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14 010 OLAF SCHULTE AND WILFRIED B.HOLZAPFEL 48

61.8 GPa5- Hg2221E 20

CDEOOg$ 16

15 '0 10

19 I+bet18

~ bctorthor.hcpOS - bct.EOS orthor. ', --- EOS - hcp

orthor.

20 I30 40pressure ( GPa )

50 60

I' a-I k l-ghep

I 70~~COCD~~ FIG. 3. Pressure-volume data of mercury at room tempera-ture. The curves represent the EOS obtained by the form givenin the text for the different phases.

9.2 GPaP-Hg

20 I30 I I I40energy ( keV )

I50 60

tern taken at 19.8 GPa which is well in the middle of thestability range of the new phase. The observed intensitiesof the diffraction lines are also given in Table I as well asthe calculated lattice spacings for the (former assumed)bct, rhombohedral, and hcp lattices. A space-groupanalysis with these rejections of the orthorhombic struc-ture was not successful, because no characteristic extinc-

6005004003002001000 0 10 20 30 40pressure ( GPa )

FIG. 2. Phase diagram ofmercury. Closed and open symbolsrepresent forward and backward transitions, respectively. Theshaded areas show the regions of hysteresis and the questionmarks indicate roughly the locations of the triple points.

FIG. 1. Diffraction patterns of Hg at room temperature andunder different pressures. (a) P-Hg (bct), (b) y-Hg (orthorhom-bic), (c) and (d) 5-Hg (hcp). g denotes diffraction lines from thegasket, e indicates escape peaks from the Ge detector. The ar-rows mark diffraction peaks of rest from the orthorhombicphase.

tions were found due to the large number of overlappinglines. Further studies are necessary to find out the spacegroup, for instance, at smaller diffraction angles to spreadout the pattern and to include possible diffraction lineswith lower indi es.With the m surements at lower and higher tempera-tures, Fig. 2 represents the present results on the variousphase transition lines. Thick solid lines show the previ-ous boundaries, ' dashed lines represent the results of thepresent study. The equilibrium transition pressures aretaken as midpoints of the hysteresis loops. A rough es-timation of the slope of the boundary lines, dp/dT,neglecting the curvature leads to values of .025GPa/K for the P-y phase boundary, .0244 GPa/Kfor the y-5, and 0.13(5)GPa/K for the a-y boundary linewith a much larger uncertainty than for the other boun-daries, since the locations of the triple points a-P-y anda-y-5 are still rather uncertain due to a lack of sufhcientdata along the a-y transition line.For further evaluation of the present results a numeri-cal representation of the equation of state (EOS) data forthe different phases can be desirable (see Fig. 3). While adetailed discussion of these data requires some special14, 15considerations about the most appropriate EOS form,which will be given for this case elsewhere, a numerical6representation can be given already here. This evaluationis strictly limited to the range of the experimental data asindicated for the three phases of Hg in the last column ofTable II. A Murnaghan-type EOS is used with the form

IV= Vr1+(p)K'/IC'] ",

which includes in addition to the original form a refer-7ence pressure p. Here, p is selected (almost arbitrarily)in the center of the stability range or experimental rangeof the corresponding p-V data to minimize the correla-tions in the three fit parameters V, K, and K', whichrepresent, respectively, the atomic volume, the bulkmodulus, and its pressure derivative at the reference pres-sure p. The results of the least-squares fitting for theMurnaghan-type EOS are given in Table II. Due to theimplicit assumption of the Murnaghan EOS that K' isconstant, a reasonable approximation for K(p) is given by

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48 PHASE DIAGRAM FOR MERCURY UP TO 67 GPa AND 500 KTABLE I. Comparison of observed lattice spacings and intensities at 19.8 GPa with calculated dvalues for an orthorhombic lattice (a =269. 1 pm, b =445.7 pm, c =645.4 pm) and for the bct, hcp, andrhombohedral lattices, respectively. Observed lines marked with an asterisk do not fit to a hypotheticalmixed phase pattern.

hkl dob (pm) d'""" (pm) I,b, (%) d'&, (pm) d,";P (pm) d rhomboh (pm)001010011002100012

101110020111003021102013112022

262. 1

248.5223.3217.0215.7

205.7193.6183.5

645.4445.7366.8322.7269.1261.4

248.4230.4222.9217.0215.1210.7206.8193.7187.5183.4

41

77317

27

259.5(110) 252.1(002)247.9(100)223.6(101) 222.5(101)

183.5(200) 176.8(102)

247.7(101)

213.8(003)205.9(102)

120103121004113023014122030031104032200123114201024130005210131211202015033132212124105220203221115025040133

155.6155.6

147.8142.0140.7

133.2133.2133.2129.1129.1129.1129.1

124.1124.1121.8121~8

115.4115.4115.4111.7111.7111.7111.7

171.6168.0165.9161.4157.2154.8151.7151.5148.5144.7138.4135.0134.6134.2132.2131.7130.7130.1129.1128.8127.5126.3124.2124.0122.3120.6119.6117.6116.4115.1114.1113.4112.6111.7111.4111.3

1036

10

141.9(211)141.0(002)

129.8(220)

123.9(112)

116.1(310)

112.3(301)111.8(202)

143.1(110)139.2(103)

126.2(004)124.5(112)124.0(200)120.4(201)

112.5(104)

111.2(202)

155.0(110)

137.7(104)

131.4(201)

125~5(113)123.8(202)

115.7(105)

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14 012 OLAF SCHULTE AND WILFRIED B.HOLZAPFEL 48TABLE II. Parameters for the representation of the p- Vdataat room temperature in the different phases by the use of a Mur-naghan equation.

bctOrthor.hcp

pr(GPa)82740

V,(nm')0.020 76(S)0.018 68(4)0.016 15(5)

E,(Gpa)81(23)267(17)271(19)

2(1)8.5(4)4.2(3)

Range(GPa)41210-4330-67

K (p )=K+(p)K'just for the limited experimental regions. An extrapola-tion of these relations to p =0 GPa to determine Eo and

Xo seems mostly not reasonable due to the large uncer-tainties in K' and requires EOS forms with more physicalinput 14 16Finally, it should be noted that the new results on thephase diagram of mercury are fully compatible with thetheoretical study, however, the new orthorhombic struc-ture was not included in these theoretical considerationsand may thus stimulate further theoretical studies to fullydescribe the phase diagram of Hg also from a theoreticalpoint of view.The authors thank the German Ministry of Scienceand Technology (BMFT) for financial support underContract No. 05 440AXI4.

W. Klement, A. Jayaraman, and G. C. Kennedy, Phys. Rev.131, 1 (1963).20. Schulte and W. B.Holzapfel, Phys. Lett. A 131,38 (1988).J.A. Moriarty, Phys. Lett. A 131,41 (1988).4W. A. Grosshans, E. F. Dusing, and W. B. Holzapfel, HighTemp. High Press. 16, 539 (1984).~H. W. Neuling, O. Schulte, T. Kriiger, and W. B. Holzapfel,Meas. Sci ~ Technol. 3, 170 (1992).6W. B.Holzapfel and W. May, in High Pressure Research Geo-physics, edited by S. Akimoto an/ H. M. Manghani, Ad-vances in Earth and Planetary Sciences Vol. 12 (KluwerAcademic, Dordrecht, 1982), p. 73.7K. Syassen and W. B. Holzapfel, Europhys. Conf. Abstr. 1A,75 (1975).SW. B. Holzapfel, in High Pressure Chemistry, edited by H.Kelm (Reidel, Boston, 1978),p. 177.B.Merkau and W. B. Holzapfel, Physica B+C 139/140, 251(1986).

G. J. Piermarini, S.Block, J.D. Barnett, and R. A. Forman, JAppl. Phys. 46, 2774 (1975)~H. K. Mao, P. M. Bell, J.W. Shaner, and D. J. Steinberg, JAppl. Phys. 49, 3276 (1977).R. A. Noack and W. B. Holzapfel, in High Pressure Scienceand Technology, edited by K. D. Timmerhaus and M. SBarber (Plenum, New York, 1979),Vol. 1, p. 748.R.G. Munro, G. J. Piermarini, S.Block, and W. B.Holzapfel,J.Appl. Phys. 67, 2 (1985).W. B. Holzapfel, Molecular Systems Under High Pressure,edited by R. Pucci and G. Piccitto (Elsevier, Amsterdam,1991),p. 61.W. B.Holzapfel, Europhys. Lett. 16, 539 (1991).O. Schulte, Ph.D. thesis, Universitat GesamthochschulePaderborn, 1993.i7F. D. Murnaghan, Finite Deformation of an Elastic Solid (Wiley, New York, 1951).