We have analyzed a large set of data in the literature as well as new data of our own to provide an improved equation of state of solid para-hydrogen.
Journal of Low Temperature Physics, Vol. 54, Nos. 3/4, 1984
An Improved Experimental Equation of State of Solid Hydrogen and Deuterium* Alfred Driessent and Isaac F. Silvera* Natuurkundig Laboratorium der Universiteit van Amsterdam, Amsterdam, The Netherlands (Received August 3, 1983) We have analyzed a large set of data in the literature as well as new data of our own to provide an improved equation of state of solid para-hydrogen and ortho-deuterium, with pressures ranging from 0 to 2 5 kbar (at the melting line). Results, including pressure, bulk modulus, and thermal expansion, are tabulated for a dense set of molar volumes as a function of temperature.
1. I N T R O D U C T I O N A detailed and accurate knowledge of the equations of state (EOS) of molecular hydrogen and deuterium is of importance due to the simplicity of the building blocks of these molecular solids, which makes many properties accessible to ab initio calculations. Indeed, in spite of the simplicity of the molecules, a number of unique and interesting phenomena occur, such as structural and orientational phase transitions, a molecular insulator to atomic metal transition, etc. In 1979 Driessen et aL 1 published an EOS for H2 and D2 dealing with both the ortho and para modifications. In this work isochoric measurements and a Mie-Gr/ineisen model were used to tie together a large array of data in the literature. Since that work, a substantial amount of new work has appeared, as as well as new measurements of our own, which lead to small but significant changes in the EOS of H2 and D2, in particular the former. In this article we reanalyze all of the data in the literature and present the EOS in tabular form up to a pressure of 25 kbar for para-H2 and ortho-D2. These new expanded tables include pressure, molar volume, temperature, bulk modulus, the coefficient of thermal expansion, the Debye temperature, and the Grtineisen parameter. The *Partial financial support provided by the Stichting FOM. tPresent address: Physics Department, Vrije Universiteit Amsterdam, The Netherlands. :~Permanent address: Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts. 361 0022-2291/84/0200-0361503.50/0 © 1984 Plenum Publishing Corporation
362
Alfred Driessen and Isaac F. Silvera
earlier model I for calculating the EOS as a function of ortho concentration remains valid. The most important new measurements that have appeared include those of the specific heat in para-H2 for six isochores by Krause and Swenson. 2-4 These measurements reproduced our previous results of the EOS within our stated error bars, but were done with greater accuracy. Liebenberg et al. 5 have also published data on the EOS of H2 and D2 at the melting line for high densities. They found 6 a severe disagreement between their molar volumes and ours in the solid. Most of this disagreement can be resolved by using their experimental melting temperature instead of our extrapolation of the lowrtemperature melting line. In the following section we will describe the procedures of getting the necessary thermodynamic functions for the EOS of H2. We start with the T = 0 K isotherm, then we calculate the Debye temperature 0D and Gr/ineisen parameter 3' as a function of volume V, and compare our results to those in the literature. In the last section we present a slightly improved EOS of D2, which differs from the previous one 1 due to use of the recent experimental melting line of Liebenberg et al. 5 at high densities. 2. T H E O R E T I C A L
BACKGROUND
We first present some thermodynamic relations used in the analysis of the EOS. This is based on the Helmholtz free energy F( V, T), which can be separated into a zero-temperature part Fo and an incremental part F*: F( V, T) = Fo( V) + F*( V, T)
(1)
where V is the molar volume. We shall deal only with para-H2 and ortho-D2. The weak dependence of the EOS on C1, the concentration of J = 1 molecules, has been discussed in Refs. 1 and 7. The pressure P, the bulk modulus B, and the thermal expansion coefficient a are determined from the thermodynamic relations P= -(aF/aV)T
(2)
B = - V(oP/o V) T
(3)
a = (1/V)(O V / O T ) p
(4)
With the aid of Eq. (3) we can write a =-(1/B)(Op/OT)v
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
363
From Eq. (1) we have
P( V, T)=Po(V)+P*(V, T)
(5)
B( V, T) = Bo( V) + B*( V, T)
(6)
and as OPo/OT is zero by definition,
1 a(V, T)
(OP*(V, T).)
B(V, T) \
0T
v
(7)
Equation (5) is of special interest for the EOS. Although the leading term P0(V), which represents the T = 0 isotherm, can be determined by ab initio calculations,8 detailed agreement with experimental data is poor. We therefore use a semiempirical analytical function, a modified Birch relation 9'1° Po(V)= y5 ~ Bi(Y2_l)i
(8)
i=l
with Y = (VoV) 1/3. Here Vo is the zero-pressure molar volume and the Bi are parameters to be determined by fitting to experiment. The thermal pressure P*( I1, T) in Eq. (5), which is caused by thermally excited phonons, gives only a small contribution to the EOS. We have found I that a MieGr/ineisen picture as used by Spain and Segall u for 4He adequately describes the thermal properties of the solid. In this picture P*( V, T) can be given in terms of a characteristic temperature, the Debye temperature 0D(V), and the Griineisen parameter 7(V): P*( v, T)
7(V) 9NokB T4 (;D
V
Oh(V)
.v
x__3__~_ ex - l d x
(9)
where 7(V) =
d In Oo(V)
dV
(10)
R = NokB is the gas constant and XD = OD/T. 3. T H E
T = 0 ISOTHERM
OF PARA-HYDROGEN
In our previous paper 1 we used an isotherm based on: 1. The Anderson-Swenson (AS) isotherm, i° 2. The experimental molar volumes along the melting line up to 400 bar by Dwyer et al., 12 with a small correction at low densities by Younglove. 13 3. Our own experimental data for the relation between zerotemperature pressure and melting pressure along an isochore.
364
Alfred Driessen and Isaac F. Silvera
TABLE I
The Coefficientsof the T = 0 Isotherm in the Birch Relation, Eq. (8)
Vo,cm3/mole B1, bar Bz, bar B3, bar B4, bar
p-H2
o-D2
23.207 2790.1 4959.5 1868 -32.16.
19.95 4766.5 10101 ---
With 2 and 3 it was possible to determine the isotherm up to 350 bar, and with 1 we could extend it from 400 bar tp 20 kbar. These data were fit to a modified Birch relation, Eq. (8), with n = 2. Krause and Swenson 2-4 measured the specific heat of solid para-Hz samples at six different molar volumes (22.79 to 16.19cm3/mole) from below 4 K up to the melting line. After each run they determined the molar volume of the sample. From the measured melting temperature T,,s (solid to liquid) they found, with aid of the melting line of Goodwin and Roder, 14 the melting pressure Pros. Using the equation
P,,,s = Po+ P*( T,,~)
(11)
they established a relation between the zero-temperature pressure P0 and the molar volume. The calculation of P * ( T ) , which was based on a careful analysis of accurate specific heat data, is very reliable. We therefore add the six P0, V points of Krause and Swenson 2-4 as additional data (input 4) to the determination of the new p-H2 isotherm. We take the Birch relation, Eq. (8), with n = 4 , and determine the coefficients Bi and Vo by minimizing
o'=
Wk(AVk/Vk)zJ
(12)
where k runs over all data points from the data sets 1-4, and Wk is the weight assigned to each point, which takes into account the accuracy of the data points. A Vk is the difference in molar volume at constant pressure between a data point and a calculated point from the Birch relation, (8). The resulting coefficients are given in Table I. 4. T H E
PRESSURE
AT
T~0
From Eqs. (9) and (10) we see that the properties at T ~ 0 are determined by only one independent variable, the Debye temperature
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
365
0D(V). Determination of the temperature dependence therefore reduces to finding 0D(V) from the experimental data available to us. We assume that 0o(V) has the same volume dependence as the frequency of the optical phonon Wph(V), within a scaling factor. For 0D(V) we use an empirical function proposed by Berkhout and Silvera 15 for Wph(V):
Oo(V) =
I~ exp (Ckxk) k=o
(13)
with x = In V - In V0. From experimental data, which we will discuss below, we form a function ,r(oD) =
wdP*(rms, Vk)exp-P*(Tms, Vk, 0D)ca,cl2J
(14)
where k runs over all .available experimental isochores with volume Vk, Wk is the weight, depending on experimental accuracy. P* (T,,~, Vk, 0D)ca~¢ is the calculated thermal pressure at the melting line, 14 using Eq. (9). The function O'(0D) in Eq. (14) is minimized by varying the coefficients Ck of 0D in Eq. (13). The resulting coefficients for the 0D(V) are given in Table II. For the calculations above we used the following experimental isochoric data: 1. 2. 3. 4.
Direct measurements from Ref. 1 (eight isochores). Direct measurements from Meyer 16 (one isochore). A new direct measurement by us (run I, Ref. 7, one isochore). Indirect measurements calculated from specific heat data of Krause and Swenson2-4 (six isochores).
The data of 4 show the least scatter and are in excellent agreement with 2, and within the stated error bars also with 1 and 3. We therefore give 4 and 2 appropriately higher weights Wk in Eq. (14). T A B L E I1 The Coefficients of 0D(V) in Eq. (13) ~ H2 Low density CO C1
C2 C3 Vo, cm3/mole
4.5991 -2.213 -0.5906 --
D2 High density
4.5987 -2.2128 -0.61192 -0.019666 23.207
Low density
High density
4.5176 -2.3064 -2.7935 -5.121
4.5525 -1.836 -0.18484 -19.95
"For an explanation of high-density values, see the text, after Eq. (15).
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Alfred Driessen and Isaac F. Silvera
5. T H E E Q U A T I O N
O F S T A T E OF S O L I D P A R A - H Y D R O G E N
With the new data sets it is now possible to give a more accurate tabulation of the EOS for moderate densities up to about 16 cma/mole. All thermodynamic functions used for the calculation are either interpolations from experimental data, the T = 0 isotherm, and the melting line, or at least obtained by direct calculation based on experimental data, in the case of the Debye temperature. The resulting table is presented in the Appendix. We give the pressure, bulk modulus, and thermal expansion as a function of temperature up the melting line for a dense set of volumes. In order to determine an EOS at higher densities it is necessary to use extrapolation procedures, with consequently less accuracy in the results. Fortunately the T = 0 isotherm for para-H2 is the most important thermodynamic function and this is based on experimental data up to 20 kbar. At T ~ 0, the main problem is the determination of 0D(V). As already stated, 0D(V) should scale in a first approximation with the frequency of the optical phonon tOph.We have found that the ratio 0D( V)/03ph (V) remains constant in the range of experimental overlap from 23 to 16 cm3/mole within small scatter. 17 To a good approximation therefore it should be possible to use experimental (..Oph(V) instead of the unavailable 0D(V) data. For O)ph(V) we have the following experimental data: 1. Own measurements (run IV, tot VIII, Ref. 7) (six points). 2. Data from Wijngaarden et al., l~sobtained in a diamond anvil cell up to about 200 kbar (13 points). It is now possible to determine the coefficients Ck of 0D(V) in Eq. (13) for the density range V = 23-5 cm3/mole by minimizing
o'( Ck) = [~n Wn[OD( V , Ck)calc-- OD(V)exp]2] 1/2
(15)
where W~ is a weight, and 0D( V)exp is determined from 1 and 2 and at low density by a set of 15 equidistant points. The latter have been obtained from Eq. (13) with coefficients from Table II, first column. The resulting new coefficients, very similar to the old ones, are given in Table II, second column. The last thermodynamic function needed for the EOS is the melting line. Recently Diatchenko and C h u 19 measured the melting line up to room temperature and reproduced the results of Lienberg et al. 5 in the region of overlap. Both sets of authors propose a modified Simon melting equation:
Pm = --0.2442+2.858 X 10-3T~ 724 with Pm given in kbar, Tm in kelvin.
(16)
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
367
We are now able to calculate the EOS for high densities ( 1 6 10 cm3/mole), with aid of the isotherm at T = 0, Eq. (8), and coefficients from Table I, and with the 0D(V) and Pro(Tin) as given above. The results are presented in the Appendix. 6. D I S C U S S I O N OF THE RESULTS F O R P A R A - H Y D R O G E N In this section we compare our new EOS with the available literature data and give an estimate of its accuracy. We are dealing with P - V - T points,
I
5-
'
I
'
I
~
I
F
8 o
i
I
0
/
8
0
T-y 0 "(3.
0
8--. o
3
-[3-[3
[]
[]
~I~I>~
-
~ i>
-
4 V[cm3/mole] -2
f
I
22
I
I
20
~
I
18
i
I
16
I
F
14
f
I
12
,.~1 10
Fig. 1. The relative change in volume at constant pressure as a function of the molar volume at T = 0 for //2. Solid lines are EOS from Appendix for T = 0 and T = Tm~ Data points for T = 0: Krause and Swenson 2-4 (fq), Anderson and Swensonl°(~), Stewart21(~l), and Durana and McTague 2° (~>). Data points for T = Tm~: Krause and Swenson 2 4 ( n ) , Dwyer et al. ~2 (x), Younglove ~3 (+), Meyer ~6 (O), Grilly 25 (4,), Kechin et al. 26 (V), and Liebenberg et aL 5 (O). The dashed line is a smoothed line through the data points.
368
Alired Driessen and Isaac F. Silvera
of which the pressure and temperature values vary by several orders of magnitude in the region under consideration, whereas the variation in the molar volume is small. As a convenient way of displaying data from different sources we suggest the presentation of Fig. 1. We plot the difference in relative volume with respect to a reference volume, i.e.,
v- v~o~.)
=av
Vref /P=const
V
as a function of the reference volume, the molar volume at T = 0. All volumes are taken at constant pressure. Our T = 0 K isotherm appears as a straight line at/~ V~ V = O. W e can distinguish two sets of points: one, around ~ V / V = 0, are the different T = 0 isotherms; the other set, at A V / V = 1 - 5 % , refer to the region of the melting line: these points are determined by _~(p) =(V(T=
Tm~,P)- V ( T = O ,
W---'-~----()~e-)
e)) P ..... t
(17)
where V ( T = O, P) is taken from our T = 0 isotherm. The solid line represents our results, i.e., V ( T = Tins, P) is taken from our EOS. We first discuss the different T = 0 K isotherms. We display the following data: I. Krause and Swenson: 2-4 six absolute volume measurements from 22.221 to 16.193 cm3/mole for p-H2. II. Anderson and Swenson: 1° four compressibility runs from 0.4 to 25 kbar. Volumes are given relative to V0 ( P = 1.1 kbar) (three runs n-H2, one run p-H2). III. Durana and McTague: 2° one compressibility run for p-H2 from 1.8 to 5 kbar. Given are the smoothed values of a Birch relation. IV. Stewart: 21 one compressibility run for n - H / f r o m 2 to 20 kbar. Volumes are given relative to Vo (P = 2 kbar). We have pinned the relative volume measurements of II, III, and IV on our T = 0 isotherm at their lowest measured pressure. This is the most accurate approach, because at these pressures our isotherm is based mainly on the direct volume measurements of Krause and Swenson, 2-4 which is much m o r e accurate than an extrapolation to zero pressures based on a Birch relation, as presented by I I - I V . As can be seen from Fig. 1, up to 12.5 cm3/mole, corresponding to 8 kbar, agreement between all authors is better than 0.3% in relative volume.
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
369
Above 12.5cm3/mole up to llcm3/mole, which corresponds to 15 kbar, the deviation of IV increases to 1.5% in relative molar volume. A similar behavior can be seen in Fig. 2 of II. 1° In this plot, Anderson and Swenson compare their different runs. Their highest density run was stated to be done with n-H2. Below 14 cm3/mole this run showed a systematic deviation to smaller molar volumes of about 0.8%. A possible qualitative explanation is that at highest densities and T = 4 . 2 K, the only slightly converted n-H2 samples of II and IV are in the ordered Icc phase, s which would reduce the volume by about 1%. The measurements of Silvera and Jochemsen22"23indicate that this would occur between 15.5 and 11 cm3/mole for the concentration of J = 1 above 50%. Sources II and IV state to have worked with n-H2 samples, but Swenson24 has communicated that the concentration during their measurements was not controlled and that their samples were more likely 50% J = 1 samples than 75 % (n-H2). From the data of II and IV and the phase diagram as proposed by Silvera and Jochemsen22'23 we would conclude that the concentration of the highest density run of II was approximately 65%, and that of IV about 55%. The above considerations and comparison give great confidence to our T = 0 isotherm, which can be used up to 11 cm3/mole (15 kbar) with a maximum error in A V / V of about 0.2% at lowest densities and to 0.4% at highest densities. A warning concerning extrapolations of the Birch relation, Eq. (8), to higher densities (below 10 cm3/mole) is that the error in volume will quickly increase, with resulting unphysical behavior due to the high number of coefficients used in the Birch relation. At T # 0 along the melting line we can compare with the following group of measurements: V. Dwyer et al., 12 with a small correction at lowest temperatures by Younglove: 13 direct volume measurements in the fluid from 0 to 400 bar. VI. Grilly: 25 only the liquid triple point volume. VII. Meyer: 16 measurement of P* directly at nearly zero-pressure volume. VIII. Krause and Swenson: 2-4 six molar volumes from 22.221 to 16.193 cm3/mole for p-H2, determined directly in the solid. IX. Liebenberg et al.: 5 compressibility measurements in the liquid from 14 to 10.5cm3/mole; they only determined relative volumes. X. Kechin et aL: 26-27 compressibility measurements at six molar volumes from 14 to 12.5cm3/mole; they determined the absolute volume by comparison with measurements at room temperature to 8 kbar by Tsiklis et al. 2s
370
Alfred Driessen and Isaac F. Silvera
Source V determined the volume in the fluid at the melting line and then calculated the volume change from liquid to solid with the aid of the Clapeyron equation. We believe this to be the most accurate technique because only in the liquid is there certainty of working with a sample of uniform density. In Fig. 1 we can see that up to 16 cm3/mole there is agreement between V - V I I I and our data (solid line), with a maximum deviation of 0.15% in A V / V . Only run 4 of VIII at 20.685 cm3/mole shows a slightly greater deviation (0.25%), which is also present in the T = 0 isotherm. The triple point volume of VI is in excellent agreement with the data of V; there, our EOS shows a deviation of 0.15% in volume. This is due to difficulties in finding an analytical function for the isotherm and the 0D that can reproduce the experimental results over a wide volume range from 23.2 to 16 cm3/mole. This is also why we had to divide the total volume range in two EOSs with different 0D values and different melting lines, one above 16 cm3/mole and one below. There is a resulting discontinuity in the solid line in Fig. 1 at 16 cm3/mole, but this does not exceed our error bars of 0.2% in A V / V at this density. Our high-density EOS is based on an isotherm with 0.3-0.4% error in A V~ V and on an extrapolation of the thermal pressure with the aid of the phonon frequencies. The resulting error in the EOS we estimate as being 0.3% at 16 cm3/mole to 0.6% at 11 cm3/mole. Above 16cm3/mole we have no direct volume measurements for comparison. Source IX gives a set of points with a large scatter (about 1% in volume), which are on the average (dashed line in Fig. 1) 1% higher in volume than our EOS. These points are the result of compressibility measurements with a piston technique. This method is useful in measuring pressure, temperature, and changes in volume, but gives no direct absolute volumes. Liebenberg et al. 5 (IX) have related their volumes to roomtemperature measurements, which by transferring to cryogenic temperatures can possibly introduce errors of 1-2% in volume. The last group, X, are a set of Russian data, which like IX are compressibility measurements with no possibility of direct volume determination. Only for one run, at N2 temperature ( T = 77.3 K), do they relate the sample volume to the volume at room temperature. In the first paper of the group 26 they determined the melting volume at T = 77.3 K to be 14.4 cm3/mole. However, based on a comparison with the other five data points with the aid of a smooth function, they came to the conclusion that the correct volume should be 14.25 cm3/mole. In the second paper 27 they stated the best value as 14.4 cm3/mole. Our EOS gives for Tm = 77.3 K and Pm= 4.92 kbar a value V = 14.23 ± 0.06 cm3/mole, which is in agreement with the Russian data, for which the error in volume is stated as being
Improved Experimental Equation ot State of Solid Hydrogen and Deuterium
371
about 1%. The data of IX when averaged (straight dashed line in Fig. 1) give, for T = 77.3 K, V = 14.42+0.15 cm4/mole. Our conclusion is that all data are in agreement within the stated error bars, but that our vaue should be preferred because it has been determined by universally minimizing a large set of data points. We would suggest that Liebenberg et al. could improve their EOS by using our melting volume at Nz temperature as a reference. At this point we can make some remarks about the zero-pressure volume V0. In our previous paper 1 we stated V0 = 23.14 + 0.08 cm3/mole. With our new EOS we get Vo -- 23.21 + 0.05 cm3/mole, very close to the value of Krause and Swenson 2-4 V0 = 23.234 + 0.05 cm3/mole. This agreement is not astonishing, as we have used the experimental data of Krause and Swenson as the most important data input for our EOS at low density. The small change in the EOS for D2 (see the following section) does not affect the zero pressure volume. Our preferred value remains V0 = 19.95 + 0.05 cm3/mole. With the aid of Eq. (7) we have calculated the thermal expansion coefficient by numerical differentiation. At low pressure (0-200 bar) we can compare our results with direct measurements by Manzhelii et aL, 29 which were performed with a capacitance method by measuring the dielectric constant. Figure 2 shows some of their results in comparison with our determination. There is good agreement within their error bars of about 10%. Manzhelii et aL 29 also observed a phase transition in the premelting range (see the isolated point, triangle, in the run at 198.1 bar). In our i
I
~ //i
3 - l~x10 3[K -1]
I
t
:3 g2 barT/ ZP---1981
/L/~ bo~
711 i i ~/////ii/// ii
2 m
/I
--
iiI
II
l/
. / " " .J'" 0
0
. ~--f2-
5
~
I
10
T[K] I
15
I
20
Fig. 2. T h e thermal expansion of p-H 2 as a function of temperature at pressures of 3.92 and 198.1 bar. Solid lines: Manzhelii et aL29; dashed lines from our EOS, given in the Appendix.
372
Alfred Driessen and Isaac F. Silvera
measurements we could not observe this effect, 1 nor did Krause and Swenson. 2-4 Also, now, after, the publication of additional experimental data in the literature, the existence and especially the nature of this phase transition remain controversial. Bereznyak and Sheinina 3° made accurate measurements of the melting line. When they subtract the melting pressure calculated with the aid of Goodwin's 3~ empirical melting line equation from their melting pressure data, a singularity is revealed, which they interpret as a possible triple point of the phase line and melting line. Vindryavskyii et al. 32 did extensive neutron diffraction studies up to 5 kbar, looking especially for a transition. However, they were unable to detect any structural phase transition. In this context it is remarkable that Bereznyak and Sheinina 3° observed a similar singularity in the melting line of D2 as in the case of H2, whereas the group of Manzhelii and Esel'son 33 did not find any sign of a transition for D2 in this region using an improved experimental setup for measuring the thermal expansion, which they had already used for H2 .29 Our conclusion is that the results of Bereznyak and Sheinina 3° for D2 and for H2 do not give compelling evidence of a phase transition. Since in these solids the energetic differences between the fcc and hcp lattices are very small, extreme care must be taken to ensure not only sample purity, but also a low strain thermodynamic equilibrium sample. 7. T H E E Q U A T I O N OF S T A T E OF S O L I D O R T H O - D E U T E R I U M
The experimental work on Dz is less extensive than that on H2. After our previous paper on the EOS, a as far as we know only Liebenberg et al. 5 publised additional data of interest. They determined the melting line at high pressure up to 20 kbar. To avoid inconsistencies between our old tables and literature data with a more accurate melting line, we decided to generate a new EOS for Dz for T ~ 0. The T = 0 isotherm, which is basically that of Anderson and Swenson 1° with a small correction to represent ortho-D2, remains unchanged. The coefficients of the Birch relation, Eq. (8) are the same as in Ref. 1, and are given in Table I, second column. At T # 0 we follow the same procedure as for H2. The main problem is the determination of 0D(V), for which we use the analytical expression (13). The coefficients in this equation were determined by minimzing an expression similar to Eq. (14). For the data input we use the experimental isochoric measurements, which are described in Ref. 1. The resulting coefficients for 0D(V) are given in Table II, third column. With the isotherm at T = 0, the Debye temperature, and the melting line, 14 we can calculate the EOS in the low-density region from 20.5 to 16 cm3/mole. The result is presented in the Appendix.
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
373
In order to determine the EOS at higher density, we used the new determination of the melting line by Liebenberg et aL, 5 Pm = -0.5431+3.666× 10 -3 T m1.677 kbar
(18)
where Tm is given in kelvins. The only problem is to extend 0D(V) up to 10 cm3/mole. Just as for Hz, we assume proportionality between 0o(V) and the frequency of the optical phonon ~Oph(V) 0D(V) = const X Wph(V)
(19)
tOph(V) has recently been determined by Lassche et al. 17 and at highest density by Wijngaarden e t a l . 18 T h e constant in Eq. (19) can be determined in the region of overlap at low density. In this way we get a semiempirical 0D(V) at high densities. We then minimize an expression like Eq. (15) and get the coefficients for 0D(V), which are given in Table II, fourth column. The resulting high-density EOS is presented in the Appendix. Similar to p-H2, we have calculated the thermal expansion coefficient of o-D2. Figure 3 gives a comparison of available literature data at low pressure with our results. Esel'son et al. 33 have measured the thermal expansion at seven pressures from 3 to 246 bar by measuring the dielectric constant of D2 as function of temperature. Their stated error is smaller than 10%. For clarity we show in Fig. 3 only the lowest and highest pressure results (3 and 246 bar, respectively). Esel'son et al. 33 also given the result of x-ray measurements by Krupskii et al. 34 at low pressure, which is drawn
61
I
I
I
I
ot x 103[K -1] /
m
/
-
/
/ / I., --
l :' P=O :' -
/13 ..:/
.."r
/ ..'/
4/
A,.X -
/,,,I/
2 --
/~'"
0
J 5
~. "
10
j~:~Y t
'"
P= 2l,,
I
T[K]
15
20
Fig. 3. The thermal expansion of o-D 2 as a function of temperature at zero pressure and 246 bar. Solid line: Nielson35; dashed lines from our EOS, given in the Appendix; dotted lines: Esel'son et a/.33; squares: Krupskii et al. 34
374
Alfred Driessen and Isaac F. Silvera
as circles in Fig. 3. Also at nearly zero pressure Nielson 3s determined the linear thermal expansion by neutron scattering with error bars of at least 10%. As can be seen, there is agreement at this pressure with all data within the error bars, but our results give values slightly too high. This can imply that at zero pressure our EOS for o - D E gives a value for the thermal pressure P* also 10-15% too high. At higher pressure P = 246 bar, which corresponds to 18.8 cma/mole, there is excellent agreement between our data and those of Esel'son et al. 33 APPENDIX
In this Appendix we present extended tables of the EOS for para-H2 (Tables III and IV) and ortho-D2 (Tables V and VI). We give for a dense set of volumes the pressure P, bulk modulus B = - V OP/O V, and the thermal expansion A = - ( 1 / V ) O V / O T along an isochore as a function of the reduced temperature T~ Tins, where T.,s is the melting temperature. For the calculation of thermal properties we use a temperatureindependent Debye temperature 0D and Grfineisen parameter 7, which is given for each isochore. Although the accuracy of the listed values for the calculated thermodynamic variables exceeds the experimental limits sometimes by two or three orders of magnitude, our presenation can be useful for interpolation and numerical calculation of other thermodynamic variables. The values are given in the following units: volume, cm3/mole; T and 0O, K; T / T m , and 3,, dimensionless; A, 10-6K-l; P and B, bar (for the low-density tables, and kbar for the high-density tables. We would like to make the following remark about the correct use of our tables along the melting line. Our EOS is fixed at T = 0. At T # 0 we calculate the properties along an isochore until we cross the melting line. As the pressure variation along an isochore as a function of temperature is small in comparison with that along the melting line, the correlation between the melting pressure Pm~ and volume V is much more accurate than that between Tm~ and V. If in the future better melting lines become available, especially for the highest densities, we recommend use of only the relation P m s - V and use of the new melting temperature at P =/'ms. For highest accuracy the following procedure can be applied: In Fig. 4, an isochore is shown with points from our table in the P - T plane, and a part of the melting lines as used in our table (solid line) and an improved one (dashed line). The correct I ! new Pm~, Tins of that isochore can be obtained by linear extrapolation of our data points, giving point A on the new melting line. Using to a good approximaticn the old Pm~, V relation, one will get point B. But working with Tin,, V, point C is the result, which introduces a substantial error.
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
375
TABLE lII Equation of State of Para-Hydrogen: Low Densities TIT m
=
0.0
0.2
0.4'
0.6
0.7
0.8
0.9
1.0
9.71 -10.6096 1736.6 1021.0
11.10 -7.6183 1719.7 1490.4
12.48 -3.4397 1697.6 2049.3
13.87 2.0755 1670.7 2683.7
V= 00= y=
23.40 T = 0.00 97.59 P = -14.9858 2.223 B = 1764.0 A= 0.0
V= 0D= y=
23.30 T = 98.53 P = 2.218 B = A=
0.00 -7.326 1813.3 0.0
2.83 -7.295 1814.8 24.2
5.66 -6.829 1811.9 193.8
8.49 -4.817 1799.6 652.8
9.91 -2,709 1787.1 1024.6
11.32 0.440 1769.4 1493.5
t2.74 4,832 1746.4 2049.9
14.15 10.617 1718.5 2679.3
V= 0D= y=
23.20 T = 99.47 P = 2.213 B = A=
0.00 0.581 1863.8 0.0
2.89 0.613 1864.4 24.4
5.78 1.104 1861.3 195,0
8.66 3.226 1848.4 656.5
10.11 5.446 1835.3 1029.5
11.55 8.759 1816.9 1498.4
13.00 13.370 1792.9 2053.1
14,44 19.432 1764.0 2678.5
V= 0D= y=
23.10 T = 100.42 P = 2.207 B = A=
0.00 8.743 1915.6 0.0
2.95 8,778 1915.0 24.5
5.89 9.295 1911.8 196.2
8,84 11.531 1898.3 660.0
10.31 13.867 1884.6 1033.8
11.78 17.348 1865.3 1502.5
13,26 22.186 1840.5 2055.0
14.73 28.532 1810.6 2676.1
V= 0D= y=
23.00 T = 101.39 P = 2.202 B = A=
0.00 17.168 1968.7 0.0
3.00 17.205 1969.2 24.6
6.01 17.749 1965.9 196.8
9.01 20.099 1951.6 661.8
10.51 22.553 1937.4 1035.5
12.01 26.205 1917.3 1502.8
13.51 31.270 1891.5 2051.9
15.02 37.903 1860.6 2667.1
V= 0D= y=
22.90 T = 102.36 P = 2.197 B = A=
0.00 25.865 2023.1 0.0
3.06 25.903 2023.8 24.7
6.12 26.477 2020.3 197.7
9.19 28.950 2005.4 664.3
10.72 31.530 1990.4 1038.4
12.25 35.363 1969.5 1504.6
13.78 40.670 1942.8 2050.8
15.31 47.607 1910.7 2660.7
V= OD= y=
22.80 T = 103.35 P = 2.192 B = A=
0.00 34.841 2079.0 0.0
3.12 34.881 2078.8 24.8
6.25 35.485 2075.1 198.9
9.37 38.091 2059.4 667.7
10.93 40.805 2043.8 1042.5
12.49 44.832 2022.0 1508.0
14.06 50.396 1994.2 2051.6
15.62 57.654 1961.1 2656.6
V= 0D= y=
22.70 T = 104.35 P = 2.187 B = A=
0.00 44.105 2136.2 0.0
3.18 44.147 2136.7 24.9
6.37 44.783 2132.8 199.7
9.55 47.523 2116.4 669.8
11.15 50.374 2100.1 1044.5
12.74 54.597 2077.4 1508.6
14.33 60.422 2048.5 2048.6
15.92 68.005 2014.4 2647.7
V= OD= y=
22.60 T = 105.36 P = 2.182 B = A=
0.00 53,666 2195.0 0.0
3.25 53.711 2192.4 25.1
6.49 54.378 2188.3 200.6
9.74 57.256 2171.1 672.3
11.36 60.246 2154.1 1047.1
12.98 64.669 2130.6 1510.0
14.61 70.757 2100.7 2046.9
16.23 78.668 2065.5 2640.7
V= 0D= y=
22.50 T = 106.39 P = 2.176 B = A=
0.00 63.533 2255.2 0.0
3.31 63.579 2257.3 25.0
6.61 64.280 2253.1 200.6
9.92 67.297 2235.1 671.6
11.58 70.428 2217.4 1044,8
13.23 75.053 2192.9 1504.3
14.88 81.408 2162.1 2035.6
16.54 89.650 2125.8 2621.3
V= 0D= y=
22,40 T = 107.42 P = 2.171 B = A=
0.00 73.72 2317.0 0.0
3.37 73,76 2318.3 25.1
6.74 74.50 2313.8 200.9
10.11 77.66 2295.1 672.0
11.79 80.93 2276.6 1044.2
13.47 85.76 2251.3 1501.1
15.16 92.38 2219.4 2027.7
16.84 100.96 2181.9 2606.7
V= 0D = y=
22.30 T = 108.47 P = 2.166 B = A=
0.00 84.22 2380.4 0.0
3.43 84.27 2378.8 25.1
6.86 85.04 2374.1 201.1
10.29 88.35 2354.6 672.2
12.00 91.76 2335.5 1043.3
13.72 96.80 2309.3 1497.5
15.43 103.70 2276.5 2019.5
17.15 112.61 2238.0 2591.6
V= 0o= 7=
22.20 T = 109.53 P = 2.161 B = A=
0.00 95.07 2445.4 0.0
3.50 95.12 2449.0 25.2
7.00 95.93 2444.2 201.8
10.50 99.41 2423.7 673.7
12.25 103.00 2403.7 1044.1
13.99 108.29 2376.4 1495.9
15.74 115.51 2342.3 2013.3
17.49 124.83 2302.~ 2578.,
376
Alfred Driessen and Isaac F. Silvera
TABLE Ul----vontinued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= 7=
20.80 T = 110.26 P = 2.155 B = A=
0.00 106.26 2512.1 0.0
4.51 107.16 2513.3 25.2
9.02 107.16 2508.3 201.6
13.53 110.78 2487.0 672.4
15.78 114.53 2466.3 1040.9
18.04 120.02 2438.1 1489.2
20.29 127.53 2403.0 2001.0
22.55 137.18 2362.3 2558.5
V= 0o= 7=
22.00 T = 111.69 P = 2.150 B = A=
0.00 117.80 2580.5 0.0
3.62 17.86 2580.0 25.1
7.24 118.74 2574.8 201.1
10.86 122.52 2552.7 670.2
12.67 126.41 2531.3 1036.4
14.49 132.12 2502.2 1480.6
16.30 139.90 2466.1 1986.4
18.11 149.90 2424.3 2535.8
V= 0D= 7=
21.90 T = 112.78 P = 2.144 B = A=
0.00 129.72 2650.7 0.0
3.70 129.78 2651.1 25.3
7.40 130.71 2645.5 202.8
11.09 134.70 2622.3 674.8
12.94 138.81 2599.9 1041.7
14.79 144.82 2569.5 1485.1
16.64 153.00 2532.1 1987.9
18.49 163.48 2488.9 2532.0
V= 0D= 7=
21.80 T = 113.89 P = 2.139 B = A=
0.00 142.02 2722.8 0.0
3.76 142.08 2720.8 25.2
7.52 143.05 2715.0 202.0
11.28 147.19 2691.0 671.5
13.16 151.46 2667.9 1035.4
15.04 157.68 2636.7 1474.0
16.92 166.14 2598.3 1970.2
18.80 176.96 2554.1 2505.7
V= 0D= 7=
21.70 T = 115.02 P = 2.134 B = A=
0.00 154.70 2796.7 0.0
3.84 154.77 2794.2 25.4
7.67 155.79 2788.1 203.3
11.51 160.16 2762.9 674.8
13.42 164.65 2738.7 1038.8
15.34 171.18 2706.3 1475.8
17.26 180.04 2666.6 1968.3
19.18 191.35 2621.0 2498.0
V= 0D= =
21.60 T = 116.16 P = 2.128 B = A=
0.00 167.80 2872.6 0.0
3.90 167.87 2872.2 25.2
7.79 168.92 2865.9 201.7
11.69 173.45 2839.9 669.1
13.64 178.09 2815.0 1028.9
15.59 184.85 2781.7 1459.9
17.54 193.99 2740.9 1944.4
19.48 205.65 2694.4 2464.2
V= 0o= 7=
21.50 T = 117.31 P = 2.123 B = A=
0.00 181.31 2950.5 0.0
3.97 181.38 2945.8 25.3
7.95 182.49 2939.2 202.9
11.92 187.25 2912.0 671.8
13.91 192.12 2886.1 1031.3
15.89 199.19 2851.6 1460.5
17.88 208.74 2809.5 1941.1
19.87 220.89 2761.6 2455.1
V= 0D= 7=
21.40 T = 118.47 P = 2.117 B = A=
0.00 195.25 3030.5 0.0
4.05 195.33 3028.5 25.4
8.10 196.49 3021.6 203.2
12.15 201.48 2993,2 672.1
14.18 206.58 2966.2 1030.0
16.20 213.97 2930.5 1455.8
18.23 223.93 2887.1 1931.0
20.25 236.58 2838.0 2437.4
V= 0D= 7=
21.30 T = 119.65 P = 2.112 B = A=
0.00 209.63 3112.6 0.0
4.11 209.71 3112.0 25.1
8.22 210.92 3104.9 201.3
12.33 216.07 3075.6 664.8
14.39 221.33 3048.0 1017.9
16.45 228.94 3011.4 1437.0
18.50 239.19 2967.1 1903.6
20.56 252.20 2916.9 2399.9
V= 0D= 7=
21.20 T = 120.85 P = 2.106 B = A=
0.00 224.48 3196.9 0.0
4,20 224.56 3197.6 25.4
8.41 225.84 3190.1 203.6
12.61 231.31 3159.2 671.0
14.71 236.88 3130.2 1025.1
16.81 244.92 3092.0 1443.4
18.91 255.71 3046.0 1907.1
21.02 269.36 2994.3 2398.1
V= 0D= 7=
21.10 T = 122.05 P = 2.101 B = A=
0.00 239.80 3283.4 0.0
4.26 239.88 3280.5 25.2
8.53 241.20 3272.8 201.5
12.79 246.84 3241.1 663.7
14.93 252.56 3211.4 1013.0
17.06 260.83 3172.3 1424.8
19.19 271.91 3125.5 1880.4
21.32 285.92 3072.7 2361.9
V= 0D = 7=
21.00 T = 123.28 P = 2.095 B = A=
0.00 255.61 3372.2 0.0
4.36 255.70 3372.1 25.4
8.71 257.10 3364.1 203.2
13.07 263.05 3330.7 667.9
15.25 269.10 3299.6 1017.2
17.43 277.80 3259.0 1427.1
19.60 289.43 3210.5 1878.7
21.78 304.10 3156.2 2354.0
V= 0D= 7=
20.90 T = 124.51 P = 2.089 B = A=
0.00 271.92 3463.5 0.0
4.42 272.01 3465.0 25.1
8.84 273.45 3456.7 200.6
13.25 279.58 3422.5 658.5
15,46 285.78 3390.8 1002.0
17.67 294.71 3349.3 1404.5
19.88 306.63 3299.9 1846.9
22.09 321.66 3244.6 2311.7
Improved Experimental Equation o| State of Solid Hydrogen and Deuterium
377
TABLE Hl----continued T/T m =
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= 7=
20.80 T = 125.76 P = 2.084 B = A=
0.00 288.76 3557.2 0.0
4.51 288.86 3556.1 25.3
9.02 290.37 3547.3 202.1
13.53 296.83 3511.5 662.2
15.78 303.36 3478.5 1005.5
18.04 312.73 3435.4 1406.0
20.29 325.21 3384.3 1844.5
22.55 340.90 3327.4 2303.5
V= 0o= ~,=
20.70 T = 127.03 P = 2.078 B = A=
0.00 306.13 3653.4 0.0
4.60 306.24 3652.0 25.4
9.20 307.83 3642.8 203.3
13.80 314.63 3605.3 664.6
16.10 321.49 3570.8 1007.0
18.41 331.31 3526.2 1404.9
20.71 344.35 3473.5 1838.7
23.01 360.71 3415.0 2291.2
V= 0o= 3,=
20.60 T = 128.32 P = 2.072 B = A=
0.00 324.06 3752.3 0.0
4.66 324.17 3750.0 25.0
9.32 325.81 3740.5 200.3
13.99 332.78 3702.3 654.2
16.32 339.79 3667.1 990.5
18.65 349.84 3621.8 1380.6
20.98 363.18 3568.1 1805.3
23.31 379.89 3508.8 2247.6
V= #D= ~,=
20.50 T = 129.61 P = 2.066 B = A=
0.00 342.57 3853.8 0.0
4.75 342.68 3851.7 25.1
9.51 344.40 3841.7 201.0
14.26 351.72 3801.7 655.1
16.64 359.07 3765.2 989.9
19.02 369.57 3718.3 1376.6
21.39 383.48 3663.1 1796.2
23.77 400.87 3602.3 2231.4
V= 0D = 3,=
20.40 T = 130.93 P = 2.061 B = A=
0.00 361.66 3958.2 0.0
4.85 361.79 3957.0 25.2
9.69 363.59 3946.6 201.4
14.54 371.26 3904.9 655.0
t6.96 378.95 3867.1 987.8
19.39 389.90 3818.6 1370.8
21.81 404.38 3761.9 1784.7
24.23 422.46 3699.6 2212.7
V= 0D= ~,=
20.30 T = 132.26 P = 2.055 B = A=
0.00 381.38 4065.4 0.0
4.94 381.50 4069.9 25.2
9.88 383.40 4059.0 201.4
14.81 391.42 4015.6 653.5
17.28 399.45 3976.4 983.6
19.75 410.87 3926.4 1362.0
22.22 425.93 3868.1 1769.6
24.69 444.68 3804.3 2189.6
V= 0o= -/=
20.20 T = 133.61 P = 2.049 B = A=
0.00 401.72 4175.5 0.0
5.03 401.86 4172.2 25.2
10.06 403.84 4160.8 201.8
15.09 412.22 4115.7 653.4
17.60 420.60 4075.1 981.6
20.12 432.48 4023.7 1356.5
22.63 448.12 3963.8 1758.9
25.15 467.56 3898.5 2172.4
V= 0D= 3,=
20.10 T = 134.97 P = 2.043 B = A=
0.00 422.73 4288.7 0.0
5.09 422.86 4287.7 24.7
10.18 424.88 4276.2 197.9
15.27 433.44 4230.3 640.4
17.82 441.97 4189.2 961.4
20.37 454.08 4137.0 1327.8
22.91 470.01 4076.3 1720.5
25.46 489.80 4010.1 2123.5
V= 0D= ~/=
20.00 T = 136.35 P = 2.037 B = A=
0.00 444.40 4405.0 0.0
5.21 444.55 4400.3 25.2
10.43 446.71 4388.0 201.3
15.64 455.83 4339.5 648.8
18.25 464.90 4296.3 971.1
20.86 477.72 4241.8 1336.9
23.46 494.53 4178.9 1726.8
26.07 515.35 4110.7 2125.1
V= 0D= "y=
19.90 T = 137.75 P = 2.031 B = A=
0.00 466.78 4524.6 0.0
5.28 466.93 4526.0 24.6
10.55 469.13 4513.5 196.9
15.83 478.42 4464.2 634.5
18.46 487.65 4420.4 949.2
21.10 500.69 4365.2 1305.9
23.74 517.78 4301.5 1685.9
26.38 538.95 4232.5 2073.4
V= 0t,= "y=
19.80 T = 139.16 P = 2.025 B = A=
0.00 489.89 4647.5 0.0
5.40 490.04 4646.7 25.0
10.80 492.39 4633.5 199.6
16.19 502.26 4581.5 640.9
18.89 512.03 4535.7 956.0
21.59 525.80 4478.3 1311.1
24.29 543.79 4412.5 1687.5
26.99 565.99 4341.5 2069.7
V= #D = 3,=
19.70 T = 140.59 P = 2.019 B = A=
0.00 513.74 4773.9 0.0
5.49 513.90 4769.4 24.9
10.98 516.34 4755.7 198.8
16.47 526.59 4702.0 636.9
19.21 536.72 4654.8 948.4
21.96 550.96 4596.0 1298.5
24.70 569.54 4528.6 1668.5
27.45 592.44 4456.3 2043.1
V= #D = ~/=
19.60 T = 142.04 P = 2.013 B = A=
0.00 538.36 4903.8 0.0
5.58 538.53 4899.0 24.7
11.16 541.06 4884.8 197.6
16.74 551.69 4829.4 631.8
19.53 562.18 4781.1 939.4
22.33 576.89 4720.8 1284.0
25.12 596.06 4652.0 1647.1
27.91 619.66 4578.4 2013.8
378
Alfred Driessen and Isaac F. Silvera
TABLEill----eontinued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0o= 3' =
19.50 T = 143.51 P = 2.007 B = A=
0.00 563.78 5037.4 0.0
5.70 563.96 5036.9 24.9
11.41 566,65 5021.9 199.3
17.11 577.89 4963.7 634.8
19.96 588.93 4913.2 941.2
22.82 604.40 4850.7 1282.7
25.67 624.48 4779.9 1640.8
28.52 649.13 4704.3 2001.1
V= 0D= 3'=
19.40 T = 145.00 P = 2.001 B = A=
0.00 590.04 5174.8 0,0
5.77 590.22 5169.9 24.4
11.53 592.94 5154.8 194.8
17.30 604.34 5095.9 620.2
20,18 615.53 5044.9 919.3
23.06 631.21 4981,8 1252,5
25.94 651.56 4910.2 1601.8
28.83 676.55 4833.9 1952.8
V= 0D= =
19.30 T = 146.50 P = 1,995 B = A=
0.00 617.15 5316.1 0.0
5,89 617.34 5317,2 24.5
11,78 620.21 5301.3 195.9
17.66 632.23 5239.8 621.6
20.61 644.00 5186.6 918.9
23,55 660.42 5121,5 1248,4
26.49 681.69 5047.9 1592.3
29.44 707.74 4969.7 1936.5
V ~
19.20 T = 148.03 P = 1.989 B = A=
0.00 645,13 5461,4 0.0
6.01 645.34 5455.3 24,7
12.02 648.37 5438.4 197.2
18,03 661.02 5374.1 623,7
21.03 673.36 5319.0 919.5
24.04 690.55 5251.8 1246.0
27.05 712.74 5175,9 1585.3
30.05 739.85 5095,9 1923.7
V= 0o= 3'=
19.10 T = 149.57 P = 1,983 B = A=
0.00 674.05 5611.0 0.0
6.13 674.26 5609.9 24.8
12,27 677.45 5592.3 197.9
18.40 690.74 5525.2 623.5
21,46 703.67 5468.1 916.8
24.53 721.62 5398.7 1239.1
27.60 744.74 5320.8 1572.7
30,66 772,92 5239.0 1904.2
V= 0D= 3' =
19.00 T = 151.13 P = 1,977 B = A=
0.00 703.90 5764.8 0.0
6.19 704.11 5766.6 24.1
12.39 707.34 5748,8 192.6
18.58 720.77 5681.1 606.9
21.68 733.84 5623.7 892.4
24.78 751.99 5553.8 1206.0
27.87 755.38 5475.3 1530.3
30,97 803.88 5392.8 1852.5
V= 0D= 3'=
18.90 T = 152.72 P = 1.970 B = A=
0.00 73d.74 5923.1 0.0
6.32 734.96 5923.6 24.2
12.63 738.35 5905.0 193.1
18,95 752.43 5834.6 606.3
22.11 766.09 5775.1 889.3
25.27 785.01 5703.1 1198.8
28.42 809,32 5622.7 1517.8
31.58 838.90 5538.4 1833.5
V= 0D= 3'=
18.80 T = 154.32 P = 1.964 B = A=
0.00 766.59 6085.9 0.0
6.44 766.83 6082.7 24.3
12.88 770.38 6063.4 193.4
19.32 785.11 5990.1 605.2
22,54 799.36 5928.8 885.5
25.75 819,05 5854.6 1191.0
28.97 844,30 5772.2 1504,5
32,19 874.95 5686.1 1813.9
V= 0t, = 3'=
18.70 T = 155,94 P = 1.958 B = A=
0.00 799.49 6253.5 0.0
6.56 799.74 6249.3 24.3
13.12 803.47 6229.1 193.3
19.68 818.86 6153.2 603.1
22,96 833,70 6089.8 880.5
26.25 854.17 6013.7 1.181.4
29.53 880,36 5929.6 1489.2
32,81 912.09 5841.6 1792.0
V= OD= 3'=
18.60 T = 157.58 P = 1,952 B = A=
0.00 833.48 6426.0 0.0
6.68 833.74 6423.4 24.2
13.37 837.63 6402.3 193,0
20.05 853.70 6323.6 600.0
23.39 869.14 6258.4 874.1
26.74 890.39 6180,1 1170.3
30,08 917,52 6094.0 1472.2
33.42 950.33 6004.5 1768.3
V= 0D= 3'=
18.50 T = 159.25 P = 1.945 B = A=
0.00 868.60 6603.6 0.0
6.81 868.87 6605.8 24.2
13.61 872.94 6584.0 192,4
20.42 889.67 6502.4 596.1
23.82 905.72 6435.4 866.5
27.23 927.75 6355.2 1157.6
30.63 955.83 6267.2 1453.3
34.03 989.73 6176.0 1742.5
V= 0D= 3'=
18.40 T = 160.93 P = 1,939 B = A=
0.00 904.9 6786.5 0.0
6.93 905.2 6786.7 24.1
13,86 909.4 6763.9 191.7
20.79 926.8 6679.7 592.2
24.25 943.5 6610.6 859.0
27,72 966.3 6528.6 1145.3
31.18 995,3 6438.7 1435.2
34,64 1030,3 6345.9 1717,8
V= 0D= 3'=
18.30 T = 162.64 P = 1,932 B = A=
0.00 942.4 6974.7 0,0
7.05 942.7 6978.4 24.0
14,10 947,1 6954.8 190.7
21.15 965.2 6867.9 587.3
24,68 982.4 6767.9 850.1
28.21 1006.1 6713.1 1131.2
31.73 1036.0 6621.5 1414,9
35.26 1072.1 6527.0 1690.7
0D= 3'=
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
379
TABLE ill---continued T~ Tm =
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1,0
V= 0o= 3'=
18.20 T = 164.37 P = 1.926 B = A=
0.00 981.1 7168.6 0.0
7.17 981.4 7168.4 23.9
14.35 986.0 7143.8 189.7
21,52 1004.8 7054.3 582.5
25.11 1022.7 6981.5 841.5
28.70 1047.1 6895.6 1117.6
32.28 1078.0 6802.1 1395.5
35.87 1115.2 6706.1 1664.9
V= 0D= ~=
18.10 T = 166.12 P = 1.919 B = A=
0.00 1021.2 7368.3 0.0
7.30 1021.5 7365.2 23.7
14.59 1026.3 7339.9 188.5
21,89 1045.7 7247.5 577.1
25.54 1064.2 7172.8 832.2
29.19 1089.4 7085.3 1103.1
32.83 1121.3 6989.9 1375.1
36.48 1159.5 6892.5 1638.1
V= 0D= 3"=
18.00 T = 167.89 P = 1.913 B = A=
0.00 1062.6 7573.9 0.0
7.48 1062.9 7577.7 24.1
14.96 1068.0 7550.9 191.4
22.44 1088.8 7453.3 582.2
26.18 1108.8 7375.6 836.2
29.92 1135.0 7284.6 1104.2
33.66 1168.6 7186.6 1371.6
27.40 1208.8 7086.8 1629.0
V= 0v= T=
17.90 T = 169.69 P = 1,906 B = A=
0.00 1105.3 7785.8 0.0
7.60 1105.7 7788.6 23.9
15.21 1111.0 7760.7 189.7
22,81 1132.5 7660.6 575.5
26.61 1152.7 7580.8 825.0
30.41 1180.1 7488.0 1087.6
34.21 1214.7 7388.3 1349.0
38.01 1255.9 7287.0 1600.0
V= 0D= 3' =
17.80 T = 171.51 P = 1.900 B = A=
0.00 1149.6 8004.0 0.0
7.72 1149.9 8007.2 23.7
15.45 1155.4 7978.5 187.8
23.18 1177.6 7875.7 568.2
27.04 1198.5 7794.2 813.2
30.90 1226.7 7699.9 1070.3
34.76 1262.2 7598.5 1325.6
38.63 1304.5 7495.5 1570.2
V= 0o= 3'=
17.70 T = 173.35 P = 1.893 B = A=
0.00 1195.3 8229.0 0.0
7.85 1195.7 8223.2 23.5
15.69 1201.3 8193.6 186.0
23.54 1224.2 8088.2 561.2
27.47 1245.7 8005.2 801.9
31.39 1274.7 7909.0 1053.9
35.31 1311.1 7805.8 1303.5
39.24 1354.5 7701.4 1542.1
V= 0D= 3'=
17.60 T = 175.21 P = 1.886 B = A=
0.00 1242.6 8460.8 0.0
7.97 1243.0 8448.1 23.2
15.94 1248.8 8417.6 183.9
23.91 1272.4 8309.5 553.7
27.89 1294.5 8224.9 790.0
31.88 1324.3 8126.7 1036.8
35.86 1361.7 8021.8 1280.6
39.85 1406.2 7916.1 1513.1
V= 0v= 3'=
17.50 T = 177.10 P = 1.880 B = A=
0.00 1291.5 8699.7 0.0
8.15 1291.9 8690.2 23.4
16.31 1298.1 8657.9 185.6
24.46 1323.1 8545.1 555.3
28.54 1346.3 8456.9 789.5
32.62 1377.6 8356.1 1032.5
36.69 1416.7 8248.4 1271.6
40.77 1463.1 8140.5 1498.7
V= 0D= 3'=
17,40 T = 179.02 P = 1.873 B =
0.00 1342.0 8946.0 0.0
8.34 1342.5 8945.1 23.6
16.68 1349.0 8911.1 186.8
25.01 1375.4 8793.0 555.7
29.18 1399.9 8701.9 787.2
33.35 1432.6 8597.8 1026.3
37.52 1473.5 8488.0 1026.3
41.69 1521.8 8377.6 1481.7
V= 0D= 3'=
17.30 T = 180.96 P = 1,866 B = A=
0.00 1394.3 9199.8 0.0
8.46 1394.8 9188.5 23.3
16.92 1401.5 9153.7 184.3
25.38 1428.6 9032.9 546.9
29.61 1453.7 8940.2 773.8
33.84 1487.2 8834.4 1007.6
38.07 1529.0 8722.9 1236.0
42.30 1578.4 8611.4 1451.7
V= 0D= 3'=
17.20 T = 182.92 P = 1,859 B = A=
0.00 1448.4 9461.7 0.0
8,58 1448.9 9451.6 23.0
17.17 1455.8 9416.1 181.4
25.75 1483.6 9292.9 537.2
30.04 1509.3 9198.6 759.2
34.33 1543.6 9091.1 987.4
38.62 1586.4 8977.9 1209.9
42.91 1636.9 8864.8 1419.7
V= 0D= y=
17.10 T = 184.91 P = 1.852 B = A=
0.00 1504.4 9731.7 0.0
8.77 1504.8 9727.1 23.1
17.53 1512.2 9689.7 182.0
26.30 1541.4 9561.3 536.0
30.68 1568.3 9463.9 755.0
35.06 1604.1 9353.4 979.1
39.45 1648.6 9237.8 1196.7
43.83 1701.0 9122,6 1401.0
V= 0D= 3"=
17.00 T = 186.93 P = 1.845 B = A=
0.00 1562.2 10010.0 0.0
8.95 1562.8 10004.0 23.2
17.90 1570.5 9965.0 182.4
26.85 1601.1 9832.0 534.4
31.32 1629.2 9731.0 750.4
35.80 1666.6 9618.0 970.4
40.27 1712.8 9500.0 1183.1
44.75 1767.2 9383.0 1382.3
380
Alfred Driessen and Isaac F. Silvera
TABLE m---contmued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= 7=
16.90 T = 188.97 P = 1.838 B = A=
0.00 1622.1 10297.0 0.0
9.07 1622.7 10289.0 22.7
18.15 1630.6 10249.0 179.1
27,22 1662.0 10114.0 523.8
31.75 1690.7 10012.0 734.9
36.29 1728.8 9897.0 949.4
40.83 1775.9 9777.0 1156.6
45.36 1831.4 9659.0 1350.1
V= 0D = 7=
16.80 T = 191.04 P = 1.831 B = A=
0.00 1684.1 10594.0 0.0
9.32 1684.7 10588.0 23.2
18.64 1693.2 10546.0 182.5
27.95 1726.8 10403.0 528.9
32.61 1757.4 10296.0 738.5
37.27 1797.8 10178.0 949.9
41.93 1847.5 10055.0 1152.8
46.59 1905.8 9934.0 1341.4
V= 0D= 7=
16.70 T = 193.14 P = 1.824 B = A=
0.00 1748.3 10900.0 0.0
9.44 1748.9 10889.0 22.8
18.88 1757.6 10845.0 178.9
28.32 1791.9 10699.0 517.8
33.04 1823.0 10591.0 722.4
37.76 1864.2 10471.0 928.5
42.48 1914.9 10347.0 1126.1
47.20 1974.2 10224.0 1309.4
V= 0D= 7=
16.60 T = 195.26 P = 1.817 B = A=
0.00 1814.7 11215.0 0.0
9.62 1815.3 11209.0 22.7
19.25 1824.4 11164.0 178.4
28.87 1860.2 11013.0 513.7
33.68 1892.6 10903.0 714.6
38.50 1935.3 10780.0 916.3
43.31 1987.7 10653.0 1108.9
48.12 2049.0 10529.0 1287.2
V= 0D= 7=
16.50 T = 197.41 P = 1,810 B = A=
0.00 1883.4 11541.0 0.0
9.81 1884.1 11541.0 22.7
19.62 1893.6 11494.0 177.6
29.42 1930.9 11339.0 508.9
34.33 1964.5 11225.0 706.2
39.23 2008.7 11100.0 903.4
44.13 2062.9 10971.0 1091.0
49.04 2126.2 10844.0 1264.2
V= 0D= 7=
16.40 T = 199.59 P = 1,803 B = A=
0.00 1954.6 11877.0 0.0
9.93 1955.3 11866.0 22.2
19.86 1965.0 11818,0 173.8
29.79 2002.9 11660.0 497.5
34.76 2037.2 11545.0 689.9
39.72 2082.1 11419.0 882.0
44.69 2137.2 11288.0 1064.6
49.65 2201.5 11160.0 1233.0
V= 0D= =
16.30 T = 201.80 P = 1.796 B = A=
0.00 2028.3 12225.0 0.0
10.18 2029.0 12210.0 22.5
20.35 2039.4 12159.0 175.8
30.53 2079.7 11994.0 499.1
35.61 2115.8 11875.0 686.3
40.70 2163.1 11744.0 877.9
45.79 2220.8 11611.0 1056.3
50.88 2288.0 11482.0 1220.1
V= 0D = 7= A=
16.20 T = 204.04 P = 1.788 B =
0.00 2104.7 12583.0 0.0
10.36 2105,4 12574.0 22.3
20.72 2116.2 12522.0 174.4
31.08 2158.0 12352.0 493.0
36.26 2195.3 12230.0 679.3
41.44 2244.1 12097.0 863,4
46.61 2303.6 11962.0 1037.0
51.79 2372.8 11830,0 1196.0
V= 0D= 7=
16.10 T = 206.30 P = 1.781 B = A=
0.00 2183.7 12954.0 0.0
10.54 2184.5 12937.0 22.2
21.09 2195.7 12883.0 173.0
31.63 2239.0 12709.0 487.0
36.90 2277.6 12584.0 669.6
42.17 2327.6 12448.0 849.4
47.44 2389.2 12311.0 1018.5
52.71 2460.3 12177.0 1173.0
V= 0D= 7=
16.00 T = 208.60 P = 1.774 B = A=
0.00 2265.6 13336.0 0.0
10.79 2266.4 13340.0 22.3
21.58 2278.3 13282.0 173.8
32.36 2324.1 13101,0 485.6
37.76 2364.6 12972.0 665.2
43.15 2417.2 12833.0 841.1
48.54 2481.1 12693.0 1005.6
53.94 2555.1 12557.0 1155.2
TABLE IV Equation of State of Para-Hydrogen: High Densities
T/Tm V= 0D= =
15.90 T = 212.42 P = 1,834 B = A=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
0.00 2.3504 13.732 0.0
11.16 2.3514 13.722 23.7
22.31 2.3648 13.658 183.6
33.47 2.4159 13.463 508.1
39.04 2.4608 13.328 692.6
44.62 2.5189 13.186 871.9
50.20 2.5892 13.046 1038.5
55.78 2.6703 12.915 1188.8
Improved Experimental Equation ot State of Solid Hydrogen and Deuterium
381
TABLE IV---continued T~ T m =
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V~ 0D= 3,=
15.80 214.89 1.830
T= P= B= A=
0.00 2.4384 14.140 0.0
11.40 2.4393 14.131 23.8
22.80 2.4535 14.064 184.1
34.20 2.5072 13,860 505.9
39.90 2.5542 13.723 687.3
45.60 2.6148 13.577 862.8
51.30 2.6879 13.435 1025.1
57.00 2.7521 13.302 1171.2
V= 0D = 3'=
15.70 217.40 1.825
T= P= B= A =
0.00 2.5295 14.562 0.0
11.65 2.5305 14.551 23.9
23.29 2.5454 14,481 184.3
34.94 2.6018 14.270 503.2
40.76 2.6509 14,128 681.5
46.58 2.7140 13,980 853.1
52.40 2.7899 13,835 1011.3
58.23 2.8772 13.701 1153.0
V= 0D = 3'=
15.60 219.95 1.820
T= P= B= A=
0,00 2.6239 14.999 0.0
11.89 2.6250 15.001 23.9
23.78 2.6407 14.927 184.0
35.67 2.6998 14.710 499.3
41.62 2.7509 14.563 674.1
47.56 2.8166 14.412 841.7
53.51 2.8954 14.265 995.5
59.45 2.9858 14.131 1132.8
V= 0D = 3,=
15.50 222.53 1.815
T= P= B= A =
0.00 2.7218 15.450 0.0
12.14 2.7229 15.448 23.9
24.27 2.7395 15.371 183.7
36.41 2.8012 15.146 495.4
42.47 2.8545 14.997 667.0
48.54 2.9227 14.843 830.7
54.61 3.0043 14.694 980.3
60.68 3.0979 14.557 1113.8
V= 0D = 3,=
15.40 225.16 1.810
T= P= B= A =
0.00 2.8233 15.917 0.0
12.38 2.8245 15.914 23.9
24.76 2.8418 15.834 183.1
37.14 2.9063 15.601 490.9
43.33 2.9617 15,448 659.1
49.52 3.0324 15.291 818.9
55.71 3.1170 15.140 964.5
61.90 3.2137 15.002 1093.9
V= 0D = 3,=
15.30 227.83 1.805
T= P= B= A=
0.00 2.9286 16,399 0.0
12.63 2.9298 16.388 23.8
25.25 2.9480 16,305 182.3
37.88 3.0152 16,065 486.1
44.19 3.0727 15.909 650.9
50.50 3.1460 15.749 807.0
56.81 3.2334 15.595 948.7
63.13 3.3333 15.457 1074,1
V= 0o= 3,=
15.20 230.54 1.801
T= P= B= A=
0.00 3.0377 16,899 0.0
12.87 3.0390 16.898 23.7
25.74 3.0580 16.811 181.1
38,61 3.1280 16.564 480.3
45.05 3.1876 16.405 641.4
51.48 3.2635 16.242 793.6
57.92 3.3539 16.087 931.2
64.35 3.4569 15,946 1052.9
V= 8D= 3'=
15.10 233.29 1.796
T= P= B= A=
0.00 3.1510 17.415 0.0
13.12 3.1523 17.393 23.6
26.23 3.1721 17.303 180.1
39.35 3.2449 17.049 474.9
45.90 3.3067 16.886 632.8
52.46 3.3851 16.720 781.3
59.02 3.4784 16.563 915.4
65.58 3.5846 16.422 1033.4
V= 0o= 3,=
15.00 236.09 1.791
T= P= B= A=
0.0T 3.2685 17.950 0.0
13.36 3.2699 17.934 23.5
26.72 3.2905 17.841 178.5
40.08 3.3660 17.580 468.4
46.76 3.4300 17.414 622.7
53.44 3.5110 17.246 767.4
60.12 3.6072 17.087 897.5
66.80 3.7166 16.944 1011.9
V= 3'=
14.90 238.93 1,786
T= P= B= A=
0,00 3.3904 18.503 0.00
13.61 3.3918 18.510 23.24
27.21 3.4133 18.414 176.52
40.82 3.4916 18.146 461.11
47.62 3.5578 17.976 611.75
54.52 3.6414 17.805 752.48
61.22 3.7405 17.644 878.79
68.03 3.8531 17,499 989.51
V= 0D = 3,=
14.80 241.81 1.782
T= P= B= A =
0.00 3.5169 19.076 0.00
13.85 3.5184 19.068 23.06
27.70 3.5408 18.969 174.77
41.55 3.6219 18.694 454.49
48.47 3.6902 18,520 601.76
55.40 3.7764 18.346 738.93
62.32 3.8785 18,184 861.70
69.25 3.9943 18.038 969.18
V= 0D = ,,/=
14.70 244.75 1,777
T= P= B= A=
0.00 3.6482 19.669 0.00
14.10 3.6498 19.669 22.82
28.19 3.6730 19.566 172.63
42.28 3.7569 19.284 447.05
49.33 3.8274 19.107 590.77
56.38 3,9162 18.932 724.21
63.43 4.0212 18.767 843.45
70.47 4.1403 18.620 947.53
V= 0D= 3'=
14.60 247.73 1.772
T= P= B= A =
0.00 3.7846 20.283 0.00
14.46 3.7863 20.282 23.15
28.93 3.8111 20.172 174.34
43.39 3.9002 19,878 446.84
50.62 3.9746 19.697 587.89
57.85 4.0680 19.517 718.08
65.08 4.1780 19.351 833.69
72.31 4.3023 19.203 934.24
382
Alfred Driessen and Isaac F. Silvera
TABLE X---continued ~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= y=
14.50 T = 250.76 P = 1.768 B = A=
0.00 3.9261 20.920 0.00
14.71 3.9279 20.916 22.86
29.41 3.9536 20.803 171.86
44.12 4.0456 20.502 438.87
51.48 4.1221 20.317 576.48
58.83 4.2181 20.134 703.12
66.18 4.3311 19.966 815.46
73.54 4.4587 19.818 912.84
V= 0o= y=
14.40 T = 253.85 P = 1.763 B = A=
0.00 4.0732 21.579 0.00
15.07 4.0751 21.564 23.11
30.15 4.1025 21.446 173.00
45.23 4.1998 21.132 437.59
52.76 4.2803 20.943 572.44
60.30 4.3808 20.757 695.87
67.84 4.4989 20.587 804.79
75.38 4.6319 20.438 898.92
V= 0o = ~=
14.30 T = 256.98 P = 1.759 B = A=
0.00 4.2259 22.262 0.00
15.32 4.2279 22.262 22.75
30.64 4.2562 22.140 170.01
45.96 4.3563 21.821 428.64
53.62 4.4390 21.628 559.93
61.28 4.5422 21.440 679.90
68.94 4.6632 21.266 785.52
76.60 4.7995 21.117 876.65
V= 0o= =
14.20 T = 260.17 P = 1.754 B = A=
0.00 4.3846 22.970 0.00
15.69 4.3867 22.968 22.91
31.38 4.4167 22.839 170.51
47.06 4.5223 22.508 426.08
54.91 4.6090 22.310 554.55
62.75 4.7168 22.119 671.24
70.59 4.8430 21.945 773.58
78.44 4.9847 21.794 861.60
V= 0D= y=
14.10 T = 263.41 P = 1.749 B = A=
0.00 4.5495 23.704 0.00
16.06 4.5517 23.710 23.03
32.11 4.5836 23.576 170.61
48.17 4.6947 23.233 422.72
56.19 4.7854 23.031 548.21
64.22 4.8979 22.835 661.70
72.25 5.0291 22.661 760.72
80.28 5.1764 22.509 845.62
V= 0D= y=
14.00 T = 266.70 P = 1.745 B = A=
0.00 4.7210 24.466 0.00
16.30 4.7232 24.469 22.60
32.60 4.7559 24.330 167.23
48.90 4.8699 23.981 413.34
57.05 4.9628 23.776 535.50
65.20 5.0780 23.579 645.76
73.35 5.2122 23.401 741.90
81.50 5.3628 23.249 824.18
V= 0D= ~=
13.90 T = 270.06 P = 1.741 B = A=
0.00 4.8992 25.256 0.00
16.67 4.9015 25.262 22.65
33.34 4.9361 25.116 166.88
50.00 5.0556 24.756 409.24
58.34 5.1526 24.546 528.50
66.67 5.2725 24.346 635.60
75.00 5.4119 24.166 728.72
83.34 5.5680 24.013 808.11
V= 0D = y=
13.80 T = 273.47 P = 1.736 B = A=
0.00 5.0845 26.075 0.00
17.04 5.0870 26.069 22.67
34.07 5.1234 25.917 166,35
51.11 5.2485 25.546 404.90
59.62 5.3496 25.331 521.29
68.14 5.4742 25.128 625.41
76.66 5.6189 24.946 715.55
85.18 5.7805 24.794 792.20
V= 0o= y=
13.70 T = 276.94 P = 1.732 B = A=
0.00 5.2772 26.925 0.00
17.28 5.2797 26.934 22.15
34.56 5.3170 26.779 162.44
51.84 5.4450 26.401 394.75
60.48 5.5483 26.185 507.82
69.12 5.6756 25.978 608.90
77.76 5.8233 25.797 696.25
86.40 5.9883 25.643 770.48
V= #D = =
13.60 T = 280.47 P = 1.727 B = A=
0.00 5.4776 27.808 0.00
17.77 5.4804 27.795 22.58
35.54 5.5206 27.630 164.43
53.31 5.6572 27.235 394.67
62.20 5.7664 27.013 505.27
71.08 5.9006 26.804 603.42
79.97 6.0558 26.620 687.83
88.85 6.2286 26.468 759.18
V= #o = =
13.50 T = 284.06 P = 1.723 B = A=
0.00 5.6862 28.724 0.00
18.02 5.6891 28.718 22.03
36.03 5.7301 28.550 160.28
54.05 5.8695 28.150 384.28
63.05 5.9810 27.924 491.75
72.06 6.1178 27.713 586.99
81.07 6.2761 27.527 668.85
90.08 6.4523 27.372 738.06
V= 0D= =
13.40 T = 287.72 P = 1.719 B = A=
0.00 5.9033 29.675 0.00
18.51 5.9064 29.653 22.36
37.01 5.9504 29.475 161.59
55.52 6.0985 29.058 383.01
64.77 6.2161 28.827 487.90
74.02 6.3599 28.612 580.36
83.27 6.5257 28.426 659.33
92.53 6.7099 28.273 725.84
V= 0D= =
13.30 T = 291.44 P = 1.714 B = A=
0.00 6.1293 30.663 0.00
18.87 6.1325 30.653 22.19
37.75 6.1785 30.469 159.77
56.62 6.3324 30.041 376.51
66.05 6.4542 29.805 478.54
75.49 6.6028 29.588 568.16
84.93 6.7739 29.400 644.55
94,36 6.9638 29.246 708.71
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
383
TABLElV--continued
T/~ =
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0o= =
13.20 T = 295.24 P = 1.710 B = A=
0.00 6.3645 31.690 0.00
19.24 6.3679 31.688 21.98
38,48 6.4159 31.496 157.79
57,72 6.5756 31.058 369.84
67.34 6.7016 30.819 469.06
76.96 6.8551 30,600 555.91
86,58 7.0316 30.411 629.79
96.20 7.2272 30,257 691.69
V= 0o= ~=
13.10 T = 299.09 P = 1,706 B = A=
0.00 6.6096 32.757 0.00
19.73 6,6132 32,746 22.18
39.46 6,6643 32,543 158.14
59.19 6.8330 32,090 366.90
69.06 6,9652 31,846 463.54
78.92 7.1258 31.624 547.67
88.79 7.3099 31.434 618.95
98.65 7.5137 31.281 678.40
V= 0o= ~=
13.00 T = 303.03 P = 1.702 B = A=
0.00 6.8648 33.866 0.00
19.98 6.8685 33.873 21.51
39.95 6.9204 33,669 153.37
59.93 7.0918 33,210 355.93
69.91 7.2262 32,963 449.66
79.90 7.3895 32.738 531.27
89.89 7.5768 32.546 600.40
99.88 7.7841 32,393 658.08
V= 0o= ~=
12.90 T = 307.03 P = 1.698 B = A=
0.00 7.1308 35.019 0.00
20.47 7.1346 35,025 21.62
40.93 7.1898 34.810 153.21
61.40 7.3703 34,336 352.24
71.63 7.5110 34.082 443.42
81.86 7.6814 33,855 522.45
92.09 7,8764 33.663 589.08
102.33 8.0919 33.510 644.53
V= 0o= ~=
12.80 T = 311.11 P = 1.693 B = A=
0.00 7.4079 36,218 0.00
20.96 7.4120 36,188 21.70
41.91 7.4705 35.963 152.90
62.87 7.6601 35,474 348,42
73.34 7.8071 35.216 437.18
8382 7,9848 34.987 513.65
94.30 8.1876 34.794 578.00
104.78 8.4113 34.643 631.30
V= 0D= ~=
12.70 T = 315.26 P = 1,689 B = A=
0.00 7.6968 37.466 0.00
21.45 7.7012 37.436 21.72
42.89 7.7629 37,200 152.15
64.34 7.9618 36.697 343.81
75.06 8.1152 36.434 430.04
85.78 8.3001 36.202 504.04
96.50 8.5109 36.009 566.04
107.23 8.7429 35,860 617.21
V= Oo= =
12.60 T = 319.50 P = 1,685 B = A=
0.00 7.9981 38.764 0.00
21.94 8.0027 38.725 21.71
43.87 8.0678 38.479 151.18
65.81 8.2760 37.960 338.91
76.77 8.4359 37.694 422.64
87.74 8.6281 37,460 494,23
98.71 8.8467 37.267 553.99
109.68 9,0871 37.118 603.23
V= 0o= ~=
12.50 T = 323.81 P = 1.681 B = A=
0,00 8.3124 40.116 0.00
22.43 8.3172 40,134 21.62
44.85 8.3857 39.877 149.72
67.28 8.6033 39.343 333.13
78.49 8.7697 39.072 414.28
89.70 8.9692 38,837 483.42
100.91 9,1958 38,644 540.89
112,13 9.4446 38.496 588.14
V= OD= ~=
12.40 T = 328.21 P = 1.678 B = A=
0.00 8.6402 41.522 0.00
22,92 8.6453 41.517 21.54
45.83 8.7173 41.248 148.51
68.75 8.9443 40,702 327.73
80.20 9.1172 40.427 406,52
91.66 9.3241 40,189 473.40
103,12 9.5588 39.996 528.81
114.58 9.8161 39.851 574.27
V= 0D= =
12.30 T = 332.69 P = 1.674 B = A=
0.00 8.982 42.988 0,00
23.41 8.988 42.983 21.40
46.81 9.063 42.704 146.68
70.22 9.300 42.143 321.88
81.92 9,479 41.864 398.30
93.62 9.694 41,623 462.98
105.32 9.936 41.430 516.36
117.03 10,202 41.285 560.17
V= 0D= 7=
12.20 T = 337.26 P = 1.670 B = A=
0.00 9.339 44.514 0.00
23.90 9.345 44.474 21.25
47.79 9.424 44.184 144.93
71,69 9,670 43.609 316.08
83.63 9.856 43.325 390.20
95.58 10.078 43.082 452.74
107.53 10.329 42,889 504.31
119.48 10.603 42.746 546.45
V= 0o = =
12.10 T = 341.92 P = 1.666 B = A=
0.00 9.712 46.105 0.00
24.39 9.718 46,097 21.03
48.77 9.801 45.797 142.78
73.16 10,056 45.208 309.57
85.35 10,249 44.920 381.39
97.54 10.478 44.675 441.78
109.73 10.738 44.482 491.45
121.93 11.021 44.342 531.96
V= 0D= y=
12.00 T = 346.68 P = 1,662 B = A=
0.00 10.102 47,763 0.00
24.88 10.108 47.769 20.79
49.75 10.194 47,459 140.54
74.63 10.459 46.856 303.05
87.0 10,659 46.564 372,64
99.50 10.896 46.317 430.97
111.94 11.163 46.125 478.82
124.38 11.455 45.984 517.82
384
Altred Driessen and Isaac F. Silvera
TABLE N--continued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0o= =
11.90 351.53 1.659
T= P= B= A=
0.00 10.509 49.493 0.00
25.37 10.515 49.470 20.54
50.73 10.605 49.149 138.28
76.10 10.880 48.532 296.68
88.78 11.086 48.237 364.12
101,46 11.330 47.988 420.54
114.14 11.606 47.795 466.72
126.83 11.906 47.657 504.30
V= 0D= y=
11.80 356.48 1.655
T= P= A=
0.00 10.934 51.296 0.00
26.10 10.941 51.270 20.83
52.20 11.037 50.930 138.74
78.30 11.330 50.293 293.94
91.35 11.547 49.993 359.17
104.40 11.804 49.742 413.43
117.45 12.093 49,553 457.64
130.50 12,407 49.419 493.46
V= 0D= =
11.70 361.53 1,651
T= P= B= A=
0.00 11.378 53.178 0.00
26.59 11.386 53.128 20.51
53.18 11,486 52.778 136.08
79.77 11.788 52.127 287.11
83.06 12.012 51.823 350.33
106.36 12.277 51.571 402.75
119.65 12.574 51.381 445.44
132.95 12.898 51.249 480.00
V= 0o= y=
11.60 366.68 1.648
T= P= B= A=
0.00 11.843 55.143 0,00
27.08 11.851 55.106 20.15
54.16 11,954 54,745 133.23
81.24 12.266 54.082 280.01
94.78 12.497 53.772 341.22
108,32 12,770 53.520 391.88
121.86 13.076 53.329 433,04
135.40 13.408 53.201 466.25
V= 0D= ~=
11.50 371.95 1.644
T= P= B= A=
0.00 12.330 57.193 0.00
27.82 12.338 57.133 20.30
55.63 12,448 56.753 132.95
83.44 12.778 56.068 276.41
97.35 13.020 55.757 335.54
111.26 13.306 55.503 384.27
125.17 13.625 55.317 423.66
139.07 13.972 55.193 455.39
V= 0D = =
11.40 377.32 1,641
T= P= B = A=
0.00 12.838 59.335 0.00
28.30 12.847 59.310 19.87
56.61 12.961 58.920 129.78
84.92 13.300 58,224 268.99
99.07 13.550 57,906 326.20
113.22 13.843 57.651 373.27
127.37 14.171 57.465 411.26
141.52 14.527 57.344 441.82
V= 0D= ~=
11.30 382.81 1.638
T= P= B= A=
0.00 13.371 61.573 0,00
29.04 13.380 61.525 19.94
58.08 13.501 61.117 129.03
87.12 13.859 60.400 264.85
101.64 14.120 60.080 320.10
116.16 14.426 59.825 365.34
130.68 14.768 59.641 401.78
145.20 15.139 59.526 431,00
V= 0~ = =
11.20 388.42 1.634
T= P= B= A=
0.00 13,929 63.912 0.00
29.53 13.938 63.855 19.47
59.06 14.063 63.435 125.75
88.59 14,430 62.704 257.51
103.36 14.698 62.380 311.02
118.12 15.013 62.123 354.74
132.89 15.363 61.939 389.93
147,65 15.743 61,825 418.11
V= 0D= =
11.10 394,15 1.631
T= P= B= A=
0,00 14.513 66.357 0.60
30.51 14.523 66.353 19.91
61.02 14.659 66.904 126,63
91.53 15.053 65.146 255.32
106.79 15.338 64.820 306.73
122.04 15.671 64.566 348.49
137.29 16.041 64.390 381.98
152.55 16.441 64.287 408.54
V= 0D= 7=
11.00 40T.01 1.628
T= P= B= A=
0,00 15.125 68.915 0,00
31,00 15.135 68.866 19,39
62.00 15,275 68.407 123,15
93.00 15.679 67.637 247.95
108.50 15.971 67.306 297.73
124.00 16.312 67.051 338.16
139.50 16.691 66.874 370.50
155.00 17.100 66.771 396.28
V= 0o = =
10.90 405.99 1.625
T= P= B = A=
0.00 15.766 71.591 0.00
31.74 15.777 71.536 19.28
63.47 15.924 71.058 121.56
95.21 16.347 70.269 242.90
111.07 16.651 69.935 290.92
126.94 17.005 69.677 329.78
142.81 17.399 69.505 360.75
158.68 17,823 69.409 385.37
V= 0D= ~=
10.80 412.11 1.622
T= P= B= A=
0.00 16.439 74.392 0.00
32.47 16.450 74.322 19.14
64.94 16.605 73.828 119.79
97.41 17.047 73.020 237.69
113.65 17.363 72.681 284.04
129.88 17.731 72.425 321.43
146.12 18.139 72.257 351,10
162.35 18.579 72.168 374.64
V= 0D= =
10.70 418.37 1.619
T= P= B= A=
0.00 17.145 77,325 0.00
33.20 17.157 77.308 18.95
66.41 17.319 76.793 117.77
99.61 17.779 75.966 232.11
116,22 18.108 75.625 276.78
132.82 18.489 75.372 312.71
149.42 18.912 75.207 341.16
166.02 19,367 75.122 363.75
Improved Experimental Equation ot State o| Sofid Hydrogen and Deuterium
385
TABLE ~---continued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= OD= y=
10.60 T = 424.77 P = 1.616 B = A=
0.00 17.885 80.398 0.00
33.94 17.898 80.293 18.75
67.88 18.068 79.759 115.80
101.82 18.547 78.914 226.88
118.79 18.888 78.568 270.00
135.76 19.283 78.314 304.54
152.73 19.721 78.154 331.96
169.70 20.t91 78.076 353.54
V= OD= y=
10.50 T = 431.32 P = 1.613 B = A=
0.00 18.662 83.617 0.00
34.92 18.676 83.590 18.88
69.84 18.858 83.024 115.10
104.76 19.365 82.156 222.93
122.22 19.724 81.810 264.31
139.68 20.139 81.562 297.32
157.14 20.597 81.408 323.37
174.60 21.089 81.344 343.86
V=
10.40 T = 438.03 P = 1.611 B = A=
0.00 19.478 86.992 0.00
35.65 19.493 86.950 18.59
71.31 19.683 86.365 112.71
106.97 20.209 85.477 217.20
124.79 20.580 85.126 257.12
142.62 21.010 84.878 288.87
160.45 21.483 84.728 313.94
178.27 21.991 84.671 333.52
V= 0D= y=
10.30 T = 444.89 P = 1.608 B = A=
0.00 20.336 90.532 0.00
36.39 20.351 90.527 18.26
72.78 20.549 89.922 110.15
109.17 21.095 89.017 211.32
127.36 21.478 88.662 249.80
145.56 21.922 88.413 280.31
163.75 22.410 88.268 304.35
181.95 22.934 88.218 323.23
V= 0o= y=
10.20 T = 451.92 P = 1.605 B = A=
0.00 21.237 94.246 0.00
37.37 21.253 94.197 18.27
74.74 21.464 93.563 109.00
112.11 22.038 92.635 207.16
130.79 22.440 92.280 244.12
149.48 22.904 92.037 273.35
168.17 23.413 91.900 296.25
186.85 23.959 91.860 314.15
V= 0o= y=
10.10 T = 459.12 P = 1.603 B = A=
0.00 22.185 98.145 0.00
38.35 22.202 98.080 18.23
76.70 22.425 97.418 107.61
115.05 23.029 96.467 202.69
134.22 23.450 96.112 238.23
153.40 23.933 95.873 266,22
172.57 24.464 95.745 288.01
191.75 25.032 95,719 305.11
V= 0D= y=
10.00 T = 466.50 P = 1.601 B = A=
0.00 23.182 102.24 0.00
39.33 23.200 102.12 18.14
78.66 23.436 101.43 106.07
117.99 24.069 100.46 198.17
137.65 24.508 100.I0 232.29
157.32 25.012 99.87 259.05
176.99 25.565 99.75 279.94
196.65 26.156 99.74 296.26
V= 0o= y=
9.90 T = 474.06 P = 1.598 B = A=
0.00 24.231 106.54 0.00
40.31 24.250 106,54 17.99
80.62 24.499 105.82 104.19
120.93 25.162 104.83 193.18
141.09 25.620 104.47 225.90
161.24 26.145 104.24 251.51
181.40 26.719 104.13 271.44
201.55 27.333 104.13 286.93
0.9
1.0
OD= y=
TABLE V Equation of State of Ortho-Deuterium: Low Densities
T/Tm= V=
0D= y=
0.0
0.2
0.4
0.6
0.7
0.8
20.50 T = 0.00 85.86 P = - 7 8 . 7 2 8 4 2.470 B = 2624.0 A= 0.0
V= 0D= y=
20.40 T = 86.89 P = 2.439 B = A=
0.00 -65.667 2718.4 0.0
V= 0D= y=
20.30 T = 87.93 P = 2.408 B = A=
0.00 -52.072 2815.4 0.0
11.73 -36.861 2691.7 1791.1
13.68 -25.473 2611.7 2625.8
16.88 -20.9260 2222.3 4877.7
18.76 1.2298 2102.7 6063.6
15.32 -24.978 2420.8 3666.7
17.23 -6.009 2310.1 4722.7
19.15 16.734 2189.9 5848.8
15.64 -10.010 2513.7 3561.2
17.59 9.498 2402.4 4570.3
19.54 32.840 2281.7 5639.2
386
Alfred Driessen and Isaac F. Silvera
TABLE V----continued T/T m
=
0.0
0.2
0.4
0.6
0.7
0.8
0,9
1.0
V= OD= 2,=
20,20 T = 88.98 , P = 2.378 B = A=
0.00 -37.923 2915.3 0.0
3,99 -37.717 2912.9 70.9
7.98 -34.640 2886.5 565.4
11.97 -22.143 2789.2 1752.2
13.97 -10.376 2708.1 2560.4
15.96 5.563 2609.3 3460.4
17.96 25.625 2497.4 4424,9
19.95 49.584 2376.4 5439.5
V= 0D= 3,=
20.10 T = 90.03 P = 2.349 B = A=
0.00 -23.201 3018.0 0.0
4.07 -22,987 3015,2 69.8
8.15 -19,787 2988.2 556.2
12.22 -6.826 2888.9 1715.2
14.25 5.336 2806.8 2498.1
16,29 21.767 2707.1 3364.6
18.33 42.402 2594.4 4287.4
20.36 66.996 2473.0 5252.1
V= 0D= y=
20.00 T = 91.08 P = 2.320 B = A=
0.00 -7,885 3123.7 0.0
4.16 -7.663 3121.8 68.7
8.31 -4.334 3094.1 547.1
12.47 9.110 2993.1 1678.7
14.55 21.679 2910.1 2436.7
16.63 38.618 2809.6 3270.4
18,71 59,843 2696.5 4152.6
20.79 85,089 2574.9 5068.1
V= 0D= y=
19.90 T = 92.14 P = 2,292 B = A=
0.00 8.04 3232.4 0.0
4.24 8.27 3231.7 67.7
8.49 11.74 3203.3 538.5
12.73 25.69 3100.5 1643.7
14.85 38.68 3016.4 2377.7
16.97 56.15 2915.2 3180.2
19.09 77.98 2801.5 4023.9
21.22 103.90 2679.8 4893.8
V= 0r)= y=
19.80 T = 93.21 P = 2.265 B = A=
0.00 24.61 3344.3 0.0
4.33 24.85 3342.7 66.8
8.66 28.46 3313.6 530.6
12.99 42.93 3208.8 1611.0
15.16 56.36 3123.8 2322.7
17.32 74.37 3021.7 3095.9
19.49 96.84 2907.5 3903.8
21.66 123.45 2785.7 4731.1
V= 0D= 3'=
19.70 T = 94.28 P = 2.238 B = A=
0.00 41.83 3459.4 0.0
4.42 42.08 3456.5 65.9
8.84 45.84 3426.7 523.2
13.26 60.86 3320.0 1579.9
15.47 74.75 3234.0 2270.0
17.68 93.33 3131.3 3015.1
19.89 116.44 3016.7 3788.9
22.10 143.77 2894.9 4576.2
V= 0D= y=
19.60 T = 95.35 P = 2.212 B = A=
0.00 59.74 3577.8 0.0
4.51 60.00 3573.1 65.1
9.02 63.91 3542.6 516.1
13.54 79,51 3434.1 1549.9
15.79 93.87 3347.1 2219.3
18.05 113.04 3243.8 2937.6
20.31 136.82 3129.0 3678.8
22.56 164.88 3007.1 4428.4
V= Or,= 3, =
19.50 T = 96.43 P = 2.187 B = A=
0.00 78.35 3699.7 0.0
4.61 78.62 3700.3 64;2
9.21 82.70 3669.0 508.2
13.82 98.89 3558.6 1517.7
16.12 113.74 3470.8 2165.6
18,42 133.50 3366.8 2856.5
20.72 157.98 3251.8 3564.8
23.03 186.79 3130.0 4276.6
V= 0o = y=
19.40 T = 97.51 P = 2.162 B = A=
0.00 97.69 3825.1 0.0
4.70 97.98 3820.4 63.6
9.40 102.23 3788.4 502.5
14.10 119.05 3676,1 1491.9
16.45 134.43 3587.4 2121.3
18.80 154.82 3482.9 2788,3
21.15 180.02 3367.6 3468.1
23.50 209.63 3246.1 4146.8
V= 0D= 3'=
19.30 T = 98.60 P = 2.138 B = A=
0.00 117.79 3954.2 0.0
4.80 118.09 3948.9 62.9
9.60 122.52 3916.0 496.4
14.40 140.01 3801.7 1465.1
16.79 155.92 3712.1 2075.8
19.19 176.97 3607.1 2719.0
21.59 202.92 3491.6 3370.4
23.99 233,34 3370.4 4016.8
V= OD= y=
19.20 T = 99.70 P = 2.115 B = A=
0.00 138.67 4087.1 0.0
4.90 138.99 4084.7 62.2
9.80 143.61 4050,9 490.2
14,69 161,79 3934.7 1437.8
17.14 178.26 3844.3 2029,8
19.59 199.99 3738.8 2649.4
22.04 226.71 3623.4 3273.0
24.49 257.98 3502.7 3887.7
V= Or,= 3"=
19.10 T = 100.80 P = 2.092 B = A=
0.00 160.37 4223.8 0.0
5.00 160.70 4224.0 61.5
10.00 165.53 4189.4 484.3
15.00 184.43 4071.3 1411.6
17.50 201.48 3980.2 1985.7
20.00 223.92 3874.3 2582.7
22.50 251.43 3759.0 3179.8
25.00 283.57 3638.7 3764.7
V= 0D= 3"=
19.00 T = 101.90 P = 2.070 B = A=
0.00 182.91 4364.6 0.0
5.10 183.25 4362.6 61.0
10.21 188.30 4327.2 479.2
15.31 207.95 4207.2 1387.9
17.86 225.60 4115.3 1945.4
20.41 248.77 4009.1 2521.4
22,96 277.11 3894.0 3094.0
25.51 310.14 3774.3 3651.7
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
387
TABLE V----contmued ~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 8D = =
18.90 T = 103.02 P = 2.049 B = A=
0.00 206.33 4509.6 0.0
5.21 206.68 4503.4 60.6
10.42 211.96 4466.9 475.0
15.63 232.42 4345.0 1366,7
18.23 250.72 4252.4 1908.5
20.84 274.66 4146.0 2464.8
23.44 303.88 4031.2 3014.4
26.05 337.86 3912.3 3546.3
V= 8D= =
18.80 T = 104.14 P = 2.029 B = A=
0.00 230.65 4658.8 0.0
5.32 231.02 4656.6 60.0
10.63 236.53 4619.3 469.6
15,95 257.81 4495.6 1342.3
18.61 276.76 4402.4 1867.6
21.27 301.48 4295.9 2403.7
23.93 331.58 4181.5 2929.9
26.59 366.52 4063.5 3436.1
V= 18.70 T = 8D= , 105.27 P = ~= 2.009 B = A=
0.00 255.90 4812.5 0.0
5.43 256.29 4804.6 59.6
10.86 262.06 4766.3 465.9
16.28 284.22 4640.6 1322.6
19.00 303.86 4546.8 1833.4
21.71 329.41 4440.2 2351.4
24.43 360.44 4326.2 2856.8
27.14 396.39 4209.3 3339.9
V= 8D= ~=
18.60 T = 106.40 P = 1.990 B = A=
0.00 282.13 4970.7 0.0
5.54 282.53 4962.5 59.2
11.08 288.57 4923.3 461.8
16.62 311.65 4795.7 1301.9
19.39 332.01 4701.5 1797.8
22.16 358.42 4594.8 2297.6
24.93 390.41 4481.6 2782.3
27.71 427.40 4365.8 3242.7
V= 8D= T=
18.50 T = 107.54 P = 1,972 B = A=
0.00 309.36 5133.7 0.0
5.66 309.79 5127.8 58.9
11.32 316.11 5087.4 458.0
16.97 340,17 4958.0 1281.9
19.80 361.30 4863.3 1763.5
22.63 388.62 4756.8 2245.6
25.46 421.64 4644.3 2710.2
28.29 459.73 4529.9 3148.8
V= 8D = ~=
18.40 T = 108.69 P = 1,955 B = A=
0.00 337.64 5301.5 0.0
5.77 338.09 5295.6 58.5
11.55 344.70 5254.3 454.1
17.32 369.76 5123.1 1262.0
20.21 391.66 5028.1 1729.7
23.10 419.90 4921.9 2194.9
25.99 453.94 4810.4 2640.4
28.87 493.14 4697.5 3058.6
V= 8o = ~=
18.30 T = 109.85 P = 1.939 B = A=
0.00 367.00 5474.3 0.0
5.90 367.47 5469.7 58.2
11.79 374.40 5427.2 450.7
17.69 400.53 5294.3 1243.2
20.63 423.24 5198.9 1697.5
23.58 452.46 5093.2 2146.4
26.53 487.59 4982.7 2573.7
29.48 527.96 4871.5 2972.3
V= 8o = T=
18.20 T = 111.02 P = 1,923 B = A=
0.00 397.48 5652.4 0.0
6.02 397.97 5648.1 57.9
12.04 405.24 5604.6 447.4
18.05 432.47 5470.0 1225.1
21.06 456.04 5374.4 1666.4
24.07 486.26 5269.3 2099.7
27.08 522.52 5160.0 2509.6
30.09 564.09 5050.8 2889.7
V= 8~= =
18.10 T = 112.20 P = 1.908 B = A=
0.00 429.13 5835.8 0,0
6.14 429.65 5833.1 57.7
12.29 437.27 5788.4 444.5
18.43 465.69 5652,0 1207.9
21.50 490.16 5556.4 1636.6
24.58 521.45 5451.8 2055.0
27.65 558.89 5344.1 2448.1
30.72 601.73 5236.8 2810.4
V= 8D = =
18.00 T = 113.39 P = 1.894 B = A=
0.00 461.98 6024.8 0.0
6.27 462.53 6022,7 57.6
12.55 470.54 5976.8 442.2
18.82 500.22 5838.8 1191.9
21.96 525.65 5743.1 1608.7
25.10 558.06 5639.3 2012.6
28.23 596.75 5533,0 2390.0
31.37 640.94 5428.3 2735.3
V= 8D= =
17.90 T = 114.59 P = 1.881 B = A=
0.00 496.09 6219.5 0.0
6.41 496.66 6213.4 57.5
12.82 505.08 6166.4 440.5
19.22 536.11 6026.8 1177.8
22.43 562.55 5931.2 1583.3
25.63 596.16 5828.5 1973.7
28.84 636.16 5724.2 2336.1
32.04 681.76 5622.0 2665.7
V= 8D= =
17.80 T = 115.80 P = 1.869 B = A=
0.00 531.49 6420.2 0.0
6.54 532.09 6420.8 57.3
13.08 540.94 6372.4 437.8
19.63 573.33 6231.4 1161.2
22.90 600.80 6136.0 1555.0
26.17 635.61 6034.4 1931.6
29.44 676.95 5932.1 2279.0
32.71 723.98 5832.9 2593.0
V= 8D= =
17.70 T = 117.02 P = 1.858 B = A=
0.00 568.24 6626.9 0.0
6.68 568.87 6623.5 57.3
13.36 578.18 6574.0 436.1 .
20.04 612.03 6431.6 1147.5
23.38 640.59 6336.7 1530.6
26.72 676.67 6236.6 1894.7
30.06 719.41 6136.7 2228.3
33.40 767.94 6040.4 2528.1
388
Alfred Driessen and Isaac F. Silvera
T A B L E V--continued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0o= =
17.60 T = 118.25 P = 1.847 B = A=
0.00 606.38 6840.0 0.0
6.82 607.05 6837.4 57.3
13.64 616.85 6786.7 434.5
20.46 652.24 6643.0 1133.7
23.88 681.95 6548,7 1506,3
27.29 719.37 6450.0 1858.0
30.70 763.60 6352.6 2178.3
34.11 813.70 6259.8 2464.2
V= 0D= y=
17.50 T = 119.50 P = 1.838 B = A=
0.00 645.98 7059,7 0.0
6.97 646.69 7051.2 57.4
13,93 657.00 6999.0 433.6
20,90 694.04 6854.0 1121.9
24.38 724,97 6760.3 1484.7
27.87 763.80 6663.4 1824.9
31.35 809.58 6568.8 2132,7
34.84 861.35 6479.4 2405.8
V= 0D= y=
17.40 T = 120.76 P = 1,830 B = A=
0.00 687.09 7286.2 0.0
7.11 687.83 7282.6 57.3
14.23 698.68 7229.2 431.7
21.34 737.40 7083.2 1107.7
24.89 769.56 6990.5 1460.3
28.45 809.83 6895.7 1788.8
32.01 857.19 6804.2 2084.0
35.56 910.64 6718.9 2344.5
V= 0D = y=
17.30 T = 122.04 P = 1.822 B = A=
0.00 729.75 7519.6 0.0
7.27 730.54 7511.8 57.5
14.53 741.99 7456.9 431.3
21.80 782.55 7310.1 1096.9
25.43 816.06 7218.2 1440.3
29.06 857.90 7125.6 1758,0
32.70 906.98 7037.6 2041.7
36,33 962.27 6956.7 2290.3
V= 0o= =
17.20 T = 123.33 P = 1.816 B = A=
0.00 774.0 7760.3 0.0
7.42 774.9 7757.4 57.6
14.84 786.9 7701,2 430,0
22.26 829.4 7553,7 1084,2
25.97 864.3 7463.3 1418.1
29.68 907.7 7373.3 1724.9
33,38 958.5 7288.9 1997.2
37.09 1015.7 7213.1 2234.2
V= 0~= y=
17.10 T = 124.65 P = 1.810 B = A=
0.00 820.0 8008.6 0.0
7.58 820.9 8003.3 57.8
15.16 833.6 7945.7 429.9
22.74 878.2 7797.6 1074.2
26.53 914.5 ~708.5 1399.4
30.32 959.7 7621.5 1696.1
34,11 1012.4 7541.4 1957.6
37.90 1071.6 7470.6 2183,8
V= 0o= ~=
17.00 T = 125.97 P = 1.806 B = A=
0.00 867.7 8264.6 0.0
7.74 868,7 8255.6 58.0
15.48 882.1 8196.5 429.5
23.22 928.7 8047.8 1063.9
27.09 966.7 7960.7 1380.6
30.96 1013.6 7876.6 1667.7
34.83 1068.3 7800.9 1919.1
38.70 1129.5 7735,7 2135.0
V= 0o= y=
16.90 T = 127.32 P = 1.802 B = A=
0.00 917.3 8528.6 0.0
7..91 918.2 8519.2 58.3
15.82 932.5 8458.4 429.7
23.73 981.4 8309.4 1054.7
27.68 1021.0 8224.1 1363.1
31.63 1069.9 8143.4 1640.8
35.59 1126.6 8072.5 1882.3
39.54 1190,1 8013.3 2088.4
V= 0o= y=
16.80 T = 128.69 P = 1,800 B = A=
0.00 968.7 8801.0 0.0
8.08 969.7 8794.3 58.5
16.15 984.7 8731,9 429.4
24.23 1036.1 8583.1 1044.5
28.27 1077.4 8499,9 1344.7
32.3t 1128.2 8423.2 1613.2
36,35 1187.1 8357.5 1845.3
40.39 1252.8 8304,6 2041.8
V= 0o = y=
16.70' T = 130.08 P = 1.799 B = A=
0.00 1022.1 9082.0 0.0
8.25 1023.2 9073.8 58.9
16.51 1039.1 9009.9 429.9
24.76 1093.0 8861.1 1036.2
28.89 1136.1 8780.3 1328.7
33.01 1189.1 8707.8 1588.5
37.14 1250.3 8647.8 1811.4
41,27 1318.4 8601.6 1999.1
V= 0o = y=
16.60 T = 131.49 P = 1.798 B = A=
0.00 1077.5 9371.9 0.0
8.43 1078.6 9363.8 59.2
16.86 1095.5 9298.4 430.0
25.29 1152.1 9150.3 1027.2
29.50 1197.1 9072.2 1312.2
33.72 1252.2 9004.4 1563.6
37.93 1315.7 8950.7 1777.8
42.15 1386.4 8912.2 1956.8
V= 0D= y=
16.50 T = 132.93 P = 1.799 B = A=
0.00 1135.0 9671.0 0.0
8.61 1136.2 9669.2 59.6
17.23 1154.0 9602.1 430.5
25~4 1213.5 9454.5 1018.8
30.15 1260.6 9379.7 1296.4
34.45 1318.0 9316,7 1539.4
38.76 1384.2 9269,4 1745.2
43.07 1457.5 9239.2 1915.9
V= 0p= y=
16.40 T = 134.39 P = 1.801 B = A=
0~00 1194.7 9979.7 0.0
8.80 1196.0 9977.3 60.2
17.61 1214.9 9908.3 431.9
26.41 1277.6 9761.7 1012.2
30.82 1326.8 9690.5 1282.7
35.22 1386.8 9632.6 1518.1
39.62 1455.6 9592.6 1715.8
44.02 1531.9 957~9 1878.6
Improved Experimental Equation o| State of Solid Hydrogen and Deuterium
389
T A B L E V---contmued ~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0o= 7=
16.30 T = 135.88 P = 1.805 B = A=
0.00 1256.7 10298.0 0.0
9.00 1258.1 10286.0 60.7
17.99 1278.2 10215.0 433.2
26.99 134.0 10069.0 1006.1
31.49 1395.5 10002.0 1270.2
35.98 1458.1 9950.0 1498.2
40.48 1529.7 9917.0 1688.5
44.98 1609.0 9905.0 1844.2
V= 0o= 7=
16.20 T = 137.40 P = 1.809 B = A=
0.00 1321.1 10627.0 0.0
9.20 1322.6 10613.0 61.3
18.39 1343.9 10540.0 434.7
27.59 1413.2 10396.0 1000.1
32.18 1467.2 10333.0 1257.6
36.78 1532.5 10287.0 1478.4
41.38 1607.1 10263.0 1661.3
45.98 1689.5 10260.0 1809.8
V= 0D= 7=
16.10 T = 138.95 P = 1.815 B = A=
0.00 1388.0 10967.0 0.0
9.39 1389.6 10963.0 61.7
18.79 1412.1 10888.0 435.4
28.18 1485.0 10746.0 992.4
32.88 1541.5 10687.0 1243.3
37.58 1609.6 10648.0 1457.0
42.27 1687.4 10633.0 1632.8
46.97 1773.1 10641.0 1774.3
V= 0o= 7=
16.00 T = 140.53 P = 1.822 B = A=
0.00 1457.4 11318.0 0.0
9.60 1459.1 11305.0 62.4
19.20 1483.0 11228.0 437.2
28.80 1559.8 11089.0 987.4
33.60 1619.0 11035.0 1232.4
38.40 1690.2 11003.0 1439.5
43.20 1771.2 10997.0 1608.7
48.00 1860.4 11017.0 1743.8
TABLE %I1 Equation of State of Ortho-Deuterium: High Densities
T~ T~ =
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= 7=
15.90 T = 142.54 P = 1.752 B = A=
0.00 1.5295 11.680 0.0
9.72 1.5311 11.673 58.1
19.43 1.5544 11.582 408.0
29.15 1.6293 11.391 927.0
34.00 1.6871 11.293 1162.2
38.86 1.7566 11.207 1364.6
43.72 1.8359 11.138 1534.4
48.58 1.9231 11.085 1674.5
V= 8o= 7=
15.80 T = 144.12 P = 1.750 B = A=
0.00 1.6043 12.054 0.0
9.93 1.6061 12.047 58.4
19.86 1.6307 11.951 407.7
29.79 1.7093 11.754 918.0
34.76 1.7695 11.654 1147.1
39.72 1.8418 11.567 1343.3
44.69 1.9240 11.498 1507.2
49.65 2.0144 11.446 1642.2
V= 0o= 7=
15.70 T = 145.73 P = 1.747 B = A=
0.00 1.6821 12.440 0.0
10.14 1.6839 12.435 58.6
20.29 1.7099 12.335 406.8
30.43 1.7922 12.132 908.0
35.51 1.8549 12.030 1130.8
40.58 1.9300 11.943 1321.0
45.65 2.0152 11.873 1479.3
50.72 2.107 11.822 1609.0
V= Oo= 7=
15.60 T = 147.37 P = 1.745 B = A=
0.00 1.7628 12.839 0.0
10.37 1.7648 12.831 59.1
20.75 1.7923 12.726 406.8
31.12 1.8787 12.517 899.5
36.31 1.9441 12.413 1116.5
41.50 2.0223 12.325 1300.7
46.68 2.1108 12.255 1453.4
51.87 2.2077 12.205 1578.2
V= 0D= 7=
15.50 T = 149.03 P = 1.743 B = A=
0.00 1.8467 13.251 0.0
10.60 1.8488 13.248 59.4
21.21 1.8779 13.138 406.0
31.81 1.9684 12.922 889.7
37.11 2.0365 12.817 1100.6
42.42 2.1178 12.728 1279.0
47.72 2.2096 12.658 1426.1
53.02 2.3099 12.609 1546.2
V= 8D= 7=
15.40 T = 150.72 P = 1.740 B = A=
0.00 1.9339 13.677 0.0
10.83 1.9361 13.666 59.6
21.67 1.9668 13.551 405.0
32.50 2.0614 13.329 879.8
37.92 2.1323 13.222 1085.1
43.33 2.2167 13.132 1257.9
48.75 2.3118 13.062 1400.1
54.17 2.4156 13.013 1515.7
V= #D = 7=
15.30 T = 152.43 P = 1.738 B = A=
0.00 2.0244 14.118 0.0
11.07 2.0267 14.102 59.9
22.14 2.0591 13.982 403.9
33.21 2.1581 13.753 869.9
38.75 2.2320 13.644 1069.5
44.28 2.3196 13.554 1236.8
49.82 2.4182 13.485 1373.8
55.35 2.5256 13.436 1485.0
390
Alfred Driessen and Isaac F. Silvera
TABLE Vl--continued TIT m =
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= 3, =
15.20 T = 154.18 P = 1.735 B = A=
0.00 2.1185 14.573 0.0
11.32 2.1210 14.554 60.2
22.63 2.1552 14.428 402.9
33.95 2.2588 14.192 860.0
39.61 2.3357 14.082 1054,0
45.26 2.4267 13.991 1215.8
50.92 2.5289 13.922 1348.1
56.58 2.6401 13.874 1454.9
V= 0D= 3,=
15.10 T = 155.96 P = 1.733 B = A=
0.00 2.2162 15.044 0.0
11.57 2.2188 15.032 60.5
23.14 2.2550 14,900 401,6
34.71 2.3635 14.658 849.5
40.49 2.4436 14.546 1037.8
46.27 2.5381' 14.454 1194.3
52.06 2.6441 14,385 1321.6
57.84 2.7592 14,339 1424.2
V= 0o= y=
15.00 T = 157.76 P = 1.731 B = A=
0,00 2.3178 15.530 0.0
11.82 2.3206 15.512 60.7
23.64 2.3587 15.374 400.1
35.46 2.4721 15.125 839.1
41.37 2.5554 15.011 1022.0
47.28 2.6535 14.919 1173.3
53.19 2.7632 14,851 1296.2
59.11 2.8823 14.805 1394.7
V= 0o= 3,=
14.90 T = 159.60 P = 1,728 B = A=
0,00 2.4233 16.034 0.0
12.09 2.4263 16.023 61.0
24.18 2.4666 15.878 398.8
36.27 2.5854 15.623 828.7
42.31 2.6722 15.507 1006.1
48.36 2.7741 15.414 1152.3
54.40 2.8879 15,347 1270.4
60.45 3.0112 15.302 1365.1
V= 0D= "/=
14,80 T = 161.46 P = 1.726 B = A=
0.00 2.5330 16.554 0.0
12.35 2.5362 16.540 61.2
24.70 2.5786 16.389 396.7
37.05 2.7026 16.127 817.4
43.22 2.7928 16.010 989.7
49.40 2.8985 15.917 1131.1
55.57 3.0162 15.849 1244.9
61.75 3.1437 15.806 1335.9
V= 0D= 3,=
14.70 T = 163.36 P = 1.723 B = A=
0.00 2.6471 17.093 0.0
12.63 2.6504 17.088 61.4
25.25 2.6952 16.930 394.8
37.88 2.8249 16.661 806.3
44.19 2.9187 16.543 973.3
50.50 3.0284 16.449 1109.7
56.81 3.1504 16.382 1219.2
63.13 3.2823 16.340 1306.5
V= 0D= 3,=
14.60 T = 165.29 P = 1.721 B = A=
0.00 2.7657 17.650 0,0
12.92 2.7692 17.639 61.8
25.83 2.8165 17.474 393.6
38.75 2.9524 17.198 796.5
45.21 3.0502 17.078 958.5
51.66 3.1642 16.985 1090.2
58.12 3.2908 16.918 1195.5
64.58 3.4273 16.878 1279.2
V= 0D= 3,=
14.50 T = 167.26 P = 1.718 B = A=
0.00 2.8890 18.227 0,0
13.19 2.8927 18.211 61.8
26.38 2.9424 18.038 391.0
39,57 3.0841 17.754 784.9
46.17 3.1856 17.633 942.0
52.77 3.3036 17.539 1069.2
59.36 3.4345 17.474 1170.8
65.96 3.5756 17.434 1251.1
V= 0D= 3'=
14.40 T = 169.26 P = 1,715 B = A=
0.00 3.0171 18.824 0.0
13.50 3.0211 18.809 62.2
27.00 3.0737 18.629 389.5
40,49 3.2221 18.338 774.7
47.24 3.3278 18.215 926.8
53.99 3.4505 18.121 1049.5
60.74 3.5863 18.056 1147.1
67.49 3.7324 18.019 1224.1
V= 0D= 3, =
14.30 T = 171.29 P = 1.713 B = A=
0.00 3,1505 19.441 0.0
13.79 3.1547 19,432 62.2
27.58 3.2100 19,244 386.5
41.37 3.3647 18,946 762.6
48.26 3.4744 18.823 909.9
55.15 3.6015 18,729 1028.4
62.05 3.7419 18.665 1122.2
68.94 3.8928 18.629 1196.2
V= 0D= y=
14.20 T = 173.36 P = 1.710 B = A=
0,00 3.2891 20.081 0.0
14.11 3.2936 20.061 62.6
28.22 3.3521 19.864 385,1
42.33 3.5141 19.559 752.7
49.39 3.6283 19.434 895.4
56.44 3.7604 19.340 1009.6
63.50 3.9060 19.277 1099.8
70.55 4.0623 19,243 1170.7
V= 0D= 3"=
14.10 T = 175.47 P = 1.708 B = A=
0.00 3.4334 20,744 0.0
14.42 3.4381 20.712 62.7
28,83 3.4996 20.508 382.2
43.25 3.6685 20.195 741.2
50.46 3.7870 20.069 879.5
57.67 3.9238 19.975 989.7
64.87 4.0744 19,913 1076.5
72.08 4.2359 19,880 1144.6
V= 0D= 3"=
14.00 T = 177.61 P = 1.705 B = A=
0.00 3.5835 21.430 0.0
14.74 3.5884 21.406 62.8
29.48 3.6532 21.193 379.4
44.21 3.8295 20.873 729.5
51.58 3.9527 20.745 863,2
58.95 4.0945 20.651 969.5
66.32 4.2504 20.591 1052.8
73.69 4.4173 20.561 1118.1
Improved Experimental Equation of State of Solid Hydrogen and Deuterium
391
TABLE ~---continued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0D= 7=
13.90 179.79 1.702
T= P= B = A =
0.00 3.7396 22.141 0.0
15.07 3.7449 22.134 63.0
30.15 3.8132 21.912 376.6
45.23 3.9975 21.584 717.9
52.76 4.1255 21.455 847.2
60.30 4.2727 21.362 949.4
67.84 4.4341 21.303 1029.4
75.38 4.6068 21.274 1091.9
V= #o = 7=
13.80 182.02 1.700
T= P= B= A=
0.00 3.9021 22.877 0.0
15.41 3.9077 22.843 63.2
30.82 3.9796 22.611 374.1
46.24 4.1719 22.277 707.3
53.94 4.3049 22.147 832.4
61.65 4.4574 22.054 931.0
69.35 4.6245 21.996 1008.1
77.06 4.8030 21.970 1067.9
V= 0D= 7=
13.70 184.28 1.697
T= P= B = A=
0.00 4.0713 23.460 0.0
15.76 4.0772 23.599 63.4
31.53 4.1530 23.358 371.5
47.29 4.3538 23.014 696.4
55.17 4.4920 22.884 817.3
63.06 4.6502 22.792 912.3
70.94 4.8233 22.736 986.2
78.82 5.0079 22.712 1043.6
V= 0o = =
13.60 186.58 1.694
T= P= B = A =
0.00 4.2473 24.432 0.0
16.13 4.2536 24.383 63.7
32.26 4.3336 24.130 369.0
48.39 4.5435 23.780 685.6
56.46 4.6873 23.649 802.5
64.53 4.8515 23.557 894.0
72.59 5.0308 23.502 964.9
80.66 5.2220 23.482 1019.7
V= 0o = 7=
13.50 188.93 1.692
T= P= B = A=
0.00 4.4307 25.252 0.00
16.48 4.4373 25.221 63.61
32.97 4.5213 24.959 365.01
49.45 4.7399 24.601 673.05
57.69 4.8889 24.469 785.86
65.94 5.0589 24.378 873.82
71.18 5.2443 24.326 941.95
82.42 5.4417 24.307 994.59
V= 0o= 7=
13.40 191.32 1.689
T= P= B= A=
0.00 4.6216 26.102 0.00
16.87 4.6286 26.074 63.80
33.73 4.7172 25.802 362.07
50.60 4.9455 25.436 661.89
59.03 5.1005 25.303 770.80
67.47 5.2768 25.212 855.49
75.90 5.4688 25.162 920.66
84.33 5.6730 25.146 970.99
V= 0D = 7=
13.30 193.75 1.686
T= P= B= A=
0.00 4.8203 26.985 0.00
17.25 4.8278 26.958 63.88
34.50 4.9210 26.673 358.67
51.75 5.1591 26.301 650.39
60.37 5.3200 26.167 755.48
69.00 5.5028 26.077 836.88
77.62 5.7016 26.029 899.45
86.25 5.9127 26.017 947.57
V= 0D= 7=
13.20 196.23 1.683
T= P= B= A=
0.00 5.0274 27.900 0.00
17.65 5.0354 27.854 64.05
35.30 5.1335 27.558 355.65
52.94 5.3821 27.178 639.56
61.77 5.5492 27.043 741.06
70.59 5.7387 26.955 819.40
79.41 5.9445 26.909 879.41
88.24 6.1628 26.899 925.50
V= #D = =
13.10 198.75 1.680
T= P= B= A=
0.00 5.2432 28.849 0.00
18.05 5.2516 28.794 64.08
36.09 5.3548 28.485 352.04
54.14 5.6138 28.098 628.17
63.16 5.7872 27.964 726.13
72.18 5.9836 27.876 801.42
81.21 6.1964 27.832 859.02
90.23 6.4220 27.825 903.07
V= #D = 7=
13.00 201.33 1.678
T= P= B = A=
0.00 5.4680 29.835 0.00
18.47 5.4769 29.822 64.19
36.95 5.5858 29.501 348.41
55.42 5.8564 29.105 616.35
64.66 6.0368 28.970 710.65
73.90 6.2405 28.884 782.80
83.13 6.4611 28.842 837.97
92.37 6.6946 28.839 879.93
V= 0o= 7=
12.90 203.95 1.675
T= P= B= A =
0.00 5.7024 30.858 0.00
18.90 5.7118 30.832 64.30
37.81 5.8264 30.498 345.00
56.71 6.1087 30.096 605.38
66.16 6.2960 29.960 696.23
75.61 6.5072 29.875 765.68
85.06 6.7356 29.836 818.43
94.52 6.9771 29.836 858.71
V= 8D= 7=
12.80 T = 206.62 P = 1.672 B = A=
0.00 5.9466 31.920 0.00
19.33 5.9566 31.868 64.32
38.66 6.0770 31.521 341.29
58.00 6.3711 31.110 594.37
67.66 6.5654 30.974 682.06
77.33 6.7842 30.891 748.79
86.99 7.0204 30.855 799.40
96,66 7.2699 30.859 837.97
V= #D = 7=
12.70 209.35 1.669
0.00 6.2013 33.023 0.00
19.79 6.2119 32.950 64.49
39.58 6.3388 32.589 338.01
59.37 6.6458 32.170 583.80
69.27 6.8478 32.035 668.21
79.17 7.0747 31.953 732.32
89.06 7.3194 31.920 780.84
98.96 7.5777 31.929 817.58
T= P= B= A=
392
Alfred Driessen and Isaac F. Silvera
TABLE H---continued
T/~
=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
V= 0o= 7=
12.60 T = 212.13 P = 1.666 B = A=
0.00 6.4668 34,169 0.00
20.25 6.4781 34.092 64.51
40.50 6.6116 33.717 334.11
60.75 6.9316 33.292 572.56
70.88 7.1412 33.156 653.92
81.00 7.3764 33,077 715.38
91.13 7.6297 33.047 761.85
101.25 7.8967 33,058 797.00
V= 0D= y=
12.50 T = 214.96 P = 1.6 B = A=
0.00 6.7438 35.360 0.00
20.71 6.7557 35,311 64.34
41.42 6.8959 34,922 329,50
62.13 7.2290 34.490 560.54
72.49 7.4464 34,354 638.78
82.84 7.6899 34.276 697.83
93.20 7.9518 34.249 742.33
103.55 8.2277 34.265 775.92
V= 0o = 7=
12.40 T = 217.85 P = " 1.660 B = A=
0.00 7.0328 36,598 0.00
21.20 7.0454 36.549 64.38
42.40 7.1930 36.145 325.60
63.60 7.5404 35.704 549.57
74.20 7.7662 35,569 624.82
84.80 8.0186 35.494 681.37
95.40 8.2898 35.472 723.93
106.00 8.5752 35.493 755.88
V= 0D= 7=
12.30 T = 220.79 P = 1.657 B = A=
0.00 7.3343 37.884 0.00
21.69 7.3477 37.826 64.31
43.38 7.5027 37,407 321.40
65.07 7.8646 36.958 538.49
75.92 8.0988 36,824 610.92
86.76 8.3603 36.751 665.13
97.61 8.6408 36,732 705.92
108.45 8.9359 36.756 736.52
V= 0D= y=
12.20 T = 223,80 P = 1,654 B = A=
0.00 7.6490 39.222 0.00
22.21 7.6632 39.160 64.36
44.42 7.8265 38,725 317.48
66,63 8.2040 38.270 527.73
77.74 8.4473 38.137 597.27
88.84 8.7186 38,065 649.32
99.95 9.0091 38,050 688.21
111.05 9.3145 38.081 717.55
V= 0D= y=
12.10 T = 226.86 P = 1.651 B = A=
0.00 7.9775 40.613 0.00
22.73 7.9925 40.555 64.27
445.46 8.1641 40,104 313.14
68.19 8.5575 39.641 516.65
79.56 8.8100 39.507 583.60
90.93 9.0910 39.440 633.40
102.29 9.3917 39,428 670.67
113.66 9.7074 39,463 698.46
V= 0D= y=
12.00 T = 229.99 P = 1.648 B = A=
0.00 8.321 42.060 0.00
23.28 8,336 41.988 64.32
46.57 8.517 41.520 309.22
69.85 8.928 41.050 506.16
81.49 9,190 40,916 570.49
93.13 9.481 40.853 618.18
104.77 9.793 40,846 653.72
116.41 10.120 40.887 680.35
V= 0D= 7=
11.90 T = 233.18 P = 1.645 B = A=
0.00 8.679 43.566 0.00
23.83 8.696 43.505 64.21
47.87 8.886 43.019 304,74
71.50 9.313 42.541 495.20
83.42 9.586 42.411 556.93
95.34 9.888 42.348 602.65
107.25 10.210 42,347 636.56
119.17 10.548 42,394 661.87
V= 0D= 7=
11.80 T = 236.44 P = 1.642 B = A=
0.00 9.053 45,133 0.00
24.39 9.071 45,049 64.02
48.77 9.270 44.545 300.19
73.16 9.715 44.061 484.45
85.35 9,997 43.931 543.77
97.54 10.310 43.873 587.67
109.73 10.644 43.877 620.09
121.93 10.993 43,929 644.32
V= 0D= y=
11.70 T = 239.76 P = 1.639 B = A=
0.00 9.444 46.766 0.00
24.97 9.463 46.690 63.88
49.93 8.672 46,167 295.66
74.90 10.136 45.677 473.68
87.38 10.429 45.548 530.64
99.87 10.753 45.493 572.59
112.35 11.098 45.501 603.57
124.83 11.460 45,559 626.67
V= 0D= 7=
11.60 T = 243.15 P = 1.636 B = A=
0.00 9.853 48.465 0.00
25,58 9.873 48.369 63.87
51.16 10.093 47.826 291.51
76.74 10.577 47,329 463.53
89.53 10.881 47.203 518.12
102.32 11,218 47.152 558.30
115.11 11.575, 47,166 587.84
127.90 11.949 47,229 609.87
V= 0D= 7=
11.50 T = 246.62 P = 1.632 B = A=
0.00 10.280 50.236 0.00
26.19 10.301 50.142 63.69
52.38 10.533 49.581 286.88
78.58 11.037 49.078 452.97
91.67 11.353 48,954 505.35
104.77 11.701 48,906 543.73
117.86 12,071 48.926 571.96
130.96 12.458 48,997 593.09
V= 0D= 7=
11.40 T = 250.16 P = 1.629 B = A=
0.00 10.727 52.081 0.00
26.83 10,749 51.976 63.61
53.67 10.993 51.395 282.51
80.50 11,518 50.884 442.78
93.92 11.846 50,761 492.98
107.34 12.208 50,720 529.65
120.76 12.592 50.743 556.74
134.17 12.992 50.824 576.68
Improved Experimental Equation of State ot Solid Hydrogen and Deuterium
393
TABLE ~--continued
T/~ = V = 0D =
3,= V= 0D =
3,= V= 0D =
3,= V= 0D =
3,= V= 0D =
3,= V= 19D =
3,= V= 3,= V= 0D =
3'= V= 0D =
3'= V= 0D =
3'= V= 0D =
3'= V= 3,= V= 0D =
3,=
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
11.30 T = 253.77 P = 1.626 B = A=
0.00 11.194 54.004 0.00
27.48 11.218 53.952 63.32
54.96 11.474 53.349 277.50
82.43 12.021 52.832 431.96
96.17 12.361 52.713 480.01
109.91 12.736 52.675 515.14
123.65 13.133 52.705 540.88
137.39 13.547 52.791 559.93
11.20 T = 257.46 P = 1.623 B = A=
0.00 11.683 56.010 0.00
28.15 11.708 55.906 63.21
56.30 11.978 55.284 273,16
84.46 12.548 54.762 422.20
98.53 12.901 54.644 468.31
112.61 13,289 54.611 501.81
126.68 13.701 54.648 526.37
140.76 14.129 54.742 544.57
11.10 T = 261.33 P = 1.619 B = A=
0.00 12.195 58.101 0.00
28.86 12.222 57,960 63.13
57.71 12.505 57.312 268.85
86.57 13.100 56.786 412.54
101.00 13.467 56.673 456.65
115.43 13.870 56.645 488.69
129.85 14.296 56.689 512.13
144.28 14.740 56.792 529.38
11.00 T = 265.08 P = 1.616 B = A=
0.00 12.730 60.284 0.00
29,56 12.759 60.190 62.38
59.12 13.057 59.521 263.87
88.68 13.676 58.988 402.15
103.46 14.057 58.876 444.41
118.24 14.475 58.855 474.91
133.02 14.916 58.906 497.35
147.80 15.376 59.017 513,73
10.90 T = 269.02 P = 1.613 B = A=
0.00 13.291 62.561 0.00
30.30 13.321 62.461 62.62
60.59 13.635 61.768 259.22
90.89 14.280 61.229 392.36
106.03 14.676 61.122 432.74
121.18 15.109 61.106 461.88
136.33 15.567 61.166 483.27
151.48 16.042 61.285 498.84
10.80 T = 273.04 P = 1.609 B = A=
0.00 13.879 64.938 0.00
31.03 13.911 64.817 62.30
62,06 14.239 64.103 254.38
93.09 14.911 63.560 382.56
108.61 15,322 63.456 421.23
124.12 15.771 63.446 449.11
139.64 16.244 63.512 469.45
155.15 16.737 63.640 484.41
10.70 T = 277.16 P = 1.606 B = A=
0.00 14.494 67.422 0.00
31.80 14.528 67.307 61.99
63.59 14.874 66.567 249.52
95.39 15.573 66.018 372.83
111.29 15.999 65.918 409.78
127.19 16.465 65.914 436.44
143.08 16.956 65.989 455.77
158.98 17.465 66.127 469.94
10.60 T = 281.36 P = 1.602 B = A=
0.00 15.139 70.015 0.00
32.62 15.176 69.898 61.86
65.25 15.540 69.133 245.06
97.87 16.270 68.580 363.49
114.18 16.713 68.484 398.80
130.49 17.197 68.488 424.15
146.80 17.706 68.573 442.51
163.12 18.234 68.722 456.06
10.50 T = 285.66 P = 1.599 B = A=
0.00 15.816 72.726 0.00
33.45 15.854 72.547 61.64
66.90 16.237 71.754 240.54
100.35 16,999 71.199 354.41
117.07 17.459 71.107 388.13
133.80 17.961 71.119 412.35
150.52 18.488 71.215 429.83
167.25 19.036 71,371 442.66
10.40 T = 290.06 P = 1.595 B = A=
0.00 16.525 75.560 0.00
34.28 16.566 75.433 61.19
68.55 16.968 74.616 235.40
102.83 17,760 74.055 344.71
119.97 18,238 73.970 376.97
137,11 18.758 73.990 399.96
154.25 19.305 74,090 416.71
171.38 19.871 74.258 428.98
10.30 T = 294.56 P = 1.592 B = A=
0.00 17.269 78.524 0.00
35.17 17.313 78.383 60.95
70.33 17.736 77.536 230.78
105.50 18.563 76.972 335.67
123.08 19.060 76.982 366.42
140.66 19.599 76,920 388.35
158.24 20.167 77,033 404.32
175.82 20.754 77.216 415.90
10.20 T = 299.17 P = 1.588 B = A=
0.00 18.051 81.625 0.00
36.05 18.097 81.471 60.57
72.11 18.541 80.596 225.94
108.16 19.402 80.030 326.59
126.19 19.918 79.958 355.89
144.21 20.478 79.994 376.84
162.24 21.066 80.116 391.93
180.27 21.674 80.307 403.13
10.10 T = 303.88 P = 1.584 B = A=
0.00 18.871 84.869 0.00
37.00 18.920 84.668 60.34
74.00 19.388 83.765 221.42
111.01 20.287 83.197 317.90
129.51 20.823 83.130 345.91
148.01 21.405 83.177 365,80
166.51 22.015 83.311 380.14
185.01 22.646 83.518 390.71
394
Alfred Driessen and Isaac F. Silvera
TABLE Vl--continued
T / T m= V=
10.00 T = 308.70 P = 1.581 B = A=
OD= ~=
I
I
p
0.0
0.2
0.4
0.6
0.7
0.8
0.9
1.0
0.00 19.732 88.267 0.0
37.92 19.784 88.098 59.78
75.84 20.274 87.166 216.30
113.76 21.210 86.596 308.78
132.72 21.767 86.535 335.53
151.68 22.370 86.588 354.45
170.65 23.002 86.734 368.19
189.61 23.655 86.953 378.06
I
I
I
I
0 ISOCHOREFROMOURTABLE /
o
I
o
o
I
I
I
0
//
I
"tl
o
~
/!
I
I T [K]
Fig. 4. Isochoric plot of P versus T. See the text for an explanation.
ACKNOWLEDGMENT We thank E. van de Poll for aid with the computer analyses of the data.
REFERENCES A. Driessen, J. A. de Waal, and I. F. Silvera, J. Low Temp. Phys. 34, 255 (1979). J. K. Krause and C. A. Swenson, Solid State Commun. 31, 833 (1979). J. K. Krause and C. A. Swenson, Phys. Rev. B 21, 2533 (1980). J. K. Krause, thesis (1978), unpublished. D. H. Liebenberg, R. L. Mills, and J. C. Bronson, Phys. Rev. B 18, 4526 (1978). R. L. Mills, priv~ite communication. A. Driessen, Thesis (1982), unpublished, Chapter VI; A. Driessen, I. F. Silvera, and E. van de Poll, to be published. 8. I. F. Silvera, Rev. Mod. Phys. 52, 393 (1980). 9. F. Birch, J. Geophs. Res. 56, 227 (1952). 10. M. S. A n d e r s o n and C. A. Swenson, Phys. Rev. B 10, 5184 (1974). 1. 2. 3. 4. 5. 6. 7.
Improved Experimental Equation o[ State oi Solid Hydrogen and Deuterium
11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27. 28. 29. 30. 31. 32. 33. 34. 35.
395
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