EXPERIMENTS AT HIGH TEMPERATURE AND PRESSURE : LASER HEATING THROUGH THE DIAMOND CELL

(1)

HAL Id: jpa-00224315

https://hal.archives-ouvertes.fr/jpa-00224315

Submitted on 1 Jan 1984

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

EXPERIMENTS AT HIGH TEMPERATURE AND PRESSURE : LASER HEATING THROUGH THE

DIAMOND CELL

R. Jeanloz, D. Heinz

To cite this version:

R. Jeanloz, D. Heinz. EXPERIMENTS AT HIGH TEMPERATURE AND PRESSURE : LASER HEATING THROUGH THE DIAMOND CELL. Journal de Physique Colloques, 1984, 45 (C8), pp.C8- 83-C8-92. �10.1051/jphyscol:1984817�. �jpa-00224315�

(2)

J O U R N A L DE PHYSIQUE

Colloque C8, suppliment au n O l l , Tome 45, novembre 1984 page C8-83

EXPERIMENTS A T H I G H TEMPERATURE AND PRESSURE :

LASER H E A T I N G THROUGH THE DIAMOND C E L L

R . J e a n l o z and D . L . Heinz

Department of Geology and Geophysics, U n i v e r s i t y of California, Berkeley, CaZifornia 9 4 7 2 0 , U.S.A.

R6sum6 - I1 e s t p o s s i b l e d e r 6 a l i s e r d e s e x p g r i e n c e s q u a n t i t a t i v e s 5 hau- t e s p r e s s i o n s e t t e m p g r a t u r e s s t a t i q u e s , e n c h a u f f a n t l ' i n t g r i e u r d ' u n e c e l l u l e 5 enclumes d e d i a r r a n t A l ' a i d e d ' u n l a s e r c o n t i n u . Des ~ e m p 6 r a - t u r e s d e 1500 2 5000K o n t 6 t 6 a t t e i n t e s d a n s t o u t e l a gamme d e p r e s s i o n s : 10 a 100 GPa. Le c h a u f f a g e e s t o b t e n u en f o c a l i s a n t l e f a i s c e a u d ' u n l a - s c r Nd: YAG e t l e s t e m p g r a t u r e s s o n t d k t e r m i n g e s p a r r a d i o m 6 t r i e a v c c une p r g c i s i o n d ' e n v i r o n 200K. Le p r o f i l d e t e m p g r a t u r e d e l a zone c h a u f - f 6 c p a r l e l a s e r e s t d g t e r m i n g p a r un f i l t r a g e s p a t i a l , o b t e n u p a r b a l a y a g e d ' u n e f e n t e . Dans c e s c o n d i t i o n s l e s t e m p 6 r a t u r e s d e f u s i o n s o n t d g t e r m i n c e s s o i t p a r l a mesure d e l a t e m p 6 r a t u r e o b s e r v g e 2 l ' i n t e r - f a c e l i q u i d e - s o l i d e , s o i t 2 p a r t i r d e l a t e m p g r a t u r e c o r r e s p o n d a n t 2 l ' a p p a r i t i o n d e l a p h a s e v i t r e u s e l o r s q u e l ' o n augmente p r o g r e s s i v e m e n t l a p u i s s a n c e d e c h a u f f a g e .

A b s t r a c t -Quantitative experiments a r e possible a t sustained high p r e s s u r e s and t e m p e r a t u r e s by means of CW-laser heating through t h e diamond-anvil cell.

T e m p e r a t u r e s of 1500 t o 5000 K have been r e a c h e d t h r o u g h o u t t h e 10 t o 100 GPa p r e s s u r e range. Heating is achieved by a focused Nd: YAG l a s e r beam, a n d t e m p e r a t u r e s a r e determined radiometrically with a n a c c u r a c y of a b o u t 200 K.

The variation of t e m p e r a t u r e a c r o s s t h e laser-heated s p o t is derived by m e a n s of spatial Altering with a slit t h a t c a n be scanned. In this way, t h e melting tem- p e r a t u r e c a n b e determined either from t h e t e m p e r a t u r e observed a t t h e liquid-solid i n t e r f a c e o r from t h e p e a k t e m p e r a t u r e a t which glass is first pro- d u c e d with increasing laser power.

IN TROD UCTION

Two of t h e most important advantages of t h e diamond-anvil cell for high-pressure r e s e a r c h derive from t h e s t r e n g t h of diamond a n d i t s t r a n s p a r e n c y across a broad range of t h e elec- tromagnetic spectrum. Thus, n o t only is i t possible t o achieve ultrahigh s t a t i c p r e s s u r e s of 100 GPa o r more, b u t t h e ability to observe t h e sample in situ a n d probe it with electromag- netic radiation while a t p r e s s u r e is a n especially i m p o r t a n t f e a t u r e of t h e diamond cell. In t h e p r e s e n t case. we u s e t h i s t r a n s p a r e n c y t o c a r r y o u t quantitative experiments a t simul- taneously high pressures a n d t e m p e r a t u r e s . CW laser radiation which is absorbed by t h e sample. b u t n o t by t h e diamond anvils. is used to achieve t e m p e r a t u r e s of several t h o u s a n d Kelvin. By t h e same token, o n e c a n observe t h e t h e r m a l radiation emitted f r o m t h e h o t sample located between t h e diamonds; t h e blackbody-like radiation makes it possible t o determine t h e sample t e m p e r a t u r e a t high p r e s s u r e s .

High t e m p e r a t u r e experiments a t elevated p r e s s u r e s a r e of i n t e r e s t for studies of phase equilibria, a s well a s for t h e synthesis of high-pressure phases t h a t c a n often be quenched a n d examined a t r o o m t e m p e r a t u r e a n d p r e s s u r e . Melting is among t h e most important transitions t h a t c a n b e examined, b u t high-pressure reactions t h a t would be kinetically impeded a t low t e m p e r a t u r e s a r e also of i n t e r e s t . As t e m p e r a t u r e s of 5000 K o r more can b e achieved a t p r e s s u r e s of 10-100 GPa, t h i s experimental technique is also of d i r e c t geophysical i n t e r e s t for studying materials a t t h e conditions of t h e Earth's interior (Fig. 1). Indeed, beginning with t h e pioneering work of Ming a n d Bassett / I / , most of t h e r e s e a r c h with laser-heated diamond cells h a s been c a r r i e d o u t by t h e geophysical community. To date.

however, this work h a s been more exploratory t h a n quantitative: t e m p e r a t u r e in t h e diamond cell h a s been roughly estimated by m e a n s of optical pyrometry. a n d little h a s been done t o control t h e t e m p e r a t u r e o r t o derive quantitative phase equilibria from s u c h experiments.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984817

(3)

JOURNAL DE PHYSIQUE

P,T Range of Diamond-Cell Experiments

L

PRESSURE (GPa)

Fig. 1 - P r e s s u r e - t e m p e r a t u r e range t h a t is accessible in diamond-cell experiments a s com- p a r e d with t h e range of estimated t e m p e r a t u r e s (geotherms) in t h e lower mantle and o u t e r c o r e of t h e Earth. Current estimates of t h e melting curves of iron and mantle silicates a r e also shown. The highest pressures so f a r achieved with t h e diamond cell a r e a t room tem- p e r a t u r e , b u t e x t e r n a l heating a n d cooling (for cryogenic experiments) allow t e m p e r a t u r e s below a b o u t 1000 K to b e reached. With l a s e r heating, t e m p e r a t u r e s exceeding 2000 t o 4000

K have been reached a t pressures u p to 100 GPa.

We describe here a spectroradiometric technique t h a t is c u r r e n t l y being developed in o r d e r to quantify t h e high-pressure laser heating experiments. Although many of t h e results a r e of a preliminary nature, o u r major conclusion is t h a t i t is possible to carry o u t phase equilibrium studies throughout t h e p r e s s u r e - t e m p e r a t u r e regime illustrated in Figure 1. The details of o u r c u r r e n t techniques, a n d some of t h e problems t h a t remain unsolved, a r e summarized in t h e following sections.

EXPERIMENTAL TECHNIQUES

The n a t u r e of laser heating a t t h e sample in t h e diamond cell is qualitatively summarized in Figure 2. Typical dimensions a r e a sample t h i c k n e s s and d i a m e t e r of 5 to 20 p m a n d 50 t o 250 p m , respectively, with t h e sample being contained by a metal gasket between t h e diamond anvils. The highest t e m p e r a t u r e s a r e achieved in t h e focal spot, which is of dimension 10 t o 50 p m depending on t h e focusing optics used ( s e e below). Because of t h e i r high t h e r - mal conductivity and large size, relative to t h e sample, t h e diamonds a c t essentially as infinite h e a t sinks. Thus. large t e m p e r a t u r e variations a p p e a r d u e to conduction both in t h e vertical (2) and radial ( T ) dimensions; a n d t h e gaussian intensity distribution across t h e focal s p o t also contributes to t h e radial t e m p e r a t u r e d e p e n d e n c e (Fig. 2).

The t e m p e r a t u r e variations with position p r e s e n t a major technical difficulty in making quantitative measurements. In particular, t h e spatial t e m p e r a t u r e Aeld must b e determined in o r d e r to c a r r y out phase equilibrium experiments. There is a n important chemical advantage, however, in t h e f a c t t h a t t h e hot, reactive p a r t of t h e sample is only in c o n t a c t with cold material of t h e same composition (cold sample material). Problems of contamination a r e minimized, and t h e diamond anvils a r e p r o t e c t e d f r o m damage caused by reactions with t h e sample. This f a c t illustrates t h e importance of properly focusing t h e laser a t t h e middle of t h e sample thickness in order t o achieve high t e m p e r a t u r e s .

Our complete l a s e r heating system is schematically illustrated in Figure 3. The 1064 n m radiation from a Nd:YAG laser with 100 W (multimode) CW power is used t o h e a t t h e sample between t h e diamond anvils. A mode-selecting a p e r t u r e is used t o isolate t h e focusable TEMOO mode. which c a r r i e s a maximum power of 2 5 t o 30 W a t t h e sample.

(4)

'\

^DIAMOND^LOWER

Fig. 2 - Cross section illustrating a sample being laser h e a t e d within t h e diamond cell. The Nd:YAG l a s e r beam is focused within the sample, which is c o n t a i n e d by a metal gasket between t h e diamond anvils. Typical dimensions a r e given. a n d t h e r a d i a l ( T ) a n d vertical (2)

d e p e n d e n c e of t e m p e r a t u r e in t h e sample is schematically illustrated.

t TEMPERATURE

Dlchro~c Mirror

Wavelength

Fig. 3 - Summary of t h e laser heating system used in t h e p r e s e n t experiments. The beam f r o m a CW Nd:YAG laser (TEMOO mode) is Focused into t h e high-pressure diamond cell by m e a n s of a microscope system containing a dichroic mirror. The dichroic mirror reflects t h e l a s e r b e a m b u t transmits t h e thermal radiation emitted from t h e sample a t visible wavelengths (wavy lines). The s p e c t r u m of t h e t h e r m a l radiation is determined by a mono- c h r o m a t o r located above t h e dichroic mirror; from t h i s s p e c t r u m t h e emissivity a n d tem- p e r a t u r e of t h e sample a r e determined. Also, t h e fluctuations in l a s e r power and sample t e m p e r a t u r e a r e monitored a s a function of time.

The focusing is achieved with a beam e x p a n d e r (optional) a n d a long working-distance objective: typically we u s e a Leitz UM 20 objective (0.33 numerical a p e r t u r e ) , which yields a beam waist of a b o u t 10 prn (or 50 p n ) a t t h e sample when using (or not using) a 6 X beam expander.

The laser power c a n be varied by changing t h e power a t t h e pump lamps. For a given experi- m e n t , however, we use a polarizer- a t t e n u a t o r s y s t e m located right a f t e r t h e b e a m expander in o r d e r t o c h a n g e t h e l a s e r power t h a t is received a t t h e sample. By changing t h e power outside t h e l a s e r cavity in this way, t h e r e is n o change in m o d e - s t r u c t u r e o r focal level of t h e l a s e r beam. The efficiency of t h i s a t t e n u a t o r is s u c h t h a t between 5 W (minimum) a n d 23 W (maximum) r e a c h t h e sample a t peak laser power.

(5)

C8-86 JOURNAL DE PHYSIQUE

The microscope system which focuses t h e laser beam is also used to observe t h e sample in t h e diamond cell. Visual observation (direct o r with a closed circuit television) is important for reproducibly focusing t h e laser in t h e sample a n d for monitoring c h a n g e s in t h e sample a t high p r e s s u r e s a n d temperatures. The thermal radiation from t h e sample passes t h r o u g h t h e "hot mirror" (high-pass dichroic Alter) t h a t reflects t h e laser b e a m t h r o u g h t h e objective. This t h e r m a l radiation is focused onto t h e e n t r a n c e slit of a holographic-grating mono- c h r o m a t o r (12 nm/rnm dispersion and 833 p m slit widths) with a silicon d e t e c t o r . Extra dichroic filters a r e placed in f r o n t of t h e e n t r a n c e slit in o r d e r t o a s s u r e t h a t none of t h e primary (1064 nm) l a s e r radiation e n t e r s t h e monochromator. Also, a low-pass (IR transmit- ting) filter located a t t h e polarizer-attenuator prevents any of t h e pump-lamp radiation f r o m contaminating t h e sample spectra. As a result, even with maximum l a s e r power almost n o radiation is observed through t h e s p e c t r o m e t e r when a reflective ( n ~ n a b s o r b i n ~ ) s u r f a c e is placed in t h e sample a r e a .

The s p e c t r a l response of t h i s system, which is summarized in Figure 4, illustrates t h e exclu- sion of radiation a t 1064 nm. The s t r u c t u r e in t h e response curve is caused mainly by t h e multilayer dichroic filters t h a t a r e used a s well a s by t h e d e t e c t o r response. As is evident, however, t h i s s y s t e m which is maximized for visible wavelengths is ideal f o r measuring t h e t h e r m a l radiation of samples a t about 1500 to 5000 K. At lower t e m p e r a t u r e s , t h e light intensity is often too low to obtain a reliable s p e c t r u m (especially for samples of low emissivity).

At higher t e m p e r a t u r e s , t h e limitation derives more from o u r d a t a reduction technique, a s described below, t h a n from fundamental optical constraints.

The d e t e c t o r o u t p u t is amplified. and smoothed as a function of time (100 to 220 pF capaci- t o r s give smoothing time c o n s t a n t s of order 1 to 2 sec.), before being r e a d by a Hewlett- P a c k a r d 9826 minicomputer which is used t o process t h e s p e c t r a l data. In o r d e r t o s c a n over a full s p e c t r u m 4 t o 8 minutes a r e usually required, b u t it is often possible to determine t h e t e m p e r a t u r e more rapidly. Speciflcally, only a fraction of t h e s p e c t r u m need be collected if t h e sample emissivity varies little with wavelength (ie., t h e greybody model applies), a s is often t h e case. Thus, t e m p e r a t u r e c a n be reliably m e a s u r e d with this system in less t h a n o n e minute. Nevertheless, sufficient time is available for characterizing t h e s p e c t r u m of t h e t h e r m a l radiation, a s continuous heating experiments lasting well over o n e h o u r have been successfully accomplished in t h e diamond cell.

WAVELENGTH (nm)

Fig. 4 - S p e c t r a l r e s p o n s e of t h e p r e s e n t radiometer system is compared with t h e l a s e r wavelength (arrow a t 1064 nm) and t h e thermal emission from blackbodies (Planck functions) a t 2000 K, 3000 K a n d 4000 K. The system response (intensity in a r b i t r a r y units) includes t h e effects of Alters. dichroic mirrors, lenses and t h e detector; c h a n g e s in o r d e r - sorting

liters

a r e shown by s h o r t vertical lines. l'here is additionally a scale f a c t o r ranging over 10 f o r t h e s y s t e m response. The Wien approximation to t h e Planck function is shown for illustrative purposes ( s e e text).

(6)

DATA REDUCTION AND SYSTEM CALIBRATION

The thermal emission from t h e Laser-heated sample is analyzed in terms of t h e greybody model which r e l a t e s s p e c t r a l intensity. I(A), t o emissivity. e, a n d temperature. 7?

with A, h, k a n d c being wavelength, Planck's c o n s t a n t , Boltzmann's c o n s t a n t a n d t h e velocity of light, respectively. In o r d e r to t e s t t h e greybody assumption t h a t & is independent of wavelength it is convenient to use Wien's linearized approximation t o t h e Planck function (1).

Thus. deflning a normalized intensity

a n d a normalized frequency

which a r e both observable, Wien's relation c a n be expressed a s a linear equation in 'I'-I:

J = lne - WT-' (3)

The problem with using (3) a s an approximation t o (1) is t h a t it is only valid a t relatively low temperatures. As is evident from Figure 4, however, t h e Wien equation accurately r e p r o - d u c e s t h e Planck relation for t h e p r e s e n t experimental conditions up to t e m p e r a t u r e s of a b o u t 5000 K. The advantage, on t h e o t h e r hand, of reducing t h e d a t a in terms of (3) is t h a t it is easy to t e s t for t h e validity of t h e greybody model (i.e.. check t h a t r is independent of A by checking t h e linearity of J versus I?. ), a n d uncertainties in t h e s p e c t r a l measurements c a n be directly propagated to t h e corresponding uncertainties in T a n d c. Starting with this analysis, high-temperature d a t a c a n be iteratively reduced t o c o r r e c t for t h e difference between t h e Wien and Planck functions. if necessary.

The spectroradiometer s y s t e m is calibrated with r e s p e c t to a s t a n d a r d tungsten-fllament lamp of spectral emittance which is known absolutely. To date, however, we have not cali- b r a t e d t h e emissivities absolutely in t h e laser-heating experiments a t pressure. The reason is t h a t t h e s u r f a c e a r e a of e m i t t a n c e in t h e diamond cell must b e accurately measured in every experiment; this is possible (using optical techniques / 2 / ) but dimcult. Still, emissivities a r e typically determined to a f a c t o r of 2 to 5, a n d what is most important is t h a t t h e relative wavelength d e p e n d e n c e of E is accurately measured. Also, t h e main c o n c e r n h a s been in measuring t e m p e r a t u r e and, a s is evident from (3). this is independent of how well t.he absolute emissivity is known.

As a check on t h e a c c u r a c y of t h e s p e c t r a l t e m p e r a t u r e determinations during laser heating, t h e zero-pressure melting of several metals has been examined between 1500 a n d 5000 K.

High-purity metal wires were heated in a n argon atmosphere to prevent oxidation. The tem- p e r a t u r e was measured a s in experiments with t h e diamond cell. The main difference with t h e high-pressure experiments is t h a t a much larger region is uniformly melted (

-

^{100 pm}

characteristic dimension) b e c a u s e of t h e absence of t h e diamond h e a t sinks.

The melting t e m p e r a t u r e was b r a c k e t e d in a c r u d e b u t unambiguous way by t h e d i r e c t observation ( o r lack t h e r e o f ) of flowage a n d formation of a bead of melt. As is evident from Figure 5, t h e p r e s e n t results a r e consistent with t h e known melting t e m p e r a t u r e s in all c a s e s b u t t h a t of tungsten, which exhibits a 5 p e r c e n t discrepancy. Although Larger t h a n t h e estimated e r r o r on t h e t e m p e r a t u r e determination (derived from t h e spectral fit to t h e greybody function), a n a c c u r a c y of 5 p e r c e n t is plausible for t h e p r e s e n t experiments. It should be noted, however, t h a t s u r f a c e tension might obscure t h e o c c u r r e n c e of liquid flow and r e s u l t in an overestimate of t h e melting t e m p e r a t u r e , a s observed. Another difficulty worth mentioning is t h a t because of t h e nonlinearity of t h e laser-sample coupling i t is not always possible to achieve t e m p e r a t u r e s n e a r t h e melting point in both t h e solid and liquid p h a s e s (cf. iron and zirconium).

FLUCTUATfONS IN LASER POWER

One important cause of uncertainties in t h e p r e s e n t experiments is t h a t t h e laser output fluctuates by a few p e r c e n t a s a function of time. These fluctuations a r e monitored by means or a silicon d e t e c t o r on the back (high reflectance) mirror of the laser: t h e r e is sufficient light leakage t o continuously monitor t h e power (Fig. 3). As a result of t h e laser-

(7)

J O U R N A L DE PHYSIQUE

Fig. 5 - Melting of four metals under t h e laser beam a t zero pressure. The difference between t h e radiometrically measured t e m p e r a t u r e and t h e known melting t e m p e r a t u r e (T,. given a t t h e bottom) is plotted f o r Fe, Zr, Mo a n d W. Open symbols r e f e r to t h e d i r e c t observation of flow whereas closed symbols indicate t h a t t h e sample a p p e a r e d solid. In all cases t h e metal was in a s t r e a m of Ar.

intensity fluctuations, sample t e m p e r a t u r e s vary by a b o u t 200 K. This value is of similar magnitude a s t h e discrepancies observed in t h e zero-pressure melting experiments. We p a r t l y s u r m o u n t t h e problems caused by t e m p e r a t u r e fluctuations by means of t h e temporal smoothing t h a t is applied to t h e s p e c t r o m e t e r o u t p u t . It is clear, however, t h a t f u r t h e r improvements a r e possible. Among o t h e r solutions, t h e laser o u t p u t could b e smoothed with a feedback system or t h e s p e c t r u m could be collected much more rapidly by mcans of a d e t e c t o r a r r a y .

From a different perspective, t h e laser-intensity fluctuations c a n actually b e advantageous.

For a sample t h a t is passively absorbing t h e l a s e r radiation, o n e would expect. t h e tempera- t u r e fluctuations to correlate with the changes in l a s e r intensity (due t o h e a t flow a loss of high-frequency components and a slight phase shift would be expected, a s is schematically shown in Fig. 3). In c o n t r a s t , t h e occurrence of reactions (in particular. melting) in t h e sam- ple would be expected t o result in a loss of correlation between t h e t e m p e r a t u r e and t h e laser intensity. That is, kinetics and t h e l a t e n t h e a t (which a c t s a s a n e x t r a h e a t sink) prevent t h e sample t e m p e r a t u r e from closely following t h e c h a n g e s in energy deposition by t h e l a s e r beam.

These expectations a r e born o u t by laser-heating experiments in t h e diamond cell (Fig. 6). A r e f r a c t o r y compound s u c h as AIZOg is solid a t elevated t e m p e r a t u r e s , a n d i t exhibits a close correlation between laser intensky a n d sample t e m p e r a t u r e (monitored h e r e by t h e intensity of t h e r m a l radiation a t 600 n m wavelength). The dominant oscillations a r e of a few Hz in frequency, a n d t h e effects of thermal conduction a r e clearly evident (phase shift and loss of high frequency components in t h e t e m p e r a t u r e fluctuatiorls).

The r e s u l t for a sample t h a t is partially molten u n d e r t h e laser b e a m is markedly different (Fig. 6). In this case. t h e correlation between laser intensity and sample t e m p e r a t u r e is poor. Qualitatively, this effect is analogous to what is observed in Differential Scanning Calorimetry experiments. Thus, although more work is required t o develop this technique, t h e correlation of laser a n d t e m p e r a t u r e fluctuations could provide a powerful tool for t h e in situ determination of high-temperature reactions, a n d specifically melting, in t h e diamond cell.

(8)

Fig. 6 - Oscilloscope t r a c e s illustrating t h e fluctuations in sample t e m p e r a t u r e associated with fluctuations in laser o u t p u t (see Fig. 3). In e a c h of t h e four r u n s t h e upper and Lower t r a c e s correspond respectively to t h e l a s e r power a n d sample t e m p e r a t u r e as functions of time. Durations for each run a r e 1 and 2 seconds. a s indicated; l a s e r intensity and sample t e m p e r a t u r e a r e in a r b i t r a r y units. The t r a c e s a r e well c o r r e l a t e d in t h e two r u n s with A1 O3 (upper half) a n d poorly correlated in t h e two r u n s with (Mg Fee, ) Si04 (oli,ne s t a r g n g material; lower half). These experiments were c a r r i e d o u t a?'%5 to$& GPa p r e s s u r e in t h e diamond cell, and a few p e r c e n t P t were mixed in with t h e AL2O3 in o r d e r to absorb t h e laser beam.

Fig. 7 - Axial v i e w in t r a n s m i t t e d white light of four glass blobs c r e a .ed by l a s e r heating in t h e diamond cell a t 30 GPa pressure. The starting material was Mgo Feo lSiOQ which was con- v e r t e d t o t h e high-pressure perovskite phase by laser heating &? ppr$ssures above 25 CPa.

The largest glass blob (top) is 18 p m in diameter.

(9)

C8-90 JOURNAL DE PHYSIQUE

MELTING EXPERIMENTS AND THE SPATIAL VARIATION OF TEMPERATURE

An alternative a n d more definitive proof t h a t samples a r e melted in t h e diamond cell is t h e formation of glass on quenching (turning off t h e laser). In this c a s e , it is advantageous t o work with silicates o r oxides t h a t a r e good glass formers. An example is illustrated in Figure 7, in which t h e s t a r t i n g m a t e r i a l is t h e high-pressure perovskite p h a s e of pyroxene; this was synthesized in situ a t a b o u t 30 GPa from starting material of composition Mg.o,88 Fe

12Si03.

Aside from its glass-forming ability this perovskite is of i n t e r e s t because it 1s c o n s i t e r e d t o b e t h e dominant mineral of t h e earth's lower mantle/3/. Indeed silicate perovskite, which is stable only above a b o u t 20 GPa, is probably t h e single most a b u n d a n t mineral within o u r planet.

Four glass blobs a r e evident in t h e microphotograph, t h e largest being formed a t t h e highest laser power. With decreasing power t h e quenched blobs become smaller, a n d a t low power n o glass is observed. Thus, a t low power t h e peak t e m p e r a t u r e in t h e diamond cell is below t h e melting point of t h e sample (Fig. 8). With increasing laser power, both t h e average a n d p e a k t e m p e r a t u r e s a r e observed t o increase, and once t h e peak t e m p e r a t u r e i n t e r s e c t s t h e melting point a small a m o u n t of glass is formed on quenching. With higher l a s e r power, a l a r g e r region is melted a n d t h e r e f o r e a larger amount of glass is observed.

Based on Figure 8, two a p p r o a c h e s a r e suggested for determining t h e melting t e m p e r a t u r e of samples in t h e diamond cell. On t h e one hand, if t h e p e a k t e m p e r a t u r e is determined f o r t h e r u n in which glass is A r s t observed with increasing laser power, this b r a c k e t s t h e melting t e m p e r a t u r e from below. On t h e o t h e r hand, t h e melting point c a n also be d e t e r m i n e d a t higher laser power by measuring t h e t e m p e r a t u r e a t t h e location of the glass-crystal interface. This is more difficult, but more satisfactory, t h a n t h e preceding technique b e c a u s e it involves a d i r e c t m e a s u r e m e n t of t h e coexistence t e m p e r a t u r e between melt a n d solid; t h a t is, t h e experiment is inherently reversed.

In e i t h e r case, i t is evident t h a t t h e t e m p e r a t u r e variation a c r o s s t h e sample (Figs. 2 a n d 8) m u s t be directly m e a s u r e d for quantitative phase-equilibrium studies to be possible. As a flrst c u t t o this problem wc t r e a t t h e laser heated spot as a disc source of light, with tem- p e r a t u r e varying a s a function 07 radial distance from t h e c e n t e r of t h e spot. Hence t h e t e m p e r a t u r e fleld c a n be directly measured by means of a movable slit which is placed directly on, a n d o r i e n t e d perpendicular to, t h e e n t r a n c e slit of t h e monochromator (Fig. 9).

t

t i

t

^glass

Distance

-

INCREASING LASER POWER

-

Fig. 8 - Schematic illustration of t h e t e m p e r a t u r e a s a function of radial distance a c r o s s t h e laser-heated spot. At low l a s e r power t h e peak t e m p e r a t u r e is below t h e melting point of t h e z m p l e . Tm ( l e f t panel). With increasing laser power t h e average t e m p e r a t u r e , TaV, i n c r e a s e s a n d t h e p e a k t e m p e r a t u r e i n t e r s e c t s t h e melting t e m p e r a t u r e (middle panel). At this point glass is formed on quenching if t h e sample material is a glass former. At higher laser power, a larger region is melted a n d h e n c e a larger amount of glass is found a f t e r t h e l a s e r is t u r n e d ofl (right panel).

(10)

SAMPLING 25pm SLIT (moveable) MONOCHROMATOR

SLIT 8 3 3 ~

(stotionory)

Fig. 9 - A vertical sampling slit can b e t r a n s l a t e d a c r o s s t h e image of t h e sample which is focused a t t h e stationary, horizontal e n t r a n c e slit of t h e monochromator. By scanning t h e slit horizontally across t h e image of t h e laser-heated s p o t it is possible to determine t h e spatial variation of t e m p e r a t u r e in t h e sample. The sampling slit is 10 t o 25 p m ' wide, t h e mono- c h r o m a t o r slit is 833 p m wide and t h e laser-heated region is typically 250 p m in diameter.

This sampling slit blocks o u t all but a thin s t r i p of t h e sample image which is focused a t t h e e n t r a n c e slit. We use sampling slits of 10 and 25 p m dimension which can be moved with a precision of 1 p m . As t h e magnification of t h e sample image is approximately 5x a t t h e slit. a spatial averaging (projected slit width) and positioning of 2 to 5 p m and 200 nm respectively, is achieved across t h e t e m p e r a t u r e field in t h e sample.

Because of t h e vertical (on-axis) variation of t e m p e r a t u r e (Fig. 2), t h e disc approximation used here must always r e s u l t in an u n d e r e s t i m a t e of t h e peak temperature. Nevertheless, t h i s gives a relatively good estimate of t h e spatial variation of t e m p e r a t u r e . The slit- sampling across a disc is a n exarnple of a tomographic problem, with t h e invcrsior~ given by a n Abel transform /4/. Therefore, t h e s p e c t r a l intensity as a function of radial d i s t a r ~ c e , T , is calculated from t h e s p e c t r a l intensity t h a t is measured a s a function of slit position, z:

Combining (4) with (1) o r ( 3 ) provides a n e s t i m a t e of t h e position-dependerit t e m p e r a t u r e a n d emissivity: T(T) and E ( 7 ) .

The result of one such scan for a l a s e r heating experiment on magnesium silicate perovskite in t h e diamond cell is shown in Figure 10. This figure illustrates sorrie of the difficulties t h a t m u s t still be resolved, a s well providing c o n c r e t e r e s u l t s from t h e p r e s e n t technique. The 7(r) curve was constrained by t h e d a t a between 5 a n d 25 p m radial dist.ance and by t h e average t e m p e r a t u r e (measured over t h e whole field of view) of 4100 (i 200) K. Near t h e c e n t e r of t h e h o t spot t h e results were extremely unstable because of t h e fluctuations in light intensity a s a function of time. That is, t h e size of t h e molten region fluctuates in response t o t h e fluctuations in laser intensity. Because of i t s small dimension (6 p m diameter, based on t h e size of t h e quenched glass). fluctuations of only I to 2 p m in t h e size of t h e molten region drastically alIect t,he amount. of t h e r m a l radiation t h a t is emitted from t h e c e n t r a l a r e a .

Beyond t h e 50 p m beam-waist diameter t h e t e m p e r a t u r e drops of! and. for t h e optical configuration used in this run, t h e decreasing light intensity produces large uncertainties in t h e t e m p e r a t u r e determinations a t T > 20 p m . We believe t h a t t h e minimum in f l ~ ) n e a r 10 prn radial distance may be d u e t o t h e laser being slightly defocused. We have found t h a t it is critical to reproducibly focus t h e laser in t h e middle of t h e sample thickness (F'ig. 2) in o r d e r to g e t reproducible profiles. Because of variation in t h e thicknesses of diamond anvils and in t h e index of refraction of diamond a s a function of pressure. t h e laser focusing must be carefully checked in e a c h experiment. One way t h a t this c a n be accomplished is by f i r ~ d i r ~ g

(11)

J O U R N A L DE PHYSIQUE

Radial Distance (,urn)

Fig. 10 - Profile of t e m p e r a t u r e a s a function of radial distance from t h e c e n t e r of t h e laser- h e a t e d s p o t for a sample of silicate perovskite a t 3 5 GPa in t h e diamond cell. The average ternperaturc a c r o s s t h e h o t regions is 4100 K a n d the beam-waist diameter is 50 p m in t h i s experiment. The t e m p e r a t u r e distribution. T(T), satisfies t h e average t e m p e r a t u r e a s well a s t e m p e r a t u r e points derived by inversion (see text). Error b a r s show t h e e s t i m a t e d u n c e r - tainties and open symbols have u n c e r t a i n t i e s well over 100 percent. Upon turning off t h e laser, a glass region 5 p m in d i a m e t e r was quenched, and t h e corresponding t e m p e r a t u r e a t t h e solid- liquid i n t e r f a c e is found to be n e a r 3000 K.

the focal position t h a t p r o d u c e s t h e narrowest t e m p e r a t u r e distribution, corresponding t o the smallest beam waist in t h c sample.

According t o Figure 10, t h e liquid-crystal interface is a t a b o u t 3000 K for t h e silicate perovskite a t 35 GPa. This value is in a c c o r d with t h e peak t e m p e r a t u r e a t which glass first a p p e a r s with increasing l a s e r power. Interestingly, t h e melting t e m p e r a t u r e of t.his perovskite a p p e a r s t o be c o n s t a n t a t a b o u t 3000 K between 30 and 60 GPa pressurc, a n d this may have important geophysical ramifications /5/.

The main conclusion from t h i s work, however, is t h a t continuous laser heating car1 be used t o achieve t e m p e r a t u r e s of several t h o u s a n d Kelvin a t p r e s s u r e s of 10 to 100 GPa in t h e diamond cell. Average t e m p e r a t u r e , a n d both t h e spatial a n d temporal variation of t e m p e r a t u r e in t h e sample can be monitored by spectroradiometry. Thus, phase-equilibrium e x p e r i m e n t s a r e possible a t high p r e s s u r e s a n d t e m p e r a t u r e over time scales of minutes t o hours.

ACKNOWLEDGEMENTS

Work s u p p o r t e d by t h e U.S. National Science Foundation, NASA a n d t h e A.P. Sloan Founda- tion.

REFERENCES

/ I / . MING. L.C.. a n d BASSETT, W.A.. Rev. Sci:Instrum., 45, (1974) 1115-1118.

/ 2 / . SCOTT, C. and JEANLOZ, R., Rev. Sci. Instrum, 55, (1984) 558-562.

/3/. JEANLOZ, R., a n d THOMPSON, A.B., Rev. Geophys. Space Phys., 21, (1983) 51-74.

/4/. DEANS. S.R.. The Radon Transform a n d Some of Its Applications, J. Wiley a n d Sons, New York (1983).

/5/. HEINZ. D.L.. a n d JEANLOZ. R.. US-Japan Conference on Partial Melting.

Proceedings. Eugene. Oregon. USA. (September 1984).