
rde
c
--
ax =
6D
dt
ax'
where Zdee lS an approximate decay time for the &ffusmn process [11], (-- d x / d t ) m a x is the maximum rate of concentratmn change obtained from the expenment, L is the hnear dlmensmn of the partmles and D is the dfffusmn constant. Taking D ~ 10 -s cm 2see -~ [11 ], (-- d x / d t ) m a ~ ~ 10 -2 H atoms/ZrV2- see and L ~ 5 x 10-3 cm, one obtains Ax ~ 0 001H atoms/ZrV2
839
H-I
>, or, o~
o~ Es E2
EI Surface
Gas
Dlsfance
Bulk from
surface
Fig 3 Schematm potentaal energy chagram of the hydrogen atom between the gas phase and the bulk el and e2 are the lowest energy levels m the bulk sites, e s is the level of the surface site and e. is the lowest energy level in the excited state whtch is located m a saddle point (EssentlaUy these levels are higher - by ½heo in the case of the parabohc potential well - than the bottom of the appropriate well ) Ea = ea -- e, is the actlvaUon energy, and Ea Is half of the dassoclatlon energy of the H2 molecule (~ 2 2 eV) which ts small compared to the x range Therefore, we assume an equfllbrmm of the hydrogen throughout the bulk and step II is rate deternunmg The potential energy of the hydrogen near the surface is described schematlcaUy m Fig 3, where E. is the actwataon energy for the recombination process H + H -* H2 The rate equation for tlus process can be written [8] d'x s dt - v ° ~
^-E/k
T.
a
2
(2)
xs,
where x s = N J M s for N s hydrogens m Ms surface sxtes, k ~s the Boltzman factor and Vo Is some attempt frequency taken to include entropy contnbutmn Vo is temperature dependent [8, 12, 13] when the spacing, hw between the energy levels at the surface s~te is much greater than k T This temperature dependence (oc T) is Irrelevant for our purposes On the case hco .~ k T , Vo does not depend on T) [12] d'N = Msd'x is the change m N s due to recombmatmn process alone, therefore d'N = d(N + Ns) where N is the number of hydrogens m the bulk Then we obtain d,xs _
d ' Ns _ Ms
d ( N + N s ) ~- dN _ Ms
Ms
M
dx,
17Ms
where M is the number of bulk sites (x = 17 . N / M ) Then dx __ __ -Ea/k T 2 dt = ve xs,
(3)
840 v -
THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2H x 17M s Uo
(3a)
M
The chemical potential/.t as equal throughout the bulk and will also determine the occupancy x s o f the surface sates by the latrine gas formula [13]
:
-o
"~
-6
e~-es)lkT xs -
1 + e Oa-es)lkT
(4)
where e s is the lowest energy level o f the proton m the surface site and we neglect excited states Let us now analyze the consequences o f the rate equation (3) Generally speaking, it predicts a curve which is exponentmlly zero at low temperature and goes to zero at htgh temperatures when all the hydrogens have desorbed and x , -+ 0 (see also [8]) In order to understand the shape o f the curve and the temperature regmns where it nses, we consider two extreme situations almost fully occupied, x . ~ 1 and the spectra will be deterrmned only b y the acttvatmn energy E a Substltutmg xs = 1 and taking the logarithm o f equation (4), we obtain In
{/( v
E
A:: 0
,, x r
x
,
dx/d/~
Fig 4 (a) Schematic diagram o f the chemical potentmls ta(x, Ta), #(x, Tz) where T1 < / ' 2 for two-sites system, where e l , e2 are the lowest energy level o f the sites and x, are the corresponding stolctuometnc concentratmns (b) The derivative d x / d # ~ (3x/a/~)r (see text)
2p ~ - - c o n s t ' T + E -
,,x%
Concentration,
order o f magnitude as an the bulk where It was found to be [7] vo ~ 101Ssec -1 Using the above values an equatmn (3a) to calculate v we obtain from equatmn (5) that E ~ / T vanes between 25 and 26, thus essentmlly constant Therefore
I # -- e s > 2 k T m this case the surface sites are
--& kT
Vol 40, No 8
(5)
A condltmn for the onset o f desorptlon will be taken as -- d x / d t > 10 -a H atom/ZrV~ see Therefore, equatmn (5) predicts a fixed onset temperature gwen by kTo = & / l n [u/(10 -a sec -1)] independent o f initial concentration This kind o f behavlour may be found for spectra (Fig 1) wathx0 ~> 3 5 where To ~ 100°C and where the onset o f desorptmn is the same for x0 between 4 27 and 3 5 II ~ { e, (or even # < e, where the following conclusmns stall stand to a good approxamatmn) This happens when the surface sates are dflutely occupied, and xs ~ e ~u-es)/kT, which after substltutmn in equation (3), and taking the logarithm, we get again equation (5) where E~ is replaced b y an effective activation energy E~ = E a + 2e, - - 2ta that depends on ts Unhke the previous case hme the onset temperature To depends on the mltml concentrations Xo through/a I n m e a s m g x o increases/~ and decreases E~ and To This b e h a ~ o u r is found for the spectra with Xo < 3 A simple interpretation for the ongm o f peaks can be obtained m case II Consider one of the spectra for xo between 0 62 and 3 0 Except for the beginning and the end o f the spectrum, -- d x / d t varies between 3 x i 0 -a and 9 x 10-3H atoms/ZrV2sec F r o m the size o f the partmles we estimate 17(Ms/M) ~ 10 -6 vo which as defined for a surface site is assumed to be o f the same
a+2%
(6)
This conclusmn stands even if errors were made an the estlmatmns o f v as long as In [v/(-- d x / d t ) ] >> 1 It is a consequence of the form of the rate equation (2) an which the term an the exponent E ~ / T dominates the desorptlon Equation (6) gives also d# cx -- dT and therefore dx
-----
dT
cc
dx -
(7)
-
d#
We conclude that, in a case o f a ddute surface, the desorptlon spectra samply reflect the reciprocal o f the denvatwe o f the chermcal potentml with regard to hydrogen concentration Therefore the mamma appear when the change m/a is small and the maxima when the change in p is large There are few models which calculate the chemical potential for a multaslte system [9, 14] Following the ideas o f these papers we may wnte the chemical potential o f the hydrogen in the tth well in the following simplified form (see also [13]) la, = k T l n
n,
+e,,
(8)
1 --n,
where n, = N,/M, as the occupaUon o f the lth type o f sites, e, as ats lowest energy level and 34, as the number o f these sites For the case o f two types of sates with equal M z we
Vol 40, No 8 THERMAL DESORPTION SPECTRA OF HYDROGEN FROM THE BULK ZrV2Hx
Acknowledgements - We wish to thank W Kohn for a helpful discussion and A Grayevsky for tus technical assistance
obtain that n2 = 2n -- nl and nl is the root of the equation +l - - 2n) (1 -- n 1)(2n --nl)
In nl(nl
_
841
e 2 -- e 1
kT
(9)
where n = (N1 + N2)/(M1 + M:) The last equation is the consequence of the equality of the chermcal potentials/al =/z2 A schematic plot of the chermcal potential vs x on the base of equations (8) and (9) for the case (e2 -- el)/kT>> 1 is presented in Fig 4 It is easy to see that m this case nl "" 2n when n < ½and nl ~-- 1, n2 = 2n -- n i when n > 12,i e only when site 1 is filled site 2 begins to be occupied The derivative (aX/~IZ)T wtuch was plotted in the right side of Fig 4 demonstrates a spectrum where the maxima occur when the sites are half-full, and the nummum occurs at the transition between the two sites, when the first one is almost full and the seond is all but empty Since/~ = T the position of the maxima in temperature wall be proportional to e, In the ZrV2H x case we have both, sites with chfferent symmetry, and sites that have the same symmetry but their bonding energies are different 0 e sites ( 2 - 2 ) occupied by hydrogens with x < 1 and sites ( 2 - 2 ) occupied by x > 1) The above picture presents an ideal situation In reahty one has to introduce corrections due to the following
REFERENCES 1
2 3
4 5 6 7 8 9 10 11
(a) An interactaon between the hydrogens must be taken into account, 1 e e I : e ~ ( x ) (b) dla/dx = (OI~/aX)T + (aMaT)~dT/dx The second additive can be neglected during the desorptlon
12
The combined result of all these corrections smooths the transition between the sites and broadens the peaks Efforts to verify these conclusions, experimentally by equilibrium measurement of the chermcal potential, and theoretically by numencal calculations based on a statistical model, are in progress now
14
13
R Burch, Chemical Physics o f Sohds and their Surfaces (Reported by W A Roberts & J M Thomas), Vol 8. The Royal Society of Chermstry, Burlington House, London (1980) M H Mendelsohn & D M Gruen, Miami lnt Symp on Metal Hydrogen Systems, p 62 (April 1981) A Pebler & E A Gulbransen, Tranz Met Soc AIME 239, 1594 (1967), H W Newkark, A Literature Survey o f Metalhc Ternary and Quaternary Hydrides, UCRL-51244 (1974) D P Shoemaker & C B Shoemaker, J Less Common Met 68, 43 (1979) J J Dldlshelm, K Yvon, P Fischer & D Shaltlel, J Less CommonMet 73,355 (1980) J J I:hdlshelm, K Yvon, P Fischer & P Tlssot, Sohd State Commun 38,637 (1981) J Shlnar, Ph D Thesis, The Hebrew University of Jerusalem (1981) AW Srmth&S Aranoff, J Phys Chem 62, 684 (1958) A L G Rees, Trans Faraday Soc 50, 335 (1954) C Wagner, Z Phystk Chem A159, 459 (1932) J V o l k l & G Alefeld, ToptcstnApphedPhystcs, Vol 28, Hydrogen m Metals I, Chapter 12 Springer Verlag, Berhn-Heidelberg-New York (1978) K W Kehr, Topics in Apphed Physws, Vol 28, Hydrogen in Metals L Chapter 8 Spnnger Verlag, Berlin-Heidelberg-New York (1978) T L Hall, An Introduction to StattstTcal Thermodynamws Addison-Wesley, New York (1961) H A Klerstead, J Less Common Metals 71,303 (1980), H A Kxerstead,J Less Common Metals 75,267 (1980)