An improved experimental equation of state of solid hydrogen and deuterium

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 25 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 B A C K G R O U N D

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 = - ( a F / a V ) T (2)

B = - V(oP/o V) T (3)

a = (1/V)(O V/OT)p (4)

With the aid of Eq. (3) we can write

a = - ( 1 / B ) ( O p / O T ) 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/O T is zero by definition,

1 (OP*( V, T).) a(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 Mie- Gr/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):

7(V) 9NokB T4 (;D x____~_ 3 P*( v, T) V Oh(V) .v e x - l d x (9)

where

d In Oo(V) 7(V) = (10)

dV

R = NokB is the gas constant and XD = OD/T.

3. T H E T = 0 I S O T H E R M O F P A R A - H Y D R O G E N

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 a l . , 12 with a small correction at low densities by Younglove. 13

3. Our own experimental data for the relation between zero- temperature pressure and melting pressure along an isochore.


TABLE I

The Coefficients of the T = 0 Isotherm in the Birch Relation, Eq. (8)

p-H2 o-D2

Vo, cm3/mole 23.207 19.95 B1, bar 2790.1 4766.5 Bz, bar 4959.5 10101 B3, bar 1868 -- B4, bar -32.16. - -

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 P R E S S U R E A T 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


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 (Ckx k) (13) k=o

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. Direct measurements from Ref. 1 (eight isochores). 2. Direct measurements from Meyer 16 (one isochore). 3. A new direct measurement by us (run I, Ref. 7, one isochore). 4. Indirect measurements calculated from specific heat data of Krause

and Swenson 2-4 (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 D2

Low density High density Low density High density

C O 4.5991 4.5987 4.5176 4.5525 C 1 - 2 . 2 1 3 - 2 . 2 1 2 8 - 2 . 3 0 6 4 - 1 . 8 3 6 C 2 - 0 . 5 9 0 6 - 0 . 6 1 1 9 2 -2 .7935 - 0 . 1 8 4 8 4 C 3 - - - 0 . 019666 -5 .121 - -

Vo, cm3/mole 23.207 19.95

"For an explanation of high-density values, see the text, after Eq. (15).


5. THE E Q U A T I O N OF STATE OF SOLID 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 interpola- tions 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~s obtained 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 (16)

with Pm given in kbar, Tm in kelvin.


We are now able to calculate the EOS for high densities (16- 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. DISCUSSION OF THE RESULTS FOR 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,

5 -

3

-2

I ' I ' I ~ I F i I / 0

8 o 8

0 T-y 0

"(3. 0

8-- . o

-[3-[3 [] [] ~I~I> ~ ~ i> - -

<>

4 V[cm3/mole]

f I I I ~ I i I I F f I ,.~1 22 20 18 16 14 12 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~.) = a v

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.

We 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 f rom 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 more accurate than an extrapolation to zero pressures based on a Birch relation, as presented by I I - IV.

As can be seen from Fig. 1, up to 12.5 cm3/mole, corresponding to 8 kbar, agreement between all authors is bet ter than 0.3% in relative volume.


Above 12.5cm3/mole up to l lcm3/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 Jochemsen 22"23 indicate 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 Swenson 24 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 Jochemsen 22'23 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


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-VIII 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 room- temperature 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 t

3- l~x10 3[K -1]

2 m

0 0

~ :3 g2 barT/ ZP---1981 / / i /L/~ bo~

ii /I --

ii I 711 II l/ iiii~/////ii///

. / " " .J'" T[K] . ~ - - f 2 - ~ I I I

5 10 15 20 Fig. 2. The thermal expansion of p-H 2 as a function of tempera ture at pressures of 3.92 and 198.1 bar. Solid lines: Manzhelii et aL29; dashed lines from our EOS, given in the Appendix.


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 STATE OF SOLID 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.


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× -3 1.677 = 10 T m 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

ot x 103[K -1]

I I I

m / /

l P=O - / :'

/ :' / - P= 2l,,

I., - - /13 . . : / .." r / . . ' / 4 / A,.X

- / , , , I / j ~ : ~ Y

2 - - / ~ ' " t I

- J ~. " ' " T [ K ]

0 5 10 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 f rom our EOS, given in the Appendix; dotted lines: Esel 'son et a/.33; squares: Krupskii et al. 34


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

A P P E N D I X

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 temperature- independent 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 some- times 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/Tm, 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 Pms-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.


TABLE lII Equation of State of Para-Hydrogen: Low Densities

T I T m = 0.0 0.2 0.4 ' 0.6 0.7 0.8 0.9 1.0

V = 23.40 T = 0.00 9.71 11.10 12.48 13.87 00= 97.59 P = -14.9858 -10.6096 -7.6183 -3.4397 2.0755

y = 2.223 B = 1764.0 1736.6 1719.7 1697.6 1670.7 A = 0.0 1021.0 1490.4 2049.3 2683.7

V = 23.30 T = 0.00 2.83 5.66 8.49 9.91 11.32 t2.74 14.15 0D= 98.53 P = -7 .326 -7.295 -6 .829 -4 .817 -2 ,709 0.440 4,832 10.617

y = 2.218 B = 1813.3 1814.8 1811.9 1799.6 1787.1 1769.4 1746.4 1718.5 A = 0.0 24.2 193.8 652.8 1024.6 1493.5 2049.9 2679.3

V = 23.20 T = 0.00 2.89 5.78 8.66 10.11 11.55 13.00 14,44 0D= 99.47 P = 0.581 0.613 1.104 3.226 5.446 8.759 13.370 19.432

y = 2.213 B = 1863.8 1864.4 1861.3 1848.4 1835.3 1816.9 1792.9 1764.0 A = 0.0 24.4 195,0 656.5 1029.5 1498.4 2053.1 2678.5

V = 23.10 T = 0.00 2.95 5.89 8,84 10.31 11.78 13,26 14.73 0D= 100.42 P = 8.743 8,778 9.295 11.531 13.867 17.348 22.186 28.532

y = 2.207 B = 1915.6 1915.0 1911.8 1898.3 1884.6 1865.3 1840.5 1810.6 A = 0.0 24.5 196.2 660.0 1033.8 1502.5 2055.0 2676.1

V = 23.00 T = 0.00 3.00 6.01 9.01 10.51 12.01 13.51 15.02 0D= 101.39 P = 17.168 17.205 17.749 20.099 22.553 26.205 31.270 37.903

y = 2.202 B = 1968.7 1969.2 1965.9 1951.6 1937.4 1917.3 1891.5 1860.6 A = 0.0 24.6 196.8 661.8 1035.5 1502.8 2051.9 2667.1

V = 22.90 T = 0.00 3.06 6.12 9.19 10.72 12.25 13.78 15.31 0D= 102.36 P = 25.865 25.903 26.477 28.950 31.530 35.363 40.670 47.607

y = 2.197 B = 2023.1 2023.8 2020.3 2005.4 1990.4 1969.5 1942.8 1910.7 A = 0.0 24.7 197.7 664.3 1038.4 1504.6 2050.8 2660.7

V = 22.80 T = 0.00 3.12 6.25 9.37 10.93 12.49 14.06 15.62 OD= 103.35 P = 34.841 34.881 35.485 38.091 40.805 44.832 50.396 57.654

y = 2.192 B = 2079.0 2078.8 2075.1 2059.4 2043.8 2022.0 1994.2 1961.1 A = 0.0 24.8 198.9 667.7 1042.5 1508.0 2051.6 2656.6

V = 22.70 T = 0.00 3.18 6.37 9.55 11.15 12.74 14.33 15.92 0D= 104.35 P = 44.105 44.147 44.783 47.523 50.374 54.597 60.422 68.005

y = 2.187 B = 2136.2 2136.7 2132.8 2116.4 2100.1 2077.4 2048.5 2014.4 A = 0.0 24.9 199.7 669.8 1044.5 1508.6 2048.6 2647.7

V = 22.60 T = 0.00 3.25 6.49 9.74 11.36 12.98 14.61 16.23 OD= 105.36 P = 53,666 53.711 54.378 57.256 60.246 64.669 70.757 78.668

y = 2.182 B = 2195.0 2192.4 2188.3 2171.1 2154.1 2130.6 2100.7 2065.5 A = 0.0 25.1 200.6 672.3 1047.1 1510.0 2046.9 2640.7

V = 22.50 T = 0.00 3.31 6.61 9.92 11.58 13.23 14.88 16.54 0D= 106.39 P = 63.533 63.579 64.280 67.297 70.428 75.053 81.408 89.650

y = 2.176 B = 2255.2 2257.3 2253.1 2235.1 2217.4 2192.9 2162.1 2125.8 A = 0.0 25.0 200.6 671.6 1044,8 1504.3 2035.6 2621.3

V = 22,40 T = 0.00 3.37 6.74 10.11 11.79 13.47 15.16 16.84 0D= 107.42 P = 73.72 73,76 74.50 77.66 80.93 85.76 92.38 100.96

y = 2.171 B = 2317.0 2318.3 2313.8 2295.1 2276.6 2251.3 2219.4 2181.9 A = 0.0 25.1 200.9 672.0 1044.2 1501.1 2027.7 2606.7

V = 22.30 T = 0.00 3.43 6.86 10.29 12.00 13.72 15.43 17.15 0 D = 108.47 P = 84.22 84.27 85.04 88.35 91.76 96.80 103.70 112.61

y = 2.166 B = 2380.4 2378.8 2374.1 2354.6 2335.5 2309.3 2276.5 2238.0 A = 0.0 25.1 201.1 672.2 1043.3 1497.5 2019.5 2591.6

V = 22.20 T = 0.00 3.50 7.00 10.50 12.25 13.99 15.74 17.49 0o= 109.53 P = 95.07 95.12 95.93 99.41 103.00 108.29 115.51 124.83

7 = 2.161 B = 2445.4 2449.0 2444.2 2423.7 2403.7 2376.4 2342.3 2302.~ A = 0.0 25.2 201.8 673.7 1044.1 1495.9 2013.3 2578.,


TABLE Ul----vontinued

T / ~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 20.80 T = 0.00 4.51 9.02 13.53 15.78 18.04 20.29 22.55 0D= 110.26 P = 106.26 107.16 107.16 110.78 114.53 120.02 127.53 137.18

7 = 2.155 B = 2512.1 2513.3 2508.3 2487.0 2466.3 2438.1 2403.0 2362.3 A = 0.0 25.2 201.6 672.4 1040.9 1489.2 2001.0 2558.5

V = 22.00 T = 0.00 3.62 7.24 10.86 12.67 14.49 16.30 18.11 0o= 111.69 P = 117.80 17.86 118.74 122.52 126.41 132.12 139.90 149.90

7 = 2.150 B = 2580.5 2580.0 2574.8 2552.7 2531.3 2502.2 2466.1 2424.3 A = 0.0 25.1 201.1 670.2 1036.4 1480.6 1986.4 2535.8

V = 21.90 T = 0.00 3.70 7.40 11.09 12.94 14.79 16.64 18.49 0D= 112.78 P = 129.72 129.78 130.71 134.70 138.81 144.82 153.00 163.48

7 = 2.144 B = 2650.7 2651.1 2645.5 2622.3 2599.9 2569.5 2532.1 2488.9 A = 0.0 25.3 202.8 674.8 1041.7 1485.1 1987.9 2532.0

V = 21.80 T = 0.00 3.76 7.52 11.28 13.16 15.04 16.92 18.80 0D= 113.89 P = 142.02 142.08 143.05 147.19 151.46 157.68 166.14 176.96

7 = 2.139 B = 2722.8 2720.8 2715.0 2691.0 2667.9 2636.7 2598.3 2554.1 A = 0.0 25.2 202.0 671.5 1035.4 1474.0 1970.2 2505.7

V = 21.70 T = 0.00 3.84 7.67 11.51 13.42 15.34 17.26 19.18 0D= 115.02 P = 154.70 154.77 155.79 160.16 164.65 171.18 180.04 191.35

7 = 2.134 B = 2796.7 2794.2 2788.1 2762.9 2738.7 2706.3 2666.6 2621.0 A = 0.0 25.4 203.3 674.8 1038.8 1475.8 1968.3 2498.0

V = 21.60 T = 0.00 3.90 7.79 11.69 13.64 15.59 17.54 19.48 0D= 116.16 P = 167.80 167.87 168.92 173.45 178.09 184.85 193.99 205.65

= 2.128 B = 2872.6 2872.2 2865.9 2839.9 2815.0 2781.7 2740.9 2694.4 A = 0.0 25.2 201.7 669.1 1028.9 1459.9 1944.4 2464.2

V = 21.50 T = 0.00 3.97 7.95 11.92 13.91 15.89 17.88 19.87 0o= 117.31 P = 181.31 181.38 182.49 187.25 192.12 199.19 208.74 220.89

7 = 2.123 B = 2950.5 2945.8 2939.2 2912.0 2886.1 2851.6 2809.5 2761.6 A = 0.0 25.3 202.9 671.8 1031.3 1460.5 1941.1 2455.1

V = 21.40 T = 0.00 4.05 8.10 12.15 14.18 16.20 18.23 20.25 0D= 118.47 P = 195.25 195.33 196.49 201.48 206.58 213.97 223.93 236.58

7 = 2.117 B = 3030.5 3028.5 3021.6 2993,2 2966.2 2930.5 2887.1 2838.0 A = 0.0 25.4 203.2 672.1 1030.0 1455.8 1931.0 2437.4

V = 21.30 T = 0.00 4.11 8.22 12.33 14.39 16.45 18.50 20.56 0D= 119.65 P = 209.63 209.71 210.92 216.07 221.33 228.94 239.19 252.20

7 = 2.112 B = 3112.6 3112.0 3104.9 3075.6 3048.0 3011.4 2967.1 2916.9 A = 0.0 25.1 201.3 664.8 1017.9 1437.0 1903.6 2399.9

V = 21.20 T = 0.00 4,20 8.41 12.61 14.71 16.81 18.91 21.02 0D= 120.85 P = 224.48 224.56 225.84 231.31 236.88 244.92 255.71 269.36

7 = 2.106 B = 3196.9 3197.6 3190.1 3159.2 3130.2 3092.0 3046.0 2994.3 A = 0.0 25.4 203.6 671.0 1025.1 1443.4 1907.1 2398.1

V = 21.10 T = 0.00 4.26 8.53 12.79 14.93 17.06 19.19 21.32 0 D = 122.05 P = 239.80 239.88 241.20 246.84 252.56 260.83 271.91 285.92

7 = 2.101 B = 3283.4 3280.5 3272.8 3241.1 3211.4 3172.3 3125.5 3072.7 A = 0.0 25.2 201.5 663.7 1013.0 1424.8 1880.4 2361.9

V = 21.00 T = 0.00 4.36 8.71 13.07 15.25 17.43 19.60 21.78 0 D = 123.28 P = 255.61 255.70 257.10 263.05 269.10 277.80 289.43 304.10

7 = 2.095 B = 3372.2 3372.1 3364.1 3330.7 3299.6 3259.0 3210.5 3156.2 A = 0.0 25.4 203.2 667.9 1017.2 1427.1 1878.7 2354.0

V = 20.90 T = 0.00 4.42 8.84 13.25 15,46 17.67 19.88 22.09 0D= 124.51 P = 271.92 272.01 273.45 279.58 285.78 294.71 306.63 321.66

7 = 2.089 B = 3463.5 3465.0 3456.7 3422.5 3390.8 3349.3 3299.9 3244.6 A = 0.0 25.1 200.6 658.5 1002.0 1404.5 1846.9 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 = 20.80 T = 0.00 4.51 9.02 13.53 15.78 18.04 20.29 22.55 0D= 125.76 P = 288.76 288.86 290.37 296.83 303.36 312.73 325.21 340.90

7 = 2.084 B = 3557.2 3556.1 3547.3 3511.5 3478.5 3435.4 3384.3 3327.4 A = 0.0 25.3 202.1 662.2 1005.5 1406.0 1844.5 2303.5

V = 20.70 T = 0.00 4.60 9.20 13.80 16.10 18.41 20.71 23.01 0o= 127.03 P = 306.13 306.24 307.83 314.63 321.49 331.31 344.35 360.71

~,= 2.078 B = 3653.4 3652.0 3642.8 3605.3 3570.8 3526.2 3473.5 3415.0 A = 0.0 25.4 203.3 664.6 1007.0 1404.9 1838.7 2291.2

V = 20.60 T = 0.00 4.66 9.32 13.99 16.32 18.65 20.98 23.31 0o= 128.32 P = 324.06 324.17 325.81 332.78 339.79 349.84 363.18 379.89

3,= 2.072 B = 3752.3 3750.0 3740.5 3702.3 3667.1 3621.8 3568.1 3508.8 A = 0.0 25.0 200.3 654.2 990.5 1380.6 1805.3 2247.6

V = 20.50 T = 0.00 4.75 9.51 14.26 16.64 19.02 21.39 23.77 #D= 129.61 P = 342.57 342.68 344.40 351.72 359.07 369.57 383.48 400.87

~,= 2.066 B = 3853.8 3851.7 3841.7 3801.7 3765.2 3718.3 3663.1 3602.3 A = 0.0 25.1 201.0 655.1 989.9 1376.6 1796.2 2231.4

V = 20.40 T = 0.00 4.85 9.69 14.54 t6.96 19.39 21.81 24.23 0D = 130.93 P = 361.66 361.79 363.59 371.26 378.95 389.90 404.38 422.46

3,= 2.061 B = 3958.2 3957.0 3946.6 3904.9 3867.1 3818.6 3761.9 3699.6 A = 0.0 25.2 201.4 655.0 987.8 1370.8 1784.7 2212.7

V = 20.30 T = 0.00 4.94 9.88 14.81 17.28 19.75 22.22 24.69 0D= 132.26 P = 381.38 381.50 383.40 391.42 399.45 410.87 425.93 444.68

~,= 2.055 B = 4065.4 4069.9 4059.0 4015.6 3976.4 3926.4 3868.1 3804.3 A = 0.0 25.2 201.4 653.5 983.6 1362.0 1769.6 2189.6

V = 20.20 T = 0.00 5.03 10.06 15.09 17.60 20.12 22.63 25.15 0o= 133.61 P = 401.72 401.86 403.84 412.22 420.60 432.48 448.12 467.56

-/= 2.049 B = 4175.5 4172.2 4160.8 4115.7 4075.1 4023.7 3963.8 3898.5 A = 0.0 25.2 201.8 653.4 981.6 1356.5 1758.9 2172.4

V = 20.10 T = 0.00 5.09 10.18 15.27 17.82 20.37 22.91 25.46 0D= 134.97 P = 422.73 422.86 424.88 433.44 441.97 454.08 470.01 489.80

3,= 2.043 B = 4288.7 4287.7 4276.2 4230.3 4189.2 4137.0 4076.3 4010.1 A = 0.0 24.7 197.9 640.4 961.4 1327.8 1720.5 2123.5

V = 20.00 T = 0.00 5.21 10.43 15.64 18.25 20.86 23.46 26.07 0D= 136.35 P = 444.40 444.55 446.71 455.83 464.90 477.72 494.53 515.35

~/= 2.037 B = 4405.0 4400.3 4388.0 4339.5 4296.3 4241.8 4178.9 4110.7 A = 0.0 25.2 201.3 648.8 971.1 1336.9 1726.8 2125.1

V = 19.90 T = 0.00 5.28 10.55 15.83 18.46 21.10 23.74 26.38 0D= 137.75 P = 466.78 466.93 469.13 478.42 487.65 500.69 517.78 538.95

"y= 2.031 B = 4524.6 4526.0 4513.5 4464.2 4420.4 4365.2 4301.5 4232.5 A = 0.0 24.6 196.9 634.5 949.2 1305.9 1685.9 2073.4

V = 19.80 T = 0.00 5.40 10.80 16.19 18.89 21.59 24.29 26.99 0t,= 139.16 P = 489.89 490.04 492.39 502.26 512.03 525.80 543.79 565.99

"y= 2.025 B = 4647.5 4646.7 4633.5 4581.5 4535.7 4478.3 4412.5 4341.5 A = 0.0 25.0 199.6 640.9 956.0 1311.1 1687.5 2069.7

V = 19.70 T = 0.00 5.49 10.98 16.47 19.21 21.96 24.70 27.45 #D = 140.59 P = 513.74 513.90 516.34 526.59 536.72 550.96 569.54 592.44

3,= 2.019 B = 4773.9 4769.4 4755.7 4702.0 4654.8 4596.0 4528.6 4456.3 A = 0.0 24.9 198.8 636.9 948.4 1298.5 1668.5 2043.1

V = 19.60 T = 0.00 5.58 11.16 16.74 19.53 22.33 25.12 27.91 #D = 142.04 P = 538.36 538.53 541.06 551.69 562.18 576.89 596.06 619.66

~/= 2.013 B = 4903.8 4899.0 4884.8 4829.4 4781.1 4720.8 4652.0 4578.4 A = 0.0 24.7 197.6 631.8 939.4 1284.0 1647.1 2013.8


TABLEill----eontinued

T / ~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 19.50 T = 0.00 5.70 11.41 17.11 0o= 143.51 P = 563.78 563.96 566,65 577.89

3' = 2.007 B = 5037.4 5036.9 5021.9 4963.7 A = 0.0 24.9 199.3 634.8

V = 19.40 T = 0.00 5.77 11.53 17.30 0D= 145.00 P = 590.04 590.22 592.94 604.34

3'= 2.001 B = 5174.8 5169.9 5154.8 5095.9 A = 0,0 24.4 194.8 620.2

V = 19.30 T = 0.00 5,89 11,78 17.66 0D= 146.50 P = 617.15 617.34 620.21 632.23

= 1,995 B = 5316.1 5317,2 5301.3 5239.8 A = 0.0 24.5 195.9 621.6

19.20 T = 0.00 6.01 12.02 18,03

19.96 22.82 25.67 28.52 588.93 604.40 624.48 649.13 4913.2 4850.7 4779.9 4704.3

941.2 1282.7 1640.8 2001.1

20,18 23.06 25.94 28.83 615.53 631.21 651.56 676.55 5044.9 4981,8 4910.2 4833.9

919.3 1252,5 1601.8 1952.8

20.61 23,55 26.49 29.44 644.00 660.42 681.69 707.74 5186.6 5121,5 5047.9 4969.7

918.9 1248,4 1592.3 1936.5

21.03 24.04 27.05 30.05 673.36 690.55 712.74 739.85 5319.0 5251.8 5175,9 5095,9

919.5 1246.0 1585.3 1923.7

21,46 24.53 27.60 30,66 703.67 721.62 744.74 772,92 5468.1 5398.7 5320.8 5239.0

916.8 1239.1 1572.7 1904.2

21.68 24.78 27.87 30,97 733.84 751.99 755.38 803.88 5623.7 5553.8 5475.3 5392.8

892.4 1206.0 1530.3 1852.5

22.11 25.27 28.42 31.58 766.09 785.01 809,32 838.90 5775.1 5703.1 5622.7 5538.4

889.3 1198.8 1517.8 1833.5

22,54 25.75 28.97 32,19 799.36 819,05 844,30 874.95 5928.8 5854.6 5772.2 5686.1

885.5 1191.0 1504,5 1813.9

22,96 26.25 29.53 32,81 833,70 854.17 880,36 912.09 6089.8 6013.7 5929.6 5841.6

880.5 1.181.4 1489.2 1792.0

23.39 26.74 30,08 33.42 869.14 890.39 917,52 950.33 6258.4 6180,1 6094.0 6004.5

874.1 1170.3 1472.2 1768.3

23.82 27.23 30.63 34.03 927.75 955.83 989.73 6355.2 6267.2 6176.0 1157.6 1453.3 1742.5

27,72 31.18 34,64 966.3 995,3 1030,3

6528.6 6438.7 6345.9 1145.3 1435.2 1717,8

28.21 31.73 35.26 1006.1 1036.0 1072.1 6713.1 6621.5 6527.0 1131.2 1414,9 1690.7

V ~

0D= 148.03 P = 645,13 645.34 648.37 661.02 3'= 1.989 B = 5461,4 5455.3 5438.4 5374.1

A = 0.0 24,7 197.2 623,7

V = 19.10 T = 0.00 6.13 12,27 18.40 0o= 149.57 P = 674.05 674.26 677.45 690.74

3'= 1,983 B = 5611.0 5609.9 5592.3 5525.2 A = 0.0 24.8 197.9 623.5

V = 19.00 T = 0.00 6.19 12.39 18.58 0D= 151.13 P = 703.90 704.11 707.34 720.77

3 ' = 1,977 B = 5764.8 5766.6 5748,8 5681.1 A = 0.0 24.1 192.6 606.9

V = 18.90 T = 0.00 6.32 12.63 18,95 0D= 152.72 P = 73d.74 734.96 738.35 752.43

3'= 1.970 B = 5923.1 5923.6 5905.0 5834.6 A = 0.0 24.2 193.1 606.3

V = 18.80 T = 0.00 6.44 12.88 19.32 0D= 154.32 P = 766.59 766.83 770.38 785.11

3'= 1.964 B = 6085.9 6082.7 6063.4 5990.1 A = 0.0 24.3 193.4 605.2

V = 18.70 T = 0.00 6.56 13.12 19.68 0t, = 155,94 P = 799.49 799.74 803.47 818.86

3'= 1.958 B = 6253.5 6249.3 6229.1 6153.2 A = 0.0 24.3 193.3 603.1

V = 18.60 T = 0.00 6.68 13.37 20.05 OD= 157.58 P = 833.48 833.74 837.63 853.70

3'= 1,952 B = 6426.0 6423.4 6402.3 6323.6 A = 0.0 24.2 193,0 600.0

V = 18.50 T = 0.00 6.81 13.61 20.42 0 D= 159.25 P = 868.60 868.87 872.94 889.67 905.72

3'= 1.945 B = 6603.6 6605.8 6584.0 6502.4 6435.4 A = 0.0 24.2 192,4 596.1 866.5

V = 18.40 T = 0.00 6.93 13,86 20.79 24.25 0D= 160.93 P = 904.9 905.2 909.4 926.8 943.5

3'= 1,939 B = 6786.5 6786.7 6763.9 6679.7 6610.6 A = 0.0 24.1 191.7 592.2 859.0

V = 18.30 T = 0.00 7.05 14,10 21.15 24,68 0D= 162.64 P = 942.4 942.7 947,1 965.2 982.4

3'= 1,932 B = 6974.7 6978.4 6954.8 6867.9 6767.9 A = 0,0 24.0 190.7 587.3 850.1


TABLE ill---continued

T~ T m = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1,0

V = 18.20 T = 0.00 7.17 14.35 21,52 25.11 28.70 32.28 35.87 0o= 164.37 P = 981.1 981.4 986.0 1004.8 1022.7 1047.1 1078.0 1115.2

3'= 1.926 B = 7168.6 7168.4 7143.8 7054.3 6981.5 6895.6 6802.1 6706.1 A = 0.0 23.9 189.7 582.5 841.5 1117.6 1395.5 1664.9

V = 18.10 T = 0.00 7.30 14.59 21,89 25.54 29.19 32.83 36.48 0D= 166.12 P = 1021.2 1021.5 1026.3 1045.7 1064.2 1089.4 1121.3 1159.5

~= 1.919 B = 7368.3 7365.2 7339.9 7247.5 7172.8 7085.3 6989.9 6892.5 A = 0.0 23.7 188.5 577.1 832.2 1103.1 1375.1 1638.1

V = 18.00 T = 0.00 7.48 14.96 22.44 26.18 29.92 33.66 27.40 0D= 167.89 P = 1062.6 1062.9 1068.0 1088.8 1108.8 1135.0 1168.6 1208.8

3"= 1.913 B = 7573.9 7577.7 7550.9 7453.3 7375.6 7284.6 7186.6 7086.8 A = 0.0 24.1 191.4 582.2 836.2 1104.2 1371.6 1629.0

V = 17.90 T = 0.00 7.60 15.21 22,81 26.61 30.41 34.21 38.01 0v= 169.69 P = 1105.3 1105.7 1111.0 1132.5 1152.7 1180.1 1214.7 1255.9

T= 1,906 B = 7785.8 7788.6 7760.7 7660.6 7580.8 7488.0 7388.3 7287.0 A = 0.0 23.9 189.7 575.5 825.0 1087.6 1349.0 1600.0

V = 17.80 T = 0.00 7.72 15.45 23.18 27.04 30.90 34.76 38.63 0D= 171.51 P = 1149.6 1149.9 1155.4 1177.6 1198.5 1226.7 1262.2 1304.5

3' = 1.900 B = 8004.0 8007.2 7978.5 7875.7 7794.2 7699.9 7598.5 7495.5 A = 0.0 23.7 187.8 568.2 813.2 1070.3 1325.6 1570.2

V = 17.70 T = 0.00 7.85 15.69 23.54 27.47 31.39 35.31 39.24 0o= 173.35 P = 1195.3 1195.7 1201.3 1224.2 1245.7 1274.7 1311.1 1354.5

3'= 1.893 B = 8229.0 8223.2 8193.6 8088.2 8005.2 7909.0 7805.8 7701.4 A = 0.0 23.5 186.0 561.2 801.9 1053.9 1303.5 1542.1

V = 17.60 T = 0.00 7.97 15.94 23.91 27.89 31.88 35.86 39.85 0D= 175.21 P = 1242.6 1243.0 1248.8 1272.4 1294.5 1324.3 1361.7 1406.2

3'= 1.886 B = 8460.8 8448.1 8417.6 8309.5 8224.9 8126.7 8021.8 7916.1 A = 0.0 23.2 183.9 553.7 790.0 1036.8 1280.6 1513.1

V = 17.50 T = 0.00 8.15 16.31 24.46 28.54 32.62 36.69 40.77 0v= 177.10 P = 1291.5 1291.9 1298.1 1323.1 1346.3 1377.6 1416.7 1463.1

3'= 1.880 B = 8699.7 8690.2 8657.9 8545.1 8456.9 8356.1 8248.4 8140.5 A = 0.0 23.4 185.6 555.3 789.5 1032.5 1271.6 1498.7

V = 17,40 T = 0.00 8.34 16.68 25.01 29.18 33.35 37.52 41.69 0D= 179.02 P = 1342.0 1342.5 1349.0 1375.4 1399.9 1432.6 1473.5 1521.8

3'= 1.873 B = 8946.0 8945.1 8911.1 8793.0 8701.9 8597.8 8488.0 8377.6 0.0 23.6 186.8 555.7 787.2 1026.3 1026.3 1481.7

V = 17.30 T = 0.00 8.46 16.92 25.38 29.61 33.84 38.07 42.30 0D= 180.96 P = 1394.3 1394.8 1401.5 1428.6 1453.7 1487.2 1529.0 1578.4

3'= 1,866 B = 9199.8 9188.5 9153.7 9032.9 8940.2 8834.4 8722.9 8611.4 A = 0.0 23.3 184.3 546.9 773.8 1007.6 1236.0 1451.7

V = 17.20 T = 0.00 8,58 17.17 25.75 30.04 34.33 38.62 42.91 0D= 182.92 P = 1448.4 1448.9 1455.8 1483.6 1509.3 1543.6 1586.4 1636.9

3'= 1,859 B = 9461.7 9451.6 9416.1 9292.9 9198.6 9091.1 8977.9 8864.8 A = 0.0 23.0 181.4 537.2 759.2 987.4 1209.9 1419.7

V = 17.10 T = 0.00 8.77 17.53 26.30 30.68 35.06 39.45 43.83 0D= 184.91 P = 1504.4 1504.8 1512.2 1541.4 1568.3 1604.1 1648.6 1701.0

y = 1.852 B = 9731.7 9727.1 9689.7 9561.3 9463.9 9353.4 9237.8 9122,6 A = 0.0 23.1 182.0 536.0 755.0 979.1 1196.7 1401.0

V = 17.00 T = 0.00 8.95 17.90 26.85 31.32 35.80 40.27 44.75 0D= 186.93 P = 1562.2 1562.8 1570.5 1601.1 1629.2 1666.6 1712.8 1767.2

3"= 1.845 B = 10010.0 10004.0 9965.0 9832.0 9731.0 9618.0 9500.0 9383.0 A = 0.0 23.2 182.4 534.4 750.4 970.4 1183.1 1382.3


TABLE m---contmued

T / ~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 16.90 T = 0.00 9.07 18.15 27,22 31.75 36.29 40.83 45.36 0D= 188.97 P = 1622.1 1622.7 1630.6 1662.0 1690.7 1728.8 1775.9 1831.4

7 = 1.838 B = 10297.0 10289.0 10249.0 10114.0 10012.0 9897.0 9777.0 9659.0 A = 0.0 22.7 179.1 523.8 734.9 949.4 1156.6 1350.1

V = 16.80 T = 0.00 9.32 18.64 27.95 32.61 37.27 41.93 46.59 0 D = 191.04 P = 1684.1 1684.7 1693.2 1726.8 1757.4 1797.8 1847.5 1905.8

7 = 1.831 B = 10594.0 10588.0 10546.0 10403.0 10296.0 10178.0 10055.0 9934.0 A = 0.0 23.2 182.5 528.9 738.5 949.9 1152.8 1341.4

V = 16.70 T = 0.00 9.44 18.88 28.32 33.04 37.76 42.48 47.20 0D= 193.14 P = 1748.3 1748.9 1757.6 1791.9 1823.0 1864.2 1914.9 1974.2

7 = 1.824 B = 10900.0 10889.0 10845.0 10699.0 10591.0 10471.0 10347.0 10224.0 A = 0.0 22.8 178.9 517.8 722.4 928.5 1126.1 1309.4

V = 16.60 T = 0.00 9.62 19.25 28.87 33.68 38.50 43.31 48.12 0D= 195.26 P = 1814.7 1815.3 1824.4 1860.2 1892.6 1935.3 1987.7 2049.0

7 = 1.817 B = 11215.0 11209.0 11164.0 11013.0 10903.0 10780.0 10653.0 10529.0 A = 0.0 22.7 178.4 513.7 714.6 916.3 1108.9 1287.2

V = 16.50 T = 0.00 9.81 19.62 29.42 34.33 39.23 44.13 49.04 0D= 197.41 P = 1883.4 1884.1 1893.6 1930.9 1964.5 2008.7 2062.9 2126.2

7 = 1,810 B = 11541.0 11541.0 11494.0 11339.0 11225.0 11100.0 10971.0 10844.0 A = 0.0 22.7 177.6 508.9 706.2 903.4 1091.0 1264.2

V = 16.40 T = 0.00 9.93 19.86 29.79 34.76 39.72 44.69 49.65 0D= 199.59 P = 1954.6 1955.3 1965.0 2002.9 2037.2 2082.1 2137.2 2201.5

7 = 1,803 B = 11877.0 11866.0 11818,0 11660.0 11545.0 11419.0 11288.0 11160.0 A = 0.0 22.2 173.8 497.5 689.9 882.0 1064.6 1233.0

V = 16.30 T = 0.00 10.18 20.35 30.53 35.61 40.70 45.79 50.88 0D= 201.80 P = 2028.3 2029.0 2039.4 2079.7 2115.8 2163.1 2220.8 2288.0

= 1.796 B = 12225.0 12210.0 12159.0 11994.0 11875.0 11744.0 11611.0 11482.0 A = 0.0 22.5 175.8 499.1 686.3 877.9 1056.3 1220.1

V = 16.20 T = 0.00 10.36 20.72 31.08 36.26 41.44 46.61 51.79 0 D = 204.04 P = 2104.7 2105,4 2116.2 2158.0 2195.3 2244.1 2303.6 2372.8

7 = 1.788 B = 12583.0 12574.0 12522.0 12352.0 12230.0 12097.0 11962.0 11830,0 A = 0.0 22.3 174.4 493.0 679.3 863,4 1037.0 1196.0

V = 16.10 T = 0.00 10.54 21.09 31.63 36.90 42.17 47.44 52.71 0D= 206.30 P = 2183.7 2184.5 2195.7 2239.0 2277.6 2327.6 2389.2 2460.3

7 = 1.781 B = 12954.0 12937.0 12883.0 12709.0 12584.0 12448.0 12311.0 12177.0 A = 0.0 22.2 173.0 487.0 669.6 849.4 1018.5 1173.0

V = 16.00 T = 0.00 10.79 21.58 32.36 37.76 43.15 48.54 53.94 0D= 208.60 P = 2265.6 2266.4 2278.3 2324.1 2364.6 2417.2 2481.1 2555.1

7 = 1.774 B = 13336.0 13340.0 13282.0 13101,0 12972.0 12833.0 12693.0 12557.0 A = 0.0 22.3 173.8 485.6 665.2 841.1 1005.6 1155.2

TABLE IV Equation of State of Para-Hydrogen: High Densities

T/Tm 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 15.90 T = 0.00 11.16 22.31 33.47 39.04 44.62 50.20 55.78 0D= 212.42 P = 2.3504 2.3514 2.3648 2.4159 2.4608 2.5189 2.5892 2.6703

= 1,834 B = 13.732 13.722 13.658 13.463 13.328 13.186 13.046 12.915 A = 0.0 23.7 183.6 508.1 692.6 871.9 1038.5 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,=

V =

0 D = 3'=

V =

0 D = 3'=

V =

0 D = 3,=

V =

0 D = 3,=

V = 0 D =

3,=

V =

0o= 3,=

V =

8 D = 3'=

V =

0o= 3,=

V =

3'=

V = 0 D =

3,=

V = 0 D =

,,/=

V = 0D=

3'=

15.80 T = 0.00 11.40 22.80 34.20 39.90 45.60 51.30 57.00 214.89 P = 2.4384 2.4393 2.4535 2.5072 2.5542 2.6148 2.6879 2.7521

1.830 B = 14.140 14.131 14.064 13,860 13.723 13.577 13.435 13.302 A = 0.0 23.8 184.1 505.9 687.3 862.8 1025.1 1171.2

15.70 T = 0.00 11.65 23.29 34.94 40.76 46.58 52.40 58.23 217.40 P = 2.5295 2.5305 2.5454 2.6018 2.6509 2.7140 2.7899 2.8772

1.825 B = 14.562 14.551 14,481 14.270 14,128 13,980 13,835 13.701 A = 0.0 23.9 184.3 503.2 681.5 853.1 1011.3 1153.0

15.60 T = 0,00 11.89 23.78 35.67 41.62 47.56 53.51 59.45 219.95 P = 2.6239 2.6250 2.6407 2.6998 2.7509 2.8166 2.8954 2.9858

1.820 B = 14.999 15.001 14.927 14.710 14.563 14.412 14.265 14.131 A = 0.0 23.9 184.0 499.3 674.1 841.7 995.5 1132.8

15.50 T = 0.00 12.14 24.27 36.41 42.47 48.54 54.61 60.68 222.53 P = 2.7218 2.7229 2.7395 2.8012 2.8545 2.9227 3.0043 3.0979

1.815 B = 15.450 15.448 15.371 15.146 14.997 14.843 14.694 14.557 A = 0.0 23.9 183.7 495.4 667.0 830.7 980.3 1113.8

15.40 T = 0.00 12.38 24.76 37.14 43.33 49.52 55.71 61.90 225.16 P = 2.8233 2.8245 2.8418 2.9063 2.9617 3.0324 3.1170 3.2137

1.810 B = 15.917 15.914 15.834 15.601 15,448 15.291 15.140 15.002 A = 0.0 23.9 183.1 490.9 659.1 818.9 964.5 1093.9

15.30 T = 0.00 12.63 25.25 37.88 44.19 50.50 56.81 63.13 227.83 P = 2.9286 2.9298 2.9480 3.0152 3.0727 3.1460 3.2334 3.3333

1.805 B = 16,399 16.388 16,305 16,065 15.909 15.749 15.595 15.457 A = 0.0 23.8 182.3 486.1 650.9 807.0 948.7 1074,1

15.20 T = 0.00 12.87 25.74 38,61 45.05 51.48 57.92 64.35 230.54 P = 3.0377 3.0390 3.0580 3.1280 3.1876 3.2635 3.3539 3.4569

1.801 B = 16,899 16.898 16.811 16.564 16.405 16.242 16.087 15,946 A = 0.0 23.7 181.1 480.3 641.4 793.6 931.2 1052.9

15.10 T = 0.00 13.12 26.23 39.35 45.90 52.46 59.02 65.58 233.29 P = 3.1510 3.1523 3.1721 3.2449 3.3067 3.3851 3.4784 3.5846

1.796 B = 17.415 17.393 17.303 17.049 16.886 16.720 16.563 16.422 A = 0.0 23.6 180.1 474.9 632.8 781.3 915.4 1033.4

15.00 T = 0.0T 13.36 26.72 40.08 46.76 53.44 60.12 66.80 236.09 P = 3.2685 3.2699 3.2905 3.3660 3.4300 3.5110 3.6072 3.7166

1.791 B = 17.950 17.934 17.841 17.580 17.414 17.246 17.087 16.944 A = 0.0 23.5 178.5 468.4 622.7 767.4 897.5 1011.9

14.90 T = 0,00 13.61 27.21 40.82 47.62 54.52 61.22 68.03 238.93 P = 3.3904 3.3918 3.4133 3.4916 3.5578 3.6414 3.7405 3.8531

1,786 B = 18.503 18.510 18.414 18.146 17.976 17.805 17.644 17,499 A = 0.00 23.24 176.52 461.11 611.75 752.48 878.79 989.51

14.80 T = 0.00 13.85 27.70 41.55 48.47 55.40 62.32 69.25 241.81 P = 3.5169 3.5184 3.5408 3.6219 3.6902 3.7764 3.8785 3.9943

1.782 B = 19.076 19.068 18.969 18.694 18,520 18.346 18,184 18.038 A = 0.00 23.06 174.77 454.49 601.76 738.93 861.70 969.18

14.70 T = 0.00 14.10 28.19 42.28 49.33 56.38 63.43 70.47 244.75 P = 3.6482 3.6498 3.6730 3.7569 3.8274 3,9162 4.0212 4.1403

1,777 B = 19.669 19.669 19.566 19.284 19.107 18.932 18.767 18.620 A = 0.00 22.82 172.63 447.05 590.77 724.21 843.45 947.53

14.60 T = 0.00 14.46 28.93 43.39 50.62 57.85 65.08 72.31 247.73 P = 3.7846 3.7863 3.8111 3.9002 3.9746 4.0680 4.1780 4.3023

1.772 B = 20.283 20.282 20.172 19,878 19.697 19.517 19.351 19.203 A = 0.00 23.15 174.34 446.84 587.89 718.08 833.69 934.24


TABLE X---continued

~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 14.50 T = 0.00 14.71 29.41 44.12 51.48 58.83 66.18 73.54 0D= 250.76 P = 3.9261 3.9279 3.9536 4.0456 4.1221 4.2181 4.3311 4.4587

y = 1.768 B = 20.920 20.916 20.803 20.502 20.317 20.134 19.966 19.818 A = 0.00 22.86 171.86 438.87 576.48 703.12 815.46 912.84

V = 14.40 T = 0.00 15.07 30.15 45.23 52.76 60.30 67.84 75.38 0o= 253.85 P = 4.0732 4.0751 4.1025 4.1998 4.2803 4.3808 4.4989 4.6319

y = 1.763 B = 21.579 21.564 21.446 21.132 20.943 20.757 20.587 20.438 A = 0.00 23.11 173.00 437.59 572.44 695.87 804.79 898.92

V = 14.30 T = 0.00 15.32 30.64 45.96 53.62 61.28 68.94 76.60 0o = 256.98 P = 4.2259 4.2279 4.2562 4.3563 4.4390 4.5422 4.6632 4.7995

~ = 1.759 B = 22.262 22.262 22.140 21.821 21.628 21.440 21.266 21.117 A = 0.00 22.75 170.01 428.64 559.93 679.90 785.52 876.65

V = 14.20 T = 0.00 15.69 31.38 47.06 54.91 62.75 70.59 78.44 0o= 260.17 P = 4.3846 4.3867 4.4167 4.5223 4.6090 4.7168 4.8430 4.9847

= 1.754 B = 22.970 22.968 22.839 22.508 22.310 22.119 21.945 21.794 A = 0.00 22.91 170.51 426.08 554.55 671.24 773.58 861.60

V = 14.10 T = 0.00 16.06 32.11 48.17 56.19 64.22 72.25 80.28 0D= 263.41 P = 4.5495 4.5517 4.5836 4.6947 4.7854 4.8979 5.0291 5.1764

y = 1.749 B = 23.704 23.710 23.576 23.233 23.031 22.835 22.661 22.509 A = 0.00 23.03 170.61 422.72 548.21 661.70 760.72 845.62

V = 14.00 T = 0.00 16.30 32.60 48.90 57.05 65.20 73.35 81.50 0D= 266.70 P = 4.7210 4.7232 4.7559 4.8699 4.9628 5.0780 5.2122 5.3628

y = 1.745 B = 24.466 24.469 24.330 23.981 23.776 23.579 23.401 23.249 A = 0.00 22.60 167.23 413.34 535.50 645.76 741.90 824.18

V = 13.90 T = 0.00 16.67 33.34 50.00 58.34 66.67 75.00 83.34 0D= 270.06 P = 4.8992 4.9015 4.9361 5.0556 5.1526 5.2725 5.4119 5.5680

~ = 1.741 B = 25.256 25.262 25.116 24.756 24.546 24.346 24.166 24.013 A = 0.00 22.65 166.88 409.24 528.50 635.60 728.72 808.11

V = 13.80 T = 0.00 17.04 34.07 51.11 59.62 68.14 76.66 85.18 0 D = 273.47 P = 5.0845 5.0870 5.1234 5.2485 5.3496 5.4742 5.6189 5.7805

y = 1.736 B = 26.075 26.069 25.917 25.546 25.331 25.128 24.946 24.794 A = 0.00 22.67 166,35 404.90 521.29 625.41 715.55 792.20

V = 13.70 T = 0.00 17.28 34.56 51.84 60.48 69.12 77.76 86.40 0o= 276.94 P = 5.2772 5.2797 5.3170 5.4450 5.5483 5.6756 5.8233 5.9883

y = 1.732 B = 26.925 26.934 26.779 26.401 26.185 25.978 25.797 25.643 A = 0.00 22.15 162.44 394.75 507.82 608.90 696.25 770.48

V = 13.60 T = 0.00 17.77 35.54 53.31 62.20 71.08 79.97 88.85 #D = 280.47 P = 5.4776 5.4804 5.5206 5.6572 5.7664 5.9006 6.0558 6.2286

= 1.727 B = 27.808 27.795 27.630 27.235 27.013 26.804 26.620 26.468 A = 0.00 22.58 164.43 394.67 505.27 603.42 687.83 759.18

V = 13.50 T = 0.00 18.02 36.03 54.05 63.05 72.06 81.07 90.08 #o = 284.06 P = 5.6862 5.6891 5.7301 5.8695 5.9810 6.1178 6.2761 6.4523

= 1.723 B = 28.724 28.718 28.550 28.150 27.924 27.713 27.527 27.372 A = 0.00 22.03 160.28 384.28 491.75 586.99 668.85 738.06

V = 13.40 T = 0.00 18.51 37.01 55.52 64.77 74.02 83.27 92.53 0D= 287.72 P = 5.9033 5.9064 5.9504 6.0985 6.2161 6.3599 6.5257 6.7099

= 1.719 B = 29.675 29.653 29.475 29.058 28.827 28.612 28.426 28.273 A = 0.00 22.36 161.59 383.01 487.90 580.36 659.33 725.84

V = 13.30 T = 0.00 18.87 37.75 56.62 66.05 75.49 84.93 94,36 0D= 291.44 P = 6.1293 6.1325 6.1785 6.3324 6.4542 6.6028 6.7739 6.9638

= 1.714 B = 30.663 30.653 30.469 30.041 29.805 29.588 29.400 29.246 A = 0.00 22.19 159.77 376.51 478.54 568.16 644.55 708.71


TABLElV--continued

T/~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 13.20 T = 0.00 19.24 38,48 57,72 67.34 76.96 86,58 96.20 0o= 295.24 P = 6.3645 6.3679 6.4159 6.5756 6.7016 6.8551 7.0316 7.2272

= 1.710 B = 31.690 31.688 31.496 31.058 30.819 30,600 30.411 30,257 A = 0.00 21.98 157.79 369.84 469.06 555.91 629.79 691.69

V = 13.10 T = 0.00 19.73 39.46 59.19 69.06 78.92 88.79 98.65 0o= 299.09 P = 6.6096 6,6132 6,6643 6.8330 6,9652 7.1258 7.3099 7.5137

~ = 1,706 B = 32.757 32,746 32,543 32,090 31,846 31.624 31.434 31.281 A = 0.00 22.18 158.14 366.90 463.54 547.67 618.95 678.40

V = 13.00 T = 0.00 19.98 39.95 59.93 69.91 79.90 89.89 99.88 0o= 303.03 P = 6.8648 6.8685 6.9204 7.0918 7.2262 7.3895 7.5768 7.7841

~ = 1.702 B = 33.866 33.873 33,669 33,210 32,963 32.738 32.546 32,393 A = 0.00 21.51 153.37 355.93 449.66 531.27 600.40 658.08

V = 12.90 T = 0.00 20.47 40.93 61.40 71.63 81.86 92.09 102.33 0o= 307.03 P = 7.1308 7.1346 7.1898 7.3703 7.5110 7.6814 7,8764 8.0919

~ = 1.698 B = 35.019 35,025 34.810 34,336 34.082 33,855 33.663 33.510 A = 0.00 21.62 153.21 352.24 443.42 522.45 589.08 644.53

V = 12.80 T = 0.00 20.96 41.91 62.87 73.34 8382 94.30 104.78 0o= 311.11 P = 7.4079 7.4120 7.4705 7.6601 7.8071 7,9848 8.1876 8.4113

~ = 1.693 B = 36,218 36,188 35.963 35,474 35.216 34.987 34.794 34.643 A = 0.00 21.70 152.90 348,42 437.18 513.65 578.00 631.30

V = 12.70 T = 0.00 21.45 42.89 64.34 75.06 85.78 96.50 107.23 0D= 315.26 P = 7.6968 7.7012 7.7629 7.9618 8.1152 8.3001 8.5109 8.7429

~ = 1,689 B = 37.466 37.436 37,200 36.697 36.434 36.202 36.009 35,860 A = 0.00 21.72 152.15 343.81 430.04 504.04 566.04 617.21

V = 12.60 T = 0.00 21.94 43.87 65.81 76.77 87.74 98.71 109.68 Oo= 319.50 P = 7.9981 8.0027 8.0678 8.2760 8.4359 8.6281 8.8467 9,0871

= 1,685 B = 38.764 38.725 38.479 37.960 37.694 37,460 37.267 37.118 A = 0.00 21.71 151.18 338.91 422.64 494,23 553.99 603.23

V = 12.50 T = 0,00 22.43 44.85 67.28 78.49 89.70 100.91 112,13 0o= 323.81 P = 8.3124 8.3172 8.3857 8.6033 8.7697 8.9692 9,1958 9.4446

~ = 1.681 B = 40.116 40,134 39.877 39.343 39.072 38,837 38,644 38.496 A = 0.00 21.62 149.72 333.13 414.28 483.42 540.89 588.14

V = 12.40 T = 0.00 22,92 45.83 68.75 80.20 91.66 103,12 114.58 OD= 328.21 P = 8.6402 8.6453 8.7173 8.9443 9.1172 9.3241 9.5588 9.8161

~ = 1.678 B = 41.522 41.517 41.248 40,702 40.427 40,189 39.996 39.851 A = 0.00 21.54 148.51 327.73 406,52 473.40 528.81 574.27

V = 12.30 T = 0.00 23.41 46.81 70.22 81.92 93.62 105.32 117.03 0D= 332.69 P = 8.982 8.988 9.063 9.300 9,479 9.694 9.936 10,202

= 1.674 B = 42.988 42.983 42.704 42.143 41.864 41,623 41.430 41.285 A = 0,00 21.40 146.68 321.88 398.30 462.98 516.36 560.17

V = 12.20 T = 0.00 23.90 47.79 71,69 83.63 95.58 107.53 119.48 0D= 337.26 P = 9.339 9.345 9.424 9,670 9.856 10.078 10.329 10.603

7 = 1.670 B = 44.514 44.474 44.184 43.609 43.325 43.082 42,889 42.746 A = 0.00 21.25 144.93 316.08 390.20 452.74 504.31 546.45

V = 12.10 T = 0.00 24.39 48.77 73.16 85.35 97.54 109.73 121.93 0 o = 341.92 P = 9.712 9.718 9.801 10,056 10,249 10.478 10.738 11.021

= 1.666 B = 46.105 46,097 45.797 45.208 44.920 44.675 44.482 44.342 A = 0.00 21.03 142.78 309.57 381.39 441.78 491.45 531.96

V = 12.00 T = 0.00 24.88 49.75 74.63 87.0 99.50 111.94 124.38 0 D= 346.68 P = 10.102 10.108 10.194 10.459 10,659 10.896 11.163 11.455

y = 1,662 B = 47,763 47.769 47,459 46.856 46.564 46.317 46.125 45.984 A = 0.00 20.79 140.54 303.05 372,64 430.97 478.82 517.82

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 = 11.90 T = 0.00 25.37 50.73 76.10 88.78 101,46 114.14 126.83 0o= 351.53 P = 10.509 10.515 10.605 10.880 11.086 11.330 11.606 11.906

= 1.659 B = 49.493 49.470 49.149 48.532 48.237 47.988 47.795 47.657 A = 0.00 20.54 138.28 296.68 364.12 420.54 466.72 504.30

V = 11.80 T = 0.00 26.10 52.20 78.30 91.35 104.40 117.45 130.50 0D= 356.48 P = 10.934 10.941 11.037 11.330 11.547 11.804 12.093 12,407

y = 1.655 51.296 51.270 50.930 50.293 49.993 49.742 49,553 49.419 A = 0.00 20.83 138.74 293.94 359.17 413.43 457.64 493.46

V = 11.70 T = 0.00 26.59 53.18 79.77 83.06 106.36 119.65 132.95 0D= 361.53 P = 11.378 11.386 11,486 11.788 12.012 12.277 12.574 12.898

= 1,651 B = 53.178 53.128 52.778 52.127 51.823 51.571 51.381 51.249 A = 0.00 20.51 136.08 287.11 350.33 402.75 445.44 480.00

V = 11.60 T = 0.00 27.08 54.16 81.24 94.78 108,32 121.86 135.40 0o= 366.68 P = 11.843 11.851 11,954 12.266 12.497 12,770 13.076 13.408

y = 1.648 B = 55.143 55.106 54,745 54.082 53.772 53.520 53.329 53.201 A = 0,00 20.15 133.23 280.01 341.22 391.88 433,04 466.25

V = 11.50 T = 0.00 27.82 55.63 83.44 97.35 111.26 125.17 139.07 0D= 371.95 P = 12.330 12.338 12,448 12.778 13.020 13.306 13.625 13.972

~ = 1.644 B = 57.193 57.133 56.753 56.068 55.757 55.503 55.317 55.193 A = 0.00 20.30 132.95 276.41 335.54 384.27 423.66 455.39

V = 11.40 T = 0.00 28.30 56.61 84.92 99.07 113.22 127.37 141.52 0 D = 377.32 P = 12.838 12.847 12.961 13.300 13.550 13.843 14.171 14.527

= 1,641 B = 59.335 59.310 58.920 58,224 57,906 57.651 57.465 57.344 A = 0.00 19.87 129.78 268.99 326.20 373.27 411.26 441.82

V = 11.30 T = 0.00 29.04 58.08 87.12 101.64 116.16 130.68 145.20 0D= 382.81 P = 13.371 13.380 13.501 13.859 14.120 14.426 14.768 15.139

~ = 1.638 B = 61.573 61.525 61.117 60.400 60.080 59.825 59.641 59.526 A = 0,00 19.94 129.03 264.85 320.10 365.34 401.78 431,00

V = 11.20 T = 0.00 29.53 59.06 88.59 103.36 118.12 132.89 147,65 0~ = 388.42 P = 13,929 13.938 14.063 14,430 14.698 15.013 15.363 15.743

= 1.634 B = 63.912 63.855 63.435 62.704 62.380 62.123 61.939 61,825 A = 0.00 19.47 125.75 257.51 311.02 354.74 389.93 418.11

V = 11.10 T = 0,00 30.51 61.02 91.53 106.79 122.04 137.29 152.55 0D= 394,15 P = 14.513 14.523 14.659 15.053 15.338 15.671 16.041 16.441

= 1.631 B = 66.357 66.353 66.904 65.146 64.820 64.566 64.390 64.287 A = 0.60 19.91 126,63 255.32 306.73 348.49 381.98 408.54

V = 11.00 T = 0,00 31,00 62.00 93.00 108.50 124.00 139.50 155.00 0D= 40T.01 P = 15.125 15.135 15,275 15.679 15.971 16.312 16.691 17.100

7 = 1.628 B = 68.915 68.866 68.407 67.637 67.306 67.051 66.874 66.771 A = 0,00 19,39 123,15 247.95 297.73 338.16 370.50 396.28

V = 10.90 T = 0.00 31.74 63.47 95.21 111.07 126.94 142.81 158.68 0 o = 405.99 P = 15.766 15.777 15.924 16.347 16.651 17.005 17.399 17,823

= 1.625 B = 71.591 71.536 71.058 70.269 69.935 69.677 69.505 69.409 A = 0.00 19.28 121.56 242.90 290.92 329.78 360.75 385.37

V = 10.80 T = 0.00 32.47 64.94 97.41 113.65 129.88 146.12 162.35 0D= 412.11 P = 16.439 16.450 16.605 17.047 17.363 17.731 18.139 18.579

~ = 1.622 B = 74.392 74.322 73.828 73.020 72.681 72.425 72.257 72.168 A = 0.00 19.14 119.79 237.69 284.04 321.43 351,10 374.64

V = 10.70 T = 0.00 33.20 66.41 99.61 116,22 132.82 149.42 166.02 0 D = 418.37 P = 17.145 17.157 17.319 17.779 18.108 18.489 18.912 19,367

= 1.619 B = 77,325 77.308 76.793 75.966 75.625 75.372 75.207 75.122 A = 0.00 18.95 117.77 232.11 276.78 312.71 341.16 363.75

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 = 10.60 T = 0.00 33.94 67.88 101.82 118.79 135.76 152.73 169.70 OD= 424.77 P = 17.885 17.898 18.068 18.547 18.888 19.283 19.721 20.t91

y = 1.616 B = 80.398 80.293 79.759 78.914 78.568 78.314 78.154 78.076 A = 0.00 18.75 115.80 226.88 270.00 304.54 331.96 353.54

V = 10.50 T = 0.00 34.92 69.84 104.76 122.22 139.68 157.14 174.60 OD= 431.32 P = 18.662 18.676 18.858 19.365 19.724 20.139 20.597 21.089

y = 1.613 B = 83.617 83.590 83.024 82.156 81.810 81.562 81.408 81.344 A = 0.00 18.88 115.10 222.93 264.31 297.32 323.37 343.86

V = 10.40 T = 0.00 35.65 71.31 106.97 124.79 142.62 160.45 178.27 OD= 438.03 P = 19.478 19.493 19.683 20.209 20.580 21.010 21.483 21.991

y = 1.611 B = 86.992 86.950 86.365 85.477 85.126 84.878 84.728 84.671 A = 0.00 18.59 112.71 217.20 257.12 288.87 313.94 333.52

V = 10.30 T = 0.00 36.39 72.78 109.17 127.36 145.56 163.75 181.95 0D= 444.89 P = 20.336 20.351 20.549 21.095 21.478 21.922 22.410 22.934

y = 1.608 B = 90.532 90.527 89.922 89.017 88.662 88.413 88.268 88.218 A = 0.00 18.26 110.15 211.32 249.80 280.31 304.35 323.23

V = 10.20 T = 0.00 37.37 74.74 112.11 130.79 149.48 168.17 186.85 0o= 451.92 P = 21.237 21.253 21.464 22.038 22.440 22.904 23.413 23.959

y = 1.605 B = 94.246 94.197 93.563 92.635 92.280 92.037 91.900 91.860 A = 0.00 18.27 109.00 207.16 244.12 273.35 296.25 314.15

V = 10.10 T = 0.00 38.35 76.70 115.05 134.22 153.40 172.57 191.75 0o= 459.12 P = 22.185 22.202 22.425 23.029 23.450 23.933 24.464 25.032

y = 1.603 B = 98.145 98.080 97.418 96.467 96.112 95.873 95.745 95,719 A = 0.00 18.23 107.61 202.69 238.23 266,22 288.01 305.11

V = 10.00 T = 0.00 39.33 78.66 117.99 137.65 157.32 176.99 196.65 0D= 466.50 P = 23.182 23.200 23.436 24.069 24.508 25.012 25.565 26.156

y = 1.601 B = 102.24 102.12 101.43 100.46 100.I0 99.87 99.75 99.74 A = 0.00 18.14 106.07 198.17 232.29 259.05 279.94 296.26

V = 9.90 T = 0.00 40.31 80.62 120.93 141.09 161.24 181.40 201.55 0o= 474.06 P = 24.231 24.250 24.499 25.162 25.620 26.145 26.719 27.333

y = 1.598 B = 106.54 106,54 105.82 104.83 104.47 104.24 104.13 104.13 A = 0.00 17.99 104.19 193.18 225.90 251.51 271.44 286.93

TABLE V Equation of State of Ortho-Deuterium: Low Densities

T/Tm= 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 20.50 T = 0.00 16.88 18.76 0D= 85.86 P = - 7 8 . 7 2 8 4 -20.9260 1.2298

y = 2.470 B = 2624.0 2222.3 2102.7 A = 0.0 4877.7 6063.6

V = 20.40 T = 0.00 15.32 17.23 19.15 0D= 86.89 P = -65.667 -24.978 -6 .009 16.734

y = 2.439 B = 2718.4 2420.8 2310.1 2189.9 A = 0.0 3666.7 4722.7 5848.8

V = 20.30 T = 0.00 11.73 13.68 15.64 17.59 19.54 0D= 87.93 P = -52.072 -36.861 -25.473 -10.010 9.498 32.840

y = 2.408 B = 2815.4 2691.7 2611.7 2513.7 2402.4 2281.7 A = 0.0 1791.1 2625.8 3561.2 4570.3 5639.2


TABLE V----continued

T / T m = 0.0 0.2 0.4 0.6 0.7 0.8 0,9 1.0

V = 20,20 T = 0.00 O D= 88.98 , P = -37.923

2,= 2.378 B = 2915.3 A = 0.0

V = 20.10 T = 0.00 0D= 90.03 P = -23.201

3,= 2.349 B = 3018.0 A = 0.0

V = 20.00 T = 0.00 0D= 91.08 P = -7,885

y = 2.320 B = 3123.7 A = 0.0

V = 19.90 T = 0.00 0D= 92.14 P = 8.04

y = 2,292 B = 3232.4 A = 0.0

V = 19.80 T = 0.00 0r)= 93.21 P = 24.61

y = 2.265 B = 3344.3 A = 0.0

V = 19.70 T = 0.00 0D= 94.28 P = 41.83

3'= 2.238 B = 3459.4 A = 0.0

V = 19.60 T = 0.00 0D= 95.35 P = 59.74

y = 2.212 B = 3577.8 A = 0.0

V = 19.50 T = 0.00 Or,= 96.43 P = 78.35

3, = 2.187 B = 3699.7 A = 0.0

V = 19.40 T = 0.00 0 o = 97.51 P = 97.69

y = 2.162 B = 3825.1 A = 0.0

V = 19.30 T = 0.00 0D= 98.60 P = 117.79

3'= 2.138 B = 3954.2 A = 0.0

V = 19.20 T = 0.00 OD= 99.70 P = 138.67

y = 2.115 B = 4087.1 A = 0.0

V = 19.10 T = 0.00 Or,= 100.80 P = 160.37

3"= 2.092 B = 4223.8 A = 0.0

V = 19.00 T = 0.00 0D= 101.90 P = 182.91

3"= 2.070 B = 4364.6 A = 0.0

3,99 7.98 11.97 13.97 15.96 17.96 19.95 -37.717 -34.640 -22.143 -10.376 5.563 25.625 49.584

2912.9 2886.5 2789.2 2708.1 2609.3 2497.4 2376.4 70.9 565.4 1752.2 2560.4 3460.4 4424,9 5439.5

4.07 8.15 12.22 14.25 16,29 18.33 20.36 -22,987 -19,787 -6 .826 5.336 21.767 42.402 66.996

3015,2 2988.2 2888.9 2806.8 2707.1 2594.4 2473.0 69.8 556.2 1715.2 2498.1 3364.6 4287.4 5252.1

4.16 8.31 12.47 14.55 16.63 18,71 20.79 -7.663 -4 .334 9.110 21.679 38.618 59,843 85,089 3121.8 3094.1 2993.1 2910.1 2809.6 2696.5 2574.9

68.7 547.1 1678.7 2436.7 3270.4 4152.6 5068.1

4.24 8.49 12.73 14.85 16.97 19.09 21.22 8.27 11.74 25.69 38.68 56.15 77.98 103.90

3231.7 3203.3 3100.5 3016.4 2915.2 2801.5 2679.8 67.7 538.5 1643.7 2377.7 3180.2 4023.9 4893.8

4.33 8.66 12.99 15.16 17.32 19.49 21.66 24.85 28.46 42.93 56.36 74.37 96.84 123.45

3342.7 3313.6 3208.8 3123.8 3021.7 2907.5 2785.7 66.8 530.6 1611.0 2322.7 3095.9 3903.8 4731.1

4.42 8.84 13.26 15.47 17.68 19.89 22.10 42.08 45.84 60.86 74.75 93.33 116.44 143.77

3456.5 3426.7 3320.0 3234.0 3131.3 3016.7 2894.9 65.9 523.2 1579.9 2270.0 3015.1 3788.9 4576.2

4.51 9.02 13.54 15.79 18.05 20.31 22.56 60.00 63.91 79,51 93.87 113.04 136.82 164.88

3573.1 3542.6 3434.1 3347.1 3243.8 3129.0 3007.1 65.1 516.1 1549.9 2219.3 2937.6 3678.8 4428.4

4.61 9.21 13.82 16.12 18,42 20.72 23.03 78.62 82.70 98.89 113.74 133.50 157.98 186.79

3700.3 3669.0 3558.6 3470.8 3366.8 3251.8 3130.0 64;2 508.2 1517.7 2165.6 2856.5 3564.8 4276.6

4.70 9.40 14.10 16.45 18.80 21.15 23.50 97.98 102.23 119.05 134.43 154.82 180.02 209.63

3820.4 3788.4 3676,1 3587.4 3482.9 3367.6 3246.1 63.6 502.5 1491.9 2121.3 2788,3 3468.1 4146.8

4.80 9.60 14.40 16.79 19.19 21.59 23.99 118.09 122.52 140.01 155.92 176.97 202.92 233,34 3948.9 3916.0 3801.7 3712.1 3607.1 3491.6 3370.4

62.9 496.4 1465.1 2075.8 2719.0 3370.4 4016.8

4.90 9.80 14,69 17.14 19.59 22.04 24.49 138.99 143.61 161,79 178.26 199.99 226.71 257.98 4084.7 4050,9 3934.7 3844.3 3738.8 3623.4 3502.7

62.2 490.2 1437.8 2029,8 2649.4 3273.0 3887.7

5.00 10.00 15.00 17.50 20.00 22.50 25.00 160.70 165.53 184.43 201.48 223.92 251.43 283.57 4224.0 4189.4 4071.3 3980.2 3874.3 3759.0 3638.7

61.5 484.3 1411.6 1985.7 2582.7 3179.8 3764.7

5.10 10.21 15.31 17.86 20.41 22,96 25.51 183.25 188.30 207.95 225.60 248.77 277.11 310.14 4362.6 4327.2 4207.2 4115.3 4009.1 3894.0 3774.3

61.0 479.2 1387.9 1945.4 2521.4 3094.0 3651.7


TABLE V----contmued

~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 18.90 T = 0.00 5.21 10.42 15.63 18.23 20.84 23.44 26.05 8 D = 103.02 P = 206.33 206.68 211.96 232.42 250.72 274.66 303.88 337.86

= 2.049 B = 4509.6 4503.4 4466.9 4345.0 4252.4 4146.0 4031.2 3912.3 A = 0.0 60.6 475.0 1366,7 1908.5 2464.8 3014.4 3546.3

V = 18.80 T = 0.00 5.32 10.63 15,95 18.61 21.27 23.93 26.59 8D= 104.14 P = 230.65 231.02 236.53 257.81 276.76 301.48 331.58 366.52

= 2.029 B = 4658.8 4656.6 4619.3 4495.6 4402.4 4295.9 4181.5 4063.5 A = 0.0 60.0 469.6 1342.3 1867.6 2403.7 2929.9 3436.1

V = 18.70 T = 0.00 5.43 10.86 16.28 19.00 21.71 24.43 27.14 8D= , 105.27 P = 255.90 256.29 262.06 284.22 303.86 329.41 360.44 396.39

~ = 2.009 B = 4812.5 4804.6 4766.3 4640.6 4546.8 4440.2 4326.2 4209.3 A = 0.0 59.6 465.9 1322.6 1833.4 2351.4 2856.8 3339.9

V = 18.60 T = 0.00 5.54 11.08 16.62 19.39 22.16 24.93 27.71 8D= 106.40 P = 282.13 282.53 288.57 311.65 332.01 358.42 390.41 427.40

~ = 1.990 B = 4970.7 4962.5 4923.3 4795.7 4701.5 4594.8 4481.6 4365.8 A = 0.0 59.2 461.8 1301.9 1797.8 2297.6 2782.3 3242.7

V = 18.50 T = 0.00 5.66 11.32 16.97 19.80 22.63 25.46 28.29 8D= 107.54 P = 309.36 309.79 316.11 340,17 361.30 388.62 421.64 459.73

T= 1,972 B = 5133.7 5127.8 5087.4 4958.0 4863.3 4756.8 4644.3 4529.9 A = 0.0 58.9 458.0 1281.9 1763.5 2245.6 2710.2 3148.8

V = 18.40 T = 0.00 5.77 11.55 17.32 20.21 23.10 25.99 28.87 8 D = 108.69 P = 337.64 338.09 344.70 369.76 391.66 419.90 453.94 493.14

~ = 1,955 B = 5301.5 5295.6 5254.3 5123.1 5028.1 4921.9 4810.4 4697.5 A = 0.0 58.5 454.1 1262.0 1729.7 2194.9 2640.4 3058.6

V = 18.30 T = 0.00 5.90 11.79 17.69 20.63 23.58 26.53 29.48 8 o = 109.85 P = 367.00 367.47 374.40 400.53 423.24 452.46 487.59 527.96

~ = 1.939 B = 5474.3 5469.7 5427.2 5294.3 5198.9 5093.2 4982.7 4871.5 A = 0.0 58.2 450.7 1243.2 1697.5 2146.4 2573.7 2972.3

V = 18.20 T = 0.00 6.02 12.04 18.05 21.06 24.07 27.08 30.09 8 o = 111.02 P = 397.48 397.97 405.24 432.47 456.04 486.26 522.52 564.09

T= 1,923 B = 5652.4 5648.1 5604.6 5470.0 5374.4 5269.3 5160.0 5050.8 A = 0.0 57.9 447.4 1225.1 1666.4 2099.7 2509.6 2889.7

V = 18.10 T = 0.00 6.14 12.29 18.43 21.50 24.58 27.65 30.72 8~= 112.20 P = 429.13 429.65 437.27 465.69 490.16 521.45 558.89 601.73

= 1.908 B = 5835.8 5833.1 5788.4 5652,0 5556.4 5451.8 5344.1 5236.8 A = 0,0 57.7 444.5 1207.9 1636.6 2055.0 2448.1 2810.4

V = 18.00 T = 0.00 6.27 12.55 18.82 21.96 25.10 28.23 31.37 8 D = 113.39 P = 461.98 462.53 470.54 500.22 525.65 558.06 596.75 640.94

= 1.894 B = 6024.8 6022,7 5976.8 5838.8 5743.1 5639.3 5533,0 5428.3 A = 0.0 57.6 442.2 1191.9 1608.7 2012.6 2390.0 2735.3

V = 17.90 T = 0.00 6.41 12.82 19.22 22.43 25.63 28.84 32.04 8D= 114.59 P = 496.09 496.66 505.08 536.11 562.55 596.16 636.16 681.76

= 1.881 B = 6219.5 6213.4 6166.4 6026.8 5931.2 5828.5 5724.2 5622.0 A = 0.0 57.5 440.5 1177.8 1583.3 1973.7 2336.1 2665.7

V = 17.80 T = 0.00 6.54 13.08 19.63 22.90 26.17 29.44 32.71 8 D = 115.80 P = 531.49 532.09 540.94 573.33 600.80 635.61 676.95 723.98

= 1.869 B = 6420.2 6420.8 6372.4 6231.4 6136.0 6034.4 5932.1 5832.9 A = 0.0 57.3 437.8 1161.2 1555.0 1931.6 2279.0 2593.0

V = 17.70 T = 0.00 6.68 13.36 20.04 23.38 26.72 30.06 33.40 8 D = 117.02 P = 568.24 568.87 578.18 612.03 640.59 676.67 719.41 767.94

= 1.858 B = 6626.9 6623.5 6574.0 6431.6 6336.7 6236.6 6136.7 6040.4 A = 0.0 57.3 436.1 . 1147.5 1530.6 1894.7 2228.3 2528.1


TABLE V--continued

T / ~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 17.60 T = 0.00 6.82 13.64 20.46 23.88 27.29 30.70 34.11 0o= 118.25 P = 606.38 607.05 616.85 652.24 681.95 719.37 763.60 813.70

= 1.847 B = 6840.0 6837.4 6786.7 6643.0 6548,7 6450.0 6352.6 6259.8 A = 0.0 57.3 434.5 1133.7 1506,3 1858.0 2178.3 2464.2

V = 17.50 T = 0.00 6.97 13,93 20,90 24.38 27.87 31.35 34.84 0D= 119.50 P = 645.98 646.69 657.00 694.04 724,97 763.80 809.58 861.35

y = 1.838 B = 7059,7 7051.2 6999.0 6854.0 6760.3 6663.4 6568.8 6479.4 A = 0.0 57.4 433.6 1121.9 1484.7 1824.9 2132,7 2405.8

V = 17.40 T = 0.00 7.11 14.23 21.34 24.89 28.45 32.01 35.56 0D= 120.76 P = 687.09 687.83 698.68 737.40 769.56 809.83 857.19 910.64

y = 1,830 B = 7286.2 7282.6 7229.2 7083.2 6990.5 6895.7 6804.2 6718.9 A = 0.0 57.3 431.7 1107.7 1460.3 1788.8 2084.0 2344.5

V = 17.30 T = 0.00 7.27 14.53 21.80 25.43 29.06 32.70 36,33 0 D = 122.04 P = 729.75 730.54 741.99 782.55 816.06 857.90 906.98 962.27

y = 1.822 B = 7519.6 7511.8 7456.9 7310.1 7218.2 7125.6 7037.6 6956.7 A = 0.0 57.5 431.3 1096.9 1440.3 1758,0 2041.7 2290.3

V = 17.20 T = 0.00 7.42 14.84 22.26 25.97 29.68 33,38 37.09 0o= 123.33 P = 774.0 774.9 786.9 829.4 864.3 907.7 958.5 1015.7

= 1.816 B = 7760.3 7757.4 7701,2 7553,7 7463.3 7373.3 7288.9 7213.1 A = 0.0 57.6 430,0 1084,2 1418.1 1724.9 1997.2 2234.2

V = 17.10 T = 0.00 7.58 15.16 22.74 26.53 30.32 34,11 37.90 0~= 124.65 P = 820.0 820.9 833.6 878.2 914.5 959.7 1012.4 1071.6

y = 1.810 B = 8008.6 8003.3 7945.7 7797.6 ~708.5 7621.5 7541.4 7470.6 A = 0.0 57.8 429.9 1074.2 1399.4 1696.1 1957.6 2183,8

V = 17.00 T = 0.00 7.74 15.48 23.22 27.09 30.96 34.83 38.70 0o= 125.97 P = 867.7 868,7 882.1 928.7 966.7 1013.6 1068.3 1129.5

~ = 1.806 B = 8264.6 8255.6 8196.5 8047.8 7960.7 7876.6 7800.9 7735,7 A = 0.0 58.0 429.5 1063.9 1380.6 1667.7 1919.1 2135.0

V = 16.90 T = 0.00 7..91 15.82 23.73 27.68 31.63 35.59 39.54 0o= 127.32 P = 917.3 918.2 932.5 981.4 1021.0 1069.9 1126.6 1190,1

y = 1.802 B = 8528.6 8519.2 8458.4 8309.4 8224.1 8143.4 8072.5 8013.3 A = 0.0 58.3 429.7 1054.7 1363.1 1640.8 1882.3 2088.4

V = 16.80 T = 0.00 8.08 16.15 24.23 28.27 32.3t 36,35 40.39 0o= 128.69 P = 968.7 969.7 984.7 1036.1 1077.4 1128.2 1187.1 1252.8

y = 1,800 B = 8801.0 8794.3 8731,9 8583.1 8499,9 8423.2 8357.5 8304,6 A = 0.0 58.5 429.4 1044.5 1344.7 1613.2 1845.3 2041.8

V = 16.70' T = 0.00 8.25 16.51 24.76 28.89 33.01 37.14 41,27 0 o = 130.08 P = 1022.1 1023.2 1039.1 1093.0 1136.1 1189.1 1250.3 1318.4

y = 1.799 B = 9082.0 9073.8 9009.9 8861.1 8780.3 8707.8 8647.8 8601.6 A = 0.0 58.9 429.9 1036.2 1328.7 1588.5 1811.4 1999.1

V = 16.60 T = 0.00 8.43 16.86 25.29 29.50 33.72 37.93 42.15 0 o = 131.49 P = 1077.5 1078.6 1095.5 1152.1 1197.1 1252.2 1315.7 1386.4

y = 1.798 B = 9371.9 9363.8 9298.4 9150.3 9072.2 9004.4 8950.7 8912.2 A = 0.0 59.2 430.0 1027.2 1312.2 1563.6 1777.8 1956.8

V = 16.50 T = 0.00 8.61 17.23 25~4 30.15 34.45 38.76 43.07 0D= 132.93 P = 1135.0 1136.2 1154.0 1213.5 1260.6 1318.0 1384.2 1457.5

y = 1.799 B = 9671.0 9669.2 9602.1 9454.5 9379.7 9316,7 9269,4 9239.2 A = 0.0 59.6 430.5 1018.8 1296.4 1539.4 1745.2 1915.9

V = 16.40 T = 0~00 8.80 17.61 26.41 30.82 35.22 39.62 44.02 0p= 134.39 P = 1194.7 1196.0 1214.9 1277.6 1326.8 1386.8 1455.6 1531.9

y = 1.801 B = 9979.7 9977.3 9908.3 9761.7 9690.5 9632.6 9592.6 957~9 A = 0.0 60.2 431.9 1012.2 1282.7 1518.1 1715.8 1878.6

Improved Experimental Equation o| State of Solid Hydrogen and Deuterium 389

TABLE V---contmued

~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 16.30 T = 0.00 9.00 17.99 26.99 31.49 35.98 40.48 44.98 0o= 135.88 P = 1256.7 1258.1 1278.2 134.0 1395.5 1458.1 1529.7 1609.0

7 = 1.805 B = 10298.0 10286.0 10215.0 10069.0 10002.0 9950.0 9917.0 9905.0 A = 0.0 60.7 433.2 1006.1 1270.2 1498.2 1688.5 1844.2

V = 16.20 T = 0.00 9.20 18.39 27.59 32.18 36.78 41.38 45.98 0o= 137.40 P = 1321.1 1322.6 1343.9 1413.2 1467.2 1532.5 1607.1 1689.5

7 = 1.809 B = 10627.0 10613.0 10540.0 10396.0 10333.0 10287.0 10263.0 10260.0 A = 0.0 61.3 434.7 1000.1 1257.6 1478.4 1661.3 1809.8

V = 16.10 T = 0.00 9.39 18.79 28.18 32.88 37.58 42.27 46.97 0D= 138.95 P = 1388.0 1389.6 1412.1 1485.0 1541.5 1609.6 1687.4 1773.1

7 = 1.815 B = 10967.0 10963.0 10888.0 10746.0 10687.0 10648.0 10633.0 10641.0 A = 0.0 61.7 435.4 992.4 1243.3 1457.0 1632.8 1774.3

V = 16.00 T = 0.00 9.60 19.20 28.80 33.60 38.40 43.20 48.00 0o= 140.53 P = 1457.4 1459.1 1483.0 1559.8 1619.0 1690.2 1771.2 1860.4

7 = 1.822 B = 11318.0 11305.0 11228.0 11089.0 11035.0 11003.0 10997.0 11017.0 A = 0.0 62.4 437.2 987.4 1232.4 1439.5 1608.7 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 = 15.90 T = 0.00 9.72 19.43 29.15 34.00 38.86 0D= 142.54 P = 1.5295 1.5311 1.5544 1.6293 1.6871 1.7566

7 = 1.752 B = 11.680 11.673 11.582 11.391 11.293 11.207 A = 0.0 58.1 408.0 927.0 1162.2 1364.6

V = 15.80 T = 0.00 9.93 19.86 29.79 34.76 39.72 8o= 144.12 P = 1.6043 1.6061 1.6307 1.7093 1.7695 1.8418

7 = 1.750 B = 12.054 12.047 11.951 11.754 11.654 11.567 A = 0.0 58.4 407.7 918.0 1147.1 1343.3

V = 15.70 T = 0.00 10.14 20.29 30.43 35.51 40.58 0o= 145.73 P = 1.6821 1.6839 1.7099 1.7922 1.8549 1.9300

7 = 1.747 B = 12.440 12.435 12.335 12.132 12.030 11.943 A = 0.0 58.6 406.8 908.0 1130.8 1321.0

V = 15.60 T = 0.00 10.37 20.75 31.12 36.31 41.50 Oo= 147.37 P = 1.7628 1.7648 1.7923 1.8787 1.9441 2.0223

7 = 1.745 B = 12.839 12.831 12.726 12.517 12.413 12.325 A = 0.0 59.1 406.8 899.5 1116.5 1300.7

V = 15.50 T = 0.00 10.60 21.21 31.81 37.11 42.42 0D= 149.03 P = 1.8467 1.8488 1.8779 1.9684 2.0365 2.1178

7 = 1.743 B = 13.251 13.248 13.138 12.922 12.817 12.728 A = 0.0 59.4 406.0 889.7 1100.6 1279.0

V = 15.40 T = 0.00 10.83 21.67 32.50 37.92 43.33 8D= 150.72 P = 1.9339 1.9361 1.9668 2.0614 2.1323 2.2167

7 = 1.740 B = 13.677 13.666 13.551 13.329 13.222 13.132 A = 0.0 59.6 405.0 879.8 1085.1 1257.9

V = 15.30 T = 0.00 11.07 22.14 33.21 38.75 44.28 #D = 152.43 P = 2.0244 2.0267 2.0591 2.1581 2.2320 2.3196

7 = 1.738 B = 14.118 14.102 13.982 13.753 13.644 13.554 A = 0.0 59.9 403.9 869.9 1069.5 1236.8

43.72 48.58 1.8359 1.9231 11.138 11.085 1534.4 1674.5

44.69 49.65 1.9240 2.0144 11.498 11.446 1507.2 1642.2

45.65 50.72 2.0152 2.107 11.873 11.822 1479.3 1609.0

46.68 51.87 2.1108 2.2077 12.255 12.205 1453.4 1578.2

47.72 53.02 2.2096 2.3099 12.658 12.609 1426.1 1546.2

48.75 54.17 2.3118 2.4156 13.062 13.013 1400.1 1515.7

49.82 55.35 2.4182 2.5256 13.485 13.436 1373.8 1485.0


TABLE Vl--continued

T I T m = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 15.20 T = 0.00 11.32 22.63 33.95 39.61 45.26 50.92 56.58 0D= 154.18 P = 2.1185 2.1210 2.1552 2.2588 2.3357 2.4267 2.5289 2.6401

3, = 1.735 B = 14.573 14.554 14.428 14.192 14.082 13.991 13.922 13.874 A = 0.0 60.2 402.9 860.0 1054,0 1215.8 1348.1 1454.9

V = 15.10 T = 0.00 11.57 23.14 34.71 40.49 46.27 52.06 57.84 0D= 155.96 P = 2.2162 2.2188 2.2550 2.3635 2.4436 2.5381' 2.6441 2.7592

3,= 1.733 B = 15.044 15.032 14,900 14.658 14.546 14.454 14,385 14,339 A = 0.0 60.5 401,6 849.5 1037.8 1194.3 1321.6 1424.2

V = 15.00 T = 0,00 11.82 23.64 35.46 41.37 47.28 53.19 59.11 0o= 157.76 P = 2.3178 2.3206 2.3587 2.4721 2.5554 2.6535 2.7632 2.8823

y = 1.731 B = 15.530 15.512 15.374 15.125 15.011 14.919 14,851 14.805 A = 0.0 60.7 400.1 839.1 1022.0 1173.3 1296.2 1394.7

V = 14.90 T = 0,00 12.09 24.18 36.27 42.31 48.36 54.40 60.45 0o= 159.60 P = 2.4233 2.4263 2.4666 2.5854 2.6722 2.7741 2.8879 3.0112

3,= 1,728 B = 16.034 16.023 15.878 15.623 15.507 15.414 15,347 15.302 A = 0.0 61.0 398.8 828.7 1006.1 1152.3 1270.4 1365.1

V = 14,80 T = 0.00 12.35 24.70 37.05 43.22 49.40 55.57 61.75 0D= 161.46 P = 2.5330 2.5362 2.5786 2.7026 2.7928 2.8985 3.0162 3.1437

"/= 1.726 B = 16.554 16.540 16.389 16.127 16.010 15.917 15.849 15.806 A = 0.0 61.2 396.7 817.4 989.7 1131.1 1244.9 1335.9

V = 14.70 T = 0.00 12.63 25.25 37.88 44.19 50.50 56.81 63.13 0D= 163.36 P = 2.6471 2.6504 2.6952 2.8249 2.9187 3.0284 3.1504 3.2823

3,= 1.723 B = 17.093 17.088 16.930 16.661 16.543 16.449 16.382 16.340 A = 0.0 61.4 394.8 806.3 973.3 1109.7 1219.2 1306.5

V = 14.60 T = 0.00 12.92 25.83 38.75 45.21 51.66 58.12 64.58 0D= 165.29 P = 2.7657 2.7692 2.8165 2.9524 3.0502 3.1642 3.2908 3.4273

3,= 1.721 B = 17.650 17.639 17.474 17.198 17.078 16.985 16.918 16.878 A = 0,0 61.8 393.6 796.5 958.5 1090.2 1195.5 1279.2

V = 14.50 T = 0.00 13.19 26.38 39,57 46.17 52.77 59.36 65.96 0D= 167.26 P = 2.8890 2.8927 2.9424 3.0841 3.1856 3.3036 3.4345 3.5756

3,= 1.718 B = 18.227 18.211 18.038 17.754 17.633 17.539 17.474 17.434 A = 0,0 61.8 391.0 784.9 942.0 1069.2 1170.8 1251.1

V = 14.40 T = 0.00 13.50 27.00 40,49 47.24 53.99 60.74 67.49 0D= 169.26 P = 3.0171 3.0211 3.0737 3.2221 3.3278 3.4505 3.5863 3.7324

3'= 1,715 B = 18.824 18.809 18.629 18.338 18.215 18.121 18.056 18.019 A = 0.0 62.2 389.5 774.7 926.8 1049.5 1147.1 1224.1

V = 14.30 T = 0.00 13.79 27.58 41.37 48.26 55.15 62.05 68.94 0D= 171.29 P = 3,1505 3.1547 3.2100 3.3647 3.4744 3.6015 3.7419 3.8928

3, = 1.713 B = 19.441 19,432 19,244 18,946 18.823 18,729 18.665 18.629 A = 0.0 62.2 386.5 762.6 909.9 1028.4 1122.2 1196.2

V = 14.20 T = 0,00 14.11 28.22 42.33 49.39 56.44 63.50 70.55 0D= 173.36 P = 3.2891 3.2936 3.3521 3.5141 3.6283 3.7604 3.9060 4.0623

y = 1.710 B = 20.081 20.061 19.864 19.559 19.434 19.340 19.277 19,243 A = 0.0 62.6 385,1 752.7 895.4 1009.6 1099.8 1170.7

V = 14.10 T = 0.00 14.42 28,83 43.25 50.46 57.67 64.87 72.08 0 D= 175.47 P = 3.4334 3.4381 3.4996 3.6685 3.7870 3.9238 4.0744 4.2359

3"= 1.708 B = 20,744 20.712 20.508 20.195 20.069 19.975 19,913 19,880 A = 0.0 62.7 382.2 741.2 879.5 989.7 1076.5 1144.6

V = 14.00 T = 0.00 14.74 29.48 44.21 51.58 58.95 66.32 73.69 0 D= 177.61 P = 3.5835 3.5884 3.6532 3.8295 3.9527 4.0945 4.2504 4.4173

3"= 1.705 B = 21.430 21.406 21.193 20.873 20.745 20.651 20.591 20.561 A = 0.0 62.8 379.4 729.5 863,2 969.5 1052.8 1118.1


TABLE ~---continued

T / ~ = 0.0 0 . 2 0.4 0.6 0.7 0.8 0.9 1.0

V = 13.90 T = 0.00 15.07 30.15 45.23 52.76 60.30 67.84 75.38 0D= 179.79 P = 3.7396 3.7449 3.8132 3.9975 4.1255 4.2727 4.4341 4.6068

7 = 1.702 B = 22.141 22.134 21.912 21.584 21.455 21.362 21.303 21.274 A = 0.0 63.0 376.6 717.9 847.2 949.4 1029.4 1091.9

V = 13.80 T = 0.00 15.41 30.82 46.24 53.94 61.65 69.35 77.06 #o = 182.02 P = 3.9021 3.9077 3.9796 4.1719 4.3049 4.4574 4.6245 4.8030

7 = 1.700 B = 22.877 22.843 22.611 22.277 22.147 22.054 21.996 21.970 A = 0.0 63.2 374.1 707.3 832.4 931.0 1008.1 1067.9

V = 13.70 T = 0.00 15.76 31.53 47.29 55.17 63.06 70.94 78.82 0D= 184.28 P = 4.0713 4.0772 4.1530 4.3538 4.4920 4.6502 4.8233 5.0079

7 = 1.697 B = 23.460 23.599 23.358 23.014 22.884 22.792 22.736 22.712 A = 0.0 63.4 371.5 696.4 817.3 912.3 986.2 1 0 4 3 . 6

V = 13.60 T = 0.00 16.13 32.26 48.39 56.46 64.53 72.59 80.66 0 o = 186.58 P = 4.2473 4.2536 4.3336 4.5435 4.6873 4.8515 5.0308 5.2220

= 1.694 B = 24.432 24.383 24.130 23.780 23.649 23.557 23.502 23.482 A = 0.0 63.7 369.0 685.6 802.5 894.0 964.9 1019.7

V = 13.50 T = 0.00 16.48 32.97 49.45 57.69 65.94 71.18 82.42 0o = 188.93 P = 4.4307 4.4373 4.5213 4.7399 4.8889 5.0589 5.2443 5.4417

7 = 1.692 B = 25.252 25.221 24.959 24.601 24.469 24.378 24.326 24.307 A = 0.00 63.61 365.01 673.05 785.86 873.82 941.95 994.59

V = 13.40 T = 0.00 16.87 33.73 50.60 59.03 67.47 75.90 84.33 0o= 191.32 P = 4.6216 4.6286 4.7172 4.9455 5.1005 5.2768 5.4688 5.6730

7 = 1.689 B = 26.102 26.074 25.802 25.436 25.303 25.212 25.162 25.146 A = 0.00 63.80 362.07 661.89 770.80 855.49 920.66 970.99

V = 13.30 T = 0.00 17.25 34.50 51.75 60.37 69.00 77.62 86.25 0D = 193.75 P = 4.8203 4.8278 4.9210 5.1591 5.3200 5.5028 5.7016 5.9127

7 = 1.686 B = 26.985 26.958 26.673 26.301 26.167 26.077 26.029 26.017 A = 0.00 63.88 358.67 650.39 755.48 836.88 899.45 947.57

V = 13.20 T = 0.00 17.65 35.30 52.94 61.77 70.59 79.41 88.24 0D= 196.23 P = 5.0274 5.0354 5.1335 5.3821 5.5492 5.7387 5.9445 6.1628

7 = 1.683 B = 27.900 27.854 27.558 27.178 27.043 26.955 26.909 26.899 A = 0.00 64.05 355.65 639.56 741.06 819.40 879.41 925.50

V = 13.10 T = 0.00 18.05 36.09 54.14 63.16 72.18 81.21 90.23 #D = 198.75 P = 5.2432 5.2516 5.3548 5.6138 5.7872 5.9836 6.1964 6.4220

= 1.680 B = 28.849 28.794 28.485 28.098 27.964 27.876 27.832 27.825 A = 0.00 64.08 352.04 628.17 726.13 801.42 859.02 903.07

V = 13.00 T = 0.00 18.47 36.95 55.42 64.66 73.90 83.13 92.37 #D = 201.33 P = 5.4680 5.4769 5.5858 5.8564 6.0368 6.2405 6.4611 6.6946

7 = 1.678 B = 29.835 29.822 29.501 29.105 28.970 28.884 28.842 28.839 A = 0.00 64.19 348.41 616.35 710.65 782.80 837.97 879.93

V = 12.90 T = 0.00 18.90 37.81 56.71 66.16 75.61 85.06 94.52 0o= 203.95 P = 5.7024 5.7118 5.8264 6.1087 6.2960 6.5072 6.7356 6.9771

7 = 1.675 B = 30.858 30.832 30.498 30.096 29.960 29.875 29.836 29.836 A = 0.00 64.30 345.00 605.38 696.23 765.68 818.43 858.71

V = 12.80 T = 0.00 19.33 38.66 58.00 67.66 77.33 86.99 96,66 8 D = 206.62 P = 5.9466 5.9566 6.0770 6.3711 6.5654 6.7842 7.0204 7.2699

7 = 1.672 B = 31.920 31.868 31.521 31.110 30.974 30.891 30.855 30.859 A = 0.00 64.32 341.29 594.37 682.06 748.79 799.40 837.97

V = 12.70 T = 0.00 19.79 39.58 59.37 69.27 79.17 89.06 98.96 #D = 209.35 P = 6.2013 6.2119 6.3388 6.6458 6.8478 7.0747 7.3194 7.5777

7 = 1.669 B = 33.023 32.950 32.589 32.170 32.035 31.953 31.920 31.929 A = 0.00 64.49 338.01 583.80 668.21 732.32 780.84 817.58


TABLE H---continued

T / ~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V = 12.60 T = 0.00 20.25 40.50 60.75 70.88 81.00 91.13 101.25 0o= 212.13 P = 6.4668 6.4781 6.6116 6.9316 7.1412 7.3764 7.6297 7.8967

7 = 1.666 B = 34,169 34.092 33.717 33.292 33.156 33,077 33.047 33,058 A = 0.00 64.51 334.11 572.56 653.92 715.38 761.85 797.00

V = 12.50 T = 0.00 20.71 41.42 62.13 72.49 82.84 93.20 103.55 0D= 214.96 P = 6.7438 6.7557 6.8959 7.2290 7.4464 7.6899 7.9518 8.2277

y = 1.6 B = 35.360 35,311 34,922 34.490 34,354 34.276 34.249 34.265 A = 0.00 64.34 329,50 560.54 638.78 697.83 742.33 775.92

V = 12.40 T = 0.00 21.20 42.40 63.60 74.20 84.80 95.40 106.00 0 o = 217.85 P = 7.0328 7.0454 7.1930 7.5404 7.7662 8.0186 8.2898 8.5752

7 = " 1.660 B = 36,598 36.549 36.145 35.704 35,569 35.494 35.472 35.493 A = 0.00 64.38 325.60 549.57 624.82 681.37 723.93 755.88

V = 12.30 T = 0.00 21.69 43.38 65.07 75.92 86.76 97.61 108.45 0D= 220.79 P = 7.3343 7.3477 7.5027 7.8646 8.0988 8.3603 8.6408 8.9359

7 = 1.657 B = 37.884 37.826 37,407 36.958 36,824 36.751 36,732 36.756 A = 0.00 64.31 321.40 538.49 610.92 665.13 705.92 736.52

V = 12.20 T = 0.00 22.21 44.42 66,63 77.74 88.84 99.95 111.05 0D= 223,80 P = 7.6490 7.6632 7.8265 8.2040 8.4473 8.7186 9.0091 9.3145

y = 1,654 B = 39.222 39.160 38,725 38.270 38.137 38,065 38,050 38.081 A = 0.00 64.36 317.48 527.73 597.27 649.32 688.21 717.55

V = 12.10 T = 0.00 22.73 445.46 68.19 79.56 90.93 102.29 113.66 0D= 226.86 P = 7.9775 7.9925 8.1641 8.5575 8.8100 9.0910 9.3917 9.7074

y = 1.651 B = 40.613 40.555 40,104 39.641 39.507 39.440 39,428 39,463 A = 0.00 64.27 313.14 516.65 583.60 633.40 670.67 698.46

V = 12.00 T = 0.00 23.28 46.57 69.85 81.49 93.13 104.77 116.41 0D= 229.99 P = 8.321 8,336 8.517 8.928 9,190 9.481 9.793 10.120

y = 1.648 B = 42.060 41.988 41.520 41.050 40,916 40.853 40,846 40.887 A = 0.00 64.32 309.22 506.16 570.49 618.18 653.72 680.35

V = 11.90 T = 0.00 23.83 47.87 71.50 83.42 95.34 107.25 119.17 0D= 233.18 P = 8.679 8.696 8.886 9.313 9.586 9.888 10.210 10.548

7 = 1.645 B = 43.566 43.505 43.019 42.541 42.411 42.348 42,347 42,394 A = 0.00 64.21 304,74 495.20 556.93 602.65 636.56 661.87

V = 11.80 T = 0.00 24.39 48.77 73.16 85.35 97.54 109.73 121.93 0D= 236.44 P = 9.053 9.071 9.270 9.715 9,997 10.310 10.644 10.993

7 = 1.642 B = 45,133 45,049 44.545 44.061 43.931 43.873 43.877 43,929 A = 0.00 64.02 300.19 484.45 543.77 587.67 620.09 644.32

V = 11.70 T = 0.00 24.97 49.93 74.90 87.38 99.87 112.35 124.83 0D= 239.76 P = 9.444 9.463 8.672 10.136 10.429 10.753 11.098 11.460

y = 1.639 B = 46.766 46.690 46,167 45.677 45.548 45.493 45.501 45,559 A = 0.00 63.88 295.66 473.68 530.64 572.59 603.57 626.67

V = 11.60 T = 0.00 25,58 51.16 76.74 89.53 102.32 115.11 127.90 0D= 243.15 P = 9.853 9.873 10.093 10.577 10.881 11,218 11.575, 11.949

7 = 1.636 B = 48.465 48.369 47.826 47,329 47.203 47.152 47,166 47,229 A = 0.00 63.87 291.51 463.53 518.12 558.30 587.84 609.87

V = 11.50 T = 0.00 26.19 52.38 78.58 91.67 104.77 117.86 130.96 0D= 246.62 P = 10.280 10.301 10.533 11.037 11.353 11.701 12,071 12.458

7 = 1.632 B = 50.236 50.142 49.581 49.078 48,954 48,906 48.926 48,997 A = 0.00 63.69 286.88 452.97 505.35 543.73 571.96 593.09

V = 11.40 T = 0.00 26.83 53.67 80.50 93.92 107.34 120.76 134.17 0 D = 250.16 P = 10.727 10,749 10.993 11,518 11.846 12.208 12.592 12.992

7 = 1.629 B = 52.081 51.976 51.395 50.884 50,761 50,720 50.743 50.824 A = 0.00 63.61 282.51 442.78 492.98 529.65 556.74 576.68

Improved Experimental Equation of State ot Solid Hydrogen and Deuterium 393

TABLE ~--continued

T/~ = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V =

0 D =

3,=

V = 0 D =

3,=

V = 0 D =

3,=

V = 0 D =

3,=

V = 0 D =

3,=

V = 19 D =

3,=

V =

3,=

V = 0 D =

3'=

V = 0 D =

3'=

V = 0 D =

3'=

V = 0 D =

3'=

V =

3,=

V = 0 D =

3,=

11.30 T = 0.00 27.48 54.96 82.43 96.17 109.91 123.65 137.39 253.77 P = 11.194 11.218 11.474 12.021 12.361 12.736 13.133 13.547

1.626 B = 54.004 53.952 53.349 52.832 52.713 52.675 52.705 52.791 A = 0.00 63.32 277.50 431.96 480.01 515.14 540.88 559.93

11.20 T = 0.00 28.15 56.30 84.46 98.53 112.61 126.68 140.76 257.46 P = 11.683 11.708 11.978 12.548 12.901 13,289 13.701 14.129

1.623 B = 56.010 55.906 55.284 54.762 54.644 54.611 54.648 54.742 A = 0.00 63.21 273,16 422.20 468.31 501.81 526.37 544.57

11.10 T = 0.00 28.86 57.71 86.57 101.00 115.43 129.85 144.28 261.33 P = 12.195 12.222 12.505 13.100 13.467 13.870 14.296 14.740

1.619 B = 58.101 57,960 57.312 56.786 56.673 56.645 56.689 56.792 A = 0.00 63.13 268.85 412.54 456.65 488.69 512.13 529.38

11.00 T = 0.00 29,56 59.12 88.68 103.46 118.24 133.02 147.80 265.08 P = 12.730 12.759 13.057 13.676 14.057 14.475 14.916 15.376

1.616 B = 60.284 60.190 59.521 58.988 58.876 58.855 58.906 59.017 A = 0.00 62.38 263.87 402.15 444.41 474.91 497.35 513,73

10.90 T = 0.00 30.30 60.59 90.89 106.03 121.18 136.33 151.48 269.02 P = 13.291 13.321 13.635 14.280 14.676 15.109 15.567 16.042

1.613 B = 62.561 62.461 61.768 61.229 61.122 61.106 61.166 61.285 A = 0.00 62.62 259.22 392.36 432.74 461.88 483.27 498.84

10.80 T = 0.00 31.03 62,06 93.09 108.61 124.12 139.64 155.15 273.04 P = 13.879 13.911 14.239 14.911 15,322 15.771 16.244 16.737

1.609 B = 64.938 64.817 64.103 63.560 63.456 63.446 63.512 63.640 A = 0.00 62.30 254.38 382.56 421.23 449.11 469.45 484.41

10.70 T = 0.00 31.80 63.59 95.39 111.29 127.19 143.08 158.98 277.16 P = 14.494 14.528 14.874 15.573 15.999 16.465 16.956 17.465

1.606 B = 67.422 67.307 66.567 66.018 65.918 65.914 65.989 66.127 A = 0.00 61.99 249.52 372.83 409.78 436.44 455.77 469.94

10.60 T = 0.00 32.62 65.25 97.87 114.18 130.49 146.80 163.12 281.36 P = 15.139 15.176 15.540 16.270 16.713 17.197 17.706 18.234

1.602 B = 70.015 69.898 69.133 68.580 68.484 68.488 68.573 68.722 A = 0.00 61.86 245.06 363.49 398.80 424.15 442.51 456.06

10.50 T = 0.00 33.45 66.90 100.35 117.07 133.80 150.52 167.25 285.66 P = 15.816 15.854 16.237 16,999 17.459 17.961 18.488 19.036

1.599 B = 72.726 72.547 71.754 71.199 71.107 71.119 71.215 71,371 A = 0.00 61.64 240.54 354.41 388.13 412.35 429.83 442.66

10.40 T = 0.00 34.28 68.55 102.83 119.97 137,11 154.25 171.38 290.06 P = 16.525 16.566 16.968 17,760 18,238 18.758 19.305 19.871

1.595 B = 75.560 75.433 74.616 74.055 73.970 73.990 74,090 74.258 A = 0.00 61.19 235.40 344.71 376.97 399.96 416.71 428.98

10.30 T = 0.00 35.17 70.33 105.50 123.08 140.66 158.24 175.82 294.56 P = 17.269 17.313 17.736 18.563 19.060 19.599 20.167 20.754

1.592 B = 78.524 78.383 77.536 76.972 76.982 76,920 77,033 77.216 A = 0.00 60.95 230.78 335.67 366.42 388.35 404.32 415.90

10.20 T = 0.00 36.05 72.11 108.16 126.19 144.21 162.24 180.27 299.17 P = 18.051 18.097 18.541 19.402 19.918 20.478 21.066 21.674

1.588 B = 81.625 81.471 80.596 80.030 79.958 79.994 80.116 80.307 A = 0.00 60.57 225.94 326.59 355.89 376.84 391.93 403.13

10.10 T = 0.00 37.00 74.00 111.01 129.51 148.01 166.51 185.01 303.88 P = 18.871 18.920 19.388 20.287 20.823 21.405 22.015 22.646

1.584 B = 84.869 84.668 83.765 83.197 83.130 83.177 83.311 83.518 A = 0.00 60.34 221.42 317.90 345.91 365,80 380.14 390.71


TABLE Vl--continued

T/T m = 0.0 0.2 0.4 0.6 0.7 0.8 0.9 1.0

V= 10.00 T= 0.00 37.92 75.84 113.76 132.72 151.68 170.65 189.61 OD= 308.70 P= 19.732 19.784 20.274 21.210 21.767 22.370 23.002 23.655

~= 1.581 B = 88.267 88.098 87.166 86.596 86.535 86.588 86.734 86.953 A = 0.0 59.78 216.30 308.78 335.53 354.45 368.19 378.06

I I I I I I / ! I

// p 0 ISOCHORE FROM OUR TABLE /

"tl o

o ~ o o

I I I I I I 0 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

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10. M. S. Anderson and C. A. Swenson, Phys. Rev. B 10, 5184 (1974).

Improved Experimental Equation o[ State oi Solid Hydrogen and Deuterium 395

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384 (1975). 30. N. G. Bereznyak and A. A. Sheinina, Soy. J. Low Temp. Phys. 6 608 (1980). 31. R. D. Goodwin, Cryogenics 2, 353 (1962). 32. B. A. Vindryavskii, S. N. Ishmaev, I. P. Sadikov, A. A. Chernyshov, V. A. Suhoparov,

and A. S. Telepnev, Phys. Lett. A76, 355 (1980). 33. V. B. Esel'son, B. G. Udovidchenko and V. G. Manzhelii, Fiz. Nizk. Temp. 7, 945 (1981). 34. I. N. Krupskii, A. I. Prokhvatilov, and G. N. Schcherbakov, in 21st All-Union Conference

on Low Temperature Physics: Abstracts of Reports (Khar'kov, 1980), Part 4, p. 82. 35. M. Nielson, Phys. Rev. B 7, 1626 (1973).

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An improved experimental equation of state of solid hydrogen and deuterium