﻿Fenner 
  — 
  Stability 
  Relations 
  of 
  Silica 
  Minerals. 
  365 
  

  

  fixed 
  for 
  any 
  given 
  condition 
  of 
  equilibrium. 
  From 
  this 
  it 
  is 
  

   but 
  a 
  short 
  step 
  to 
  suppose 
  that 
  when 
  a 
  solid 
  crystallizes 
  from 
  

   such 
  a 
  liquid 
  not 
  only 
  one 
  but 
  two 
  or 
  several 
  molecular 
  species 
  

   go 
  to 
  form 
  it. 
  The 
  proportions 
  of 
  the 
  several 
  molecular 
  

   species 
  in 
  the 
  solid 
  and 
  liquid 
  will 
  differ 
  from 
  each 
  other 
  but 
  a 
  

   certain 
  equilibrium 
  will 
  exist 
  between 
  the 
  two 
  phases. 
  In 
  the 
  

   crystallization 
  of 
  such 
  a 
  system 
  the 
  substance 
  in 
  question 
  may 
  

   behave 
  as 
  a 
  unary 
  substance. 
  This 
  is 
  accounted 
  for 
  by 
  the 
  

   fact 
  that 
  the 
  condition 
  of 
  inner 
  equilibrium 
  in 
  the 
  melt, 
  when 
  

   disturbed 
  by 
  the 
  appearance 
  of 
  a 
  new 
  phase, 
  is 
  immediately 
  

   restored 
  by 
  the 
  necessary 
  transformation 
  of 
  molecular 
  species, 
  

   and 
  in 
  this 
  manner 
  equilibrium 
  is 
  constantly 
  maintained. 
  

   When, 
  however, 
  the 
  molecular 
  transformations 
  are 
  not 
  accom- 
  

   plished 
  with 
  sufficient 
  facility 
  to 
  maintain 
  equilibrium 
  under 
  

   rapidly 
  changing 
  conditions, 
  the 
  binary 
  or 
  ternary 
  nature 
  of 
  

   the 
  substance 
  will 
  show 
  forth. 
  The 
  crystallization 
  of 
  such 
  a 
  

   pseudo-unary 
  substance 
  will 
  be 
  analogous 
  to 
  that 
  of 
  mixed 
  

   crystals 
  and 
  should 
  show 
  a 
  similar 
  temperature-range 
  of 
  crys- 
  

   tallization. 
  Inversions 
  in 
  the 
  solid 
  state 
  should 
  be 
  character- 
  

   ized 
  by 
  similar 
  phenomena. 
  When 
  inversion 
  occurs 
  the 
  

   components 
  of 
  the 
  pseudo-unary 
  mix-crystals 
  unmix, 
  as 
  Smits 
  

   expresses 
  it, 
  and 
  the 
  temperature 
  of 
  inversion 
  will 
  depend 
  

   upon 
  the 
  relative 
  proportions 
  of 
  the 
  two 
  or 
  more 
  species 
  of 
  

   molecules 
  as 
  determined 
  at 
  the 
  time 
  of 
  formation. 
  

  

  A 
  further 
  thesis 
  as 
  stated 
  by 
  Smits 
  is 
  " 
  that 
  this 
  theory 
  

   requires 
  that 
  every 
  substance 
  which 
  shows 
  a 
  transition 
  point 
  

   must 
  consist 
  of 
  two 
  different 
  kinds 
  of 
  molecules, 
  which 
  are 
  in 
  

   equilibrium 
  at 
  every 
  temperature."* 
  The 
  necessity 
  of 
  this 
  as 
  

   a 
  consequence 
  of 
  the 
  main 
  theory 
  is 
  not 
  wholly 
  evident 
  and 
  

   certain 
  phenomena 
  which 
  will 
  be 
  described 
  later 
  tend 
  to 
  throw 
  

   doubt 
  upon 
  its 
  validity 
  as 
  a 
  universal 
  proposition. 
  We 
  may 
  

   suppose 
  that 
  a 
  liquid 
  consisting 
  of 
  the 
  molecular 
  species 
  X 
  and 
  

   fM 
  in 
  the 
  proportions 
  demanded 
  by 
  equilibrium 
  starts 
  to 
  crystal- 
  

   lize, 
  but 
  that 
  the 
  requirements 
  of 
  the 
  distribution 
  of 
  forces 
  

   within 
  the 
  crystal-structure 
  can 
  be 
  met 
  only 
  by 
  the 
  species 
  X. 
  

   Then 
  the 
  crystallizing 
  solid 
  will 
  withdraw 
  X 
  only 
  from 
  the 
  

   liquid, 
  leaving 
  a 
  surplus 
  of 
  /x. 
  This, 
  however, 
  will 
  be 
  met 
  by 
  

   a 
  transformation 
  of 
  some 
  of 
  the 
  /jl 
  molecules 
  into 
  X 
  until 
  equi- 
  

   librium 
  is 
  restored, 
  and 
  this 
  process 
  will 
  continue 
  until 
  the 
  

   whole 
  has 
  crystallized 
  in 
  X 
  molecules. 
  Moreover 
  such 
  a 
  crys- 
  

   tal 
  may 
  possess 
  an 
  inversion-point. 
  The 
  process 
  here 
  will 
  

   not 
  be 
  an 
  unmixing 
  of 
  molecular 
  species 
  as 
  Smits 
  conceives, 
  

   but 
  it 
  will 
  be 
  more 
  probably 
  a 
  rearrangement 
  of 
  the 
  one 
  kind 
  

   of 
  molecule 
  within 
  the 
  crystal 
  structure 
  due 
  to 
  the 
  fact 
  that 
  

   the 
  equilibrium 
  of 
  forces 
  has 
  become 
  unstable 
  when 
  a 
  certain 
  

  

  *A. 
  Smits, 
  Koninklijke 
  Akademie 
  van 
  Wetenschappen 
  te 
  Amsterdam, 
  

   Proceedings 
  of 
  Mar. 
  26, 
  1910 
  (English 
  text). 
  

  

  