American Mineralogist, Volume 82, pages 441-451, 1997

A simulation study of induced failure and recrystallization of a perfect MgO crystalunder non-hydrostatic compression: Application to melting in the diamond'anvil cell

ANaror,v B. Bu,oNosHKo AND LnoNrn S. DunnovINSKY

Theoretical Geochemistry Program, Institute of Earth Sciences, Uppsala University,Box 555, 5-752 36 Uppsala, Sweden

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Recent experimental studies revealed that the thermal pressure in a diamond-anvil cell

with laser heating can be large. Accounting for this pressure is therefore important for

treatment of experimental results. In earlier studies, we developed an MgO model that was

demonstrated to perform very well for calculations of thermoelastic properties. Here, we

study the effect of thermal stress on the behavior of MgO under high pressure and tem-perature conditions using molecular dynamics and the earlier developed interatomic po-

tential. The simulations show that thermal stress can produce such effects as dynamic

recrystallization, which may be interpreted as onset of convective-like motion and which

may cause a change in the slope of laser power-temperature curve. Because these two

criteria are used for the identiflcation of melting, it is possible that what was interpretedas melting in previous experiments with MgO was in reality recrystallization.

INrnooucltroN

The use of the diamond-anvil cell (DAC) experimentaltechnique with laser heating has generated a significantadvance in our knowledge of material properties underextreme pressure (P) and temperature (7) conditions (e.9.,Boehler and Chopelas 1991; Jephcoat and Besedin 1996).Simultaneously, advances in computational methods al-low us to assess material properties with increasing reli-ability. Obviously, neither experimental techniques norcomputational methods are perfect. It is of crucial im-portance to examine carefully the reasons for any dis-crepancy between experiment and theory each time it ap-pears. It helps us to advance both theoretical andexperimental methods, and it is especially importantwhen experimental results are either controversial as inthe case of MgSiO. perovskite melting (e.g., Knittle andJeanloz 1989;Zerr and Boehler 1993) or are not yet con-firmed by alternative experiments, as in the case of MgOmelting (Zer and Boehler 1994).

In this paper, we examine the possible reasons for thediscrepancy between existing theoretical predictions (Be-lonoshko and Dubrovinsky 1996b, 1996c; Cohen andGong 1994; Cohen and Kluge 1995; Cohen and Weitz1996; Jackson 1977; Ohtani 1983; Vocadlo and Price1996) and experimental measurements (Zen and Boehler1994) of the melting curve of periclase. As one can seefrom Figure 1, all the available theoretical predictionsprovide significantly higher melting temperatures at highpressure than those measured experimentally. Among theeight predictions shown in Figure 1, the melting curve byCohen and Gong (1994) shows significantly higher tem-peratures than the other seven. The explanation of theseerroneously high melting temperatures was provided by

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Belonoshko and Dubrovinsky (1996b)' Barring the melt-ing curve of Cohen and Gong (1994), the remaining sev-en predictions are internally consistent, and the ability of

MD simulation to predict correctly the room pressure

melting temperature of periclase was also demonsffatedby Ferneyhough et al. (1994). Vocadlo and Price (1996)

used three interatomic potentials in their simulations and

obtained close results. Their melting curves are somewhathigher than that calculated by Belonoshko and Dubrov-insky (1996b, 1996c) at high pressures. This can be ex-plained by the different potentials used, unavoidableoverheating in their simulation or both. Cohen and Kluge(1995) calculated the melting curve of periclase, whichis somewhat lower than the curve by Cohen and Gong(1994) and is more consistent with the Belonoshko and

Dubrovinsky (1996b, 1996c) predictions. Recently, Co-hen and Weitz (1996) provided a melting curve that is

also generally consistent with the other molecular dynam-ics predictions.

Therefore, there is a consistent set of theoretical pre-

dictions of periclase melting (in fact, the degree of con-

sistency has no precedent in the literature) and an exper-imental determination, which provides significantly lower

melting temperatures at high pressures in relation to thepredictions. The difference between experiment and the-

ory amounts to more than 1000 K at 30 GPa. Notwith-

standing the fact that temperature measurements in the

DAC are subject to some errors owing to the neglect of

the dependence of emissivity on temperature and pres-

sure, which can amount up to 300 K at temperature of

4000 K (Shen 1994; Zerr and Boehler 1994), the differ-

ence of more than 1000 K cannot be explained solely by

that. Of course, one can argue that all the theoretical pre-

441

442 BELONOSHKO AND DUBROVINSKY: MD SIMULATION oF Mso

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Thermal pressure (or rather stress, because it is clearthat thermal pressure is different in differently heatedparts of a sample) was assessed both theoretically (Heinz1990) and experimentally (Andrault et al. 1996' Fiquet etal. 1996a,1996b). These studies demonstrated that ther-mal pressure can be significant; for example, Fiquet et al.(1996a) obtained a thermal pressure of about 15 Gpawhen an MgO sample was heated to 3500 K. Experi-mental studies showed that stress in MgO can be signif-icant and amount to up to 15 GPa at pressure of a fewdozen GPa (Duffy et al. 1995). Other measurements gavevalue of stress up to 4 GPa (Weidner et al. 1994) at pres-sures up to 40 GPa (Meade and Jeanloz 1988).

Thus, there is a gap between theoretical studies ofmelting under hydrostatic conditions and experimentalconditions, which are nonhydrostatic because of eitherthermal stress even when the pressurizing medium is qua-si-hydrostatic or deviatoric stress when the medium is nothydrostatic. This study is aimed at filling this gap and atsimulating the behavior of MgO at high temperarure andnon-hydrostatic stress.

Briefly, the pattern of the paper is as follows. We es-timate thermal stress in a sample, making reasonable as-sumptions based on experimental data about the temper-ature distribution in the sample during laser heating. Thisprovides us with the conditions for further simulation. Wesimulated a slab of MgO pressurizedby argon and sub-jected to superimposed stress in the direction parallel tothe slab. In the course of simulation under the conditionscorresponding to the highest P-T tn the 7,en and Boehler(1994) experiment (cold pressure of approximately 35GPa and temperature of about 4000 K), we observed thatwhen the applied stress is higher than 18 GPa, the slabbegins to recrystallize. We calculated how large overes-timation of the strength can be by comparing the simu-lated values of stress necessary for failure of MgO at Ibar with the experimental data. We discuss further whatimpact recystallization might have on visual observationand the power-temperature curve. We come to the con-clusion that it is possible that the simulated process canbe realized under experimental conditions and such phe-nomena might be interpreted as onset of melting.

JusrrmcnrroN oF THE coNDrrroNs FoR MDSIMULATIONS

We have to make some assumptions to calculate ther-mal stresses to which a sample in DAC is subjected.These assumptions actually reduce somewhat the valuesof calculated stresses. The periclase sample in the Zenand Boehler (1994) experiment is approximately rectan-gular in shape with the dimensions 100 x 100 x <15pm. We neglect stress (and temperature gradient) in thedirection perpendicular to the sample surface and assumethat the sample has cylindrical shape [accounting for rect-angular shape will lead to increase of resulting stress (Ti-moshenko and Goodier 1951)1. We neglect ih" p".p"n-dicular gradient not because we think it is not imponant,but simply because there is no experimental data on tem-

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FrcurB 1. The existing data on the melting of periclase. Alltheoretical predictions are internally consistent up to 30 Gpa,except the one by Cohen and Gong (1994), which is likely ro beerroneous (Belonoshko and Dubrovinsky 1996b). The predictionsby Ohtani (1983) and Belonoshko and Dubrovinsky (1996b) aredifferent above 30 GPa most likely because of Ohtani's (19g3)extrapolation of the melting curve by the Simon (1930) equation.

dictions are incorrect. However, because of the consisten-cy among many theoretical predictions, we decided toexamine in detail the experimental technique that mightbe responsible for the discrepancy.

It is well known that because of the particulars of theexperimental technique the sample in a DAC is heatedinhomogeneously. It is appreciated that such inhomoge-neous heating influences the precision of temperaturemeasurements (Heinz et al. 1994; Boehler and Zen

sample is heated to abour 2000 K (Boehler et al. 1990).Such gradients are likely ro have some influence on themeasured properties of a sample. Note that the use of a

pressure can easily be understood. The outer part of asample remains essentially cold, and this maintains thesame volume of a sample during partial heating (of itspaft). Naturally, pressure in the heated part of the sampleduring heating is higher than compared to that beforeheating because the volume has been maintained constantby the unheated portion of the sample. Some relaxationdecreases thermal pressure, but it is not sufficient to re_lease the stress completely because the temperaturc gra_dient is maintained by inhomogeneous laseiheating.

BELONOSHKO AND DUBROVINSKY: MD SIMULATION OF MgO

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Frcunn 2. Assumed radially symmetric temperature distributions (a) on the surface of the sample in a DAC heated by a laser

and corresponding values of the radial component of thermal stresses (b) as a function of distance from the center of a round sample,

given in ctEunits; crE is equal to 7.3 bar/K at 3000 K and I bar and to 22 5 bar/K at 4000 K and 30 GPa, therefore, the approximate

esrimate of thermal stress ranges from 0.5 GPa at 3000 K and 1 bar to 3.3 GPa at 4000 K and 30 GPa in the range of Zetr and

Boehler (1994) experimental conditions. Shape of symbols in (b) corresponds to the temperature distributions shown in (a).

443

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perature gradient in the direction perpendicular to the sur-face of a sample. Accounting for the vertical temperaturegradient would probably increase the total magnitude ofthe stress. If temperature T(r) as a function of distance rfrom the center of sample is known, the radial (o,) andtangential (o*) thermal stresses can be calculated as fol-lows (Timoshenko and Goodier 1951):

where a is the thermal expansivity, E is the Young mod-ulus, and b is the radius of the sample. Note that radialstress vanishes at the border of sample; therefore the re-quirement of mechanical equilibrium is fulfilled.

Boehler et al. (1990),Lazor et al. (1993), and Shen(1994) have shown that the temperature distributionacross the sample can be described by Gaussian function.Indeed, such a distribution is justified by solving the heattransfer equation when a laser is the source of heat (Kar-lov et al. 1995). Therefore, for describing the temperatureprofile as a function of distance from the center of thehot spot, the following expression has been used

where To is the value of temperature measured in the cen-ter of hot spot and rn is an adjustable parameter that canbe determined either by assuming certain temperature atthe border of the sample [slightly higher than room tem-perature (A. Zen, personal communication)] or from re-ported values of temperature gradients (Boehler et al.1990; Boehler and Zen 1994; Heinz et al. 1994; Shen1994).

The stresses were calculated with the use of tempera-ture distributions shown in Fieure 2a. These distributions

0 1 0 2 0 3 0 4 0 5 0

Distance from center (micrometers)

[T(r)l were calculated assuming T(0) as 3000 and 4000K [approximately the lowest and the highest temperaturesof periclase melting measured by Zerc and Boehler(1994)l and corresponding (Fig. 2a) values at the sampleborder; there are four combinations of T(0) and T(R)which were composed from high and low values in thecenter and at the border of a sample. Maximum temper-ature gradients are well within the limits of those mea-sured in DAC (Lazor et al. 1993; Shen 1994; Shen et al.1993). Using these T(r), thermal stresses were calculated(Fie. 2b).

The analysis above shows that thermal stress can besignificant, ranging from 0.5 to 4 GPa, depending on tem-perature distribution, and therefore needs serious consid-eration. The estimated values of thermal stress are in rea-sonable agreement with the values provided by Heinz(1990), which is not surprising because we used the sameanalytical procedure.

Mor-ocur-ln DYNAMICS SIMULATIoN

The consideration of the thermal stress given aboveshows that previous simulations of the melting of MgOare not adequate for the conditions in the diamond anvilcell. We maintained hydrostatic conditions during a two-phase simulation (Belonoshko 1993; Belonoshko andDubrovinsky 1996b, 1996c). Consideration of the thermalstress in DAC suggests that to make direct comparisonbetween measured and simulated melting curves one hasto carry out simulation under non-hydrostatic conditions.The goal of the present MD simulations is to study thebehavior of MgO subjected not only to confining hydro-static pressure but also to superimposed non-hydrostaticstress, which inevitably exists as a result of inhomoge-neous laser heating.

It is well known that the theoretical approach provides

significantly higher values of yield sffength in comparisonwith experimental values (Selinger et al. 1993; Lynden-

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444 BELONOSHKO AND DUBROVINSKY: MD SIMULATION OF MsO

Bell 1995). Several obvious reasons for that result includeneglect of polycrystallinity, defects, particular orientation,and a very high pace of loading. To estimate the magni-tude of overestimation of the strength of MgO, we decid-ed first to calculate the impact of stress on MgO at lowpressure where experimental data exist (Weidner et al.1994) and then to proceed with simulations at 4000 Kand 35 Gpa, approximately the highest p-Z conditions inthe experiment of Zen and Boehler (1994). The purposeof these simulations is to determine whether we can ob-serve any drastic changes in MgO when we apply non-hydrostatic stress instead ofhydrostatic pressure and whatis the value of stress necessary to initiate such changes.

Computational cells at I bar and 35 GPaTo simulate the effect of stress on the behavior of a

sample at I bar, we arranged computational cell in theway shown in Figure 3a. The cell consists of 8 x 8 x 4MgO unit cells with each unit cell containing 4 MgOformula units and contains 2048 atoms overall. The upperhalf of the cell remained empty. The vertical size waskept constant. Constant pressure (stress) was applied inX ard Y directions.

The cell was arranged in a similar way to study theimpact of stress at 35 GPa. In addition, we used 400 Aratoms as the pressurizing medium placed above (in Z di-rection) the MgO parr (Fig. 3b). The MgO part of the cellconsisted of 6 x 6 x 6 MgO unit cells with each unitcell containing 4 MgO formula units and with 1728 Mgand O atoms overall. The size in Z direction was chosento correspond to initial pressure of 35 Gpa and was keptconstant during simulations. An additional (on top of the35 GPa) stress was applied in the X and y directions.Periodic boundary conditions have been applied in bothcases as usual.

Interatomic interaction

The Mg-Mg, Mg-O, and O-O inreractions have beencalculated using the inreraction potential (Ip) describedby Belonoshko and Dubrovinsky (1996b). The Ar-Ar Ipwas the same as applied for modeling Ar melting (Be-lonoshko 1992). The Ar-Mg and Ar-O inreractions werecalculated using the Ar-Ar IP The variation of Ar-Mgand Ar-O interaction parameters within the range typicalfor fluids (Belonoshko and Saxena l99Z) did, not influ-ence the obtained results.

Technical details of the simulationsThe molecular dynamics simulations were carried out

using the Parrinello-Rahman (1981) method. Temperaturewas maintained constant using the Nose-Hoover algo-rithm (Allen and Tildesley 1989; Hoover 1985; Nose1984). Coulomb interactions were calculated using theEwald technique. The time step ranged from 1 to 2 fs.Calculations were continued up to 20 000 time steps (upto 40 ps) if no drastic changes in moving averages wereobserved and for about 2000 time steps if such changeswere observed. Such long computational experiments

with considerable number of atoms (more than two thou-sand) were possible with the use of IBM SP2 massivelyparallel computers (Maui and Stockholm High-Perfor-mance Computing Centers).

Simulations at I bar

The simulations at I bar were done to see how signif-icantly we overestimate the yield strength of MgO. Thestress in X and Y directions (in the plane of slab) havebeen gradually increased. At 300 K and up to 28 GPa nodrastic changes were observed. At32 GPa the slab failedand the resulting configuration was similar to the oneshown in Figure 3c.

The same simulations were done at 3000 K. The max-imum value of stress that the slab was able to sustain isabout 8 GPa (Fig. 4). When the slab fails the a and bsizes decreases because the atoms begin to move into theempty half of the computational cell. The resulting con-figuration is liquidlike (Fig. 5) in full agreement wirh theresults by Lynden and Bell (1995), who also noticed ap-pearance of a liquidlike structure when crystal failed.

Since the yield strength measured by Weidner et al.(1994) is about 3 GPa at 300 K and decreases with in-creasing temperature, we can conclude that we overesti-mate the value of strength by about an order of magnitudeas a result of the neglect of dislocations, vacancies, po-lycrystallinity, and the very high speed of loading.

Simulations at 35 GPa and 4000 K

The pressure and temperature conditions of these sim-ulations were the highest melting P-T of the Zen andBoehler (199a) MgO melting curve, approximately 4000K and 35 GPa. The initial configuration was prepared inthe following way. The size of MgO part was calculatedusing the equation of state (Belonoshko and Dubrovinsky1996a,1996b) at 4000 K and 35 GPa. This gave us thesize of MgO cube equal to 24.24 A. The argon part ofcomputational cell was prepared by melting an fcc crystalof Ar at 4000 K and 35 GPa, maintaining the pressure inZ direction constant and the size in X and Y directionsequal to 24.24 A. Then the MgO and Ar parts of the cellwere put together in the configuration shown in Figure3b.

To model the impact of thermal pressure on the behav-ior of the sample, we kept the size in Z direction constantand applied cold pressure plus stress in X and Y direc-tions. We chose cold pressure equal to 35 GPa and variedvalue of stress from 0 to 28 GPa. Simulations under hy-drostatic pressure of 35 GPa at temperature 4000 Kshowed that the size and shape of the cell did not change.Only a slight change of Z size was observed because ofthe adjustment of Ar and MgO pafis to each other to formthe interface.

When the imposed pressure in X and Y directions be-came higher than 53 GPa (sffess of 18 GPa), drasticchanges in the behavior of the computational cell wereobserved (none of these changes was observed below 53GPa). The MgO part of the sample started to recrystallize

BELONOSHKO AND DUBROVINSKY: MD SIMULATION OF MgO 445

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Flcuns 3, Configurations of MgO which were used in themolecular dynamics simulation at I bar (a) and 35 GPa (b). Theupper and lower (4 surfaces are free in the case of I bar andexposed to liquid Ar (upper portion of the figure) in the case of35 GPa. Periodic boundary conditions are applied in X and Ydirections. If the pressure in the X and Y directions (stress) wereless than 8 GPa at a temperature of 3000 K, the final configu-ration would be about the same as in part (a). The higher mag-nitude of stress (9 GPa and higher) was suflicient to destroy theslab and produce liquid-like configuration (c).

446 BELONOSHKO AND DUBROVINSKY: MD SIMULATION OF MsO

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Flcurn 4. Dependence of size of computational cell at 3000K containing 2048 Mg and O atoms on the applied in X and, ydirections stress. Resulting pressure tn the Z direction is 0 belowapproximately 8 GPa and becomes equal to stress in Xy directionif the stress is above 8 GPa.

(Fig. 6a-e) forming finally (Fig. 6e) a crysral of l0 x 12x 14 layers insread of the initial (Fig. 6a) 12 x 12 x 12atomic layers. The incommensurate .,rest', of atomsformed incomplete layers at the top of MgO part. Themechanism of the observed recrystallization is glide of twoparts of crystal along the (110) surface (Fig. 6d). Becauseof recrystallization, a larger portion of the cell in Z direc-tion is occupied by MgO atoms. Because the size in the Zdirection was kept constant, the Z component of pressureincreased but still remained lower than 53 Gpa (pressurein X and I directions), the value of stress decreased, andthe process of recrytallization stopped. The observedchange of cell size is illustrated in Fisure 7.

The recrystallization is accompaiied by changes ofstructure. Figure 8 shows Mg-O radial distribution func-tion (RDF) during the simulation. One can see how theRDF goes through stages of distorlion, broadening ofpeaks, and finally back to the RDF typical of cubic oxide.

DrscussroNReal vs. ideal

In fact, after we finished this study, we felt that we aretrying to prove what is already self evident, namely, thatMgO cannot sustain some sufficiently high stress and thatsome changes will be inevitably noticed if stress is higherthan some critical value. It is possibly fortuitous that thevalue of the stress at which the drastic chanses are ob-served is close to the value of thermal pr".r,ir" becauseour simulated system, even being closer to a real one thanever simulated, still is very far from the real situation. Areal sample has defects, whereas the simulated one doesnot. A real sample is polycrystalline, whereas the simu-lated one is a single oriented crystal. It is possible toname other reasons, such as rate of loading, for example.However, these differences act in opposite way, cancelingeffects. On the one hand, a real sample is more capableof relaxing the stress due to defects and different orien-

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Frcunn 5. Radial Mg-O distribution functions at stresses of7.5 (diamonds) and 9 (spheres) GPa and 3000 K. The RDF ar7.5 GPa is typical for solid and the RDF ar 9.0 GPa is rypicalfor liquid state.

tation of crystallites. On the other hand, the same defectsand polycrystallinity is likely to decrease strength of asample in about the same degree as they are capable ofstress relaxation. The value of the thermal pressure (18GPa) that we use as a thermal sffess is likely not the valueof thermal stress in a sample. However, it is likely that areal sample has lower sffength compared with that of anideal crystal. It is also of interest to note that Fiquet etal. (1996a, 1996b) measured thermal pressure in MgOabout 15 GPa and were ptzzled how a powder samplecan sustain such a high sffess.

The overestimation of yield strength of MgO is aboutan order of magnitude, as the comparison of the simulatedvalue at I bar (30 GPa) wirh experimenral data (3 Gpa)demonstrates. It is possible that the critical value of stressequal to 18 GPa is also higher by approximately an orderof magnitude in comparison with the real one. If so, thenthe magnitude of calculated thermal stress (0.5 to 4 GPa;see above) is quite sufficient to initiate the simulatedchanges at 4000 K and 35 GPa. Of course, it is possiblethat the magnitude of the thermal stress in a sample re-mains below the critical value. In this case none of theobserved phenomena would be developed. However, inthe case of thermal stress of about 4 GPa the overesti-mation could be below a factor of five.

Impact of recrystallization on indication of meltThe decision about the appearance of melt in the DAC

with laser heating is based mainly on two criteria (weconsider here the technique employed by Boehler andcoworkers).

One criterion is visual observation. In earlier papers,"convective motion" or "vigorous convection" or "flu-id-like movement" (Boehler et al. 1990; Boehler 1992;Shen et al. 1993) were reported. Jeanloz and Kavner(1996) argued that it cannot be "convective motion,"moreover "vigorous convection." Nevertheless, it is ev-ident that movement of material is indeed observed. What

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kinds of motion are possible? First, it is possible that theobserved motion is indeed an indication of melting maybe convection, for example, movement of melting andsolidification fronts. The second possibility is the processof dynamic recrystallization simulated in this study. Be-cause the different crystallites are subjected to differentstresses due to temperature gradient and different orien-tation, the recrystallization would occur not simulta-neously, but rather in chaotic regime, possibly giving theimpression of convection. Jeanloz and Kavner (1996) de-scribed other possibilities.

The second criterion for indication of melting in DACexperiments is the change of the slope in the laser power-temperature curve. Recrystallization is likely to cause thechange for several reasons. First, the texture is likely tochange. Second, release of thermal stress leads to Joule-Thompson effect. When pressure on a substance is adi-abatically released, temperature drops by approximatelyVAP|C., where V is volume (if we neglect its change, thevolume of MgO at 4000 K and 35 GPa is about l0 cmi/mol), AP is the value of pressure release (according toour estimates, it varies from 0 to 18 Gpa), and C. is heatcapacity of the substance (about 100 J/mol.K). One cansee that the temperature effect can be large, a few hun-dred degrees, depending on the amount of the substancewhich was released from thermal pressure. The so called"yo-yo" oscillating pattern can also be explained, be-cause as soon as thermal pressure is released, inhomo_geneous laser heating generates thermal stress again andthe process can go on forever. However, there is anotherphysical process that acts in the opposite way, namelyviscous heating. This process due to the dissipation ofenergy required to initiate the process of recrystallizationcan lead to a fast increase in temperature.

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The observation of typical circular features of meltingin annealed samples can be also due to recrystallizationor be produced by subsequent run-away melting at highertemperatures. For example, Shen et al. (1993) wrote:"Note that if we turn off the laser power after the firstchange in texture, we do not observe typical circular fea-ture of melting." However, this is exactly the first changein texture that is accepted as an indication of melting.Interestingly, our simulation also produces (Fig. 6e) suchfeatures (atoms at the top and bottom of recrystallizedMgO slab). We should, however, admit that this is a ratherremote analogy.

The melting temperatures at I bar and moderate pres-sures measured in DAC with laser heating are in goodagreement with the experimental data provided by alter-native techniques. While we cannot neglect the possibilitythat this is simply because the method has no intrinsicdeficiencies with regard to the suggested phenomenon ofrecrystallization, it could also be explained by the follow-ing reasons. First, textural changes (recrystallization?) areobserved, and they indeed change the slope of power-temperature curve, but well before the melting tempera-ture at a pressure of I bar (S.K. Saxena, personal com-munication). Second, high thermal sffess might notappear because of other mechanisms of sffess release atlow pressures (e.9., brittle mechanism). This is a wellknown problem in mechanical tests, when study of plasticdeformation in brittle materials requires creation of highconfining hydrostatic pressure to prevent them from fail-ing by fracture. This is the principle of the Griggs ap-paratus (Poirier 1985). In this regard DAC serves as avery efficient Griggs apparatus (when pressure is high)preventing microcracks from growing. Third, at low andmoderate pressures melting temperature and the temper-ature at which recrystallization begins might be indistin-guishable within rather large experimental temperatureetTors.

To conclude, we can say that the effects that serve as

BELONOSHKO AND DUBROVINSKY: MD SIMULATION OF MgO 449

indications of melting at high pressure might be as welldue to the process of dynamic recrystallization which wesimulated. The opposite conclusion (that it cannot be)could be reached only on the basis of thorough experi-mental studies with full control of all relevant parameters(temperature, pressure, deviatoric and thermal stress, andstructure).

Melting of MgSiO. perovskite and iron

Belonoshko (1994) simulated the melting of MgSiO.perovskite in good agreement with experimental data(Zen and Boehler 1993; Boehler and Zen 1994). Whyare experimental and simulated melting curves of MgSiO.perovskite in good agreement while those of MgO aretotally different? Apart from other possible reasons andaccording to our suggested possibility of a high impactof thermal pressure on measured melting curves, it meanseither that MgSiO. perovskite is significantly harder thanpericlase (and it is) and is able to sustain thermal stressor that thermal stress was not as high in the perovskiteexperiment as in the experiment on periclase. Unlike theexperiment on MgO, the initial material in the experimenton perovskite was different (enstatite). During heating thephase transition of initial enstatite material to perovskitewith a negative volume effect could significantly releasethermal pressure. It is also possible that the release ofstress in perovskite was a result of the brittle mechanism.Indeed, Figure 2b of Zen and Boehler (1993) shows thatthe perovskite part of the sample has a few clearly visibledeep fractures. There are no such fractures in MgO sam-ple [Fig. I in paper by Zen and Boehler (1994)].

The peculiar feature of MgO melting curve is that ther-mal pressure along the curve is almost constant and equalto 18 GPa fthe thermal pressure was calculated using theequation of state by Belonoshko and Dubrovinsky(1996a, 1996b), which is very precise in experimentaldata rangel. Interestingly, the thermal pressure along theiron melting curve (Boehler, 1993) from 100 to 200 GPais also practically constant and equals to 22 GPa (thethermal pressure was calculated using the latest assess-ment of the equation of state for (1 iron). Deformationmaps (Frost and Ashby 1982) of MgO and Fe are verysimilar. Therefore, the simulated effect might be relevantin the case of iron as well. According to the deformationmaps of Fe and MgO, dynamic recrystallization beginsat high stresses (more than 0.01-0.1 of shear modulus)and high temperatures (T/T^ > 0.7-0.8). Hence, if thesuggested phenomenon is indeed what has been observedinstead of melting, the corrected iron melting tempera-tures would be higher than that measured by Boehler(1993) by 25 to 40Vo at 200 GPa, i.e., 5000 to 5600 K.This is in good agreement with the data of Williams etal. (1987), the recent revision of shock-wave data on ironmelting (Anderson and Ahrens 1996), and the Brown andMcQueen (1986) melting point (5625 K at 240 GPa, ac-cording to Boness and Brown (1990). A similar coffec-tion of MgO melting temperatures would lead to very

good agreement with the existing theoretical predictions(Fig. 1).

CoNcr-usrous

This study demonstrates that accounting for thermalstress in DAC experiments with laser heating might beimportant. Thermal stress, when achieving some criticalvalue can activate phenomena that have not been takeninto account previously. The dependence on visual ob-servation of melting can be misleading. In our opinion,there are two major reasons for the existing controversiesbetween melting curves obtained by different (includingtheoretical) methods. First, the physical processes thattake place in DAC are poorly understood, or, better said,we are not aware of what kind of physical effects areessential for this or that particular behavior. Second, allthe experimental determinations of melting curves usedtechniques that did not allow in situ control of pressure,temperature, stress, and phase composition in the sample.Even the latest experiments (Mao et al. 1996) do not pro-vide data on sffess in the sample. If stress is high enough,once activated, recrystallization can become a stationaryprocess. As it was demonstrated, the structure of a ma-terial during a stationary recrystallization process be-comes liquidlike. Therefore, even the absence of sharppeaks in measured X-ray pattern, characteristic of liquidstructure, cannot guarantee measurement of a truly hy-drostatic melting temperature.

Measurements of pressure before and after heating (notduring the experiment) in the pressurizing medium (not

in the sample) might be misleading. Depending on thesize of the spot, the type of laser radiation used, particulargeometry of a cell, the size and shape of a sample, con-ditions might be very different. To no surprise, whenpressurizing media are different (Williams et al. 1987;Boehler 1993) and different criteria are used for the iden-tification of onset of melting, the obtained temperaturesof melting are quite different. Despite the significantprogress achieved in the assessment of high-pressuremelting transitions, one has to admit that a definite an-swer has yet to be provided by careful experiments withfull in situ control of all relevant parameters.

It was also suggested (H. Keppler, personal commu-nication) that the discrepancy between theoretical and ex-perimental MgO melting temperatures can be explainedby other reasons. For example, it was pointed out thatMgO is a very hygroscopic material. Because a few per-cent of HrO dramatically decrease the melting point ofsilicates and oxide systems, this could easily account forthe low melting points observed in the experiments. Thisexplanation is possible. However, the room-pressure MgOmelting point was measured rather close to the previouslydetermined. Because the room-pressure Z- was measuredwithout a gasket, it is unlikely that the sample in thatcase contained less HrO than when it was subjected toconfining pressure of argon at high pressure.

Another reason for the discrepancy could be that ne-glect of defects leads to overheating in computer exper-

450 BELONOSHKO AND DUBROVINSKY: MD SIMULATION OF Meo

iments. We should note, however, that we calculated MgOmelting curve using two-phase modeling, which resolvesthe problem of overheating.

In conclusion, we want to emphasize that all the aboveis presented not to provide definite answers but rather tosuggest consideration of the impact of thermal stress onthe behavior of a sample in the DAC when undertakingan experimental study.

AcrNowr,nocMENTS

We are deeply thankful to K. Refson for providing rhe computer pro_gram Moldy. Comments and suggestions made by H. Keppler and H.J.Reichmann were very helpful. Discussions with R. Boehler, D. Heinz, R.Jeanloz, HK. Mao, LL Perchuk, S K Saxena, G Serghiou, S Soloma_tov, T Yagi, and A Zen are gratefully acknowledged part of the calcu_lations were done using IBM SP2 in the Maui Hish-performance andStockholm Parallel Computer Centers. Visualization o] stmcture was doneusing the program Xmol. L.D. acknowledges financial support from Swed_ish Royal Academy of Sciences. The research was supported by the Swed_ish Natural Sciences Research Council (Naturvetenskapliga Forsknings_rridet) grant no. G-GU 06901-301.

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